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The Journal of

Financial PerspectivesEY Global Financial Services Institute July 2013 | Volume 1 — Issue 2

The EY Global Financial Services Institute brings together world-renowned thought leaders and practitioners from top-tier academic institutions, global financial services firms, public policy organizations and regulators to develop solutions to the most pertinent issues facing the financial services industry.

The Journal of Financial Perspectives aims to become the medium of choice for senior financial services executives from banking and capital markets, asset management and insurance, as well as academics and policy-makers who wish to keep abreast of the latest ideas from some of the world’s foremost thought leaders in financial services. To achieve this objective, a board comprising of leading academic scholars and respected financial executives has been established to solicit articles that not only make genuine contributions to the most important topics, but are also practical in their focus. The Journal will be published three times a year.

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The articles, information and reports (the articles) contained within The Journal are generic and represent the views and opinions of their authors. The articles produced by authors external to EY do not necessarily represent the views or opinions of EYGM Limited nor any other member of the global EY organization. The articles produced by EY contain general commentary and do not contain tailored specific advice and should not be regarded as comprehensive or sufficient for making decisions, nor should be used in place of professional advice. Accordingly, neither EYGM Limited nor any other member of the global EY organization accepts responsibility for loss arising from any action taken or not taken by those receiving The Journal.

EditorShahin Shojai EY LLP

Advisory EditorsDai Bedford EY LLPShaun Crawford EY LLP Carmine DiSibio EY LLP

Special Advisory EditorsBen Golub Blackrock Anthony Neoh Bank of China Kishore Ponnavolu Metlife

Editorial BoardViral V. Acharya New York UniversityJohn Armour University of OxfordTom Baker University of Pennsylvania Law SchoolPhilip Booth Cass Business School and IEAJosé Manuel CampaIESE Business SchoolKalok Chan Hong Kong University of Science and TechnologyJ. David Cummins Temple UniversityAllen Ferrell Harvard Law SchoolThierry Foucault HEC ParisRoland Füss University of St. GallenGiampaolo Gabbi SDA BocconiBoris Groysberg Harvard Business SchoolScott E. Harrington The Wharton SchoolPaul M. Healy Harvard Business SchoolJun-Koo Kang Nanyang Business SchoolTakao Kobayashi Aoyama Gakuin UniversityHoward Kunreuther The Wharton SchoolDeborah J. Lucas Massachusetts Institute of Technology

Massimo Massa INSEADPatricia A. McCoy University of Connecticut School of LawTim Morris University of OxfordJohn M. Mulvey Princeton UniversityRichard D. Phillips Georgia State UniversityPatrice Poncet ESSEC Business SchoolMichael R. Powers Tsinghua UniversityAndreas Richter Ludwig-Maximilians-UniversitaetPhilip Rawlings Queen Mary, University of LondonRoberta Romano Yale Law SchoolHato Schmeiser University of St. GallenPeter SwanUniversity of New South WalesPaola Musile Tanzi SDA BocconiRolf Tilmes EBS UniversityMarno Verbeek Erasmus UniversityIngo Walter New York UniversityBernard Yeung National University of Singapore

Editorial

Ratan Engineer EY LLP David Gittleson EY LLP Bill Schlich EY LLP

Anthony M. Santomero Citigroup Nick SilitchPrudential Financial

The Journal of Financial Perspectives

Part 1 11 Gresham’slawincorporatefinance

Gordon S. Roberts, CIBC Professor of Financial Services, Schulich School of Business, York University

17 Financial development in 205 economies, 1960 to 2010MartinČihák, Lead Economist, World BankAslıDemirgüç-Kunt, Director of Research, World BankErik Feyen, Senior Financial Specialist, World BankRoss Levine, Willis H. Booth Chair in Banking and Finance, University of California at Berkeley

37 Estimating the probability of a lost decade for U.S. and global equityBlake LeBaron, Abram L. and Thelma Sachar Chair of International Economics, International Business School, Brandeis University

47 Challengesforcentralbanks:widerpowers,greaterrestraints–thefinancialcrisisandits aftermathPhilip Middleton, Head of Central Banking, EY LLPDavid Marsh, Chairman, Official Monetary and Financial Institutions Forum (OMFIF)

67 Stress-testingbanks'profitability:thecaseofFrenchbanksJérômeCoffinet, Head of Statistical Engineering Division, Directorate General Statistics, Banque de France Surong Lin, Economist, Banque de France

81 Stress-testing models: a strategic risk management toolBalvinder Sangha, Principal and Leader, Credit and Capital Analytics team, Financial Services Risk Management Practice, EY LLPJane Lin, Senior Manager, Financial Services Risk Management Practice, EY LLP

Part 2 93 Calculating damages in ERISA litigation

Allen Ferrell, Greenfield Professor of Securities Law, Harvard Law School Atanu Saha, Senior Vice President, Compass Lexeco

105 Levered exchange-traded products: theory and practice John Mulvey, Professor of Operations Research and Financial Engineering, Princeton UniversityThomas Nadbielny, President, Benchmark Advisors, LLCWoo Chang Kim, Assistant Professor, Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology (KAIST)

119 Regulating insurance groups: a comparison of risk-based solvency modelsHato Schmeiser, Professor of Risk Management and Insurance Economics, University of St. GallenCaroline Siegel, Project Leader and Senior Research Associate, Institute of Insurance Economics University of St. Gallen

133 Determinants of the interest rate premium on contingent convertible bonds (CoCos)George M. von Furstenberg — J.H. Rudy Professor of Economics Emeritus, Department of Economics, Indiana University

145 Risk-on/risk-off,capitalflows,leverageandsafeassetsRobert N McCauley, Senior Advisor, Monetary and Economic Department, Bank for International Settlements

6 The Journal of Financial Perspectives

Gresham’slawincorporatefinanceby Gordon S. Roberts, CIBC Professor of Financial Services, Schulich School of Business, York UniversityGresham’s law: bad money drives out good appears applicable in modern day corporate finance. This article shows that where demand for a specific type of financing causes it to become overvalued, it becomes the financing mechanism of choice, as was the case during the Internet boom of the 1990s, where overvalued equities became the preferred method of payment for acquisitions. Consequently, this article helps us improve our understanding of corporate financing choices in both crisis and non-crisis times and highlights what regulators and investors should look out for when appraising and monitoring acquisitions.

Financial development in 205 economies, 1960 to 2010byMartinČihák, Lead Economist, World Bank, AslıDemirgüç-Kunt, Director of Research, World Bank, Erik Feyen, Senior Financial Specialist, World Bank, and Ross Levine, Willis H. Booth Chair in Banking and Finance, University of California at BerkeleyA growing body of evidence suggests that financial institutions and financial markets exert a powerful influence on economic development, poverty alleviation, and economic stability. This paper looks at how the Global Financial Development Database, which is an extensive dataset of financial system characteristics around the world since 1960s, is providing an improved way of measuring the functioning of financial systems. The paper highlights the multidimensional nature of financial systems and that focusing on only one characteristic, such as financial stability, or type of institution, say banks, means missing important characteristics of financial systems. This article helps us to assess linkages between finance and economic development and to assess the efficacy of different financial policies and regulation.

Estimating the probability of a lost decade for U.S. and global equityby Blake LeBaron, Abram L. and Thelma Sachar Chair of International Economics at the International Business School, Brandeis UniversityThis paper estimates the probability of equity investments losing value over a ten year period. It suggests that while lost decades are often treated as events that are extremely rare, they are not be as unlikely as many believe. Using data from U.S. and international markets over a very long period it finds that the likelihood of a lost decade is around 7%. This paper also highlights the importance of volatility in stock markets, even over the long term.

Executive summaries

7The Journal of Financial Perspectives

Challengesforcentralbanks:widerpowers,greaterrestraints—thefinancialcrisisand its aftermathby Philip Middleton, Head of Central Banking, EY LLP, and David Marsh, Chairman, Official Monetary and Financial Institutions Forum (OMFIF)A fundamental debate is taking place about the position of central banking, its relationship to government, and its role in the determination of public policy. This article questions the political position and accountability of central bankers, highlighting the challenges of adapting to an increasingly public role: it recommends that, in order to adapt, central banks must balance their greater responsibility with greater restraint.

Stress-testingbanks’profitability:thecaseofFrenchbanksbyJérômeCoffinet, Head of Statistical Engineering Division, Directorate General Statistics, Banque de France, and Surong Lin, Economist, Banque de FranceOver the last decades, banking systems of developed countries have experienced major changes regarding their sources of revenue. Ensuring the banking system’s solvency and identifying the vulnerabilities of banks’ profitability are crucial. This article presents a stress-testing framework to evaluate the sensitivity of banks’ profitability to plausible but severe adverse macroeconomic shocks. The results suggest that there is a statistically significant relationship between the macro environment and the profitability of the banking industry. Looking specifically at the resilience of French banks between 1993 and 2009, the findings show that, even in a severe recession, the French banking system would remain profitable.

Stress-testing models: a strategic risk management toolby Balvinder Sangha, Principal and Leader, Credit and Capital Analytics team, Financial Services Risk Management Practice, EY LLP, and Jane Lin, Senior Manager, Financial Services Risk Management Practice, EY LLPStress-testing has become a critical component of risk management, but the information it produces is only as reliable as the underlying model used. As such, this paper highlights the importance of using a variety of models and methodologies to produce a diagnosis of a bank’s health.

Calculating damages in ERISA litigationby Allen Ferrell, Greenfield Professor of Securities Law, Harvard Law School , and Atanu Saha, Senior Vice President, Compass LexecoWhilst Employment Retirement Income Security Act (ERISA) class action suits, which focus on the management and handling of pension and retirement plans, are becoming increasingly common, there has been limited discussion as to how to calculate ERISA damages. This paper presents and discusses four different methodologies for calculating ERISA damages using data from actual ERISA litigation. These different methods can result in strikingly different damage estimates, from U.S.$3 million with one method, to well over U.S.$2 billion with another in the same set of circumstances. To choose the appropriate method, this article highlights the importance of linking the damage method to the cause of the ERISA liability.


Levered exchange-traded products: theory and practiceby John Mulvey, Professor of Operations Research and Financial Engineering, Princeton University, Thomas Nadbielny, President, Benchmark Advisors, LLC, and Woo Chang Kim, Assistant Professor, Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology (KAIST) When levered exchange products were first introduced, they were heralded as a convenient mechanism for investors to achieve a better result than with more traditional borrowing and leveraging strategies. This article shows that rebalancing decisions have a major impact on the performance of levered and inverse strategies, especially during periods of high volatility. It considers the actual benefits of levered exchange-traded products, which do not always provide returns in line with their anticipated performance, and discusses the best rebalancing approaches. It demonstrates, through empirical testing, situations when daily rebalance leveraging is likely to outperform term borrowing leverage, and vice-versa.

Regulating insurance groups: a comparison of risk-based solvency modelsby Hato Schmeiser, Professor of Risk Management and Insurance Economics, University of St. Gallen, and Caroline Siegel, Project Leader and Senior Research Associate, Institute of Insurance Economics University of St. GallenRegulators are developing capital standards to monitor insurance groups more effectively. This paper provides a qualitative overview of the current approaches to group-wide solvency regulation through both a numerical and theoretical comparison of a consolidated and a legal-entity approach. The results reveal that the choice of a particular group solvency approach has a substantial influence on capital charges and shortfalls, provoking thinking around future business strategy.

Determinants of the interest rate premium on contingent convertible bonds (CoCos)by George M. von Furstenberg — J.H. Rudy Professor of Economics Emeritus, Department of Economics, Indiana UniversityCoCos are a promising but underutilized financial-reform instrument. Well-designed CoCos are cost-effective. This paper considers the impact of CoCos on a bank’s stakeholders: it states that the addition of CoCos to the balance sheet of systemically important financial institutions would strengthen the self-insurance of the financial system and relieve taxpayers of the burden of bail-outs.

Executive summaries


Risk-on/risk-off,capitalflows,leverageandsafeassetsby Robert N McCauley, Senior Advisor. Monetary and Economic Department, Bank for International SettlementsThis paper describes the international flow of funds associated with calm and volatile global equity markets. During calm periods, portfolio investment by real money and leveraged investors in advanced countries flows into emerging markets. When central banks in the receiving countries resist exchange rate appreciation and buy dollars against domestic currency, they end up investing in medium-term bonds in reserve currencies. In the process they fund themselves by issuing safe assets in domestic currency to domestic investors. Thus, calm periods, marked by leveraged investing in emerging markets, lead to an asymmetric asset swap (risky emerging market assets against safe reserve currency assets) and leveraging up by emerging market central banks. In declining and volatile global equity markets, these flows reverse, and, contrary to some claims, emerging market central banks draw down reserves substantially. In effect, emerging market central banks then release safe assets from their reserves, supplying safe havens to global investors. This paper traces the international flows of funds and leverage and concludes that the international flow of funds produces not an exchange of risky assets, but an acquisition of risky assets on one side and acquisition of safe assets on the other.

Part 1:

Gresham’s law in corporate finance

Financial development in 205 economies, 1960 to 2010

Estimating the probability of a lost decade for U.S. and global equity

Challenges for central banks: wider powers, greater restraints — the financial crisis and its aftermath

Stress-testing banks’ profitability: the case of French banks

Stress-testing models: a strategic risk management tool


Part 1

Gresham’s law in corporatefinanceGordon S. RobertsCIBC Professor of Financial Services, Schulich School of Business, York University1

AbstractFinancing patterns in corporate takeovers and private equity deals over the last twenty years demonstrate the widespread application of Rolnick and Weber’s (1986) extension of one of the most venerable principles of monetary economics: Gresham’s law. Two currencies, corporate securities (bad money) and cash (good money) circulate together with the former playing the dominant role of par money in times when investors exhibit irrational enthusiasm. Heightened social pressure in the form of herding combined with greater uncertainty about the degree and duration of the overvaluation of securities jointly play the role of transactions costs creating a preference for payment in the par money and most deals are financed with equity or debt securities rather than cash. To illustrate, overvalued bank loans were the most common form of financing in the credit bubble up to 2008 while stock deals predominated in takeover financing during the Internet bubble period of the late 1990s. Normal markets, not characterized by irrational enthusiasm, display the use of both corporate securities and cash in funding takeovers with cash deals (good money) enjoying a premium in the form of more favorable stock market reaction. The analysis provides useful insights for both monetary economists and researchers in corporate finance. For the former, it brings a fresh currency to the interpretation and extension of Gresham’s law relating the classic debate to contemporary, as opposed to historical, events. For the latter, the lesson is that principles of monetary economics can enhance understanding of corporate financing choices.

1 The Social Sciences and Humanities Research Council of Canada provided support for this research.


Gresham’slawincorporatefinance

IntroductionGresham’s law is widely known: “Bad money drives out the good.” An historical review traces examples back to ancient Greece [Bernholz (2011)]. In its original form, in order to hold, the law requires a key assumption: a legal tender law mandating equal valuation of good and bad money. Less widely known, however, is that, in the absence of a legal tender law, but with fixed transactions costs associated with paying a premium on undervalued currency (or exacting a discount on overvalued money), bad and good money can co-exist with one playing the role of the dominant, par money [Rolnick and Weber (1986); Selgin, (1996)]. Good money is not driven out but circulates at a premium (or bad money at a discount) as shown in the historical examples provided in Rolnick and Weber. When transactions costs become large, par money dominates. These insights have valuable applications beyond currency valuation.

In corporate finance, two “currencies” exist: cash and corporate securities. Securities can be either overvalued (bad money) or undervalued (good money) in the presence of investor irrationality. When this occurs there are two effects of interest. First, transactions occur in par money which may be either bad or good depending on whether the market is in a bubble period. Firms issue overvalued securities (bad money) creating value distortions for shareholders [Baker and Wurgler (2012)]. Issuance of overvalued mortgage-backed securities by investment banks contributed to the recent financial crisis [Baker and Wurgler (2012), Romero (2012)]. After the resulting stock market plunge, many companies announced share buyback programs using cash (good money). Transactions costs in the form of difficulty in determining the degree of over or undervaluation result in the majority of transactions moving to the par currency. Second, in normal markets, good and bad money may coexist with good money trading at a premium. For example, takeover offers are for either cash or shares. Overvalued firms use stock offers (bad money) while undervalued firm with growth options unrecognized by the market use cash (good money) and benefit from a premium in the form of a more favorable share price reaction [Savor and Lu (2008)].

This analysis provides a perspective on corporate finance placing current research in an historical and conceptual context. Doing so generates new evidence for Rolnick and Weber’s and Selgin’s clarifications of Gresham’s law by demonstrating their application

outside the realm of currency valuation. To achieve these goals, the paper restates the traditional version of the law and examines the relevant aspects of the debate in the context of currency applications. We then turn to relevant cases in corporate finance, including the recent financial crisis.

Understanding the lawGresham’s law is one of the more venerable principles of economics and finance: Macleod (1858) coined the term referencing a letter written by Sir Thomas Gresham to Queen Elizabeth I in 1558. Historical evidence demonstrates that the principle was understood widely considerably earlier. This long lineage notwithstanding, the law and its application have engendered considerable debate among modern economists. Selgin (1996) restates Gresham’s law as follows: “the proposition that, when an official fixed equivalence is imposed on two economically distinct monies (for example, silver coins of different weight), the “bad” (relatively less valuable) money will drive the “good” (relatively more valuable) one out of circulation (p638)”.

According to Selgin (2003), the term Gresham’s law was coined by Macleod in 1858 although an earlier Victorian economist reproduced the famous quote from Gresham’s letter to Queen Elizabeth I: “good and bad coin cannot circulate together” [Burgon, (1839)]. Sir Thomas Gresham made this remark in his role as a prominent merchant and the royal representative in Antwerp shortly after Elizabeth became queen. On taking the throne, she inherited a debased currency resulting from previous monarchs’ policy of reducing the amount of silver in coins.2 Strict legal tender laws were in force prohibiting exchange of coins at anything other than their face values. Purchasers paid their bills in “bad” (debased) coins and sellers quoted prices in these coins, resulting in inflation. “Good” coins with higher silver content were removed from circulation and either hoarded, exported to jurisdictions not subject to the legal tender law where they could circulate at a premium, “sweated” and reminted privately by moneychangers with superior information on their value, or returned to the mint at higher values [Dutu (2004, 2005)]. In short, “bad” money drove out the “good.” This ended in 1560 when the Queen “decried” the debased coins, officially devaluing them. At the same time new money was issued with higher silver content and declared legal tender.

2 This historical discussion is drawn principally from Selgin (1996).


Selgin (1996) interprets this example of the operation of Gresham’s law in the context of a Prisoner’s Dilemma. In the absence of a legal tender law, sellers can choose whether to request payment in “good” or “bad” money and set prices accordingly. When the law makes this illegal, sellers cannot discount “bad” money due to the fear that buyers might report them to the authorities. Similarly, a seller who insisted on payment in “good” money only would risk being forced to accept “bad” at face value. The result is a “bad” money equilibrium.

Although the interpretation in terms of the Prisoner’s Dilemma is a modern one, understanding of the basic principle underlying Gresham’s law goes back to ancient times. Aristophanes’ play, The Frogs, written around 400 B.C. contrasts “sterling pieces, all of pure Athenian mold” with “the worthless pinchbeck coins of yesterday, vilest die and basest metal [which] now we always use instead” [quoted in Bernholz (2011)]. Further evidence that Gresham’s law operated in ancient times comes from the study of coin hoards uncovered by modern archaeologists. Dating the approximate time that the hoards were buried, researchers established that the majority of the hoards consisted of older coins of greater value [Bolin (1958) as cited in Mundell (1998)].

Removing the legal tender lawThe discussion above highlights the importance of legal tender regulations to the operation of Gresham’s law. In the absence of such rules (laissez-faire exchange) Rolnick and Weber (1986) show that the outcome depends on the cost of non-par exchange, which involves evaluating coins and maintaining current information on the rate of exchange. When exchange is costless (or nearly so), both “good” and “bad” money can circulate and prices can be posted in either. When sellers price their goods and services in terms of “good” money, they will accept “bad” money at a discount. Conversely, with pricing in “bad” money, “good” money commands a premium. In contrast, when the costs of exchange are significant, buyers and sellers minimize these costs by transacting only in par money. In this case, par money (which could be either “good” or “bad”) will drive out non-par money. Selgin (1996) terms this statement, Rolnick and Weber’s Law. The costs of exchange reflect societal preferences and information asymmetry on the exchange rate and as these costs increase, the amount of non-par money in circulation declines.

The conclusions of Rolnick and Weber differ from Gresham’s law in two important respects. First, it is possible that two types of money can circulate together. Second, when par money drives out non-par, the par money can be either “good” or “bad” depending on which is more popular and therefore lower cost. As clarified by Selgin, Rolnick and Weber err when they claim that their analysis contradicts Gresham’s law. More correctly, they extend the analysis to cases which cannot be explained by Gresham’s law because no legal tender law existed.

A case highly relevant to our present day application in corporate finance occurred in the U.S. during and after the Civil War. In 1862, the U.S. government (the North) suspended payments in gold and silver and issued greenbacks, its first paper currency, to finance the war. This effectively set aside the legal tender law under which the two types of money were equivalent. At the time it was far from clear that the North would win the war and resume the issue of gold and silver coins and as a result, the greenbacks traded at a discount to specie (gold), priced as low as 40 cents on the dollar. As Rolnick and Weber state, “specie was the undervalued money and greenbacks were the overvalued money.” The overvalued (bad) paper currency became the par money throughout most of the northern states largely because banknotes were already widely accepted and hence lower cost. Gold coins were hoarded or had limited circulation at a premium. The exception occurred in California where gold coins were the most popular form of payment and greenbacks only rarely circulated.3 According to Greenfield and Rockoff (1995): “…Social pressure to use gold, a major export, proved insurmountable. California had shown a preference for hard money even before the War. The [state] constitution, written in 1849, prohibited paper money. A few private banks had issued notes, defying the law, but these notes had difficulty swimming against the tide of public opinion. Greenback inflation, of course, did nothing to warm Californians toward paper money. Social preferences became private costs. Debtors who tried repaying in greenbacks found themselves denounced for “greenbacking,” their names published in the newspapers.”

3 Greenfield and Rockoff (1995) show that the circulation of non-par currency during the U.S. Civil War was more limited than envisaged by Rolnick and Weber. Selgin (1996) points out that this is consistent with Rolnick and Weber’s Law but suggests that the costs of circulation for non-par money was more substantial than they believed.



The case demonstrates the working of Rolnick and Weber’s extension of Gresham’s law. In the East, the dominance of greenbacks (bad money) as par money accompanied by the highly restricted circulation of gold coins, approximated the situation predicted by Gresham’s law. In California, “social pressure” to pay in gold (good money) supported its role as par money and suppressed the circulation of greenbacks.

TwocurrenciesincorporatefinancingIn corporate finance, two “currencies” exist: cash and equity.4 Equity can be either overvalued (bad money) or undervalued (good money) in the presence of investor irrationality. One form of irrationality is investor tastes, which can explain share mispricing in the presence of limits to arbitrage [Baker (2009)]. In this vein, Greenwood and Hanson (2009) explain over — and undervaluation in terms of factor mispricing which “may fluctuate due to time-varying investor enthusiasm for different themes such as ‘internet’ or ‘small stocks.’” They identify the characteristics of firms (share price, distress status, industry, size, profitability and payout policy) and link them to net equity issuance (new shares minus repurchases). Characteristics of net issuers predict future returns — positive net issuance is associated with negative future abnormal returns while net repurchasers enjoy positive abnormal returns in future.

Enthusiasm can occur either at the industry or firm level. In the case of an industry bubble, share issues are used to finance takeovers in industries whose characteristics generate investor enthusiasm. Managers of overvalued acquirers seek to purchase hard assets with shares and when they succeed, wealth transfers from target to acquirer’s shareholders [Schleifer and Vishny (2003].

In the parlance of Rolnick and Weber’s extension of Gresham’s law, shares become the par money for takeovers in these industries and, since shares are overvalued in a bubble, the par currency is bad money in this case. As in the case of gold versus greenbacks discussed earlier, social pressure to “follow the herd” and invest in popular stocks works to create demand for par money shares. In their paper modeling herd behavior by investors, Scharstein and Stein [(1990), page 465] give the

4 The analysis here focuses on equity securities. The next section considers debt.

example of investor thinking leading up to the crash of October 1987: “The consensus among professional money managers was that price levels were too high — the market was, in their opinion, more likely to go down rather than up. However, few money managers were eager to sell their equity holdings. If the market did continue to go up, they were afraid of being perceived as lone fools for missing out on the ride. On the other hand, in the more likely event of a market decline, there would be comfort in numbers — how bad could they look if everybody else had suffered the same fate?”

The greater the investor enthusiasm and as a result, the bigger the bubble, the greater the percentage of transactions financed by stock. When investor enthusiasm for an industry wanes and the bubble bursts, net stock issuance becomes negative with share buybacks predominant. The number of takeovers declines and any that are made are likely to be financed with cash.

Savor and Lu [(2009), Figure 1] document “the equity-financed merger wave occurring in the second half of the 1990s.” They track U.S. mergers from 1978 through 2003 and show that the number of merger bids increased dramatically above historical levels in 1994 and remained elevated through 2000. In these years, roughly corresponding to the Internet bubble, the majority of bids were financed with stock, in contrast to roughly half in the non-bubble years, prior to 1990 and after 2001.

Investor enthusiasm for a “new paradigm” creates a form of social pressure to conform. During the Internet bubble, those reluctant to invest in untried companies were scorned as “failing to understand the new paradigm,” not unlike the disdain directed at those accused of “greenbacking” in California in the 1860s. As a substitute for investor enthusiasm, high transactions costs in the form of uncertainty about the degree of overvaluation provide an alternative explanation for the preponderance of overvalued shares as the par currency for takeovers during a bubble. As explained above and illustrated with the example of uncertainty over which side would win the U.S. Civil War, such high costs restrict the use of the non-par currency, cash in this case.

In the absence of a bubble, this effect can also occur at the firm level with some firms in an industry being overvalued and others undervalued. In this case, investor enthusiasm and uncertainty about the degree of overvaluation (transactions costs) are


more moderate and as a result both types of takeover financing are observed. As observed by Greenwood and Hanson (2009) and discussed earlier, overvalued firms issue shares to make an acquisition. Undervalued firms possessing growth options unobserved by investors make cash acquisitions. Such firms benefit from more favorable stock price reaction to the takeover announcement as the use of cash is seen as a signal that the acquirer’s management believes its shares are undervalued.

TwocurrenciesinfinancialintermediationThe discussion to this point has focused on the role of corporations as issuers of overvalued equity, but the same principles apply to financial intermediaries issuing overvalued debt.5 During the credit bubble prior to 2008, commercial and investment banks capitalized on investor enthusiasm for overpriced debt. While the best known example of that period was securitized subprime mortgages, there was also a large market providing financing for private equity deals directly related to our discussion above on corporate takeovers. As with the use of overpriced securities in corporate acquisitions, investor enthusiasm for debt of seemingly low risk kept the market going. This was coupled with difficulty in determining how long the bubble would last. Charles Prince, then CEO of Citigroup, was referring to the market for private equity financing in his well-known quote as is clear when the context is provided [Nakamoto and Wighton (2007)]: “Chuck Prince on Monday dismissed fears that the music was about to stop for the cheap credit-fuelled buy-out boom, saying Citigroup was “still dancing.” The Citigroup chief executive told the Financial Times that the party would end at some point but there was so much liquidity it would not be disrupted by the turmoil in the U.S. subprime mortgage market.

He denied that Citigroup, one of the biggest providers of finance to private equity deals, was pulling back. “When the music stops, in terms of liquidity, things will be complicated. But as long as the music is playing, you’ve got to get up and dance. We’re still dancing.”

When banks like Citigroup provided debt financing for private equity deals, they catered to investor enthusiasm and evidence suggests that the financing was overpriced. Bank-affiliated deals

5 The discussion here draws on Baker and Wurgler (2012).

in which the private equity fund was an arm of the bank benefited from more favorable financing terms than did deals of similar ex-ante risk sponsored by outside private equity funds. Further, when the deals sponsored by banks occurred at credit market peaks, the ex-post risk measured by subsequent debt downgrades was higher [Fang et al. (2012].

ConclusionsThe realm of corporate takeovers and private equity deals demonstrates the widespread application of Rolnick and Weber’s (1986) extension of Gresham’s law. Two currencies, corporate securities (bad money) and cash (good money) circulate together with the former playing the dominant role of par money in times when investors exhibit irrational enthusiasm. Heightened social pressure in the form of herding combined with greater uncertainty about the degree and duration of the overvaluation of securities jointly play the role of transactions costs, creating a preference for payment in the par money and most deals are financed with equity or debt securities rather than cash. As examples, during the Internet bubble period of the late 1990s, stock deals predominated while in the credit bubble of 2007, overvalued bank loans were the most common form of financing. Normal markets, not characterized by irrational enthusiasm, display the use of both corporate securities and cash in funding takeovers with cash deals (good money), enjoying a premium in the form of more favorable stock market reaction.

The analysis provides useful insights for both monetary economists and researchers in corporate finance. For the former, it brings a fresh currency to the interpretation and extension of Gresham’s law relating the classic debate to contemporary events. For the latter, the lesson is that principles of monetary economics can enhance understanding of corporate financing choices in both crisis and non-crisis times.



ReferencesBaker, M., 2009, “Capital market-driven corporate finance,” Annual Review of Economics, 1, 181-205Baker, M., and J. Wurgler, 2012, “Behavioral corporate finance: an updated survey,” in Constantinides, G. M., M. Harris, and R. M. Stulz (eds.), Handbook of the economics of finance: Volume 2, Elsevier Press, AmsterdamBernholz, P., 2011, “Understanding early monetary developments by applying economic laws: the monetary approach to the balance of payments, Gresham’s and Thier’s laws,” Available at SSRN: http://ssrn.com/abstract=1799983 Bolin, S., 1958, State and currency in the Roman Empire to 300 A.D., Stockholm, Almqauist & WiksellBurgon, J. W., 1839, The life and times of Sir Thomas Gresham, Royal Exchange, LondonDutu, R., 2004, “Moneychangers, private information and Gresham’s law in late medieval Europe,” Revista de Historia Economica (Second Series) 22(3), 555-571Dutu, R., E. Nosal, and G. Rocheteau, 2005, “The tale of Gresham’s law,” Economic Commentary, Federal Reserve Bank of Cleveland (October)Fang, L. H., V. Ivashina, and J. Lerner, J., 2012, “Combining banking with private equity investing,” AFA 2011 Denver Meetings Paper; Harvard Business School Finance Working Paper No. 10-106. Available at SSRN: http://ssrn.com/abstract=1571921 or http://dx.doi.org/10.2139/ssrn.1571921Greenfield,R.L.,andH.Rockoff,1995,“Gresham’s law in nineteenth century America”, Journal of Money, Credit and Banking, 27(4), 1086-1098Greenwood, R., and S. G. Hanson, 2012, “Share issuance and factor timing,” Journal of Finance, 67(2), 761-798Macleod, H. D., 1858, Elements of political economy, Cosimo: New York (2007)Mundell, R., 1998, “Uses and abuses of Gresham’s law in the history of money,” Zagreb Journal of Economics, 2(2), 57-72Nakamoto, M., and D. Wighton, 2007, “Citigroup chief stays bullish on buyouts, Financial Times (July 9), http://www.ft.com/intl/cms/s/0/80e2987a-2e50-11dc-821c-0000779fd2ac.html#axzz2OYyOFb00 Rolnick, A. J., and W. E. Weber, 1986, “Gresham’s law or Gresham’s fallacy?”, Journal of Political Economy, 94(1), 185-199Romero, P., 2012, “Why did the U.S. market for mortgage backed securities unravel?” Available at SSRN:http://ssrn.com.abstract=2123455Savor, P. G., and Q. Lu, 2008, “Do stock mergers create value for acquirers?”, Journal of Finance, 44(3), 1061-1097Scharfstein, D. S., and J. C. Stein, 1990, “Herd behavior and investment” American Economic Review, 80(3), 465-479Selgin, G., 1996, “Salvaging Gresham’s law, the good, the bad and the illegal,” Journal of Money, Credit and Banking, 28(4), 637-649Selgin, G., 2003, “Gresham’s law,” E.H. Net Encyclopedia, Whaples, R., (ed), URL http://eh.net/encyclopedia/article/sekgub,gresham.law Shleifer, A., and R. Vishny, 2003, “Stock market driven acquisitions,” Journal of Financial Economics, 70, 295-311


Part 1

Financial development in 205 economies, 1960 to 2010MartinČihákLead Economist, World Bank

AslıDemirgüç-KuntDirector of Research, World Bank

Erik FeyenSenior Financial Specialist, World Bank

Ross LevineWillis H. Booth Chair in Banking and Finance, University of California at Berkeley1

AbstractThis paper describes our construction of the Global Financial Development Database and uses the data to compare financial systems around the world. The database (available at www.worldbank.org/financialdevelopment) provides information on financial systems in 205 economies over the period from 1960 to 2010 and includes measures of (1) size of financial institutions and markets (financial depth), (2) degree to which individuals and firms can and do use financial services (access), (3) efficiency of financial intermediaries and markets in intermediating resources and facilitating financial transactions (efficiency) and (4) stability of financial institutions and markets (stability).

1 The database builds on previous data compilation work, in particular Beck, Demirgüç-Kunt and Levine (2000, 2010). The findings, interpretations and conclusions in this paper are those of the authors and do not necessarily represent the views of the World Bank, its Executive Directors or the countries they represent. The paper benefited from comments by Thorsten Beck, Sergio Schmuckler, Roberto Rocha, Stijn Claessens, Augusto de la Torre, Norman Loayza, Tunc Uyanik and participants of several seminars. Amin Mohseni, Mauricio Pinzon Latorre and Subika Farazi provided research assistance. Katie Kibuuka, Diego Sourrouille, Ed Al-Hussainy, Haocong Ren and Andrea Coppola helped with compiling parts of the dataset. All remaining errors are those of the authors.



IntroductionA growing body of evidence suggests that financial institutions (such as banks and insurance companies) and financial markets (including stock markets, bond markets and derivative markets) exert a powerful influence on economic development, poverty alleviation and economic stability [Levine (2005)]. For example, when banks screen borrowers and identify firms with the most promising prospects, this is a key step that helps allocate resources efficiently, expand economic opportunities and foster growth. When banks and securities markets mobilize savings from households to invest in promising projects, this is another crucial step in fostering economic development. When financial institutions monitor the use of investments and scrutinize managerial performance, this is an additional ingredient in boosting the efficiency of corporations and reducing waste and fraud by corporate insiders. But, that is not all. When equity, bond and derivative markets enable the diversification of risk, this encourages investment in higher-return projects that might otherwise be shunned. And, when financial systems lower transactions costs, it facilitates trade and specialization — fundamental inputs to technological innovation [Smith (1776)].

But, when financial systems perform these functions poorly, they tend to hinder economic growth, curtail economic opportunities and destabilize economies. For example, if financial systems simply collect funds with one hand and pass them along to cronies, the wealthy and the politically-connected with the other hand, this slows economic growth and prohibits many potential entrepreneurs from even attempting to realize their economic dreams. And, if financial institutions fail to exert sound corporate governance over the firms that they fund, this makes it easier for managers to pursue projects that benefit themselves rather than the firm and the overall economy. When financial institutions create complex financial instruments and sell them to unsophisticated investors, this might boost the bonuses of the financial engineers and executives associated with marketing the new-fangled instruments while simultaneously distorting the allocation of society’s savings and impeding economic prosperity [Barth et al. (2006, 2012)].

Although the evidence on the role of the financial system in shaping economic development is substantial and varied, there are serious shortcomings associated with measuring the central concept under consideration: the functioning of the financial

system. Researchers do not have good cross-country, cross-time measures of the degree to which financial systems (1) enhance the quality of information about firms and hence the efficiency of resource allocation, (2) exert sound corporate governance over the firms to which they funnel those resources, (3) provide effective mechanisms for managing, pooling and diversifying risk, (4) mobilize savings from disparate savers so that these resources can be allocated to the most promising projects in the economy and (5) facilitate trade. Instead, researchers have largely — though not exclusively — relied on measures of the size of the banking industry as a proxy. But, banking sector size is not a measure of quality, or efficiency, or stability. And, the banking sector is only one component of financial systems.

The major contribution of this paper is the construction of improved measures of the functioning of financial systems in 205 economies from 1960 to 2010. We call the resultant database the “Global Financial Development Database.” It is available at www.worldbank.org/financialdevelopment and http://data.worldbank.org/data-catalog/global-financial-development.

To quantify the functioning of financial systems, we develop several measures of four broad characteristics of financial institutions and markets: (1) the size of financial institutions and markets (financial depth), (2) the degree to which individuals can and do use financial institutions and markets (access), (3) the efficiency of financial institutions and markets in providing financial services (efficiency) and (4) the stability of financial institutions and markets (stability). These four characteristics are measured both for (1) financial institutions (mostly for banks, which are the major financial institution in most economies, but also for insurance companies and other financial institutions) and (2) financial markets (equity and bond markets), thus leading to a 4x2 matrix of financial system characteristics. The paper then uses these measures to characterize and compare financial systems across countries and over time.

In focusing on these four characteristics of financial institutions and markets, we seek to provide empirical shape and substance to the complex, multifaceted and sometimes amorphous concept of the “functioning of financial systems.” We recognize that financial depth, access, efficiency and stability might not fully capture all features of financial systems, but they reflect features on which much of the empirical literature has been concentrating.


We make these new and improved measures of financial development available so that others can use them to benchmark national financial systems and test particular hypotheses. The analyses presented in this paper, together with the underlying datasets, highlight the multi-dimensional nature of financial systems. Deep financial systems do not necessarily provide high degrees of financial access; highly efficient financial systems are not necessarily more stable than the less efficient ones, and so on. The paper illustrates that financial systems come in different shapes and sizes, and they differ widely in terms of the 4x2 matrix of characteristics.

Theconceptoffinancialdevelopmentanditslinkstoeconomic development There has been a considerable debate among economists on the role of financial development in economic growth and poverty reduction, but the balance of theoretical reasoning and empirical evidence suggests that finance has a central role in socio-economic development [Levine (1997, 2005)]. Economies with higher levels of financial development grow faster and experience faster reductions in poverty levels. This section introduces the concept of financial development and provides a brief review of the literature on the linkages between financial development, economic growth and poverty reduction.

Markets are imperfect. It is costly to acquire and process information about potential investments. There are costs and uncertainties associated with writing, interpreting and enforcing contracts. And, there are costs associated with transacting goods, services and financial instruments. These market imperfections inhibit the flow of society’s savings to those with the best ideas and projects, curtailing economic development and retarding improvements in living standards.

It is the existence of these costs — these market imperfections — that creates incentives for the emergence of financial contracts, markets and intermediaries. Motivated by profits, people create financial products and institutions to ameliorate the effects of these market imperfections. And, governments often provide an array of services — ranging from legal and accounting systems to government-owned banks — with the stated goals of reducing these imperfections and enhancing resource allocation. Some economies are comparatively successful at developing

financial systems that reduce these costs. Other economies are considerably less successful, with potentially large effects on economic development.

At the most basic, conceptual level, therefore, financial development occurs when financial instruments, markets and intermediaries mitigate — though do not necessarily eliminate — the effects of imperfect information, limited enforcement and transactions costs. For example, the creation of credit registries tended to improve acquisition and dissemination of information about potential borrowers, improving the allocation of resources with positive effects on economic development. As another example, economies with effective legal and regulatory systems have facilitated the development of equity and bond markets that allow investors to hold more diversified portfolios than they could without efficient securities markets. This greater risk diversification can facilitate the flow of capital to higher return projects, boosting growth and enhancing living standards.

Defining financial development in terms of the degree to which the financial system eases market imperfections, however, is too narrow and does not provide much information on the actual functions provided by the financial system to the overall economy. Thus, Merton (1992), Levine (1997, 2005), Merton and Bodie (2004) and others have developed broader definitions that focus on what the financial system actually does.

At a broader level, financial development can be defined as improvements in the quality of five key financial functions: (1) producing and processing information about possible investments and allocating capital based on these assessments; (2) monitoring individuals and firms and exerting corporate governance after allocating capital; (3) facilitating the trading, diversification and management of risk; (4) mobilizing and pooling savings; and (5) easing the exchange of goods, services and financial instruments. Financial institutions and markets around the world differ markedly in how well they provide these key services. Although this paper sometimes focuses on the role of the financial systems in reducing information, contracting and transactions costs, it primarily adopts a broader view of finance and stresses the key functions provided by the financial system to the overall economy.



Economists have long debated the role of the financial sector in economic growth. Lucas (1988), for example, dismissed finance as an over-stressed determinant of economic growth. Robinson (1952, p. 86) quipped that “where enterprise leads finance follows.” From this perspective, finance responds to demands from the non-financial sector; it does not cause economic growth. At the other extreme, Miller (1988, p.14) argued that the idea that financial markets contribute to economic growth “is a proposition too obvious for serious discussion.” Bagehot (1873) and others rejected the idea that the finance-growth nexus can be safely ignored without substantially limiting the understanding of economic growth.

Recent literature reviews, such as Levine (2005) and Demirgüç-Kunt and Levine (2008), conclude that the preponderance of evidence suggests a positive, first-order relationship between financial development and economic growth. In other words, well-functioning financial systems play an independent role in promoting long-run economic growth: economies with better-developed financial systems tend to grow faster over long periods of time, and a large body of evidence suggests that this effect is causal.

Moreover, research sheds light on the mechanisms through which finance affects growth — the financial system influences growth primarily by affecting the allocation of society’s savings, not by affecting the aggregate savings rate. Thus, when financial systems do a good job of identifying and funding those firms with the best prospects, not those firms simply with the strongest political connections, this improves the capital allocation and fosters economic growth. Such financial systems promote the entry of new, promising firms and force the exit of less efficient enterprises. They also expand economic opportunities, so that the allocation of credit — and hence opportunity — is less closely tied to accumulated wealth and more closely connected to the social value of the project. Furthermore, by improving the governance of firms, well-functioning financial markets and institutions reduce waste and fraud, boosting the efficient use of scarce resources. By facilitating risk management, financial systems can ease the financing of higher return endeavors with positive reverberations on living standards. And, by pooling society’s savings, financial systems make it possible to exploit economies of scale — getting the biggest development bang for available resources.

The4x2frameworkforbenchmarkingfinancialsystemsTo capture the key features of financial systems, one would ideally like to have direct measures of how well financial institutions and financial markets (1) produce information ex-ante about possible investments and allocate capital; (2) monitor investments and exert corporate governance after providing finance; (3) facilitate the trading, diversification and management of risk; (4) mobilize and pool savings; and (5) ease the exchange of goods and services. So, if measurement was not an issue, one would like to be able to say that in terms of producing information about possible investments and allocation of capital, the financial sector in Country A, for example, scores 60 on a scale from 0 to 100, while Country B’s financial sector scores 75; in terms of monitoring investments and exerting corporate governance after providing finance, Country A scores 90, while Country B scores only 20 on a scale from 0 to 100, and so on. But, researchers have so far been unable to obtain such direct measures of these financial functions.

The goal of this paper is to construct measures of four important characteristics of financial systems: (1) depth, (2) access, (3) efficiency and (4) stability. These financial system characteristics are proxies of the services provided by the financial system. For example, “financial depth” is not a function in itself, but it is a proxy of the overall extent of services provided by the financial system. Similarly, our measures of “access” do not directly measure how well the financial system identifies good investments, regardless of the collateral of the individual; but it provides an (imperfect, ex-post) approximation of the breadth of use of particular financial institutions and instruments. For each of the four characteristics, this paper presents measures for both financial institutions and financial markets. The resulting 4x2 matrix of financial system characteristics (Table 1), which builds on a large literature seeking to compare financial systems empirically, illustrates the multi-dimensional nature of financial systems.2

2 In each of the cells in the 4x2 matrix, Table 1 shows several variables. In some cases, the variables in the same cell are complementary (for example, total assets of banks to GDP and total assets of non-bank financial institutions to GDP are expressed in the same units and complement each other, so they can be summed up to approximate total assets of financial institutions to GDP). In other cases, the variables measure similar concepts in different ways, with different degrees of comprehensiveness. For example, private credit to GDP and total assets of financial institutions to GDP are both proxies for financial institutions’ size. Private credit to GDP covers a sub-set of assets but is available for a larger number of economies. In Table 1, variables with the highest country coverage are highlighted in bold. The competing indicators tend to be highly but not perfectly correlated. For example, the correlation coefficient for private credit to GDP and banking sector’s total assets to GDP is 0.9.


The resulting database that we construct — Global Financial Development Database — builds on, updates, and extends previous efforts, in particular the data collected for the “Database on Financial Development and Structure” by Beck et al. (2000, 2010). The database also incorporates data from the Financial Access Survey (fas.imf.org) and the Global Findex (www.worldbank.org/globalfindex).

Financial depth With regards to financial depth, the variable that has received much attention in the empirical literature on financial development is private credit to GDP. More specifically, the variable is defined as domestic private credit to the real sector by deposit money banks as a percentage of local currency GDP. The private credit, therefore, excludes credit issued to governments, government agencies and public enterprises. It also excludes credit issued by central banks. Private credit to GDP differs widely across countries, and it correlates strongly with income level. For example, private credit to GDP in high-income countries is 103% in high-income

countries, more than four times the average ratio in low-income countries (Table 2). Based on this measure, economies with deep financial systems include many of those in Europe; Canada, Australia and South Africa are also among those in the highest quartile in terms of private credit to GDP. China’s financial system is also in the highest quartile in terms of this measure, higher than other major emerging markets such as Russia, Brazil and India. The United States’ financial system, while above average, is not as deep as China’s. This reflects in part the more market-based nature of the U.S. financial system.

Financial depth, approximated by private credit to GDP, has a strong statistical link to long-term economic growth; it is also closely linked to poverty reduction [see, for example, Demirgüç-Kunt and Levine (2008)]. To illustrate, Table 3 summarizes the relationship between per capita GDP growth and various measures of financial intermediary depth. The reported cross-country growth regressions update the earlier analyses by King and Levine (1993b) by enhancing and extending their data. Figure 1

Financial institutions Financial markets

Dep

th

Private credit to GDPFinancial institutions’ assets to GDPM2 to GDPDeposits to GDPGross value-added of the financial sector to GDP

Stock market capitalization plus outstanding domestic private debt securities to GDPPrivate debt securities to GDPPublic debt securities to GDP International debt securities to GDP Stock market capitalization to GDP Stocks traded to GDP

Acc

ess

Accounts per thousand adults (commercial banks)Branches per 100,000 adults (commercial banks)% of people with a bank account% of firms with line of credit (all firms)% of firms with line of credit (small firms)

Percent of market capitalization outside of top 10 largest companiesPercent of value traded outside of top 10 traded companies Government bond yields (3 month and 10 years) Ratio of domestic to total debt securities Ratio of private to total debt securities (domestic) Ratio of new corporate bond issues to GDP

Effic

ienc

y

Net interest marginLending-deposits spreadNon-interest income to total income Overhead costs (% of total assets)Profitability (return on assets, return on equity)Boone indicator (or Herfindahl or H-statistics)

Turnover ratio (turnover/capitalization) for stock marketPrice synchronicity (co-movement) Private information trading Price impact Liquidity/transaction costs Quoted bid-ask spread for government bonds Turnover of bonds (private, public) on securities exchange Settlement efficiency

Stab

ility

Z-score (or distance to default) capital adequacy ratiosasset quality ratiosliquidity ratiosOther (net foreign exchange position to capital etc.)

Volatility (standard deviation/average) of stock price index, sovereign bond indexSkewness of the index (stock price, sovereign bond)Vulnerability to earnings manipulationPrice/earnings ratioDurationRatio of short-term to total bonds (domestic, international) Correlation with major bond returns (German, U.S.)

Table1:The4x2matrixoffinancialsystemcharacteristicsNote: In bold, we highlight those measures within each category that are the most widely available.



provides a basic illustration of the link between financial depth, approximated by the ratio of private sector credit to gross domestic product, and income inequality, approximated by changes in the Gini coefficient. The figure illustrates that higher levels of financial development are associated with declines in inequality. These observations are in line with more in-depth empirical research based on microeconomic data.3

Nonetheless, a high ratio of private sector credit to GDP is not necessarily a good thing. Indeed, all the eight countries with the highest ratios of private sector credit to GDP as of 2010 (Cyprus,

3 For example, evidence suggests that access to credit markets increases parental investment in the education of their children and reduces the substitution of children out of schooling and into labor markets when adverse shocks reduce family income [Belley and Lochner (2007)]. Better-functioning financial systems stimulate new firm formation and help small, promising firms expand as a wider array of firms gain access to the financial system. Moreover, better-functioning financial systems will identify and fund better projects, with less emphasis on collateral and incumbency. Not only do they allow new, efficient firms to enter, they also force old, inefficient firms to leave, as evidenced by data [Kerr and Nanda (2009)].

Ireland, Spain, the Netherlands, Portugal, the U.K., Luxembourg and Switzerland, going from the highest to the lowest) had a banking crisis episode since 2008.4

An alternative to private credit to GDP is total banking assets to GDP, a variable that is also included in the Global Financial Development Database. It is arguably a more comprehensive measure of size, because it includes not only credit to private sector, but also credit to government as well as bank assets other than credit. However, it is available for a smaller number of economies and has been used less extensively in the literature on financial development. In any case, the two variables are rather closely correlated (with a correlation coefficient of about 0.9 over the whole sample).

4 Hong Kong SAR, a jurisdiction that is not a country but reports data on a separate basis, would rank between U.K. and Luxembourg in terms of the variable.

Private credit to GDP (%) Number of countries

Average Median Standard deviation

Minimum Maximum Weighted average1

World 173 56.3 38.8 54.6 3.2 361.7 89.9By developed/developing economiesDeveloped economies 48 113.3 100.1 68.6 3.3 361.7 103.0Developing economies 125 34.5 26.3 24.9 3.2 112.0 60.5By income levelHigh income 48 113.3 100.1 68.6 3.3 361.7 103.0Upper middle income 49 48.6 44.5 28.0 8.0 112.0 67.8Lower middle income 49 30.8 27.0 18.7 3.2 96.8 36.6Low income 27 15.4 12.8 9.9 3.3 44.7 24.9By regionHigh income: OECD 30 124.0 109.4 52.2 43.2 228.2 103.7High income: non-OECD 17 97.3 65.6 90.7 3.3 361.7 80.7East Asia and Pacific 17 46.8 38.8 34.6 3.3 111.1 100.1Europe and Central Asia 19 44.9 41.1 19.6 16.0 88.1 40.4Latin America and Caribbean 29 41.5 32.0 24.2 12.3 112.0 33.4Middle East and North Africa 12 34.5 29.1 26.0 5.5 71.8 32.1South Asia 8 35.3 34.6 17.3 7.9 66.1 41.1Sub-Saharan Africa 41 20.1 16.4 16.9 3.2 80.8 38.7

Table2:Depth—financialinstitutions(2008–2010)Source: Authors’ calculations are based on the Global Financial Development Database.Note: Domestic private credit to the real sector by deposit money banks as percentage of local currency GDP. Data on domestic private credit to the real sector by deposit money banks is from the International Financial Statistics (IFS) line 22D published by the International Monetary Fund (IMF). Local currency GDP is also from IFS. Missing observations are imputed by using GDP growth rates from World Development Indicators (WDI). Arithmetic average of annual observations for 2008–2010. 1 To calculate the group averages, country-by-country observations are weighted by nominal GDP.


Despite the literature’s focus on banks, the recent crisis has highlighted issues in non-bank financial institutions (NBFIs). The coverage of NBFIs by data is much less comprehensive than that of banks. Nonetheless, to acknowledge this point, the Global Financial Development Database includes total assets of NBFIs to GDP, which includes pension fund assets to GDP, mutual fund assets to GDP, insurance company assets to GDP, insurance premiums (life) to GDP and insurance premiums (non-life) to GDP.

For financial markets, earlier work by Levine and Zervos (1998) indicates that the trading of ownership claims on firms in an economy is closely tied to the rate of economic development. In the database, financial market depth is approximated using a combination of data on stock markets and bond markets. To approximate the size of stock markets, a common choice in the literature is stock market capitalization to GDP. For bond markets, a commonly used proxy for size is the outstanding volume of private debt securities to GDP. The sum of these two provides a

rough indication of the relative size of the financial markets in various countries.

There is substantial variation among countries, by size and by income level (Table 4). For example, over the 2008–2010 period, the world-wide average value of this ratio was 131%, but individual country observations ranged from less than 1% to 533%. The average for developed economies was 151%, while the average for developing economies was about a half, at 76%. Also, in bigger countries, financial markets tend to play a relatively larger role relative to the size of the economy.5 Countries in the highest quartile of the world-wide distribution include not only the U.S., Canada, Japan and other major developed economies, but for example also China and Malaysia.

5 In Table 4, this is illustrated by the fact that the world-wide median is only 49%, while the weighted average (with nominal GDP as weight) is 131%.

Dependent variable Depth Bank Privy

Real per capita GDP growth 2.4** 3.2** 3.2**

(0.007) (0.005) (0.002)

R2 0.5 0.5 0.52

Real per capita capital growth 2.2** 2.2** 2.5**

(0.006) (0.008) (0.007)

R2 0.65 0.62 0.64

Productivity growth 1.8** 2.6** 2.5**

(0.026) (0.010) (0.006)

R2 0.42 0.43 0.44

Table 3: Financial depth and economic growth (1960-2010) Source: Authors’ update on King and Levine (1993b), Table VII, using the Global Financial Development Database.Notes: King and Levine (1993b) define 2% growth as 0.02; here, 2% growth is 2.00. * significant at the 0.10 level, ** significant at the 0.05 level, p-values in parentheses, Observations: 77Variable definitions: Depth = Liquid liabilities/GDP, Bank = Deposit bank domestic credit/(deposit bank domestic credit + central bank domestic credit), Privy = Gross claims on the private sector/GDP,Productivity growth = Real per capita GDP growth – (0.3)*(Real per capita Capital growth)Other explanatory variables included in each of the nine regression results reported above: logarithm of initial income, logarithm of initial secondary school enrollment, ratio of government consumption expenditures to GDP, inflation rate, and ratio of exports plus imports to GDP.

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Figure 1: Financial depth and income inequality (1960-2010)Source: Authors’ update on Beck, Demirgüç-Kunt and Levine (2007), using data from the Global Financial Development Database.Note: The Gini coefficient is on a scale from 0 (total equality) to 1 (maximum inequality). The chart is a partial scatter plot, visually representing the regression of changes in the Gini coefficient between 1960 and 2010 on the private credit-to-GDP ratio (logarithm, 1960—2010 average), controlling for the initial (1960) Gini coefficient. Variables on both axes are residuals. The abbreviations next to some of the observations are the three-letter country codes as defined by the International Organization for Standardization.



The size of financial institutions relative to the size of financial markets is central to the study of “financial structures” — [Demirgüç-Kunt and Levine (2001), Demirgüç-Kunt et al. (2012)]. The literature on financial structures seeks to assess whether and under which conditions the mixture of financial institutions and financial markets in an economy exerts an influence on economic development that is independent of the overall level of financial development. Does the mixture of financial institutions and markets matter? We find that financial structure differs markedly across economies. Over the full sample period, the annual average value of the financial structure ratio is 279. Countries such as Australia, India, Singapore and Sweden have this ratio at or below 2.35 (10th percentile), while Bolivia, Bulgaria, Serbia and Uganda are examples of countries where this ratio is over 356 (90th percentile).

Financial access Better functioning financial systems allocate capital based more on the expected quality of the project and entrepreneur and less on the accumulated wealth and social connections of the entrepreneur. Under many conditions, therefore, better functioning financial systems that overcome market frictions will more effectively identify and fund the most promising firms and not just funnel credit to large companies and rich individuals. Thus, to develop informative proxies of financial development, it is useful to move beyond financial depth and also include indicators of financial access — the degree to which the public can access financial services. As with the other measures, both financial institutions and financial markets are examined.

With regards to access to financial institutions, a common proxy variable is the number of bank accounts per 1,000 adults. Other variables in this category include the number of bank branches per 100,000 adults (commercial banks) and the percentage

Stock market capitalization plus outstanding domestic private debt securities to GDP (%)

Number of countries




Table4:Depth—financialmarkets(2008–2010)Source: Authors’ calculations are based on the Global Financial Development Database.Note: Stock market capitalization plus the amount of outstanding domestic private debt securities as percentage of GDP. Market capitalization (also known as market value) is the share price times the number of shares outstanding. Listed domestic companies are the domestically incorporated companies listed on the country’s stock exchanges at the end of the year. Listed companies does not include investment companies, mutual funds, or other collective investment vehicles. Data is from Standard & Poor’s, Global Stock Markets Factbook and supplemental S&P data, and is compiled and reported by the WDI. Amount of outstanding domestic private debt securities is from Table 16A (domestic debt amount) of the Securities Statistics by Bank for International Settlements. The amount includes all issuers except governments. Arithmetic average of annual observations for 2008–2010.1 To calculate the group averages, country-by-country observations are weighted by nominal GDP.


of firms with line of credit (all firms, small firms). When using these proxies, one needs to be mindful of their weaknesses. For example, the number of bank branches is becoming increasingly misleading with the move towards branchless banking. The number of bank accounts does not suffer from the same issue, but it has its own limitations. In particular, it focuses on banks only, and does not correct for the fact that some bank clients have numerous accounts.

Much of the data for the financial access dimension of the Global Financial Development Database come from the recently established Financial Access Survey database (fas.imf.org), which is based on earlier work by Beck et al. (2007) and currently contains annual data for 187 jurisdictions for the period 2004 to 2011. A portion of the financial access data is from the newly constructed Global Financial Inclusion Indicators, or “Global Findex” dataset [Demirgüç-Kunt and Klapper (2012)]. The Global Findex is the first public database

of indicators that consistently measures individuals’ usage of financial products across economies. It can be used to track the potential impact of global financial inclusion policies and facilitate a deeper and more nuanced understanding of how adults around the world save, borrow, and make payments. It is based on detailed interviews with at least 1,000 people per economy in some 150 economies about their financial behavior through the Gallup World Poll survey.

Table 5 illustrates the wide dispersion in access to finance across countries, using the provider-side data. World-wide, there were about 1.34 bank accounts per adult in 2008–2010, but the observations ranged from less than 0.01 to 7.19 accounts per adult. The average for developing economies was 0.69 accounts per adult, a mere fraction of the 3.76 per adult in developed economies.

Accounts per thousand adults from commercial banks

Number of countries




Table5:Access—financialinstitutions(2008–2010)Source: Authors’ calculations are based on the Global Financial Development Database.Note: Number of depositors with commercial banks per 1,000 adults. For each type of institution the calculation follows: (reported number of depositors)*1,000/adult population in the reporting country. Number of commercial bank depositors is from the Financial Access Survey (fas.imf.org). Adult population data is from WDI. Arithmetic average of annual observations for 2008–2010.1 To calculate the group averages, country-by-country observations are weighted by total adult population.



The disparity between developed and developing economies in terms of financial access is confirmed also by user-side data from the Global Findex (Figure 2). Here, the focus is on account penetration, that is, the percentage of adults that have at least on account at a formal financial institution. Again, account penetration differs enormously between high-income and developing economies. While it is nearly universal in high-income economies, with 89% of adults reporting that they have an account at a formal financial institution, it is only 24% in low income economies. Globally, more than 2.5 billion adults do not have a formal account, and a majority of this group resides in developing economies. In several economies (such as Cambodia, the Democratic Republic of Congo, Guinea, the Kyrgyz Republic, Turkmenistan and the Republic of Yemen) less than 5% of adults have a formal account.

Data on access to financial markets is relatively more scant. To approximate access to stock and bond markets, measures of market concentration are used, the idea being that a higher degree of concentration reflects greater difficulties for access for newer or smaller issuers. The variables in this category include the percentage of market capitalization outside of top 10 largest companies, the percentage of value traded outside of top 10 traded companies, government bond yields (3 month and 10 years), ratio of domestic to total debt securities, ratio of private to total debt securities (domestic) and ratio of new corporate bond issues to GDP.

Table 6 provides a summary for one of these measures of access to financial markets contained in the Global Financial Development Database, namely the share of market capitalization that is outside of the top ten largest issuers. Interestingly, the difference between developed economies and developing economies is not as large as for some of the other indicators in the database. This suggests that in this case, factors other than income level play important roles. One of the other factors may be size: some large developing economies, such as China and India, have relatively dispersed financial markets, scoring in the top quartile of this proxy for financial market access.

FinancialefficiencyFor intermediaries, efficiency is primarily constructed to measure the cost of intermediating credit. Efficiency measures for institutions include indicators, such as overhead costs to total

assets, net interest margin, lending-deposits spread, non-interest income to total income, and cost to income ratio (Table 1). Closely related variables include measures such as return on assets and return on equity. While efficient financial institutions also tend to be more profitable, the relationship is not very close. For example, an inefficient financial system can post relatively high profitability if it operates in an economic upswing, while an otherwise efficient system hit by an adverse shock may generate losses.

Table 7 summarizes the key statistics for the lending-deposit spreads. The weighted average for developed economies is 2.2%, compared to 7.3% in developed economies, for a world-wide weighted average of 6.9%. There are relatively large disparities among regions, with Latin America and Caribbean reporting the highest spreads, at 16.9%. We find that even within the same region, there are wide disparities, so Latin America and Caribbean contain both countries with very high spreads (such as Brazil) and those with low spreads (such as Colombia). Similarly, while Sub-Saharan Africa reports generally high spreads (12.8% on average), Ethiopia (3.3%) is an example of a country with very low spreads.

Figure2:Access—financialinstitutions(2011)Source: Global Findex [Demirgüç-Kunt and Klapper (2012)]Note: Adults (defined as individuals aged 15 and older) with an account at a formal financial institution.Population data is from WDI.

0—1516—3031—50

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Adults with an account at a formal financial institution (%)


Market capitalization out of top 10 largest companies (%)

Number of countries



World 46 44.8 44.8 18.2 3.7 74.2 63.6By developed/developing economiesDeveloped economies 25 42.4 42.6 20.8 3.7 74.2 64.4Developing economies 21 47.6 51.2 14.6 24.6 72.1 60.9By income levelHigh income 25 42.4 42.6 20.8 3.7 74.2 64.4Upper middle income 15 45.7 45.8 14.6 24.6 71.6 59.9Lower middle income 6 52.4 54.3 14.6 26.8 72.1 66.7Low income 0 By regionHigh income: OECD 20 43.5 43.2 20.2 3.7 74.2 64.9High income: non-OECD 5 38.0 39.6 24.8 5.8 65.0 55.2East Asia and Pacific 5 58.2 53.2 8.8 51.2 71.6 69.6Europe and Central Asia 2 41.6 41.6 10.4 34.3 49.0 37.4Latin America and Caribbean 6 37.0 35.0 11.0 24.6 53.7 42.1Middle East and North Africa 4 41.8 42.3 15.3 26.8 56.0 44.8South Asia 2 63.7 63.7 11.9 55.3 72.1 72.2Sub-Saharan Africa 2 54.7 54.7 18.3 41.8 67.6 68.4

Table6:Access—financialmarkets(2008–2010)Source: Authors’ calculations are based on the Global Financial Development Database.Note: Ratio of market capitalization outside of top ten largest companies to total market capitalization. The World Federation of Exchanges provides data on the exchange level. This variable is aggregated up to the country level by taking a simple average over exchanges. Arithmetic average of annual observations for 2008–2010.

Lending-deposit spread (%) Number of countries



World 129 7.7 6.3 6.4 0.1 41.5 6.9By developed/developing economiesDeveloped economies 28.0 3.8 3.5 2.0 0.2 8.1 2.2Developing economies 101 8.8 6.9 6.7 0.1 41.5 7.3By income levelHigh income 28 3.8 3.5 2.0 0.2 8.1 2.2Upper middle income 43 6.7 6.2 5.3 0.1 34.0 6.5Lower middle income 39 8.8 8.0 4.7 2.4 24.8 6.0Low income 19 13.7 10.2 10.1 3.3 41.5 13.0By regionHigh income: OECD 14 2.6 2.7 1.2 0.2 4.7 1.9High income: non-OECD 13 5.1 4.9 1.9 1.8 8.1 5.1East Asia and Pacific 17 7.3 5.5 4.7 2.4 20.2 3.6Europe and Central Asia 17 7.7 6.2 5.2 0.4 20.8 6.7Latin America and Caribbean 27 9.6 7.2 6.8 4.1 34.0 16.9Middle East and North Africa 10 4.6 4.9 2.6 0.1 9.5 4.6South Asia 5 5.9 5.9 0.5 5.2 6.4 6.0Sub-Saharan Africa 26 11.7 8.8 8.9 3.3 41.5 12.8

Table7:Efficiency—financialinstitutions(2008–2010)Source: Authors’ calculations are based on the Global Financial Development Database.Note: Lending rate minus deposit rate. Lending rate is the average rate charged by banks on loans to the private sector and deposit interest rate is the average rate paid by commercial or similar banks for demand, time or savings deposits. Both lending and deposit rates are from IFS line 60P and 60L, respectively. Arithmetic average of annual observations for 2008–2010.1 To calculate the group averages, country-by-country observations are weighted by nominal GDP.



Lending-deposit spreads are relatively crude measures of efficiency. For some economies, it is possible to calculate efficiency indices based on more sophisticated measures. For example, Angelidis and Lyroudi (2006) apply data envelopment analysis and neural networks to measure efficiency in the Italian banking industry. However, the data required for this type of analysis is available only for a small sub-set of economies.

For financial markets, a basic proxy for efficiency in the stock market is the turnover ratio, that is, the ratio of stock market’s annual turnover to its capitalization. The logic of using this variable is that higher turnover means more liquidity, which in turn allows the market to be more efficient. In the bond market, the most commonly used variable is the tightness of the bid-ask spread (with the U.S. and Western European markets showing low spreads, and Vietnam, Peru, Qatar, Dominican Republic and Pakistan reporting high spreads) and the turnover ratio (although the measurement of the latter often suffers from incomplete data).

A range of other proxies for efficiency in financial markets has been used in empirical literature (Table 1). One of them is price synchronicity, calculated as a degree of co-movement of individual stock returns in an equity market. The variable aims to capture the information content of daily stock prices, as a market operates efficiently only when prices are informative about the performance of individual firms. Another proxy variable for efficiency is private information trading, defined as the percentage of firms with trading patterns that arise from trading conducted through privately obtained information. This calculation is based on the examination of daily price-volume patterns, and helps indicate the prevalence of trading in a stock based on private or privileged information. Finally, efficiency can be approximated by the real transaction cost. Based on daily return data of the listed stocks, this variable attempts to approximate the transaction costs associated with trading a particular security. This variable helps determine the barriers to efficiency in the market. All these indicators are constructed by compiling and statistically processing firm-level data from a variety of market sources.

Stock market turnover ratio (%) Number of countries




Table8:Efficiency—financialmarkets(2008–2010)Source: Authors’ calculations are based on the Global Financial Development Database.Note: Stock market turnover ratio, calculated as total value of shares traded during the period divided by the average market capitalization for the period. Average market capitalization is calculated as the average of the end-of-period values for the current period and the previous period. Data is from Standard & Poor’s, Global Stock Markets Factbook and supplemental S&P data, and is compiled and reported by the WDI. Arithmetic average of annual observations for 2008–2010.1 To calculate the group averages, country-by-country observations are weighted by nominal GDP.


Table 8 summarizes the results for the stock market turnover ratio, illustrating the wide dispersion across countries and regions, as well as by income groups. The world-wide weighted average of the turnover ratio is 198%, but the country-by-country observations range from less than 1% to 343%. Developing economy average is 127%, compared to developed economy average of 218%. Among the regions, East Asia and Pacific scores the highest, at 167%, and Sub-Saharan Africa the lowest, at 62%. Again, country size is a helpful factor: countries scoring highly include not only the developed economies of Europe and North America, but also large emerging markets and developing economies, such as China, India, Russia, Turkey and Saudi Arabia.

Financial stabilityA common measure of financial stability is the z-score. It explicitly compares buffers (capitalization and returns) with risk (volatility of returns) to measure a bank’s solvency risk. The z-score is defined as z (k )/+/ n v, where k is equity capital as percent of assets, z (k )/+/ n v is return as percent of assets, and z (k )/+/ n v is standard deviation of return on assets as a proxy for return volatility. The popularity of the z-score stems from the fact that it has a clear (negative) relationship to the probability of a financial institution’s insolvency, that is, the probability that the value of its assets becomes lower than the value of its debt [see, for example, Boyd and Runkle (1993); Beck et al. (2006); Demirgüç-Kunt et al. (2008); Laeven and Levine (2009); Čihák and Hesse (2010)]. A higher z-score, therefore, implies a lower probability of insolvency.

The z-score has several limitations as a measure of financial stability. Perhaps the most important limitation is that the z-scores are based purely on accounting data. They are thus only as good as the underlying accounting and auditing framework. If financial institutions are able to smooth out the reported data, the z-score may provide an overly positive assessment of the financial institutions’ stability. Also, the z-score looks at each financial institution separately, potentially overlooking the risk that a default in one financial institution may cause loss to other financial institutions in the system. An advantage of the z-score is that it can be also used for institutions for which more sophisticated, market based data are not available. Also, the z-scores allow comparing the risk of default in different groups of institutions, which may differ in their ownership or objectives, but face the risk of insolvency. For other indicators, such as the regulatory capital to risk-weighted assets and nonperforming loans to total gross loans, the Global

Financial Development Database cross-refers to financial soundness indicator database available on IMF’s website (fsi.imf.org). Variables such as the nonperforming loan ratios may be better known than the z-score, but they are also known to be lagging indicators of soundness [Čihák and Schaeck (2010)]. One alternative indicator of financial instability is “excessive” credit growth, with the emphasis on excessive. A well-developing financial sector is likely to grow. But very rapid growth in credit is one of the most robust common factors associated with banking crises [Demirgüc-Kunt and Detragiache (1997); Kaminsky and Reinhart (1999)]. Indeed, the IMF (2004) found that about 75% of credit booms in emerging markets end in banking crises. The credit growth measure also has pros and cons. Although it is easy to measure credit growth, it is difficult to assess ex-ante whether the growth is excessive.

Interestingly, there is not much of a difference between the reported measures of financial stability in different groups of countries (Table 9). For example, the reported z-scores in developed economies and developing economies appear identical (Table 9). This is in line with the global financial crisis experience: financial instability occurred both in developed economies and in developing economies. The distinguishing factors were other things, such as quality of the regulatory and institutional framework, rather than the level of development.

For financial markets, the most commonly used proxy variable for stability is market volatility, although other proxies are also included in the database (Table 1). One of these variables is the skewness of stock returns, because a market with a more negative skewed distribution of stock returns is likely to deliver large negative returns, and likely to be prone to less stability. Another variable is vulnerability to earnings manipulation, which is derived from certain characteristics of information reported in the financial statements of companies that can be indicative of manipulation. It is defined as the percentage of firms listed on the stock exchange that are susceptible to such manipulation. In the U.S., France, and most other high-income economies, less than 10% of firms have issues concerning earnings manipulation; in Zimbabwe, in contrast, almost all firms may experience manipulation of their accounting statements. In Turkey, the number is close to 40%. Other variables approximating volatility in the stock market are the price-to-earnings ratio and duration, which is a refined version of the price-to-earnings ratio that takes into account factors such as long-term growth and interest rates.



Z-score weighted average from commercial banks

Number of countries




Table9:Stability—financialinstitutions(2008–2010)Source: Authors’ calculations are based on the Global Financial Development Database.Note: Z–Score weighted average from commercial banks is estimated as (ROA + Equity/Assets)/(standard deviation of ROA). Return of assets (ROA), Equity and Assets are from Bankscope. The standard deviation of ROA is estimated as a 5-year moving average. Arithmetic average of annual observations for 2008–2010.1 To calculate the group averages, country-by-country observations are weighted by nominal GDP.

Asset price volatility Number of countries




Table10:Stability—financialmarkets(2008–2010)Source: Authors’ calculations are based on the Global Financial Development Database.Note: Annual standard deviation of the price of a 1-year sovereign bond divided by the annual average price of the 1-year sovereign bond (both based on end-month data). Arithmetic average of annual observations for 2008–2010.1 To calculate the group averages, country-by-country observations are weighted by nominal GDP.


Table 10 provides a summary of the measures of asset price volatility in 2008–2010. Developing economy markets show a relatively higher volatility than developed economy markets but the difference is not significant (it is smaller than the cross-country standard deviation). Also a comparison across regions does not show a clear pattern, suggesting that all regions were affected by the increased volatility during the global financial crisis.

SelectedfindingsOverall comparisons by levels of development and by region (Table 11) confirm that while developing economy financial systems tend to be much less deep, somewhat less efficient, and provide less access, their stability has been comparable to developed economy financial systems. Table 11 summarizes the recent data from the Global Financial Development Database (2008–10) for the eight key characteristics of financial systems. For the purpose of these calculations, we provide “winsorized” and “rescaled” variables. To prepare for this, the 95th and 5th percentile for each variable for the entire pooled country-

year dataset are calculated, and the top and bottom 5% of observations are truncated. Specifically, all observations from the 5th percentile to the minimum are replaced by the value corresponding to the 5th percentile, and all observations from the 95th percentile to the maximum are replaced by the value corresponding to the 95th percentile. To convert all the variables to a 0-100 scale, each score is rescaled by the maximum for each indicator, and the minimum of the indicator. The rescaled indicator can be interpreted as the percent distance between the “worst” (0) and the “best” (100) value of the respective financial system characteristic, defined by the 5th and 95th percentile of the original distribution.

Financial systems are multidimensionalOne basic, yet important, observation highlighted by the Global Financial Development Database is that the four financial system characteristics are far from closely correlated across countries (Figures 3 and 4). This underscores the point that each dimension captures a very different, separate facet of financial

Financial institutions (Mean)High income East Asia and

PacificEurope and Central Asia

Latin America and the Caribbean

Middle East and North Africa

South Asia

Sub-Saharan Africa

Depth 69 43 37 37 33 32 17Access 43 23 35 30 14 16 10Efficiency 80 70 65 62 83 81 51Stability 42 52 20 35 57 38 32Financial markets (Mean)Depth 43 38 12 21 24 17 20Access 46 80 56 40 50 85 77Efficiency 29 40 17 8 24 49 7Stability 66 60 43 64 81 56 54

Financial institutions (Mean)High income Upper middle

incomelower middle

incomeLow income

Depth 84 44 28 13Access 55 32 19 5Efficiency 86 75 61 42Stability 35 38 40 35Financial markets (Mean)Depth 51 27 16 10Access 53 58 69 29Efficiency 45 19 20 21Stability 53 60 53 44

Table 11: Financial system characteristics: summary Source: Authors’ calculations are based on the global financial development database.Note: Financial institutions — depth: private credit/GDP (%); access: number of accounts per 1,000 adults, commercial banks; efficiency: net interest margin; stability: z-score. Financial markets — depth: (stock market capitalization + outstanding domestic private debt securities)/GDP ; access: percent market capitalization outside of the top 10 largest companies (%); efficiency: stock market turnover ratio (%); stability: asset price volatility. The statistics are winsorized and rescaled to 0-100, as described in the text.



systems. In other words, looking only at financial depth would not be sufficient. Similarly, focusing only on financial stability or on access or on efficiency would not suffice. Also, covering only financial institutions or only financial markets would be insufficient: our findings underscore the large differences between financial systems that are bank-centric (such as those in most of Europe) and those that center more on financial markets (such as those in the U.S., Korea, and Hong Kong SAR). Moreover, attempts to run a more rigorous “horse race” among the indicators from the four dimensions tend to end in a tie: that is, none of the indicators is clearly superior to the others in explaining long-term growth or poverty reduction.

Therearemassivedisparitiesinfinancialsystemsaround the globeA comparison at the regional level shows major differences in financial systems among the key regions (Table 11). The results are by and large in line as one could expect, with Sub-Saharan Africa scoring the lowest on average on most of the dimensions, and high income economies scoring the highest on most dimensions. A remarkable number is the relatively low score of Middle East and North Africa on access to finance (Table 11, upper panel). This resonates with the complaints heard during the unrest in the region in 2011. Much of the differences among regions are correlated with differences in income levels. Countries that have lower income tend to also show lower degrees of financial development as approximated by the 4x2 framework (Table 11, lower panel).

Behind these regional and peer group averages are vast differences among individual countries. These do not always mirror country size. For example, Russia’s financial system is dwarfed by China’s, and Germany’s is bigger than the combined financial systems of all the countries in Sub-Saharan Africa. The largest financial system in the sample is more than 34,500 times the smallest one. Even if the financial systems are re-scaled by the size of the corresponding economies (that is, by their gross domestic product), the largest (deepest) financial system is still some 110 times the smallest (least deep) one. And even if the top and bottom 5% of this distribution are taken out, the ratio of the largest to the smallest is about 28 — a large degree of disparity, considering that these are not raw figures but ratios relative to the size of economy. To put this in a more anthropomorphic perspective, the tallest adult person on Earth is less than 5 times

taller than the smallest person (www.guinessworldrecords.com). Large disparities are observed also for other characteristics of the financial system. For example, Denmark has 99.7% of adults covered by bank accounts, compared to only 0.4% in Turkmenistan (246 times higher coverage). Interestingly, Demark is also the country with the highest turnover/capitalization ratio in securities markets, at 538, with many countries having that ratio below 1. In short, when one examines country-level data, there are vast differences in financial system characteristics.

Financial systems have converged somewhat during the crisisThe most notable changes during the global financial crisis include large declines in the stability index, which in turn reflects the increased volatility in returns by financial institutions in some countries and in most financial markets. But the charts also illustrate that stability has not been the only dimension in decline and that to some extent it has been accompanied also by difficulties along with other characteristics, such as reduced depth and access to finance and in some cases also reductions in efficiency, particularly in financial markets.

Overall, financial system disparities have somewhat subsided during the crisis, as financial sectors in many medium- and low-income countries were relatively more isolated from the global turmoil, and therefore less affected by the global liquidity shocks. In addition, financial institutions on average rebounded faster than markets, showing improvements in depth and efficiency after the crisis. This seems to have been the case so far for example for Brazil and other Latin American countries [de la Torre et al. (2011)], China, and many Sub-Saharan African countries [see, for example, World Bank (2012)]. The medium-term effect of the crisis on financial systems still remains to be seen.


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Access versus StabilityCorrelation = 0.02

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Figure3:Correlationsamongfinancialsystemcharacteristics–financialinstitutionsSource: Authors’ calculations are based on the Global Financial Development Database.Notes: see Table 1.



Low incomeLower middle income

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AUS

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Depth versus EfficiencyCorrelation = 0.47*

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ck m

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t cap

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ing

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GDP

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ck m

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GDP

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Percent market capitalization out of the top 10 largest companies (%)


Depth versus AccessCorrelation = 0.39*

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IRL

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ITA

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Access versus EfficiencyCorrelation = 0.51*

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Depth versus StabilityCorrelation = −0.09

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)

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Efficiency versus StabilityCorrelation = 0.24*

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JPNKOR

LUXMLT

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10 20 30 40 50


Access versus StabilityCorrelation = −0.21

Figure4:Correlationsamongfinancialsystemcharacteristics–financialmarketsSource: Authors’ calculations are based on the Global Financial Development Database.Notes: see Table 1.


ConclusionThis paper has presented the Global Financial Development Database, an extensive dataset of financial system characteristics around the world since 1960s. The database is a one-stop, cleaned-up database that builds on previous efforts, in particular the data collected and the categorization of variables proposed by Beck et al. (2000, 2010).

The dataset can be used to illustrate cross-country and time-series patterns in financial systems. The data can be used to better assess linkages between finance and economic development and to assess the efficacy of different financial policies and regulations. The database can be used to analyze financial sector development and trends in 205 jurisdictions around the world. The Global Financial Development Database goes back some 50 years (to 1960), although some of the variables, such as the only recently defined financial stability indicators, go back only to the 1990s.

The database and this paper highlight the multidimensional nature of financial systems. Focusing on only one characteristic — say, financial stability — means missing important characteristics of financial systems. And, focusing only on financial institutions, or just on banks, misses important components of the overall financial system as equity and bond markets are crucial components in many economies.

This paper illustrates that financial sectors come in different shapes and sizes, and they differ widely in terms of their performance. The paper also emphasizes a need for humility, and for further research. Despite the remarkable progress in gathering data and intelligence on financial systems around the world in recent years, researchers and practitioners still do not have precise measures of the functioning of financial systems.

References Angelidis, D., and K. Lyroudi, 2006, “Efficiency in the Italian banking industry: data envelopment analysis and neural networks,” International Research Journal of Finance and Economics, 5, 155-165Bagehot, Walter, 1873, Lombard Street, Richard D. Irwin Publishers, Homewood, ILBarth, J., G. Caprio, and R. Levine, 2006, Rethinking bank supervision and regulation: until angels govern, Cambridge University Press, NYBarth, J., G. Caprio, and R. Levine, 2012, Guardians of finance: making regulators work for us, MIT Press, Cambridge, MABeck,T.,A.Demirgüç-Kunt,andM.S.MartínezPería,2007,“Reaching out: access to and use of banking services across countries,” Journal of Financial Economics, 85(1), pp. 234—66Beck,T.,A.Demirgüç-Kunt,andR.Levine,2000,“A new database on

thestructure and development of the financial sector,” World Bank Economic Review, 14(3), 597-605Beck,T.,A.Demirgüç-Kunt,andR.Levine,2007,“Finance, inequality and the poor,” Journal of Economic Growth, 12(1), 27—49Beck,T.,A.Demirgüç-Kunt,andR.Levine,2010,“Financial institutions and markets across countries and over time,” World Bank Economic Review, 24(1), 77—92Belley, P., and L. Lochner, 2007, “The changing role of family income and ability in determining educational achievement,” NBER Working Paper No. w13527Boyd, J. H., and D. E. Runkle, 1993, “Size and performance of banking firms: testing the predictions of theory,” Journal of Monetary Economics, 31, 47—67Čihák,M.,andH.Hesse,2010,“Islamic banks and financial stability: an empirical analysis,” Journal of Financial Services Research, 38(2-3), 95-113Čihák,M.,andK.Schaeck,2010,“How well do aggregate prudential ratios identify banking system problems?” Journal of Financial Stability, 6(3), 130—144de la Torre, A., A. Ize, and S. L. Schmukler, 2011, Financial development in Latin America and the Caribbean: the road ahead, Washington, DC: World BankDemirgüç-Kunt,A.,andE.Detragiache,1997,“The determinants of banking crises in developing and developed countries,” IMF Staff Papers, 45, pp. 81-109Demirgüç-Kunt,A.,andL.Klapper,2012,“Measuring financial inclusion: the global Findex,” Policy Research Working Paper 6025, World Bank, Washington, DCDemirgüç-Kunt,A.,andR.Levine,2008,“Finance, financial sector policies, and long run growth,” M. Spence Growth Commission Background Paper, No 11, World Bank, Washington, DCDemirgüç-Kunt,A.,andR.Levine,2009,“Finance and inequality: theory and evidence,” Annual Review of Financial Economics, 1, 287—318Demirgüç-Kunt,A.,E.Detragiache,andT.Tressel,2008,“Banking on the principles: compliance with Basel core principles and bank soundness,” Journal of Financial Intermediation, 17(4), 511—42Demirgüç-Kunt,A.,E.Feyen,andR.Levine,2012,“The evolving importance of banks and securities markets,” World Bank Economic Review, World Bank, Washington, DCKaminsky, G., and C. Reinhart, 1999, “The twin crises: the causes of banking and balance of payments problems,” The American Economic Review, 89(3), 473—500Kerr, W., and R. Nanda, 2009, “Democratizing entry: banking deregulations, financing constraints, and entrepreneurship.” Journal of Financial Economics, 94(1), 124—49King, R., and R. Levine, 1993a, “Finance and growth: Schumpeter might be right,” Quarterly Journal of Economics, 103, 717-737King, R., and R. Levine, 1993b, “Finance, entrepreneurship, and growth: theory and evidence,” Journal of Monetary Economics, 32(3), 513-542Laeven, L., and R. Levine, 2009, “Bank governance, regulation, and risk taking,” Journal of Financial Economics, 93(2), 259-275Levine, R., 1997, “Financial development and economic growth: views and agenda,” Journal of Economic Literature, 35(2), 688-726Levine, R., 2005, “Finance and growth: theory and evidence,” in Aghion, P., and S. Durlauf (eds.), Handbook of economic growth, edition 1, volume 1, chapter 12, 865—934Levine, R., and S. Zervos, 1998, “Stock markets, banks, and economic growth,” American Economic Review 88, 537—58Lucas, R., 1988, “On the mechanics of economic development,” Journal of Monetary Economics, 22, 3—42Merton, R., and Z. Bodie, 2004, “The design of financial systems: towards a synthesis of function and structure,” NBER Working Paper Number 10620Merton, R., 1992, “Financial innovation and economic performance,” Journal of Applied Corporate Finance, 4, 12—22Miller, M. 1998, “Financial markets and economic growth,” Journal of Applied Corporate Finance, 11, 8—14


Part 1

Estimating the probability of a lost decade for U.S. and global equityBlake LeBaronAbram L. and Thelma Sachar Chair of International Economics, International Business School, Brandeis University

AbstractThis paper estimates the probability of a “lost decade,” where equity investments lose value over a 10-year period. The findings are a reminder that equity investments are risky even over longer time periods, and investors should take this into consideration when making portfolio choices. It also introduces a simple method to allow the reader to combine beliefs about long-run stock returns along with computer simulated return distributions. Finally, the results for the U.S. are augmented with international data which strengthen the case for large long horizon risk.



IntroductionIt is often assumed that in the long-run equity markets always generate positive returns for investors. This paper looks at this question using data from U.S. and international markets, concentrating on real and nominal losses over a decade. While the probability of generating a loss over a decade might not easily fit into many standard asset pricing models, it does give investors an intuitive measure of downside risk. This measure is similar in spirit to value-at-risk calculations in that it will be concentrated on a specific aspect of the return distribution.

There is a vast literature exploring the long-range properties of financial market data. The exploration of the equity premium is the most extensive.1 This paper considers equity returns alone, and only a single feature of their distribution. There are several reasons for doing this. As already discussed, the first reason is that decade losses can be an interesting measure of long-run risk. Second, it avoids having to estimate or proxy for risk-free rates of return in early periods when this might be difficult. Finally, it keeps the bootstrap methodology relatively simple and assumption free.

A long series of U.S. returns is constructed by merging two annual data sets. This set of returns is used with a bootstrapping technique to estimate decade length return distributions, and from these decade loss probabilities. Though small, these loss probabilities are probably higher than what most investors expect. The methodology also allows for readers to estimate loss probabilities using their own beliefs about future expected returns. In the final section, the U.S.-centered data perspective will be augmented using the cross-sectional country return series from Dimson et al. (2002) and Dimson et al. (2008). This dataset contains a comprehensive asset return cross-section from 18 industrialized countries starting at the beginning of the 20th century. These series are used as outside information that should influence investors’ beliefs about the U.S. empirical experience.

1 There are many collections of classic papers on this topic. These include Goetzmann and Ibbotson (2006), Mehra (2008), and most recently Hammond et al. (2011). Many books have covered the topic using extensive long-range data sets both U.S. and international. These include Cornell (1999), Dimson et al. (2002) and Siegel (2002). Also, looking at the most recent decade alone, Arnott and West (2010) show that investment losses are far from uniform across various asset classes.

Return summaryThe long return history is built by merging two stock return datasets. The first is the monthly return series described in Schwert (1990), which extends back to 1802. The second is the annual series from 1871–2010, constructed by Shiller, and used in Shiller (2000).2 Shiller’s dataset also includes inflation series from 1872 onward. This is augmented with inflation series obtained from “Measuring Worth.”3 From 1918 onward, the stock returns are from the S&P composite portfolio. From 1872–1917 the stock market information is from the indices created in Cowles and Associates (1939) to track aggregate stock market movements. Earlier returns were assembled by Schwert to best track aggregate market movements. They involve several different sources, and become relatively narrow indices as one moves back in time.4 In the earliest period they are mostly bank stocks, and in later periods they include railroad stocks. There are obvious survivorship biases in these indices. Also, many are constructed as monthly averages from bid and ask prices, making precise time series analysis at higher frequencies difficult.5

Figure 1 gives an overall picture of lost decades. The y-axis plots the total decade return including dividends for the 10 years ending on the year given by the x-axis. Both nominal, and inflation adjusted real returns are plotted. For the decade ending in 2009 both real and nominal returns are negative, indicating that investors would have lost value on their equity investments. In this figure, lost decades appear to be relatively rare. The decades ending in 1858, 1939, and 1940 are the only other decades with negative nominal equity returns. If one considers real returns, then several others appear. The most recent of these would be the decades ending in the late 1970s and early 1980s, where large U.S. inflation adds a heavy cost to a relatively flat market. This picture is interesting, but not informative as to how likely these events are. The analysis below addresses this question.

The first two rows of Table 1 provide summary statistics for the annual holding period returns used to construct the previous

2 Both of these datasets are available at the authors’ websites.3 See http://www.measuringworth.com/ for full information on the methodology behind the

early inflation estimates.4 Also, dividend yields can only be approximated for the earliest samples from the first part of

the 19th century.5 See Schwert (1990) for detailed discussions.


figure. The mean nominal and real annual returns of 9.1 and 7.8% respectively, represent this 209-year U.S. history of equity returns. The table also reports the standard deviation of about 17% per year for both series. This estimate will not be surprising to most investors familiar with the properties of long-range return series. The table also presents skewness and kurtosis levels for these series. These are quick tests of whether a normal distribution would be a reasonable approximation. Skewness is

near zero, and kurtosis near 4, which is larger than its value of 3 for a normal distribution. The last column in the table presents a simple test for normality, the Jarque-Bera test. The values given are the p-values corresponding to the normal null hypothesis with unknown mean and variance.6 The first two rows indicate a weak rejection of normality for the nominal returns, and a borderline p-value of 0.09 for the real returns.

Long horizon returns should not be expected to follow a normal distribution since they are compounded short horizon returns,

r (1 r ) 1t,A t jj 0

ll

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% are monthly returns. The logged annual returns would then be

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If these annual logged returns are independent with finite second moments, then geometric, or log returns at longer horizons must approach normality. Lines 3 and 4 of table 1 report the same set of summary statistics for the logged annual nominal and

6 Since small sample properties of the Jarque-Bera test are questionable, the p-values report results from a 100,000 length monte-carlo.

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Series Mean Standard deviation

Skewness Kurtosis Normal(p-value)

Nominal returns 9.1 16.8 0.18 3.79 0.04Real returns 7.8 17.1 0.10 3.68 0.09Nominal log 7.5 15.9 -0.53 4.55 0.00Real log 6.2 16.4 -0.53 3.91 0.00Nominal (1802–1871) 6.9 14.0 1.18 7.34 0.00Nominal (1872–2010) 10.2 18.1 -0.13 3.13 0.78Real (1802–1871) 7.1 15.6 0.64 5.90 0.00Real (1872–2010) 8.1 17.8 -0.10 2.99 0.89

Table 1: Summary statistics Annual arithmetic and geometric returns. Sample length is 209 years covering returns from years ending 1802–2010. All returns include dividends. Mean and Std. estimates are in annual percentages. Kurtosis estimates the kurtosis in the return distribution. This value would be 3 for a normal distribution. Normal refers to a Jarque-Bera test for normality. The value reported is the p-value for the normal null hypothesis. The period 1802–1871 uses the data from the Schwert (1990), series. The period 1872–2010 uses the dataset contained in the Shiller (2000), annual series.



real returns. Results are similar to those for the holding period returns, except for a moderate increase in kurtosis. This shows up in the Jarque-Bera statistics yielding a p-value of zero in both cases. A visual test for normality is presented in figure 2, which shows the density for the nominal holding period and log returns superimposed with a normal density. The figures suggest that the

practical deviations from normality in these series may be quite small. This will be checked in the later simulations.

The last four rows in table 1 present subsample estimates using 1871 as a break date. This is the date when the Schwert series ends, and the Shiller series begins. Also, a plot of the full return time series is presented in figure 3. The figure shows no obvious visual changes in the series. The table shows that the earlier subsample contains a reduced mean and standard deviation as compared to the full sample. It also displays much larger kurtosis. In the latter periods kurtosis falls enough so that the Jarque-Bera test is unable to reject normality for both real and nominal returns.7

Independent returnsMany of the results presented here will be based on a form of bootstrapping where the 209 years of return data are expanded out to 250,000 years by repeatedly drawing years from the original 209 with replacement until a new very long series is built. This is unusual for the bootstrap which usually redraws samples with length less than or equal to that of the original sample. The difference here is that by scrambling the time order we are creating novel decade periods which did not occur in the original series, so the bootstrap is adding to our information beyond the original 209 data points. This does depend critically on assumptions about return independence. Assumptions about independence will be weakened in the next section.

Figure 4 uses the simulated decade returns to generate a histogram of ending wealth levels for an investor starting with a one dollar investment at the beginning of a decade. Two important features should be noted. First, the area to the left of the black line indicates the lost decades, or periods when the investment lost money. Although small, the area is not insignificant. The well-known near log normality of this distribution drives the strong right skew which is evident in the figure. At decade lengths it is interesting to note that probabilities are not insignificant for wealth doubling, or even increasing six-fold.

7 One might initially suspect that there are more tail events driving the larger kurtosis in the first subsample, but this does not seem to be the case. In looking at figure 3 one sees similar tail behavior, but a higher concentration of smaller return years (in absolute value) in the earlier part of the dataset. This might be driven by the fact that this is a relatively narrow index, and some years may not have many large information events in the industries covered.

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Figure 3: Annual returns

Figure 4: 10-year portfolio values


Table 2 presents estimates of decade loss probabilities from the long time series sampling exercise with T=250,000 years, using overlapping decades. The first column and row correspond to the simulation presented in the previous figure. This is a bootstrap using the actual returns in the data, and yields a probability of 0.072.8 It is generated from the nominal returns with a mean of 9.1% per year. The second column repeats this estimation for real returns where the mean return falls to 7.7% per year. The probability of a lost decade in this case rises to 0.12. The second line in the table reports bootstrap standard errors for each of the probability estimates. These values are calculated by drawing a new set of 209 annual returns with replacement from the original data, and then using these as a sample for the expansion to the long T sampling methodology for decade return estimation as is done for the actual returns. The bootstrap procedure is repeated 1,000 times, and the standard deviation across this simulations is shown in parenthesis. For the first two return assumptions standard errors of 0.034 and 0.047 show that the estimated probabilities still contain a large amount of uncertainty. This is a reminder that with 200 years of data we will not be able to make strong statements about the tails of decade return distributions.

The sample mean returns from the data may not be the best estimate of expected returns for future decades. This paper does not take a strong stand on what future returns should be, but other return assumptions can easily be applied to the simulations.9 The last three columns in table 2 estimate loss probabilities assuming annual mean returns of 10, 6, and 4% respectively. The sample mean is subtracted from the historical series, and one of the three expected return assumptions is added to the returns. It is clear that the estimated loss probabilities change dramatically as assumptions about returns change. For example, if investors only expect a 6% return, then they should prepare for a loss over a decade occurring with probability 0.186. For optimists, expecting a ten% annual return, the decade loss probability falls to 5%.

8 Since this estimator is built from a bootstrapping experiment there will be some uncertainty from the finite length of the bootstrap itself. This can be kept small by keeping the simulation sizes large. The standard error for this estimate will be approximately p(1 p)/n- using the asymptotic approximation to the binomial trial. For p = 0.07 this yields an estimate of 0.0016 which was confirmed with a slightly lower value of 0.0015 from a monte-carlo experiment which used the longer sample, and overlapping decades. Therefore, T is sufficiently large to ignore the error coming from the bootstrap.

9 Investors may not agree with either of these long-run expected return levels. See Hammond et al. (2011) for many different perspectives on this. Also, Welch has conducted survey results that are reported on his website http://research.ivo-welch.info/equpdate-results2009.html.

Figure 5 shows the impact of various return assumptions on the expected decade loss probabilities. Readers can quickly put their own return assumption on the x-axis to assess their long-term chances of a loss. The probabilities are calculated for a discrete set of expected returns using the same bootstrap long-range sampling methods used in table 2. For example, at an expected annual return of 8%, the decade loss probability is approximately 10%. This falls to 2.5% for assumed long-range returns of 12%.

Annual return

Simulation 9.1% (Nominal)

7.7% (Real)

10% 6% 4%

Bootstrap 0.072(0.034)

0.120(0.047)

0.052(0.028)

0.186(0.061)

0.300(0.075)

Bootstrap: 1872–2010

0.067(0.042)

0.122(0.060)

0.073(0.045)

0.218(0.082)

0.332(0.098)

Log-normal 0.069(0.036)

0.118(0.048)

0.047(0.028)

0.191(0.062)

0.313(0.078)

Table 2: Probability of decade loss — independent returns Probabilities of a loss in equity portfolios compounded with dividends over decades. All mean returns are adjusted to the given annual mean return shown in the column heading. Bootstrap uses actual returns with readjusted means. Returns are drawn independently from the set of all annual returns. Log Normal uses estimated means and standard deviations along with a standard normal distribution to estimate the decade losses.

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Figure 5: Decade loss probabilities



The next two rows in table 2 check whether the results are driven by returns coming from the earliest part of the sample. The sample is restricted to the period from 1872–2010, and the same loss probabilities are estimated. The decade loss probabilities of 0.067 and 0.122 for the real and nominal returns show little change from the full sample. The mean adjusted returns are again used in the last three columns. For these simulations the means will again be adjusted to the given values, but other aspects of the distributions will be different, reflecting the later sample period.

The results presented so far have made minimal assumptions for the return distributions. The final results in table 2 assume that long horizon returns are log normal. In this case, estimating the loss probability involves only estimating the mean and standard deviation for log returns, expanding these to decade length, and then using a normal cumulative distribution function (CDF). Results of this estimation are given in the row labeled “log normal.” The numbers do not change substantially from the corresponding bootstrap values. For example, for real returns, the probability goes from 0.120 for the data to 0.118 under the log normal assumption. The numbers in parenthesis correspond to bootstrap standard errors estimated by redrawing the annual returns, and using the new series for mean and standard deviation estimation. In other words, it recreates the estimation error on the two moments which go into the log normal probability estimates.

The 10-year horizon explored in table 2 may be viewed as a short horizon for some long-term investors. Figure 6 displays loss probability estimates over a range of time horizons using real returns. These values are estimated using the methods from table 2 with both the bootstrap and log normal assumptions. As the horizon increases, the probabilities fall as expected. However, even for a 20-year horizon, the point estimate of the probability of a real loss is still near 5%, which is not zero. One has to move to the 40- and 50-year horizons to consider the loss probabilities as negligible. Also, beyond the very short horizons, normality becomes a good approximation for the return series.

Dependent returnsUp to this point returns have been assumed to be independent over time. If long-range returns were dependent this could change the estimated risk of decade returns. Figure 7 presents the estimated autocorrelations for the real and nominal returns with asymptotic 95% confidence bands around the uncorrelated null hypothesis. Evidence for any correlation in these series is very weak. Combining the first five autocorrelations into a Ljung/Box test yields a p-value of 0.07 for the nominal returns, and 0.16 for the real returns. Figure 8 looks at another measure of long-range dependence, the variance ratio. Assuming σ2 is the variance of annual log returns, independence gives m period return variances of mσ2. Deviations from this are a direct measure of how risk is increasing with horizon lengths.10 The figure shows the variance ratio declining, indicating some long-range mean reversion, but the asymptotic confidence bands remind us that the sample length is still too short to say anything significant about these values.11

The results on dependence show some weak indications of mean reversion. A cautious tester should consider some form of dependent bootstrapping to explore the possible impact of this. Two different methods for generating dependence in the annual returns series will be used here. First, a parametric bootstrap is performed, using an estimated autoregressive model with five lags, an AR(5), for the returns process. The model and residuals are estimated, and the residuals are then redrawn with replacement and used along with the parameter estimates to

10 See Lo and MacKinlay (1988) and Poterba and Summers (1988) for early examples of this.11 The 95% confidence bands are generated as in Lo and MacKinlay (1988).

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generate a new simulated time series of length T=250,000.12 The independent loss probabilities are repeated in the first row of table 3 for comparison. The second row presents the estimated loss probabilities using the AR(5) null model, using overlapping decades on the long sample as in table 2. There is some reduction for both the real returns, and the nominal returns series, indicating the data has some weak information about long-run mean reversion. However, the probabilities are still not trivial.

A second simulation experiment uses the stationary bootstrap to replicate the dependence in a nonparametric fashion.13 This form of bootstrap draws returns in contiguous blocks where block length is controlled by a random variable, Xt which is 1 with probability m, and 0 with probability 1−m. Assume a new time series is being constructed at the current point t, and is drawn from point τ in the original series. The next point, t+1, will come from 1+x , if X 0t = , and will come from a new point xc , if X 1t = . This generates a series containing blocks of varying lengths from the old series, where the lengths are controlled by the behavior of X 0t =.14 Results for this simulation are given in the second line of the table. For these runs, m = 0.2, which gives an average block length of five years.15 The values are close to those from the AR(5) simulation, and indicate that these two methods may be replicating a similar amount of dependence for the long-range returns.

12 See Efron and Tibshirani (1993) for a basic description of the parametric bootstrap, and Maddala and Li (1996) for financial applications. Killian and Berkowitz (2000) is a useful survey which covers many issues on modeling dependence in time series. Given the reported autocorrelations, the AR(5) would appear to be an overfit model. Kilian (2001) shows that when bootstrapping standard errors, the dangers of under parameterization outweigh those of over parameterization.

13 See Politis and Romano (1994) for the original derivations. Also, see Sullivan et al. (1999) for a financial application.

14 The varying block lengths follow a geometric distribution with mean 1/m.15 Values for 10 and 20 years have also been tried, generating similar results.

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Figure 8: Variance ratiosEstimated variance ratios Vm/mV1. Estimate and asymptotic 95% confidence band under IID null (ratio = 1).

Figure 7: Annual return autocorrelationsAutocorrelations and 95% confidence bounds around uncorrelated null (zero).

Simulation Real (7.7%) Nominal (9.1%)Independent 0.120 0.072Autoregressive: AR(5) 0.081 0.042Stationary 0.106 0.051

Table 3: Probability of decade loss — dependent returns Autoregressive estimates an autoregressive model with 5 lags on the return series, and uses the estimated parameters and resampled residuals to generate dependent data. The stationary bootstrap draws random blocks from the original time series.



Figure 9 explores the possibility that weaker long-range dependence might yield evidence for lower decade loss probabilities. The parametric AR simulation is run for lags of 1 through 25, and the loss probabilities, estimated using the previous methodology are plotted. This figure uses the merged real returns as the starting data series. There is an early sharp drop off in probabilities as the lags increase from 1 to 5. However, at this point the probabilities stabilize near 0.07–0.08, which is consistent with table 3. Adding further lags appears unlikely to dramatically reduce estimated long-range losses. This is consistent with the evidence that long-range mean reversion is weak.

International cross-sectionUp to this point, the analysis has concentrated only on long-range series built from U.S. returns and inflation series. Series used in Dimson et al. (2002) provide a useful long-range cross-section for comparison.16 The series are annual, and extend from 1900 though 2010 for 111 years of data. Only real equity returns will be used here.

16 These series are available from Morningstar. Another important study on the international cross-section is Jorion and Goetzmann (1999).

Table 4 presents the results for the international returns. It includes all the countries in the dataset along with value and equal weighted portfolios. The first two columns record the annual mean and standard deviation for the logged returns. The column labeled “Bootstrap” repeats the long resampling procedure, taking each series out to 250,000 observations to estimate the decade loss probability. The column labeled “Normal” uses the independent log normal return assumption, with the sample means and standard deviations.

The results from table 2 reported a decade loss probability for real returns in the U.S. of 0.12. Comparison of this number with values in table 4 shows that relative to the rest of the world, the U.S. is a safer country than most when it comes to long-run tail risk. Using the bootstrap estimator, countries vary from a high of 0.396 for Italy to a low of 0.108 for Australia. Similar to the previous results, the normal approximations do not have a large impact on the results, continuing to support the idea that normality is a good approximation at long horizons.

A graphical summary of this table is given in figure 10, which displays a histogram of the bootstrapped loss probabilities from table 4. This gives a clear picture of where the U.S. falls in terms of long-run risk. Also, it shows that if investors are going to use this data to adjust their beliefs about risk in the U.S., they should increase their risk assessment. Finally, the last two lines in table 4 present results for both value and equal weighted global portfolios. These results show surprisingly small reductions in risk from either form of diversification. The equal weighted portfolio reduces the decade loss probability to 0.10, which is lower than the individual countries, as it has to be, but the gain is small. Furthermore, given various impediments to international investing over the early parts of this sample, the feasibility of achieving these returns should be viewed with some skepticism.

Table 5 performs some additional experiments, exploring the cross-sectional dimensions of the real return data, and how it impacts investors. All the experiments are bootstrap simulations done with 10,000 replications. For calculating the loss probabilities, each simulation uses the normal approximation using estimated means and standard deviations.

The first experiment, labeled “Country draw,” assumes a random draw of new returns data which is structured by country. First,

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one of the countries is drawn at random from the pool. Then its returns are redrawn with replacement giving a new sample which is used to estimate the mean and standard deviation. The investor here is viewing the countries as different, but could potentially face data that looks like any one of them going into the future. The columns report the 0.1, 0.5, 0.9 quantiles for the decade loss probability distribution. The median value of 0.245 is consistent with the cross-sectional results, and the graphical information in figure 10, all of which show that the probability of a lost decade is large in the international returns series. The bootstrap runs generate a large amount of dispersion as shown by the 0.1 and 0.9 quantiles, which are estimated at 0.099 and 0.445.

The second row of the table, labeled “Full sample,” pools the entire dataset into one set of returns, and then draws country samples from this pooled population. This implements a null hypothesis that all country returns come from the same population. Pooling all the data reduces the dispersion from the separate country sampling method as is seen in the narrowing of the extreme quantiles to 0.136 and 0.415. However, the median value of 0.260 does not change much by moving to the pooled sample.

The last two rows test the impact of dependence on the results. None of the international returns series show much evidence for return autocorrelation, but the importance of this is tested by repeating the parametric bootstrap that was used before with the U.S. returns. Two models, an AR(2), and an AR(5) are used as a simple dependent null hypothesis. These are estimated once on each country, and then simulated for T=250,000 years to estimate the decade loss probability. The quantiles represent the cross-section across the countries. The results again show little change from the earlier results that assumed independence in

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Australia 0.072 0.179 0.108 0.103Belgium 0.025 0.228 0.360 0.364Canada 0.057 0.166 0.136 0.139Denmark 0.050 0.187 0.194 0.200Finland 0.052 0.276 0.268 0.274France 0.030 0.226 0.329 0.337Germany 0.030 0.345 0.326 0.391Ireland 0.037 0.233 0.287 0.309Italy 0.020 0.291 0.396 0.415Japan 0.037 0.326 0.306 0.358Netherlands 0.049 0.203 0.220 0.225Norway 0.041 0.238 0.285 0.292New Zealand 0.057 0.184 0.157 0.166South Africa 0.071 0.204 0.132 0.137Spain 0.035 0.209 0.291 0.299Sweden 0.061 0.215 0.179 0.184Switzerland 0.041 0.189 0.238 0.244United Kingdom 0.052 0.193 0.186 0.197U.S. 0.061 0.199 0.166 0.167World 0.053 0.173 0.165 0.165Equal weighted 0.061 0.148 0.100 0.097

Table 4: Probability of decade loss — country real equity returns Summary statistics and decade loss probabilities for developed country returns. Bootstrap repeats methods from table 2, and Normal assumes a log normal return distribution.

Figure 10: Country loss histogram

Experiment q0.10 q0.50 q0.90Country draw 0.099 0.245 0.445Full sample 0.136 0.260 0.415AR(2) 0.127 0.252 0.347AR(5) 0.102 0.233 0.350

Table 5: Probability of decade loss — cross-section experimentsColumns represent quantiles from 10,000 bootstrapped distributions for estimated decade loss probabilities. Country draw assumes investors face a random draw of a country. Full sample pools all the return data into one large sample. AR(2) and AR(5) assume autoregressive models with two and five lags respectively.



the returns. The median loss probabilities for the two dependent cases are 0.252 and 0.233 for the AR(2) and AR(5) respectively. Evidence from the international returns again suggest that long-range return dependence should not reduce investors’ beliefs about the riskiness of decade returns.

SummaryLost decades are often treated as a kind of “black swan” event that are almost impossible. Results in this paper show that while they are a tail event, they may not be as far out in the tail as the popular press would have us think. Allowing the data to speak directly in an independent bootstrap, with two centuries of return time series, the estimate of a portfolio loss over a decade is about 7%. For the investor concerned with real returns the results are more depressing, with decade loss probabilities of 12%. The bootstrap methodology is not dependent on distributional assumptions about annual returns. However, in the reported estimates, normality assumptions for annual returns do not have a major impact on decade length results.

The estimated loss probabilities are checked for robustness in two ways. First, the independent null hypothesis is weakened by using several methods for simulated dependent long-range returns. In all the tests there is only a small reduction in the decade loss probability, which is consistent with the very weak mean reversion present in aggregate long-range returns. Second, the U.S. experience is compared with international equity data using several different tests. Consistent with other research, global data do not give U.S. investors any increased confidence in terms of risk. On the contrary, long-run results across the globe consistently appear riskier in terms of decade losses in real equity returns.

The simple message here is that stock markets are volatile. Even in the long-run volatility is still important. These results emphasize that 10-year periods where an equity portfolio loses value in either real or nominal terms should be an event on which investors put some weight when making their investment decisions.

ReferencesArnott, R. and West, J. (2010), “Was it really a lost decade?”, Index Universe .Cornell, B. (1999), The Equity Risk Premium: The Long-Run Future of the Stock Market, Wiley, New York, NY.Cowles, III, A. and Associates (1939), Common Stock Indexes, number 3 in “Cowles Commision Monograph”, 2nd edn, Principia Press, Bloomington, Indiana.Dimson, E., Marsh, P. & Staunton, M. (2002), Triumph of the Optimists: 101 Years of Global Investment Returns, Princeton University Press, Princeton, New Jersey.Dimson, E., Marsh, P. & Staunton, M. (2008), The worldwide equity premium: A smaller puzzle, in R. Mehra, ed., “The Handbook of the Equity Risk Premium”, Elsevier, Amsterdam, Netherlands.Efron, B. & Tibshirani, R. (1993), An Introduction to the Bootstrap, Chapman and Hall, New York.Goetzmann, W. N. & Ibbotson, R. G. (2006), The Equity Risk Premium, Oxford University Press, Oxford, UK.Jorion, P. & Goetzmann, W. N. (1999), “Global stock markets in the twentieth century”, Journal of Finance 54, 953—980Hammond, P. B., Leibowitz, M. L. & Siegel, L. B. (2011), Rethinking the Equity Risk Premium, CFA InstituteKilian, L. (2001), “Impulse response analysis in vector autoregressions with unknown lag order”, Journal of Forecasting 20, 161—179.Killian, L. & Berkowitz, J. (2000), “Recent developments in boottrapping time series”, Econometric Reviews 19(1), 1—48.Lo, A. W. & MacKinlay, A. C. (1988), “Stock prices do not follow random walks: Evidence from a simple specification test”, Review of Financial Studies 1, 41—66.Maddala, G. S. & Li, H. (1996), Bootstrap based tests in financial models, in G. S. Maddala & C. R. Rao, eds, “Handbook of Statistics”, Vol. 14, North-Holland, Amsterdam, pp. 463—488.Mehra, R., ed. (2008), Handbook of the Equity Risk Premium, Elsevier, Amsterdam, the Netherlands.Politis, D. & Romano, J. (1994), “The stationary bootstrap”, Journal of the American Statistical Association 89, 1303—1313.Poterba, J. M. & Summers, L. H. (1988), “Mean reversion in stock prices: Evidence and implications”, Journal of Financial Economics 22, 27—59.Schwert, G. W. (1990), “Indexes of United States stock prices from 1802-1987”, Journal of Business 63, 399—426.Shiller, R. J. (2000), Irrational Exuberance, Princeton University Press, Princeton, NJ.Siegel, J. J. (2002), Stocks for the Long-run: The Definitive Guide to Financial Market Returns and Long-Term Investment Strategies, 3rd edn, McGraw-Hill, New York, NY.Sullivan, R., Timmerman, A. & White, H. (1999), “Data-snooping, technical trading rule performance and the bootstrap”, Journal of Finance 54, 1647—1691.


Part 1

Challenges for central banks: wider powers, greater restraints — thefinancialcrisisandits aftermathPhilip MiddletonHead of Central Banking, EY LLP

David MarshChairman, Official Monetary and Financial Institutions Forum (OMFIF)

AbstractThis paper argues that whatever the macro- and micro-outcomes of the current economic, financial and regulatory crises, the roles of central banks worldwide are changing fundamentally. These changes will not be uniform, and different models of central banking, especially with regard to strategic remit and operational activities, will be seen in different jurisdictions. However, as a general rule, the role of the central bank will become bigger, riskier and more complex. In many instances, a re-evaluation of a central bank’s fundamental relationships, both formal and informal, will be required. These will include the institutional and governance relationships with both state governments and pan-national institutions, links with banks and financial firms over which the central bank may have monetary, fiscal and regulatory power, relationships with the media and communication with the electorate as a whole. Many central bankers will find this new transparency and accountability as irksome as it is novel, but attention will be required if the extended powers of the central bank are to be seen as legitimate. The paradox is that as central banks become inexorably more powerful and influential, the reins on their long-cherished independence will become tighter.


Challengesforcentralbanks:widerpowers,greaterrestraints—thefinancialcrisisanditsaftermath

As recently as five years ago, most central bank governors could walk down the main street of their country’s capital city unnoticed, their names and faces familiar only to avid readers of specialist journals. Today, in many countries, they are as well known as the government leaders they serve, and their words and deeds are the subject of heated debate in newspapers, bars and taxis. The continuing financial and economic crises have thrust central bankers center stage and cast them as leading actors, simultaneously berated as progenitors of the crisis and hailed as potential saviors.

It is not clear that all central bankers welcome this transition from membership of a hitherto largely anonymous technocratic elite to an increasingly public role. This paper argues that central bankers need to adjust to an increasingly public and prominent position on the political stage. A fundamental debate about the position of central banking and its relationship to government is now under way.

Central bankers have achieved a new prominence and become pivotal members of the policy-making establishments of both national and intergovernmental organizations. As a result of a growing responsibility for financial stability, coupled with their injection of massive amounts of liquidity into the financial system, central banks in many jurisdictions have extended their powers and remit beyond their traditional responsibilities to conduct monetary policy and act as a “lender of last resort” to banks. We believe that this extension of powers is unlikely to be temporary and may not be entirely desirable. It raises far-reaching questions about the accountability and transparency of the principal activities of central bankers.

In addition to their traditional monetary policy and lender of last resort roles, as well as acting as banker to the government in many jurisdictions, central banks have become national and global firemen with growing responsibility for the resilience of economies, the stability of financial systems and individual financial institutions, macro- and micro-prudential supervision, and macroeconomic and quasi-fiscal policy. They have gleaned far greater exposure to the media, politics and electorates. They have also taken on a whole range of new strategic and operational tasks and become exposed to far greater financial, reputational, and operational risks. As their responsibilities have grown, so have their balance sheets and the accompanying risks.

From acting largely behind the scenes, central banks have now entered the political arena in a very public manner. Whether central banks act as principals, agents, or advisers, their activities have a strong political dimension. If that is the case, to what extent and how should central banks strive to maintain political neutrality? Should fiscal policy, for example, be an arena restricted to elected politicians, or should the views of central bankers be publicly aired as well? To whom should central bankers be accountable, and how transparent should that accountability be to the media and to electorates?

If this expanding remit of new roles and activities is to become permanent, what targets should be set for a central bank, and who should decide whether these targets have been met? While it is comparatively straightforward to set a target for inflation, how does one measure “financial stability,” and just what degree of financial instability is deemed acceptable?

We argue in this paper — which draws on extensive primary and secondary research with participation from current and former central bankers, politicians, academics, senior officials, members of OMFIF staff and Advisory Council, and contributors from EY to analyze the recent activities of central banks — that the role of central bankers is changing and will continue to change fundamentally and irreversibly. There are multiple challenges, ranging from the grandly philosophical and strategic to more prosaic concerns. Paradoxically, in the final analysis, it may well be that expanded powers and responsibilities for central banks will lead to a full or partial loss of the independence that has, particularly in the Western world, become the cherished hallmark of central banking. Having been forced center stage as a result of the financial crisis, it is doubtful that central bankers will be able to escape the limelight, so they will have to define and adapt to an increasingly public role.

Overview — the new centrality of central bankersSeminal shift in central banks’ policy-making rolesMoney has been with us for more than 4,000 years; for most of that time, we did without central bankers. During the past 150 years in which they have played an important role in the economic lives of leading nations, central banks’ influence has waxed and waned. But since the eruption of the global financial crisis in 2007 and the accompanying large-scale increase in government debt in the U.S., Europe and Japan, they have undergone a seminal


shift with few precedents. Central bankers have risen significantly in the economic rankings to become a pivotal part of the policy-making establishment in both industrialized countries and in emerging market economies. The new landscape brings a range of consequences on a global scale, with repercussions on financial and business practices in many parts of the world.

In nearly all cases, central bankers are unelected officials who, until relatively recently, were operating largely unseen in technical areas. Now, central banks have become ubiquitous. As part of emergency action to combat the crisis, many of the world‘s leading central banks have moved into new fields — or back into old ones — of responsibility. Some interpretations are that they are under-resourced and not subject to sufficient oversight or accountability. In some countries they now appear to be engaged in both fiscal and monetary policy; they have become judges of probity, arbiters of capital markets, rescuers of banks, backstops to governments, and overarching umpires of the financial system. They operate in an economic and political environment of “shared objectives” that has become harsher, more complex, and less forgiving. They have become more vulnerable to risks of all kinds, whether from fluctuations in capital markets, from changes in political and public opinion, or from broader macroeconomic developments.

In two critical, interlinked areas — by taking charge in many cases of the wider stability of the financial system, and by systematically expanding their balance sheets to inject liquidity into government bond markets and commercial banks’ balance sheets — central banks have amassed great influence. Yet they attract manifold criticism for real or alleged misdemeanors and shortcomings. There are two interlinked paradoxes here. First, they have been widely blamed for not spotting the buildup of the financial crisis, for not taking action to forestall it, and for following one-sided policies such as inflation-targeting that may have exacerbated it. Nevertheless, they have been granted wider duties and remits for action. Second, as their field of maneuver has widened, they have simultaneously become more constrained. Reflecting the extreme attention that they attract and the far-reaching consequences of their actions, central banks are confronted with acute and many-sided tests of their abilities and acumen. Greater exposure to politics and the media and fresh operational tasks require them to increase diversity of recruitment. In some cases, they are required to be more market-oriented and focused on profitability while also being more aware of commercial and financial risk — for example,

in managing official reserves of gold and foreign exchange, or in handling collateral in the shape of government bonds that may no longer be risk-free.

A complex trade-off between power, risk, and responsibility is under way. Many central banks have admitted their (partial) responsibility for the circumstances generating the present set of international economic and financial problems — and have pledged to do better. Ben Bernanke, Chairman of the Board of Governors of the Federal Reserve, told the U.S. Congress in 2009, “There were mistakes made all around. … We should have done more [in banking supervision]. We should have required more capital, more liquidity. We should have required tougher risk management controls.” Such declarations have brought in their wake wider powers coupled with greater restraints.

There is an important distinction between the behavior of central banks in developed countries and those in emerging market economies. On the whole, those in emerging market economies have withstood economic turbulence better than their Western counterparts, although in many instances the conditions of their financial sectors were different, not least in the lack of exposure of the banking system to residential mortgage-backed securities (RMBS). This implies that there is no one size that fits all: we have to keep changing central banking functions as the need changes. We can see that over time in the same jurisdiction and across countries at the same time. We need to acknowledge this and then act accordingly. We need different horses for different courses.”

A strong backlash from politicians, in the most extreme cases, could tend to deprive central banks in developed economies of much of their hard-won autonomy. This could even propel them back to the position some of them had before, as little more than government bookkeepers. That juxtaposition may be the defining equation in the next 10 years in the multifaceted relationship among central banks, governments, and the financial system.

Different kinds of pressureIn many countries and regions, “who controls whom?” is a central question. As central banks have intruded more directly into the political arena, engaging considerably greater sums of public money, demands have grown in intensity for greater political oversight and scrutiny and new standards of transparency and accountability. Different kinds of pressure arise in different ways



in various countries. In the most well-known central banks — the Federal Reserve (Fed), the Bank of Japan (BoJ), the European Central Bank (ECB), the Bank of England (BoE) and even the firmly state-controlled People’s Bank of China (PBOC) — the new strains are noticeable. The same is true for many other central banks in industrialized and developing countries. Jens Weidmann, President of the German Bundesbank, still by far the most influential national central bank (NCB) in the euro area, conceded in a press conference in March 2012 that central banks in many jurisdictions have been brought “to the limits of their mandates” by their new roles. Weidmann openly cites the pressure on central banking colleagues who are being increasingly called to account by parliaments, which believe central banks have moved into areas that need to be “democratically legitimized or controlled.” Even the ECB, whose independence is entrenched in a treaty, has found itself under different kinds of political pressure for most of its existence. Partly because these pressures are growing as a result of the strains in economic and monetary union (EMU) in Europe, and partly because of the greatly increased complexity of the ECB’s operations, the ECB now concedes that it must be more open in its deliberations and its policy declarations.

The changing conduct and status of central banks provide an important illustration of broader global patterns. Economic and financial power and resources are moving toward the emerging market economies, away from the industrialized West. Mohan, the former Reserve Bank of India Deputy Governor, points out that central banks face different policy imperatives, and this must necessarily affect monetary policies. “For example, there has been a persistence of inflation differentials between developed countries and emerging market economies for an extended period of time. This implies a corresponding nominal interest rate differential, leading to arbitrage capital flows that then put further upward pressure on exchange rates and even more arbitrage flows: is there any alternative for emerging market economies other than to practice regular foreign exchange intervention and some degree of capital account management?”1

The influence of the emerging market economies can be seen in another field, too. A large part of Western central banks’ apparent success in bringing down inflation to targeted levels in the early

1 Mohan, R., 2012, “Diversity to combat groupthink,” OMFIF May Bulletin, 6-7

2000s was through globalization of the world economy. This coincided with what in hindsight turned out to be an overreaction to the mild recession of 2001/2 (partly prompted by fears of deflation), shortcomings in policing wider financial stability criteria and a failure to control the adverse effects of certain financial innovations. Developing countries sharply increased exports to the West, depressing price levels without damping the formation of asset bubbles. The aftermath of the crisis has ushered in a further stage of world economic transformation, with important consequences for central banks in industrialized as well as emerging market countries. Central banks in the former have been propelled by the upheavals to extend their duties and responsibilities but are, in general, growing less independent. Those in the latter, in general less encumbered by the financial crisis, are increasing their focus on monetary tasks and are consequently becoming more autonomous.

It is worth dwelling briefly on what is meant by “central bank independence.” Central banks are given a mandate, which may be price stability, financial stability, or some other measure of economic well-being, by the political authorities of the jurisdiction concerned. Central banks are emphatically not at liberty to select their own mandate and must report periodically to government on how and how well they have executed that mandate. “Independence” resides in the bank’s choice of methods, priorities, and timing for executing that mandate. These mandates are broad, the constraints on the bank’s freedom of execution are limited, and day-to-day external oversight of the bank’s activities is ipso facto absent. Although most governments have the power to nominate the head of the central bank, many governors have fixed-term mandates and only can be removed for reasons of gross negligence, misconduct, or criminal behavior. There is now growing debate about whether central banks are sufficiently “accountable;” whether some of their activities (e.g., government financing or direct lending to non-financial institutions) are outside of their mandate; and whether the previously accepted belief that “independence” guaranteed freedom from “political interference” is sustainable or indeed desirable.

Lessons from recent central banking historyThe Federal Reserve: change of guard, change of styleThe high point of Alan Greenspan’s reputation was perhaps 1999, when then U.S. presidential candidate John McCain declared that he would reappoint him even if he was dead. Handled with


respectful deference during his semiannual pilgrimage to testify in Congress about monetary policy, and praised for the Delphic quality of his remarks about interest rates, Greenspan urged regulators to liberate markets and allow markets relatively free rein. He philosophized that central banks could not deflate bubbles, only clean up the wreckage after they burst. The man once lionized as “The Maestro” admitted later that he had placed misguided faith in the self-correcting power of free markets. “Those of us who have looked to the self-interest of lending institutions to protect shareholders’ equity, myself included, are in a state of shocked disbelief,” he said in a Congressional testimony in 2008. Greenspan stuck to an ideology that emphasized regulatory inactivity, allowing the perception of considerable latitude of action. By contrast, Ben Bernanke, with his background in academia, originally approached the Fed with the intention of emphasizing its inflation-fighting role. This had to be abandoned to deal with the immediate financial crisis. But with the setting of a “near-formal” inflation target of 2% in 2012, the issue has returned. It is also notable that the FOMC has been less unanimous under Bernanke.

Bernanke’s willingness in the heat of the financial crisis to push the Fed’s independence to the limit angered some U.S. lawmakers, who perceived the central bank as acting in a high-handed fashion, even though the Fed acted in close cooperation with the Secretary of the Treasury. Though the Fed is under no formal requirement to seek the opinion of Congress regarding the particular monetary or supervisory steps that the Fed might decide to take, many legislators felt that such momentous decisions should be subject to more stringent oversight than that afforded by after-the-fact hearings in Congress on Fed decisions.

Along with other banking regulators, the Fed was accused of inattention in allowing risk to build up in the financial system to such an extent. As a result, there was also talk of stripping the Fed of its regulatory functions and making monetary policy its sole activity. In the end, the Fed lost none of its statutory powers and even gained further influence. A last-ditch effort to consolidate banking regulation in a single agency — which would have removed 850 state-chartered banks from direct Fed supervision — ultimately failed. However, Congress did mandate that the Treasury rather than the Fed chair the Financial Stability Oversight Council (FSOC) that would be responsible for the design and implementation of macro-prudential supervision in the United States.

Changes in monetary policyUnder Bernanke the Fed markedly changed the implementation of monetary policy. It departed from relying solely on adjusting the Fed funds rate, used for overnight loans to banks. It put the Fed funds rate down to zero, kept it there and announced that it intended to keep it there until at least the end of 2015. It also elected to supplement this interest rate policy with three rounds of quantitative easing. This involved massive purchases of government securities in the open market, including long-term securities to bring down long-term rates (a return to “Operation Twist” from the 1960s) as well as mortgage-backed securities (to remove distortions in that market and reverse the collapse in the housing market). All this represented financial market activism on an unprecedented scale.

A second major change under Bernanke’s chairmanship has been the move toward more disclosure regarding Fed’s policies and policy intentions. He has accelerated a gradual opening-up that started even before the financial crisis with regular testimony of the Fed chairman to Congress and the delayed publication of the minutes (by three weeks) and of the full transcripts (by five years) of the FOMC meetings. In 2011, Bernanke began holding press conferences following certain FOMC meetings, with the plan to hold at least four a year, primarily to talk about the Fed’s view of the economic outlook. In addition, in 2012, the Fed began publishing a number of documents showing the views of individual FOMC members (without giving their names) regarding growth, inflation, and Fed funds rates. In this manner, the public can get an idea of the range of expectations within the panel and where consensus seems to be headed.

Controversies at the Bank of EnglandIn the 15 years before the 2007 credit crunch, the BoE’s approach to monetary policy was substantially transformed, as was the quality of its economic analysis. This was largely the work of Sir Mervyn King in his successive roles as Chief Economist, Deputy Governor, and Governor of the Bank. Sir Mervyn was an early advocate of flexible inflation-targeting whereby interest rates were set in response to forecasts of future inflation. An underlying assumption was that achieving price and output stability would be sufficient to ensure financial stability. However, during Sir Mervyn’s governorship, the Bank downgraded its financial stability objective and put increased emphasis on monetary policy. Like the Fed, the BoE believed at the time that the best way for central banks to minimize the likelihood of macroeconomic instability arising from extreme fluctuations in asset



prices was to focus on monetary policy. They believed that asset price bubbles were hard to identify, difficult to pop safely and best cleaned up after the event.

Critics argue that the Bank failed to foresee the financial crisis and was slow to grasp its severity when it struck. The Bank might quibble about its perceived lack of foresight, but the Governor has acknowledged that he and others at the Bank should have shouted from the rooftops that the system was unstable. Although the Bank did not provide liquidity to the banking system as freely as the ECB did (particularly at the start of the crisis), the Bank did progressively expand its provision of liquidity and did restructure its discount window policies to allow it to deal more effectively with market-wide and bank-specific problems. The Bank has also embarked on a massive — and in some quarters controversial — Quantitative Easing program (QE).

DifficulttasksineuroareaThe governance of the euro makes arrangements within the Economic and Monetary Union (EMU) a special case.

Early confidence in the sustainability of EMU after it was set up in 1999 coincided with persistent inflows of international capital, fueled by expectations of European economic convergence and solid growth prospects, allowing governments across the euro area to borrow more or less at the same low interest rates as the government of the European country with the most stable post-war economic track record: Germany. A sharp reduction in the interest rate spread between better-class and less-good borrowers convinced politicians that EMU was succeeding far more than many had expected or hoped. Governments in the peripheral countries experiencing booms fueled by low interest rates appeared to have no further incentive to carry out unpopular structural reforms at home, even though such measures were necessary to underpin EMU’s long-term health.

With the restoration of financial market risk aversion after the trans-Atlantic bubble burst, the true level of danger confronting overstretched debtors suddenly became apparent. Europe had to cope not only with the cost of years of unrealized reforms in many countries that had lived beyond their means, but also with the economic challenges of financing persistent current account imbalances and capital flight in EMU members that could no longer adjust by devaluing their currencies.

Sensitivities on the balance sheetECB President Mario Draghi has presided over a very large increase in the balance sheet of the Eurosystem, which is regarded by many central bank watchers (especially in Germany and other more economically orthodox EMU members in Northern Europe) as a portent of higher inflation. However, the Governing Council of the] ECB has been showing a united front toward governments in an effort to ensure it is not left with an unfair share of the burdens of stabilizing EMU.

The ECB’s widespread belief in the necessity of fiscal consolidation explains its long-running support for the fiscal compact agreed to by Member States in March 2012 to instill greater discipline into the single currency arrangements. However, a much greater form of political union is needed to bring together EMU’s fragmented structures. It remains to be seen whether the proposals for the outright monetary transactions (OMT) program and the mooted banking union encompassing a single supervisor for banks in the Eurozone provide merely a temporary reprieve or lay the foundations for greater stability delivered through more federal European structures.

The divergence in confidence levels between and in northern and southern Europe is starkly illustrated by the divergence in the Target 2 intra-euro area payment balances between AAA Germany, Finland, Luxemburg, and Netherlands and the “peripheral” GIIPS: Greece, Italy, Ireland, Portugal and Spain. With downgrades and bailouts impacting GIIPS there has been a notable flight to safety to the northern nations by depositors and investors.

The divergence between the trajectory of Germany’s Target 2 balance and the rest of Europe’s highlights Germany, as the largest AAA country, has attracted the greatest volume of capital inflows, which have as their counterparty a corresponding build-upon of the Bundesbank’s claims on the ECB. (However, on the basis of GDP, Luxembourg’s claims on the ECB are larger.) A country-specific picture shows that the deterioration of balances is greater for a country believed to be needing assistance than for one that has already been bailed out.

As central banks have acted to increase liquidity in capital markets, they have increasingly embarked on targeted asset purchase schemes, which, alongside their increased collateral


based lending, have led to a significant growth in balance sheet risk for both national and regional central banks.

Increased prominence for the People’s Bank of ChinaThe higher profile in China and abroad of the People’s Bank of China partly reflects the public stance of Governor Zhou Xiaochuan, now on the Board of the Bank for International Settlements in Basel. The process of greater accountability and transparency is undoubtedly moving forward in China. Zhou has to appear before the finance and economic committee of the Chinese parliament once every three months to answer questions on the implementation of China’s monetary policy.

Zhou has lent prominence to the PBOC’s role in encouraging Chinese financial liberalization to promote both capital inflows and outflows for China’s up-to-now tightly circumscribed financial markets. China sees three major benefits from capital account liberalization. First, more foreign investment will flow into the domestic market, generating growth and employment. Second, overseas investment will provide Chinese entrepreneurs with more opportunities to diversify their businesses and provide Chinese citizens with more financial products to spread their savings. Third, opening up the financial services industry and the capital account is a crucial step to promote much-needed domestic financial competition and innovation.

Defusing tensions with the U.S.In promoting financial liberalization, the PBOC and Zhou also have a role to play in defusing long-running tensions with the U.S. on trade and currency issues. One powerful incentive for the U.S. to take such liberalization moves seriously is that it could buttress the position of U.S. and other foreign asset managers seeking to do business in China. Moving toward a more flexible currency regime by announcing a wider trading band for the renminbi2 would help China develop a more independent monetary policy, setting interest rates to meet domestic objectives rather than being constrained by fears of vulnerability to flows of foreign

2 China has been hesitant about widening the renminbi’s trading band because of the possibility of surges of speculative inflows. But in early 2012, pressures for renminbi appreciation have eased. This is partly because export growth has slowed as a result of weakness in the major advanced economies in Europe and elsewhere: consequently, China’s reserve accumulation diminished markedly in 2011, with forecasters expecting little or no appreciation of the renminbi in 2012–13. This may be one reason why the trading band was doubled from 0.5% to 1% in the spring of 2012.

capital. This in turn assists financial sector reforms by allowing the central bank to use interest rates to guide credit allocation and rebalance growth toward domestically generated expansion — a major theme of the current 5-year Plan.

Growing politicization of the Bank of Japan: cautious approach on debt monetizationJapan’s experience of unconventional monetary policy started relatively early. It was initiated by the BoJ in March 2001, one week after the Japanese Government announced the economy was in “mild deflation.” (As a result of the fallout of the Asian financial crisis in 1997—98, the BoJ had already begun to expand its balance sheet some years earlier.) The policy in 2001 included zero interest rates as well as quantitative easing, although the manner of the policy was highly cautious. It was also associated in 2003—04 with massive intervention on the foreign exchanges to depress the yen.

The BoJ set a ceiling on government bond purchases equal to the size of the banknote issue, on the grounds that the central bank wished to prevent debt monetization. The BoJ also announced credit easing through the purchase of asset-backed securities, asset-backed commercial paper, and equities from financial institutions. The purchase of equities was implemented as part of macroprudential policy; the Japanese banks held large volume of equities of customer firms, and the collapse of equity prices had a cumulatively detrimental effect on the banks’ capital base and hence their ability to lend. One reason why the BoJ was more cautious about purchasing government bonds was that the costs involved in the transactions were not indemnified by the Ministry of Finance (in contrast to the BoE, but comparable to the Fed and the ECB).

Although Governor Masaaki Shirakawa has maintained a stout defense against more aggressive QE, in early 2012 the BoJ diverged from previous practice both in moving to expand government bond purchases and in announcing a price stability goal (at 1%) to encourage economic recovery. In line with “Abenomics,” the new Governor, Haruhiko Kuroda, has announced “quantitative and qualitative monetary easing,” whereby the BoJ will double Japan’s monetary base with the aim of pushing Japan’s inflation to about 2% which alongside fiscal measures is designed to reverse Japan’s deflationary slump.



The new risk landscape for central bankingConfronting risksTraditionally, central banks have enjoyed being positive role models, as advisers on good economic policy, upholders of monetary discipline, guardians of sound public finance, and reliable sources of government income (from passing on profits from their money market and foreign exchange operations as well as seigniorage profits from notes and coins in circulation). Now, these relatively comfortable positions have been turned on their head.

One of the greatest risks concerns encroachment on central banks’ independence caused by the multiplicity of burdens put on them.

Central banks, notably in the West, enjoyed a period of considerable success and enhanced status from the 1980s to the beginning of the financial crisis in 2007. This stemmed from their success in conquering inflation, notably in the U.S., starting with the massive spike in interest rates (and the consequent recession) in 1981. Recessions became fewer, shorter, and shallower, giving rise to the belief that the achievement of price stability (for goods and services) had produced what economists came to call the “Great Moderation” — a belief that monetary policy had effectively tamed the business cycle and set the stage for more rapid and more consistent economic growth. In light of this apparent triumph, a consensus emerged that central banks’ main, if not sole, target should be combating inflation. Following the reintroduction of inflation-targeting, commonly attributed to the Reserve Bank of New Zealand in the early 1990s, this model has spread and is now followed by most advanced-economy central banks as well as by a large number of institutions from emerging markets.3 Moreover, a view also emerged that the best way to assure that central banks achieve their inflation targets was to make them independent — to give them the right to decide the timing and magnitude of changes in interest rates necessary

3 There were and are, however, several notable exceptions. The U.S. Fed has a dual mandate of stable prices and maximum employment, although it has recently moved to setting a de facto 2% inflation target. The ECB acts like an inflation-targeting central bank but with some crucial omissions, notably a lack of sanction if the target is breached. The BoJ, even though it has recently moved in the direction of inflation-targeting, is not formally following such a goal. A number of important Asian central banks such as the People’s Bank of China and the Monetary Authority of Singapore follow exchange rate targets. Taiwan’s Central Bank of China, perhaps uniquely among central banks, has no formal target at all.

to achieve price stability. That seemed to be the lesson from the Bundesbank and from the Fed (it received this power in 1951), and it was followed in the U.K. in 1997 and in the design of the ECB at the end of the 1990s.

In the troubled aftermath of the financial crisis, three sets of paradigms fractured. First, although they were frequently praised for speedy action to pump in liquidity and lower interest rates, central banks’ evident unpreparedness has been a factor undermining the model of independence. Further, central banks faced criticism that interest rate policies — at least in the trans-Atlantic world — contributed to the destabilizing forces that fueled the buildup of the financial crisis. In the supervisory arena, their hands-off approach was an important factor behind the steady rise in risks that almost brought down the financial system.

Second, the tools and instruments previously at their disposal were shown to have been insufficient and new ones were needed (or old ones brought back). The mantra that central banks’ policy priority of maintaining stable prices would be sufficient to promote stable economic growth was revealed as misplaced, as central banks seemingly lost sight of one of their key original tasks: providing financial stability. There was a similar undermining of the belief that “microsupervision” of the banking system — that is, scrutiny of individual components of it without regard to the whole structure — would suffice to keep it on an even keel. The same was true of the view that price movements on financial markets would turn out to be self-correcting without large-scale government intervention.

Third, the new policy landscape was itself fraught with difficulties amid general disagreement about whether the new policies are really appropriate and what their effects would be.

Into new territoryAs they gradually recovered their poise, central banks moved into new territory. As outlined above, they have designed and implemented new monetary policy tools, such as QE, that border on fiscal policy. They have also broadened their extension of liquidity to the banking and financial system and adjusted their collateral criteria with large-scale implications both for central banks’ own finances and for the overall health and liquidity of capital markets.

Central banks have also embraced the concept of macroprudential supervision. They have effectively resolved the so-called “lean


versus clean” debate in favor of “lean.” Central banks have come to the view (together with finance ministries and other policy makers) that they should “lean against the wind” in taking pre-emptive action to guard against bubbles building up in financial or other asset markets during upswings in the credit cycle. This echoes the philosophy that the central bank should “take away the punch bowl just as the party gets going.” Raising rates was the tool that the author of the phrase, William McChesney Martin, Chairman of the Federal Reserve Board from 1951 to 1970, originally had in mind. Today’s central bankers have a much broader — but still untested — set of macroprudential tools in mind, such as varying capital and/or leverage ratios at banks. In this respect, the “lean” school is paying respect to the reservations of the “clean” school, which holds that raising rates is a counterproductive way to “lean against the wind,” for it threatens to bring about the very recession that the central bank should seek to avoid.

But wielding macroprudential tools to counter financial instability when inflation may be under control significantly widens central banks’ remit. This is an ill-defined task that, almost by definition, will turn out to be rather thankless and exposes central banks to conflicts of interest and creeping political influence.

Balance sheet hazardsThe biggest quantifiable risk comes from balance sheet hazards in lending to banks and purchasing government and other securities. The latter is predominantly a risk where government securities purchased by the central bank are in currency that the government in question cannot itself issue, giving rise to exchange rate and/or default risk. Here central banks are confronted with the possibility of losses in cases where the measures fail to work and debtors’ difficulties get worse. Such cases represent a significant extension of the famous “lender of last resort” dictum of 19th-century British essayist Walter Bagehot that central banks should lend freely (i.e., liberally) at a high rate to solvent but illiquid banks that have good collateral. All the main industrialized country central banks have undergone large-scale expansion of their balance sheets, albeit at different times during the development of the financial crisis, in different ways, and for different reasons.

The BoE registered the biggest proportionate increase in the balance sheet, up 250% since the beginning of 2007, followed by the Fed (up 230%) and the ECB (up 162%). The BoJ, which carried out large-scale QE during the 1990s, reflecting the effects

of an earlier severe recession in Japan, has registered a much smaller rise in the balance sheet of only 20% since January 2007 (data as of March 2012). As well as moving in smaller steps, the BoJ has resorted to less conventional actions, with forays into the stock markets and corporate bonds, while the Fed and the BoE have concentrated on purchases of government bonds, usually of relatively short duration. The ECB and the NCBs (i.e., the Eurosystem) roughly doubled their overall balance sheets in the first 18 months after the U.S. subprime-mortgage crisis hit markets, then kept them relatively steady until the deepening of the euro area debt unrest in summer 2011. In the period to spring 2012, the Eurosystem balance sheet rose a further 50%, much more than for the other large central banks, mainly reflecting a big increase in unconventional lending to banks in December 2011 and February 2012 under the ECB’s so-called long-term refinancing operation (LTRO). Expressed as a proportion of the GDP of their areas of jurisdiction, as the Bundesbank itself has pointed out, the Eurosystem’s balance sheet increased as of March 2012 to 32%, above the comparative figures for the BoJ (31%), the BoE (22%), and the Fed (19%).

Sir Andrew Large, former Deputy Governor of the BoE, points to the danger of “a loss of credibility and policy traction when people figure out the hole in central banks’ balance sheets, with effects on the quality and credit standing of sovereign owners.”4 This has been brought into focus by discussion in Europe over “burden-sharing” and over potential losses by the ECB and the Eurosystem combining the ECB and NCBs, Large says. Engineering an “exit” from what Jean-Claude Trichet calls the “historically abnormal” expansion of central banks’ balance sheets is one of the biggest, and most intractable, challenges facing central banks in the leading industrialized countries. Since, through seigniorage, central banks have access to present and future revenue streams from the profits of printing banknotes and minting coins (effectively non – interest rate-bearing loans to the currency issuer from the rest of the financial system), it is difficult (but not impossible) for them to become technically bankrupt, but balance sheet strength is still politically and symbolically significant.5

4 Andrew Large, statement to OMFIF, emailed response to survey on 1 February 2012.5 One risk of technical bankruptcy would be where a central bank’s liabilities in foreign currencies

rise dramatically through devaluation of the domestic currency, where seigniorage cannot be used to stem the weakness of its balance sheet.



Pressures in emerging market economiesIn emerging market economies, too, additional pressures have emerged from extended burdens on central banks’ balance sheets, albeit for different reasons. The massive increase in foreign exchange reserves in Asia and Latin America reflects the authorities’ efforts both to dampen local currency appreciation and protect export-oriented economies, and also to build up financial arsenals to guard against a repeat of unrest of the sort that occurred during the 1997–98 Asian financial crisis. These much-enlarged stocks of foreign exchange (largely in U.S. dollars, but with a sizable component in euros) represent a form of self-insurance against the buffeting of world capital flows, as well as a reaction against what was considered to be ill-conceived conditions from the International Monetary Fund accompanying loans made at the height of the Asian crisis.

But such insurance comes at a price. Greatly increased reserve holdings may appear outwardly a sign of virility and growing maturity of the fast-growing parts of the world. In an important sense, this interpretation contains a good deal of truth. But, paradoxically, sharply higher asset volumes are also a source of vulnerability that is directly connected to the relatively poor economic performance of (and lower returns in) the industrialized nations that provide the lion’s share of the world’s reserve currencies. This reflects recent tendencies for reserve currencies to depreciate against the local currencies in which emerging markets’ central bank balance sheets are denominated and, furthermore, the historically low interest rates in the U.S. and Europe. These developments expose central banks to “negative carry” in their reserve operations in which their holdings of unprofitable foreign exchange cause significant falls in income and sometimes outright losses. This can add further to strains on central banks’ balance sheets that are recovering only gradually from the results of the longer-term bailout actions undertaken during the Asian crisis 15 years ago.

With this in mind, some emerging economy central banks are energetically diversifying their reserve management operations. The aim in many cases is to maintain a traditional leaning toward conservatism and liquidity yet to include more active return-boosting techniques, such as expanding the range of instruments and currencies and even moving into non-standard fields such as real estate and private equity. Emerging market economies’ exposure to the travails of the dollar and euro provide an

illuminating case study on risk transference between the private and official sectors in certain countries. By seeking to shield their nascent manufacturing companies from the effects of relative economic decline in the developed markets on which they depend for exports, emerging market economies (and others in a similar position) are opening themselves to potential financial fragility in their official institutions that could spill over to the nation’s economic core.

Conflicts,accountabilityandindependenceBalance of diverging opinionsFinding a balance in the new landscape is fraught with real and potential conflicts of interest, all with large repercussions for central banks’ accountability and independence. Hanging over central bankers is a specter that has been prevalent throughout the history of official monetary policy and especially during the financial crisis: moral hazard, or the development of counterproductive incentives that promote rather than hinder destabilizing behavior by financial market participants. This is an especially large issue regarding the political, economic, and legal tussle surrounding EMU and over the status and remit of the ECB. These differences of emphasis about credit policies in Europe are part of a wider central banking debate in which opinion around the world has moved toward greater pre-emptive stringency, adapting to signs of excess monetary growth and asset price bubbles through “leaning against the wind” earlier in the credit cycle.

There is plenty of room for conflicts of interest between previously separated operational structures of financial and monetary stability, now being brought together in a way that, in many cases, amounts to reversion to an old form of central banking architecture. For example, the tightening of capital requirements for banks under the Basel III accords at least partly contradicts the need to prompt recession-defeating flows of bank funding to businesses. The separation or “ring-fencing” of retail commercial banking structures to protect them from risks in investment banking has been put forward for many countries, predominantly in Europe, as a way of avoiding the need for taxpayers to bail out risk-prone banking operations. (It should be noted that investment banking is not necessarily or inherently riskier than retail banking; an early bank failure in the financial crisis was the British retail bank and former building society Northern Rock.)


Imbalance in democratic accountabilityThe upheavals in the central banking landscape have substantial repercussions in the sphere of politics and public opinion, as shown in the U.S., Europe and Japan, as well as in emerging market economies. The substantial upgrading and widening of central banks’ roles have taken place while they have maintained a high degree of statutory independence from governments, part of a compact to preserve their freedom of monetary policy action and guard against irresponsible and inflationary government policies. Politicians’ scrutiny and control rights over central banks’ actions have, however, not increased in line with the considerable expansion in central banks’ realm of action and de facto power. This has sometimes given rise to searching debates about democratic accountability.

One particularly important part of this debate is the specialist field of accounting policies and standards. It is argued in some quarters that the absence of common accounting policies among central banks is also a barrier to transparency. In this section we discuss some of the most important new accounting questions facing central banks and consider their implications.

Central banking in emerging market economies, too, has undertaken an important transition as a result of the general pressures on economic policies in recent years. Yet these changes have been less radical than in the industrialized nations. As they have come of age in the past two or three decades, central banks in emerging market economies have been traditionally closer to the core of government, more prone to government influence, and holding sway over a greater variety of economic and social tasks, often involving national development goals.

Since the impact of the trans-Atlantic economic crisis on these countries has been less acute, and since their central banks already commanded a relatively wide field of action, they have not been confronted with the operational widening that has been such a challenging transition for central banks in the West.

Pressures on independenceShortcomings displayed by central banks — and subsequent pressures on their independence — have been epitomized by Alan Greenspan, widely praised during his 18 years as Chairman of the Board of Governors of the U.S. Federal Reserve. Ben Bernanke, his successor, himself a member of the Board of Governors of the Fed from 2002 to 2005 before he took over as Chairman in February

2006, has faced a political backlash that has been all the fiercer because of the unquestioning enthusiasm that preceded it.

The debate over the role of the Fed and other central banks underlines how the threat to independence is very far from being a matter of theoretical dispute: it has entered into the realms of realpolitik. In a sense, it is not surprising that the historically somewhat anomalous position of statutorily autonomous central banks is now under pressure. The ECB’s independence is still more solidly embedded into law than that of the German central bank, since it is part of an international treaty. But as a result of compromises with governments caused by the strains confronting EMU, the high-water mark of ECB independence may now have passed. Niels Thygesen of Copenhagen University says the ECB in its first years of existence probably exaggerated its independence.

According to Lord Desai of the London School of Economics, the shift in opinion on the necessity and efficacy of independence is part of a steady historical pattern: a changing carousel of central banking doctrine. Now, he says, the world is moving to a new form of central banking multilateralism. Desai is somewhat cynical about the lags in the central banks’ reactions to changes in the economic or political environment and believes that “Free-standing central banks pursuing their own national agenda are on the way out.” Precisely what will take their place is, of course, a matter of conjecture.

Accounting questions for central banksThe recent unprecedented growth in central bank balance sheets and the complexity of the operations that these institutions now undertake have introduced a new set of questions into the hitherto placid waters of central bank accounting. These questions are not just simply of a technical accounting nature (although the complications here are real enough) but also have serious policy implications in both financial and political arenas. To give just one example, the turmoil surrounding a number of sovereign bond markets raises the question of just how should a central bank account for its holdings in such bonds. The choice between using a fair value or historical cost measure can be far reaching, not only for the impact on the central bank‘s results, but also, for example, the message that any change to the valuation, or lack thereof, can send to the market. In many instances, the central bank is by far the single largest investor in a particular market and acts by policy to affect prices in the markets.



Below we consider some of the key questions and challenges we see for central banks:• Accounting policies: while most large commercial

organizations report under well-recognized accounting frameworks (e.g., IFRS or national GAAPs), accounting and reporting standards used by central banks diverge widely. In a number of cases, central banks use a recognized GAAP as a base but make adjustments where they feel it does not appropriately represent their operations. This is perhaps understandable as many GAAPs were developed with commercial organizations in mind and so may not be the answer for some specific operations of a central bank; however, in the absence of standard accounting frameworks, it is currently both difficult and occasionally contentious to attempt to draw detailed comparisons of central bank accounts either at the overall or the specific technical levels.

• Valuation uncertainty: whether the aim is to obtain a fair value or to determine whether an impairment has occurred, valuation is a complex and potentially subjective area, and this has been shown in the varied accounting for sovereign bonds by a number of commercial organizations. Further challenges can also occur for central banks who may have significant concentrations in a particular market or may be expecting a different treatment to commercial organizations in a bailout or restructuring, and whose valuation decisions — for example, whether to impair — may have political and market consequences far beyond the accounting implications.

• Treatment of government interventions: in many countries, central banks have been engaged in complex market operations including quantitative easing, emergency liquidity assistance, asset protection, and support to extraordinary activities of the domestic authorities. Existing accounting policies may not always represent such actions well and therefore call for developing policies and disclosures that may not only raise significant accounting questions but also influence the way these actions are understood and ultimately judged.

• Exposure to international agencies: the growing interconnectivity of the global financial system and the scale of central bank involvement with international institutions such as the International Monetary Fund (IMF) or the ECB give rise to some unique accounting transactions and hence reporting requirements. It also raises issues about exposures and potential liabilities to international payments systems such as Target 2, for example.

• Risk management: as stakeholders seek to better understand central banks’ risks, the volume of risk information, historically not generally an area of extensive disclosure, is likely to increase. Judged by traditional commercial banking yardsticks, the level of market, credit, liquidity, and concentration risk run by central banks from areas such as foreign exchange and bond holdings can appear significant. A key element to consider in any risk management disclosure is, therefore, not only the quantitative information but the context that it is placed in. The way this risk is viewed can ultimately significantly affect the way it is managed and the appetite of a central bank to engage in certain activities.

• Transparency: a central theme to the items above is transparency, and how much is appropriate for a central bank must be considered. The increasing prominence of central banks is likely to give rise to ever more public scrutiny, and this can significantly affect organizations not used to such attention. While there is a general push for transparency in global markets, the unique role of central banks also presents many situations where full transparency may not be desired. Central banks may, for example, be sensitive about providing details of transactions with related parties and may not want to provide financial support information for fear of its impact on the market.

Macroprudential supervisionBefore the crisis: how “clean” won over “lean.” In an increasingly politicized world of central banks, attention is now being focused on the precise extent of macroprudential supervision and financial stability measures.

Before the crisis, it was a different story. Taking their cue from Alan Greenspan, some central bankers downgraded the goal of financial stability, believing that state-of-the-art monetary policy conducted by independent central banks would be sufficient to stabilize the economy. In addition, the Fed took an asymmetrical view on asset prices, in that it did not believe it had the responsibility to step in to check asset price bubbles but was ready to intervene to support prices should they fall — an important contributory factor in the buildup to the financial crisis. Following the Fed’s lead, most central bankers more or less ignored those economists, most notably Hyman Minsky, who argued that the economy was hostage to financial instability and that it was most endangered when conditions appeared most benign.


Those who argued for “leaning against the wind,” among them the Reserve Bank of Australia and leading economists at the BIS, were given short shrift. Even though many central bankers were clearly aware of growing risks in the system, the neatness of a central banker approach that assigned different tools to different objectives proved highly seductive. A number of factors militated in favor of “cleaning” the credit cycle after any upset, rather than taking pre-emptive action to mitigate asset bubbles. Some of these are far more than mere technicalities, since they go to the heart of the makeup of central banking.

• Bubbles are hard to detect — the benefits of pricking a bubble need to be seen against the costs of attempting to offset long-running sustained movements in asset prices. In addition, if the bubble is spotted only later in the credit process, raising interest rates late could be counterproductive.

• Bubbles do not burst easily — combating them requires that a central bank raises interest rates significantly to bring asset prices back into line, and this would depress economic activity as well as inflation. Reactive monetary policy is not quite as complicated as is sometimes alleged. Monetary policy is sufficiently flexible and powerful to cope with the task of “cleaning up” after the bubble bursts and then restoring the path to monetary stability.

• A less visible explanation for inactivity was that central banks were keen not to take on or expand their financial stability mandates. They deduced that this was a thankless and extraordinarily difficult job that threatened to conflict with their monetary policy goals.

In fact, the financial crisis revealed a fundamental flaw in the regulatory structure. After 2007–08, central banks and the myriad players who follow or react to their actions focused on the need for a new approach that would rectify the shortcomings of a system that had evidently failed. Macroprudential policy, including an arsenal of preventive weapons to mitigate systemic risk, was called upon to fill the gap. Not for the first time in the chronicles of central banking, the monetary authorities reached back to past methods.

Back to the futureJean-Claude Trichet, then ECB President, summed up the change in 2009: “Recent experience has demonstrated the limitations of a wait-and-see approach.” What was needed, he said, was “a systematic approach ... that leans against the emergence of asset

price booms as well as dealing with asset price busts. ... Such an approach should make cycles of boom and bust less likely.”6 In fact, the reshaping of priorities in many cases represented a return to the previous status quo, and in many ways this involves policies that turned out to be imperfect. Until relatively recently, central bankers over many years were deeply preoccupied with systemic risk and conscious that, since monetary policy was implemented through the financial system, it was vital to keep a close eye on financial markets and institutions. Moreover, in financial crises, the goal of financial stability has historically always trumped that of price stability. Many macroprudential tools such as capital and liquidity ratios or loan-to-value ratios are long-standing central bank instruments. As Alexandre Lamfalussy pointed out in a speech in 2010, macroprudential policy tools were deployed in the 1970s — with success that he termed as “mild, patchy and uncertain” — in attempting to reconcile the concerns of supervisors monitoring international banks’ exposures to Latin American countries with the broader objective of stabilizing the region’s economy.

In finding a workable policy, listing financial stability objectives in broad terms and assembling tools to meet them is in a sense the easy part. The extreme difficulty lies in the detailed implementation. The overall approach entails macroprudential analysis, which was, in fact, conducted by many central banks before the crisis but not acted upon; macroprudential supervision, which uses the analysis to influence the behavior of financial intermediaries; the deployment of preventive macroprudential tools; and crisis management, notably the lender and market-maker-of-last-resort roles.

The tools can be divided into two main categories. The first is structural measures, such as resolution regimes for the orderly closure of financial institutions, capital controls, increased capital requirements for systemically important institutions, and putting more derivatives trading onto central clearing counterparties. The second category is instruments designed to prevent or mitigate imbalances and address pro-cyclicality — these include countercyclical capital requirements, loan-to-value and debt-to-income limits, margin requirements, and limits on leverage, maturity, and currency mismatches.

6 Jean-Claude Trichet, President of the ECB, Keynote speech at the 19th Frankfurt European Banking Congress: “After the Crisis,” Frankfurt am Main, Alte Oper, 20 November 2009, www.ecb.int/press/key/date/2009/html/sp091120.en.html.



As the recent history shows, reconciling financial stability and monetary policy is fraught with pitfalls. Central banks once again find themselves in waters that, if not exactly uncharted, are full of obstacles, both visible and hidden.

DefiningtargetsOne set of problems centers on setting a clearly defined, quantified target for a complicated dual objective, one half of which — “financial stability” — is clearly identifiable only by its absence. The practical deployment of weaponry brings great challenges. One of the reasons central banks shied away from the task in the past was the perception that if interest rates were to be deployed solely in the service of price stability for goods and services (whilst ignoring asset price inflation), those charged with financial stability had no weapons to deploy, except perhaps to make speeches and write reports. A lot of effort has been put into developing tools, such as loan-to-value limits or countercyclical capital provisions, that central banks could use to restrain financial activities or institutions deemed to be too risky. However, implementing these policies could be excruciating.

One main problem is the possibility of a clash with monetary policy. It seems clear, for example, that if central banks were to follow macroprudential objectives, interest rates would differ from what they would otherwise be — as shown by the meeting of inflation targets in the period when crisis-inducing imbalances built up before 2007. The BoE argued that: “Monetary policy would not have been able to curb these emerging financial balances without diluting the inflation objective. An attempt to curb banks’ balance sheet growth through monetary policy may have been seriously destabilizing for the real economy over this period.”7

There is a fascinating corollary in the case of EMU in Europe. Macroprudential policy, it is said, would have prevented or mitigated the buildup of imbalances in states such as Spain or Ireland that experienced overheating as a result of lower-than-optimal interest rates in the early 2000s. Jens Weidmann claimed at a Chatham House event in 2012 that similar tools could have an effect in curbing “inflationary pressures” in Germany, resulting from low interest rates and high liquidity levels introduced

7 Bank of England discussion paper, The role of macroprudential policy, 19 November 2009, accessed at: www.bankofengland.co.uk/publications/Documents/other/financialstability/ roleofmacroprudentialpolicy091121.pdf.

throughout the euro area to combat the threat of banking and sovereign state failures.

Most of the macroprudential tools being considered are largely untried, so — unlike with monetary policy — central banks will not be able to cite experience or evidence to justify them. On this basis, financial intermediaries whose business is to be constrained by them will complain loudly, and possibly justifiably, that their business is being hobbled on the basis of a theory. Finally, it will never be clear whether policy has worked. If crisis recurs, then whatever the central bank did will not have been enough. If on the other hand the central bank successfully reins in, say, commercial property lending and no stability problems emerge, this success may well be held up as evidence of heavy-handed dirigiste policy-making.

The political dimensionEqually problematic is the political dimension. Many financial imbalances have arisen historically in housing finance. Housing booms, particularly in the English-speaking countries, are popular, not least with politicians. Charles Goodhart of the London School of Economics points out that central banks will require strong nerves if they decide — on the basis of “superior wisdom” — to take away the punch bowl just as the party is getting going. If we assume that the central bank does succeed in deflating the property balloon quietly and successfully, he adds, then it will be told that its restrictive actions were not necessary in the first place. Note, too, that in Spain, which used countercyclical provisioning before the crisis, the central bank came under considerable pressure from private banks and from business to loosen the regime just as the construction and real estate party was becoming potentially dangerous.

At the very least, governance arrangements for the macroprudential role, which logically should sit in the central bank (apart from crisis management, which involves taxpayers’ money), will need a clear mandate and a high degree of transparency to ensure that it gains wider legitimacy. Since macroprudential policy requires such difficult judgments about the nature of the cycle and scale of the threat implicit in financial imbalances, there are bound to be mistakes. That further underlines the importance of transparent explanations. One leading central banker explains: “We have to be clear-cut and avoid fuzziness about the mandate.”


Precisely; in fields where there is so much interaction between politics and finance — and so many cross-border repercussions into countries and regions of different jurisdiction and standards — that precision is very difficult to achieve.

Central banks in a new environmentThe framework1 Accountability, independence and limits to power The Great Recession pushed new roles and new responsibilities onto central banks. Some of the new tasks were welcome, some less so. But every expansion of power carries risks. The pressure to do everything may produce an ability to do nothing very well. Moreover, central banks cannot automatically expect the independence they have enjoyed when restricted to inflation-fighting to carry over into their non-monetary functions. Moreover, with multiple tasks comes the risk of conflicting tasks. Central banks will have to be careful to spell out what they can do, and, more importantly, what they cannot do. One particular problem here is that success can be a non-event — e.g., the absence of a crisis — which makes it more difficult to justify action. They will, therefore, have to be prepared for greater political interference and demands for accountability and transparency, as well as to take broader consequences of their actions into account. Central banks also need to define the legal framework for their activities so there is unambiguous division between operations that are decided and implemented by the bank itself and those undertaken by the bank acting as an agent of the government. This provides the best means of imposing a clear demarcation line between the central bank and its ultimate overseer, the political authority.

This will require skillful communications management — even more so given the high likelihood of increased political pressure. Criticisms of Western central banks for being out of touch with ordinary people facing economic hardships, or for being insufficiently communicative to political representatives, are signs that the broad consensus that has sustained central bank independence could break down — or maybe is doing so already. In the emerging market economies, too, central banks require more deft communications skills to overcome criticism that they may be presiding over imbalanced economic growth, taking insufficient action to ward off currency pressure or making losses in management of official foreign exchange and gold reserves.

In the sphere of financial stability, the public does not need reminding of the costs of letting the financial system get out of control. However, nobody has much idea, or much previous experience, in making financial stability policy comprehensible. As well as being ineffective, the financial stability reports published before the crisis were usually comprehensible only to the cognoscenti. They also tended to embrace a backward-looking approach rather than a forward-looking discussion of risks and potential future issues. One of the top priorities for central banks facing greatly expanded roles should be to explain precisely what they plan to do, especially if those actions are likely to be controversial. If central banks can secure support for the principle of intervening to slow incipient bubbles, they have some defense against criticism from those who are disadvantaged by any particular initiative.

2 Macroprudential policy and institutional structuresParticularly when they interact with government more fully through macroprudential measures (as well as in other areas, such as purchases of government bonds), central banks must recognize the many-sided nature of their governance arrangements. Especially with regard to macroprudential aspects, several important functional areas need to be engaged. The main stakeholders are the fiscal authority, which is likely to be called upon in a crisis; the central banks as creators of money, a vital ingredient to restoring confidence; and the supervisors with relationships to individual institutions.

Information about macroprudential risks should be presented by a separate institution, or at least one that reports directly to the board of a new-style central bank where the macroprudential approach is given equal weight to monetary policy-making. This is similar to the separation of powers in a private sector asset management company, where the investment manager (analogous to the central bank) is balanced by an independent risk management function (the macroprudential risk committee), which focuses purely on identifying, quantifying, and mitigating risks.

Establishing an appropriate corporate governance framework for macroprudential policy is difficult. Unlike monetary policy, where the rate of inflation provides a measurable, comprehensible benchmark, there is no single, continuously observable metric to describe the buildup of systemic risk. A further problem is that the benefits of macroprudential policy are long-term and not readily



grasped by politicians and the public, whereas the costs may be highly visible and felt immediately. There is thus an inbuilt bias toward inertia. The grant of operational independence may also be more controversial than with monetary policy. It follows that for credible accountability, a clear mandate is vital, along with a high degree of transparency and good communications.

Extension of central banking roles has brought great challenges as well as opportunities for management at central banks, at both senior and intermediate levels. The search for operational excellence in central banks has now taken on a new urgency. The challenge is to find (via internal or external appointments), incentivize, and retain appropriate staff. The opportunity is to restructure management systems that may have been preserved for many years in spite of changing external circumstances and adapt personnel hierarchies and individual staff positions to the new environment, introducing a new spirit of dynamism and flair into the operation of highly traditional institutions.

There are diverse areas where central banks need to import expertise and know-how from non-central-banking fields to improve their management practices. At the same time, the interlinked nature of the financial crisis and the new emphasis on cross-border cooperation has brought fresh imperatives for central banks to cooperate more fully both with other central banks and with other public sector authorities around the world. The new environment highlights the requirement for skill sets that have always been part of central banking expertise but are now returning to the fore with greater intensity.

Given the bias toward inertia, it is important that the institutional arrangements for macroprudential policy should strengthen the ability and willingness of policy-makers to act. The institutional architecture must also reflect the need for coordination and consultation where macroprudential policy overlaps with related policy areas. Central bankers and prudential agencies must clearly be involved, as should securities regulators in financial systems where capital markets play a large role in financial intermediation. The involvement of treasuries, while potentially helpful, needs to be carefully managed to avoid operational independence being compromised.

The tasks3 Early warning systemsCentral banks are coming under increasing pressure to provide early warnings of when economies are becoming unstuck. They will face having to prescribe harsh economic medicine to counter predicted but unquantifiable threats. This will require a heightened level of alertness in assessing signs of stress in the economy stemming from both domestic and international factors. Such an approach will frequently involve acting preemptively when the need for action is not generally accepted. In addition to developing early warning systems, this once more highlights the crucial need for central bank communications skills.

4 Central banking targets and instrumentsThe limits of inflation-targeting as a unitary central banking goal have been cruelly exposed. A new framework must solve the conceptual challenge of finding appropriate instruments and targets and how to meet multiple targets. The issue of whether central banks have any effective macroprudential tools has yet to be resolved. The same is true for the pros and cons of the countercyclical instruments typically favored in Europe, such as “dynamic provisioning” (as in Spain). Central banks must see the real possibility that adoption of multiple targets (i.e., a reduction in the importance of the inflation target) would automatically raise fears of higher inflation and thus gravely set back their agenda of promoting low-inflation growth.

In the macroprudential sphere, it is vital that regulators and central banks work out what they mean by “financial stability” and set down concrete objectives that will allow them to measure progress (or lack of it). They need, too, a mechanism to handle the conflicts of objectives that inevitably arise.

5 Lender-of-last-resort functionOne of the most pressing challenges is the idea that a central bank should act as a “lender of last resort.” Central banks should make clear where they see the dividing line between normal financing activities that help execute monetary policy and emergency liquidity assistance to particular institutions. Realizing a satisfactory exit from the latter is a major priority for central banks. It is a particularly complicated issue in Europe in view of the heterogeneous nature of the euro area economy and the absence of European political or fiscal union.


Central banks face pressure from time to time to act as a provider of extensive liquidity support to the bonds of sovereign borrowers, as has been advocated for the ECB with regard to peripheral states in EMU — an issue highlighted by controversy over the ECB’s OMT program. Central banks in other developed and emerging market economies have also purchased government bonds via QE, but this has been carried out as part of the overall macroeconomic policy to add liquidity to financial markets and lower interest rates within the economy as a whole. When calls are made for a central bank specifically to provide massive liquidity to support the market for government debt, such calls can be viewed as equivalent to the central bank being asked to directly fund illiquid sovereigns, either via direct interventions on the primary market or by extending direct credit lines. But this is a fraught field. Any central bank that undertook aggressive funding of its sovereign in an overt fashion would be likely to see its currency and financial assets downgraded in the marketplace. Although this is a legal and political gray area, central banks will need to take care, for a mixture of reputational, governance, and economic reasons, if contemplating extending significant market support operations for the debt of their own government. Central banks, in effect, are always lenders of last resort to governments that issue their own currency. The unique feature of the euro is that the currency is itself independent from the Member States. In this sense, the euro bears some resemblance to the gold standard.

6 Central bank balance sheetsCentral banks have had to use their balance sheets as rarely before. During the last five years, they have become progressively more exposed to credit risks and issues of collateral adequacy that were previously not a constraint. Purchases of assets in markets under stress imply a financial risk for the central bank’s balance sheet. In theory, a central bank can fail, since it cannot create unlimited money at will. Moreover, since central banks are normally part of the public sector, they can call on the tax-raising powers of the state. But, because of the potential political difficulties associated with this, balance sheet weakness is likely sooner or later to spill over into reputational and political weakness that can affect financial market outcomes.

This is an acute question for the ECB and the NCBs of the Eurosystem, since large-scale recapitalizations for creditor central banks in EMU that suffer losses because of defaults or impairments affecting counterparties from the private or public sector will be

financially irksome and politically controversial. However, the issue is preoccupying emerging market economies, too, because of the “negative carry” generated by many developing country governments’ and central banks’ investments in low-interest-bearing foreign government bonds issued by industrialized countries. These governments and central banks, like their opposite numbers in the West, are also concerned about the impact on international and domestic public opinion of losses caused by such disadvantageous investment policies.

7 RegulatingandsupervisingthefinancialsystemThe experience of the past five years has taught central banks and regulators that they almost certainly need to support an activist approach to banking regulation and supervision, including such previously ignored issues as bonuses and the impact of dividends on banks’ capital. One potential pitfall here is macroeconomic: overzealous regulation may drive banks to avoid the type of risks they should be taking in financing sound corporate or public investments, stifling the financing enterprise. Regulation must be subject to cost-benefit analysis to avoid this trap. The second is more microeconomic: a simplification approach to bank capital adequacy rules may result in many different relative risks being grouped together into a single category and assigned a single risk weight where because of a broad capital bucket the capital charge understates the risks. Regulatory arbitrage may ensue: banks will accumulate those assets for which they believe the risks are underestimated and avoid those for which they believe the risks are overestimated. If, to overcome this, regulators impose a disproportionately high risk weight, then this constricts economic growth. Furthermore, differing regimes across regions engender counterproductive regulatory arbitrage.

Central banks need to have, and communicate, a clear idea of the kind of banking systems they are aiming for, even though they clearly do not possess the powers to shape structures in what they may consider to be a beneficial direction. At a minimum, central banks need to know more about how their banks make their profits. In the recent past, substantial profits were treated as reassuring, but, as we now know, it depends how they are made. If such profits arise from “rent seeking” or from speculation, then they may turn out to be unsustainable. As part of their supervisory function, central banks should be trained to recognize such phenomena and act accordingly.



One of the reasons why central banks are being pushed into the forefront of efforts to deal with financial system weakness is that politicians have taken a back seat. Some actions that hold genuine promise for reducing global systemic risk — for instance, creating a credible international resolution regime for global banks — cannot be undertaken by central banks or even groups of central banks. They require concerted political action and international diplomacy and coordination. Central banks must not allow themselves to be backed into a corner with weak and untried tools because politicians are unwilling to make structural changes to the financial system. Just as central bank governors sometimes need to grit their teeth and criticize spendthrift fiscal policy, they may have to start calling their political masters on failure to make progress risk-proofing the financial system.

Central banks have to heed widespread public antagonism toward what is often perceived as misguided, foolhardy, or self-centered action by commercial and investment banks contributing to the financial crisis. As a priority, they must explore the need for much stricter conditions for and surveillance of new and potentially risky financial products, building on and extending the strictures of Basel III.

The international dimension8 Policing disequilibria in the world monetary systemThe financial crisis that started in 2008 demonstrated that central banks need to think beyond their own borders. Disequilibria in the world monetary system provides a considerable source of risk for central banks in implementing their objectives in both the monetary and financial stability areas. Failure to cope with current account imbalances and other sources of macroeconomic instability was a key contributor to the financial crisis.

Another area for enhanced central banking activity is in the management and oversight of the International Monetary Fund, which has greatly expanded its activity, especially in Europe. A third field is in enhanced regional monetary cooperation seen in most continents. All this has far-reaching implications for the operations and management of central banks, for the way that they interact with diverse sets of players on the financial markets, for their public communications and accountability, and for the way they are monitored and assessed by their own supervisory bodies, by governments, and by the public.

9 The role of foreign exchange reservesCentral banks are in the vanguard of the gradual evolution of a multiple reserve currency system, but there is little certainty whether this will turn out to be more or less stable than the constellation that has pertained hitherto. Global foreign exchange reserves rose from 6% of gross world GDP in 1999 to more than 16% in 2011. Driving the trend was reserve accumulation in emerging market economies, which account for more than 67% of total official foreign exchange reserves of U.S.$10.2tr. China alone has amassed official reserves of U.S.$3.2tr. As a percentage of GDP, reserve holdings in emerging market economies have risen fivefold to 25% from the 1980s average of about 5%. This is generally perceived to be far in excess of what these countries need for self-insurance against balance-of-payments crises, sudden stops in external funding, or as a means of smoothing exceptionally volatile flows. Much of the buildup has been a by-product of mercantilist growth strategies aimed at keeping exchange rates competitive.

As a result of the enormous increase in world monetary reserves, central banks’ practices as custodians and/or managers of their countries’ official assets have come under increased scrutiny. Unless there is a mandatory sale of foreign currency to the central banks, or the central bank follows an exchange rate target, there is no clear-cut reason why the central bank should be the manager of foreign exchange reserves. If anything, concerns about the effect on FX reserves could risk dividing central bank attention from other goals.

Where they do have responsibility for reserve management, central banks have to strive for balance between the different considerations of maintaining conservatively managed stocks of liquid assets, helping to police the exchange rate, and achieving profitability (or at least avoiding large losses) on their operations. Adequate coordination with domestically attuned policy-makers is needed to ensure that management of foreign exchange reserves does not conflict with the financial stability and lender-of-last-resort functions. As a general maxim, financial stability considerations should take priority over optimizing returns on official reserves.

Central banks need to bear in mind the reasons for expansion of official reserves — partly because of efforts at maintaining competitive exchange rates, and partly because of a desire to build up “self-insurance” against future foreign exchange crises. There


has also been an element of windfall from higher commodity prices, especially oil. With the decline in yields on traditional assets — most notably U.S. Treasury bills and bonds — central bankers have come under pressure to raise returns. Critics argue that the high opportunity cost of holding low-yielding assets is harmful from a social welfare perspective.

Another worry for central bankers has been their concentration of holdings in the dollar, the world’s pre-eminent reserve currency, backed by deep and liquid markets in the world’s largest, but heavily debt-laden, economy. The ability to divest or diversify without incurring foreign exchange losses is severely constrained.

Central banks are under no illusions that their opportunity to emulate the private sector is limited. A foreign exchange reserve portfolio is just one part of the assets and liabilities of a country and of the central bank balance sheet. Reserve management has to be highly sensitive to the potential impact on central bank capital and to wider economic priorities such as insuring against a halt to capital inflows or repatriation of external capital.

ConclusionWhile rethinking roles and constitutions in the depth of the crisis may seem to most central bank boards to be akin to changing the airplane’s engines while in flight, satisfactory answers to a series of fundamental questions will be required. These will include considerations of:• Strategy: has the bank’s remit been comprehensively

defined and new roles adequately specified? Is there clarity on quantitative targets and objectives for the bank and the measures of success? Does the bank have the requisite powers and authorities to accomplish its mission? What are the delineations between national, transnational, and supranational responsibilities and authorities?

• Governance: are the bank’s institutional framework and accountabilities in line with the strategic mission defined above? In particular, are authorities, reporting lines, and responsibilities sufficiently well delineated? How independent is the bank to be, and how far does the remit of politicians extend?

• Risk management: if the bank’s balance sheet and financial markets operations have significantly expanded, are the right skills and processes in place to measure, assess, and manage the enhanced risk?

• Operational platform: does the bank have sufficient and

suitable operational capabilities to manage an increased workload, and in particular are IT systems up to scratch? Is the bank being managed as efficiently and effectively as it could be? Is there a need to review the distinction between “policy requirements” and “executive requirements”?

The answers to these questions will vary markedly depending on institutional circumstance, but it will be imperative that central banks wrestle with them if they are to cope successfully with the significant challenges and major increases in the remits that lie ahead.

In summary, we arrive at three major conclusions:• The crisis has fundamentally changed the roles of central banks

and central bankers, and there will be no reversion to the previous status quo. Adjusting to an increasingly public and prominent position on the political stage will be one of the lasting legacies for central bankers of the current crises. The role of the central banker has become inherently more powerful, more complex and more contentious.

• The price of the extension of the activities and powers of central banks is likely to be a restriction of their hitherto sacrosanct independence. In many countries there will be a growing and vigorous debate about the transparency of the activities of central bankers and of accountability to government and the wider electorate.

• Many central banks are confronting a new set of policy and operational challenges. In a palette of disciplines ranging from overall strategy and governance, through risk management, and on to the core operational platform, there is much work to be done in attaining organizational fitness to manage significantly increased and more complex roles.

We maintain that the role of central bankers is changing and will continue to change fundamentally. There are multiple challenges, ranging from the grandly philosophical and strategic to more prosaic concerns. It may well be that expanded powers and responsibilities for central banks will lead to a full or partial loss of the independence that has, particularly in the western world, become the cherished hallmark of central banking. Having been forced center stage as a result of the financial crisis, central bankers are adapting with difficulty to an increasingly public role. As a condition for wielding wider power, they will have to accept greater restraints.


Part 1

Stress-testing banks’ profitability:thecaseof French banks1

JérômeCoffinetHead of Statistical Engineering Division, Directorate General Statistics, Banque de France

Surong LinEconomist, Banque de France

AbstractWe propose a stress-testing framework to evaluate the sensitivity of banks’ profitability to plausible but severe adverse macroeconomic shocks. Specifically, we test the resilience of French banks’ profitability over the period 1993–2009. First, we identify the macroeconomic and financial variables (GDP growth, interest rate maturity spread, stock market’s volatility) and bank-specific variables (size, capital ratio, ratio of non-interest income to assets) that significantly determine banks’ profitability. Second, we propose macroeconomic stress-testing exercises showing that French banks’ profitability is resilient to major adverse macroeconomic scenarios. Specifically, our findings highlight that even severe recessions would leave the French banking system profitable.

1 The opinions expressed in the paper do not necessarily represent those of the Banque de France or the French Prudential Supervisory Authority.


Stress-testingbanks’profitability:thecaseofFrenchbanks

IntroductionOver the last decades, banking systems of developed countries have experienced major changes regarding their sources of revenue. The traditional interest revenue has been increasingly replaced by fees and commissions, and trading incomes. According to some observers, this development could lead to a weaker resilience of banks’ revenues to adverse shocks. Yet, several banking systems, among which the French one, went through the current financial crisis without any failure and their profitability remained strong in spite of a strong economic and financial downturn. As a matter of fact, the French banking system as a whole proved profitable even through the crisis.

From the supervisory perspective of ensuring the banking system’s solvency, identifying the vulnerabilities of banks’ profitability is crucial. First, profits prove to be a, if not the main, driver of bank capital [Gropp and Heider (2009)]. Hence, any trouble regarding banks’ profitability is likely to be transmitted to the solvency ratios, eventually threatening the banking system’s strength. Second, in line with the “bank capital channel” literature [van den Heuvel (2002)], banks facing a slump in profits, combined with difficulties to issue additional equity, are likely to ration credit in order to meet regulatory constraints, and finally to weigh on the economic growth. Third, profits are known to be reliable early-warning indicators of financial distress [Demirgüç-Kunt and Detragiache (1999)], though they are available, at best, on a quarterly basis. The low profitability data frequency, combined with their backward-looking nature, makes it fundamental for regulators to identify the main determinants of profits in order to run accurate forecasts and determine vulnerabilities in a more forward-looking manner.

The early research dedicated to banks’ earnings sources focuses on net interest margins [Ho and Saunders (1981)]. In that respect, Allen (1988), Saunders and Schumacher (2000), and Demirgürc-Kunt and Huizinga (2000) highlight a robust relationship between interest margins and the business cycle. Nevertheless, the growing importance of non-interest income (fees and commissions, and trading incomes) progressively lessens the importance of net interest income. On average, the share of income generated by traditional interest activities has progressively fallen in the U.S. and in Europe over the two last decades. Consequently, recent research has focused on the determinants of bank profitability accounting for both interest

and non-interest activities. Alternatively, the literature on bank interest margins has considered the impact of non-interest activities on optimal loan price and margin setting [Carbo Valverde and Rodriguez Fernandez (2007)]. In this paper, because we are concerned about the safety and soundness of the banking system and the ability of individual banks to generate income to prevent sharp equity changes, we focus on aggregate profit measures such as the return on equity (ROE) and the return on assets (ROA). Earlier work on bank profitability has focused on three types of determinants which are generally found as significant determinants of banks’ profitability: firm-specific variables (the amount of capital, bank expenditures, the size of the bank proxied by its total assets, and the risk borne by the financial institution) as stated by Goddard et al. (2004), Kosmidou et al. (2006), Athanasoglou et al. (2008), and Albertazzi and Gambacorta (2009); variables linked to the market’s structure (the market power of the bank, and the share of non-interest income), as established by Smirlock (1985), Berger (1995), and Lepetit et al. (2008); and finally macroeconomic and financial variables (GDP growth, interest rate spread, inflation, stock market’s return and volatility, and loan growth), as established, among others, by Revell (1979), Molyneux and Thornton (1992), Demirguc-Kunt and Huizinga (2000), Beckmann (2007), Athanasoglou et al. (2008), and Albertazzi and Gambacorta (2009).

In order to assess the resilience of financial institutions to macroeconomic and financial shocks, we rely on the recent stress-testing frameworks developed by supervisors and central banks over recent years. In contrast to the methods implemented by banks themselves, those implemented by supervisors focus on the resilience of the financial system as a whole. Jones et al. (2004), Sorge (2004), and Foglia (2009), among others, provide extensive literature reviews on those practices. The purpose of such methodologies is to test the capability of the financial system to survive severe but plausible scenarios. Hence, they appear as particularly relevant tools to assess the effects of adverse scenarios on banks’ profitability, like our paper’s objective, since they prove forward-looking and adapted to various unfavorable hypothetical scenarios.

In the present paper, we propose a framework to evaluate the resilience of banks’ revenues to adverse macroeconomic shocks, and apply it to French supervisory data. For this purpose, we first identify the main determinants of French banks’ profitability


— measured by their return-on-assets (RoA) — by considering the most relevant macro and bank-specific factors used in the literature. Second, we develop an innovative stress-testing framework to evaluate the resistance of French banks’ RoA to adverse macroeconomic shocks.

Our contribution to the existing literature is twofold. First, we build up an original and comprehensive (i.e., not restricted to sensitivity analysis) macro-econometric stress-testing framework that allows us to test for the resilience of banking profitability in the current downturn context. Second, although Goyeau et al. (1998) and Goyeau et al. (2002) extend the model developed by Flannery (1981) to analyze the profitability of French banks their focus is on the sensitivity of bank profits to interest rate changes. To our knowledge, our paper is the first to use individual supervisory bank data to study the determinants of French banks’ profits and their sensitivity to changes in the economic environment as a whole and therefore accounting for a large number of macro variables, such as interest rates but also GDP growth, inflation, stock prices, and exchange rates.

Our results show that banks’ profitability significantly depends on macroeconomic and financial variables (GDP growth, interest rate spread, stock market’s volatility) and bank-specific variables (size, capital ratio, ratio of non-interest income to assets). However, simulating major macroeconomic shocks and looking at the magnitude of their effects on banks’ profitability, we find that French banks’ profitability is resilient to major adverse macroeconomic scenarios. These outcomes are likely to give quantitative grounds to the fact that, at the current juncture, one did not observe any disastrous loss among the French banking system.

Data and empirical modelDataIn this paper, bank-specific variables come from the supervisory dataset BAFi, consisting of a panel of individual French banks’ consolidated data over a relatively long period (1993–2009) on an annual basis. The dataset, called ‘BAFi,’ which stands for ‘Base des Agents Financiers’ (Basis of financial agents), belongs to the French banking supervisor (Prudential Supervisory Authority). Relying on such supervisory data allows us to consider the whole French banking system on a consolidated basis in a comprehensive manner. In particular, it turns out that the quality of the data with

regards to non-interest and, specifically, trading income appears much better than that of private data providers, especially at the very beginning of the sample. The panel is unbalanced, that is to say, some banks may appear or disappear from time to time, essentially because of mergers and acquisitions. Hence, we finally get an overall number of 370 different groups over the whole sample, about 170 on average each year.

Dependent variableOur dependent variable is banks’ profits. Alternative profitability measures could be considered for the purpose of this study, such as RoA, defined as the ratio of the net income after taxes to total assets, and return-on-equity (RoE), defined as the ratio of the net income after taxes to total equity. Net interest margin, defined as the ratio of the net interest income after taxes to total assets could also be used as a proxy. However, as the net interest margin is solely based on interest activities, whose importance in terms of the share of total income has experienced a continuous decline over the recent years [Coffinet et al. (2009)] and does not constitute an aggregate measure of profitability, we do not consider it as a relevant endogenous variable for the purpose of this paper.

0%

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15%

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0,8%

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1993 1995 1997 1999 2001 2003 2005 2007 2009

roa (left)net interest marginroe (right)

Figure1:Evolutionofbanks’profitability(1993–2009)

Coefficient of correlation RoA Net interest margin

RoE

ROA 1Net interest margin -0.60 1ROE 0.93 -0.59 1



With regards to ROE and ROA, the latter is more consistent with supervisory concerns than the former. First, it is directly related to the quality of loans, as opposed to ROE, which takes on the shareholder’s perspective. Second, ROA may be computed as the ratio of ROE to leverage, and thus integrates the latter explicitly, which is of special interest at the current juncture. However, to some extent there might be inconsistencies between the numerator and the denominator of the ROA because the former is related to profits generated from all activities and the latter covers only the balance sheet activities. Nevertheless, ROA reflects the ability of banks to generate profits from all activities related to their assets. It seems particularly relevant for banks with noteworthy intermediation activities, and specifically most French banks. Hence, we focus on ROA as the key ratio for evaluating banks’ profitability, which is consistent with our supervisory objectives and the recommendations of the International Monetary Fund (2002) and numerous studies like, for instance, Athanasoglou et al. (2008).

Figure 1 displays the evolution of banks’ profitability during the period under consideration according to these three measures after removing outliers, defined as observations beyond the 95% percentile and below the 5% percentile.

From the outset, one notices that the overall French banking system’s RoA seems to move in tandem with the business cycle, falling significantly in the years 1993–1994, 2001–2002, and 2007–2009, coinciding with economic slowdowns or downturns, and increasing in the periods 1994-2000 and 2003–2006, corresponding to robust economic growth. Besides, Figure 1 shows that RoA and RoE behave in a very similar manner over the whole sample period. The correlation between both series is very high (93%). Hence, we can infer from that figure that results obtained on the basis of RoA figures are robust to the choice of the profitability measure (RoA versus RoE). On the contrary, as expected, NIM is less correlated to RoA and RoE, and behaves in an opposite manner (as shown by the negative sign of the correlation coefficients). This demonstrates that the aggregate profitability of banks is, over the sample period, more strongly linked to non-intermediation activities than to traditional interest revenues.

Nonetheless, the French banking system is composed of institutions with different legal statuses, such as commercial banks, financial and investment firms, and mutual and cooperative banks. The

sample (Table A1 in the Appendix) seems well balanced between different types of institutions with, for a total of 2896 bank-year observations, 920 commercial banks, 1070 mutual and cooperative banks, and 906 for financial and investment firms. The average RoA for the whole French banking system was 0.67%. It is homogenous across the three groups and ranges from 0.55% for commercial banks to 0.88% for financial and investment firms. The standard deviation of ROA for financial and investment firms is more than twice that for mutual and cooperative banks, indicating a greater degree of heterogeneity among members of the former group. Moreover, consistent with the empirical literature, we find that smaller banks generate higher RoA and, in accordance with the too-big-to-fail hypothesis, are generally better capitalized.

Independent variablesWith regards to bank-specific determinants of banks’ profitability, the related literature generally considers the amount of capital, the size of the bank, the risk borne by the bank, and the expenditures of the bank as suitable proxies [Goddard et al. (2004); Kosmidou et al. (2006); Athanasoglou et al. (2008); Albertazzi and Gambacorta (2009)]. The amount of capital is likely to positively impact profitability, as capital may be interpreted as the amount of own funds available to support the bank’s business, and hence as a buffer against adverse developments. This relationship may have been strengthened by the M&A activities that took place in the late 1990s. A high capital ratio may be viewed as a signal that bank expects high profitability. The size of the bank could be a possible determinant of its profitability, as size can be considered a proxy for capital adequacy, since large banks can raise capital at a lower cost. Nevertheless, the empirical evidence is mixed and sometimes points to a significantly negative relationship between size and profitability. A possible interpretation might be that large banks could experience negative effects due to bureaucratic reasons. Conversely, too-big-too-fail considerations may lead to a positive relationship. In terms of the risk borne by the bank, it is generally accepted that an increase in exposure to credit risk would decrease a bank’s profitability. The risk proxy mostly used in the literature is the ratio of loan-loss provisions to total loans and is specific to credit risk, which might not be as relevant given the growing share of non-interest income in total income. In the literature, this relationship is generally unambiguously negative, though sometimes not significant. The expenditures ratio of the banks (i.e., operating cost over assets) is expected to be negatively related to profitability, as improved management of those expenses


may increase efficiency and raise profits. The market power proxy assumes that firms with large market shares and differentiated products are able to use their market power and enjoy a more secured income position. Another possible source of profitability is linked to the source of revenues: ceteris paribus, a higher share of revenue stemming from a more profitable business is likely to act positively on the overall profit. In that respect, the increase in non-interest income could have a positive effect on banks’ profitability. Hence, in this paper, we also control for business differences.

All in all, we consider the following bank-specific variables:• The “capital” variable is defined, for each bank, as the ratio of

equity to total assets.• The ratio of non-interest income “nnii” is the ratio of the sum of

fees and commissions, trading income, and dividends to total assets.2

• The “expenditures” ratio is defined as the ratio of total expenditures to total assets.

• The size of the bank variable is built as dummy variables: “large” for banks whose balance sheet amount is in the upper quartile and “small” for those whose balance sheet is in lower quartile.

• The “risk” variable is the ratio of loan loss provisions to total loans.• The “market power” variable is the individual net operating income

over the total net operating income of the banking industry.

The macroeconomic and financial determinants reflect the economic and financial environment that can also affect banks’ performances. They are the same across banks and hence represent many of the cross-sectional common factors. Six macroeconomic and financial variables are generally considered: economic growth, inflation, interest rate spread (split or not between short-term and long-term), stock index return and volatility, and loan growth. There are several reasons why output growth may have a positive impact of bank profitability. First, higher growth may result in a higher loan distribution (increased demand) and indirectly higher revenues from financial markets, due to higher stock market returns. Second, with expectations of higher profits, provisions could decrease in economic upturns

2 Alternative measures could be the ratio of non-interest income to total income or the ratio of net non-interest income to total net operating income [DeYoung and Roland (2001); Stiroh (2004); Stiroh and Rumble (2006); Lepetit et al., (2008)]. However, these measures do not lead to robust results in our regressions, or make the other variables’ significance less robust. Hence, we decided to rely on that ‘nnii’ measure, yielding very robust specifications of the model, and already used by Smith et al. (2003) and DeYoung and Rice (2004).

and hence capital may have a positive impact on profitability. Empirically, many studies find a significantly positive relationship between GDP growth and banking profitability. However, the effect of inflation on profitability is ambiguous and depends on whether the bank’s expenses grow faster than inflation, i.e., whether inflation is accurately forecasted by the banks or not. A significantly positive effect of inflation on profitability is generally interpreted as a good predictor of future inflation by banks, yielding an accurate adjustment of interest rates and thus resulting in revenues growing faster than costs. In most recent papers, the effect of inflation on profitability is found to be significantly positive. The implications of the interest rate spread are related to the traditional maturity transformation activity of banks, yielding revenues essentially related to loans. Banks are assumed to receive and remunerate short-term deposits and grant long-term loans, from which they receive interest. Hence, a higher interest rate spread is likely to be beneficial to banks. This effect is to be more significant when tested on the NIM subcomponent of revenues. Loan growth is linked to the traditional sources of revenue for banks, which stem from credit distribution. It is expected to positively impact not only net interest income, but also fees related to credit. Stock market returns are directly related to revenues derived from trading income. They are also strongly correlated with GDP growth, which makes it difficult to use as a proxy for overall banking profitability; even more so since GDP growth is jointly considered. Stock market volatility, which may increase banks’ trading opportunities, yields higher non-interest income and profitability, but also increases provisions because of higher uncertainty, which leads to smaller profits.

We use the following explanatory variables for our regressions on ROA:• “GDP growth” is defined as the year-on-year change in the real

French GDP in volume, extracted from the OECD database. The choice of the national GDP growth is consistent with the choices made by Athanasoglou et al. (2008) and Albertazzi and Gambacorta (2009), among others. It assumes that, even on a consolidated database, profitability of French banks essentially depends on the French growth, irrespective of those of the countries where international groups may own assets. Nevertheless, it seems reasonable, first as French GDP growth does not prove, on average, uncorrelated to that of countries where French banks might own assets, and second because the international merger and acquisitions of French banks took place only in the very recent years. Another more practical



reason behind this decision is that we can only observe the path of French GDP growth to perform stress tests and do not want to impend artificially on the effect of a recession on ROA (conservative assumption on stress tests).

• The “inflation” variable is defined as the year-on-year variation in the French consumer price index.

• The “yield curve” variable is the difference between the 10-year French Treasury bond rate and the 3-month Euribor (Pibor before 1999) rate.

• The “stock market index’s return” (volatility) variable is measured as the year-on-year growth of the SBF250 index’s return (the annual historical volatility of the SBF250 index).

• The loan growth is the year-on-year relative change in the total credit volume in the French economy.

Figure 2 shows the developments in some of the main macroeconomic variables (GDP growth the yield curve) used in our model.

ModelOur objective is to identify the macroeconomic, financial, and bank-specific determinant of banks’ profitability. For this purpose, as shown in Figure 2, bank profits seem to persist over time. Hence, following Berger et al. (2000), we allow for the existence of an autoregressive component of RoA. More specifically, we consider a dynamic model specification including a lagged endogenous variable, to account for persistence. The model is written, for each date t, as:

jZiRb X

c ki,t 1 i,t 1

jtj k

i,tk

i,t= + + + +r { r fR

- (1)

where r is RoA and c a constant, i is the i-th bank of the sample, Xj indicates the j-th macroeconomic variable which is common to all banks, Zk corresponds to k-th bank-specific variable and

v ui,t i i,t= +f is a residual term composed of a bank-specific fixed effect vi and a normal residual ui,t.

Econometric investigationOur econometric investigation is performed in four steps. As a first step, we test for the stationarity of the panel, using unit root tests for unbalanced panels (the Levin, Lin, and Chu test, complemented by a Fisher test). Results are presented in Table 1 and tend to confirm the stationarity of the panel.

The stationarity of the macroeconomic variables is also tested using a Dickey Fuller test but is not that relevant given the small number of observations (17 for each variable).

As a second step, we identify whether some explanatory variables might be endogenous. There are two good candidates: apart from the credit risk measure, which will not be retained in the end because of its insignificance, the capital ratio and the share of non-interest income in total assets. Following Athanasoglou et al. (2008), we run model (1) with these variables as strictly exogenous, strictly endogenous, or one exogenous and the other endogenous. The Sargan tests, though they indicate that both could be considered as endogenous, appear in favor of considering nnii, i.e., the share of income coming from non-interest activities as endogenous and capital as exogenous. This may seem surprising as the equity ratio, as a target variable, is generally considered endogenous in most papers [Athanasoglou et al. (2008)].

A third question that may arise is the treatment of mergers and acquisitions (M&A). Following Athanasoglou et al. (2008) and Albertazzi and Gambacorta (2009), we chose to disregard any detailed treatment of mergers and acquisitions, and to estimate an unbalanced panel. There are two reasons for this: first, including a dummy variable for each merger may limit dramatically the number of degrees of freedom of the system;

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roa (left)GDP growth (right)

Figure 2: Evolution of GDP growth and yield curve (1993–2009)


second, as argued by Athanasoglou et al. (2008), the capital variable already accounts indirectly for potential M&A effects.3

Fourth, with regards to the estimation stricto sensu, we use the Arellano-Bond (Arellano and Bond, 1991) two step estimator for dynamic panel-data models and robust option to report standard error. We use two types of instruments for our difference equation: all exogenous variables (X and Z) as additional standard instruments except non-interest income (nnii)4 and lagged endogenous variables (r and nnii) as difference GMM-type instruments. The difference equation used in our model is:

Zj + f

DiRb XDki,t 1 i,t 1

jtj k

i,tk

i,t= + +r { rD DR

- (2)

ResultsBaseline equationOur aim is to estimate the impact of economic and financial shocks on banks’ profitability. We begin by considering the whole vector of possible variables, as identified in the literature: GDP growth, spread, inflation rate, stock market return, stock market volatility, loan growth, share of non-interest income, capital, expenditures, risk, and the constant.

3 To check for robustness, we re-run our regressions excluding observations corresponding to a yearly increase in assets by more than 20%. This leaves the results unchanged.

4 Non-interest income is directly linked with net income. By running several models, regression results show inherently that non-interest income is better modelled as an endogenous variable.

Firstly, we chose the stock market index’s return as the measure of market activity. However, the coefficient of this variable proves not significant in our regressions, especially when estimated with other macroeconomic variables. Then, we find that the positive coefficients of the yield curve and the market index return are not simultaneously significant. Besides, this variable is highly and negatively correlated to inflation, with a correlation coefficient of – 0.60 during the studied period. For that reason, in the remainder of the paper, we only consider stock market volatility as a proxy for market risk.

Regarding the other macroeconomic variables, we find that the inflation rate is not significant when combined with GDP growth. This may result from the strong relationship between these two variables. Loan growth is never significant and has been dropped from the remaining equations. Furthermore, among the banking specific variables, we find that the variables “risk” and “expenditures” are not significant but keep the former in the remaining results to be consistent with the underlying theoretical models.

Table 2 presents the final results, which are those that we will consider for the remainder of the paper as the main equation results.

The significant coefficient on the lagged endogenous variable confirms the dynamic specification. The coefficient of the lagged RoA, which equals to 0.171, indicates that profitability seems to be moderately persistent over time. According to Athanasoglou et al. (2008), a small value of that coefficient means that the banking industry is fairly competitive (high speed of adjustment) or that informational opacity is low [Berger et al. (2000)].

The regression results confirm our prediction that a higher GDP growth, steeper yield curve, or higher inflation rate increase banks’ profitability. The coefficient on GDP growth means that an increase in GDP growth by 1% increases the overall RoA of the whole French banking system by about 0.04%, which is quite important given the average RoA over the sample (0.67%). The same reasoning applies to the yield curve. Contrary to the market index return, market index volatility is negatively linked with banking profitability. An interpretation is that higher stock market volatility is associated with higher uncertainty, leading to lower profits. To test whether the relationship is still relevant when economic growth slows down,

Levin, Lin and chu Fisher test

Variables W-stat p-stat 2| p-statRoA -13 0.00 448 0.00Capital -167 0.00 487 0.00Risk -593 0.00 690 0.00NNII -19 0.00 494 0.00ResultsofthestationaritytestsforthemacroeconomicandfinancialvariablesVariables Dickey-Fuller ERS

T-stat 1% critical value 10% critical valueGDP growth -1.21 -2.73 -1.60Spread -1.81 -2.73 -1.60Loan growth -1.39 -2.73 -1.60Inflation -1.82 -2.73 -1.60SBF return -3.22 -2.73 -1.60SBF volatility -1.62 -2.73 -1.60

Table1:Resultsofthestationaritytestsforthebank-specificvariables



we re-run the main equation with a cross-variable which equals the economic growth times a time dummy for periods when economic growth is lower than 2%. The results remain unchanged.

With regards to the effects of banking structure on banking profitability, we observe that both the leverage ratio (the inverse of the capital-to-asset ratio included in our estimation) and the non-interest income have positive effects. The fact that the intensity in the use of capital increases banks’ profitability can be interpreted as a proxy for the “efficiency” of the capital, particularly important in banks’ risky businesses. Besides, we find evidence that small banks have higher RoA than other banks, consistent with descriptive statistics and the empirical literature.

Back testing of the resultsIn order to test the reliability of our model, the following standard tests for linear dynamic panel models are presented in the result table of each regression: the Wald-test indicates significance of coefficients of explanatory variables; the Sargan-test shows no evidence of over-identifying restrictions; the negative statistic value for the first-order autocorrelation test on errors

is expected in dynamic panel models; and the second-order autocorrelation test on errors have been rejected so that there is no autocorrelation of order 2 of differenced errors.

Additional robustness checksBaseline equation re-estimated with group-effectsAs shown in Table A1, the panel used may exhibit slight differences in the behavior of sub-samples of the panel. In this subsection, we re-estimate the main equation with specific effects linked to the legal status or to the size of the individuals.

Individual effects linked to banks’ legal statusWe estimate a further regression for RoA where the variable GDP growth has been substituted by GDP growth times indicators (X I1

q), which are dummy variables on banks’ legal status. The aim is to test the differentiated effects of banks’ legal statuses in events of macroeconomic shocks.

Arellano-Bond dynamic panel data estimation (t = 1993–2009)Number of Obs. = 2292Number of groups = 370ROA coefficient p coefficient p coefficient pLag1 (Roa) 0.171** 0.034 0.173** 0.035 0.171** 0.041GDP growth 0.039*** 0.001 0.043*** 0.000 0.041*** 0.000CPI -0.015 0.334 Spread 0.047*** 0.002 0.057*** 0.000 0.056*** 0.000L1. SBF volatility -0.00004** 0.044 -0.00003* 0.064 -0.00004* 0.058Small 0.002 0.182 Large -0.001* 0.084 Capital 0.013*** 0.003 0.013*** 0.003 0.013*** 0.003NNII 0.065** 0.019 0.065** 0.020 0.065** 0.020Risk -0.002 0.311 Market power 0.031 0.617 Low-growth* GDP -0.002 0.849Wald test chi2(11) = 74 p>chi2 = 0.00 chi2(6) = 51 p>chi2 = 0.00 chi2(7) = 64 p>chi2 = 0.00Sargan test of over-identifying inst. chi2(238) = 225 p>chi2 = 0.71 chi2(238) = 223 p>chi2 = 0.70 chi2(238) = 226 p>chi2 = 0.70Autocorrelation test AR(1) z = -3.02 p>z = 0.00 z = -3.02 p>z = 0.00 z = -3.01 p>z = 0.00Autocorrelation test AR(2) z = 0.26 p>z = 0.80 z = 0.24 p>z = 0.81 z = 0.24 p>z = 0.81Overall R² 45% 39% 38%Between R² 61% 52% 51%Within R² 18% 17% 16%

Table 2: Results for the main equations


ql +ZiR t

lb qGDPdXIki,t 1 i,t 1

tl k

i,tk

q i,t= + + + fr { rR

-

R (3)

I :q thq - dummy variable; for example, I 1bmc = for mutual and cooperative banks, 0 otherwise.

Table 3 presents the results for this alternative estimation. Our main findings are that mutual and cooperative banks appear less impacted by GDP growth shocks than commercial banks, with a sensitivity of 0.01 against 0.052.

Individual effects linked to banks’ balance sheet sizeWe differentiate banks’ size according to the size of their balance sheet; banks that are in the 75%–100% percentile region of the largest balance sheet are classified as large banks, and banks in the bottom 25% percentile region are classified as small banks.

Our main finding is that small banks seem to be more affected than other banks by shocks on GDP growth. All in all, the results can be summarized as follows: we do not find a clear homogeneity of the panel with regards to the sensitivity of

each category’s RoA to GDP growth. Nevertheless, as our goal is to study the resilience of the whole French banking system to adverse macroeconomic scenarios, we will consider only the results of the main equation in the remainder of the paper.

Restricting the time-windowAs a complementary robustness check, we propose to re-run the main equation on a narrower time-window that would cover the period 2000–2009. A reason for choosing this restricted period is that some authors find that ROA’s reaction to macroeconomic variables are somewhat different in the post–1999 period. This is due to the introduction of the euro; a different business model of banks; and a growing influence of securitization, that would threaten the old model of profits through maturity transformation, and thus alter the sensitivity of ROA to spread fluctuations.

In addition, despite the fact that the gap is in general small, we find that the model, as estimated over the whole period, systematically overestimates the actual RoA from 1994 to 1999, as it is the opposite in the remaining period. Results of the main

Arellano-Bond dynamic panel data estimation (t = 1993–2009); Number of Obs. = 2292; Number of groups = 370 (t = 2000–2009); Number of Obs. = 1358;

Number of groups = 246ROA Coefficient p Coefficient p Coefficient pLag1 (L.Roa) 0.169** 0.021 0.176** 0.015 0.120* 0.075GDP growth 0.035** 0.021Spread 0.066*** 0.000 0.060*** 0.000 0.082*** 0.000L1. SBF volatility -0.00005*** 0.008 -0.00004** 0.043 -0.00007*** 0.002Capital 0.013*** 0.002 0.013*** 0.002 0.012*** 0.005NNII 0.066** 0.024 0.066** 0.026 0.061** 0.024Bank*GDP 0.052*** 0.010 Cm*GDP 0.010 0.318 IF*GDP 0.104*** 0.000 Large*GDP 0.034** 0.014 Average*GDP 0.037*** 0.006 Small*GDP 0.087** 0.024 Wald test chi2(8) = 58 p>chi2 = 0.00 chi2(8) = 59 p>chi2 = 0.00 chi2(6) = 64 p>chi2 = 0.00Sargan test of over-identifying inst. chi2(238) = 235 p>chi2 = 0.54 chi2(238) = 223 p>chi2 = 0.74 chi2(208) = 193 p>chi2 = 0.74Autocorrelation test AR(1) z = -3.10 p>z = 0.00 z = -3.08 p>z = 0.00 z = -3.35 p>z = 0.00Autocorrelation test AR(2) z = 0.26 p>z = 0.80 z = 0.26 p>z = 0.80 z = -0.68 p>z = 0.49Overall R² 44% 43% 32%Between R² 58% 57% 42%Within R² 19% 18% 14%

Table 3: Results for the equations with individual effects



model re-estimated over the 2000–2009 sub-period presented in the last column of Table 3 clearly support the robustness of the model, as regards the magnitude of the coefficients, even if the significance of the coefficients is slightly altered. But for our stress-testing purpose, only the magnitude of the various coefficients matters. In addition, changing the coefficients with those re-estimated over the 2000–2009 sub-period leaves the gap between estimated and actual ROA unchanged (chart available upon request).

Orthogonalizing the macroeconomic variablesAs our three variables of interest (GDP growth, interest rate spread, stock market volatility) prove somewhat correlated, we re-estimate the main model after orthogonalization of those variables. For this purpose, we keep our GDP growth variable unchanged. We regress the spread on the GDP growth and a constant term and define the orthogonalized spread* as the residuals of this equation. Moreover, we regress the volatility of the stock market on the GDP growth, the spread, and a constant term and define the residuals of that equation as the new stock market volatility. We re-run all the equations above using those new variables. We find that, on the whole, our main results are robust.

UsinganalternativemeasureofproductdiversificationAs our measure of product diversification ‘nnii’ is by construction an element of the RoA and might appear very specific to financial and investment firms (for which it exhibits the highest values), we estimate an alternative model which relies on another measure of product diversification, that is to say the ratio of loans to the total assets, as proxy for the loan activity of banks. When we re-run the Sargan test, we find that our new variable loans/assets has to be specified as an exogenous variable, whereas the ratio of capital now appears endogenous and is specified as such in the regression. Our findings are fully consistent with the main results of Table 2.

Macroeconomicstress-testsofFrenchbanks’profitabilityStress-tests focused on banking profitability seek to identify the most important economic and financial channels of contagion of an initial shock that may affect the stability of the banking sector. Indeed, as the previous section showed, the economic and financial market environment may affect banks’ profitability. The aim of stress-test exercises is to study the effects of some

macroeconomic or financial variables paths derived from various scenarios — a forecast and some adverse variants – on relevant banking variables, such as profitability.

The stress-testing frameworkThe approaches by Lehmann and Manz (2006) and Rouabah (2006), focusing on Switzerland and Luxemburg respectively, conclude that the impact of macroeconomic and financial shocks on banks’ profits is relatively modest, demonstrating that the two banking sectors are resilient. But the analysis carried out in these papers, albeit interesting, is limited to sensitivity analysis and does not consider the effect of a comprehensive adverse scenario on banking variables, especially profitability.

Here, it is very important to notice that our aim is not to only study the impact of one shock of one specific explanatory variable on the income subcomponents, regardless of the impact of such a shock on the other variables. On the contrary, the impact of stress scenarios on the relevant risk factors is consistently determined with the Banque de France’s [Baghli et al. (2005)] forecast models (Mascotte and Nigem). This means that we simulate the effects of various exogenous shocks (in our stress test exercise, demand shocks yielding recession scenarios, a yield curve flattening, and an exchange rate shock), conditionally on these models, on the “stressed” output variables of the macroeconomic model (that prove to be our “stressed” explanatory variables for the banking model), which are then used as “stressed” inputs in our revenue model. Hence, we get “stressed” profitability, which is compared to the value obtained without any stress (i.e., in line with the basis line of the forecast). The advantage of using such a macroeconomic model is that it offers a lot of flexibility in the design of the scenario and that it ensures the consistency of the forecasted and stressed paths of the various macroeconomic variables.

A limitation to this approach lies in a feature of traditional macroeconometric models. Even though it provides an integrated and consistent framework to link the different effects of exogenous shocks on key macro variables, such as GDP growth, loans, or interest rates, the model is not clearly devoted to analyzing financial relationships and how different agents in the system may be financially constrained. Hence, in such models, there is no limit to credit demand from households. Another limitation is related to the fact that our model does not aim to take into account “second round” effects, as it only captures the effect of macroeconomic


shocks on banking variables and not directly that of banking variables on macroeconomic and financial ones. In addition, our stress-test exercises are carried out ceteris paribus: in particular, we do not model any portfolio reallocation, leading to a shift from interest income to trading income, in case of, for instance, a negative shock on the spread, leading to a decrease in net interest revenues. For these reasons, it seems much more relevant to restrict our stress-test exercise to the first year of shock, given that it is likely to avoid any unreliable results.

Results of the stress-test The macroeconomic baseline scenario stems from the Broad Macroeconomic Projection Exercise for France, which is produced by the DG Economics of the Banque de France. Stressed-scenarios are defined as severe but plausible in comparison with the baseline scenario. In April 2009, we designed and tested five hypothetical stress-scenarios which were all found at the time to be consistent with the definition of stress-test scenarios (severe but plausible), though their probability of occurrence is from a statistical and historical point of view likely to be different. It is important to note that the design of stress-scenarios rely strongly on expert judgment. It should also be noted that our goal is not to quantitatively compare the magnitude of the effects of each adverse scenario on others. We are much more interested in the qualitative comparison of different outputs of various scenarios and the absolute magnitude of the effects of scenarios over a certain threshold, for instance, negative profitability of banks. Hence, the five scenarios that were worth simulating were as follows:

• Internal demand shocks: –1% GDP growth, –2% GDP growth, –3% GDP growth.

• Financial shocks: a 25% depreciation of the dollar against the euro; a flattening of the yield curve [–200 bp Euribor 3-month and -400 bp OAT (government bonds) 10-year].

In order to determine whether the recession shocks tested, though they appear ‘severe’ enough, were plausible, we also studied the distribution of GDP growth in France from 1875 to 2008, excluding the war years, in order to calibrate the probability of recession. The results of the non-autocorrelation tests demonstrated that GDP growth is a White Noise process. Moreover, GDP growth does not follow a normal distribution according to the normality tests. Thanks to the distribution of GDP growth, we simulate the probability of the three recession scenarios defined previously.

According to this distribution, the average value of GDP growth is 2.7% and the cumulative probability associated with it is about 58%. Hence, the probability that the GDP growth is greater than the average value is equal to 42%. We find that the probability of GDP growth being smaller than –1% is 14%, 2% is 8% and –3% is 5%.

As stated earlier, the impacts of the stress scenarios on the relevant macro risk factors (GDP, loan growth, interest rates) for the years 2009–2010 are determined by using the Banque de France Mascotte model [Baghli et al. (2005)] and NIGEM, with the latter being provided by the NIESR (National Institute of Economic and Social Research) and used to introduce international interactions.

Table 4 presents the effects of these scenarios on the variables used as inputs in our profitability models. Table 5 presents the results of stress tests using the baseline model presented in table 2.Our results demonstrate that the French banking system is resilient to the set of comprehensive adverse scenarios tested. Only the severe recession scenarios (-2% growth and –3% growth) would generate negative profits. On the contrary, other

In deviation from the basis lineGDP growth

T+1 T+21 – 1% GDP growth -0.8 -2.12 – 2% GDP growth -2.1 -3.03 – 3% GDP growth -2.7 -4.04 – 25% depreciation of U.S.D/EUR -0.6 0.05 Flattening of the yield curve 0.0 0.4

Table 4: Design of scenarios

RoA -1% GDP

growth

-2% GDP

growth

-3% GDP

growth

-25% depreciation

of U.S.D/EUR

Flattening of the yield curve (-200bp ST, –

400bp LT)Aggregated data

T+1 0.04% -0.01% -0.03% 0.05% 0.07%

T+2 0.01% -0.03% -0.07% 0.10% 0.11%

Cooperative banks

T+1 0.09% 0.08% 0.08% 0.10% 0.10%

T+2 0.07% 0.06% 0.05% 0.09% 0.09%

Commercial banks

T+1 0.05% -0.01% -0.04% 0.06% 0.09%

T+2 0.03% -0.03% -0.08% 0.14% 0.16%

Financial firms

T+1 0.00% -0.13% -0.19% 0.02% 0.08%

T+2 -0.03% -0.14% -0.25% 0.19% 0.23%

Table 5: Results of stress-tests using the main equation results



scenarios (flattening of the yield curve, exchange rate shock, and moderate recession) would yield positive profits. In comparison with the actual figures for the French banking system recorded in 2009, our results are consistent with the reporting of banks. Indeed, as the GDP growth forecast for 2009 is likely to be in the range [-2.4%; -2%] (see for instance recent OECD’s and IMF’s outlooks), our –2% stress scenario constitutes a good benchmark. The annual RoA of –0.01% forecasted by the model is not that far from the actual figure, which equals 0.02% for the French banking industry in aggregated consolidated data. This means that the diagnosis of relatively good results recorded by the French banking system in the context of the current crisis could have been rather accurately forecasted by the model, especially relatively to the mean of RoA over the sample (0.67%). This reveals the robustness of our model as a backtesting check. In addition, the first actual figure obtained for French banks’ RoA, 0.063%, is close to that obtained by simulating our model using the actual path for explanatory variables, providing, again, support of the robustness of our model.

In order to answer the question of why French banks and the French banking system as a whole proved that resistant to strong economic shocks, we would need to dig deeper and analyze income subcomponents [Coffinet et al. (2009)], something which is beyond the scope of this article. Nevertheless, the interpretation of the main equation’s results can provide some intuition. Indeed, one of the three main macroeconomic drivers — the interest rate maturity spread — is clearly linked to the traditional maturity transformation activity of banks. GDP growth could also be associated to that income subcomponent as stronger economic growth could enhance the credit demand and hence support the loan activity and profitability of banks. Another significant driver of overall banks’ profitability — stock market volatility — is clearly specific to trading revenues (and indirectly GDP growth). As a result, a conclusion that can be drawn from these results is that the French model of universal banking — that is to say the diversification of products and revenues by banks — could lead to opposite developments in income subcomponents in depressed situations. The higher risk and lower profits generated by trading activities and economic downturn being compensated by a more profitable traditional credit activity, driven by a widening of the yield curve in downturns — e.g., due to interest rate cuts by the central bank. Consequently, our results can be viewed as a support for the model of universal banking as a source of resilience.

ConclusionOur results provide evidence of statistically significant relationships between the macro environment and the profitability of the banking industry. In particular, we provide strong evidence that the overall French banking system’s profitability positively depends on the French GDP growth, the stock market return, the interest rate maturity spread, the share of non-interest income, and the capital owned by banks, and negatively on the bank’s size and credit risk. These results are consistent with those obtained in the banking literature.

Our stress-testing analysis suggests that the impact of economic shocks may be relatively modest in terms of profitability, the French banking system being quite resilient and well capitalized to absorb extreme macroeconomic and financial variations. In particular, the model would have performed well in forecasting the good results of the French banks in spite of the current depressed environment. These results could be interpreted as a vindication for the model of universal banking, though further work should be carried out to arrive at definite conclusions in that regard.

However, a lot of work remains to be done, as other risk channels may affect banks’ profits but are not simulated in our framework, such as the sudden illiquidity in specific banking activities observed in August 2007 at the beginning of the subprime crisis (illiquid structured products, tensions in the money market, etc.). Moreover, the model may be refined in terms of econometrics, as it fails to explicitly account for nonlinearities that may arise in extreme events. Since we are especially interested in the extreme losses arising from stressed-scenarios, it would be of particular interest to implement quantile regressions.


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Jones, M., P. Hilbers, and G. Slack, 2004, “Stress-testing financial systems: what to do when the governor calls,” IMF Working Paper 04/127Kosmidou, K., E. Pasiouras, M. Doumpos, and C. Zopounidis, 2006, “Assessing performance factors in the U.K. banking sector: a multicriteria approach,” Central European Journal of Operations Research, 14(1), 25-44Lehmann, H., and M. Manz, 2006, “The exposure of Swiss banks to Macroeconomic Shocks: an Empirical Investigation,” Swiss National Banks Working Papers, 2006-4Lepetit, L., P. Rous, and A. Tarazi, 2008, “Bank income structure and risk: An empirical analysis of European banks,” Journal of Banking and Finance, 32(8), 1452-1467Molyneux, P., and J. Thornton, 1992, “Determinants of European bank profitability: A note,” Journal of Banking and Finance, no. 16, 1173-1178Revell, J., 1979, “Inflation and financial institutions” Financial Times, London.Rouabah, A., 2006, “La sensibilité de l’activité bancaire aux chocs macroéconomiques: une analyse en panel sur des données de banques luxembourgeoises,” BCL working papers cahier_etude_21, Central Bank of LuxembourgSaunders, A., and L. Schumacher, 2000, “The determinants of bank interest rate margins: an international study,” Journal of International Money and Finance, 19, 813-832Smirlock, M., 1985, “Evidence on the (non) relationship between concentration and profitability in banking,” Journal of Money, Credit and Banking, 17(1), 69-83Smith, R., C. Staikouras, and G. Wood, 2003, “Non-interest income and total income stability,” Bank of England Working Paper No. 198, AugustSorge, M., 2004, “Stress-testing financial systems: an overview of current methodologies,” BIS working papers no.165Stiroh, K., 2004, “Diversification in banking: is non-interest income the answer?” Journal of Money, Credit, and Banking, 36(5), 853—882Stiroh, K., and A. Rumble, 2006, “The dark side of diversification: The case of U.S. financial holding companies,” Journal of Banking and Finance, 30(8), 2131-2161Van den Heuvel, S., 2002, “Does bank capital matter for monetary transmission?”, Federal Reserve Bank of New York, Economic Policy Review, 8(1), 258—265



1993–2009 All banks Commercial banks Mutual and cooperative banks

Financial and investmentfirms

Large banks Average banks Small banks

RoAAverage 0.7% 0.5% 0.6% 0.9% 0.4% 0.7% 0.9%Std. 0.7% 0.7% 0.3% 1.0% 0.4% 0.7% 1.0%Min -1.6% -1.6% -0.7% -1.5% -1.5% -1.6% -1.6%Max 4.1% 4.1% 3.2% 4.1% 3.0% 4.1% 4.1%Obs. 2896 920 1070 906 724 1448 724Capital/assetsAverage 10% 8% 8% 14% 6% 9% 17%Std. 12% 13% 4% 15% 4% 7% 19%Min -3% 0% -3% 0% 0% -3% 0%Max 100% 100% 31% 97% 23% 81% 100%Non-interest income/assetsAverage 3% 2% 2% 4% 1% 2% 5%Std. 9% 4% 1% 15% 1% 3% 16%Min -16% -16% 0% -3% 0% -16% -3%Max 210% 33% 7% 210% 7% 68% 210%Expenditures/assetsAverage 3% 3% 2% 5% 2% 3% 6%Std. 8% 3% 1% 14% 1% 2% 15%Min 0% 0% 0% 0% 0% 0% 0%Max 195% 30% 6% 195% 6% 59% 195%Individual net operating income/total operating incomeAverage 0.6% 1.1% 0.4% 0.2% 2% 0.2% 0.0%Std. 1.9% 3.1% 1.1% 0.8% 4% 0.1% 0.0%Min 0% 0% 0% 0% 0% -0.2% 0.0%Max 23% 23% 11% 12% 23% 1.3% 0.4%Loans/assetsAverage 74% 72% 84% 66% 73% 77% 72%Std. 24% 21% 9% 32% 16% 23% 29%Min 0% 4% 40% 0% 3% 0% 0%Max 100% 99% 96% 100% 98% 99% 100%Loan loss provisions/loansAverage 3% 3% 1% 5% 1% 2% 7%Std. 10% 12% 5% 12% 2% 8% 16%Min 0% 0% 0% 0% 0% 0% 0%Max 100% 100% 96% 99% 21% 99% 100%Ln (Assets)Average 15 15 16 14 17.5 15 12Std. 2 2 1.1 2.1 1.3 0.7 0.9Min 7 10 12 7 16 14 7Max 22 22 21 21 22 16 14

Table A1: Descriptive statistics of RoA


Part 1

Stress-testing models: a strategic risk management toolBalvinder SanghaPrincipal and Leader, Credit and Capital Analytics team, Financial Services Risk Management Practice, EY LLP

Jane LinSenior Manager, Financial Services Risk Management Practice, EY LLP

AbstractThis paper discusses the role of models in conducting stress-tests for regulatory and risk management purposes, and presents some approaches that may enhance their ability to estimate outcomes in a stressful environment. Unlike a conventional model that is designed for a steady state environment, we argue that a stress-testing model needs to be developed with a different design to capture the implications of abnormal business and economic conditions. Developing such a model may require a combination of qualitative and quantitative adjustments to capture the stress or boundary conditions. Consequently, the governance needs of stress-testing models require more rigor than steady state models to effectively challenge the underlying construct and assumptions. It is critical that senior management appreciate these nuances before using the output of such models for key strategic decisions.



Risk management in the financial services industry has continued to evolve and adapt to new or unforeseen combination of risks. The recent financial crisis has highlighted the previously unrecognized high degree of correlation across and within asset classes, particularly when faced with a deteriorating economic environment. During this period, the common economic shocks (e.g., decline in house prices, rise in the unemployment rate, increased volatility in the stock market, etc.) affected multiple portfolios simultaneously, albeit with different lag times. During this turbulent time, the fundamental weaknesses in the market coupled with in some instances a lack of an ability to anticipate the degree of concentrated risks brought many institutions in the U.S. and elsewhere to the brink of insolvency. This resulted either in outright bankruptcy, an orderly acquisition engineered by the regulators, or recapitalization of the bank by regulators. The need for stress-testing in financial services was accentuated during this tumultuous period as this crisis unraveled and the ability to understand the implications of likely future projections became critical both for regulators and the industry. The concept of using a stress-testing framework gained immense strategic importance as bank senior management and the board of directors, as well as the regulators, tried to grapple with the outcome of the domino effects. Coming out of the crisis, stress-testing has emerged as one of the most critical regulatory tools in a post-crisis effort to avoid such outcomes in the future.

The term “stress-testing” is commonly applied in the medical profession, where cardiologists routinely stress-test the human cardiovascular system to evaluate adequate supply of blood to vital organs. The stress-testing of the banking system focuses on ensuring adequate capital, which is not too far from the analogy of the human body since capital serves as the life blood of a financial institution and an abrupt shortage of which could not only cause financial distress but also potential insolvency. However, the parallel between the banking and medical stress-tests breaks down in the implementation of this concept across the two fields. While the human body can be stressed in a limited manner under controlled conditions to evaluate the body’s cardiovascular response to potentially stressful conditions requiring higher than normal levels of exertion, the same realistic experiment cannot be conducted on a bank to evaluate different stressful scenarios even on a limited basis without causing significant financial losses and business disruptions. The practical

approach, therefore, is to use a model1 (or a set of models) that represents a bank’s balance sheet and portfolio to simulate the stressful scenarios. The model proxies the bank’s portfolio and provides an assessment of its financial condition under various circumstances, simulating alternative future outcomes.

Consequently, it is imperative that such models have the capability to simulate alternative macroeconomic or other scenarios as realistically as possible to assess the bank’s solvency, as well as build in sufficient portfolio sensitivity to those scenarios. The models need to impose appropriate profit and loss implications to draw some realistic conclusions about the bank’s financial condition under multiple stress conditions. Needless to say, the effectiveness of the underlying models used to conduct the stress-tests is critical in reaching a viable diagnosis of a bank’s financial health, otherwise we may cause unnecessary alarm and panic or alternatively fail to identify a significant risk (also referred to in statistical terms as Type I or Type II error, otherwise known as false positives or false negatives). The effectiveness of the entire stress-testing exercise, therefore, relies heavily on the ability of the model(s) to adequately represent the bank’s portfolio, and its ability to capture the impact on the portfolio of a stressful internal or external scenario.

The quality of information coming out of a stress-testing exercise is dependent on the thoroughness of the process and the effectiveness of the underlying models. The results of a robust stress-testing process can provide immense insight into the probable scenario-driven outcomes, and offer a valuable means of preparing for the potential challenges. Institutions with these capabilities are able to anticipate and prepare for the adverse conditions. Stress-testing is also an important element of the prudential supervision process that permits regulators to draw conclusions about the health of a bank and develop appropriate regulatory responses based on that outcome. Conversely, model risks and limitations associated with the stress-testing models, if not understood and mitigated where necessary, can lead to false conclusions about the bank’s ability to sustain a stressful outcome. Hence, of all the different requirements that are necessary for conducting stress-testing, a well-functioning model(s) represents a crucial component of that process.

1 The term model is used generically to describe a qualitative or quantitative approach that forms the basis of future projections.


Have never created or implemented any new

stress-testing methodologies

Have not implemented new stress-testing

methodologies in the past 12 months

Created and implemented new stress-testing

methodologies prior to January 2011

Created and implemented new stress-testing

methodologies in the past 12 months

0%

10%

20%

30%

40%

50%

60%

70%

80%

0%

6%

54%

75%

Table 1: Firms continue to implement new stress-tests2

Source: EY/IIF 3rd Annual Survey of Risk Governance (2012)Greatest problem is speed — stress-tests take 3 months or more and are too cumbersome to use as a flexible management tool

As stress-testing is evolving in the banking industry, this paper describes some of the modeling challenges in stress-testing and offers insights into methodologies used in the industry, regulatory expectations, and the means to ascertain the effectiveness of such models. Furthermore, this paper offers critical insights to senior management as they utilize the stress-testing results for strategic needs, such as determining the risk appetite of the bank, and provides them with guidance on how to effectively challenge the underlying models before accepting their output.

BackgroundEven though the Basel II global capital accord formulated in the early 2000s specifically called out the need for conducting stress-testing, their criticality and the value did not become fully apparent as an important risk management tool until the 2007–2008 financial crisis in the U.S. As the crisis was unraveling, a number of financial institutions hurriedly undertook significant stress-testing exercises focused primarily on their mortgage exposures to fully comprehend the impact of changing housing market conditions. Some of the early adopters were able to plan ahead and partially mitigate the impact of the “housing bubble.” A number of post-crisis regulatory initiatives and subsequent

2 Percentages in the figure across choices may sum up to more than 100%, as not all survey choices are mutually exclusive.

legislation emphasized stress-testing of bank portfolios as an important prudential supervisory tool. The Supervisory Capital Adequacy Program (SCAP) conducted by the Federal Reserve in early 2009 drew significant media and public attention as it was the first publicly disclosed effort to ascertain the health of the banking sector post–2008 financial meltdown. Since then, the stress-testing exercise has been codified in the U.S. via standard regulatory tools for ongoing prudential supervision, namely the Comprehensive Capital Analysis and Review (CCAR) and the Dodd-Frank Act Stress Tests (DFAST) requirements.3 CCAR is an annual exercise by the Federal Reserve to ensure that the largest bank holding companies have sufficient capital to continue operations throughout periods of economic and financial stress, as well as robust, forward-looking capital planning processes that account for their unique risks.4 Based on the outcome of the CCAR stress-tests and qualitative review, U.S. regulators may approve, curtail, or reject any proposed capital actions planned by the bank during the year. Furthermore, public disclosure of the stress-testing results puts added pressure on bank management to appropriately inform investors about their risks. The regulatory requirements specify the economic scenarios that banks have to utilize to project their stress-testing outcomes. These future scenarios include baseline or neutral and (severely) adverse scenarios. Over time, the number of economic variables provided by the regulators, against which the stress-testing outcomes have to be projected, have grown, recognizing both the increasing reliance by regulators on stress-testing for supervision purposes as well as the multi-faceted linkages to a bank’s portfolios. For example, some of the earlier stress-testing requirements immediately after the financial crisis were limited to scenarios defined by a handful of economic drivers such as GDP, home price, and unemployment. These have recently been expanded to also include macro-economic changes in the Eurozone that has implications for internationally-active banks. As part of the CCAR process, U.S. regulators have developed an independent set of stress-testing models designed to use bank data to analyze the impact of different economic conditions. The independent regulatory stress-testing models are a mechanism to guard

3 Similar to the Dodd-Frank Act in the U.S., other jurisdictions like the FSA in the U.K. have also enacted similar regulations that require banks to conduct periodic stress-testing of their portfolios.

4 Currently, there are 18 BHCs that are required to submit their capital plans to the Federal Reserve on an annual basis as part of the CCAR. In addition, there are an additional set of 11 BHCs that are also required to submit their capital plans as part of the Capital Review Process (CapPr).



against overreliance of a common industry modeling approach that may fail to pick up critical negative implications of the scenarios. Clearly, the stress-testing exercise is becoming more institutionalized as an important ongoing regulatory tool.

Even though the genesis of the current focus on stress-testing in the industry has been in part driven by evolving regulatory requirements, increasingly bank senior management have responded to the changing paradigm by explicitly recognizing it as a critical part of the risk management function. Many banks have expanded their stress-testing exercises beyond the regulatory mandates to also gain important strategic risk management insights to evaluate and understand the “worst-case” or “nightmare” scenarios utilizing concepts like reverse stress-testing. The concepts of stress-testing are also feeding into an institution’s economic capital needs under various scenarios, product pricing, as well as determination of risk appetite at the strategic level. Banks continue to invest heavily in the underlying ingredients of stress-testing: internal and external data, and models to implement and analyze the stressful scenarios.

Industry efforts on stress-testingThe focus on stress-testing is a global endeavor for the industry, with banks across the world investing in improving and building out their stress-testing efforts. A recent survey of global financial industry covering 75 large banks and insurance companies across 38 countries by EY/IIF confirmed a significant ongoing effort across the industry in recent years on creating and implementing new stress-testing methodologies.

Unique challenges of stress-testing modelsThe evolving model governance doctrine5 stresses the importance of aligning modeling choices and methodological options with the business purpose of the model. For stress-testing models, the purpose is to produce outcomes not under average or normal business conditions, but under extreme or boundary conditions. This implicit requirement challenges the traditional or conventional wisdom in modeling, where analysts seek to mimic the long-term average expectations when building models. Any model that adequately captures the long-term or average

5 In the U.S., primarily spurred by the joint regulatory guidance issued by the Federal Reserve and the Office of Comptroller of Currency in April, 2012 (FRB SR 11–7 and OCC Bulletin 2011–12 respectively).

trends and also builds in the average asset value correlations will often fail to pick up the likely impact under stressful conditions. Put differently, the steady state models need to be designed to produce good predictions over the long-term under normal business and market conditions, whereas the stress-testing models need to capture the rare 1 in 10-, 50-, or a 100-year event. The modeling choices may not be the same for the two objectives articulated above, and this key distinction forms the basis of the authors’ argument for a differential modeling approach between the steady state and stress-testing modeling.

To illustrate this point, it is instructive to consider a hypothetical mortgage portfolio and its evolution across the recent financial crisis. The implications of economic changes on a real estate related portfolio are insightful as the impact of home price movements and their impact on mortgages have become better understood since the U.S. market endured its implications in the recent crisis. A model developed on historical experience in the U.S. covering the pre-2007 period would invariably emphasize the importance of credit history as an important driver of a mortgage portfolio performance. In relationship to the role of asset values or loan-to-value (LTV), credit history typically emerged as the predominant predictor of default during the period of rising home values. However, the relationship switched during the crisis when LTV became the dominant driver of mortgage default as home prices started to decrease, and even mortgage holders with good credit started to default once they realized that the value of their property had fallen well below their outstanding mortgage balance (referred to as strategic default). Similar anecdotes may be found in a host of other portfolios as well, where models based on long-term data and trends fail to pick up the anomalous behavior patterns during a period of crisis or upheaval. Consequently, a robust model that captures the dynamics of any portfolio in the long-term and has immense value in predicting outcomes in a steady-state economic environment may fail to capture the likely outcomes in a stressful period. For example, some institutions have re-estimated their mortgage model after the crisis, updating the parameters to include the implications of macro-economic data such as the home price index and unemployment to account for the downturn, but also used the data prior to and after the downturn to train their model. They evaluated the efficacy of their updated models by recasting the actual economic environment from 2007–2008 period to estimate the projected losses estimated by the model.


Not surprisingly, the models generally fail to account for the magnitude of the actual losses incurred during the financial crisis by a significant amount, primarily because they are not capturing the changing consumer behavior that became evident during the crisis and the degree of cross-correlation across regions with falling home prices (higher asset value correlations than average). Both of these patterns manifested themselves only in the recent housing market collapse and could not have been predicted using a long-term or steady state economic data. Such anomalies also occur in other non-mortgage portfolios as part of the CCAR exercise, where recently developed methods/models fail to produce the level of losses that occurred in the crisis even under particularly stressful scenarios. While the above illustration is loss-centric, similar modeling challenges exist when projecting revenue or balance sheet elements under stressful circumstances.

The above discussion produces a dilemma for banking institutions when developing stress-testing models. On the one hand, they need to use historical data to train, parameterize, and validate their models, but on the other hand they need to ensure that the models are designed so as to pick up the sensitivities that will only emerge in a rare stressful environment. The obvious conclusion being that a good stable model that produces robust estimates in the long-run may not necessarily be a reliable stress-testing model.

Designing stress-testing modelsAs discussed earlier, a significant challenge exists in building and designing stress-testing models in that the business use of such models may require a significantly different approach than the standard modeling methods that focus on using long-term data to build models with robust predictive powers in the steady state circumstances. However, unlike models designed for the steady state it is clear that stress-testing models need the predictive capability to estimate the boundary conditions or the tail events around the normal or steady state. The first consideration that an institution needs to address is, therefore, whether the stress-testing model should simply extrapolate the predictions from business-as-usual steady state models, or, alternatively design and develop stress-testing models specifically to capture the tail events. Having struggled with the ability of their models to pick up the stressful environment, many banks are moving in the direction of considering developing specific models for stress-testing purposes alone.

An argument can be made that given the limitations of an empirical model discussed above and the need to think about capturing non-historical trends in the analysis, whether a purely judgmental approach to stress-testing may be appropriate. In many instances where portfolios reflect idiosyncratic patterns, it is indeed desirable to consider expert judgment approaches to capture such unique outcomes. However, the use of judgment is not the panacea for designing stress-testing models as qualitative inputs are difficult to validate and justify. If anything, more judgment will necessitate more substantiation and support to authenticate the use of the qualitative model. Nevertheless, in the discussion that follows we will consider a purely qualitative or an expert judgment approach as a model, where a model is defined broadly as a framework.

Based on the evolving industry practices, we offer the following suggestions in designing stress-testing models. For purposes of the discussion below, we assume that stress-testing models specifically include macroeconomic factors as drivers of portfolio dynamics, or in other words, the outcome of these models is influenced by these factors. Further, we abstract from other modeling decisions, such as the underlying lag structure of the timing of the macro impact, and assume that standard modeling methods are employed to ascertain those. Additionally, the discussion is agnostic to the type of model used (loan-level, panel, time series model, etc.). Some of the following considerations challenge the conventional wisdom on acceptable modeling practices.

The most general formulation of the problem may be represented mathematically as:

(a) yss ssx= + +a b f, where y is the outcome variable and x represents a vector of portfolio and macro-economic factors, estimated under a steady state (SS) or long-term environment. ssb represents the estimated relationship between y and x.

(b) yST STX= + +a b f, where y is the outcome variable and x represents a vector of portfolio and macro-economic factors, estimated under a stressed (ST) environment. STb represents the estimated relationship between y and x under stressful conditions.



The discussion below focuses on estimating STb in so far as there is a reason to believe that ST SS!b b . Some of the specific suggestions include:

Combining business insights into modeling: given the unique business use of the stress-testing models, conduct a pre-development feasibility exercise to evaluate the data, judgment, potential methodology choices, and likely risks and limitations of alternative approaches. Unlike the usual steady state modeling approach, where the business lines outsource the modeling exercise to a quantitative group within the institution that uses the data provided to develop a model based on the agreed-upon specifications, stress-testing requires much more thought and business line input in designing a model that is able to capture portfolio dynamics in an abnormal or an extreme period. This approach also forces the business line to critically evaluate the stressed circumstances and the degree of adverse consequences under such scenarios, making them more resilient if such an event were to materialize. Consequently, it is very important that the business insight into how the portfolio would react under stressful conditions is embedded in the model rather than simply reliant on historical data. This collaborative approach between modeling and business area is critical for determining how much judgment may be required in the process, what is the appropriate time period to cover the stressful environment, and determine the optimal modeling choice.

Parsimonious modeling: another fundamental difference between developing a stress-testing versus the steady state model is the need to build a more general model for stress-testing purposes such that the model can accommodate a wide variety of environments and not be tailored or fitted to a particular set of conditions. Usually, one of the goals in developing a steady state model is to fit it to the long-term data and produce model specification with the highest predictive abilities — for example, Basel II rules require a minimum of 5 years of data to develop credit risk models for retail exposures. However, in building a stress-testing model care should be taken not to fit or “fine tune” the model to a certain data period as the primary purpose of the model is to estimate portfolio behavior in a non-normal environment. Thus, a more general or parsimonious approach is more useful when designing a stress-testing model as it would be less tied to a particular data environment. The modeling community, therefore, has to balance the need between the

stress-testing model’s predictive capabilities against the more general and adaptable abilities of the model. Using a minimal set of predictors would produce a model which is better suited in the context of stress-testing models, as the model offers more degrees of freedom to adapt to different economic and market scenarios, a requirement which is at the core of the stress-testing principles. Clearly, such a model would not be as predictive as a model with additional variables fitted to a dataset over the longer horizon, but likely to perform better during the turns in a business cycle. Generally, modelers are trained to optimize on goodness-of-fit metrics where the model specifications with the best fit are selected, but designing a stress-testing model requires a constrained optimization exercise where the modeler deliberately selects a sub-optimal solution from a goodness-of-fit perspective, and favors a parsimonious and general structure.

Parameterselectionusingouterconfidenceintervals: most modeling exercises rely on the principle of maximum likelihood or least squares estimation techniques to estimate the parameter values of the explanatory variables at the central tendency or mean of the distribution. As opposed to a judgmental determination of which variables to select, some modelers may prefer to rely on an empirical approach, but instead choose the model parameters not around the mean but outer confidence intervals to recognize the 1 in 10- or a 100-year event. In theory, assuming a rich dataset with sufficient observations, it may be argued that rather than selecting parameter values for a variable that predicts the mean, for stress-testing models it may be more appropriate to consider parameter values at ± 1 standard error (commensurate with outcomes likely to occur only 1/3 of the time), or ± 2 standard error (commensurate with outcomes likely to occur less than 1 in 20+ years). The benefit of this approach is that it is empirically driven but the parameter values represent the outer limits of likely occurrences. The approach is consistent with the empirical analyses that form the basis of most modeling exercises, except by design it specifically considers the less probable outcomes. In effect, the standard errors around a model’s estimated parameter value represent a distribution of likely values that those parameters may assume with the mean of the distribution indicating the most likely value, and lower probable outcomes with parameter values as you move away from the distribution mean in both directions. In this approach, parameter values at the tail that produces higher losses or lower revenue (depending on the nature of the model) may be


selected as the stress-testing parameter value for each variable. For example, for a credit loss model, the model developer may choose parameter values at 1 standard error towards the higher losses for each parameter. In modeling terms, making the distinction between βSS and βST such that the stress-testing model parameters specifically take into consideration the basic purpose of the model to estimate outcomes away from the mean.

Conditional estimators: one criticism of using parameter values at some outer confidence intervals is that the outer tail may not represent different economic environments but rather the simple noise in the data, which can come from a single and stable economic environment. The inability of the previous approach to disentangle the effect of different economic conditions may be addressed by specifically identifying periods of historical stress or downturn, and then producing a number of estimators separately for each downturn period. For example, banks with sufficient historical data may pick recessionary periods corresponding to the recessions in early 80s, 91–93, 2001 9/11, and 2007–2009. For each of these time frames, a separate estimate may be generated: ST1b , ST2b , ST3b , and ST4b , corresponding to each of the previous recessionary periods. For purposes of stress-testing, either the bank may use specific historical experience that is closest to the future scenario, or use the multiple points to develop a distribution of parameter values under stressful times to compute a ST2cb from that distribution as any metric that measures the central tendency of that distribution. For many institutions, lack of sufficient historical data may limit their ability to execute this approach.

Event study approach: recognizing that the lack of data around economic downturns may limit a bank’s ability to robustly estimate their conditional estimators, and furthermore not all recessionary periods are sufficiently long enough to estimate a reasonable model. One strategy could be to combine the entire dataset over the long horizon, but use additional indicator variables to tag periods of down-turn (which may be as little as a few months in some instances), and then estimate the model to compute the STb as an interaction term with the tagged common downturn variable. This method is conceptually very similar to the conditional estimator approach described above but uses a different implementation approach to estimate the mean STb . The approach also presents some flexibility in estimating parameters across the different time periods in a business cycle.

Reversion to a pure optionality assumption under stress: another approach to build-in the stress-testing elements into a model is to redefine the model and limit it to a pure option-theoretic framework. In other words, the obligor “put” option is the only consideration for a stress-testing framework, while many other aspects are evaluated in the steady state model for the same portfolio and purpose. In the mortgage example discussed earlier, the pure optionality would suggest that the only factor that should be considered is the borrower’s loan-to-value and should the home value drop below the outstanding loan amount, the borrower will ruthlessly exercise his option to default. Similarly, while for a C&I portfolio, a bank may utilize a rich set of rating scorecards by industry sector in a steady state environment, an obligor may exercise their put option to default when the value of the collateral drops below the loan amount, or the rent from an income-producing asset falls below the debt service levels, both of which optionalities are typically not explicitly captured in the scorecards. Similar extensions of the ruthless put option view may be utilized for the loss exposure models for stress-testing purposes ignoring other elements that are typically considered in steady state conditions.

As a practical matter, banks may choose a hybrid approach combining elements from multiple considerations presented above to suit the specific needs of their specific portfolios. However, the key is to recognize that alternative methods, adjustments, assumptions, and judgments may be necessary when it is clear that ST SS!b b . Furthermore, some banks may choose to continue using the traditional steady state models for stress-testing as their core methodology, but supplement the analysis of the associated risks and limitations of those steady state models using some of the considerations suggested above. For example, the potential model risk of a long-term model used for stress-testing may be quantified using the “event study” or pure “option” approach, such that the bank may be able to use that to ensure adequate capital buffer for model risk. When it comes to stress-testing models, every bank faces a unique set of challenges, be it data, resources, materiality of the portfolio, and so on — all of which will determine the appropriate modeling strategy for that institution. The term model strategy is used to emphasize that no one modeling approach may suffice, but a combination of different methods may be necessary to produce a core estimate of the future scenarios which needs to be coupled by either corroborative methods to support that conclusion,



or alternatively measure model risk associated with the core estimate. Either way, it is critical to think beyond the traditional modeling methods when designing the modeling strategy for stress-tests.

Governance of stress-testing modelsA fair question may be raised in the context of different unconventional strategies discussed earlier as to how the “independent validation” team can validate the myriad of approaches suggested in the previous section. Most model validation groups are geared towards evaluating empirically-driven models using standard or commonly accepted modeling methods. The recent regulatory guidance emphasizes the role of back-testing as a fundamental basis for model risk guidance as well.

The key point to address this dilemma is that model governance does not equate to back-testing alone. If one looks at the period prior to the financial crisis, one finds that most institutions were using models that had been back-tested on a routine basis, producing very standardized validation reports. So much so that there was a significant trend among banks to off-shore model validation functions under the premise that back-testing is a repeatable compliance exercise requiring minimal oversight. Yet, even with frequently back-tested and compliant models, which is akin to looking in the rear view mirror, those models faced credibility questions at the onslaught of the financial crisis. Stretching the analogy, even though banks were equipped with spotless rear view mirrors, few had the tools to look beyond the curve in the road ahead. We argue, therefore, that the key to effective model governance is to focus on “effective challenge” as the primary tool to manage model risk, as opposed to singular concepts such as back-testing. The need for effective challenge is arguably the single biggest theme of the recent regulatory guidance on model risk management as well — the guidance specifically includes processes with qualitative inputs but producing quantitative outputs as being within the definition of a model. The considerations for stress-testing models to better align the model output with realistic stressful scenarios would be within the bounds of model risk management, albeit different types of skills may be necessary to apply effective challenge to such models.

The governance of a stress-testing-model involves a much more holistic assessment of the model than mere back-testing. It has to take into consideration the model design, its adaptability to different economic conditions, sensitivity to changing environment, reasonable benchmarking to alternative methodologies, and appropriateness of model outputs. The need for diverse approaches to estimate stress models is imperative as it provides a benchmark for what may happen under extreme conditions from multiple methodological perspectives. The worst outcome from this initiative would be if everyone converges to one standard view for modeling the future extreme conditions, and the obvious fear is that if that approach fails to pick up a turn in the cycle we would be no wiser than we were going into the last recession. Consequently, prudent model governance requires that senior bank management challenge the stress-testing model methodologies sufficiently, and not accept the absolute outcome of such models without questioning the model’s ability to pick up changing business environments or comparing their output against some reasonable benchmarks, including expert judgment for corroborating the output. It will never be possible to back-test or “validate” the stress-test model predictions, unless the extreme conditions materialize with sufficient frequency to reach such conclusions. The management, therefore, needs to focus more on understanding the risks and limitations of such models to formulate their view of how the model will perform in adverse conditions, even if such views are based on a qualitative assessment of the models.


ConclusionStress-testing models form the basis for evaluating a bank’s performance, capital position, and sustainability under a stressful environment, and are designed to serve as the proverbial “canary in a coal mine.” As stress-testing becomes an ever more critical component of risk management, given the recent industry experience through the financial crisis, it becomes important that senior management develop confidence and comfort with the bank’s stress-testing models. The most important aspect of these models is that by design, they are not, and should not, resemble the long-term steady state models that are used in so many applications within the bank to project likely or average outcomes. Instead, these models should try to focus on capturing the extreme events. The design and governance of such models has to keep that important purpose in the forefront, which requires a significant amount of qualitative and quantitative adjustments.

It is critical that senior management through its review and challenge process gain adequate insights into the risks and limitations of stress-testing models in order to develop confidence in the model output, and be in a position to make any qualitative adjustments to the output as these models will continue to serve important strategic business imperatives.

Part 2:

Calculating damages in ERISA litigation

Levered exchange-traded products: theory and practice

Regulating insurance groups: a comparison of risk-based solvency models

Determinants of the interest rate premium on contingent convertible bonds (CoCos)

Risk-on/risk-off, capital flows, leverage and safe assets


Part 2

Calculating damages in ERISA litigationAllen FerrellGreenfield Professor of Securities Law, Harvard Law School

Atanu SahaSenior Vice President, Compass Lexecon1

AbstractIn this paper we will present and discuss four different methodologies for calculating ERISA damages — what we will label the “best-performing fund,” “portfolio redistribution,” “most similar fund,” and “10b-5 style” ERISA damage methods. For purposes of demonstrating how these ERISA damage methods work in practice we will use facts and data from an actual ERISA litigation matter. These different ERISA methods can result in strikingly different damage estimates. In the ERISA matter we analyze, for instance, aggregate damages can range from less than U.S.$3 million, using the “most similar fund” approach, to well over U.S.$2 billion using the “best-performing fund” ERISA damage method.

1 This paper utilizes for illustrative purposes the facts of a case that one of the authors worked on as an expert (which has subsequently been resolved). We would like to thank the John M. Olin Foundation in Law, Economics and Business at Harvard Law School for financial support, and Paul Ferrillo, Warren Stern, and participants at the Harvard Law School Law and Economics Workshop for helpful comments.



IntroductionEmployment Retirement Income Security Act (ERISA) class actions, which focus on the management and handling of pension and retirement plans such as a company’s 401(k) plan, constitute an important component of overall U.S. securities litigation activity. In particular, in the aftermath of the stock market collapse in 2001 and the credit crisis of 2007–2008 a number of ERISA lawsuits were filed as many companies’ 401(k) and Employee Stock Ownership plans (ESOPs) plans suffered substantial losses. The ERISA litigation wave after 2001 includes lawsuits filed against Enron, Global Crossing, and Lucent and, in the wake of the credit crisis, ERISA lawsuits against AIG, Bank of America, Bear Stearns, Citigroup, Countrywide, Merrill Lynch, Morgan Stanley, State Street, UBS, Washington Mutual, and many others. ERISA cases can be attractive to bring as there is no need to prove that the defendants acted with scienter, i.e., acted with intent or recklessly, in order to establish liability under ERISA, a major hurdle for plaintiffs bringing a Rule 10b-5 action.2 Rather, ERISA liability rests on a breach of a fiduciary obligation.

The settlement value of this litigation can be substantial. For instance, State Street recently settled its ERISA lawsuit for U.S.$89.75 million with Merrill Lynch settling its ERISA lawsuit for U.S.$75 million. Washington Mutual settled two different ERISA class action lawsuits, one for U.S.$49 million and the second for U.S.$20 million. Countrywide also recently settled its ERISA lawsuit for U.S.$55 million. They are not alone.3 The record for the largest ERISA settlement remains to this day, however, the Enron ERISA litigation, in which there was an initial partial settlement for U.S.$85 million covered by Enron’s insurance policies. A later settlement resulted in a further U.S.$356 million, albeit in the form of an unsecured claim against the bankruptcy estate.

Despite the commonality of these suits and their settlement value, there are no papers that we have been able to identify that address the issue of how to calculate ERISA damages. In this paper, we will present and discuss four different methodologies for calculating ERISA damages — what we will label the “best-performing fund,”

2 If ERISA liability is based on a respondent superior theory, which is often the basis for a company’s alleged liability in an ERISA suit, then most courts require a showing of scienter.

3 Some other notable ERISA settlements include Global Crossing (U.S.$79 million), Lucent (U.S.$69 million), the Williams Company (U.S.$55 million), Xerox (U.S.$51 million), Worldcom (U.S.$48 million), Household International (U.S.$46.5 million), and Dynegy (U.S.$30.75 million).

“portfolio redistribution,” “most similar fund,” and “10b-5 style” ERISA damage methods. For purposes of demonstrating how these ERISA damage methods work in practice we will use facts and data from an actual ERISA litigation matter. These different ERISA methods can result in strikingly different damage estimates. In the ERISA matter we analyze, for instance, aggregate damages can range from less than U.S.$3 million, using the “most similar fund” approach, to well over U.S.$2 billion using the “best-performing fund” ERISA damage method.

The next section will first present the two common plaintiffs’ theories for ERISA liability — provision of an “imprudent” plan investment option and inadequate disclosures affecting the value of company stock which has been offered as an investment option. The following section will then present some descriptive statistics concerning our illustrative ERISA litigation matter. The penultimate section will then turn to presenting, discussing, and comparing the four ERISA damage methods. As we will discuss, the appropriate damage method will be informed by the basis for ERISA liability. In cases where liability is based on an inadequate disclosure claim, we will argue that “10b-5 style” damages are likely to be the most appropriate method. In other cases, the most appropriate damage method will often be the “most similar fund” approach.

Typical ERISA class action claimsThere is a high degree of uniformity in the basic types of allegations presented in an ERISA action brought on behalf of a class of plan participants in a company’s ERISA plan, such as the company 401(k) plan. More specifically, ERISA complaints typically present one, or both, of two basic breaches of fiduciary obligations theories as a basis for ERISA liability.4 These lawsuits are often brought after plan participants have suffered substantial stock market losses as a result of holdings in the plan of company stock.

The first basic theory often presented is the claim that the plan fiduciaries provided inadequate disclosures to plan participants by either failing to disclose material information or disseminating misleading information, typically information relevant to the market’s assessment of the value of the company stock. Plan participant stock losses are then realized once the market belatedly

4 Only fiduciaries can have fiduciary obligations and as a result an extensive area of litigation in the ERISA context is whether a party is a “fiduciary” as that term is defined in Section 3(21)(A) of ERISA, 29 U.S.C. Section 1002(21)(A).


learns the truth as a result of a disclosure, finally correcting earlier inadequate disclosures. Liability on this basis is quite similar to a typical Rule 10b-5 class action alleging that the firm (and its officers and directors) disseminated fraudulent misinformation to the market (or failed to disclose material information that they had a duty to disclose) and thereby harmed the firm’s shareholders who purchased at an inflated stock price.

The second basic theory also often presented as a basis for liability is the claim that the plan fiduciaries offered, and continued to offer, as an investment option to plan participants company stock when the fiduciaries knew or should have known that the company stock was an “imprudent” investment. One of the main factors often pointed to in order to substantiate the claim of “imprudence” is the inadequate disclosures relied upon when invoking the first theory. In this sense, the second theory can be a derivative of the first theory, hence the reason why the two theories are often simultaneously invoked.5

Consider, by way of example, the Countrywide ERISA complaint.6 Both of these two theories are presented in this complaint as a basis for liability. Countrywide’s 401(k) plan offered as an investment option Countywide stock to plan participants, Countrywide employees. And a number of plan participants in fact chose to place a portion of their 401(k) investment in Countrywide stock. According to the complaint, the value of Countrywide stock held by plan participants fell in value over the class period from U.S.$350 million to U.S.$80 million.

As for the first theory, the complaint alleges a breach of fiduciary obligation by the 401(k) Countrywide plan fiduciaries: as “Defendants failed to provide participants, and the market as a whole, with complete and accurate information regarding the true financial condition of the Company. As such, participants in the Plan could not appreciate the true risks presented by investments in Company stock and therefore could not make informed decisions regarding their investments in Company stock in the Plan.”7 As for the second theory, the complaint also asserted liability based on the claim that an “adequate or even cursory investigation by

5 See Niden, C., 2007, “Economic analysis in ERISA class actions involving employee investments in company stock,” 44 Benefits & Compensation Digest 1, April

6 For the complaint, see http://www.oakbridgeins.com/clients/blog/countrywideerisacomplaint.pdf7 Countrywide Complaint, ¶181.

Defendants would have revealed to a reasonable fiduciary that, under these circumstances, investment by the Plan in Countrywide stock was excessively and unduly risky, and, thus, imprudent. A prudent fiduciary acting under similar circumstances would have acted to protect participants against unnecessary losses and would have made different investment decisions.”8 This claim of imprudence is explicitly tied to the inadequate disclosure claim. The undisclosed problems at the firm are alleged to have caused “Countrywide’s stock price and the price of the Fund [to be] artificially inflated making them an imprudent investment for the Plan.”9

We will use for illustrative purposes the facts and data from an actual ERISA litigation matter. In this matter, a firm, call it ABC, had a 401(k) plan in which the value of the company’s stock, one of the plan’s available investment options (the ABC Company Stock Fund), fell substantially in value. Plaintiffs allege that the ABC 401(k) plan fiduciaries, in breach of their fiduciary obligations, failed to provide to plan participants certain disclosures that would have revealed that the company, and hence its stock, was worth far less than the market price. These disclosures should have been made, according to plaintiffs, as early as 31 July 2001. The disclosures to plan participants (and the market more generally) occurred only on 22 July 2002 and 23 July 2002, approximately a year later. The 22 July and 23 July 2002 corrective disclosures were associated with significant stock price drops in the price of ABC stock. In addition, plaintiffs further allege that the failure to provide these disclosures during the 31 July 2001 — 23 July 2002 time period resulted in a further breach of fiduciary obligations, given that the plan fiduciaries offered the company’s stock as a plan investment option despite knowing that the company’s stock was an “imprudent” investment. The price of ABC company stock fell during the class period by approximately 36%.

The class period in our illustrative ERISA matter therefore ran from 31 July 2001 to 23 July 2002, with class members consisting of any plan participants who held company stock in the 401(k) plan at any point during this time period. It is worth noting that unlike a Rule 10b-5 class action, class members in an ERISA matter can potentially include investors who merely held securities during the class period, such as a plan participant who invested in the ABC

8 Countrywide Complaint, ¶171.9 Countrywide Complaint, ¶167



Company Stock Fund prior to 31 July 2001 and continued to hold that position throughout the class period. In other words, there is no general requirement that investors, in order to be members of an ERISA class, purchase or sell securities during the class period.

The next section will present some descriptive statistics concerning the 401(k) plan in the ABC litigation matter that will provide the necessary context for our calculations of ERISA damages presented below.

Descriptive statistics for the ABC 401(k) planBefore presenting some descriptive statistics for the ABC 401(k) plan it is worth briefly highlighting the nature of the individual ABC 401(k) plan participant data available to us during the class period. We have data on all plan participants’ monthly fund level activity (withdrawals and deposits) and ending balances. We also have data on loans and loan repayments by participants from their 401(k) plan, which we will treat as withdrawals and deposits. Given the monthly frequency of our data, we assume that participants’ withdrawals and deposits occur at the end of the month. We will use as a proxy, because of the frequency of our data, for participants’ holdings as of 23 July 2002 (the end of the class period) plan participants’ holdings as of 31 July 2002. Finally, we will present data only for plan participants that invested in the ABC Company

Stock Fund for at least one point in time during the class period. This focus on participants that invested in the ABC Company Stock Fund for at least one point during the class period is simply a function of the fact that we are interested in calculating potential ERISA damages where the asserted basis for ERISA liability is the handling of the ABC Company Stock Fund. This is reflected in the fact that the ERISA class in the ABC matter consists of any plan participant that held a position in the ABC Company Stock Fund at any point during the class period.

Table 1 presents a summary of ABC’s 401(k) fund options and plan participation (fund name, strategy, participation by amount invested) as of July 2001 and July 2002 as it relates to the ABC Company Stock Fund (which is solely invested in ABC stock) and the next top ten funds, as measured by the amount collectively invested by plan participants.10 In addition, the number of participants investing in each of these funds as of July 2001 is also presented with the total number of plan participants at this time

10 The total amount of funds invested by plan participants as of July 2001 in the twenty funds not separately listed in Table 1 constitute 9.1% of the total aggregate value (approximately U.S.$10.1 billion) of the 401(k) plan (excluding participants that never invested in the ABC Company Stock Fund during the class period). These twenty funds included funds with a variety of investment strategies, including fixed income government, fixed income/equity, equity international, equity/value, equity/growth, and equity large cap.

July 2001 dollars July 2002 dollarsFund Strategy Participants1 Value Percent Value Percent

(1) ABC Company Stock Fund Equity/growth 117,132 5,545,956,643 54.8% 3,547,985,159 46.3%(2) Stable value fund Fixed income 33,906 1,071,420,592 10.6% 1,220,224,185 15.9%(3) S&P 500 index Equity/growth 41,463 747,112,693 7.4% 540,313,742 7.1%(4) Aggressive growth2 Equity — small growth 28,361 458,976,762 4.5% 295,160,168 3.9%(5) Appreciation Equity — large-cap 15,964 292,475,937 2.9% 241,964,417 3.2%(6) Emerging growth Equity/growth 11,218 224,477,915 2.2% 133,047,644 1.7%(7) Russell 2000 Index Equity/growth 22,664 203,804,945 2.0% 177,013,238 2.3%(8) Money funds cash portfolio Fixed income – short term 12,485 193,553,590 1.9% 222,709,740 2.9%(9) Moderate focus Fixed income/equity 14,482 165,610,031 1.6% 140,935,138 1.8%(10) Large-cap value Equity/value 9,554 159,324,437 1.6% 118,059,373 1.5%(11) Fixed income securities3 Fixed income 11,855 127,726,423 1.3% 166,510,582 2.2%(12) Other4 n/a n/a 924,237,057 9.1% 857,960,335 11.2% Total 117,182 10,114,677,025 7,661,883,720 100.0%

Table 1: Summary of retirement plan investment options and plan participation for company ABC (July 2001–July 2002)Notes: 1 Participant count as of July 2001.2 The fund considered to perform most similar to the company stock fund from July 2001 through July 2002.3 The fund considered to be the best-performing fund from July 2001 through July 2002.4 Twenty other fund options were offered to plan participants from July 2001 through July 2002.


being 117,182. Putting aside the ABC Company Stock Fund, Table 1 documents a substantial degree of stability over the class period in terms of the percentage of the aggregate 401(k) funds allocated to each of the funds.

Turning to the ABC Company Stock Fund, Table 1 reports that the aggregate value of the ABC Company Stock Fund as of July 2001, approximately U.S.$5.5 billion, represents over half the aggregate value (54.8%) of the ABC 401(k) plan (again this figure excludes plan participants who never invested in the ABC Company Stock Fund). As of July, 2002, the aggregate value of the ABC Company Stock Fund held was approximately U.S.$3.5 billion, representing close to half the aggregate value (46.3%) of the 401(k) plan. Given the substantial allocation of the 401(k) funds to the ABC Company Stock Fund in conjunction with the approximately 36% decline suffered by ABC stock during the class period, it is not surprising that the U.S.$2 billion decrease in the value of the ABC Company Stock Fund during the class period represents a significant portion of the roughly U.S.$2.5 billion decrease in the aggregate value of the 401(k) plan over the class period.

Table 2 provides further information on fund participants’ investment activities as of July 2001. Approximately 21% of fund participants invested in just one fund as of July 2001, representing 12.5% of the aggregate value of the 401(k) plan. The overwhelming majority of these participants were solely invested in the ABC Company Stock Fund. Given the roughly 36% decline in the price of ABC company’s stock over the class period, these participants were particularly hard hit. Another

approximately 20% of plan participants were invested as of July 2001 in only two funds; for the overwhelming majority of these participants one of these two funds was the ABC Company Stock Fund. As Table 2 documents, almost a third of the aggregate value of the 401(k) represents the investments of plan participants that invested either in just one or two funds. It is worth noting in this context that the number of participants invested in each fund remained relatively constant over the class period. Various additional cut-offs in terms of number of funds invested in as of July 2001 are also reported in Table 2.

We will now turn to calculating ERISA damages, assuming that there is ERISA liability as a result of the alleged mishandling of the ABC Company Stock Fund during the class period. ERISA damagesSection 409(a) of ERISA11 requires that a plan fiduciary “make good to [the] plan any losses to the plan resulting from each such breach.” The “breach” referenced in Section 409(a) is a breach of a fiduciary obligation. The definition of “losses,” however, is left undefined in the ERISA statute and as a result courts have looked towards the common law of trusts for guidance. In an important and well-known opinion the Second Circuit in Bierwirth v. Donovan, 754 F.2d 1049 (1985), referencing the common law of trusts and prior ERISA case law, held that in some circumstances “losses” can refer to the difference between what was actually

11 29 U.S.C. Section 1109(a)

July 2001Dollars Participants

Number of funds Value Percent Number Percent(1) One fund 1,261,732,369 12.5% 24,887 21.2%(2) Two funds 2,019,102,307 32.4% 24,323 42.0%(3) Three funds 1,621,189,251 48.5% 18,540 57.8%(4) Four funds 1,502,170,065 63.3% 17,066 72.4%(5) Five funds 1,225,525,468 75.4% 12,482 83.0%(6) Six funds 887,263,611 84.2% 7,831 89.7%(7) Seven funds 672,838,579 90.9% 5,284 94.2%(8) Eight or more funds 924,855,374 100.0% 6,769 100.0% Total 10,114,677,025 100.0% 117,182 100.0%

Table 2: Number of funds participants invested in July 2001



earned by the plan as a result of an imprudent investment versus “what the Plan would have earned had the funds been available for other Plan purposes.” This line of inquiry suggested by the Donovan court is focused on a claim in which the asserted basis for ERISA liability is the offering by plan fiduciaries of an “imprudent” investment.

At the same time, the Donovan Court discussed a second line of inquiry in terms of estimating ERISA damages. The court further explained that in cases where liability was based on stock prices being “manipulated by the defendants or [a claim that] information that would affect the market price was improperly withheld” then “it well may be that the best measure of damages is one that awards the plaintiff the difference between what as paid for the stock, and what would have been paid had the plaintiff been aware of the concealed information, or had the market price not been manipulated.” The latter method of calculating ERISA damages, however, was found by the Donovan Court to be inapplicable as the “case at bar [ ] does not involve fraud, or the withholding of information, or the manipulation of prices.”12 As was emphasized above, claims of “imprudence” are

12 For a recent case drawing this distinction see Taylor v. Keycorp (Northern District of Ohio) (2010) (emphasizing for damages purposes that the gravamen of the ERISA complaint was a disclosure claim).

commonly based, at least in substantial part, on allegations of inadequate disclosures.

We will first discuss the first line of inquiry suggested by the Donovan court — calculating ERISA damages based on measuring what the 401(k) plan “would have earned” but for the imprudent investment option being offered in the first place — and will then turn to the second Donovan line of inquiry — calculating ERISA damages where the basis for ERISA liability is grounded in allegations of inadequate disclosures.

Measuring what the plan “would have earned” but for the imprudent investmentFocusing on the first line of inquiry suggested by the Donovan Court, there are at least three potential methods that can be used as a basis for determining what the plan “would have earned” but for the imprudent investment. One approach is to assume that the funds placed in the imprudent investment, which in the ABC case would be the funds placed by plan participants in the ABC Company Stock Fund, would have been placed — but for the imprudent investment option having been offered — in the “best-performing fund” that was available as an investment option during the class period. A second approach is to assume that the funds placed in the imprudent investment would have been placed in the investment option that is the “most similar” to the imprudent investment. A third approach is to assume that the imprudently invested funds would have been invested by a plan participant in the same proportion across the rest of the participant’s plan investments excluding the imprudent investment option (portfolio redistribution).

In order to explore these three possibilities in more detail, we will return to the ABC litigation matter. Table 3 lists the cumulative returns during the class period of the ABC Company Stock Fund as well as the next ten largest funds, as measured by plan participants’ holdings, offered as investment options during the class period. These cumulative returns are derived from individual monthly participant data. They are based on the median of the monthly returns for all participants that had an outstanding balance in a particular fund but no activity (buying or selling shares of the fund) in that month. We then verified these calculations, where possible, with return data from Bloomberg.

Fund

Correlation withcompany stock

Cumulativereturn

(1) ABC company stock 1.00 -35.6%(2) Stable value fund 0.24 6.7%(3) S&P 500 index 0.88 -24.5%(4) Aggressive growth2 0.92 -40.0%(5) Appreciation 0.88 -17.8%(6) Emerging growth 0.86 -36.4%(7) Russell 2000 index 0.81 -22.7%(8) Money funds cash portfolio -0.01 2.2%(9) Moderate focus 0.89 -7.6%(10) Large-cap value 0.87 -25.5%(11) Fixed income securities3 -0.57 10.0%

Table 3: Cumulative returns of retirement plan fund options1 and their correlation with ABC Company Stock Fund (July 2001–July 2002) Notes: 1 Only the largest fund options are depicted.2 The fund considered to perform most similar to the company stock fund from

July 2001 through July 2002.3 The fund considered to be the best-performing fund from July 2001 through

July 2002.


As Table 3 documents, the ABC Company Stock Fund has a –35.6% return during the class period with the Aggressive Growth Fund, with a –40.0% return, and the Emerging Growth Fund, with a –36.4% return, suffering roughly similar declines. The best-performing fund during the class period is the Fixed Income

Securities Fund, which had a 10% return. The fund with the highest correlation of returns with the ABC Company Stock Fund during the class period is that of the Aggressive Growth Fund, at 0.92.

Figure 1 provides information on the aggregate value of the 401(k) plan both with and without plan participants’ holdings in the ABC Common Stock Fund. The actual portfolio return was –25.9% and is –14.7% when excluding the performance of the ABC Common Stock Fund. Plan losses during the class period are therefore not solely a function of investments in the ABC Common Stock Fund, although holdings in that fund did make the losses steeper.

Figure 2 graphs the value of a $100 investment as of the start of the class period in the “most similar fund”, i.e., the Aggressive Growth Fund if one uses class period return correlations, the “best-performing fund”, i.e., the Fixed Income Securities Fund with its positive 10% return, and “portfolio redistribution.” The value of the $100 investment is very different depending on which of these three alternatives is used. The “most similar fund” generates a class period return of –40.0%, the “best-performing fund” a positive return of 10%, and the weighted average plan participant “portfolio redistribution” a return of –18.1%. We wish to emphasize that in calculating “portfolio redistribution” we calculated for each individual plan participation their “portfolio redistribution” and then aggregated these individual “portfolio redistributions,” as presented in Figure 2.

These three different bases for estimating what each plan participant “would have earned” on their funds if they had not been invested in the ABC Common Stock Fund generates three very different aggregate damage estimates. Under the “most similar fund” approach, each plan participant’s ABC Common Stock Fund investments earns the return of the Aggressive Growth Fund. Under the “best-performing fund,” each plan participant’s ABC Common Stock Fund investments earns the returns of the Fixed Income Securities Fund. Finally, each plan participant earns their individually calculated “portfolio redistribution” return on their ABC Common Stock Fund investments. In calculating what each participant “would have earned” we assume that participants would have chosen to withdraw the same dollar value in this hypothetical “but for” world as they do in the actual world and would choose to exit their plan investments at the same point in time under both scenarios.

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Figure 2: Results of $100 investment in ABC Common Stock Fund and alternative “but-for” investment scenarios used in ERISA style damage calculations (July 2001–July 2002)

Figure 1: Aggregate portfolio return with and without ABC Common Stock Fund (July 2001–July 2002)



Aggregate damages are then simply the sum of each individual plan participant’s damages so calculated. We will present later in the paper the actual figures, in terms of the median and average plan participant’s individual damages and, perhaps of most import, the aggregate damage figures utilizing each one of these three approaches. Needless to say, the damage estimates vary dramatically.

Before one can assess the meaning of these three different bases and the returns presented in Figure 2, however, it is first necessary to discuss the basis for selecting the “most similar” and the “best-performing” funds and how the “portfolio redistribution” calculation is actually done. As for the “most similar fund”, the Aggressive Growth Fund, as was already mentioned, had the highest class period correlation of returns with the ABC Common Stock Fund. Correlation of returns was utilized as the metric for measuring “similarity,” as this captures information on whether two funds share similar risk and performance characteristics, characteristics that are presumably important to investors. However, calculating correlation of returns based on the class period returns, as we have done, entails the use of ex-post information, i.e., information that plan participants would not have had at the beginning of the class period. The preferable approach would be to measure fund correlations in the period immediately prior to the beginning of the class period, such as data covering the July 1998 — July 2001 time period, information that would have been available to plan participants both in the actual world and the hypothetical world in which the imprudent investment, the ABC Common Stock Fund, was not offered during the class period. We were unable to do so in the ABC matter, however, as a result of data limitations.

On a similar note, the Fixed Income Securities Fund, which has been designated the “best-performing fund,” was also selected based on class period data and hence also has the disadvantage of utilizing ex-post information. The preferable approach for selecting the “best-performing fund” would be to base the selection solely on information available as of the beginning of the class period. In other words, selecting the “best-performing fund” by comparing fund returns in the period immediately prior to the beginning of the class period. Again, in the ABC matter this was not possible as a result of data limitations.

As for the “portfolio redistribution” results presented in Figure 2, this is based on reallocating for each plan participant any holdings in the ABC Common Stock Fund proportionally across other plan investment options already utilized by that plan participant. So, for instance, if a plan participant had 20% of their ABC 401(k) holdings as of July 2001 in the ABC Common Stock Fund, 40% in the Fixed Income Securities Fund and 40% in the Aggressive Growth Fund, “portfolio redistribution” would entail reallocating the 20% to the other two funds: half would be allocated to the Fixed Income Securities Fund and the other half to the Aggressive Growth Fund. The plan participant then is assumed to receive whatever the return would be on this position. For plan participants solely invested in the ABC Common Stock Fund, we reallocate the ABC Common Stock Fund investments to the “most similar fund”, i.e., the Aggressive Growth Fund.

Of these three possibilities, the “most similar fund” approach is the most convincing representation of the “but for” world, the world that would have been obtained “but for” the imprudent investment option being offered. This judgment is based on the fundamental, long-established, and well-known point from finance theory that selecting a security or an investment fund can be conceptualized as selecting in effect a future payoff stream with a certain risk/return profile. Greater non-diversifiable risk implies higher expected returns. An investor who chooses a particular fund has exhibited a revealed preference for a certain risk/return profile. Indeed, whether the investor in fact realizes it or not, they have in fact assumed an investment with a certain risk/return profile. It is, therefore, natural to posit that in the “but for” world the investor would have allocated those funds to the available plan investment option with a similar risk/return profile. It is far more difficult to motivate the assumption, on the other hand, that plan participants — if they had been unable to invest in the ABC Common Stock Fund — would have switched all their ABC Common Stock Fund investments (which after all represented over half of the aggregate value of the 401(k) plan as of July 2001) to a fixed income fund, which is the assumption underlying the “best-performing fund” approach.

However, the calculations under different assumptions of what the plan “would have earned” does not answer the question as to whether the right framework is to ask what would have happened if the imprudent investment option had not been offered. Under the second Donovan line of inquiry, if the basis for ERISA


liability is inadequate disclosures, such as the dissemination of misinformation or concealment of material information that distorts the value of company stock held in an ERISA plan, the damage analysis called for becomes fundamentally different.

Measuring losses caused by inadequate disclosuresHarm caused to investors as a result of inadequate disclosures is the type of damage analysis routinely addressed in the Rule 10b-5 context. This analysis addresses whether a security’s price was distorted (or equivalently “inflated”) by the inadequate disclosures, and by how much, and whether particular types of investors in fact suffered losses as a result of any distorted prices. Indeed, in addition to allegations of inadequate disclosures, it is quite common for ERISA complaints to explicitly allege “artificially inflated” and “distorted” stock prices in presenting the case for ERISA liability.

We will not reproduce our discussion presented elsewhere of how to calculate Rule 10-5 damages.13 Suffice to say for present purposes, measurement of stock price inflation resulting from inadequate disclosures is often done via a regression analysis measuring the market’s reaction to a disclosure correcting the disclosure inadequacies (a so-called “corrective disclosure”). It is also common to then use the dollar value of any such market reaction to estimate the “inflation” in the stock price during the class period and, therefore, the losses suffered by investors who purchased at the inflated price and held through the corrective disclosure.

We will do so here. While not endorsing the constant dollar inflation approach as necessarily the most accurate Rule 10b-5 method, we will present such calculations in order to provide a baseline Rule 10b-5 damages calculation. Table 4 presents the market model that will be used in measuring the market’s reaction to the corrective disclosures plaintiffs alleged occurred on 22 July 2002 and 23 July 2002 in the ABC matter. The market model is estimated based on ABC log daily return data over the 31 July 2001– 21 July 2002 (the period immediately prior to the 22 July 2002 corrective disclosure) period using the S&P 500 and an industry index as explanatory variables. The industry index, it should be noted, does include ABC stock

13 See Ferrell, A., and A. Saha, 2011, “Forward-casting 10b-5 damages: a comparison to other methods,” 37 Journal of Corporation Law 36.

but it constitutes only 5% of the index. As can be seen from the t-statistics reported in Table 4, both explanatory variables are statistically significant at the 1% level.

As Table 5 documents, both the 22 July and 23 July 2002 corrective disclosures are associated with statistically significant negative residual stock price reactions (stock price reactions that cannot be attributed to contemporaneous S&P 500 and industry index movements) with a total negative residual dollar change of U.S.$5.23 (a drop of U.S.$2.22 on 22 July 2002 and U.S.$3.01 on 23 July 2002).

Inflation in the stock price as a result of the alleged disclosure inadequacies that create ERISA liability, utilizing the constant dollar method, is simply a constant U.S.$5.23 over the class period, except for 22 July 2002 when the inflation drops to U.S.$3.01. Figure 3 graphs the constant dollar inflation over the

Regression statisticsR-squared 0.8285Number of observations 242CoefficientofexplanatoryvariablesIntercept

0.0002(0.34)

S&P 500 index

0.3266(2.89)

Industry index

1.0183(9.94)

Table 4: Results of event study analysis for ABC company stock (31 July 2001–21 July 2002) Source: Bloomberg LP. Notes: “t” statistics are in parentheses under coefficient.

Event DateAdjusted percent

changeAdjusted dollar

changeDisclosure 1 22 July 2002 -6.86%

(t = – 6.52) -$2.22Disclosure 2 22 July 2002 -10.63%

(t = – 9.78)-$3.01

Total -$5.23

Table 5: Estimation of market-adjusted changes in ABC common stock on disclosure days of 22 July 2002 and 23 July 2002 Source: Bloomberg LP.Notes: Market-adjusted change is the residual return from the regression of the company stock returns on the S&P 500 Index and an industry index over the estimation period of 31 July 2001 – 23 July 2002.“t” represents the t-statistic. Statistically significant changes are in bold.



class period. It is worth noting that under a constant percentage inflation method (inflation remains a constant percentage of the stock price), the inflation estimates remain fairly close to that produced by constant dollar.

It is worth noting that plan participants only suffered damages under this approach if they purchased ABC common stock during the class period, the period during which the inadequate disclosures were allegedly inflating the stock price, and held onto those shares through at least the first corrective disclosure on July 22, 2002. Plan participants who merely held ABC common stock at one point in the class period would not necessarily have been harmed by the inadequate disclosures. Purchasing and selling at an inflated price does not necessarily result in damages.

To estimate aggregate damages, we first estimate each plan participant’s individual damages based on whether they purchased at an inflated ABC stock price and suffered losses as a result of a corrective disclosure removing the inflation in the stock price.14 We then aggregate the individual damages to arrive at an aggregate damage figure.

14 To determine the sale date of a particular share purchase, and therefore whether it occurred prior or after 22 July 2002, we assumed first in, first out (FIFO).

The bottom line: the damage estimatesWe have presented four different damage approaches, three for measuring what the plan participants “would have earned” but for the offering of an imprudent investment (the first Donovan line of inquiry) and one addressing the harm resulting from inadequate disclosures (the second Donovan line of inquiry). Whether the former or latter set of calculations is the appropriate way to frame the damages issue will turn on the gravamen of the ERISA liability theory.

The differences can, and often are, enormous in terms of estimated aggregate ERISA damages. Table 6 presents the resulting ERISA damages, both in terms of the average and median individual plan participant’s damages. Aggregate damages for the class are also presented. Taking the largest and smallest estimates of aggregate damages, the “best-performing fund” approach generates aggregate damages of U.S.$2.15 billion while the “most similar fund” approach generates damages of not even U.S.$3 million. The Rule 10b-5 style approach results in damages of approximately U.S.$84 million with the “portfolio redistribution” calculation resulting in the second highest level of damages at approximately U.S.$785 million. Simply put, the stakes in ERISA litigation are vastly different, at least in this matter, if one uses a “most similar fund” or 10b-5 style damages approach versus a “best-performing fund” or even a “portfolio redistribution” approach.

It is interesting to note that damages using the “most similar” approach is still positive, albeit very modestly so, despite the fact that the “most similar fund”, the Aggressive Growth Fund, underperformed the ABC Company Stock Fund over the class period (-40% versus –35.6%). There are sub-periods, however, when the Aggressive Growth Fund outperforms the ABC Company Stock Fund (such as July–September 2001). Damages using the “most similar fund” approach can, therefore, occur as a result of participants depositing and withdrawing funds from the ABC Company Stock Fund during these times. Approximately 11% of class members suffered damages as a result of such activity, albeit with median damages of only U.S.$7.

ConclusionERISA lawsuits are common occurrences which form an important component of overall securities litigation activity. Despite their importance, how to calculate damages based on a

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Figure 3: Actual and estimated prices for ABC company stock alleged class period: (31 July 2001–23 July 2002)


claim of ERISA liability has been an issue left unaddressed by the literature. Filling this gap, this paper presents and discusses the “best-performing fund,” “portfolio redistribution,” “most similar fund” and “10b-5 style” ERISA damage methodologies. Moreover, the paper discusses how these methodologies are implemented in practice using the facts and data from an actual ERISA matter. The choice among these competing methodologies can be quite important. In the ERISA matter we analyze, for instance, aggregate damages can range from less than U.S.$3 million to well over U.S.$2 billion.

When the gravamen of the ERISA liability claim is based on an inadequate disclosure theory, “10b-5 style” damages will often be, we argue, the most appropriate damage methodology. On the other hand, if the gravamen of the ERISA liability claim is one based on an allegation that the plan fiduciaries knew or should have known that the company stock was an “imprudent” investment, the “most similar fund” methodology could potentially serve as an appropriate damage methodology given that this approach is based on the revealed preference of the plan participants.

Participants damagedScenario Aggregate damage value Number Percent Average damage(U.S.$) Median damage (U.S. $)Best performing1 U.S.$2,152 million 127,995 99.0% U.S.$16,817 U.S.$3,391Portfolio redistribution 2 U.S.$785 million 98,805 76.5% U.S.$7,942 U.S.$1,369Most similar3 U.S.$3 million 13,699 10.6% U.S.$209 U.S.$710b(5) style calculation4 U.S.$84 million 117,292 90.8% U.S.$719 U.S.$147

Table 6: Alleged damages for participants invested in ABC Company Stock Fund (July 2001–July 2002) Notes: 1 The Fixed Income Fund was the best-performing fund with 10% return from July 2001 through July 2002. 2 The dollars investment in ABC Company Stock Fund are redistributed proportionately across participant’s other chosen portfolio allocations. Participants 100% invested in

the ABC Company Stock Fund were redistributed to the Aggressive Growth Fund (the most similar fund).3 The Aggressive Growth Fund performed most similar to the company stock fund. 4 The 10b5-style calculations assumes the stock price was artificially inflated by U.S.$5.23.


Part 2

Levered exchange-traded products: theory and practice1

John MulveyProfessor of Operations Research and Financial Engineering, Princeton University

Thomas NadbielnyPresident, Benchmark Advisors, LLC

Woo Chang KimAssistant Professor, Dept of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology (KAIST)

AbstractThe introduction of levered exchange-traded products was heralded as a convenient mechanism for investors to enhance performance over traditional borrowing and leverage strategies. In many cases, these products have not generated the anticipated benefits. Because multi-period returns for levered and inverse products can depend on the path of the underlying asset’s returns, the rebalancing strategy is a crucial determinant of their success. The standard ETF approach is to rebalance on an end-of-day daily basis. Naive investors may base their expectations of these products on the expected performance of traditional “buy and hold” leverage. Optimal rebalancing decisions depend upon several interrelated factors, including the expected return pattern of the underlying asset and the investor’s time horizon. Empirical tests illustrate the pros and cons of two types of levered products under various scenarios. We find that in a majority of outcomes, term borrowing performs better than end-of-day daily rebalance leverage and increasingly so as volatility increases and holding periods expand. Daily rebalance leverage performs better in trending and in certain extreme market conditions.

1 The authors would like to thank Hongseok Namkoong for his efforts in running the simulation model. The opinions and viewpoints expressed are those of the authors and are for informational purposes only, and should not be construed as a recommendation of any specific security or strategy. Investors should always consult an investment professional before making any investment. One of the authors has a business relationship with EdgeShares LLC.



IntroductionThe traditional approach for levering a portfolio utilizes a margin loan from a brokerage firm to invest the proceeds in the target securities. This approach can be expensive for individual investors. As an alternative, exchange-traded products (ETPs) and related securities have been developed to offer investors leverage without direct borrowing by the investor. These products are often used in accounts where traditional leverage is restricted (e.g., self-directed retirement accounts). These products are called levered and inverse products in this report.

ETPs can be less expensive than traditional leverage due to economies of scale and other features. For instance, the originating firm can employ futures contracts, swap agreements, and other derivative instruments to increase efficiency. Accordingly, leverage ETPs have grown in the amount of assets under management. Since their introduction in the U.S. in 2006, levered and inverse ETFs have grown to over U.S.$30.2 billion (leveraged to U.S.$13.5 billion and inverse to U.S.$16.7 billion) in assets by year-end 2012 — about 2.2% of the overall U.S. ETF marketplace.2

This growth has not come without controversy. For investors with horizons longer than one day, the standard levered ETF products have not provided returns in concert with their anticipated performance.3 Two of the more egregious examples are cited by the Financial Industry Regulatory Authority (FINRA) in regulatory notice #09-31 (June 2009) regarding Nontraditional ETFs. For “most leveraged and inverse ETFs,” FINRA states that “due to the effect of compounding, performance over longer periods of time can differ significantly from the anticipated performance (or inverse of performance) of their underlying index during the same period of time. For example, between December 1, 2008 and April 30, 2009:

• The Dow Jones U.S. Oil & Gas Index gained 2%, while an ETF seeking to deliver twice the index’s daily return fell 6% and the related ETF seeking to deliver twice the inverse of in the index’s daily return fell 26% (Figure 1).

2 Source: IndexUniverse.com, Dave Nadig, and Olly Ludig, “ETF fund flows: GDX Adds $370.6M,” 1 January 2013.

3 Naive investors often fail to understand the adverse consequences of daily rebalancing inherent in many of these products.

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Figure 2: Russell 1000 Financial Services Index and related Bull (3X) and Bear (-3X) ETFs1 December 2008 (= 100.0) to 30 April 2009

Figure 1: Dow Jones Oil & Gas Index and related Bull (2X) and Bear (-2X) ETFs1 December 2008 (= 100.0) to 30 April 2009


• An ETF seeking to deliver three times the daily return of the Russell 1000 Financial Services Index fell 53% while the index actually gained around 8%. The related ETF seeking to deliver three times the inverse of the index’s daily return declined by 90% over the same period (Figure 2).”4

Over this five-month period, the Dow Jones U.S. Oil & Gas Index experienced 48% annualized volatility of returns, while the Russell 1000 Financial Services Index suffered 91% annualized volatility. Periods of high volatility are particularly difficult for most levered and inverse products, for reasons shown in this report.

At a fundamental level, a levered exchange-traded product (ETP) is a combination — portfolio – of an investment in the underlying security (“underlying” herein) plus an amount of borrowed cash. Rebalancing decisions determine the mix of these two “assets” at selected time points over the life of the product. For the most part, difficulties with levered products spring from the type and frequency of rebalancing the level of equity and borrowing. For example, consider an initial $100 investment in a double-levered fund. At the start, we can view the levered investment as two parts: $200 in equity, and $100 in borrowing. Next, assume that equity increases by 10% to $220 during the first trading day. At this point, the security is no longer a doubled-levered fund; it is a 2.2 times levered fund while the investors initial stake has grown to $120. Typically, to maintain the two times leverage ratio, the portfolio manager will rebalance the fund before the start of the next trading day, called daily rebalancing, herein. Borrowing an additional $20 will further enhance the fund’s equity position, currently $220. The $20 can be employed to purchase an incremental $20 stake in the underlying security, so that the mix is now $240 equity and $120 borrowing — again doubled levered.5 Assume that the equity decreases by 9.09% over the next trading day so that the underlying asset returns to its initial price. Now the fund’s $240 in equity declines to $218.18 while the amount borrowed remains at $120. At this point the fund is a 1.82 times levered fund. To restore the fund to 2.0 times leverage, $21.82 in equity must be sold and the proceeds

4 Non-traditional ETFs: FINRA reminds firms of sales practice obligations relating to leveraged and inverse exchange-traded funds,” FINRA Regulatory Notice 09-31, https://www.finra.org/web/groups/industry/@ip/@reg/@notice/documents/notices/p118952.pdf, June 2009.

5 An alternative process would be to return part of the capital to the investor as would be the case if the investor were utilizing futures contracts, but this step is rarely, if ever, done with levered ETPs.

returned to the lender. Once this happens, the fund will have $196.36 in equity with $98.18 in borrowing to yield a leverage ratio of 2.0. In this case, although the underlying equity’s value has remained the same over the 2 day period (+10%, –9.09%), the investor’s initial stake of $100 has now shrunk to $98.18 for a 2-day loss of 1.82%. Had the fund not rebalanced at the end of the first trading day, the investor’s stake would have returned to $100 at the end of the second trading day leaving the investor flat for the two days.

This simple example shows how the performance of a levered product depends upon the return patterns of the underlying security and the rebalancing decisions. As shown in this paper, the latter issue becomes especially pertinent during periods of high volatility and major market moves.

Theory of rebalancingThis section analyzes the performance of levered products based on previous research on rebalancing the assets in a portfolio over time. Rebalancing can be done in a variety of ways. The simplest way is to not rebalance at all — called the “do-nothing” or “buy-and-hold” strategy. This approach is the one assumed by the traditional Markowitz portfolio model over the investment planning horizon (for example one year ahead). We call this approach “point-to-point” or “term borrowing” leverage.

We can separate rebalancing decisions into two fundamental types: 1) momentum based, and 2) fixed/target proportions.6 The distinguishing feature between the two involves the decision to purchase or sell the underlying asset during a period of increasing or decreasing performance. For momentum based rebalancing, we add to the amount of equity as equities increase — as discussed in the previous section; whereas in fixed/target rebalancing, we decrease the equity level. The situation reverses when the equity returns are negative, i.e., selling equity for momentum based, and purchasing equity in target proportions. Buying equities during increasing return periods (and selling during market downturns) fits within the context of “portfolio-insurance” strategies. In contrast, selling equities during bull

6 The fixed/target proportion-based rebalancing strategy should not be confused with the end-of-day daily rebalancing typically employed by constant leverage strategies. In the former, outperforming assets are sold, whereas with the latter, they are bought. Likewise, with the former strategy, underperforming assets are bought, whereas with the latter, they are sold.



markets fits the fixed-mix strategy. Perold and Sharpe (1988) and Tokat (2007) discuss the pros and cons of these opposing strategies.

To start, we propose a stochastic process for the underlying equity element within a self-contained fund. The standard approach models equity prices with geometric Brownian motion (GBM). First, we compare the buy-and-hold (do nothing) portfolio with a strategy that constantly rebalances from the perspective of a portfolio of n-assets. Recall the performance of the buy-and-hold strategy from the Markowitz model. Suppose there are n securities whose mean return is n, and covariance matrix R. Assuming normality, the average buy-and-hold portfolio return with weights, wBH, does not have a closed form expression as the sum of the log normal random variables is not a log normal random variable. However, assuming that the number of the securities in the portfolio is large enough, one can approximate the return as a normal random variable. That is, r N(w , ) N(w ,w w)BH T

p2 T Tv+ /n n R .

Next, consider the rebalanced portfolio constructed from the same securities with the same weight () as the previous buy-and-hold portfolio. Since it is rebalanced at every intermediate juncture, security prices must be modeled as stochastic processes. We model them as an n-dimensional geometric Brownian motion whose return distribution for a unit time length is the same as in the previous case. Then, the price process of security can be written as the following SDE: dS /S ( /2)dt dBt

iti

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Since the portfolio is rebalanced continuously to the initial weight (w), its instantaneous growth rate is the same as the weighted sum of instantaneous growth rates of the constituent securities at any given juncture. Consequently, the SDE for the portfolio wealth can be written as:

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i 1

n

i ii2

ti= = + +n

v= =R R a k& 0.

With a little algebra, one can show that, for the standard 1-dimensional Wiener process P

dP w 21 w dt dW

tFMtFM

T

i 1

n

i i2

p2

t= + +n v vR=

a k ,

PdP w 2

1 w dt dWtFMtFM

T

i 1

n

i i2

p2

t= + +n v vR=

a k .

Hence, the return of the fixed mix portfolio for a unit time length can be given as

r N w 21 w 2

1 , N w 21 w 2

1 w w,w wFM T

i 1

n

i i2

p2

p2 T

i 1

n

i i2 T T+ - + -+ /n v v v n v R RR R

= =a ak k

Consequently, returns of both buy-and-hold and continuously rebalanced fixed mix are normally distributed with the same variance p

2v , while the mean of the latter one contains extra terms, w /2i 1

ni i

2p2-v vR =^ h . These extra terms, which are referred

to as rebalancing gain or volatility pumping [Luenberger (1998), Mulvey and Kim (2008)], represent the value of an option to rebalance the portfolio to the target fixed-proportions.

To observe its effects more closely, consider the following example: suppose we have n securities where the expected return and the volatility of each are 0n and v, and the correlation is t. Assuming that the portfolio is equally weighted, the amount of the rebalancing gain (RG) is:

n1

n1

n1

n1

n1

2nn 1 1

RG 21

i 1

n2

T 2

- =- -

= g gvv t

RR=

a a^ ^

k kh h

& 0 .

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

0 0.05 0.1 0.15 0.2 0.25 0.3

Reb

alan

cing

gai

n

Volatility (σ)

ρ = 0.0

ρ = 0.9

ρ = 0.6

ρ = 0.3

Figure 3: Effects of volatility and correlation on rebalancing gains


Now it is evident that the continuously rebalanced strategy has benefit over the static buy-and-hold rule, even without mean-reversion: the rebalancing gain is always positive, except in the case where all security returns are perfectly correlated, in which it becomes zero. Note that the rebalancing gain is an increasing function of the number of securities n and the volatility v and is a decreasing function of the correlation t. Therefore, with the wisdom from the portfolio theory, one can see that volatile securities should not be penalized when a portfolio is constructed with the fixed mix rule, as long as their correlations to other securities are low and they have reasonable and positive expected returns. They can serve as good sources of rebalancing gains, while their risks can be effectively eliminated via diversification. See Figure 3 for the graphical illustrations for the effects of to rebalancing gains from Monte-Carlo simulations.

In general, rebalancing gains accrue when the better performing assets are systematically sold and the underperforming assets are systematically bought — as shown above. The critical feature is to lower risks when risky assets do well relative to other assets, such as with the fixed-mix investment strategy. Of course, rebalancing gains can be turned into rebalancing losses when the expected returns (the drift terms) are negative or when the better performing assets are systematically bought and the underperforming assets are systematically sold (as is often the case when a leveraged portfolio is rebalanced to a pre-set leverage ratio on a discrete time basis, such as daily).

Rebalancing decisions are critical to performance, along with the standard performance paths. Rebalancing gains are generally difficult to achieve with levered and inverse funds on their own, outside a generic portfolio. Daily rebalancing (DR) leverage strategies increase equities and beta risks during upward movements, rather than during down moves as is the case with the discussion above. Thus, in trendless and volatile markets, the drift term for DR strategies is negative because they are buying more of the outperforming assets rather than selling them [i.e., the constant leverage trap (CLT)].7

In addition, transaction costs and market impact costs affect performance in the context of rebalancing a portfolio. The general

7 Remember that the stated Brownian motion processes must have positive drift terms.

approach for addressing transaction costs for fixed mix investors is to construct a no-trade zone around the target allocation percentage and to not trade while asset levels remain within the designated zone. For example, suppose that we are interested in preserving a 50/50 fund. Then, we might select a zone equal to 49% to 51%. In this situation, the fund would only rebalance the portfolio to the 50% target when prices fell or gained enough to place it outside the no-trade zone. In this example, trading is done on a price driven basis, as compared with time dependent trading rules such as daily rebalancing [see Mulvey and Simsek (2002), and Kritzman and Page (2009) for further details]. The advantages of fixed mix strategies are best expressed in markets that are trendless with relatively high volatility and low transaction costs.

Empirical testsIn this section, we explore the boundaries of the buy and hold [term borrowing (TB) leverage] and daily rebalance leverage strategies and give some insight into when one is superior to the other in a controlled set of experiments.

In general, there is a tradeoff between the probability of positions experiencing early termination with TB strategies and the re-levering gains and losses associated with DR strategies. With TB strategies, there is no re-levering; the main concern is being cashed out prematurely on an adverse move. In practice, TB strategies will likely self-liquidate before losing all their capital.8 However, TB strategies generally do not suffer volatility-induced asset erosion. Thus, if the TB strategy does not terminate early, then one can predict with relative certainty how much the TB strategy will be worth for a given underlying asset value at the end of a target term.9 Conversely, daily rebalance strategies are path-dependent. For multi-periods, one cannot predict with any certainty how much a DR strategy will be worth at the end of the term. As volatility and noise increase, the end-of-day DR-levered strategies become increasingly vulnerable to rebalancing losses because they increase borrowing and exposure only after the underlying asset appreciates and decrease borrowing and exposure only after the underlying asset depreciates. In essence, they generally buy high and sell low, subjecting them to the sometimes severe negative consequences of noise in markets (i.e., “volatility” losses).

8 An early termination of a TB fund would require the investor to re-establish his position in another security if he intended to maintain his position.

9 The possibility of early termination for TB strategies makes them partially path-dependent.



Many investors find a daily DR strategy counterintuitive from the standpoint of temporal considerations, and prefer a TB strategy with a fixed term when the investor’s horizon is longer than one day. With a TB strategy, the amount borrowed stays constant while the leverage ratio floats. With an end-of-day DR strategy, the amount borrowed floats so that the leverage ratio remains constant on a daily basis (Table 1). We note that over 90% of the 274 levered and inverse-levered ETFs available in the marketplace as of September 30, 2012 employ an end-of-day DR strategy.10 TB solutions for the ETF marketplace are extremely limited; an exception is EdgeShares LLC,11,12 which has developed an effective solution for achieving targeted leverage in a TB strategy.

Through our simulated return environments, we outline the boundaries of when TB strategies outperform DR strategies, and vice versa. For each of the two types of strategies (TB and DR), we simulate four distinct leveraged and inverse-leveraged strategies: double leverage (2X), triple leverage (3X), double inverse leverage (-2X) and triple inverse leverage (-3X).13

In our experiments, we evaluate 21 expected period returns ( 0n) ranging from –50% to +50% in increments of 5%, along with 18 annualized volatilities (v) ranging from 5% to 90%, also in increments of 5% for the underlying risky asset. We simulate two time periods: 126 trading days, representing a half-year period, and 252 trading days, representing a full trading year. We group all the simulation trials together (21 x 18 x 250,000) and sort outcomes based on the realized return (r) and realized

10 See BlackRock ETP 2012 Landscape Global Handbook at http://www.indexfunds.com.cn/userfiles/file/1358232962976.pdf

11 See Kiron, K., “Securitization system and process” United States Patent Application 20110191234. Filed February 2, 2011.

12 See Kiron, K., “Securitization system and process II” United States Patent Application 20130046673. Filed August 15, 2012.

13 The 2X strategy simulated borrowing an amount equal to an investor’s initial equity and investing so that the investor received 200% of the return of the underlying risky asset. The 3X strategy simulated borrowing an amount equal to twice the investor’s initial equity and investing the entire amount so that the investor received 300% of the return of the underlying risky asset. The –2X strategy simulated shorting an amount equal to twice the investor’s initial equity in the risky asset so that the investor received –200% of the return of the underlying risky asset. Likewise, the –3X strategy simulated shorting an amount equal to three times the investor’s initial equity in the risky asset so that the investor received –300% of the underlying return of the risky asset.

standard deviation (v) of each simulation.14 We then select only those outcomes that result in realized returns that are within ±0.5% of a target return (ri) and realized volatilities that are also within ±0.5% of a target volatility ( jv ). All other simulation results are discarded for the tables. Furthermore, because all (r ,i jv ) are not equally likely, results for some (r ,i jv ) pairs that are deemed incredibly unlikely (e.g., r 50%, 5%i j=- =v ) are not shown and appear as blank cells in the tables. For all simulated underlying risky asset return series pertaining to a respective outcome pair (r ,i jv ), the returns of each of the four variations of simulated TB and DR strategies are then generated by overlaying each respective strategy (eight in all) onto each daily return series of the underlying risky asset. The results for each strategy variation are then averaged into each respective outcome pair (r ,i jv ) for that respective variation.

We employ a stylized framework to compare strategies by assuming a virtual perfect world for leveraged and inverse-leveraged investors. We assume no borrowing costs, transaction

14 We sort and analyze the Monte Carlo simulation results based on realized return and realized volatility to directly compare the likely return differences between (a) term borrowing (buy and hold) leveraged and inverse-leveraged strategies with those of (b) constant daily rebalanced leverage and inverse-leverage strategies for given market outcomes (return and volatility combinations). This allows comparison of the average returns of each strategy when the paths taken by the underlying asset to generate a given return and volatility combination vary from run to run.

Strategy Code Amount borrowed

Rebalance frequency

Leverage ratio

Other names

Term borrowing

TB Fixed amount for term

None Floats, never reset

Point-to-point leverage

Daily rebalance

DR Updates daily

Daily Rebalanced to target at end of day

Constant proportional leverage

Table 1: Characteristics of two rebalancing strategies

Index name Time frame Return Volatility 2X ETF return

-2X ETF return

Dow Jones Oil & Gas Index

1 Dec 2008 to 30 April 2009

2% 45% -6.0% -26.0%

Table 2A: Dow Jones Oil & Gas Index and ETFs (1 Dec 2008– 30 April 2009)


costs, management fees, and taxes.15 We did not model initial and maintenance margin amounts and assumed no credit or counter-party risk.16 In short, we focused on the interaction between time and volatility to differentiate the two strategies. Each simulation of the underlying asset price changes is modeled as a geometric Brownian motion (GBM) continuous time pricing process using the multiplicative form to discretize the price process. The result is the following formula:

SS t e tk 1 kt t tk=++c veD D

^ ^^

h hh

Where, 0n = expected period return = –50%, –45%, … , +50%v= target volatility = 5%, 10%, … , 90%

122= -c n v

t = timeS(t) = asset price at time tkn = number of days in periodk = 0 … n-1

A standard variance reduction method – antithetic variables – is employed to reduce the standard errors over all runs. Thus, for each pair of simulations, the sign of the random terms for each sequence is opposite that of its corresponding paired simulation. This increases the accuracy of the results by reducing the variance of the simulated paths. Thus, to run 250,000 trials for each given pair, we generate only 125,000 unique sequences of random variables.

Results of the experimentsSorting by realized return and variance allows us to identify the relative advantages of TB versus end-of-day DR strategies.17 As a test of the model’s robustness, we refer to the two examples cited by FINRA at the beginning of this paper. In the first case, the index gained 2%, while the 2X ETF fell 6% and the related –2X ETF fell 26%. The annualized volatility of the Dow Jones U.S. Oil & Gas Index during the 1 Dec 2008 to 30 April 2009 period was

15 For the sake of brevity, we excluded borrowing and transaction costs. Since transaction costs will vary depending on market and implementation, turnover data is available from the authors. Borrowing costs are not a major differentiating factor between the two strategies particularly in a low-interest rate environment. Initially, borrowing costs will be the same for both strategies.

16 In practice, no regulatory authority or counterparty would knowingly let an investor’s equity totally evaporate and leverage ratio sky rocket before taking action.

17 Because of our simplifying assumptions, real-world outcomes may differ considerably from what we present here.

45% (Table 2A). Over a simulated six-month period, when realized volatility is 45% and return of the underlying is 0%, a 2X DR strategy returns an estimated –9.6% while it returns an estimated –0.3% when the return of the underlying is 5% (Table 2B). When realized volatility is 45% and return of the underlying is 0% over six months, a –2X DR strategy returns an estimated –26.2% while it returns an estimated –33.1% when the return of the underlying is 5%. Although, the time period is slightly longer, these results are roughly in-line with this example.

In the second example, the 3X ETF fell 53% while the index actually gained around 8%. The related – 3X ETF declined by 90% over the same period. The annualized volatility of the Russell 1000 Financial Services Index during the same five-month period was 91% (Table 3A). Over six months when realized volatility is

2X simulated six-month horizonAsset return

Annualized volatility

Naïve E(return)

2X TB E(return)

Prob(TB termination)

2X DR E(return)

DR 1-way turnover

TB – DR E(return)

0% 45% 0% 0% -- -9.6% 556% 9.6%5% 45% 10% 10.0% -- -0.3% 583% 10.3%

-2X simulated six-month horizon0% 45% 0% -2.7% 2.7% -26.2% 506% 23.5%5% 45% -10% -13.7% 4.1% -33.1% 484% 19.4%

Table 2B: Simulated leverage and inverse DB and TB strategies*TB – term borrowing; DR – daily rebalance; E(return) – expected return

Index name Time frame Return Volatility 3X ETF return

-3X ETF return

Russell 1000 Financial Services Index

1 Dec 2008– 30 April 2009

8% 91% -53.0% -90.0%

Table 3A: Russell 1000 Financial Services Index and ETFs (1 Dec 2008–30 April 2009)

3X simulated six-month horizonAsset return

Annualized volatility

Naïve E(return)

3X TB E(return)

Prob(TB termination)

3X DR E(return)

DR 1-way turnover

TB – DR E(return)

5% 90% 15% -24.8% 34.6% -66.5% 2,843% 41.6%10% 90% 30% -10.0% 30.7% -61.4% 3,061% 51.4%

-3X simulated six-month horizon5% 90% -15% -70.2% 64.9% -93.4% 1,658% 23.2%10% 90% -30% -78.8% 69.8% -94.3% 1,552% 15.5%

Table 3B: Simulated leverage and inverse leverage strategies*TB – term borrowing; DR – daily rebalance; E(return) – expected return



90% and return of the underlying is 5% and 10%, respectively, the 3X DR strategy returns an estimated –66.5% and –61.4%, respectively (Table 3B). For the same terms: the –3X DR strategy returns an estimated –93.4% and –94.3%, respectively. Again, although the time period is slightly longer, our simulated results are similar to this real-world example.18

It is worth noting that in both examples illustrated above, for similar return and risk characteristics, on average TB strategies would have handily outperformed the DBL strategies (Tables 2B and 3B). However, for the index and time period in question, a 3X TB strategy would have experienced early termination when the actual index was down by 34.8% from 1 Dec 2008 to 6 March 2009.

Tables 4A through 7A show the semiannual return differences between TB and DR strategies for the four leverage and inverse leverage levels modeled (2X, –2X, 3X, –3X), while Tables 4B through 7B show the annual results. Overall, in very-low-volatility directional markets, DR strategies generally outperform TB strategies because

18 In this case, with volatility at these extreme levels, subjecting a DR strategy to an extra month of volatility losses compared to the results from the actual ETF can account for some of the observed difference. Other factors may be at work as well. For example, the simulations assume the investor is able to execute at the closing level and have no market impact. During crash periods, certain funds may not even be able to trade, let alone trade at or near the close.

there are minimal reversals while the amount levered (relative to the initial stake) continually increases as the underlying asset generally moves in one’s favor, thereby magnifying gains. Similarly, if the underlying asset generally moves in an adverse direction, there are minimal reversals while leverage is steadily decreased, thereby mitigating losses and preventing the threat of early termination in all but the most extreme of circumstances.

There is a broad range of return outcomes where the 2X TB strategies dominate the 2X DR strategies (see Tables 4A and 4B). In particular, TB overwhelmingly dominates when underlying asset returns are modest (-5% to +5%) and increasingly (see light shaded area in tables) so as volatility and holding period increase.

Overall, 2X TB generally outperforms 2X DR in an ever-expanding realized return space plume spreading from lower to higher volatility, and increasingly so for longer holding periods (annual versus semiannual). The only caveat to this generalization is when the underlying asset moves in an extreme adverse direction, then the back leg of the plume tapers off as the model’s measured probability of early termination for TB strategies starts to become a significant factor. Tables 5A and 5B show similar results for the –2X strategies.

Target underlying asset realized annualized volatility ±0.5(%)

Targ

et u

nder

lyin

g as

set

real

ized

sem

iann

ual r

etur

n ±0

.5(%

)

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90-50 -24.3 -24.1 -23.8 -23.4 -22.9 -22.5 -21.9 -21.3 -20.7 -20.1 -19.4 -18.7 -18.0 -17.2 -16.5-45 -19.6 -19.3 -19.2 -19.2 -19.2 -19.2 -19.3 -19.2 -19.1 -18.9 -18.5 -18.0 -17.6 -16.9 -16.4-40 -15.5 -15.2 -14.8 -14.4 -13.9 -13.7 -13.6 -13.7 -13.7 -13.9 -14.0 -14.1 -13.9 -13.8 -13.3 -12.8-35 -11.7 -11.3 -10.9 -10.3 -9.7 -9.1 -8.7 -8.4 -8.3 -8.6 -8.5 -8.7 -8.5 -8.4 -8.8 -8.6-30 -8.4 -8.0 -7.4 -6.8 -6.0 -5.2 -4.5 -3.7 -3.4 -3.1 -2.9 -3.3 -3.1 -3.2 -3.0 -3.5-25 -5.9 -5.6 -5.1 -4.5 -3.7 -2.9 -1.9 -0.9 0.0 0.8 1.6 1.9 2.1 1.9 2.1 2.1 2.5-20 -3.7 -3.3 -2.7 -2.0 -1.2 -0.2 0.9 2.1 3.3 4.6 5.4 6.1 6.7 7.5 7.6 7.6 7.2-15 -2.1 -1.9 -1.4 -0.8 0.0 0.9 2.0 3.3 4.7 6.1 7.6 8.9 9.9 11.0 11.3 12.0 12.5 12.4-10 -0.9 -0.6 -0.1 0.6 1.5 2.6 3.8 5.2 6.8 8.4 10.1 11.8 13.1 14.4 15.6 16.7 16.8 18.0-5 -0.1 0.2 0.8 1.5 2.5 3.7 5.1 6.7 8.4 10.3 12.2 14.1 16.1 17.9 19.5 20.0 21.0 21.80 0.1 0.5 1.1 2.0 3.1 4.4 5.9 7.6 9.6 11.7 13.9 16.2 18.2 20.4 22.2 23.7 25.3 25.95 -0.1 0.3 1.0 1.9 3.1 4.6 6.3 8.2 10.3 12.6 15.1 17.7 20.0 22.5 24.7 26.8 28.4 29.3

10 -0.8 -0.4 0.3 1.4 2.7 4.3 6.1 8.2 10.6 13.1 15.9 18.7 21.6 24.3 26.9 29.4 31.7 33.015 -2.1 -1.6 -0.8 0.4 1.8 3.5 5.6 7.8 10.4 13.2 16.2 19.2 22.5 25.6 28.7 31.2 34.0 36.220 -3.3 -2.4 -1.1 0.4 2.3 4.5 7.0 9.8 12.8 16.1 19.5 23.1 26.5 29.9 33.2 36.3 38.325 -5.4 -4.5 -3.1 -1.4 0.6 3.0 5.7 8.7 12.0 15.5 19.2 23.1 26.9 30.8 34.4 37.7 40.730 -7.0 -5.6 -3.8 -1.6 1.0 3.9 7.2 10.7 14.6 18.6 22.8 27.0 31.3 35.1 39.4 41.735 -10.1 -8.6 -6.6 -4.2 -1.4 1.7 5.2 9.0 13.2 17.5 22.1 26.8 31.2 35.7 39.8 43.340 -13.7 -12.0 -9.9 -7.3 -4.4 -1.0 2.8 6.9 11.4 16.1 20.9 25.9 30.9 36.4 40.8 44.745 -15.9 -13.7 -10.9 -7.7 -4.1 -0.1 4.3 9.1 14.1 19.4 24.9 30.4 35.9 41.1 45.550 -20.3 -17.9 -15.0 -11.6 -7.7 -3.4 1.3 6.4 11.9 17.5 23.4 29.4 35.6 40.8 47.1

Table 4A: 2X term borrowing (TB) leverage minus 2X daily rebalance (DR) leverageAverage TB – DR realized semiannual return differences (%)



Targ

et u

nder

lyin

g as

set

real

ized

ann

ual r

etur

n ±0

.5(%

)

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90-50 -24.3 -23.9 -23.4 -22.8 -22.0 -21.2 -20.3 -19.4 -18.4 -17.3 -16.3 -15.2 -14.1 -13.0 -12.0 -11.0-45 -19.6 -19.3 -19.3 -19.5 -19.6 -19.6 -19.3 -18.8 -18.0 -17.3 -16.4 -15.5 -14.5 -13.3 -12.4 -11.3-40 -15.6 -15.2 -14.6 -14.1 -13.8 -13.9 -14.1 -14.4 -14.3 -14.4 -13.7 -13.7 -13.0 -12.0 -11.5 -10.3 -9.5-35 -11.8 -11.3 -10.6 -9.7 -8.9 -8.5 -8.7 -8.8 -9.0 -9.1 -9.0 -9.2 -8.4 -8.3 -8.2 -7.4 -6.1-30 -8.5 -7.9 -7.1 -6.0 -4.9 -4.1 -3.6 -3.5 -3.6 -3.6 -3.5 -3.8 -3.9 -4.2 -4.0 -2.6 -1.5-25 -5.7 -5.0 -4.0 -2.8 -1.5 -0.1 0.9 1.5 1.5 2.3 2.0 1.3 1.2 1.3 1.6 2.0 3.0-20 -3.8 -3.4 -2.6 -1.5 -0.1 1.5 3.1 4.7 5.6 6.3 6.8 6.7 6.8 6.7 6.7 6.5 7.3 7.5-15 -2.1 -1.5 -0.6 0.6 2.1 4.0 6.0 7.9 9.3 10.8 11.3 12.0 11.8 11.4 11.9 11.9 11.8 11.7-10 -0.8 -0.2 0.8 2.2 3.9 6.0 8.3 10.6 12.7 14.2 15.8 16.5 16.5 17.0 16.6 16.5 17.3 16.6-5 0.0 0.6 1.8 3.3 5.2 7.5 10.1 12.9 15.4 17.8 19.2 20.2 20.9 21.7 22.3 22.0 22.0 23.30 0.2 1.0 2.2 3.9 6.0 8.6 11.5 14.6 17.8 20.3 22.6 24.4 25.3 26.9 26.5 27.5 28.2 27.15 0.0 0.8 2.2 4.1 6.4 9.2 12.4 15.9 19.5 22.8 25.5 27.5 29.4 30.5 32.5 31.8 33.3 34.7

10 -0.7 0.2 1.7 3.7 6.3 9.4 12.9 16.7 20.8 24.5 27.9 31.0 32.7 34.5 36.1 36.8 37.8 37.715 -1.9 -0.9 0.7 2.9 5.7 9.1 12.9 17.2 21.6 26.2 29.9 33.7 36.0 38.5 39.4 40.5 41.8 44.320 -3.6 -2.6 -0.8 1.6 4.7 8.4 12.5 17.2 22.2 27.1 31.6 35.7 38.8 41.7 42.8 45.2 47.3 48.325 -4.7 -2.8 -0.1 3.2 7.2 11.7 16.8 22.2 27.7 33.2 37.3 41.2 45.5 46.5 51.1 52.2 53.230 -7.3 -5.2 -2.4 1.2 5.5 10.4 15.9 21.7 27.8 33.3 39.0 44.0 47.2 51.3 53.6 55.1 55.335 -10.4 -8.2 -5.1 -1.2 3.4 8.7 14.6 20.9 27.7 33.9 39.5 45.4 49.8 53.6 56.8 59.4 60.640 -14.0 -11.6 -8.3 -4.1 0.8 6.5 12.9 19.7 27.0 33.8 40.5 46.5 52.3 56.8 60.1 62.1 66.545 -15.5 -12.0 -7.5 -2.2 3.9 10.7 18.2 25.9 33.3 40.4 47.7 53.5 59.4 63.1 67.5 69.550 -19.9 -16.1 -11.3 -5.6 0.9 8.2 16.1 24.5 32.7 40.8 48.0 53.7 61.0 66.7 69.7 74.0

Table 4B: 2X term borrowing (TB) leverage minus 2X daily rebalance (DR) leverageAverage TB – DR realized annual return differences (%)


Targ

et u

nder

lyin

g as

set

real

ized

sem

iann

ual r

etur

n ±0

.5(%

)

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90-50 -173.2 -161.2 -146.9 -131.0 -113.3 -94.4 -74.6 -54.5 -33.8 -14.3 4.4 21.5 37.9 52.9 66.6-45 -119.3 -109.3 -97.5 -84.1 -69.5 -53.7 -37.3 -20.6 -4.5 11.2 26.8 40.0 50.3 64.1 72.3-40 -87.2 -80.4 -71.9 -62.0 -50.7 -38.4 -25.1 -11.4 2.5 15.6 28.5 40.4 50.1 60.4 68.6 74.6-35 -58.0 -52.2 -45.0 -36.5 -26.8 -16.2 -4.9 6.7 17.9 29.0 39.3 48.0 56.7 64.0 70.4 73.6-30 -36.9 -31.9 -25.6 -18.2 -9.9 -0.7 9.0 18.9 28.8 37.4 45.1 51.9 58.8 63.7 66.8 73.0-25 -24.8 -21.7 -17.3 -11.8 -5.3 1.9 9.9 18.3 26.6 34.6 42.0 47.4 52.7 57.4 59.8 64.0 64.9-20 -13.8 -11.0 -7.1 -2.3 3.4 9.8 16.8 23.9 31.1 37.2 42.3 47.4 51.3 53.2 55.9 58.9 60.4-15 -7.8 -6.3 -3.8 -0.4 3.9 9.0 14.7 20.7 26.8 32.4 37.3 41.2 45.1 46.9 49.3 50.8 52.6 54.5-10 -3.0 -1.6 0.6 3.7 7.5 12.0 17.1 22.4 27.4 32.2 34.8 38.7 41.3 42.5 44.4 44.8 46.2 45.0-5 -0.4 0.8 2.8 5.6 9.0 13.1 17.6 22.1 26.1 29.4 32.2 34.6 35.4 36.9 37.2 39.4 38.7 39.80 0.4 1.5 3.3 5.8 8.9 12.5 16.5 20.1 23.5 25.4 27.5 28.3 29.2 29.9 31.4 31.5 32.2 33.35 -0.4 0.6 2.3 4.6 7.4 10.7 14.1 16.8 19.4 20.8 21.5 22.0 22.5 22.7 24.6 23.6 24.9 25.3

10 -2.3 -1.4 0.1 2.2 4.7 7.6 10.3 12.4 14.1 14.8 15.0 14.8 15.3 16.9 16.6 16.5 17.9 18.015 -5.3 -4.5 -3.1 -1.2 1.1 3.6 5.6 7.1 7.6 7.6 8.1 8.0 8.4 9.6 9.4 10.7 10.7 10.920 -8.4 -7.1 -5.4 -3.3 -1.3 0.1 0.8 0.6 0.4 0.7 1.0 1.2 2.0 2.8 3.5 4.5 6.025 -13.0 -11.8 -10.2 -8.5 -7.2 -6.5 -6.7 -6.6 -6.8 -6.3 -6.0 -5.5 -4.4 -3.0 -2.1 -0.7 0.830 -17.1 -15.7 -14.4 -13.9 -13.7 -13.9 -14.2 -13.7 -13.2 -12.4 -11.7 -10.1 -8.9 -7.1 -5.2 -4.035 -22.9 -21.8 -21.2 -21.1 -21.4 -21.7 -21.2 -20.4 -19.2 -18.1 -16.7 -14.8 -13.1 -11.2 -9.5 -7.440 -29.2 -28.8 -28.8 -29.0 -28.7 -28.2 -27.1 -25.6 -24.0 -22.5 -20.4 -18.1 -16.1 -14.0 -12.3 -10.345 -36.4 -36.3 -35.8 -34.7 -33.2 -31.4 -29.3 -27.3 -25.0 -22.7 -20.4 -18.1 -16.0 -14.0 -12.050 -41.5 -40.2 -38.5 -36.7 -34.6 -32.5 -30.2 -27.8 -25.5 -23.1 -20.8 -18.5 -16.4 -14.4 -12.5

Table 5A: –2X term borrowing (TB) leverage minus –2X daily rebalance (DR) leverageAverage TB – DR realized semiannual return differences (%)




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set

real

ized

ann

ual r

etur

n ±0

.5(%

)

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90-50 -172.2 -153.4 -130.7 -104.8 -76.8 -48.0 -19.5 6.5 30.2 50.2 65.9 78.6 91.2 97.1 101.3 103.8-45 -118.0 -102.4 -83.6 -62.2 -39.0 -15.5 7.7 27.5 45.4 60.3 72.6 82.5 91.9 92.4 98.8 98.2-40 -88.9 -79.1 -66.0 -50.1 -32.0 -12.6 6.7 25.5 42.2 55.5 65.9 76.0 82.6 84.2 90.0 90.2 90.8-35 -59.3 -50.9 -39.8 -26.2 -10.8 5.3 21.6 36.3 49.3 58.8 67.5 73.7 76.5 81.1 82.6 83.5 81.5-30 -37.8 -30.6 -20.9 -9.2 4.1 17.9 31.1 43.1 51.7 60.2 65.6 69.1 73.1 73.9 75.9 73.1 74.5-25 -22.4 -16.1 -7.7 2.6 13.9 25.6 36.7 45.3 52.5 58.2 62.4 66.2 66.0 66.3 66.9 67.3 64.5-20 -15.0 -11.6 -6.0 1.4 10.4 20.4 30.3 38.7 45.2 50.7 55.4 56.9 60.2 58.9 58.5 59.6 58.6 56.8-15 -7.3 -4.3 0.6 7.2 15.1 23.7 31.8 38.1 43.1 47.4 48.7 51.1 50.5 52.2 50.8 50.9 51.4 51.2-10 -2.5 0.2 4.6 10.5 17.4 24.8 31.5 35.9 39.3 41.5 43.8 44.2 43.8 43.3 43.5 44.4 44.5 42.6-5 0.0 2.5 6.4 11.7 17.9 24.2 28.5 31.8 34.4 36.0 36.2 37.3 35.6 37.0 37.5 37.4 36.7 35.30 0.7 2.9 6.5 11.3 16.7 21.5 24.9 26.9 28.1 29.7 29.0 29.3 29.3 28.8 29.9 29.0 29.2 30.85 0.0 2.0 5.2 9.5 14.1 17.7 20.0 21.4 21.3 21.9 21.9 22.1 22.0 23.5 22.8 23.6 23.1 21.0

10 -2.0 -0.2 2.7 6.6 10.3 12.8 14.0 14.2 14.7 15.2 15.0 14.5 16.5 15.7 17.4 17.9 17.0 18.015 -5.0 -3.4 -0.7 2.7 5.6 6.4 6.7 7.0 6.9 7.9 7.5 9.1 9.6 10.6 12.1 12.2 12.0 12.320 -8.9 -7.4 -4.9 -2.1 -0.3 0.1 -0.3 -0.4 0.4 0.8 1.2 3.5 4.4 5.9 6.6 7.3 7.6 9.125 -12.1 -9.9 -7.7 -7.0 -7.3 -7.6 -7.3 -6.8 -5.4 -4.3 -2.3 -1.1 0.5 2.3 2.9 4.4 5.230 -17.4 -15.4 -14.2 -14.3 -14.7 -14.6 -14.1 -12.5 -11.7 -8.8 -6.9 -5.0 -3.2 -1.6 -0.1 1.1 2.435 -23.2 -21.7 -21.5 -22.0 -22.0 -21.4 -20.0 -17.8 -15.7 -13.0 -10.5 -8.3 -6.2 -4.3 -2.8 -1.2 0.140 -29.5 -28.9 -29.3 -29.3 -28.2 -26.7 -24.3 -21.8 -18.7 -15.9 -13.1 -10.7 -8.4 -6.4 -4.5 -3.0 -2.045 -36.7 -36.3 -34.9 -32.8 -30.0 -27.0 -23.8 -20.6 -17.5 -14.6 -11.9 -9.6 -7.5 -5.7 -4.3 -3.150 -41.3 -39.2 -36.7 -33.7 -30.6 -27.3 -24.0 -20.7 -17.6 -14.8 -12.2 -9.8 -7.8 -6.1 -4.7 -3.6

Table 5B: –2X term borrowing (TB) leverage minus –2X daily rebalance (DR) leverageAverage TB – DR realized annual return differences (%)


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lyin

g as

set

real

ized

sem

iann

ual r

etur

n ±0

.5(%

)

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90-50 -11.6 -11.2 -10.8 -10.2 -9.7 -9.0 -8.4 -7.7 -7.1 -6.4 -5.8 -5.1 -4.5 -4.0 -3.4-45 -15.5 -15.0 -14.4 -13.7 -12.9 -12.1 -11.2 -10.3 -9.5 -8.6 -7.7 -6.9 -6.1 -5.3 -4.6-40 -20.7 -20.2 -19.5 -18.7 -17.8 -16.8 -15.7 -14.6 -13.5 -12.3 -11.2 -10.1 -9.0 -7.9 -6.9 -6.0-35 -26.4 -25.7 -24.9 -23.8 -22.7 -21.4 -20.1 -18.7 -17.2 -15.7 -14.3 -12.8 -11.5 -10.1 -8.9 -7.7-30 -23.2 -23.2 -23.3 -23.1 -22.7 -21.9 -20.9 -19.8 -18.3 -16.9 -15.4 -13.7 -12.3 -10.8 -9.4 -8.2-25 -16.5 -15.7 -14.8 -14.2 -14.0 -14.2 -14.3 -14.0 -13.6 -13.2 -12.4 -11.4 -9.8 -8.7 -7.7 -6.3 -4.7-20 -10.4 -9.4 -8.2 -6.8 -5.8 -5.2 -5.0 -5.0 -5.4 -5.4 -4.9 -4.1 -3.5 -2.2 -1.9 -0.3 0.1-15 -6.1 -5.5 -4.3 -2.8 -1.0 1.0 2.3 3.1 3.4 3.4 3.2 3.9 3.6 4.4 4.6 5.6 6.2 6.9-10 -2.6 -1.8 -0.5 1.4 3.6 6.2 8.4 10.1 11.5 11.9 12.1 12.3 12.4 12.5 13.7 14.1 14.4 15.3-5 -0.4 0.5 2.1 4.2 6.9 10.0 13.2 15.8 18.1 19.7 20.8 20.5 20.8 21.4 22.6 22.3 23.2 24.00 0.4 1.5 3.3 5.8 8.9 12.5 16.5 20.1 23.4 25.7 27.4 28.7 29.4 29.5 30.5 31.2 32.1 31.95 -0.3 0.9 3.0 5.9 9.5 13.8 18.5 23.1 27.3 30.5 33.2 35.7 37.1 38.1 38.5 40.6 40.9 41.6

10 -2.6 -1.1 1.3 4.6 8.7 13.6 19.0 24.6 30.2 34.7 38.7 42.0 45.1 45.4 48.5 47.7 50.1 51.415 -6.5 -4.8 -2.0 1.7 6.4 12.0 18.3 24.7 31.5 37.0 42.5 46.9 50.0 52.4 54.7 56.2 58.6 60.120 -10.1 -7.0 -2.8 2.6 8.9 16.0 23.6 31.5 38.5 45.1 51.0 55.5 58.4 61.9 63.1 66.3 67.325 -17.2 -13.7 -8.9 -2.9 4.2 12.3 21.0 29.9 38.8 46.8 53.3 58.7 63.9 67.5 69.9 73.1 75.530 -22.2 -16.8 -10.0 -2.0 7.0 16.9 27.1 37.0 46.5 54.5 61.8 67.9 73.5 76.9 82.0 83.835 -32.5 -26.5 -18.9 -10.0 0.1 11.1 22.8 34.2 45.2 55.1 64.5 71.6 77.2 83.2 88.1 89.040 -44.8 -38.0 -29.6 -19.7 -8.4 3.9 16.7 30.3 42.8 54.8 65.0 74.0 80.6 87.9 93.0 96.045 -51.5 -42.2 -31.2 -18.7 -5.0 9.2 24.2 38.5 52.2 65.0 74.6 84.1 91.8 99.2 103.750 -67.0 -56.7 -44.5 -30.8 -15.6 0.4 17.0 33.1 49.1 61.5 74.2 85.2 98.1 103.1 113.1

Table 6A: 3X term borrowing (TB) leverage minus 3X daily rebalance (DR) leverageAverage TB – DR realized semiannual return differences (%)



Targ

et u

nder

lyin

g as

set

real

ized

ann

ual r

etur

n ±0

.5(%

)

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90-50 -11.6 -11.0 -10.3 -9.5 -8.6 -7.6 -6.7 -5.8 -4.9 -4.1 -3.4 -2.7 -2.2 -1.7 -1.3 -1.0-45 -15.5 -14.7 -13.7 -12.6 -11.4 -10.2 -8.9 -7.7 -6.6 -5.5 -4.5 -3.7 -2.9 -2.3 -1.8 -1.3-40 -20.9 -20.1 -19.1 -17.8 -16.4 -14.9 -13.2 -11.6 -10.1 -8.6 -7.2 -5.9 -4.8 -3.8 -3.0 -2.3 -1.7-35 -26.6 -25.6 -24.3 -22.7 -20.9 -18.9 -16.9 -14.8 -12.8 -10.9 -9.1 -7.5 -6.1 -4.9 -3.8 -2.9 -2.2-30 -23.4 -23.3 -23.5 -23.0 -21.9 -20.3 -18.3 -16.1 -14.0 -11.9 -9.8 -8.0 -6.3 -5.0 -3.7 -2.7 -1.9-25 -15.9 -14.7 -14.3 -14.6 -14.7 -14.2 -13.8 -12.2 -10.7 -8.7 -7.1 -5.4 -3.9 -2.6 -1.5 -0.4 0.3-20 -10.8 -9.7 -7.9 -6.1 -5.5 -5.7 -6.2 -5.5 -5.1 -4.5 -3.1 -2.1 -1.3 0.6 2.0 2.7 3.3 4.4-15 -5.9 -4.6 -2.4 0.3 2.2 2.8 2.9 3.0 3.0 3.0 3.9 5.3 5.7 6.5 7.9 8.2 9.1 8.7-10 -2.3 -0.7 1.9 5.2 8.5 10.5 11.3 11.6 11.3 11.9 11.6 12.2 12.7 13.6 14.6 15.2 15.1 14.4-5 -0.1 1.8 4.8 8.9 13.3 16.6 18.6 19.3 20.2 19.8 20.7 20.4 21.4 22.2 22.1 21.8 21.7 22.30 0.7 2.9 6.5 11.3 16.7 21.6 25.3 26.8 28.6 29.4 29.3 29.9 30.1 29.9 30.6 29.9 29.1 27.35 0.1 2.6 6.8 12.3 18.8 25.1 29.9 33.4 35.6 36.4 36.8 39.1 38.2 38.4 39.2 38.2 37.6 38.9

10 -2.1 0.8 5.6 11.9 19.5 27.1 33.6 38.9 42.8 43.8 46.4 47.5 47.6 48.5 47.9 45.4 45.0 45.515 -5.9 -2.6 2.8 10.0 18.7 28.1 36.8 43.4 47.3 52.1 53.7 54.9 55.8 56.8 55.8 54.8 55.5 54.520 -11.5 -7.7 -1.5 6.7 16.6 27.5 37.6 46.6 52.3 57.8 61.8 63.2 64.4 65.1 65.0 64.3 62.4 61.525 -14.5 -7.6 1.7 13.0 25.3 37.4 48.5 57.6 63.2 68.0 70.5 74.3 73.2 74.5 76.8 72.5 71.830 -23.1 -15.3 -4.9 7.8 21.8 36.3 49.3 58.8 67.9 72.9 78.0 81.3 83.0 83.5 83.4 83.5 78.235 -33.6 -24.9 -13.2 0.9 16.9 33.0 48.7 61.2 71.6 78.8 84.9 89.3 90.0 90.3 94.2 91.8 88.840 -46.0 -36.3 -23.3 -7.5 10.2 28.7 46.3 61.6 73.4 83.9 91.1 95.7 100.6 100.1 98.3 99.9 99.045 -49.7 -35.3 -17.8 2.1 22.7 43.2 60.8 75.2 85.9 94.7 102.0 106.5 109.3 110.9 109.7 109.150 -65.1 -49.1 -29.8 -7.9 15.4 38.2 59.8 76.5 91.0 100.2 107.8 113.4 114.7 118.9 120.0 124.0

Table 6B: 3X term borrowing (TB) leverage minus 3X daily rebalance (DR) leverageAverage TB – DR realized annual return differences (%)


Targ

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lyin

g as

set

real

ized

sem

iann

ual r

etur

n ±0

.5(%

)

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90-50 -447.3 -403.5 -353.2 -299.1 -242.1 -184.9 -129.1 -77.3 -28.6 13.7 48.5 78.2 102.0 121.8 134.9-45 -291.6 -258.3 -220.3 -179.0 -136.2 -93.0 -52.4 -13.3 21.1 50.8 74.7 94.3 109.0 123.3 128.9-40 -208.4 -187.2 -161.3 -131.9 -99.9 -66.7 -33.9 -2.4 25.3 50.5 70.0 87.7 101.2 112.2 116.8 120.3-35 -133.1 -116.2 -95.8 -72.4 -47.2 -21.2 4.2 27.0 48.4 65.7 80.0 92.0 100.4 105.3 109.5 112.2-30 -81.4 -67.8 -51.3 -32.5 -12.3 7.9 27.6 45.5 59.7 72.8 84.2 87.8 94.5 98.3 98.7 102.8-25 -54.3 -46.0 -35.0 -21.4 -6.1 10.2 26.7 41.0 53.3 63.4 74.4 77.7 82.4 87.1 87.9 88.8 86.6-20 -29.2 -22.4 -13.2 -2.0 10.5 23.6 36.0 46.8 55.5 63.8 68.4 72.2 74.6 75.3 77.2 77.5 76.0-15 -16.4 -12.9 -7.2 0.5 9.9 20.3 30.5 39.8 46.8 53.0 58.5 60.6 63.7 64.6 65.6 66.2 65.3 65.4-10 -6.1 -3.1 1.7 8.2 16.1 24.6 32.6 39.5 44.3 48.5 49.5 52.7 53.8 54.1 55.7 54.6 54.5 52.5-5 -0.8 1.8 5.9 11.5 18.1 24.8 30.7 34.4 38.3 39.7 41.1 42.6 42.8 42.8 43.1 45.2 43.3 41.70 0.7 2.9 6.5 11.2 16.7 21.7 25.7 28.0 29.8 30.5 31.0 31.6 31.7 32.9 33.3 33.1 32.4 33.35 -0.7 1.2 4.2 8.3 12.6 16.1 17.8 19.3 20.0 20.2 20.7 20.7 22.1 22.3 23.9 22.6 24.0 23.2

10 -4.5 -2.9 -0.2 3.2 6.3 7.9 8.4 9.2 9.8 9.8 10.5 11.0 11.8 13.8 13.9 14.7 14.9 15.515 -10.2 -8.8 -6.4 -3.8 -2.3 -1.7 -1.6 -1.5 -1.2 -0.9 1.4 2.1 4.3 5.4 6.0 7.3 8.2 8.320 -16.1 -14.1 -12.7 -12.7 -12.7 -12.4 -11.5 -10.5 -9.1 -6.8 -5.0 -3.1 -1.0 0.3 1.4 3.0 3.725 -24.6 -23.3 -23.3 -23.4 -23.1 -22.0 -20.2 -18.0 -15.4 -12.9 -10.4 -7.8 -6.0 -4.0 -2.4 -1.0 0.230 -34.4 -34.0 -32.7 -30.7 -28.0 -25.2 -22.1 -19.1 -16.1 -13.3 -10.8 -8.5 -6.6 -4.8 -3.5 -2.335 -37.8 -35.8 -33.5 -30.8 -27.8 -24.8 -21.7 -18.7 -15.9 -13.2 -10.8 -8.7 -6.8 -5.3 -4.0 -3.040 -33.9 -32.1 -30.0 -27.5 -24.9 -22.2 -19.4 -16.7 -14.2 -11.8 -9.7 -7.8 -6.1 -4.7 -3.6 -2.745 -28.8 -26.9 -24.7 -22.4 -19.9 -17.5 -15.0 -12.7 -10.6 -8.7 -7.0 -5.5 -4.2 -3.2 -2.450 -26.0 -24.3 -22.3 -20.2 -18.0 -15.7 -13.5 -11.5 -9.5 -7.8 -6.3 -4.9 -3.8 -2.9 -2.1

Table 7A: –3X term borrowing (TB) leverage minus –3X daily rebalance (DR) leverageAverage TB – DR realized semiannual return differences (%)



3X leveraged strategy results are shown in Tables 6A and 6B while –3X results are found in Tables 7A and 7B. In general, TB strategies are generally superior at all modest return levels and increasingly so as volatility and holding period increase. It is worthwhile noting that when the underlying asset moves in one’s favor accompanied by high volatility, for the range of outcomes we examine, one is usually better off with TB leverage.

Our results confirm what other researchers have noted [Bush (2009), and Cheng and Madhavan (2009)]. In almost every scenario and time period studied, the TB strategy does increasingly better than end-of-day DR strategy as volatility increases. For example, for a six-month holding period, when the underlying asset returns 10%, the 2X TB strategy outperforms the 2X DR strategy by an average of 0.3% when realized volatility is 15%, by an average of 4.3% at 30% volatility, by an average of 10.6% at 45% volatility, and by an average of 18.7% when realized volatility is 60% (See Table 8).

For readers interested in delving deeper into these topics, the raw expected returns of the four respective TB and DR strategy simulations (2X, –2X, 3X and –3X), the model’s measured

probability of early termination for each TB strategy outcome and the expected average one-way turnover associated with each DR strategy outcome are available upon request.

ConclusionsThis paper has shown that the best strategy for rebalancing a levered fund depends upon, among other things, the expected pattern of returns of the underlying target security and the investor’s time horizon. There are two fundamental types of rebalancing strategies: 1) momentum-based, such as portfolio insurance, and 2) fixed-mix (also called fixed-proportions). The main difference involves the change in the amount of the risky assets, such as equity, during market increases and decreases. Momentum strategies increase exposure to risky assets during sustained prices rises, whereas the risky assets are sold during price rises for fixed-mix strategies. For levered funds, the traditional end-of-day daily rebalancing to target leverage approach is a momentum strategy. The term-based borrowing strategy can be interpreted as a buy-and-hold approach.

If one is to rebalance a portfolio on a regular basis in the context of fixed-mix strategies, there are distinct advantages


Targ

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.5(%

)

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90-50 -443.0 -375.0 -297.4 -215.5 -135.0 -61.2 1.5 49.2 88.1 116.5 130.9 135.2 140.6 138.3 133.5 131.7-45 -287.0 -235.8 -177.1 -115.7 -55.2 -3.1 41.6 74.6 99.8 119.1 124.9 129.1 130.6 123.9 121.8 114.8-40 -213.8 -182.9 -143.2 -97.9 -50.6 -5.6 33.9 65.2 87.9 105.4 112.7 119.1 118.5 114.4 112.8 106.5 101.9-35 -136.7 -112.4 -81.1 -45.3 -9.3 24.4 52.2 75.0 90.1 100.7 105.7 107.5 103.9 103.1 98.3 94.3 86.5-30 -84.0 -64.4 -39.3 -10.9 17.7 43.6 62.5 77.6 88.1 93.2 94.3 94.5 93.3 90.3 87.7 79.5 74.6-25 -48.0 -32.0 -11.5 11.3 33.0 51.1 66.2 75.3 81.6 84.5 85.9 84.9 80.7 77.7 73.5 68.3 63.8-20 -32.2 -23.8 -10.6 6.2 24.5 41.6 54.1 63.0 69.2 72.2 73.5 73.9 72.9 69.8 64.6 60.8 56.2 53.5-15 -15.3 -8.3 2.7 16.7 31.3 43.5 51.3 57.8 61.6 62.4 62.5 61.2 60.1 57.8 53.3 50.4 48.3 45.2-10 -5.1 0.8 10.1 21.7 32.8 41.2 46.7 49.7 51.3 51.1 52.8 51.7 48.5 46.0 43.7 40.8 38.6 37.7-5 0.1 5.1 13.0 22.5 30.7 35.5 37.8 40.2 40.9 42.8 40.0 39.7 37.4 36.1 34.2 32.7 31.4 29.60 1.5 5.8 12.5 20.1 25.4 27.9 28.7 29.8 29.6 30.8 30.7 29.6 28.1 27.4 26.4 24.6 24.0 22.35 -0.1 3.6 9.4 14.8 17.5 18.5 19.1 20.2 20.6 20.5 20.9 21.6 20.4 20.5 18.4 18.7 16.9 15.0

10 -4.0 -0.7 4.0 7.4 7.9 8.3 8.6 8.8 10.6 12.5 13.0 12.3 13.6 13.0 13.1 12.2 11.7 11.415 -9.7 -6.9 -3.4 -2.3 -2.5 -2.7 -1.6 0.1 2.5 4.4 5.4 7.1 7.7 8.2 8.2 7.7 7.2 6.820 -17.0 -14.5 -12.7 -13.2 -13.2 -12.2 -10.0 -7.5 -4.3 -2.0 -0.2 1.8 3.0 3.6 3.7 4.0 3.8 3.725 -23.6 -23.8 -23.9 -22.5 -19.8 -16.5 -12.9 -9.5 -6.4 -4.1 -2.0 -0.8 0.2 1.0 1.2 1.3 1.630 -34.7 -34.2 -31.9 -28.3 -24.2 -19.9 -15.7 -12.0 -8.8 -6.1 -4.1 -2.6 -1.5 -0.7 -0.3 0.1 0.335 -38.2 -35.4 -31.9 -27.8 -23.5 -19.3 -15.3 -11.8 -8.7 -6.3 -4.4 -2.9 -1.9 -1.2 -0.7 -0.4 -0.240 -34.2 -31.7 -28.5 -24.9 -21.0 -17.2 -13.7 -10.5 -7.8 -5.6 -3.9 -2.6 -1.7 -1.1 -0.6 -0.4 -0.245 -28.5 -25.7 -22.4 -18.9 -15.5 -12.3 -9.4 -7.0 -5.1 -3.5 -2.3 -1.5 -0.9 -0.6 -0.3 -0.250 -25.8 -23.2 -20.2 -17.1 -14.0 -11.1 -8.5 -6.3 -4.5 -3.2 -2.1 -1.4 -0.8 -0.5 -0.3 -0.2

Table 7B: –3X term borrowing (TB) leverage minus –3X daily rebalance (DR) leverageAverage TB – DR realized annual return differences (%)


of rebalancing based on price movements, rather than fixed time periods. The fixed-mix rules are ideally suited to trendless markets with considerable noise and low transaction costs. Conversely, momentum-like strategies perform best when markets exhibit trends with few reversals.

Levered and inverse funds are clearly derivatives of the underlying security. Thus, investors will naturally compare the performance of the levered fund to that of the underlying security. When the investor’s horizon is greater than one day, term borrowed levered products are more consistent with most investors’ expectations about the performance of these funds relative to that of the underlying asset.

The standard ETF approach, daily rebalancing, is a momentum-like strategy; it tends to outperform when underlying asset returns are trending in one direction or the other with relatively few reversals. In low volatility directional markets, daily rebalancing strategies are generally superior to buy-and-hold strategies because the amount levered (relative to the initial stake) increases as the underlying asset generally moves in one’s favor with few, if any, reversals, thereby magnifying gains.

Similarly, if the underlying asset generally moves in an adverse direction, leverage is steadily decreased, thereby mitigating losses and preventing the threat of early termination in all but the most extreme of circumstances.

Daily rebalancing performs poorly in trendless markets when there is a small or no change in the underlying asset value and in high volatility markets except for the most extreme movements. Over longer time periods, it is a tail strategy. Its relative performance generally worsens vis-à-vis the term borrowing strategy as the holding period increases. For the majority of outcomes, term borrowing performs better and increasingly so as volatility increases and as the holding period expands.

Lastly, daily rebalance ETFs buy and sell billions of dollars of market exposure over time, which increases turnover and transactions costs, generally resulting in reduced longer term investor returns vis-à-vis what is possible with term borrowing strategies. The macro-benefits of having a term borrowing based ETF solution versus the daily rebalance alternative may result in more stable investment environment and generally better overall return patterns for investors.

2X six month horizonAsset return Annualized volatility 2X TB E(return) Prob(TB termination) 2X DR E(return) DR 1-wayturnover TB – DR E(return)

10% 15% 20% -- 19.7% 207% 0.3%10% 30% 20% -- 15.7% 411% 4.3%10% 45% 20% -- 9.4% 609% 10.6%10% 60% 19.8% 0.1% 1.2% 809% 18.7%

2X one year horizon10% 15% 20% -- 18.3% 415% 1.7%10% 30% 20% -- 10.6% 820% 9.4%10% 45% 19.6% 0.3% -1.1% 1206% 20.8%10% 60% 15.4% 3.8% -15.6% 1578% 31.0%

-2X six month horizon10% 15% -20% -- -20.1% 170% 0.1%10% 30% -20.2 0.2% -27.8% 328% 7.6%10% 45% -24.9 6.2% -39.1% 465% 14.1%10% 60% -37.2 21.6% -52.1% 571% 14.8%

-2X one year horizon10% 15% -20% -- -22.8% 337% 2.7%10% 30% -24.1 5.1% -36.9% 627% 12.8%10% 45% -40.5 25.6% -55.1% 841% 14.7%10% 60% -57.8 47.2% -72.3% 965% 14.5%

Table 8: Selected results DR versus TB, 2X & –2X



Rebalancing (or not rebalancing) decisions have a major impact on the performance of levered and inverse strategies. We have shown through empirical tests when daily rebalance leverage is likely to outperform term borrowing leverage, and vice versa. The performance characteristics of levered and inverse products should be well understood by investors before they invest in these products. Caveat emptor!

ReferencesBlackRock ETP 2012 Landscape Global Handbook, http://www.indexfunds.com.cn/userfiles/file/1358232962976.pdfBush, M., 2009, “Gearing up for leverage: an in-depth review of a growing market phenomenon,” Index Universe, May 10Cheng, M., and A. Madhavan, “The dynamics of leveraged and inverse exchange-traded funds,” Journal of Investment Management, (7)4, 43-62FINRA Regulatory Notice 09-31, June 2009. “Non-traditional ETFs. FINRA reminds firms of sales practice obligations relating to leveraged and inverse exchange-tradedFunds.” https://www.finra.org/web/groups/industry/@ip/@reg/@notice/documents/notices/p118952.pdf.Kiron, K., 2011, “Securitization system and process,” United States Patent Application 20110191234. Filed February 2, 2011Kiron, K., 2012, “Securitization system and process II” United States Patent Application 20130046673. Filed August 15, 2012Kritzman, M., and S. Page, 2009, “Optimal rebalancing: a scalable solution,” Journal of Investment Management, 7, 9-19Little, P. K., 2010, “Inverse and leveraged ETFs: not your father’s ETF,” The Journal of Indexing, 1(1), 83-89Luenberger, D., 1997, Investment science, Oxford University Press: New YorkMulvey, J., and K. Simsek, 2002, “Rebalancing strategies for long-term investors,” in Kontoghiorghes, E. J., B. Rustem, and S. Siokos (eds.), Computational methods in decision-making, economics and finance: optimization models, Kluwer, 1 5-33, 2002.Mulvey, J. M., B. Pauling, and R. E. Madey, 2003, “Advantages of multiperiod portfolio models”, Journal of Portfolio Management, 29, 35—45Mulvey, J., and W. Kim, 2009, “Constantly rebalanced portfolio — is mean reversion necessary?” Encyclopedia of Quantitative Finance, WileyNadig, D., and O. Ludwig, 2013, “ETF fund flows: GDX adds $370.6M,” IndexUniverse.com. January 1Perold, A., and W. Sharpe, 1998, “Dynamic strategies for asset allocation,” Financial Analysts Journal, Jan-Feb, 7-18Tokat, Y., N. W. Wicas, 2007, “Rebalancing in theory and practice,” Journal of Investing, 16(2), 52-59


Part 2

Regulating insurance groups: a comparison of risk-based solvency modelsHato SchmeiserProfessor of Risk Management and Insurance Economics, University of St. Gallen

Caroline SiegelProject Leader and Senior Research Associate, Institute of Insurance Economics, University of St. Gallen

AbstractRegulators are currently developing group-wide capital standards that are intended to enable the effective monitoring of insurance groups. Some jurisdictions are taking steps toward models with a focus on the groups’ consolidated balance sheets, while other models focus on the interrelations of the groups’ legal entities. This paper compares two general approaches to group-wide solvency in light of the regulatory challenges of regulatory inconsistency, risk dependencies, and risk aggregation: a consolidated approach and a legal entity approach. In order to contribute to the current discussion on the regulation and risk management for insurance groups, we support our line of reasoning by using a generalized model of Gatzert and Schmeiser (2011). Our findings show that a solely consolidated viewpoint is likely to underestimate shortfall risks in times of financial crises, whereas while a sole focus on the interrelated legal entities generally makes it possible to display different group structures it cannot control regulatory arbitrage.



IntroductionThe increasing importance of internationally operating financial groups has given rise to a debate about capital adequacy and appropriate safety levels within the financial services industry. In the past, supervisors and regulators focused primarily on the single legal entity and the protection of its customers’ claims. Consequently, capital requirements were typically computed on a stand-alone basis [Mälkönen (2004)]. However, more recent risk-based capital standards also aim to consider group effects by implementing capital requirements at the corporate level. One group-solvency approach, which treats the insurance group as a set of interrelated legal entities, calculates capital charges on a legal entity basis by accounting for capital and risk transfer instruments (CRTIs) [IAIS (2009b)]. Another approach to group-wide solvency assessment takes a consolidated point of view by considering the group as one integrated entity and assuming that the legal entities can access each other’s cash flows and freely transfer risks [Keller (2007), IAIS (2009b)].

In practice, a variety of models to group-wide solvency assessment are used, many of which can be regarded as intermediate approaches because they have the characteristics of both a legal entity focus and a consolidated viewpoint. Nevertheless, current examples of group solvency models with a greater emphasis on the legal entity are the NAIC Legal Entity Method of the U.S. and the Swiss Group Structure Model [IAIS (2009b)]. Examples of jurisdictions that are moving towards models with a more consolidated focus are the European Union, Canada, and Australia [IAIS (2009b)].

This paper contributes to the literature by comparing these two approaches to assessing group-wide solvency in order to determine which of the two is more appropriate for regulating insurance groups, given different assumptions and economic circumstances.

To date, the literature on financial groups can be divided into two categories: either they explore the issues and practical challenges regulators face when establishing a risk-based capital standard of group-wide solvency assessment, or they attempt to explore group structures and quantify the risks and diversification effects within financial groups.

In the latter category, a number of studies examine whether financial groups trade at a discount compared to single line firms. While the majority of studies find evidence of a conglomerate discount in financial groups [Ammann and Verhofen (2006), Laeven and Levine (2005), Schmid and Walter (2009)], there is also mixed evidence [van Lelyveld and Knot (2009)] for a sample of European bank-insurance conglomerates. Here, the diversification discount is found to be varying considerably for different conglomerate structures. Furthermore, Gatzert and Schmeiser (2011) simultaneously assess the diversification benefit and conglomerate discount of a two-entity financial conglomerate, given fair pricing for the stakes of equityholders and policyholders. They find that diversification benefits within financial conglomerates are much less considerable when stakeholders obtain risk-adjusted returns. Freixas et al. (2007) compare the risk-taking appetite of single firms and financial conglomerates and find that, in comparison to stand-alone financial institutions, the diversification in conglomerates can increase risk-taking incentives. Analyzing moral hazard within financial groups, Kahn and Winton (2004) propose a model framework to explain the “bipartite” subsidiary structure often found within banking conglomerates. With regard to the group-level Swiss Solvency Test, Keller (2007) and Luder (2007) model risks and diversification effects and calculate capital charges when capital and risk transfers between the legal entities of the insurance group take place. Within the same context, Filipović and Kupper and Filipović and Kupper (2007 and 2008) derive optimal capital and risk transfer instruments in order to explore group diversification under convex risk measures.

Another segment of the literature deals with the group effects of financial conglomerates and their impact on systemic risk. In light of the subprime financial crisis, Harrington (2009) discusses, from a theoretical perspective, the question of whether insurance generally exhibits systemic risk. Other studies take an empirical approach. As an indicator of the systemic risk potential in the U.S. and Europe, De Nicolo and Kwast (2002) and Schüler (2002) examine the interdependencies among banks proxied by the correlations of the banks’ stock returns. Both empirical studies find evidence that consolidation contributes to the interdependencies between firms and, thus, to an increase in systemic risk. Allen and Jagtiani (2000) create “synthetic universal banks” in order to analyze the effect of investments and insurance activities on the banks’ total risks and conclude that


conglomeration leads to an increase in both systematic market risk and systemic risk.

Most of the literature that deals with the issues and practical challenges of establishing group-wide solvency standards takes a nonquantitative perspective. Siegel (2013) provides an overview and comparison of three current supervisory frameworks that regulate group solvency: the “Solo-Plus”-approach of the U.S., Switzerland’s Group Structure Model, and the E.U. Solvency II Directive’s solvency assessment for groups. The paper reveals a clear need for further revisions regarding the U.S. framework, whereas the European approaches provide a solid solvency assessment, in particular the Swiss Model. Diereck (2004) discusses the legal structures of financial conglomerates and the conglomerates’ relevant risks and benefits from a supervisory perspective. Mälkönen (2004), Morrison (2003), and Schilder and van Lelyveld (2003), derive the possible causes of the establishment of financial groups, set out justifications for their regulation, and address the issues and challenges with which supervisors of financial conglomerates are confronted. In addition, Mälkönen (2004) examines limitations to solvency regulation by comparing a silo approach with a consolidated view. Along the lines of these studies, the paper on group-wide solvency assessment and supervision prepared by the International Association of Insurance Supervisors discusses the regulatory issues of the solvency assessment for insurance groups and identifies four main challenges to group supervision [IAIS (2009b)]:

1. Regulatory inconsistency that is “capital gearing” and “regulatory arbitrage”

2. “Fungibility1 of capital and transferability of assets”3. “Measurement of risk dependencies and aggregation of risks”4. “Treatment of nonregulated entities”

The paper also provides a qualitative overview of current approaches to group-wide solvency regulation. Our paper makes both a theoretical and a numerical comparison between the different approaches to group-wide solvency assessment by quantifying risks and capital requirements. It determines which approach is more appropriate in which situation when dealing

1 In the following, we will define “fungibility” as the ability to transfer capital easily and freely within the insurance group [Filipović and Kupper (2007)].

with different regulatory challenges. Our analyses are based on the model framework proposed by Gatzert and Schmeiser (2011). Their study simultaneously assesses the diversification benefit and conglomerate discount with respect to the capital charges and shortfall risks of a two-entity financial conglomerate with and without accounting for the altered shareholder value. The authors derive capital requirements in the context of the tail value at risk concept of the Swiss Solvency Test.

Generalizing the model framework by Gatzert and Schmeiser (2011) to N+1 legal entities (one parent company and N subsidiaries), we aim to compare the two approaches to assess the solvency of insurance groups in light of different regulatory issues under the real world measure P. Within a one-year solvency horizon, we compare results from a legal entity approach, which takes different capital and risk transfer instruments (CRTIs) into account, and a consolidated approach. Keeping the capital structure fixed, we study shortfall risk and capital charges under different parameter assumptions. In order to derive the capital requirements we apply the value at risk measure of the proposed Solvency II regulatory framework. Since, in general, no closed-form solutions can be derived, numerical results are generated by means of a Monte Carlo simulation. We interpret our findings in light of two main challenges to group-wide solvency regulation: regulatory inconsistency and risk interdependencies, with a special focus on the latter.

Model frameworkBasic settingGeneralizing the model framework proposed by Gatzert and Schmeiser (2011), we consider a set F ={0,...,N} of firms denoted by i = 0, ... ,N within an insurance group. The index i = 0 denotes the parent company; i = 1, ... ,N stand for the subsidiaries.

The market value of liabilities and the market value of assets of the ith entity are given by Lt,i and At,i, respectively, with the time index t = 0, 1. t 0,1.A0,i= is defined as the sum of the initial payments of equityholders E0,i and policyholders D0,i to firm i: A E D0,i 0,i 0,i= + . The development of assets and liabilities is modeled by means of correlated geometric Brownian motions.

At t = 1, two scenarios are possible. In the first, company i e F is able to cover its liabilities, so policyholders and other debt holders obtain the value of the liabilities and equityholders receive the



difference between the market value of assets and the market value of liabilities. In the second scenario, the liabilities cannot be met in full, therefore policyholders receive the total value of assets and equityholders leave empty handed. The payoff to policyholders can be expressed by the value of liabilities less the payoff of the default put option at time t = 1 [Doherty and Garven (1986)]:

D L max L A ,0l,i l,i l,i l,i= - -^ h, (1)

Where Max max L A ,0 DPOl,i l,i l,i- =^ h constitutes the default put option value of firm i at time t [Doherty and Garven (1986)]. The payoff to equityholders can be expressed as a call option on the firm’s assets, while the liabilities represent the strike price. Thus, for the equityholders of entity i at time 1, one obtains [Doherty and Garven (1986)]:

E A D max A L ,0 .l,i l,i l,i l,il,i= - = -^ h (2)

Economic CapitalWe derive available and necessary economic capital based on fixed amounts of initial debt and equity payments [Gatzert and Schmeiser (2011)]. In insurance regulation, available economic capital (AEC) is often called risk-bearing capital, as in the Swiss Solvency Test [FOPI (2006)], or risk-based capital, as in the U.S. NAIC method [NAIC (2009c)]. Following Keller (2007), and Filipović and Kupper (2007), we define the AEC of company i at time t as the market value of assets less the market value of liabilities.

The necessary economic capital (NEC), also called solvency capital requirement (Solvency II) or target capital (Swiss Solvency Test), is the economic capital needed at t = 0 to limit the probability of default to a prespecified confidence level [FOPI (2004)]. The NECa depends on the underlying stochastic model, the input parameters, and the risk measure chosen. For the latter, value at risk (VaR) is applied, in line with Solvency II [EC (2009)]. The value at risk for a given confidence level 1 - a is given by the quantile of the distribution F 1 a- ^ h, such that VaR X inf x F xi x= | $ aa ^ ^h h" ,. For the ith firm, we set Xi to:

X AEC e AECi 1,i fr

0,i= -$ - (3)

That is, we define VaR (Xi) as the value at risk of the change of available economic capital of firm i during one time period [FOPI (2006)]. Consequently, the necessary economic capital for i e F is given by:

NEC VaR Xi i=-a a ^ h (4)

We set the minimum level of economic capital (ML) as the level below which financial resources are not supposed to fall [EC (2009)], the so-called minimum capital requirement under E.U. solvency regulations for nonlife insurers, to the maximum of the premium basis (PBi) and the claims basis (CBi) of an insurance company i [EC (2002a)]2:

ML max PB ,CBi i i= ^ h. (5)

The premium basis and the claims basis for firm i are calculated according to EC (2002a):

PB 0.18 min p ; 50million 0.16 max p 50million;0i i i= + -$ $* *^ ^h h6 6@ @

(6)CB 0.26 min C ; 35million 0.23 max C 35million;0i i i= + -$ $* *^ ^h h6 6@ @

(7)

where Pi stands for the net premium income of insurer i at t = 0 and Ci denotes the average net claims of company i – in general based on the last three years.

Legal entity approachA group-wide solvency assessment approach with a legal entity focus treats the insurance group as a collection of interdependent legal entities [IAIS (2009b)]. Capital requirements and risks are determined for each legal entity, taking into account intra-group transactions. In this section, we extend the model framework provided by Gatzert and Schmeiser (2011) to the general case of N + 1 legal entities which are separately capitalized. Within this framework, firm i = 0, the parent company, covers its subsidiaries’ liabilities only in the presence of legally binding transfer contracts [Keller (2007)]. This approach, therefore, relies on different assumptions regarding the capital and risk transfer between entities [Gatzert and Schmeiser (2011)].

2 For the sake of simplification we ignore reinsurance coverage.


The first one is that the parent company i = 0 can access its subsidiaries’ surplus capital.

Furthermore, a going concern assumption for the subsidiaries after t = 1 is included, which requires that the subsidiaries i = 1, ... ,N must at least be endowed with the minimum level of economic capital at time 1, A L ,MLl,i l,i i-^ h. Thus, the available economic capital of a subsidiary i = 1, ... ,N in t = 1 can be expressed by mini A L ,MLl,i l,i i-^ h. Taken together, these assumptions imply that the parent can sell its subsidiaries for the value of

max A L ML ,0i 1N

1,i 1.i i- -R = ^ h. In line with Gatzert and Schmeiser (2011), our analysis examines two different CRTIs: a guarantee and a quota-share retrocession when each is transferred from the parent company to one subsidiary and when each is transferred from one subsidiary to another.

Under the guarantee, we assume that the transferring company, denoted by i ibfc tr! , covers the shortfall DPO max L A ,0l,ibfc l,ibfc l,ibfc= -^ h of the beneficiary ibfc with i ibfc tr! only, when the transferor’s available economic capital at time 1 is above the minimum level. Thus, the transfer T to the benefiting firm is restricted to max A L ML ,0l,itr l,itr itr- -^ h .

The second type of CRTI considered is a quota-share retrocession in which q denotes the quota that the transferring company is legally obligated to assume. Consolidated approachFollowing Gatzert and Schmeiser (2011), we define available economic capital under the consolidated approach as the difference between the sum of the legal entities’ assets and the sum of the liabilities. Under this approach, individual and joint shortfall probabilities coincide such that P Pind

mjoint= and

P Pind,MLmjoint,ML= , for any m = 1, ... ,N + 1.

Numerical analysis and implicationsIn our numerical analyses, we present results for a stylized example. For the sake of simplicity, we consider an insurance group that is comprised of three legal entities: two subsidiaries and their parent company.

Our analysis examines the introduction of a guarantee and a quota-share retrocession transferred either from the parent company 0 to subsidiary 1 or from subsidiary 2 to subsidiary 1.

The numerical example is conducted via a 100,000-run Monte-Carlo simulation, each run employing the same set of random numbers [Glasserman (2004)].

Parameter settingsIn the following, we assume that the three firms (i.e., the two subsidiaries and their parent) have the same asset-liability structure but that the parent company is twice as large as its subsidiaries. We set the nominal value of the liabilities of subsidiaries 1 and 2 to L L 500,1 0,2= = mln currency units (CU) and the market value of the liabilities of the parent company 0 to L CU0,0 = 100 mln. The equity capital of the two subsidiaries E0,1 and E0,2 is fixed at CU 15 mln and for the parent E0,0 at CU 30 mln. The initial values of the default put option are fixed at CU 100,000 for company 0 and at CU 50,000 for the subsidiaries, so the value of the debt capital of subsidiaries 1 and 2 is given by D D CU0,1 0,2= = mln, and the value of the debt capital of the parent company is given by D CU0,0 = 99.9 mln. Thus, the market value of the assets of the two subsidiaries A0,1 and A0,2 is CU 65 mln and for the parent company it amounts to A CU0,0 = 130 mln. The net premium income of subsidiaries 1 and 2 is set to P P CU1 2= = 7.5 mln and that of the parent is set to P CU0 = 15 mln. We assume the average net claims over the last three years to be C C CU1 2= = 4.5 mln for the subsidiaries and C CU0 = 9 mln for the parent company. Drift and standard deviation of the assets and liabilities are given by 5%, 10%A A= =n v (for assets) and 3%, 0.5%L L= =n v (for liabilities). The risk-free rate of return is set to r 2%f = , and the quota of the quota-share retrocession is assumed to be q = 5%. The correlation coefficients between pairs of assets and liabilities are fixed at: A ,L 0.2i i =t^ h and

A ,L A ,L 0.0i j j i= =tt^ ^h h , with i j! and i, j = 0, 1, 2. For a more profound comparison of the two solvency models, we compare results for different values of A ,A L ,Li i jj= =t t t^ ^h h, with i j! and i, j = 0, 1, 2. We show outcomes for the uncorrelated case

0.0=t^ h, for a case of moderate correlation 0.4=t^ h, and for a case of relatively high correlation 0.8=t^ h.

Numerical results and interpretation

Risk dependenciesWe follow the working definition of risk dependencies by the International Association of Insurance Supervisors [IAIS (2009b)]. Our discussion, therefore, focuses on two main drivers of risk dependencies: risk concentration and risk diversification.



According to the IAIS, risk concentration refers to common risk factors that are able to threaten the financial soundness of the entire insurance group, while diversification effects cause the aggregated risks of the entire group to be in general lower than the sum of the individual companies’ risks. We take two perspectives in comparing the different solvency approaches with regard to how they assess shortfall risks and concentration, as

well as diversification effects within the insurance group. In the first step, we assess the riskiness of each financial institution by considering individual shortfall probabilities (Figure 1) and the necessary economic capital (Figure 2). In the second step, we focus on the institutions’ exposure to common risk factors and their interconnectedness, measured by joint shortfall probabilities (Figure 3).

LELE G0/1

LE G2/1

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Cons

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Pind for ρ = 0.0 Pind,ML ρ = 0.0

Pind,ML ρ = 0.4

Pind,ML ρ = 0.8

0

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0

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Pind for ρ = 0.8

Company 1Company 2

Company 0

Figure1:Individualshortfallprobabilitiesforρ=0.0,0.4and0.8LE = legal entity approach without CRTIs; LEG0/1 = legal entity approach with a guarantee from company 0 to subsidiary 1; LEG2/1 = legal entity approach with a guarantee from subsidiary 2 to subsidiary 1; LER0/1 = legal entity approach with a retrocession from company 0 to subsidiary 1; LER2/1 = legal entity approach with a retrocession from subsidiary 2 to subsidiary 1; Cons = consolidated approach


TheriskinessoftheindividualfinancialinstitutionOur simulation results, shown in Figure 1 and Figure 2, are based on the fixed capital structure given above. Figure 1 shows individual shortfall probabilities (left column) as well as the probabilities that the available economic capital in time 1 will

fall below the minimum level (ML) (right column) for different specifications of the correlation coefficient t. The left column of Figure 1 0.0=t^ h shows that under our legal entity approach, the parent company’s shortfall probability is practically reduced to zero due to the group diversification [Gatzert and Schmeiser (2011)].3 The subsidiaries’ shortfall probabilities, on the other hand, depend on the transfer case, considered. With no CRTIs in place, the subsidiaries do not participate in the diversification effects.

By contrast, the introduction of a CRTI leads to a considerable reduction in the shortfall probability of the subsidiary benefiting from the transfer, although the extent of the reduction depends on the type of CRTI and on the transferring company’s solvency. A guarantee reduces the beneficiary’s shortfall probability to practically zero, regardless of whether the transferor is the parent company or another subsidiary. By contrast, the introduction of a quota-share retrocession reduces the benefiting company’s shortfall probability to a lesser degree, particularly when it is the other subsidiary that is making the transfer. The parent company’s shortfall probability is unchanged and close to zero in all cases, since the transfer from the parent is undertaken only when the company is solvent. Only one bar is shown for the consolidated approach, because the insurance group is treated as one consolidated entity. As a consequence, individual and joint shortfall probabilities are indistinguishable in this framework. Due to a maximum realization of diversification effects and synergies under this solvency approach, the probability of shortfall is close to zero for 0.0=t^ h. The right column of Figure 1 shows the probability that the available economic capital at time 1 will fall below the minimum level of economic capital, meaning that the firms will not be able to continue in business unless they raise additional capital. Thus, Pind,ML includes Pind. Under the legal-entity approach, the benefiting subsidiary’s Pind,ML remains stable both with and without a guarantee, but it is reduced in case of a quota-share retrocession. The parent’s individual shortfall probability and the consolidated model’s PML are, again, close to zero. Turning to the second and third row of Figure 1, we find that the higher the correlation coefficient t, the more diversification effects are reduced in both group solvency approaches and consequently the individual shortfall probabilities are increased in all cases.

3 Here, diversification effects can arise because assets and liabilities of the three companies are not fully correlated [Gatzert and Schmeiser (2011)].

60

50

40

30

20

10

0

LELE G0/1

LE G2/1

LE R0/1

LE R2/1

Cons

LELE G0/1

LE G2/1

LE R0/1

LE R2/1

Cons

LELE G0/1

LE G2/1

LE R0/1

LE R2/1

Cons

NEC for ρ = 0.0

60

50

40

30

20

10

0

NEC for ρ = 0.4

60

50

40

30

20

10

0

NEC for ρ = 0.8

Company 0 Company 1 Company 2

Figure2:Necessaryeconomiccapitalforρ=0.0,0.4and0.8LE = legal entity approach without CRTIs; LEG0/1 = legal entity approach with a guarantee from company 0 to subsidiary 1; LEG2/1 = legal entity approach with a guarantee from subsidiary 2 to subsidiary 1; LER0/1 = legal entity approach with a retrocession from company 0 to subsidiary 1; LER2/1 = legal entity approach with a retrocession from subsidiary 2 to subsidiary 1; Cons = consolidated approach



Figure 2 shows the capital requirements for the entire insurance group under both approaches. The different shades of gray in the cases of the legal entity approach indicate the entities’ individual contribution to the group capital charge. Considering the uncorrelated case in the first row, we see that under the legal entity approach, the parent’s necessary economic capital is substantially lower compared to the NECs of the two subsidiaries. The introduction of a guarantee leads to a slight decrease in the NEC of the benefiting subsidiary, but to a slight increase in the

capital requirement of the parent company. Consequently, the group NEC remains relatively constant.

By contrast, when a quota-share retrocession is in place, the increase in the parent’s NEC is substantial, so that the group capital requirement is higher than in the case without any CRTIs. Turning to the consolidated approach, where the insurance group is considered on the basis of its consolidated balance sheet, the NEC shown is already the capital requirement for the entire

IIIII

I

0.01

0

0.005

LELE G0/1

LE G2/1

LE R0/1

LE R2/1

Cons

LELE G0/1

LE G2/1

LE R0/1

LE R2/1

Cons

LELE G0/1

LE G2/1

LE R0/1

LE R2/1

Cons

LELE G0/1

LE G2/1

LE R0/1

LE R2/1

Cons

LELE G0/1

LE G2/1

LE R0/1

LE R2/1

Cons

LELE G0/1

LE G2/1

LE R0/1

LE R2/1

Cons

Pjoint for ρ = 0.0

0.01

0.015

0

0.005

Pjoint,ML for ρ = 0.0

0.01

0

0.005

Pjoint for ρ = 0.4

0.01

0.015

0

0.005


0.01

0

0.005

Pjoint for ρ = 0.8

0.01

0

0.005


Figure3:Jointshortfallprobabilitiesforρ=0.0,0.4and0.8LE = legal entity approach without CRTIs; LEG0/1 = legal entity approach with a guarantee from company 0 to subsidiary 1; LEG2/1 = legal entity approach with a guarantee from subsidiary 2 to subsidiary 1; LER0/1 = legal entity approach with a retrocession from company 0 to subsidiary 1; LER2/1 = legal entity approach with a retrocession from subsidiary 2 to subsidiary 1; Cons = consolidated approach


insurance group. Comparing the necessary economic capital of the two solvency models, we find that they are very similar to each other.

With an increase in t, the necessary economic capital for company 0 increases substantially within the legal entity approach due to group diversification effects. This is particularly evident when looking at the entities’ contribution to the overall group capital charge. While the subsidiaries’ necessary economic capital remains approximately the same, the capital requirement of the parent company increases considerably. The necessary economic capital under the consolidated approach increases to a similar extent for higher correlation coefficients.

Interconnectedness within the insurance group – in the next step, joint shortfall probabilities are calculated based on the capital structure of the numerical example. Results are presented in Figure 3. Again, we consider three different values for t. In the uncorrelated case (left column of Figure 3), we find that the probability that all three entities, or two out of three of them, will default at the same time (P andPIII

jointIIjoint) is close to zero for

both approaches. Since under the consolidated approach joint shortfall probabilities correspond to the individual ones, PI

joint and P andPIII

jointIIjoint are not defined [Gatzert and Schmeiser (2011)]. The

probability that exactly one firm defaults (PIjoint) is lowest for

the case of a guarantee under the legal entity approach.

In the case of a quota-share retrocession, PIjoint is significantly higher

when the transfer is made from one subsidiary to another than when the transfer is made from the parent company to one of the subsidiaries. Similar results can be observed in the right column of Figure 3. However, the legal entity approach results in the lowest probabilities that the available economic capital of exactly one firm will fall below the minimum level of economic capital in the presence of a quota-share retrocession.

The second and last row of Figure 3 depict the results for higher correlations. While the probability that only one entity of the insurance group will default is reduced significantly when assets and liabilities of the different entities are highly correlated, the joint shortfall probabilities II and III are significantly increased in all cases. Comparing the two solvency models, the probability of all three firms defaulting at the same time is approximately three times higher in the consolidated framework than in all cases of the legal entity approach.

Regulatory inconsistencyAccording to Mälkönen (2004), regulatory inconsistency occurs in the presence of regulatory arbitrage and double/multiple gearing of capital. Regulatory arbitrage is the process of taking advantage of the discrepancies between different regulatory regimes and is sometimes referred to as “capital arbitrage” or “jurisdictional arbitrage” [Freixas et al. (2007)]. In the context of financial conglomerates and insurance groups, regulatory arbitrage can be defined as the possibility of separately capitalized legal entities transferring assets to the divisions that are subject to the lowest capital charges.

According to the Joint Forum on Financial Conglomerates (1998), double gearing of capital occurs if one legal entity of a financial group holds solvency capital issued by another legal entity, and the issuing company counts the capital in its own balance sheet. Thus, external capital of the group is counted twice, so it may serve to fulfill capital adequacy requirements in both entities. Multiple capital gearing occurs when the externally generated capital is geared up multiple times, such as when a company that holds regulatory capital issued by another legal entity downstreams this capital to a third-tier legal entity.

With regard to the legal entity approach, intra-group transfers are properly assessed because this approach models the web of CRTIs. However, regulatory arbitrage between countries and financial sectors is generally possible whenever capital charges are calculated differently in different jurisdictions (Table A1 in the Appendix). On the other hand, this approach models the market value of the subsidiaries as an asset of the parent company, so double/multiple gearing is avoided by splitting up the value of a subsidiary i = 1, ... ,N into two parts: the transferable value to the parent max A L ML ,0l,i l,i i- -^^ hh, and the subsidiary’s available economic capital min A L ML,l,i l,i i-^^ hh, which at least equals the minimum level [Gatzert and Schmeiser (2011)].

Finally, considering our consolidated approach, we find that due to the implicit assumption of full fungibility and transferability of capital and risks and the fact that capital adequacy requirements are based on one consolidated balance sheet, regulatory arbitrage and double/multiple gearing of capital are not possible [Freixas et al. (2007)].



ComparisonThe comparison in this section aims to determine which of the two group solvency approaches considered is more appropriate under which circumstances. The consolidated approach treats the insurance group as one integrated entity, so all intra-group transactions cancel out. Thus, the approach implicitly controls for regulatory inconsistency. Yet, Keller (2007) points out that it is a valid group solvency approach only when its assumption of full mobility of capital and risks between members of the insurance group holds, allowing for a maximum realization of synergies and diversification. These effects are reflected in our simulation results for the individual shortfall probabilities, as the consolidated approach produces the lowest probabilities, regardless of the value of t (Figure 1). In line with Keller’s reasoning, the Committee of European Insurance and Occupational Pensions Supervisors points out, that such an assumption is particularly problematic during financial crises because diversification benefits tend to diminish or at least do not operate the same way they do in normal times [CEIOPS (2009c)]. In addition to the problematic assumption of full transferability, the consolidated approach does not provide any information about the individual entity or its risk contribution to the total risk faced by the insurance group as it is based on a consolidated balance sheet.

On the other hand, the analysis presented above suggests that the consolidated approach is the more conservative approach when it comes to computing the probability that all legal entities within an insurance group will default at the same time (Figure 3). By contrast, the legal entity approach to group solvency provides for the shortfall risk of each institution and its individual capital endowment by taking into account risk and capital transfer instruments. As it is based on the individual entities’ balance sheets, and therefore does not need to assume full transferability of capital and risks within the insurance group, Keller (2007) argues that it is a group solvency approach directly compatible with a solo assessment of the solvency of an individual entity. Despite the problem of not being able to account for regulatory arbitrage, in our model framework the legal entity approach is more conservative with regard to the risk assessment of the individual members of the insurance group (Figure 1). It is also able to control for capital gearing. However, it is likely to be the most complex to implement in practice and therefore probably the more expensive group-wide solvency approach

[IAIS (2009b)]. Nevertheless, if the web of CRTIs is modeled accurately, the legal entity approach can model all kinds of group structures, including the extreme case of no intra-group transactions at all, as well as the case when capital and risks are freely transferable among the legal entities. Consequently, it is the more generally applicable framework.

Summary This paper compares two approaches to group-wide solvency assessment of insurance groups in light of the regulatory challenges of regulatory inconsistency and risk dependencies: a legal entity approach and a consolidated approach. Generalizing the model framework by Gatzert and Schmeiser (2011), we examine capital charges, individual shortfall risks, as well as joint shortfall for an insurance group of N + 1 legal entities — one parent company and N subsidiaries — and interpret the results with respect to the supervisory challenges of regulatory inconsistency and risk dependencies, with a special focus on the latter one.

Our findings contribute to the current discussion of regulating and managing large financial groups, especially insurance groups. Firstly, we present the two group solvency approaches emphasizing the different implicit and explicit assumptions made in each framework since these are of special relevance from a regulatory perspective. The results of our numerical analyses reveal that the choice of a particular group solvency approach has a substantial influence on capital charges and shortfall risks. Individual shortfall risks decrease considerably with the level of consolidation assumed by each of the different solvency approaches, although this effect diminishes as the correlation between the entities’ returns on assets and liabilities increases. Secondly, the two solvency approaches are compared in terms of their advantages and shortcomings, and it is determined under which circumstances each approach is more appropriate. The assumptions of a consolidated framework are particularly problematic when asset and liability returns become highly correlated as the effects of diversification diminish. On the other hand, our numerical analyses show that the consolidated approach is more conservative than the legal entity framework with respect to the calculation of joint shortfall probabilities. In addition, the legal entity approach provides for each entity’s individual shortfall risk and capital endowment by taking into account the web of CRTIs, whereas a consolidated approach


provides no information about the individual entity or its contribution to total risk [Gatzert and Schmeiser (2011)]. Finally, the legal entity framework is more complex to implement and cannot control regulatory arbitrage.

We conclude from the analyses that a legal entity approach is more generally applicable, as it is able to take different group structures into account and find it therefore, despite its shortcomings, superior to an approach that is solely based on a consolidated viewpoint. Although the models used to assess group-wide solvency in practice are intermediate models with characteristics of both the legal entity and the consolidated approach, a comparison of these two extremes on a theoretical and numerical basis in light of regulatory challenges is especially important as regulators and practitioners alike work toward designing and implementing sound solvency models for the risk management of insurance groups.

ReferencesAllen, L., and J. Jagtiani, 2000, “The risk effects of combining banking, securities, and insurance activities,” Journal of Economics and Business, 52(6), 485—497Ammann, M., and M. Verhofen, 2006, “The conglomerate discount: a new explanation based on credit risk,” International Journal of Theoretical and Applied Finance, 9(8), 1201—1214Committee of European Insurance and Occupational Pension Supervisors (CEIOPS), 2009, Lessons learned from the crisis, available at: https://eiopa.europa.euDe Nicolo, G., and M. Kwast, 2002, “Systemic risk and financial consolidation: are they related?” Journal of Banking and Finance, 26(5), 861—880Diereck, F., 2004, “The supervision of mixed financial services groups in Europe,” European CentralBank Occasional Paper Series, No. 20, European Central Bank, FrankfurtDoherty, N., and J. Garven, 1986, “Price regulation in property-liability insurance: a contingent-claims Approach,” Journal of Finance, 41(5), 1031—1050European Commission (EC), 2002, Directive 2002/13/EC of the European Parliament and of the Council Amending Council Directive 73/239/EEC as regards the “Solvency margin requirements for non-life insurance undertakings,” available at: http://eur-lex.europa.euEuropean Commission (EC), 2009, Directive 2009/138/EC of the European Parliament and of the Council of 25 November 2009 on the “Taking-up and pursuit of the business of insurance and reinsurance (Solvency II),” Official Journal of the European Union, available at: http://eur-lex.europa.euFilipović,D.,andM.Kupper,2007,“On the group level Swiss solvency test,” Bulletin of the Swiss Association of Actuaries, 1(1), 97—115Filipović,D.,andM.Kupper,2008,“Optimal capital and risk transfer for group diversification,” Mathematical Finance, 18(1), 55—76Freixas, X., G. Loranth, and A. Morrison, 2007, “Regulating financial conglomerates,” Journal of Financial Intermediation, 16(4), 479—514Gatzert, N., and H. Schmeiser, 2011, “On the risk situation of financial conglomerates: does diversification matter?” Financial Markets and Portfolio Management, 25(1), 3—26Glasserman, P., 2004, Monte Carlo methods in financial engineering, Springer, New York

Harrington, S., 2009, “The financial crisis, systemic risk, and the future of insurance regulation,” Journal of Risk and Insurance, 76(4), 785—819International Association of Insurance Supervisors (IAIS), 2009, Issues paper on group-wide solvency assessment and supervision, available at: www.iaisweb.orgJoint Forum on Financial Conglomerates, 1998, Capital adequacy principles paper, www.bis.orgKahn, C., and A. Winton, 2004, “Moral hazard and optimal subsidiary structure for financial institutions,” Journal of Finance, 59(6), 2531—2575Keller, P., 2007, “Group diversification,” Geneva Papers on Risk and Insurance — Issues and Practice, 32(3), 382—392Laeven, L., and R. Levine, 2005, “Is there a diversification discount in financial conglomerates?” Journal of Financial Economics, 85(2):331—367Luder, T., 2007, “Modelling of risks in insurance groups for the Swiss solvency test,” Bulletin of the Swiss Association of Actuaries, 1(1), 85—97Mälkönen, V., 2004, “Capital adequacy regulation and financial conglomerates,” Journal of Banking Regulation, 6(1), 33—52Morrison, A., 2003, “The economics of capital regulation in financial conglomerates,” Geneva Papers on Risk and Insurance — Issues and Practice, 28(3), 521—533National Association of Insurance Commissioners (NAIC), 2009, Risk-based capital — general overview, available at: www.naic.orgSchilder, A., and I. van Lelyveld, 2003, “Risk in financial conglomerates: management and supervision,” in Herring, R., and R. Litan (eds.), Brookings-Wharton Papers on Financial Services, pages 195—224. Brookings Institution Press, Washington, DCSchmid, M., and I. Walter, 2009, “Do financial conglomerates create or destroy economic value?” Journal of Financial Intermediation, 18(2), 193—216Schüler, M., 2002, “The threat of systemic risk in banking – evidence for Europe,” Quarterly Journal of Business and Economics, 41(3/4), 145—165Siegel, C., 2013, “Solvency assessment for insurance groups in the United States and Europe – a comparison of regulatory frameworks,” Geneva Papers on Risk and Insurance – Issues and Practice, forthcoming SwissFederalOfficeofPrivateInsurance(FOPI),2004,White paper of the Swiss solvency test, available at: www.finma.chSwissFederalOfficeofPrivateInsurance(FOPI),2006,Technical document on the Swiss solvency test, available at: www.finma.chvan Lelyveld, I., and K. Knot, 2009, “Do financial conglomerates create or destroy value? Evidence for the EU,” Journal of Banking & Finance, 33(12), 2312—2321

Appendix A. Derivation of individual and joint shortfall probabilitiesIn line with Gatzert and Schmeiser (2011), we assume that shortfall can occur in two cases:

1. Either the available economic capital in t = 1 falls below zero, so the insurer is insolvent, or

2. P AEC MLiind,ML

1,i i= 1^ h falls below the minimum level P AEC MLiind,ML

1,i i= 1^ h, meaning that firm i is not insolvent, but cannot continue in business, unless it raises additional capital.

Thus, the individual shortfall probabilities for the ith entity can be calculated by [Gatzert and Schmeiser (2011)]:



P AEC 0iind

1,i= P 1^ h (1)

P AEC MLiind,ML

1,i i= P 1^ h. (2)

The probability of a joint shortfall of exactly m = 1, ... ,N + 1 legal entities can be expressed by:

P AEC 0 AEC 0mjoint

i F* 1,i i F\F* 1,i= / / /R 2 2P e e^ ^h h6 @ F* 1 F|F*|=m

(3)

The sum runs over all subsets F* of F counting exactly m elements.4 The first term inside the square brackets describes the joint shortfall of all legal entities within the subset F*, given that the residual firms of F (the second term inside the square brackets) are solvent at t = 1. Similarly, the probability that the available capital of m = 1, ... ,N + 1 legal entities simultaneously falls below the minimum level, is:

P AEC ML AEC MLmjoint

i F* 1,i i i F\F* 1,i i= / / /R 2 2P e e^ ^h h6 @ F* 1 F|F*|=m

(4)

B. Legal entity approach — values of the CRTIs The value of the guarantee TG can be expressed by:

T min DPO ,max A L ML ,0G1,i 1,i 1,i itr tr trbfc= - -^^ hh. (1)

For the quota share retrocession, the value can be calculated as:

T min q L ,max A L ML ,0R1,i 1,i 1,i ibfc tr tr tr= - -$ ^^ hh. (2)

C. Derivation of available economic capital

1. Legal entity approach — considering the case of a transfer from the parent company i = 0 to the benefiting subsidiary, ibfc, we can express available economic capital in t = 0 for all i = 0, ... ,N, by: AEC A L0,i 0,i 0,i= - . At time t = 1 the AEC of the beneficiary is:

AEC min A L ,ML T1,i 1,i 1,i ibfc bfc bfc bfc= - +^ h . (1)

4 |F*| denotes the cardinality of the subset F* (m is the number of legal entities insolvent at t = 1).

For the parent company i = 0, we obtain at t = 1:

AEC A L max A L ML ,0 max A L ML 0 T1,0 1,0 1,0 1,i 1,i i

N

1,i 1,i ibfc bfc bfc

bfc

= - + - - + - - -Ri 1i i=!

^ ^^h hh

(2)

For all other subsidiaries i 1,...,N, i ibfc= ! , we receive:

AEC A –L ,MLmin1,i 1,i 1,i i= ^ h (3)

For the case in which a transfer is made from one subsidiary itr to another subsidiary ibfc, with itr, given i 0bfc ! , the available economic capital in t = 0 is again defined by AEC A L0,i 0,i 0,i= - for all i = 0,...,N. The AEC of the transferor and the beneficiary in t = 1 can be expressed by:

AEC min A L T,ML1,i 1,i 1,i itr tr tr tr= - -^ h (4)andAEC min A L T,ML T1,i 1,i 1,i ibfc bfc bfc bfc= - - +^ h

Finally, we receive for the available economic capital of the parent company in t = 1:

RN

AEC A L max A L ML T,0

max A L ML T,0 max A L ML ,0

1,0 1,0 0,1 1,i 1,i i

1,i 1,i i

i i ;i i

1,i 1,i i

tr tr tr

bfc bfc bfc

bfc tr

= - + - - - +

- - + + - -! !

i 1=

^

^ ^^

h

h hh

(5)

2. Consolidated approach — on the basis of consolidated accounts, the available economic capital of the concern can be calculated by [Gatzert and Schmeiser (2011)]:

AEC A Ltcons

i 1

N

t,ii 1

N

t,i= - -R R= =

(6)

for t = 0, 1.


Three-entity example – for an insurance group comprised of three entities, one parent company and two subsidiaries, the calculation of available economic capital reduces to the following formulas: under the legal entity approach, available economic capital at t = 0 for the ith legal entity is determined by AEC A L0,i 0,i 0,i= - , whereas it is given by AEC A A A L L L0

cons0,0 0,1 0,2 0,0 0,1 0,2= + + - - -

for the consolidated approach.

The AEC for the different transfer cases under the legal entity approach as well as the consolidated available economic capital at t = 1 are summarized in the table below [Gatzert and Schmeiser (2011)].

AEC1,0 AEC1,1 AEC1,2

Legal entity A Lmax A L MLmax A L ML

1,0 1,0

1,1 1,1 1,0

1,2 1,2 2,0

-+ - -+ - -

^

^

h

h

min A L ,ML1,1 1,1 1-^ h min A L ,ML1,2 1,2 2-^ h

Legal entity G0/1 A Lmax A L MLmax A L ML T

1,0 1,0

1,1 1,1 1,0

1,2 1,2 2,0G

-+ - -+ - - -

^

^

h

h

min A L ,ML T1,1 1,1 1G- +^ h min A L ,ML1,2 1,2 2-^ h

Legal entity G2/1 A Lmax A L ML T ,0max A L ML T ,0

1,0 1,0

1,1 1,1 1G

1,2 1,2 2G

-+ - - -+ - - +

^

^

h

h

min A L ,ML T1,1 1,1 1G- +^ h min A L T ,ML1,2 1,2

G2- -^ h

Legal entity R0/1 A Lmax A L MLmax A L ML T

1,0 1,0

1,1 1,1 1,0

1,2 1,2 2,0R

-+ - -+ - - -

^

^

h

h

min A L ,ML T1,1 1,1 1R- +^ h min A L ,ML1,2 1,2 2-^ h

Legal entity R2/1 A Lmax A L ML T ,0max A L ML T ,0

1,0 1,0

1,1 1,1 1R

1,2 1,2 2R

-+ - - -+ - - +

^

^

h

h

min A L ,ML T1,1 1,1 1R- +^ h min A L T ,ML1,2 1,2

R2- -^ h

Cons A A A L L L1,0 1,1 1,2 1,0 1,1 1,2+ + - - - -- --

Table A1: Available economic capital at t = 1 for the two approaches of group solvency assessmentLegal entity = legal entity approach without CRTIs; Legal entity G0/1 = legal entity approach with a guarantee from company 0 to subsidiary 1; Legal entity G2/1 = legal entity approach with a guarantee from subsidiary 2 to subsidiary 1; Legal entity R0/1 = legal entity approach with a retrocession from company 0 to subsidiary 1; Legal entity R2/1 = legal entity approach with a retrocession from subsidiary 2 to subsidiary 1; Cons = consolidated approach


Part 2

Determinants of the interest rate premium on contingent convertible bonds (CoCos)George M. von FurstenbergJ.H. Rudy Professor of Economics Emeritus, Department of Economics, Indiana University

AbstractRuling out default prior to conversion of high-trigger (going-concern) CoCos, this paper concentrates on estimating the conversion risk premium on CoCos. It does so by estimating the cost of hedging that risk with a contingent put option, exercisable only in the event of conversion, whose strike price is set at the conversion price per share (CPS). In this situation, the level of the common equity tier-1 (CET1) capital ratio at the time that the CoCos are issued plays a central role: it determines the probability of conversion during the term of the CoCos and the level of the CPS, relative to the market price per share (MPS) at the time of CoCos issuance, that must be set to stabilize the expected replacement rate, here at 80%. This replacement rate implies that CoCos holders can expect to lose 20% of the face value of CoCos in the event of conversion and are moved to exercise debt discipline. At the same time, existing shareholders derive sufficient comfort from conversion, for the losses leading up to it, not to oppose the issuance of CoCos in the first place. If the issuing companies have initial Basel III-based capital ratios that are at least 3 percentage points above the 7% going-concern trigger, covering the conversion risk should cost only a third as much as the average premium now required on equity into which, upon conversion, the CoCos would turn. By issuing such CoCos, banks can thus equip themselves with a form of contingent equity line. That line is activated automatically when triggered by adversity to rebuild their capital at a bargain without causing dilution for existing shareholders.



General introduction and motivationThis paper works through an integrated dynamic leading from a bank’s issuance of CoCos, whose terms are conditioned on the strength of its initial capitalization, to their ultimate conversion and its consequences for stakeholders. It aims to provide internally consistent specifications and numerical estimates of the probability of conversion, the choice of conversion price, and expected recovery rates, to solve for the conversion-risk premium and the resulting interest rates that could make CoCos attractive for prudential and business purposes.

CoCos are debt securities that convert outside bankruptcy to common equity tier-1 (CET1) automatically when, now usually Basel III, CET1 — henceforth understood to be expressed in percent of Basel-III risk-weighted assets (RWA) – falls below a specified level. As here, this trigger level most often is 7%. CoCos provide remedial equity capital of assured loss-absorption capacity, coupled with debt relief, to a going concern automatically just when such capital is most needed and too expensive and/or dilutive to be raised directly by public offering.

CoCos thus are a promising, and as yet underutilized, financial-reform instrument. Their addition to the balance sheet, particularly of systemically important financial institutions, would strengthen the self-insurance of the financial system and relieve taxpayers from implicit bail-out obligations. Yet issuance of CoCos by banks too big to fail so far has been confined to a few European countries. They are the United Kingdom, the Netherlands, Switzerland, Cyprus (CoCos already converted) and Belgium and, most recently, for masking government deficits, Portugal and Spain. The 15 billion dollars’ worth of “Enhanced Capital Notes” (ECNs) issued by a major UK bank in 2009, detailed in von Furstenberg (2011a, pp. 10-13, and 2011b, pp. 32-33), played a pioneering role in that regard. However, the skimpy conversion terms and low trigger level of ECNs have not proved exemplary, and interest rates have been into the double digits on pounds sterling and U.S. dollar issues of the series of low-rated CoCos that were offered in exchange for other debt or hybrids. The integrated analytical framework, previewed next, shows what links and choices need to be made at each step to make CoCos attractive to issuers and investors without government aid or mandates. CoCos deserve regulators’ acknowledgment of their merits in shoring up capital and meeting part of regulatory capital requirements to reward private prudential innovation and self-insurance, and not as a favor to the banking industry.

An integrated trajectory from CoCos issuance to conversion: technical previewThe paper first considers whether CoCos conversion should be dilutive, non-dilutive, or the opposite of dilutive to existing shareholders so as to lower, leave unchanged, or raise book value and/or market value per share, depending on the criterion chosen for dilution. The size of the bank’s CET10 capital buffer percentage above its trigger level at the time it issues CoCos (indicated by subscript 0) helps determine the probability of conversion. Its terms, in turn, affect the quality of corporate governance and the viability of issuing CoCos.

To determine the most appropriate setting of conversion terms, I estimate the empirical link between the fall in the capital ratio in the firm that would eventually lead to the trigger point and the rate of decline in the share price of its common stock. This link is needed to determine the expected recovery rate, R, which is the fraction of the principal of CoCos that may be recovered from the market value of the shares received in conversion. Next to the probability of conversion (Pc) or its complement, the probability of survival (PS) until repayment at maturity, R is crucial. It is given equivalently by the market price per share expected to prevail at the time of conversion (indicated by subscript c), MPSc, divided by the intentionally higher conversion price per share, CPS, so that R MPS /CPS 1CPSc= 1 determines the number of shares (Nc) of common stock that are to be received in conversion. This is because, by definition, Nc is equal to the principal amount of the CoCos concerted, PAC, divided by CPS, so that N PAC/CPSc / . Multiplying both sides of the identity by MPSc then yields the expected market value MPS N R PACc c =^ ^h h.

Further specifications are that the conversion terms are varied in response to changes in the probability of conversion that are associated with differences in CET10. The closer CET10 is to the trigger level when the CoCos are issued, the higher the probability of conversion before maturity and the lower the rate of share price decline from the already depressed level of the market price per share at the time the CoCos are issued, MPS i, which is normalized at 1, to its level at conversion, MPS 1c 1 . To keep the expected recovery rate, MPS /CPSc , the same at the time of issue for all CoCos, any change in MPSc produced by a difference in the initial capital ratios of particular CoCos issues must be compensated by an equal percentage change in CPS. The resulting conversion prices, like the probability of CoCos


being converted within their 10-year term to maturity, Pc, are inversely related to CET10. They are designed to leave the losses from conversion expected by CoCos holders uniformly at about 20% of the PAC converted to facilitate standardization and focusing on differences in CoCos features other than their recovery rate.

The last step for deriving the CoCos conversion-risk premium is to price a 10-year put option whose strike price is CPS and whose market price is set equal to the expected MPSc rather than the current MPS0. This is done because conversion must occur before the contingent put option can be exercised.1 Buying such on option for the number of shares to be issued at conversion, Nc, which is equal to 1/CPS when PAC is set equal to 1 as already explained, and weighting by the cumulative probability of conversion prior to maturity, Pc, because the exercise of the option is contingent on conversion, yields a rough estimate of the expected cost of the hedge against conversion risk. Put options are, therefore, used as a theoretical device for pricing the risk of losses from conversion facing CoCos investors by what it would cost to hedge this risk in perfect capital markets.2

The resulting schedule of premiums over the riskless interest rate, derived with conversion-contingent options coverage of the risk of losses, is then compared with the results reported in an earlier paper. That paper [von Furstenberg (2012a)] contained estimates of the cost of CDS coverage of the conversion losses for CoCos investors when conversion is treated as a default event. This comparison gives confidence that if the stand-alone credit profile (SACP) of the issuing bank and the buffer above the trigger level of the CET1 capital ratio together are adequate to support an initial investment-grade rating for CoCos, CoCos are a highly competitive contingent source of equity capital. That source is tapped automatically when it is most needed because other sources have dried up while capital ratios were shrinking. This concludes the introductory section and its technical preview.

1 Certain complexities are passed over here. For instance, while the cumulative probability of conversion, Pc, is later deduced from a random-walk expansion process, the survival curve of CoCos from the time of issue to maturity, other than its end point, is not made explicit, nor is the market price expected to prevail at the uncertain time of CoCos conversion discounted to the time of issue before it is used in the put option.

2 The condition that CPS > MPSc, while holding ex-ante by design, may be violated ex-post in rare instances. Ignoring this slight upside potential makes the present estimate of the conversion risk premium a little too high and leaves the complete estimate closer to the estimate based on hedging with CDS.

Corporate governance and how stakeholders fare in CoCos conversionTo be motivated to exercise debt discipline, investors in CoCos should expect to be subjected to losses in the event of conversion. They could then be relied upon to exercise influence over management to avoid excessive risk taking and to keep the designated capital ratio well above the trigger point. Prompt corrective action may then follow. Certain groups of stakeholders, such as unsecured senior creditors, naturally favor adding CoCos financing as long as such financing does not displace an equal amount of common equity, because CoCos would be loss-absorbing outside bankruptcy after conversion has been triggered. On the other hand, if conversion terms are so dilutive as to make conversion harmful to existing shareholders in spite of any help in avoiding bankruptcy it could provide, it may not be possible to get CoCos issued by any firm unless there are regulatory CoCos mandates to do so. Such mandates, not further considered in this paper, have been imposed on Switzerland’s two largest banks. They have also been imposed under quite different circumstances on failing banks in Spain and Portugal to precede their recapitalization through equity injections by government agencies.

CoCos can become worthless only if the stock into which they convert when triggered is expected to have no value whatsoever so that bankruptcy is at hand. However, the debt cancellation associated with conversion strengthens the balance sheet of the firm by providing for more equity and less interest-bearing debt.3 The safety cushion that CoCos provide for firms struggling to maintain viability will then be generally appreciated, and disputes over the terms of conversion will yield to concern for what conversion can do to help the firm recover. Well away from bankruptcy and CoCos-induced changes in the dynamics of the firm’s survival, however, the terms of CoCos conversion appear zero-sum, with redistribution primarily taking place between CoCos holders and existing shareholders. Relations between

3 For this restoration of value to existing shareholders to occur in a going concern, conversion would have to be into shares that would otherwise have been worthless, and not into shares of a new legal entity or successor company, established in resolution, as a recent joint paper by the Federal Deposit Insurance Corporation and Bank of England (2012) has proposed. Conversion terms are immaterial under that proposal because the holders of the highest levels of debt not written off in resolution, through conversion of that debt, would alone capitalize the shrunken successor company. The total value of the shares in this new legal entity is determined by the value of its net assets and not by the number of shares issued at conversion.



the conversion price (CPS), book value (BVS), and market price (MPS), all per share (S), are crucial to which group gains and which loses from conversion and when conversion produces theoretical stock-value and earnings-per-share dilution or its opposite. After explaining the metric of dilution, a sequence of accounting snapshots in Table 1 – from CoCos issuance through conversion – applies this metric to show which group gains and which loses from conversion. The distributions that result depend on the alternative values of CPS specified in Table 1 and hence on the number of shares issued to the CoCos holders in conversion. One such distribution key may dominate the others by containing adequate incentives to get CoCos issued while also providing CoCos debt discipline to discourage excessive risk-taking. Definingandmeasuringdilutionfromconversion, and its oppositeEquating CoCos conversion automatically with dilution and regarding only write-down CoCos that do not convert to equity when triggered as non-dilutive for existing shareholders is commonplace in financial reporting and commentaries [see Durand (2011) for a case in point]. In fact, however, write-down-only CoCos that convert into thin air and not shares are not just non-dilutive but strongly anti-dilutive, making a gift of CoCos

debt write-off to existing shareholders.4 Although partial write-down, or complete permanent write-off “cliff” CoCos have been issued by at least four banks in recent years, the market for such contingently canceled debt claims is likely to remain very small. When triggered, their holders would be worse off than under regular bankruptcy, where subordinated debt holders would not be first to absorb losses, ahead of stockholders, and their losses might not be total. Write-off CoCos have been likened to regular CoCos with a CPS of infinity so that N PAC/CPS 0c =/ . There is no need to go to such an extreme value for CPS to satisfy the no-dilution condition for existing shareholders, CPS MPSc$ .

Some prominent groups of academics have taken the opposite, equally extreme, position of wanting the terms of conversion to be made ruinous for existing shareholders rather than CoCos holders. Specifically, von Furstenberg (2011b, p. 5) references the Interim Report of the (U.K.) Independent Commission on Banking [ICB (2011, p. 182)], Goodhart (2011, p. 117), Calomiris and Herring (2011, p. 18), Flannery and Perotti (2011, p. 4), and

4 Write-down CoCos that provide for partial or full reinstatement of the debt claim after the firm has recovered to a specified degree have so many debilities, including the creation of an ugly debt overhang problem and regulatory uncertainty, as to be left out of account here.

Initially CoCosissued

Conversiontriggered

CoCos converted at CPS of:

0.2 0.4 0.5 1Column: (1) (2) (3) (4) (5) (6) (7)Liabilities (U.S.$)CoCos 25 25Other liabilities 1290 1275 1275 1275 1275 1275 1275Equity (CET1) 110 100 40 65 65 65 65Total liabilities 1400 1400 1340 1340 1340 1340 1340Number of shares pre-existing 110 100 100 100 100 100 100 from conversion 125 62.5 50 25 Total 110 100 100 225 162.5 150 125BVS (U.S.$) 1 1 0.4 0.2889 0.4 0.4333 0.5200Ownership % Pre-existing shareholders 100% 100% 100% 44.44% 61.54% 66.67% 80.00%Former CoCos holders 55.56% 38.46% 33.33% 20.00%Ownership (U.S.$)Pre-existing shareholders 110 100 40 28.89 40.00 43.33 52.00Former CoCos holders 36.11 25.00 21.67 13.00Memos: Risk-weighted assets are U.S.$575. CET1 ≤ U.S.$40 triggers conversion under the 7% trigger. BVS is calculated as the book value of CET1 divided by the total number of shares.

Table 1: Gains and losses of shareholders and CoCos holders from CoCos conversion at selected values of the conversion price per share (CPS)


the (U.S.) Shadow Financial Regulatory Committee [SFRC (2010)] as having favored CoCos with conversion terms that hold out the prospect of “death by dilution” or at least “severe” dilution. These authors expected such confiscatory terms of conversion to compel existing shareholders to impress upon management to keep the institution’s capital ratio well above the trigger level by all means at its disposal. Should conversion ever be triggered nonetheless, it would decimate the stake of existing shareholders while the former CoCos holders would end up with the great majority of shares and seize control. What tying such deadly threats to CoCos conversion ignores is that existing shareholders would be ill-advised to consent to the issuance of “Damocles” CoCos in the first place.

Hence extreme arrangements, where either CoCos holders or existing shareholders are set up to lose everything in conversion, are likely to succeed only in discouraging CoCos from being issued. Such arrangements boost, typically underpriced, tail risks by making rare events devastating to one group or the other, should they occur, with adverse ripple effects on counterparties. Thus there will be no chance for these ill-designed CoCos to make a contribution to financial stability through greater self-insurance and provisioning of financial institutions. In between these extremes there is a continuum of outcomes that can be reached by varying the conversion price per share, CPS.

The treatment that follows assumes that CoCos remain at their principal or face amount, PAC, on the balance sheet until converted5 and that the number of shares issued in conversion, Nc, is always equal to PAC/CPS and hence CPS PAC/Nc= . PAC is known from the time of CoCos issuance. Nc and CPS are generally known from the time of issue as well, as knowing one allows solving for the other. This advance knowledge facilitates the pricing and hedging of CoCos in financial markets and is indispensable to their success.

One method of conversion that has been used simply sets CPS equal to MPS around the time of CoCos issuance, MPS0. Another determines CPS, subject to a minimum, from stock price data

5 If CoCos liabilities had been marked to market, the boost to book equity from write-off of PAC at conversion is less by the amount of the prior markdown. Because that markdown anticipates some of the benefits of complete write-off should it occur, it could be added back to estimate the total benefit of the debt write-off at conversion.

around the time of CoCos conversion rather than issuance. Then CPS equals the actual MPSc known only at conversion, provided it lies above a specified minimum value. In practice, as documented in von Furstenberg (2012a, pp. 59-62), the minimum value set on CPS when CoCos are issued by initially well-capitalized banks has tended to be around 0.5MPS0 while MPSc is expected to be around 0.4MPS0 for these banks. Assuming that the minimum will in fact be binding, the number of shares to be issued in conversion is thus known already at the time of CoCos issuance as it is when CPS is set equal to the MPS0.

The two groups most directly affected by conversion are CoCos holders and existing shareholders. In the comparative-static setting of a going concern, losses to one of these two groups imply gains for the other since conversion, viewed as an accounting operation, cannot create net wealth. CoCos holders would be subject to losses from conversion on the principal amount of their claim if the market value of the shares obtained through conversion is less than PAC. This will happen when MPS CPSc 1 and hence MPS N PACc c 1^ h . Existing shareholders would then end up with net gains from the debt cancellation accompanying conversion even though the number of shares outstanding has increased. Conversely, if CoCos holders can expect to get value exceeding PAC from the shares obtained through conversion because MPS CPSc 2 , pre-existing shareholders stand to lose from conversion and oppose the issuance of CoCos by the firm.6

CoCos issuance to conversion: a process with alternative endings, depending on CPSThe numerical account in Table 1 lays out balance sheet modifications from CoCos issuance to conversions, which are conducted on alternative terms. In the table, the initial composition of a financial institution’s liabilities in column (1) is affected by the $25 CoCos issued in column 2. Of this $10 (40%) is used for stock buyback and $15 (60%) as a substitute for other debt. Total liabilities and book value per share (BVS) so far do not change. The capital position of the firm then deteriorates drastically: column (3) shows the book value of equity falling from

6 The combination of inequalities CPS < BVSc and CPS > MPSc may be encountered so that conversion can reduce BVSc, because CoCos holders are overcompensated at conversion by the BVS criterion, while at the same time increasing MPSc, because CoCos holders are not fully compensated by the MPS criterion. Hence which criterion for dilution is chosen can make a difference.



100 to 40, and BVS from $1 to $0.40 on the 100 shares held by existing shareholders. RWA is calculated with a weighted-average risk weight of 42.91% applied to total assets of $1,340 in this illustration. CoCos conversion is triggered because CET1/RWA now falls below 7% as explained in the memo to the table.

How many shares are issued to the former CoCos holders depends on the conversion price per share that is specified in the CoCos covenant. CPS values shown range from $0.2 to $1 in columns (4) to (7) of Table 1. The first major recent CoCos issue, made in the U.K. in 2009, specified a CPS equal to the MPS0. For financial firms, BVS and MPS0 are often close during relatively good times which are most suitable for issuing CoCos. However, BVS tends to be appreciably greater than MPSc when capital ratios have deteriorated toward the trigger point of CoCos. If CPS is $1 but BVS has fallen from $1 to $0.4, the last column of Table 1 shows that conversion at that CPS would transfer an amount equal to $52 – $40 = $12 from the former CoCos holders to pre-existing shareholders. For them, the result of conversion at such a high CPS thus would be strongly anti-dilutive.

Almost the precise opposite would happen in this comparative-static setting if CPS had been as low as $0.2. In that case, CoCos holders (unless legally entitled to no more value than PAC) would get about $36.11 – $25 = $11.11 more than the PAC of $25 in shares, while the original shareholders are left that much short of $40, which is the value of their equity prior to conversion shown in column (3).

The logic underlying these results is this: in the example just given, CoCos debt cancellation contributes 25/65, or 38.46%, of the equity of $65 outstanding after conversion when CPS BVS 0.4c= = . If the former CoCos holders were to end up with a larger share in the total number of shares outstanding after conversion, as in column (4), they would benefit at the expense of pre-existing shareholders. Conversely, if their part of the total number of shares is less than 38.46%, as in columns (6) and (7), pre-existing shareholders benefit from conversion on these terms at the expense of the former CoCos holders. Only when CPS = BVSc (= $0.4 in column(5)) is there no redistribution judging by book values. Under the latter terms, the former CoCos holders obtain the full value of PAC = $25 in shares, while pre-existing shareholders suffer neither dilution nor anti-dilution of their prior stake of $40. Judging by market rather than book values,

the same results would be obtained if CPS would be equal to the expected future value, MPSc. However, such a distributionally neutral outcome can only be intended, not guaranteed, by fixing CPS, or equivalently the number of shares to be issued in conversion. Furthermore, as next argued, aiming for such a “fair” outcome would not yield the optimal structure of incentives.

Reflecting on the appropriateness of the distribution of gains and losses from conversion for CoCos and existing shareholders, it appears that when BVSc and/or MPSc is expected to be around $0.4 at conversion, CPS = $0.5 is the best choice. As shown in column (5), existing shareholders then would receive some comfort from conversion for the large losses already suffered as their stake would be raised from $40, down from $100, to $43.33. Thus, existing shareholders would remain exposed to large losses of capital that would make them averse to venturing onto the road to conversion even though the act of conversion itself would provide a measure of relief.

At the same time, CoCos holders get to collect only $21.67 on the PAC of $25 from the shares issued in conversion. Even though the number of shares obtained from conversion is 20% less (50 compared with 62.5) at a CPS of 0.5 rather than 0.4, the recovery rate from Table 1 would be 21.67/25.00 and thus over 80% (86.7%, to be exact). The reason is that BVS and MPS rise in the process of shifting to the higher value of CPS because the number of shares outstanding declines (from 162.5 to 150). Such an effect would become immaterial if CoCos were a much smaller percentage of total liabilities than assumed in Table 1. Hence the uniform R adopted in the next part of the paper is much closer to 80% than the R deduced above. CoCos holders would thus suffer significant losses from conversion and oppose any course of action by the firm that would predictably carry an appreciable risk of ending in decapitalization to the trigger point. Goodhart’s recommendation that CoCos holders should have governance representation on the board of directors and relevant committees of the bank [see von Furstenberg (2013, p.101)] may have to be adopted to strengthen not only these holders’ incentive, but also their ability, to exercise CoCos debt discipline over management.7

7 This recommendation runs counter to the earlier support for severely penalizing existing shareholders in Goodhart (2010) because it implies, correctly in my view, that CoCos holders, not pre-existing shareholders, should suffer losses at conversion and be empowered to better guard against management’s actions that could lead to conversion.


Pricing the conversion risk of CoCos with CDS spreads or contingent put options My first simplified approach to pricing CoCos, exposited in a previous paper [von Furstenberg (2013)], followed Zhu (2004) in applying an arbitrage theorem that involved Credit Default Swaps (CDS). That approach showed that CDS spreads (annualized quarterly premium payments in percent of notional, N), c r= -t, should be approximately equal to the credit spreads (yield rates minus riskless rate), c-r. Zhu showed that, in complete markets, the fundamental equilibrium relation would be c r= -t = c-r because there would be arbitrage profits to be made otherwise. For instance, if c r= -t > (c-r) or equally ( c r= -t+r) > c, an investor can sell the CDS in the

derivatives market (earning c r= -t), buy a risk-free bond (earning r), short the corporate bond in the cash market (owing c), and make profits until c r= -t has declined and/or c has risen to restore the equality of c r= -t and (c-r). If the bond defaults, the profit on the short matches the payout on the CDS, [(1-R)N]. The problem of pricing the credit spread on CoCos was thus handled by pricing a CDS with specified survival and recovery rates and treating CoCos conversion as a default event.

A second, equally simplified, approach to estimating the conversion risk premium commanded by CoCos, over the interest rate on risk-free debt of equal maturity, prices contingent put options rather than CDS. This is the approach explored here. Results using both approaches are compared at the end of this part.

Contingent put options may be exercised just like regular options but only if and when the underlying CoCos have been converted during their term-to-maturity, assumed to be 10 years. The price of such options thus is equal to that of regular options — with the current market price, the strike price, the risk-free interest rate, the annualized volatility, and contract maturity specified — times the probability that the CoCos are triggered and duly converted into common equity rather than being paid off in full at maturity.

The probability of CoCos being converted rather than paid off depends on how far the issuer’s CET10 capital ratio was above the trigger point when the CoCos were issued, and how much time has elapsed since then, up to maturity. When one analyzes the data for common equity tier 1 (CET1) Basel-III-based capital ratios of the largest U.S. banks, obtained from 10-Q and 10-K reports filed with the SEC, one finds that the average capital ratio reported rose from 7.15% to almost 9% between 2010 and 2012. The standard

deviation of the changes in CET1, CET1tT , to the end of one quarter (t) from that of the previous quarter (t-1) through 2012-Q3 is 0.465 or 0.93 at an annual rate and 2.94 over 40 quarters when a random-walk diffusion process applies. Then if the CET1 ratio is 5 percentage points above its 7% trigger level to start with, so that CET1 12%0 = , there would be a 4.46% probability (Pc) that conversion would be triggered within 10 years since the z-score on a standard normal distribution would have to be – 5/2.94 = – 1.7 or less for the trigger event to occur. Table 2 shows that Pc rises to almost 37% if CET0 is only about 1% above the trigger level of 7% to start with, as still is the case for a few of the banks analyzed. The cumulative probability of conversion thus falls strongly, ceteris paribus, with the rise in the initial capital buffer above 7%. This percentage, with the 2.5% conservation buffer included, may soon be the lowest of the minimum regulatory Basel III CET1 capital ratios that have to be maintained by any class of internationally active banks.

Implementing the contingent-options approach for pricing the CoCos conversion riskTo implement the contingent options approach to CoCos pricing it is further necessary to associate the decline in CET1c to the trigger level with the expected fall in the market price of the company’s shares of common equity. In estimating this relationship with data for the largest U.S. banking institutions for CET1 CET1 CET1t t t 1= -T - and from Yahoo Finance for the rate

of change in adjusted stock prices at the close of trading between ends of quarters, ln MPS /MPSt t 1-^ h, intertemporal relations are important. Though dealing with 10-K annual, rather than 10-Q quarterly report filings with the SEC, the following quote may lead us into the issue: [I]nvestors’ reaction to information in 10-K appears sluggish in that future stock prices continue to drift in the same direction as the immediate market response to the information… [F]or every 1% of immediate market reaction to 10-K, there is a delayed response [over the 12 month period after the annual report filing] of about 0.7% [You and Zhang (2007)].

CET10 Pc

12% 4.46%11% 8.69%10% 15.39%9% 24.83%8% 36.69%

Table 2: Relationship between CET10 and Pc



“Large accelerated filers” must submit their reports to the SEC and release them to the public within 40 (10-Q) and 60 (10-K) days from the close of the respective quarter or year. Hence You and Zhang (2007) would expect the market’s reaction to the change in the capital ratio to occur when the data to calculate that change is reported and shortly thereafter, and not in the earlier quarter for which it is reported. This leads to the specification ln MPS /MPS b CETt 1 t 1 t= T+ $^ h .8 However, the estimate of the regression coefficient b1 obtained with the 40 CET1tT observations that can be constructed for the banks through 2012:Q39 was weak, as Table 3 shows with standard errors of estimate in parentheses.

The simultaneous relation, ln MPS /MPS b CET1t t 1 2 t= T-^ h , was slightly more successful. This specification is also quite plausible because large companies tend to provide earnings and dividend guidance and announce planned major reserve set-asides that could affect CET1 during any quarter while that quarter is still unfolding. Finally, there is the idea that markets unaccountably know quite well what is going to happen to CET1 before the accountants are able to tell. In that case the market is two quarters ahead of the quarterly release date of the latest report needed to construct CET1tT and one quarter ahead of the end-of-quarter to which that report would apply. However, the specification ln MPS /MPS b CET1t 1 t 2 3 t= T- -^ h received no empirical support as b3 unexpectedly turned out to be negative.

On balance, the best estimate appears to be that the response of stock prices to changes in a company’s CET1 ratio is simultaneous

8 The constant term was dropped after its estimate turned out to be minute and statistically insignificant.

9 The closing stock price at the end of March 2013, past this paper’s deadline for submission, is needed to implement this specification with ∆CET1t through 2012:Q4. Hence the quarterly change in CET1 during the fourth quarter that could be calculated with year-end 2012 data available by 1 March 2013 could not be used in any of the three regressions to allow their results to be comparable.

in quarterly data and presumably co-integrated but anemic. The signal-to-noise ratio in CET1tT may have been raised by the Federal Reserve’s declining to require and supervise the adoption of Basel III standards for reporting tier-1 common equity and RWA. The Fed did not provide adequate and uniform guidance even to the largest U.S. banks in that regard. Thus self-selection in choosing to initiate reporting of Basel III-based capital ratios may have led to varying degrees of upward bias. In addition, errors may well arise in CET1, and likely also in CET1tT , from measurement inconsistencies across time and companies. Raising the preferred regression coefficient, b2, by 2.326 times its estimated standard error from 0.0734 to 0.2067 implies choosing a coefficient on CET1tT so high as to allow only a 1% chance that the true coefficient is even higher. Such an adjustment may provide adequately for the jump in the sensitivity of stock prices to evidence of decapitalization that is to be expected in a financial crisis. The equation used to predict the rate of change in the stock price from its initial position at CET10 to its level at CoCos conversion – when CET1 has declined to the trigger level of 7% – is therefore:

ln MPS /MPS 0.2067 CET1c 0 c= T^ h . (1)

To give an example of how this equation is used, if CET10 were 12%, it would take a 5 percentage point decline to trigger CoCos. Hence substituting -5 for CET1cT in the equation above yields ln MPS /MPS 1.0335c 0 =-^ h and, taking antilogs, MPS 0.3558MPSc 0= . By the time of CoCos conversion the market price of the company’s common shares thus would be expected to have fallen to 35.58% of its initial level.

If, at the lower end, CET10 would be only 8%, just 1 percentage point above the trigger level, the probability of conversion, Pc, prior to the assumed maturity of 10 years, would be much higher and already factored into the market price per common share at the time the CoCos are issued. As shown in the Table 4, that expected price at conversion, MPSc, would then be down only to 81.33% of its level at the time of CoCos issuance, rather than down to 0.81335 = 35.58% as in the earlier example. Hence if the conversion price, CPS, were set equal to the market price per common share at the time of CoCos issuance, MPS0, unhedged CoCos holders would expect to lose on account of conversion an amount equal to about 20% (18.67%) of the face value of CoCos issued at CET10 of 8%.

b1 0.0399(0.0582)

b2 0.0734(0.0573)

b3 -0.0805(0.0599)

Table3:Estimatesofregressioncoefficient


This same expected loss rate is preserved for all starting values of the CET1 percentage as MPS /CPSc is 0.8133 for all values of CET10 in Table 4. The higher CET10, the more severe the reversal of a company’s fortunes and capitalization would have to be to bring on CoCos conversion. Hence to keep CoCos holders’ losses from conversion to the same percentage, the number of common shares issued in conversion, Nc, per face value of CoCos, would also have to be higher, and CPS correspondingly lower, the greater CET10. Only if the company is initially very well capitalized, with a CET10 of 11% -12%, could the conversion price be set as low as half of MPS0 according to Table 4 and still remain well above MPSc.10

Making the contingent-put-option approach to hedging conversion risk operationalThe risk of loss from conversion arises from the expected market price per common share issued at conversion, MPSc, being less than the conversion price, CPS. The product of CPS and Nc is required to be equal to the face value of CoCos, PAC, but MPS Nc c will be less than PAC, if CPS MPSc2 as here intended by the choice of CPS. To hedge against this risk of losses from conversion, investors could, notionally if not realistically, purchase a 10-year American contingent put option on the number of shares received in conversion. Analogous to a barrier option, this “contingent” put option, absent conversion, would not be exercisable, however, even if it were in the money otherwise. The value of the shares received in conversion thus would equal PAC if the shares could be put at a strike price of CPS once CoCos conversion has been triggered. Hence the expected market price at conversion, MPSc, is the then relevant spot price

10 This finding contradicts some of my earlier design suggestions for CoCos, as for instance in von Furstenberg (2013, p. 101), that did not take differences in CET10, and their implications for the expected level of MPS /MPSc 0 , into account and did not seek to hold the expected recovery rate constant at a value well below 100% to generate appropriate incentives for corporate governance and CoCos issuance.

used in calculating the value of the contingent put option whose contingency clause has been satisfied. Finally, MPSc equals MPS /MPSc 0 (see above) because MPS0 functions as numeraire.

Additional parameter values are required to price the contingent put option. Assuming a random walk in stock prices co-integrated with CET1, the quarterly volatility of 0.1924, equal to the standard deviation of the 41 observations on lnMPS /MPSt t 1- introduced earlier, translates into an annual volatility of 0.3848. The U.S. Treasury rate on a 10-year issue is taken to be either at a low of 2% or at a more normal level of 4%, with both percentages equally split between real interest and inflation premium. With these alternative riskless interest rates and an expected share price conditional on conversion of MPSc, potential investors in CoCos can determine the expected cost of a 10-year put option with a strike price of CPS. Buying such an option for the number of shares to be issued in conversion, which is CPS 1- times the face amount of CoCos, and multiplying by the probability of conversion, Pc, would yield a rough approximation to the expected cost of the hedge in perfect capital markets. Arbitrage would then ensure that investors would be compensated fully through a premium over the riskless rate, later represented as AAA/Aaa corporate bond yield, for the up-front costs they would have to incur if they hedged against conversion risk and the resulting loss in the manner here described.11

Comparing results from the CDS and contingent-put approaches to pricing CoCosResults derived with the first approach to pricing CoCos are laid out in von Furstenberg (2012, p. 71). They show the annualized fixed premium leg in percent of notional for a par value CDS for (i) CoCos survival curves with different 10-year terminal probabilities of survival (PS) to maturity, and (ii) different recovery rates, R, from the shares of common stock obtained through conversion.

The second approach, applied here, links the probability of CoCos conversion explicitly to the degree to which a company’s CET10 is above the 7% trigger level when its CoCos are issued. PS under

11 As for the CDS, the arbitrage condition can again be represented as c = r + ρ, where c is the yield rate on PAC=1, r is the riskless interest rate, and ρ the annualized interest rate premium corresponding to the up-front cost of the contingent put of PAC/CPS shares. For instance, if c > r + ρ, the investor can make an assured arbitrage profit by buying CoCos (earning c), going short on the risk-free bond (owing r) and buying the put (owing ρ).

CET10 MPSc/MPS0 CPS/MPS0

12% 0.3558 0.437511% 0.4375 0.538010% 0.5380 0.66159% 0.6615 0.81338% 0.8133 1

Table 4: MPS expected at conversion and CPS, both relative to MPS at the time of CoCos issue, as a function of the capital ratios at that time



the first approach is the same as 1-Pc under the second. However, the expected recovery rate is made independent of CET10 by varying the conversion price CPS, and hence the number of shares to be issued at CoCos conversion, in such a way that the expected recovery rate is always just above 80% (81.33%). With regard to the choice of interest rates, the first approach uses the discount-factor curve of 1 February 2012 when the rate on Treasuries with a constant maturity of 10 years was 1.87%. The second applies alternative risk-free rates of 2% or 4% per annum in option valuation. These rates are also used to translate up-front costs of buying contingent put options into equivalent annualized interest rate premiums. These premiums, like the CDS premiums, are treated as add-ons to the yield on AAA/Aaa-rated corporate bonds.

When compared at approximately matching values of the probability of survival (PS) and of not being converted (1 – Pc), the estimated percentage premiums under the CDS approach are appreciably less than under the contingent-put approach. A 2% riskless discount rate is most compatible with a CDS calculated with the interest rate level of February 1, 2012. Then the difference is over 50% and greatest for the highest PS values in the Table 6. No exact agreement could have been expected since the two elementary approaches employ different simplifying assumptions, though both are compared at a recovery rate of about 80%. Inconsistencies in the selectively reported Basel III CET1 variable reported by the largest U.S. banks and unresolved timing issues in valuation weaken the application of the contingent put option approach in particular. Nevertheless, these estimates provide useful information about the range in which the conversion premium for any PS may lie and how the premiums rise as the probability of CoCos conversion increases.

For instance, the three columns of premium estimates in Table 6 agree that, at a PS (and 1-Pc) of about 0.6 on the last line, the premium should be 4 to 5 times as high as at a PS of about 0.9 on line 2.

Interpretation of resultsTable 6 shows that under the worst of circumstances considered, when the CET1 buffer is only 1 percentage point above the 7% trigger level and the probability of CoCos surviving until maturity is down to about 60%, the CoCos conversion premium over the nearly riskless rate is just over 1% when its size is estimated with the CDS approach. When estimated with the contingent-put approach this premium is a little over 1-1/2% if the riskless rate on 10-year Treasury notes is 2%, as it was in February 2013. The premium is only about 1-1/4% if the riskless rate is represented by the 4% yield required in the same month on Moody’s Aaa-rated bonds, whose effective maturity is about 10 years. Because CoCos are corporate bonds with the risk of conversion added it is attractive to think of that premium as an add-on to the Aaa rate for pricing purposes.

Conversion risk includes the probability of conversion and the losses expected on the shares received in conversion, which are measured by the cost of hedging against these losses either with CDS or, as in this paper, with contingent-put options. The question then is whether CoCos may be expected to be cheaper to issue than equity into which some of them ultimately may turn. The literature on the “equity premium puzzle,” ably reviewed and extended by Benartzi and Thaler (1993), implicitly cautions against comparing a model-deduced premium on one type of instrument with the actual risk premium observed on another. The reason for the caution is that the actual premium may be

CET10 Pc CPS Put(r = 2%)

Put(r = 4%)

{Up-front cost} and Interest rate premium for

hedgea (r = 2%)

{Up-front cost} and interest rate premium for

hedgea (r = 4%)12% 0.0446 0.4375 0.1640 0.1184 {0.0167} 0.20% {0.0121} 0.19%11% 0.0869 0.5380 0.2023 0.1461 {0.0327} 0.38% {0.0236} 0.33%10% 0.1539 0.6615 0.2482 0.1793 {0.0577} 0.66% {0.0417} 0.56%9% 0.2483 0.8133 0.3055 0.2206 {0.0933} 1.16% {0.0673} 0.88%8% 0.3669 1 0.3758 0.2714 {0.1379} 1.56% {0.0996} 1.29%

Table 5: Cost of hedging the CoCos conversion risk through contingent put options as a function of the initial capital ratio CET1 and associated values of the probability of conversion and the conversion price per share a The up-front cost is Pc/CPS times the cost of the put. The latter was obtained with the riskless rate r = 2% or 4% using the calculator at http://www.erieri.com/BlackScholes. Like the Black-Scholes theorem, this calculator was developed for European options and stocks that do not pay dividends. The compensation for that up-front cost is calculated in terms of a higher annual rate on coupons paid semiannually to investors in 10-year CoCos.


much higher than what accepted valuation models would yield with plausible calibration of central parameters, such as the degree of risk aversion. Hence there is the possibility that CoCos would pose a premium puzzle like stocks, requiring an actual rate premium over the Aaa rate on corporates that is much greater – as research referenced just below suggests, twice as high – than plain models would predict.

If CoCos were priced like equity from the start, I would accept the highly informed judgment of Fernandez (2012) that the incremental return of a diversified portfolio (the market) over the risk-free rate — traditionally the return on Treasury securities, now sometimes trumped by Aaa-rated corporate bonds — required by an investor is about 4% so far this century. Furthermore, I infer from Benartzi and Thaler (1993) that the model-deduced premium over a time horizon coinciding with the 10-year term to maturity of the CoCos here considered is around 2%. This would leave the remaining difference of (4 – 2)% = 2% unexplained by a standard valuation model with plausible calibration.

CoCos issues have been few, and conversions so far have occurred only once (in Cyprus) though, more will occur on the Iberian Peninsula by prior arrangement in the next five years. This means that CoCos still bear innovation, non-standardization, and illiquidity risks. In addition they are subject to intense regulatory scrutiny and exposed to regulatory interference with their terms. For all these reasons it is difficult to parse the actual returns required on CoCos and to predict how much their required return would fall once volume builds and their market deepens. Hence the only valid, apples-to-apples comparison that can be struck is to compare the model range of premium estimates in the last text table for specified levels of the probability of CoCos survival, PS40 quarters- , with a model-

deduced stock market premium of 2% for a 10-year horizon. By that standard, the cost savings from CoCos are modest, being under 100 bps for PS = 0.6 and around 100 bps for PS = 0.7. They are impressive only for higher values of PS of 0.8 and over, which are associated with initial levels of capitalization, CET10, 3 or more percentage points above the trigger level of 7%. As von Furstenberg (2013, p. 99) shows, such strong capital buffers when combined with no less than a stand-alone credit profile (SACP) rating of a-, that is commanded by most global systemically important banks, would allow these institutions to issue investment-grade CoCos.

ConclusionTo be incentive-compatible, CoCos investors must have reason to expect to lose from conversion. For existing shareholders to support CoCos issuance, they must expect to get some consolation from conversion for the losses of equity already suffered in the process of the company’s decapitalization to the trigger point. Aiming for a uniform recovery rate of just over 80% from CoCos in setting conversion terms under different initial conditions meets these distributional objectives. It turns out that CoCos with such a high recovery rate and a probability of survival until maturity of 85% would warrant a conversion risk premium of 66 bps or less if they are rated investment grade. To merit such an initial rating, the CET1/RWA capital ratio of the issuer has to be at least 10%, three percentage points above the trigger level of 7%. (At year-end 2012, the vast majority of the largest banks in the U.S. had Basel-III CET1/RWA ratios that still fell 1 or 2 percentage points short of that level.) Results obtained with the CDS approach to hedging in my previous work [von Furstenberg (2012a)] indicated a premium that would be even smaller. Hence high-grade, high-recovery CoCos may be expected to command

Approach:Recovery

rate ≈ 80%

CDSa

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premium Contingent put

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(r = 2%)

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0.9554 0.20% 0.19%0.9 0.21% 0.9131 0.38% 0.33%0.8 0.45% 0.8461 0.66% 0.56%0.7 0.72% 0.7517 1.16% 0.88%0.6 1.03% 0.6331 1.56% 1.29%

Table6:CDSandcontingentputpremiumscomparedasestimatorsoftheCoCosconversionriskpremiumatspecifiedsurvivalratesa Source for CDS results: von Furstenberg (2012a, p. 71). The probability of survival, PS, for 40 quarters under the CDS approach is conceptually the same as the complement of the probability of CoCos being converted, Pc, rather than repaid at their 10-year maturity, under the contingent-put approach.



only a small fraction of the premium (over AAA/Aaa-rated corporates) required on the equity into which, upon conversion, they would turn.

Even before considering the likely deductibility from taxable income of interest paid on high-trigger CoCos,12 this makes CoCos deliver contingent capital at a bargain relative to issuing more equity, but only after the CET1/RWA capital ratio of the issuer has been built up to 10% or more. This could make the firm’s capital buffer high enough to issue investment-grade CoCos with a 7% trigger. Under these conditions the model-deduced CoCos conversion risk premium turns out to be equal to one-third of the model-deduced equity premium and equal to only one-sixth of the actual equity premium.

For estimating the effect of adding CoCos on the cost of capital overall, the conclusion, that well-designed CoCos are a cost-effective instrument innovation, is based on the assumption that CoCos issuance does not increase leverage in a way that would raise the required rate of return on equity along Modigliani-Miller lines. The reasoning why it should not be expected to do so is that the additional debt is a hybrid that, in a pinch, is loss-absorbing by turning automatically into equity. Furthermore, the leverage that CoCos provide when issued is automatically reversed in conversion that boosts equity just when the need is great because the capital ratio has fallen to the trigger point. CoCos thus do the work of common equity at the interest cost of high-grade debt with compensation for the conversion risk premium added.

ReferencesBarth, J. R., and A. Prabha, 2012, “Too-big-to-fail: a little perspective on a large problem,” Paper delivered at the Fifteenth Annual International Banking Conference, “The social value of the financial sector: too big to fail or just too big?” Federal Reserve Bank of Chicago, November 15-16, available at http://www.chicagofed.org/digital_assets/others/events/2012/international_conference/barth_111512.pdf . Benartzi, S., and R. H. Thaler, 1993, “Myopic loss aversion and the equity premium puzzle,” NBER Working Paper, No. 4369, May. http://www.nber.org/papers/w4369.pdf?new_window=1Calomiris, C. W., and R. J. Herring, 2011, “Why and how to design a contingent convertible debt requirement,” working paper, available on SSRNDurand, H., 2011, “Deals: IFR bankers welcome Barclays planned non-dilutive CoCo,” http://mobile.reuters.com/article/Deals/idUSLDE7591IC20110610?irpc=932

12 In von Furstenberg (2012a, pp. 66-67) and (2012b, pp. 1-2) I have provided an assessment of the U.S. tax treatment of CoCos in this regard.

Federal Deposit Insurance Corporation and Bank of England, 2012, “Resolving globally active, systemically important, financial institutions,” A joint paper by the FDIC and the BoE, Dec. 10, http://www.bankofengland.co.uk/publications/Documents/news/2012/nr156.pdf .Fernandez, P., 2012, “Market risk premium used in 56 countries in 2011: a survey with 6,014 answers,” Brussels, October 10, available at http://www.cfasociety.org/belgium/Events%20Presentations/SurveyEquityPremiumBrusselsOctober2012.pdf .Flannery, M., and E. Perotti, 2011, “CoCo design as a risk preventive tool,” Vox, 9. FebruaryGoodhart, C. A. E., 2010, “Are CoCos from cloud cuckoo-land?” Central Banking, 21(1), 29-33Goodhart, C. A.E., 2011, “The Squam Lake Report: a commentary, Journal of Economic Literature, 49(1), 114-119.ICB, 2011, “Interim report: consultation on reform options,” AprilSFRC, 2010, “The case for a properly structured contingent capital requirement,” Statement No. 303. von Furstenberg, G. M., 2011a, ‘Contingent capital to strengthen the private safety net for financial institutions: CoCos to the rescue?” Deutsche Bundesbank Discussion Paper, series 2: Banking and Financial Studies, No 01/2011, available at http://www.bundesbank.de/Redaktion/EN/Downloads/Publications/Discussion_Paper_2/2011/2011_02_07_dkp_01.pdf?_blob=publicationFilevon Furstenberg, G. M., 2011b, “Concocting marketable CoCos,” HKIMR Working Paper No. 22/2011, Hong Kong Institute for Monetary Research, July, available from http://ssrn.com/abstract=1895984von Furstenberg, G. M., 2012a, “Mega-banks self-insurance with CoCos: a work in progress,” Global Credit Review, Risk Management Institute, NUS, Vol. 2, 53-78von Furstenberg, G. M., 2012b, “Minimum requirements for CoCos to be included in regulatory capital and for getting an S&P investment-grade rating,” August, available through http://ssrn.com/abstract=2135146von Furstenberg, G. M., 2013, “Who or what has been hobbling CoCos: three essentials for making CoCos a success,” Journal of Financial Transformation, 36, 95-105You, H., and X-J. Zhang, 2007, “Investor under-reaction to earnings announcement and 10-K Report,” November, available from http://www4.gsb.columbia.edu/filemgr?file_id=16535Zhu, H., 2004,”An empirical comparison of credit spreads between the bond market and the credit default swap market,” BIS Working Papers No. 160, August, available at www.bis.org/publ/work160.htm


Part 2

Risk-on/risk-off, capitalflows,leverageand safe assetsRobert N. McCauleySenior Advisor, Monetary and Economic Department, BIS1

AbstractThis paper describes the international flow of funds associated with calm and volatile global equity markets. During calm periods, portfolio investment by real money and leveraged investors in advanced countries flows into emerging markets. When central banks in the receiving countries resist exchange rate appreciation and buy dollars against domestic currency, they end up investing in medium-term bonds in reserve currencies. In the process they fund themselves (or “sterilize” the expansion of local bank reserves) by issuing safe assets in domestic currency to domestic investors. Thus, calm periods, marked by leveraged investing in emerging markets, lead to an asymmetric asset swap (risky emerging market assets against safe reserve currency assets) and leveraging up by emerging market central banks. In declining and volatile global equity markets, these flows reverse, and, contrary to some claims, emerging market central banks draw down reserves substantially. In effect, emerging market central banks then release safe assets from their reserves, supplying safe havens to global investors.

1 Paper prepared for the ADBI/PRI Conference “Achieving financial stability – lessons from the Eurozone crisis for macroeconomic and financial stability,” Tokyo, 14 March 2012, and published in Public Policy Review, vol 8, no 3, Policy Research Institute, Ministry of Finance, Japan, August 2012, pp 281-297. Reprinted from Working Paper no. 382, with permission of the BIS. The author thanks Michela Scatigna for research assistance, the discussant Tsuyoshi Oyama and, for comments, Stephen Cecchetti, Takatoshi Ito, Patrick McGuire, and Vladyslav Sushko. The views expressed in this paper are those of the author and not necessarily the views of the BIS.


Risk-on/risk-off,capitalflows,leverageandsafeassets

IntroductionThis paper traces the international flows of funds and leverage that accompany risk-on and risk-off markets. When global equity markets are calm, leveraged portfolios expand and capital flows from advanced economies [Bruno and Shin (2012)]. What has not been sufficiently recognized is that capital inflows into emerging markets systematically lead to leveraging by central banks there, and that capital outflows lead to deleveraging. Given the investment and financing habits of emerging market central banks, their leveraging tends to remove duration from global bond markets. As a result, their response to risk-on markets tends to put downward pressure on global bond yields, reinforcing the risk-on mode. When they deleverage, however, they accommodate a flight to quality by global investors by selling safe assets.

The international flow of funds during risk-on markets has to be understood as involving gross flows [Shin (2012) and Borio and Disyatat (2011)]. It involves not only current account deficit countries like Brazil and India, but also countries running current account surpluses, apart from China, which has to date used capital controls to remain mostly outside of this circuit. In the terms of Obstfeld and Taylor (2004), the alternation of risk-on and risk-off markets is not development finance — a one-way flow of capital that finances a current account deficit. Rather, it is a kind of international asset swap, in which gross flows allow investors in different countries to alter their risk profile.

Yet, the gross flows are asymmetric in their risk character. The usual asset swap can be modeled as two islands at different latitudes, and therefore with different weather, that exchange claims on each other’s harvest, allowing smoother consumption over time. In this textbook example, the claims swapped are similar in their risk character. By contrast, when risk is on, global investors acquire risky emerging market assets that respond disproportionately to global growth, and emerging market central banks invest in safe obligations of governments in the reserve currency countries.

Moreover, the asymmetric asset swap is not a stable, buy-and-hold position. When risk is off, global investors sell risky emerging market assets, and repurchase the low-risk reserve assets from emerging market central banks. In effect, global investors purchase a call option on emerging market growth, holding

equities for the upside and selling them for the downside. And emerging market central banks provide safe assets — reserve currency government bonds — to global investors when risk is off.

Risk-onIn what follows, we trace the risk-on international flow of funds

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Figure1:GlobalvolatilityandAsiannetportfolioequityinflows1 Net foreign purchases of equities in India (data start in 1999), Indonesia, Korea (KOSPI and KOSDAQ), Philippines, Chinese Taipei, and Thailand, in billions of U.S. dollars.Source: CEIC; Bloomberg

Figure2:GlobalvolatilityandAsiannetportfolioequityinflows1 Net foreign purchases of equities in India, Indonesia, Korea (KOSPI and KOSDAQ), Philippines, Chinese Taipei and Thailand, in billions of U.S. dollars.Source: CEIC; Bloomberg


through three steps: capital flow by the global investor; domestic swap from risky to safe asset by the emerging market investor; and exchange rate intervention and leveraged investment into reserve currency bonds by the emerging market central bank. CapitalflowsbyglobalinvestorsWhen global equity markets are calm and the VIX is low, investors in mature economies, both real money and leveraged, purchase risky equities and bonds in emerging markets [Figure 1, updating McCauley (2010, p 132)]. If the investor is a real money investor, the investment is financed by sale of low-risk domestic assets. If the investor is leveraged, one can think of the investment as being financed in short-term markets like that for repo. In the latter case, the transaction represents a net increase in demand for duration.

At higher frequency, it is evident how global investors buy and sell on a hair trigger (Figure 2). Periods of calm in global equity markets tend to lead to inflows into Asia. The CGFS (2011) cautions against interpreting the VIX as a measure of global risk aversion, but for leveraged portfolios with risk management keyed off of value-at-risk (VaR) measures, higher volatility can be associated with lower leveraging [Bruno and Shin (2012)].

While these daily data provide useful perspective, other capital flows measured at lower frequency also tend to track aggregate equity market volatility. CGFS (2011), drawing on McGuire and von Kleist (2008) and McGuire and von Peter (2008), shows how international bank flows co-vary with the VIX (Figure 3). [See also Borio et al. (2011) and Avdjiev et al. (2012).]

The capital outflow tends to raise equity and bond prices and to lead to currency appreciation. This is the finding of Richards (2005) and Chai-Anant and Ho (2008) using daily data from stock exchanges in East Asia. Using data that allow them to distinguish equity purchases that are accompanied by currency hedges from those that are not, Gyntelberg et al. (2009) find that generally unhedged foreign purchases of Thai stocks put upward pressure on the exchange rate.

The upshot is clear. When global investors feel confident, capital flows towards emerging financial markets. This flow tends to put upward pressure on exchange rates. Before we turn to the official reaction to such pressure, let us consider the matter from the perspective of the emerging market investor.

The emerging market investorThe emerging market investor who sells the equity to the foreign investors receives in the first instance a bank deposit in return. To the extent that the inflow into the local equity market is pushing up prices, the bank deposit can help maintain the balance of the local investor’s portfolio between risky and safe assets. However, the local investor may bid up the price of local assets that are not in demand by global investors, both secondary equities and local real estate [Aliber (2011)]. Thus, through the portfolio rebalancing of domestic investors, asset price rises diffuse from the often-narrow focus on the most liquid large-capitalization emerging market stocks (or benchmark domestic-currency bonds) by global investors.

Sterilized currency intervention by the emerging market central bank Eventually, the emerging market central bank resists the appreciation by purchasing dollars, leveraging its balance sheet. If the central bank were simply to purchase dollars, local bank reserves would become excessive and short-term interest rates would tend to fall to zero. To keep this from happening, the central bank will offset the addition to local bank reserves, often by selling its own interest-bearing liability [Ho and McCauley

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1 The stacked areas indicate the contributions to the total year-on-year rate of growth in international claims, which include all BIS reporting banks’ cross-border credit and local credit in foreign currency. Source: Bloomberg; BIS locational banking statistics by residence.



(2009)]. If the central bank is operating monetary policy by setting a short-term rate, the effect of the intervention on bank reserves is simply folded into all the other (autonomous) factors influencing bank reserves, including, not least, fiscal flows like tax receipts, interest payments, and so on. In this context, it is highly stylized, and not necessarily useful, to see the central bank as offsetting (sterilizing) the foreign exchange purchase in particular.

A key observation is that the central bank’s financing (sterilization) of its larger holding of foreign exchange assets produces a safe asset in domestic currency. The investor who sold domestic equity to the foreign investor is unlikely to hold the central bank bill on his own account, but his bank can hold it as the asset corresponding to his deposit. From the standpoint of the domestic bank and its depositors, the central bank bill is a safe asset. Contrary to those who posit some shortage of safe assets in emerging markets, central banks can and do provide copious safe assets as a by-product of their foreign exchange policy. The Bank of Korea, for instance, has issued a larger stock of monetary stabilization bonds (of up to two years’ maturity) than the Korean government has in outstanding bonds. Truly, one observes an elastic supply of low-risk governmental obligations in many emerging markets.

Emerging market central bank investment in reserve currency bonds The emerging market central bank not only leverages up in the process of resisting currency appreciation, it also systematically takes duration out of the portfolios of global bond investors. Thirty years ago, central banks invested mostly at the short end of the yield curve in bank deposits linked to Libor and in Treasury bills. The long bull market in bonds, however, taught central banks in Pavlovian fashion to invest further out on the yield curve. Indeed, not only did higher returns reinforce the extension of maturities, but also the trend dollar depreciation punished central banks that did not extend the maturity of their foreign exchange reserve portfolios. For instance, dollars invested in Treasury bills and compounded over 1980-2010 did not keep up with a compounded SDR liability, with its inclusion of euro, yen, and sterling [McCauley and Schenk (2012)]. By running a mismatch between their short-term liabilities in domestic currency and a medium-term portfolio of foreign exchange reserves, central banks could harvest a term premium to offset dollar depreciation.

Some of the most comprehensive data on the maturity of official portfolio is produced by the U.S. Treasury and Federal Reserve survey of holdings of Treasury securities. This shows (Figure 4) that relative to overall supply, foreign officials are underinvested in Treasury bills and very long-term bonds. They are overinvested in the so-called belly of the curve, that is, in bonds of one-to-five-year maturity [McCauley and Rigaudy (2011)].

This reserve management behavior helps provide perspective on findings that official purchases of U.S. bonds put downward pressure on their yields. Bernanke et al. (2004) found that intervention by the Japanese Ministry of Finance in 2003–2004, for which daily data are eventually released, was associated over a short window with something like 1 basis point lower 10-year bond yields per U.S.$1 billion in intervention (and eventual investment). Using monthly Treasury International Capital data, Warnock and Warnock (2009) find a similar response to all official investment in U.S. bonds. Gerlach et al. (2012) find that the Japanese intervention of 2003–04 tended to push down global bond yields broadly in industrialized economies and in emerging markets with more globally integrated bond markets.

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Figure4:MaturityofforeignofficialholdingsofTreasurysecuritiesandtotaloutstanding, June 2009 (in percentage)1 Number of months.Source: Department of the Treasury, Federal Reserve Bank of New York, Board of Governors of the Federal Reserve System, Survey of foreign portfolio holdings as of 30 June 2009, April 2010; U.S. Treasury.


Summary: the risk-on circuit as a positive feedback loopThus, at the end of the circuit of international fund flows is a demand by foreign exchange reserve managers for safe assets, that is, the obligations of governments deemed to be of low risk of default. But they do not demand assets that are utterly safe in relation to interest rate risk, such as Treasury bills. Since the investments of emerging market central banks in major bond markets are of longer duration than the domestic currency liabilities that they issue to finance them, the net effect is to remove duration from global bond markets. To the extent that bills and bonds in global bond markets are imperfect substitutes, the net effect of the leveraging of emerging market central bank balance sheets is to lower the yield on safe assets of medium maturity in major bond markets.

If the discount rate applied to future cash flows associated with equities is thereby reduced, the response of emerging market central banks to capital inflows feeds back in a positive fashion to global equity prices, further encouraging the “risk-on.”

The risk-off circuitWhen, for some reason, global equity markets turn down and the VIX rises, this process works in reverse. Seeking to limit losses, leveraged global investors liquidate risky positions, including those in emerging market equities and bonds. Local investors buy back the equities and bonds from global investors. Eventually, emerging market central banks step in to sell dollars. In the process they eventually shrink their balance sheets, selling the safe assets bought in major bond markets and reducing their liabilities in domestic currency.

When equity market volatility rises, there is a marked tendency for higher yielding currencies to depreciate. The spike in the VIX in 2008, the largest to date, was accompanied by a sell-off in higher-yielding currencies (Figure 5).2 The cross-sectional relationship is very strong, with short-term interest rates in the six months between February and July 2008 accounting for 44% of the variation in dollar exchange rate changes. High-yielding currencies like the Brazilian real, Indonesian rupee, or Turkish lira reliably decline during risk-off periods against the dollar, while the yen tends to rise.

2 See McCauley and McGuire (2009). Clarida et al. (2009) and Gyntelberg and Schrimpt (2011) discuss this in terms of exchange rate volatility. In addition to the pervasive VaR-based risk management emphasized by Bruno and Shin (2012), variations in unhedged cross-border investment in equities link equity and currency volatility.

This can be interpreted as reflecting in part leveraged carry trades in which low-yielding currencies are used to fund investments in high-yielding currencies. When risk is on, such positions produce a run of smallish gains; when risk is off they can produce sudden large losses. The slope of the regression line in Figure 5 is about three, indicating that three years of yield differential was lost to depreciation in nine weeks. For example, the Colombian peso (COP) was yielding almost 10% between February and July 2008, but it fell almost 30% against the dollar in the nine weeks. Such periods are the nightmares of “carry-traders.”

Even those central banks that well recognize the presence of carry-traders in their foreign exchange markets tend at some point to use their reserves in an attempt to limit depreciation of the domestic currency. And when they do, they deleverage, selling their safe assets in reserve currencies and reducing their own borrowing in domestic currency. Oddly, though, there is not an agreement on the question of whether central banks sell reserves extensively during persistent risk-off periods, or whether they are afraid to do so, preferring to allow currency depreciation to bear the weight of changes in global market sentiment.

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Figure 5: Unwinding of carry trades with rising volatility (21 August–28 October 2008)Source: IMF, International Financial Statistics; Bloomberg; BIS calculations.



Do emerging central banks really sell reserves?The risk-on, risk-off flow of funds involves not only purchase of foreign exchange reserves by emerging market central banks in the face of capital inflows but also their sale of foreign exchange reserves in the face of capital outflows. However, it is a widely held view that emerging market central banks sell remarkably little of their foreign exchange reserves in the face of capital outflows. Aizenman and Sun (2009) termed this “fear of losing international reserves,” while Aizenman and Hutchison (2010) went for pith with “fear of reserve loss.” At a conference on global liquidity at the ECB, Pierre-Olivier Gourinchas took issue with the assertion that emerging market central banks actually sell down their foreign exchange reserves during risk-off periods. Thus, this section lays out the facts of effective reserve use in 2008–09 by Asian central banks.

An oft-cited case in point that seems to support this “fear of reserve loss” view was the market speculation that the Korean authorities regarded U.S.$200 billion in reserves as a minimum. At first blush, the data is not inconsistent with this view, with headline Korean reserves3 peaking at $U.S.264 billion in March 2008 and bottoming in December 2008 at U.S.$201 billion, but only if one ignores the forward book.4 In fact, the Korean authorities started with net forward dollar purchases of U.S.$22 billion in March 2008 and ended up in February 2009 with a net U.S.$11 billion in dollars sold forward, taking their net reserves to U.S.$190 billion at the minimum in February 2009. Thus, net Korean reserves peaked at U.S.$286 billion (U.S.$264 billion cash and U.S.$22 billion forward) and fell not only by the U.S.$63 billion drop in cash reserves but also the U.S.$33 billion swing in the forward position. Properly understood, Korean reserves dropped not by 24% (U.S.$63 billion/U.S.$264 billion), but rather by 33% (U.S.$96 billion/

3 Here we use reserves as reported in the IMF, International Financial Statistics, including foreign exchange, SDR, and reserve position in the IMF, but excluding gold.

4 On the SDDS template, foreign exchange reserves are listed as number 1 under “I.A. Official reserve assets,” while the forward book is listed under “II. Predetermined short-term net drains on foreign currency assets (nominal value),” under “2. Aggregate short and long positions in forwards and futures in foreign currencies vis-à-vis the domestic currency (including the forward leg of currency swaps).” In effect, the SDDS treats a long forward (i.e., buy dollars) position as a short-term dollar loan out of reserves that does not count as reserves. In contrast, the view taken here is that, after a central bank has intervened in the foreign exchange market to buy U.S. dollars, it is of second-order importance whether it sterilizes the increase in domestic bank reserves using its own bills, a repo in domestic currency, or a foreign-exchange swap. According to the SDDS, the first two sterilization approaches would leave official reserve assets higher as a result of the dollar purchase, while the foreign exchange swap would leave official reserve unchanged.

U.S.$286 billion). This difference between Korea’s net and cash reserves in 2008 can be seen in the center panel of Figure 6. Table 1 shows that peak-to-trough reserve drawdowns elsewhere in East Asia were generally substantial, too.

One could interpret this to support the “fear of [headline] reserve loss”: when intervening to slow depreciation, the authorities run down the stock of their forward dollar purchases instead of cash reserve holdings in order to “window-dress” the headline reserve figure. They might do this on the assumption that market participants do not bother to consult the disclosures of the forward position. Such neglect would be ironic, since the IMF’s special data dissemination standard (under which forward positions are reported) in part responded to the discovery in 1997–98 that the Korean authorities had placed much of their reserves with Korean banks and that the Thai authorities had run up a big forward sale of dollars. If this window-dressing interpretation is accepted,5 analysts should all use the more comprehensive measure of net reserve holdings, lest their measure of reserve loss be subject to systematic errors, rather than subject merely to noise.

5 Other interpretations are possible. Central banks could view forward dollar purchases as low quality foreign exchange reserves, since they entail the risk that the counterparty does not deliver dollars at the maturity of the contract. This might be a particular concern if the counterparties are domestic banks. Or central banks may view swaps as an inferior sterilization instrument to central bank liabilities. Or central banks may minimize costs.

Peak month

Peak amount

Trough month

Trough amount

Net reserve

drawdown

China Sep-08 $1,908 Nov-08 $1,888 1.0%Hong Kong SAR Sep-08 $160 Oct-08 $155 3.5%India Apr-08 $322 Feb-09 $238 26.2%Indonesia Jun-08 $57 Feb-09 $48 15.9%Korea Mar-08 $286 Feb-09 $190 33.5%Malaysia Apr-08 $144 Apr-09 $87 39.5%Philippines Feb-08 $45 Oct-08 $34 24.4%Singapore Apr-08 $267 Feb-09 $193 27.6%Thailand Apr-08 $128 Nov-08 $111 13.4%Total excluding CN, HK $1,250 $901 27.9%

Table 1: Foreign exchange reserve and forward book drawdown in Asia in 2008-09 Source: IMF, IFS; SDDS, as reported by Filardo and Yetman (2012) in Figure 6.


Whatever the reason for the behavior of the forward book, overlooking it can lead to an understatement of the extent of emerging market central banks’ use of their reserves. As reserves are accumulated, central banks may find themselves for one reason or another depending more on swaps to sterilize dollar purchases. In particular, after a central bank has bought dollars in the spot market, it can then sterilize the increase in bank reserves by swapping dollars against domestic currency. When the swap counterparty delivers

domestic currency to the central bank, the expansive effect of the original dollar purchase on local bank reserves is extinguished. The combination of the spot purchase of dollars and then the swap of dollars against domestic currency leaves nothing but a forward purchase of dollars. It is evident in Figure 6 that most Asian central banks entered the global financial crisis with a stock of forward dollar purchases. When the pressure in the exchange market reversed, they tended to draw first on the reserves that they had financed not on

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Figure 6: Foreign exchange reserves1 and net forward positions2 (in billions of U.S. dollars)1 Official reserves excluding gold, in billions of U.S. dollars. Includes SDRs and reserve positions in the IMF. 2 Long positions in forwards and futures in foreign currencies vis-à-vis the domestic currency, minus short positions. 3 Data of net forward positions are not available for China.Source: IMF, International Financial Statistics; IMF, International Reserves and Foreign Currency Liquidity; national data.



balance sheet (e.g., with central bank bills) but rather on the reserves that they had in effect financed off their balance sheet, that is, their forward book of dollar purchases. To resist depreciation of the domestic currency, the central bank sold dollars spot, and two days later a maturing forward dollar purchase provided the dollars. Heavy use of swaps during the latter stages of risk-on periods, followed by an unwinding of the forward book in the early stages of risk-off periods, means that not taking into account forward transactions leads to an understatement of the scale of effective reserve use in an episode of downward pressure on emerging market currencies.

In particular, the neglect of forward positions, in combination with central banks’ last-hired-first-fired use of swaps as a sterilization instrument, results in very significant understatement of the use of reserves in Asia. Among major Asian central banks for which we have information, only Bank Indonesia does not use swaps much, and the Reserve Bank of India uses them only to a limited extent. Other central banks show huge differences between reserve drawdowns including or excluding forwards (first and second columns of Table 2).

Both by imposing a common window for reserve losses and by not taking forwards into account, Aizenman and Hutchison (2010) seriously understate the reserve drawdowns in the region, overstating the evidence for their “fear of reserve loss.” The last column in Table 2 shows their understatement of reserve use, of 7–15% of peak reserves for India, 15–17% for Korea, 12–22% for Malaysia, 25% for the Philippines, and 22% for Thailand.

Dominguez (2012) and Dominguez et al. (2012) reject the claim that emerging market authorities did not use reserves during the global financial crisis. Their approach is very thorough in recognizing that, without intervention, reserves should grow owing to investment returns and, when the dollar weakens against other reserve currencies, valuation gains. In these respects, their analysis goes well beyond that in Table 1. In addition, they implicitly criticize Aizenman and Sun (2009) for imposing a common window for reserve drawdowns and opt for a window defined by peak-to-trough real GDP. Certainly, their general point, that the reserve drawdown associated with the global financial crisis is systematically understated by Aizenman and Sun (2009), is well taken.

Still, it appears that Dominguez et al. (2012) also understate the extent of the reserve drawdown both because their macroeconomically defined windows do not coincide with peak-to-trough movements in reserves and because of their non-inclusion of forward positions. Table 3 again shows in the first two columns the reserve drawdown as calculated by the author. The next column shows the macroeconomically defined window used by Dominguez et al. (2012), and the next column shows the drawdown in cash reserves for that window.6 Judging from the Asian sample at least,

6 It should be underscored that this fourth column would be the main input into Dominguez et al.’s reserve drawdown, but it lacks their netting out of imputed investment earnings (always positive) and currency valuation gains (positive when the dollar is weak against other reserve currencies). But the first column does not net out imputed investment earnings or valuation gains either, so the differences should be regarded as arising from differences in the window used and from the inclusion or exclusion of forward transactions.

Author’s Aizenman and HutchisonAuthor including forwards

less Aizenman and Hutchison (wide, narrow)Including forwards Excluding forwards

Wide: July 2008–February

2009

Narrow: September 2008–December 2008

China na 1.0% -3.6% -2.1% 4.6%, 3.1%Hong Kong SAR 3.5% 3.5%India 26.2% 21.4% 19.3% 11.1% 6.9%, 15.1%Indonesia 15.9% 15.6% 17.3% 9.9% -1.4%, 6.0%Korea 33.5% 23.7% 18.7% 16.2% 14.8%, 17.3%Malaysia 39.5% 29.4% 27.5% 16.9% 12.0%, 22.6%Philippines 24.4% -0.6% -0.6% -0.1% 25.0%, 24.5%Singapore 27.6% 7.0%Thailand 13.4% 3.1% -8.1% -8.4% 21.5%, 21.8%Total excluding CN, HK 27.9%

Table 2: Foreign exchange reserve drawdown: contrasting estimates I Source: Aizenman and Hutchison (2010), and IMF, IFS; SDDS, as reported by Filardo and Yetman (2012) in Figure 6.


Dominguez et al. (2012) seem to understate the reserve drawdown during the global financial crisis.

The risk of understating reserve loss during the big risk-off period of 2008–09 by not taking forward positions into account is not limited to Asia. According to Stone et al. (2009), the Central Bank of Brazil had built up a U.S.$22 billion long dollar stock position in the domestic currency futures market by early 2008 as it resisted real appreciation. Its subsequent intervention in this market took this net long dollar position to a net short dollar position of U.S.$12 billion, for a net swing of U.S.$34 billion. Stone et al. (2009) report that it also sold U.S.$14.5 billion in the spot foreign exchange market between late September 2008 and early May 2009. These spot sales represented 7% of the original holdings of U.S.$208 billion, while the combined spot and futures sales represented almost a fifth.

The upshot is that it is easy to understate the extent to which central banks use their reserves during an extended risk-off period. As a result, it is also easy to understate the extent to which the combined official and private sector in emerging markets sell dollar assets during such a period.7

7 When a central bank buys dollars forward against domestic currency, the private sector in effect acquires a synthetic domestic currency asset. A bank, for instance, can buy a U.S. dollar asset that, combined with a forward sale of dollars to the central bank, amounts to a domestic currency asset. In this manner, the central bank delegates to the private sector the choice of dollar asset, rather than making that choice as part of its reserve management. Similarly, when the central bank runs down its forward purchases of dollars and even sells dollars forward, the private sector can square its position by selling the dollar asset and buying a domestic currency asset.

An important observation is the exceptional behavior of the reserves of China, the largest reserve holder. In 2008, its reserve use, if any, was very limited. This is owing to the capital controls of China, which, for instance, have split the Hong Kong and New York markets for Chinese equities from those in Shanghai and Shenzhen. When risk is off, Chinese share prices in Hong Kong fall relative to those onshore [McCauley (2011)], but non-resident selling of shares in Shanghai and Shenzhen is limited. However, this might be changing. If one looks carefully at Figure 6, upper left-hand panel, one can see a reserve drop in the risk-off period of late 2011. The suggestion is that, as China opens up its capital account, including allowing the use of the renminbi offshore, its reserve holdings could decline during risk-off periods, and the global flow of funds described in this paper could as a result be larger. ConclusionThe international flow of funds associated with risk-on and risk-off markets are gross flows with asymmetric risk characteristics. In risk-on markets, leveraged and unleveraged global investors position themselves in high-beta emerging market assets. In response, emerging market central banks that manage their currencies tend to increase their reserves, investing them in safe assets in reserve currencies. To the extent that this investment pushes down global bond yields, the risk-on is reinforced. The international flow of funds produces not an exchange of risky assets but an acquisition of risky assets on one side and an acquisition of safe assets on the other.

Author’s Foreign exchange drawdown over Dominguez et al. (2012) window

Author including forwards less reserve decline over Dominguez et al. (2012)

window Including forwards Excluding forwards Window Reserve decline excluding forwards

China na 1.0% 08:4-09:1 -0.4% 1.4%Hong Kong SAR 3.5% 3.5% 07:4-09:1 -22.0% 25.5%India 26.2% 21.4% 08:4-09:1 2.1% 24.1%Indonesia 15.9% 15.6% 08:3-08:4 9.9% 6.0%Korea 33.5% 23.7% 08:4-09:1 21.3% 12.2%Malaysia 39.5% 29.4% 08:3-09:1 22.1% 17.4%Philippines 24.4% -0.6% 08:4-09:1 -3.9% 28.3%Singapore 27.6% 7.0% 07:4-09:1 -2.0% 29.6%Thailand 13.4% 3.1% 08:4-09:1 -4.7% 18.1%Total excluding CN, HK 27.9%

Table 3: Foreign exchange reserve drawdown: contrasting estimates II Source: Dominguez et al. (2012), Table 2, and author’s calculations.



When risk is off, the international flow of funds reverses. An implication is that global investors are behaving as if they were replicating a call option on risky emerging market assets. Another implication is that emerging market investors and central banks accommodate global investors: emerging market investors buy back the risky assets when risk is off (providing market liquidity at times of financial strain), and emerging market central banks sell back safe assets into global investors’ flight to quality bid. In these senses, one could say that emerging markets provide liquidity to global investors in risk-off markets.

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