option-adjusted delta credit spreads: a cross-country analysis

European Financial Management, Vol. 18, No. 2, 2012, 183–217doi: 10.1111/j.1468-036X.2009.00527.x

Option-Adjusted Delta Credit Spreads:a Cross-Country Analysis

Leonardo BecchettiUniversita Tor Vergata, Roma, Facolta di Economia, Dipartimento di Economia e Istituzioni,Via Columbia 2, 00133 Roma, ItalyE-mail: [email protected]

Andrea CarpentieriBancoPosta Fondi sgr, via Marmorata 4, 00153, Roma, and Universita Tor Vergata,Facolta di Economia, Via Columbia 2, 00133 Roma, ItalyE-mail: [email protected]

Iftekhar HasanRensselaer Polytechnic Institute, Lally School of Management, 110 8th Street, Troy, New York,12180-3590, USA and Bank of Finland, 00101 Helsinki, FinlandE-mail: [email protected]

Abstract

This study analyses the determinants of the variation in option-adjusted creditspreads (OASs) using a unique database and enlarges the traditional analysisto include disaggregated indexes, new variables, and a complete set of markets(USA, UK, and the Eurozone). An extended set of regressors explains almost halfthe variability of OASs in the three markets. We find that institutional tradingactivity significantly affects corporate bond spreads, signalling either variationin perceptions of risk or the existence of an indirect measure of liquidity. We alsofind that US business cycle indicators significantly affect the variability of OASsin the UK and the Eurozone. Finally, we find evidence that stock returns havemore influence on high-yield bonds in the Eurozone than in the USA.

Keywords: option adjusted credit spread, corporate bonds.

JEL classification: G11, G12

1. Introduction

Empirical analysis on the determinants of bond returns has greatly benefited in the lastdecades from the progressively enhanced availability of data. For example, in the first

We thank an anonymous referee for helpful comments and suggestions. Any opinionexpressed is of the authors, and not of BancoPosta Fondi sgr, or the Bank of Finland.

C© 2010 Blackwell Publishing Ltd

184 Leonardo Becchetti, Andrea Carpentieri and Iftekhar Hasan

empirical papers in this field, Fama and French (1989, 1993) evaluate the relationshipbetween aggregate stock and bond returns. Cornell and Green (1991) and Kwan (1996)also analyse the relationship between the stock and bond markets at the aggregate andfirm levels. All find that low-grade bond returns are relatively more correlated withstock returns, but high-grade bond returns are more correlated with government bondreturns.

More recent empirical analyses have changed the focus from bond yields to changesin the yield differential between corporate and government bonds at the same maturity(delta credit spreads). The idea is that credit spreads measure the excess return investorsrequire for the additional risk involved in holding corporate bonds instead of governmentbonds. In this perspective, delta credit spreads represent a good proxy of the dynamicsof corporate credit risk.1 Researchers generally consider five sources of risk affectingthese credit spreads: (1) the issuers’ default risk; (2) the market’s perception of thisrisk; (3) observed and expected dynamics of financial volatility; (4) uncertainty aboutdefault timing; and (5) uncertainty about the recovery value or the value bondholdersmight receive at maturity. Business cycle is obviously an important driver for many ofthese risks.

The empirical literature on the determinants of delta credit spreads is still in itsinfancy and includes few contributions. However, Pedrosa and Roll (1998) providea first descriptive analysis of delta credit spreads for fixed bond indexes, classifiedfor grade, industry, and maturity. Collin-Dufresne et al. (2001) explain around 25%of the variability in the delta credit spreads of Lehman Brothers US bond investment-grade indexes. The authors find that regression residuals are highly cross-correlated andthat a principal component largely explains spread variability, which they interpret asgenerated by local demand and supply shocks. In another study, Elton et al. (2001)explain corporate bond returns mainly in terms of systematic nondiversifiable riskpremium and, after that, default risk premium and fiscal components. Using the three-factor risk model of Fama and French (1995), they explain up to 30% of the variabilityof the spreads not explained by default risk.2 Likewise, Huang and Kong (2003) usenine Merrill Lynch investment-grade and high-yield US indexes to explain up to 30%of investment-grade and 60% of high-yield credit spreads. Additionally, Schaefer andStrebulaev (2008), in a general framework, show that structural credit risk models,even if they are poor predictors of corporate bond prices, can be good at predicting thesensitivity of bond returns to changes in equity value.3 Ericsson et al. (2007) analyse UScorporate bonds and credit-default swap (CDS) spreads, highlighting the importance ofomitted risk factors. Comparing actual with theoretical spreads, they find that CDSdo not underestimate as corporate bonds. Rather, the latter should include in theirpremia nondefault risk factors such as illiquidity. De Jong and Driessen (2005) showthat liquidity risk is priced into the expected returns on corporate bonds, explaining a

1 This argument is consistent with practitioners’ behavior if we consider that investment bankproprietary desks were long on corporate bonds and short on government bonds when theywanted to assume credit risk but not interest rate risk.2 Elton et al. (2001) aim to explain the determinants of risk premium in corporate bonds.They conclude that systematic equity risk determines a large portion of risk.3 In this way, they study not only the sign but the size of the estimated coefficients and ifthese are consistent with the theory; their finding can be useful for hedging corporate debt.Moreover, they find that bond prices are related to other factors, as the Fama-French SMBfactor.


Option-Adjusted Delta Credit Spreads 185

risk premium between 0.45% and 1% for long-term investment-grade and speculative-grade bond expected returns, respectively. Boss and Scheicher (2002) make one ofthe first attempts to analyse Eurozone corporate spreads. They use two Euro indexes,industrial and financial, and swap data. They find that interest rate variables mainlyexplain spread changes, and, to a lesser extent, stock market variables. Additionally,Avramov et al. (2007) analyse US corporate bonds using aggregate and firm-levelvariables as regressors. They find that individual volatility and price-to-book ratio playa role in explaining credit spreads on corporate bonds. Longstaff et al. (2005), using CDSand corporate bonds, find that the majority of corporate spread is due to default risk, butthe residual is time-varying and correlated to bond-specific issues and macroeconomicmeasures of bond market liquidity. These results contrast with other works (such asElton et al, 2001; Huang and Huang, 2003) that find default risk accounts for only afraction of corporate bond spreads.

Not all recent works focus on credit spread changes; they investigate levels insteadof differences. For example, Campbell and Taskler (2003) and Cremers et al. (2008),among others, choose to analyse corporate yield levels. However, differences are harderto explain than levels, and therefore a regression on the former should provide a morestringent test. Thus, Ericsson et al. (2009), using CDS premia both in levels anddifferences, find that leverage, volatility, and interest rates are important determinants ofCDS premia, explaining 60% of the variability in levels but only 23% of the variabilityin spread changes. This study will focus, therefore, on corporate spread changes.

The goal of this paper is to extend the analysis on corporate spread changes for the firsttime to more disaggregated indexes (combining industry, grade, and maturity levels),new variables (trading volumes for institutional investors as well as monthly data ondowngrades and defaults), and a complete set of markets (USA, UK, and the Eurozone),focusing in the meantime on the interlinkages among different markets. At the sametime, we intend to test whether institutional investors’ trading activity has an importantrole in these markets and a relevant impact on corporate credit risk. The significanceof this variable would support the hypothesis that institutional sales/purchases signalthe presence of additional information to the market – information not incorporated inother regressors, such as stock performance, or in business cycle indicators.

The paper is divided into six sections. Section 2 discusses credit spread data andillustrates theoretical rationales justifying the inclusion of various regressors thatproxy different underlying components. Section 3 describes our database and thevarious covariates used in the paper. Section 4 presents our econometric findings, andSection 5 includes the results of robustness checks. Section 6 concludes.

2. The Determinants of Credit Spreads

Theories about credit spreads take two distinct approaches: the structural approach,developed by Merton (1974) and subsequent works,4 and the reduced-form approach.The last and more recent path (among the others, Lando, 1998; Duffee, 1999; Duffieand Singleton, 1999; Duffie and Lando, 2001; Collin-Dufresne and Goldstein, 2001)relies on the concept of default intensity, a related process that behaves in its simplestformulation as a Poisson process. The approach considers the default event unpre-dictable, not guided by observed economic variables, and modelled along many of the

4 Among the many are Longstaff and Schwartz (1995), Zhou (2001), Collin-Dufresne andGoldstein (2001).



same technical lines of stochastic term-structure models. The structural approach, on theother hand, uses contingent claim analysis (CCA) to identify theoretical determinantsof credit spreads. We use this approach in our analysis.

Firm structure is the basis of bond valuation in this approach. With firm valuemodelled as a geometric Brownian motion, the bond value equals the value of a risk-free bond minus the value of a put option on the firm’s assets. Consequently, using theCCA, the credit spread is a function of leverage (or distance to default) and volatility.Among the numerous successive contributions to Merton’s seminal work, Longstaffand Schwartz (1995) introduce stochastic interest rates into the model. Most of thevariables in this study are similar to the structural approach in Merton (1974) andsubsequent contributions. For example, equity volatility and volatility skew (or smile)are proxies for asset volatility and distance to default for our purposes; this secondvariable in particular accounts for large negative jumps in equity value. We also useinterest rate variables because, as discussed in Longstaff and Schwartz (1995), spotrates influence the risk-neutral drift of a firm’s value. Moreover, we use equity returnsbecause they measure the value of firm assets and indirectly influence the probabilityof failure; macroeconomic indicators are better used as business cycle measures. Infact, the business cycle can influence expected recovery rates (Collin-Dufresne et al.,2001; Duffie and Singleton, 2003), and, even with constant default probability, can havean impact on credit spreads via the Loss Given Default (LGD5). Other variables arenot linked to the structural approach, but, following the methods in many other papers(among the others, Collin-Dufresne et al. 2001), are added to control for the presenceof omitted factors. In our work, these factors are default rates and transition matrices,liquidity variables, and trading activity among institutional investors. We add defaultrates and transition matrices to check the market reaction to downgrades and to testsignals of worsening aggregate credit risk.

Some studies have shown that liquidity is an important determinant of credit spreads(among others, Driessen, 2005; De Jong and Driessen, 2005; Longstaff et al, 2005).In particular, De Jong and Driessen (2005) show that liquidity risk is priced intothe expected returns on corporate bonds. In this respect, we include different market-liquidity variables.

The last variable is the aggregate trading volume of corporate bonds registered byLehman Brothers with institutional clients. These data on institutional investors, otherthan providing an indirect measure of liquidity in the market, can signal the presence ofadditional information to the market.

Even if the structural approach predicts a nonlinear relationship among variables, mostof the literature in this area – and this study – uses linear regression analysis. For example,Collin-Dufresne et al. (2001), among others, use some of the variables used in this paperas theoretical determinants of corporate bond spreads in a structural approach (Merton,1974). They use changes in 10-year yield, slope, stock returns, implied volatility, slope ofthe volatility smile, and leverage as explanatory variables. They add other variables, suchas liquidity variables, Small-Minus-Big (SMB), and High-Minus-Low (HML) factorsamong others, to capture other omitted factors eventually, even if they are not strictlylinked with the structural approach. They also perform a simulation to demonstrate thatusing linear regression analysis, even when theory predicts a nonlinear relationship,

5 Loss Given Default is the loss for the bondholder, once that the default is given for certain;in other words, it is the loss (nominal value minus recovery rate) without considering theprobability of default.



does not influence the results. Campbell and Taskler (2003) do a similar linear analysisbut use levels instead of changes in bond spreads. Cremers et al. (2008) choose, likethe others, linear regression, focusing on implied volatility. Ericsson et al. (2009) useCDS premia, both in levels and differences, with linear regressions as well. They findthat leverage, volatility, and interest rates are important determinants of CDS premia.

2.1. Corporate bond spreads and CDS

Some empirical works (for example, Zhu, 2006) argue that CDS prices contain betterquality data than bond prices. However, CDS data can be misleading if it does notaccount for the basis (i.e., the difference between CDS and corporate bond spreads).The basis links to the presence of covenants on the bonds (Mahanti et al, 2007) and tothe delivery option embedded in CDS (Jankowitsch et al., 2006), even over liquiditypremiums (Cossin and Lu, 2005). Jankowitsch et al. (2006) find that correcting for thedelivery option6 in a reduced-form approach eliminates the mispricing between CDSand corporate bonds, but they also find no significant evidence, after the adjustment, ofthe influence of liquidity proxies. Cossin and Lu (2005) find that the cheapest-to-deliveroption, market segmentation, and a time-dependent liquidity premium contribute to thepricing differences between corporate bonds and CDS. Levin et al. (2005) show thatmarket frictions can cause divergence in the basis, and that idiosyncratic causes explainthe differences.

Moreover, though in the long run the CDS spread should equal the corporate bondspread,7 this is not always true. In particular, CDS spreads can reflect temporary marketconditions and frictions in the arbitrage mechanism because investment banks use themprimarily for hedging purposes. On the other side, direct owners, such as institutionalinvestors, are the primary holders of corporate bonds, and their activity therefore tendsto reflect ‘fundamental value’ more accurately.

Dotz (2007), continuing the study of Blanco et al. (2005), shows that althoughinformation about CDS markets is slightly superior to information about bond marketsin the price-discovery process, the opposite is true during market turbulence, when bondmarkets dominate. Mahanti et al. (2007), using ‘latent liquidity’ (the weighted-averageturnover of funds holding a bond), find that bonds with higher latent liquidity are moreexpensive relative to CDS contracts; they also find that several firm-level variablesrelated to credit risk8 negatively affect the basis, implying that CDS spreads do not fullycapture the credit risk in corporate bonds.

Given this evidence, researchers could prefer to use corporate bond data if a reliabledatabase is available, particularly if the focus is on the fundamental relationships between

6 Subsequent to a default, the protection buyer in a CDS contract has the option to deliverthe cheapest of a group of bonds (and even loans) linked to the issuer, receiving from thecounterparty the nominal face value. This can be arranged also by simply exchanging moneyand without giving the securities (cash settlement versus physical settlement), dependingon the provisions of the contract. The value of the cheapest-to-deliver option is anywayunaffected.7 All things being equal, first of all maturity, and, as mentioned, taking into account seniority,covenants, etc.8 Leverage; tangible assets as a measure of recovery rates; short-term interest coverage,measured with the ratio of current assets to current liabilities.



corporate bonds and other variables. Given the high quality of our database, explainedin Section 3, we therefore choose to focus on corporate bond spreads.

3. The database

Our dependent variable is represented by option-adjusted spreads (OASs) calculatedfor a set of global, corporate bond indexes (investment-grade and high-yield) providedby Merrill Lynch. We choose OASs because many corporate bonds are callable or havecall options, which allow issuers to repurchase them at a convenient time in orderto refinance their debt at lower interest rates. OASs therefore have the advantage ofsegregating changes in credit risk from changes in the value of the options attached tocorporate bonds.9

Our dataset is more extended than most of those traditionally used in the literatureand explores for the first time the dynamics of corporate bond indexes in the UK andEU markets10 in an extensive manner. An additional advantage is that the data comesfrom investment banks that provide the information (and fixed-income indexes) to themarket. This lends quality and accuracy to the data, and it is superior to data from marketmakers, which do not directly provide index data.11 Collin-Dufresne et al. (2001) takethis argument seriously and exclude from their Lehman Brothers sample those bondsthat are not part of the index data Lehman Brothers provides directly to the market. Eltonet al. (2001) and Duffee (1999) use that the same approach to preserve data quality.

A final advantage of our dataset is that it includes only quoted prices and does notinclude ‘matrix prices’12 or matrix interpolation of missing observations with adjoiningdata. The data appears in the widely used Lehman Brothers Fixed Income Database

9 Computing OAS is common practice in the marketplace, and it is a standard methodologyfor determining the embedded value of the eventual call option of the bond. The OAS is notonly computed by the investment banks providing indexes to institutional investors, but alsoby Bloomberg for almost all the bonds in the market. For this reason, the data used in thisstudy is reliable for the analysis. Moreover, the option value is zero for a noncallable bond,and this is the case for the majority of investment-grade bonds in our sample.10 Boss and Scheicher (2002) make one of the first attempts on analysing Euro (but non-UK)corporate spreads. However, they use only two indexes; our dataset includes 118 indexesfor the Eurozone. Moreover, Boss and Scheicher (2002) have a limited set of explanatoryvariables.11 Corporate bond markets are far more illiquid than government bond markets. Transactioncosts on corporates may reach 1% or 2% of nominal value in the case of high-yield bonds,but they are normally not greater than 0.10–0.30% on governments. These bid-ask spreadsare valid for institutions, and for normal market sizes they can vary from only hundredsof thousands of Euros for high-yield bonds, up to €50 million for governments. Of coursethese numbers are subject to market conditions and vary depending on the relative liquidityof the specific bond; thus they are only indicative costs.12 Quoted prices are ‘quoted’ directly by the trader (so, they are real prices). Instead, matrixprices are generated as a sort of interpolation of other prices. This is done to give a priceeventually to some bonds (the scope can range from pricing a bank’s or client’s portfolio, or forrisk-management purposes, when the series does not have all the data). This ‘matrix’ problemarises in the Lehman database (also called Warga database), which has been extensivelyused in the past. To overcome the problem, researchers normally excluded from the databasematrix prices.



used in most empirical analyses (Sarig and Warga, 1989; Collin-Dufresne et al., 2001;Elton et al. 2001). This underlines the reliability of our database.

3.1. Option-adjusted spreads

Bond indexes in our database cover three areas: the USA (207 indexes), the UK (125indexes), and the EU (118 indexes). The observation period goes from January 1997 toNovember 2003. Data availability varies across areas. The EU series begins in January1999.

The US dataset includes 87 investment-grade (IG) indexes (from AAA to BBB rating)and 120 high-yield (HY) indexes13 (from BB to C rating). The UK dataset includes 119investment-grade and six high-yield indexes, and the EU database has 108 investment-grade and 10 high-yield indexes. Rating classification is available for macroindustries(financials, industrials, and, for the USA, utilities) and at the industry level. Maturitiesare classified according to the following buckets: 1-3,14 3-5, 5-7, 7-10, 10+ years (aswell as 10-15 and 15+ for the USA and the UK only). We show here a subset15 of indexes(42 for the USA, 36 for the UK, and 35 for Eurozone). All indexes are rebalanced on thelast day of the month to account for entries, exits, or changes in rating or maturity classesfor individual bonds. To prevent these changes from affecting our dependent variables,we calculate OASs as differences between the first day of the month (in which therebalancing has already occurred) and the day before the revision.

Descriptive statistics for the synthesis of our fixed bond indexes are available uponrequest. These statistics16 show that OAS volatility monotonically increases credit risk17

but is quite stable along the maturity curve.

3.2. Interest rate variables

Interest rate changes are among the main determinants of credit spreads. Longstaff andSchwartz (1995) in particular show that spot rates influence the risk-neutral drift in afirm’s value.

13 HY Merrill Lynch US indexes do have industry breakdowns, but the UK and Eurozoneindexes do not. This is due to the different development methods of HY bonds in the threefinancial markets. In the USA the HY index includes on average 1,270 bonds, comparedwith 31 and 94 in the UK and in the Eurozone, respectively.14 Merrill Lynch excludes bonds with residual maturities below one year from the universeof assets it considers when building the indexes.15 Complete results are available upon request.16 The maximum change of the total US IG index is 45 bps and around 20/30 bps for the UKand the Eurozone. Skewness, kurtosis, and Jarque-Bera tests show that our OAS series arenonnormal and have excess kurtosis exactly as stock return series. First-order autocorrelationcoefficients and Box-Pierce diagnostics reveal some autocorrelation in these series.17 As expected, HY indexes have much higher volatility than IG indexes, with a maximummonthly change in the aggregate HY index of 211 bps. Air transportation, insurance, andtelecom have the highest volatility HY indexes in the USA (with a maximum monthly changeof more than 1,200 bps). The presence of the first two sectors among those with the highestvolatility may clearly relate to the effects of the terrorist attacks of September 11, 2001, onthe financial markets.



Furthermore, empirical literature on term-structure stochastic models identifies twocomponents explaining most of the time variability of risk-free returns. Ex post, thesecomponents are highly correlated (in decreasing order) with the level of interest rates andthe slope of the yield curve.18 These variables are thus natural candidates for inclusionas regressors in empirical estimates. Returns on a 10- or five-year benchmark or ona government-bond index generally represent interest rates (government bond data arefrom Bloomberg). The spread between two different maturities generally represents theslope of the yield curve.

Some models include return volatility as an additional explanatory variable (see,among others, Longstaff and Schwartz, 1995). We follow this path by using Bloombergmonthly data on the implicit volatility19 options on bond futures, where bonds at themost significant maturities (such as five, 10, or 30 years in the USA, UK, and Germany)represent the underlying assets.20 As is well known, implicit volatility is forward-lookingand expresses better than historical volatility current investors’ expectations for thevolatility itself. Despite that, because options on bond futures are mainly developed inthe USA, we also compare historical volatility in different markets. Historical volatilityrefers to benchmark government bonds from Bloomberg data. Our variable is themonthly change of the monthly historical and implied volatility calculated using dailyprices.

We collect also the implicit volatility of over-the-counter (OTC) options such as swapoptions, which represent the most liquid and widely used hedging instrument in thebond market.21 The swap rate is a ‘refreshed AA credit quality rate’;22 therefore it isa benchmark rate for the corporate market and its volatility should be a fundamentalcomponent of bond valuation.

3.3. Stock market variables

Structural models predict the effect of stock market variables on credit spreads (Merton,1974) and illustrate how positive stock returns increase the value of firm assets andreduce the probability of failure. The same structural models predict the positive effectof firm asset volatility on credit spreads.

18 Collin-Dufresne et al. (2001) argue that yield-curve slope can represent the expected pathof future short rates.19 Even if previous empirical literature shows that Treasury bond returns are not stronglycorrelated with volatility, volatility could affect credit spreads and the underlying risk-freeinterest rates (bonds volatility), not just the assets, as suggested by Merton’s work (i.e., equityvolatility for empirical reasons). In fact, investors could demand a premium in the marketsto hold a corporate bond that is mainly valued on a spread basis if the underlying risk-freerate is more volatile.20 The 10-year Bund is the reference future in the Eurozone.21 Other measures we evaluated the first stages of our analysis were the skewness of optionson bond futures and the implicit volatility of options at long maturities (or vega).22 The credit-risk difference between an AA corporate bond and a generic swap rate (whichis an AA by definition, being based on the LIBOR rate) depends on the latter having nodowngrade risk, because we assume that the rating is constant in any resetting. The parallelwith a corporate index is clear: corporate indexes, when defined according to the ratinggrade, have a ‘refreshed credit quality.’ Consider though that an individual bond rating mayvary before rebalancing given that the bond will be excluded from the index only at the endof the month.



We proxy this variable with the historical volatility of stock market indexes and withimplicit options volatility. Moreover, we also include the skew of implicit volatilities(namely, the difference between implicit volatilities of out-of-the-money, OTM, and at-the-money, ATM, put options). The rationale is that an increase in this specific skewmeasure implies an increase in the perception of risk (‘jump risk’) generated by largenegative movements in stock prices (Collin-Dufresne et al., 2001).Given that the priceof a corporate bond is equivalent to a risk-free bond minus the value of a put optionon the firm’s assets (Merton, 1974), we expect the skew to correlate positively withcredit spreads.23 We calculate the skew as: skew = σ (strike) − σ (ATM), where σ is theimplicit volatility and the OTM option strike is 20% below the ATM option strike.24

We calculate the skew for the most liquid maturities and try alternatively the one-monthand three-month ones. As an additional stock market variable we include the orthogonalrisk factor SMB built by Fama and French (1995) as a proxy of specific small-size risk.Given that this variable is constructed as a differential in stock performance of smallversus large firms, it therefore can link to a spread reduction in corporate bonds (and to apositive return) in the same way the SMB factor in the Fama-French approach connectsto an increase in stock returns.25

3.4. Macroeconomic indicators

Because credit spreads measure excess corporate risk, government bonds are obviouslyexpected to be negatively correlated with the business cycle (see, among others, Duffieand Singleton, 2003). Business cycles can influence expected recovery rates (Collin-Dufresne et al., 2001; Duffie and Singleton, 2003), and even with constant defaultprobability can have an impact on credit spreads.

To evaluate this effect we use Conference Board leading, coincident, and laggingindicators. The leading indicator is the weighted average of 10 indexes;26 the coincidentindicator is an average of four indexes27 that measure the current state of the economy,

23 Because the put option is on the index and not on the individual stock, the observedempirical relationship may be weaker than the theoretical one. The same reasoning appliesto stock index returns or for their implied volatility. Listed options are always defined onmore liquid and representative large-capitalisation indexes (such as the Standard & Poor’s100), but corporate bond indexes generally cover more of the universe of bonds tradedin the market. This is another factor that inevitably weakens the links between theoreticalframework and empirical analysis. Cremers et al. (2005), using implied volatility levels andthe volatility skew starting from individual stock option data, find that aggregate (stockindex) implied volatility and skew has less economic impact than individual data.24 We also tried to use a strike price 5% or 10% below the ATM strike. We finally decided touse 20% both because it better measures jump risk, and because we did not want collinearityproblems with simple ATM implied volatility, which was used as a regressor.25 In a parallel way, we also constructed the HML factor of Fama and French (1995) basedon the market-to-book ratio. Both SMB and HML factors include the relevant stock marketindex constituents, different for the three areas.26 The ‘leading’ indicator is a weighted average of average work week, jobless claims, con-sumer orders, stock prices, vendor performance, capital orders, building permits, consumerexpectations, money supply, and interest rates.27 The ‘coincident’ indicator is a weighted average of nonfarm payroll, personal income,industrial production, and trade sales.



and the lagging indicator is an average of seven indexes.28 ven though these indicatorsincorporate some of the individual variables included in our estimates, those variablesare weakly correlated with such indicators and have a different meaning. We thereforeinclude them in our analysis.29

For the UK we use leading and coincident Conference Board indicators. As inthe USA, these indicators are averages of (respectively, nine and four) individualcomponents.30 For the Eurozone we use the Handesblatt leading indicator,31 theEconomic Sentiment Indicator (ESI), and the European Commission’s ‘business climateindicator.’32

3.5. Default rates and transition matrices

Default rates and information on downgrades/upgrades issued by ratings agencies areanother group of variables that may significantly affect OASs. From a theoretical point ofview, a bankruptcy may affect credit spread indexes if the market does not anticipate theevent and interprets it as a signal of worsening aggregate credit risk. In this perspective,company failures in a given industry should affect credit spread indexes for that industrymore, and the downgrade of a large representative firm may have stronger impact thandowngrades on small firms. Default rates and downgrades are generally anticyclical(see, among others, Duffie and Singleton, 2003).

To test the effect of these variables we use Moody’s default rates, divided into IGand HY groups for the USA, UK, and Europe rating transition matrices33 for differentareas on a monthly basis. Default rates represent the share of firms (IG or HY in theUS, UK, or Eurozone) that defaulted among those observed by Moody’s. Transitionmatrices indicate the frequencies of firms falling into different rating classes in a givenperiod. We exploit the unique advantage of having these data on a monthly basis to builda monthly downgrade ratio calculated as down = down grades

all , where the denominator isthe relevant group of corporations observed by Moody’s in a given geographical areaor aggregate asset class. We therefore have three indicators for any area (IG, HY, andtotal).

28 The ‘lagging’ indicator is a weighted average of average duration, inventory/sales ratio,labor cost per unit ratio, prime rate, loans, credit/income ratio, and CPI of services.29 Huang and Kong (2003) follow the same approach.30 The UK ‘leading’ indicator is a weighted average of order book, output volume, consumerconfidence, house starts,31 The leading indicator is built using Handesblatt information and is a weighted averageof industrial confidence, consumer confidence, industrial production, monetary aggregates,harmonised inflation, and curve.32 The Economic Sentiment Indicator is a weighted average of industrial confidence, con-sumer confidence, construction confidence, and retail trade confidence. Service confidence,an indicator for European Commission, is not part of the ESI. The relationship between yields(not spreads) and ESI has been studied in particular by Ferreira et al. (2000).33 This matrix is generally called transition probability matrix. Strictu sensu the definitionis not correct, because we have historical transition frequencies and not ex ante transitionprobabilities.



3.6. Liquidity variables

In a typically illiquid OTC market, such as the corporate bond market, investors expectliquidity effects to influence credit risk changes significantly (Driessen, 2005; DeJong and Driessen, 2005; Longstaff et al., 2005). In particular, De Jong and Driessen(2005) show that liquidity risk is a priced factor for the expected returns on corporatebonds. Bid-offer spreads represent the exact measure of transaction costs, but thisvariable is not available for academic research or in investment bank databases, whichconventionally quote bond bid prices in their indexes. Typical proxies are bid-offerspreads on government bonds and possibly more illiquid, nonbenchmark governmentbonds.

Furthermore, it is well known that given an increased perception of market risk, a‘flight-to-quality’ may increase the spread between benchmark (or ‘on-the-run’) andex-benchmark (or ‘off-the-run’) government bonds.34 We therefore build a series ofthese spreads for the USA, the UK, and Germany35 with 10–30-year maturities.36

Another liquidity indicator that typically appears in the literature is the swap spread,which is the spread between government bonds and the swap rate. The assumption isthat reduced liquidity in the swap market implies a parallel and amplified effect in thecorporate bond market (Collin-Dufresne et al. 2001). In reality, the swap market hasbecome increasingly more liquid, so changes in the swap spread are unlikely to indicatesignificant liquidity effects.

Moreover, the swap spread is a measure of the excess return on a generic AA-ratedfinancial corporate bond over a government bond. The measure relies on LIBOR, whichgenerally applies to an AA-rated (banking sector) issuer. Because the index resetsevery half year or every year, LIBOR can be considered a ‘refreshed credit quality’yield and therefore intrinsically less risky than an AA-rated corporate bond whosecreditworthiness may deteriorate over time. Hence, the swap spread is a downward-biased proxy of the risk differential between a high-grade corporate bond and agovernment bond. To analyse this effect we collect the monthly changes in swap spreads(measured in basis points) for five-, 10-, and 30-year maturities in the USA, UK, andin the Eurozone from Bloomberg.37

3.7. The role of institutional investors

Buy and sell activity on corporate bonds, as recorded by Lehman Brothers from 1998, isthe last proxy of liquidity. These data measure monthly sales and purchases (in billions ofdollars) institutional investors transact with Lehman Brothers. Even though the variablerefers only to the US market and only to transactions in which Lehman Brothers is themarket maker, it represents a significant share of total volume given the investmentbank’s leadership in the fixed-income market.

34 Benchmark (‘on-the-run’) bonds typically have a longer time to maturity and, consequently,a higher theoretical yield to maturity than ‘off-the-run’ bonds. With a flight to quality, theyield curve may invert (in that point) with a liquidity premium, which justifies, for the‘on-the-run’ bond, a yield to maturity lower than that of the ‘off-the-run’ bond.35 As mentioned, investors generally use German bonds as a reference point for the Eurozone.36 Consider that liquidity and changes in the perception of risk may coincide, because ahigher perception of risk generates flight-to-quality effects that induce investors to movefrom less liquid to more liquid bonds.37 The swap spread for the Eurozone is built with German government bonds.



Martell (2008) uses as a regressor inflow data in equity and bond funds as measured byInvestment Company Institute (ICI). Nevertheless, these inflows are not actual tradingdata for institutional investors and do not benefit from the distinction between buy andsell signs38 or between investment-grade and high-yield corporate bonds flows. Martellalso relies on the analysis of US-dollar-denominated bonds, both corporate and foreignsovereign, to find links and similarities between the two markets, whereas this studyfocuses on USA, UK, and European (IG and HY) corporate debt markets.

We introduce institutional buy-sell activity to test whether institutional investors signalthe presence of additional information not incorporated in other regressors (such as stockperformance or in business cycle indicators). In particular, an increase in purchases(sales) could signal reduced (increased) perception of risk and therefore have negative(positive) impact on bid-ask spreads. Transaction data can also closely mirror thesupply/demand shocks that much of the literature considers important, beginning withCollin-Dufresne et al. (2001).

4. Empirical findings on separate estimates39

Section 3 provided rationales for including all the variables described in the estimates.The number of these variables, though, is too high and some of them proxy for thesame underlying factors. Hence, including all of them in the estimates may createserious problems of multicollinearity. We therefore divide the empirical analysis into twosteps.

In order to evaluate the significance of different variables, we perform separateestimates for each subgroup of variables as a first step. We use as a dependentvariable corporate bond indexes of different subgroups classified by rating, maturity,and industry.40 In a second step we use a selected group of indicators that aresignificant at least 20% of the time in separate estimates. Among interest rate variables,we select the five-year yield and the spread between US and UK (or Euro) bondyields as regressors;41 among stock market variables, we select the return on therelevant index, the implied volatility on the index, and the SMB factor;42 amongthe business cycle indicators, we select the US leading indicator;43 among liquidity

38 Inflows can turn or not in actual buying, depending on the asset manager’s view. Moreover,leaving aside equity fund inflows that are not very in line with the analysis, inflows ingeneric bond mutual funds without distinction in corporate/sovereign, or IG/HY, are notvery informative. Instead, actual transaction data that distinguishes IG/HY corporate bondflows can be much more informative.39 For an extensive analysis of the data and associated results, also, see Becchetti et al. (2009).40 In a table available upon request, we report synthetically the number of times (in percent)the variable is significant in these estimates.41 We find equivalent results using bond index returns and bond yield variation, and wetherefore choose to use the latter. Moreover, we find yield curve and both implied (includingskew and vega) and historical yield volatility not very powerful in explaining credit spreadchanges.42 We instead exclude HML factor and skew.43 The US leading indicator proves much more reliable even for UK and the Eurozone withrespect to ‘local’ indicators, showing the link between credit spreads and the US economy.



indicators, the swap spread.44 We also use the institutional investor data45 for USestimates.

Finally, we check the robustness of our results by repeating the estimates for differentsubsample splits, performing structural break tests, and incorporating higher (weekly)data frequency. We also use principal-component analysis to validate our choice ofavailable variables.

Given the autocorrelation and nonnormality of OAS evidenced by descriptive statis-tics, we use heteroskedasticity and autocorrelation robust Newey-West (1987) standarderrors. The optimal selection of the truncation lag is achieved by following the automaticselection approach followed by Newey and West (1994).

4.1. Empirical findings on the final selected specification for the US area

This section outlines an empirical specification that includes a selected number of thedescribed regressors. Following Huang and Kong (2003), we select them from a largerset to perform a parsimonious estimate.

The chosen specification for US delta credit spread is the following:

DCSt = α + β1�(5y)t + β2(russ2)t + β3�(riv)t + β4(smb)t

+ β5�(lead)t + β6�(swsp5)t + β7�(hy b)t + β8�(hy s)t + εt

(1.1)

where DCS (delta credit spread) is the change in the option-adjusted credit spread,5y is the five-year Treasury bond yield, russ2 is the return on the Russell 2000, rivis the implicit volatility of the options on the Russell 2000, smb is the Fama-FrenchSmall-Minus-Big factor, lead is the Leading Indicator from the Conference Board,swsp5 is the spread between the swap and yield of a five-year government bond, andhy b (hy s) are total HY US bond purchases (sales) of professional investors throughLehman Brothers.46

Our results, presented in Table 1A, show that this set of regressors explains asignificant part of credit-spread variability. The adjusted R2 ranges from 52.33% forthe overall IG index to 56.89% for the HY index. The five- to seven-year High Yieldindex has the highest R2 (61.67%). All of the selected variables maintain significantexplanatory power when jointly considered. The change in the interest rate level (5y)is statistically significant for almost all indexes.47 The telecommunications and autoindustry indexes aremore sensitive to this variable.

44 The spread between on-the-run and off-the-run government bonds is significant in the UKand the Eurozone but not in the USA; given it has a very small coefficient, however, weexclude it from the regressor set. We also exclude bid-ask spread variations.45 We exclude instead the downgrade and default ratios. They are significant only in theEurozone, but further analysis reveals that this result comes from a unique default notexpected in the market (Ahold, October 2002). This confirms that credit spreads on averageare sensitive only to unexpected and relevant credit events. This is consistent with the factthat rating agencies are prudent in rating revisions, resulting in delayed rating adjustments,with spread-implied ratings possibly anticipating future movements in agency ratings (Kouand Varotto, 2008).46 In a robustness check, we also add the lagged values of the regressors in our specificationand find that results are robust to their inclusion, being not statistically significant.47 An increase in the yield of the five-year Treasury bond of 10 basis points reduces thespreads by 1 bp (8 bps) for the aggregate investment-grade (high-yield) index.



Tabl

e1

The

dete

rmin

ants

ofop

tion

adju

sted

cred

itsp

read

chan

ges

for

bond

inde

xes

Thi

sTa

ble

repo

rts

the

dete

rmin

ants

ofop

tion

adju

sted

cred

itsp

read

chan

ges

for

bond

inde

xes

Dep

ende

ntva

riab

les

are

mon

thly

chan

ges

ofO

ptio

nA

djus

ted

Spr

eads

ofM

erri

llLy

nch

Cor

pora

tein

dexe

s.E

ach

chan

geis

calc

ulat

edbe

fore

mon

thly

reba

lanc

ing

inor

der

toen

sure

inva

rian

ceof

inde

xco

nsti

tuen

tsfo

ra

give

nsp

read

chan

ge.

Inde

xes

are

divi

ded

for

rati

ng,

mat

urit

yan

din

dust

ries

.D

ata

are

mea

sure

din

basi

spo

ints

.E

ach

tabl

ere

port

ses

tim

ated

coef

fici

ents

,t-

stat

san

dad

just

edR

-squ

ared

.T-

stat

sar

eca

lcul

ated

byus

ing

Het

eros

keda

stic

ity

and

Aut

ocor

rela

tion

Con

sist

ent

Cov

aria

nces

wit

hth

eN

ewey

-Wes

tco

vari

ance

mat

rix

esti

mat

or(t

runc

atio

nla

gis

sett

oth

ree)

.Pan

elA

repo

rts

find

ings

for

the

US

mar

ketf

ora

sam

ple

peri

odra

ngin

gfr

om1/

1997

to11

/200

3.T

hesp

ecif

icat

ion

isth

efo

llow

ing:

DC

S t=

α+

β1�

(5y)

t+

β2(r

uss2

) t+

β3�

(riv

) t+

β4(s

mb)

t+

β5�

(lea

d)t+

β6�

(sw

sp5)

t+

β7�

(hy

b)t+

β8�

(hy

s)t+

εt

whe

reD

CS

(Del

taC

redi

tSpr

ead)

isth

ech

ange

ofth

eop

tion

adju

sted

cred

itsp

read

,5y

isth

e5-

year

Tre

asur

ybo

ndyi

eld,

russ

2is

the

retu

rnof

the

Rus

sell

2000

,riv

isth

eim

plic

itvo

lati

lity

ofth

eop

tion

son

the

Rus

sell

2000

,sm

bis

the

Fam

a-Fr

ench

Sm

all-

min

us-B

igfa

ctor

,lea

dis

the

Lea

ding

Indi

cato

rde

lC

onfe

renc

eB

oard

,sw

sp5

isth

esp

read

betw

een

swap

and

yiel

dof

5-ye

argo

vern

men

tbo

nd,

hyb

(hy

s)ar

eto

tal

HY

US

bond

purc

hase

s(s

ales

)of

Leh

man

Bro

ther

spr

ofes

sion

alin

vest

ors.

Pane

lB

repo

rts

find

ings

for

the

UK

mar

ket

for

asa

mpl

epe

riod

rang

ing

from

1/19

98to

11/2

003.

The

spec

ific

atio

nis

the

foll

owin

g:

DC

S t=

α+

β1�

(5y)

t+

β2�

(sp5

y)t+

β3(f

tse

all)

t+

β4�

(fts

eiv

) t+

β5(s

mb)

t+

β6�

(lea

dus

) t+

β7�

(sw

sp10

) t+

εt

whe

re5y

isth

e5-

year

UK

Tre

asur

yyi

eld,

sp5y

isth

esp

read

betw

een

the

5-ye

arU

San

dU

Kgo

vern

men

tbo

nd,f

tse

all

isth

ere

turn

ofth

eF

tse

All

Sha

rein

dex,

ftse

ivis

the

impl

icit

vola

tili

tyof

opti

ons

onth

eF

tse

100,

smb

isth

eFa

ma-

Fren

chS

mal

l-m

inus

-Big

fact

or,l

ead

usis

the

Lea

ding

Indi

cato

rof

the

US

Con

fere

nce

Boa

rd,s

wsp

10is

the

spre

adbe

twee

nth

esw

apra

tean

dth

e10

-yea

rgo

vern

men

tbo

ndyi

eld.

Pane

lC

repo

rts

find

ings

for

the

Eur

ozon

em

arke

tfo

ra

sam

ple

peri

odra

ngin

gfr

om1/

1999

to11

/200

3.T

hesp

ecif

icat

ion

isth

efo

llow

ing:

DC

S t=

α+

β1�

(5y)

t+

β2�

(sp5

y)t+

β3(e

usto

x)t+

β4�

(dax

iv) t

+β

5(s

mb)

t+

β6�

(lea

dus

) t+

β7�

(sw

sp5)

t+

εt

whe

re5y

isth

eyi

eld

onth

e5-

year

Ger

man

gove

rnm

ent

bond

,sp

5yth

esp

read

betw

een

the

5-ye

arU

San

dG

erm

ango

vern

men

tbo

nd,e

usto

xis

the

retu

rnof

the

Eur

osto

xxin

dex,

dax

ivis

the

impl

icit

vola

tili

tyof

the

opti

ons

onD

ax,

smb

isth

eFa

ma-

Fren

chS

mal

l-m

inus

-Big

fact

or,

lead

usis

the

Lea

ding

Indi

cato

rof

the

US

Con

fere

nce

Boa

rd,s

wsp

10is

the

spre

adbe

twee

nth

esw

apra

tean

dth

e10

-yea

rgo

vern

men

tbo

ndyi

eld.

Pane

lA

:T

heD

eter

min

ants

ofO

ptio

nA

djus

ted

Cre

dit

Spre

adC

hang

esfo

rU

SB

ond

Inde

xes

alfa

5yru

ss2

Riv

smb

Lea

dsw

sp5

hyb

hys

t(al

fa)

t(5y

)t(

russ

2)t(

riv)

t(sm

b)t(

lead

)t(

swsp

5)t(

hyb)

t(hy

s)R

2

US

Cor

pora

te2.

02−0

.10

−0.4

30.

56−1

.01

−5.0

70.

33−1

7.31

19.2

51.

10−2

.58

−2.4

92.

28−2

.52

−1.7

82.

95−2

.56

3.05

52.3

3%U

SC

orp

AA

A−0

.75

−0.0

7−0

.17

0.21

−0.0

90.

130.

23−7

.92

7.36

−0.9

1−3

.50

−1.5

51.

08−0

.46

0.07

3.82

−2.7

42.

6950

.54%



US

Cor

pA

A0.

04−0

.04

−0.1

70.

35−0

.37

−3.3

90.

29−9

.49

9.53

0.03

−1.8

6−1

.35

1.65

−1.3

9−1

.73

4.67

−2.4

83.

1147

.37%

US

Cor

pA

1.28

−0.0

8−0

.30

0.45

−0.8

3−4

.62

0.31

−10.

8614

.02

0.86

−2.4

5−2

.15

1.64

−2.5

8−1

.78

3.34

−2.1

73.

0148

.56%

US

Cor

pB

BB

4.18

−0.1

3−0

.75

0.80

−1.7

0−6

.09

0.37

−26.

8929

.37

1.49

−2.3

7−2

.82

2.39

−2.7

3−1

.47

2.00

−2.2

42.

6050

.01%

US

Cor

p1-

3Y

rs3.

82−0

.12

−0.3

40.

46−1

.56

−2.7

60.

18−2

3.25

26.0

31.

48−2

.96

−1.6

81.

53−2

.71

−0.8

61.

14−2

.60

3.01

36.9

6%U

SC

orp

3-5

Yrs

2.01

−0.1

0−0

.44

0.34

−1.1

0−4

.19

0.33

−15.

5421

.56

0.91

−2.6

0−2

.24

1.23

−2.5

6−1

.57

2.71

−1.9

92.

8046

.91%

US

Cor

p5-

7Y

rs1.

76−0

.09

−0.4

60.

68−1

.12

−4.9

60.

34−1

4.47

17.9

30.

86−2

.47

−2.2

82.

51−2

.86

−1.6

02.

63−2

.20

2.83

50.0

8%U

SC

orp

7-10

Yrs

1.63

−0.1

2−0

.50

0.62

−0.6

7−4

.91

0.39

−17.

3017

.68

0.99

−2.7

6−2

.68

2.34

−1.7

4−1

.49

3.76

−2.6

53.

1255

.98%

US

Cor

p10

-15

Yrs

1.84

−0.0

2−0

.56

0.41

−0.9

2−2

.36

0.29

−19.

2719

.21

1.13

−0.3

9−2

.47

1.45

−2.0

3−0

.76

2.94

−2.7

12.

9443

.45%

US

Cor

p15

+Y

rs1.

05−0

.06

−0.4

70.

77−0

.90

−7.5

90.

39−1

5.39

14.3

00.

70−1

.43

−2.3

53.

58−1

.67

−2.0

33.

49−2

.70

2.81

55.8

8%

US

Fina

ncia

lC

orp

0.98

−0.1

0−0

.28

0.39

−0.8

7−5

.42

0.39

−11.

8415

.76

0.49

−2.6

6−1

.62

1.10

−2.0

4−1

.74

3.22

−1.9

92.

5940

.54%

US

Cor

pB

anki

ng−1

.08

−0.0

6−0

.11

0.36

−0.2

3−5

.16

0.35

−7.9

68.

79−0

.89

−2.1

5−0

.84

1.79

−0.9

0−1

.90

4.41

−2.0

22.

9943

.19%

US

Cor

pB

roke

rage

−0.6

9−0

.10

−0.0

60.

52−0

.40

−7.0

60.

44−1

1.62

12.5

9−0

.44

−2.2

6−0

.24

2.04

−1.2

4−2

.51

5.14

−2.2

73.

4342

.30%

US

Cor

pFi

nanc

e&

3.11

−0.1

7−0

.45

0.23

−1.6

5−4

.50

0.48

−17.

5526

.10

1.03

−2.7

0−2

.13

0.38

−2.0

1−0

.93

2.31

−1.8

02.

1430

.47%

Inve

stm

ent

US

Cor

pIn

sura

nce

3.06

0.06

−0.9

41.

11−1

.12

−6.4

0−0

.20

−0.2

34.

260.

930.

65−1

.79

1.53

−1.7

7−1

.50

−0.6

1−0

.03

0.97

8.37

%U

SIn

dust

rial

Cor

p2.

61−0

.08

−0.5

40.

78−1

.13

−6.1

20.

29−2

0.21

20.1

71.

27−1

.84

−2.9

93.

81−2

.07

−1.8

62.

25−2

.64

2.96

50.3

6%U

SC

orp

Aut

oG

roup

3.89

−0.2

2−0

.71

1.00

−2.0

8−1

0.36

0.43

−18.

0825

.84

0.98

−2.2

4−2

.62

1.28

−2.2

9−1

.52

1.51

−1.2

22.

0627

.99%

US

Cor

pB

asic

1.56

−0.0

6−0

.43

0.62

−1.1

0−3

.56

0.14

−9.5

011

.37

1.04

−1.8

8−2

.52

2.28

−2.8

2−1

.16

1.00

−1.0

91.

3738

.23%

Indu

stry

US

Cor

pC

onsu

mer

3.28

−0.0

7−0

.48

1.11

−2.0

7−7

.82

0.27

−9.8

611

.54

1.23

−1.0

6−2

.36

3.94

−2.0

5−1

.78

1.53

−1.3

12.

0738

.61%

Cyc

lica

lsU

SC

orp

Cap

ital

2.22

−0.0

3−0

.38

0.56

−0.8

1−6

.66

0.14

−9.5

614

.22

1.27

−0.8

2−2

.40

2.60

−1.4

5−1

.75

1.01

−1.0

71.

9431

.97%

Goo

dsU

SC

orp

Con

sum

er0.

460.

02−0

.36

0.37

−0.8

0−3

.94

0.19

−4.2

74.

920.

430.

74−2

.61

2.04

−2.0

7−1

.95

2.49

−1.2

21.

8139

.05%

Non

-Cyc

lica

lU

SC

orp

Ene

rgy

1.78

−0.1

3−0

.54

0.31

−0.7

72.

860.

36−1

9.66

18.7

70.

78−3

.11

−1.9

10.

82−1

.73

0.68

2.77

−2.0

92.

0542

.31%



Tabl

e1

Con

tinu

ed.

Pane

lA

:T

heD

eter

min

ants

ofO

ptio

nA

djus

ted

Cre

dit

Spre

adC

hang

esfo

rU

SB

ond

Inde

xes

alfa

5yru

ss2

Riv

smb

Lea

dsw

sp5

hyb

hys

t(al

fa)

t(5y

)t(

russ

2)t(

riv)

t(sm

b)t(

lead

)t(

swsp

5)t(

hyb)

t(hy

s)R

2

US

Cor

pM

edia

−1.2

5−0

.16

−0.7

30.

71−0

.97

−2.4

80.

75−4

3.44

40.2

2−0

.36

−1.8

9−2

.00

1.95

−1.5

5−0

.44

3.14

−1.8

61.

7940

.44%

US

Cor

pR

eal

Est

ate

−0.7

9−0

.09

−0.0

20.

54−0

.62

−4.4

20.

16−3

.71

3.28

−0.3

8−1

.74

−0.0

62.

11−1

.13

−1.6

70.

97−0

.71

0.89

12.0

8%U

SC

orp

Ser

vice

s8.

770.

01−0

.81

1.34

−2.3

1−1

1.51

−0.0

5−1

3.44

13.5

92.

540.

25−2

.42

1.90

−2.9

0−2

.71

−0.2

0−1

.06

1.22

26.9

4%C

ycli

cal

US

Cor

pS

ervi

ces

1.91

0.01

−0.7

4−0

.85

−2.2

1−0

.13

−0.1

6−1

5.05

11.3

10.

560.

12−1

.65

−0.6

5−1

.91

−0.0

2−0

.42

−1.4

61.

2113

.52%

Non

-Cyc

lica

lU

SC

orp

2.48

−0.2

0−0

.62

1.49

−0.5

5−1

3.13

0.48

−49.

9548

.09

0.47

−1.7

4−1

.76

2.54

−0.3

9−1

.44

1.16

−1.8

91.

9823

.35%

Tele

com

mun

icat

ions

US

Cor

pTe

chno

logy

8.26

−0.0

9−0

.65

0.55

−1.8

1−6

.79

0.44

−16.

2715

.90

2.00

−1.3

5−2

.15

2.00

−2.4

3−1

.20

1.95

−1.2

11.

4331

.80%

Ele

ctro

nics

US

Uti

lity

Cor

p4.

07−0

.17

−0.4

4−0

.13

−1.6

52.

640.

31−2

9.54

39.0

21.

11−2

.16

−1.0

2−0

.22

−1.8

30.

421.

40−1

.37

1.59

23.8

1%

US

Hig

hY

ield

Inde

x9.

93−0

.81

−2.4

63.

24−3

.50

−13.

931.

71−2

9.74

21.0

91.

12−4

.49

−2.8

32.

30−1

.57

−0.8

33.

61−1

.23

1.13

56.8

9%U

SH

YB

B6.

38−0

.65

−2.0

22.

72−2

.19

−9.2

40.

88−3

3.54

25.9

21.

16−4

.82

−2.9

92.

22−1

.22

−0.7

42.

38−1

.54

1.61

51.7

5%U

SH

YB

12.1

7−0

.92

−2.4

53.

20−3

.60

−17.

702.

26−2

4.57

19.4

51.

08−3

.96

−2.5

22.

13−1

.40

−0.8

93.

96−0

.90

0.94

57.3

9%U

SH

YC

CC

and

24.8

5−1

.12

−4.2

36.

34−1

0.90

−24.

822.

65−1

3.50

−12.

601.

21−3

.44

−2.2

22.

51−3

.23

−0.7

82.

43−0

.25

−0.2

944

.70%

Low

er

HY

US

1-3

Yrs

10.0

9−0

.85

−2.2

010

.61

−4.1

6−2

3.06

2.04

−138

.295

.19

0.60

−3.2

2−1

.05

2.78

−0.8

5−0

.87

1.86

−1.8

41.

5520

.64%

HY

US

3-5

Yrs

10.1

5−0

.88

−2.3

13.

43−4

.38

−18.

031.

45−4

1.12

19.9

01.

09−5

.62

−2.4

92.

19−2

.20

−1.2

93.

13−1

.54

0.80

57.3

5%H

YU

S5-

7Y

rs8.

96−0

.93

−2.0

32.

75−4

.58

−9.1

61.

51−8

.83

6.24

1.06

−5.2

4−2

.44

2.05

−2.9

8−0

.55

3.39

−0.4

20.

4261

.67%

HY

US

7-10

Yrs

9.51

−0.7

7−2

.47

3.13

−2.4

2−1

1.02

1.67

−19.

9215

.13

1.16

−3.8

0−2

.82

2.19

−1.0

5−0

.63

3.45

−0.9

91.

0155

.05%

HY

US

10-1

5Y

rs3.

62−0

.50

−1.9

11.

95−2

.38

−10.

130.

27−3

3.50

19.8

90.

52−4

.21

−2.9

51.

84−1

.79

−0.8

90.

86−1

.36

1.16

49.1

0%H

YU

S15

+Y

rs−4

.83

−0.5

5−0

.97

1.72

−0.7

4−1

1.35

1.05

−54.

9536

.00

−1.0

7−4

.11

−1.9

31.

84−0

.35

−0.8

52.

89−1

.96

2.03

40.1

8%

HY

US

Lar

geC

ap12

.42

−0.8

9−1

.39

2.20

−4.6

10.

302.

32−2

8.37

22.9

21.

32−5

.30

−0.8

10.

79−1

.55

0.02

3.51

−0.9

91.

1620

.92%

HY

US

Sm

all

Cap

15.2

3−0

.93

0.01

0.49

−10.

36−1

.97

1.98

−29.

6825

.36

1.32

−4.7

60.

010.

16−2

.63

−0.0

91.

94−0

.79

0.79

5.07

%



Pane

lB

:T

heD

eter

min

ants

ofO

ptio

nA

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ted

Cre

dit

Spre

adC

hang

esfo

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KB

ond

Inde

xes

alfa

5ysp

5yft

seal

lft

seiv

smb

lead

ussw

sp10

t(al

fa)

t(5y

)t(

sp5y

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ftse

all)

t(ft

seiv

)t(

smb)

t(le

adus

)t(

swsp

10)

R2

Ste

rlin

gC

orpo

rate

Inde

x0.

720.

01−0

.02

−0.3

60.

05−0

.66

−3.7

10.

520.

880.

03−0

.60

−1.4

60.

10−1

.73

−1.9

34.

9740

.02%

Ste

rlin

gC

orp

AA

A0.

400.

020.

01−0

.02

0.09

−0.4

8−1

.50

0.52

0.63

0.71

0.48

−0.0

80.

37−1

.59

−1.0

25.

9738

.20%

Ste

rlin

gC

orp

AA

0.43

0.02

0.01

−0.2

50.

06−0

.57

−2.9

20.

570.

690.

68−0

.16

−1.2

80.

17−1

.57

−1.8

96.

4344

.68%

Ste

rlin

gC

orp

A0.

85−0

.01

−0.0

3−0

.44

0.11

−0.5

9−4

.45

0.51

0.80

−0.1

8−0

.79

−1.5

30.

33−1

.24

−1.8

03.

8031

.71%

Ste

rlin

gC

orp

BB

B1.

39−0

.09

−0.0

9−0

.54

−0.0

9−1

.02

−6.0

30.

471.

03−1

.56

−1.4

5−1

.14

−0.4

1−1

.99

−1.9

32.

9239

.04%

Ste

rlin

gC

orp

1-3

Yrs

0.06

−0.0

1−0

.03

−0.1

80.

26−1

.00

−0.3

00.

210.

07−0

.41

−1.3

1−0

.71

1.37

−3.4

1−0

.17

2.54

25.5

8%S

terl

ing

Cor

p3-

5Y

rs1.

66−0

.03

−0.0

6−0

.49

0.17

−0.9

6−2

.31

0.33

1.94

−0.9

1−1

.46

−1.9

10.

71−3

.41

−0.9

92.

8642

.89%

Ste

rlin

gC

orp

5-7

Yrs

2.02

−0.0

4−0

.05

−0.3

0−0

.12

−0.6

7−8

.13

0.54

1.85

−0.9

0−1

.22

−0.9

6−0

.58

−1.4

3−3

.49

4.72

48.8

9%S

terl

ing

Cor

p7-

10Y

rs0.

92−0

.03

−0.0

3−0

.37

−0.0

1−0

.76

−5.0

10.

620.

99−0

.74

−0.8

5−1

.21

−0.1

4−1

.58

−2.1

75.

6144

.43%

Ste

rlin

gC

orp

10-1

5Y

rs1.

010.

02−0

.03

−0.4

10.

04−0

.64

−4.9

10.

610.

820.

36−0

.56

−1.3

40.

08−1

.17

−1.8

44.

3828

.27%

Ste

rlin

gC

orp

15+

Yrs

0.35

0.04

0.01

−0.3

80.

08−0

.42

−3.9

50.

660.

310.

890.

03−1

.29

0.22

−0.7

4−1

.53

4.39

27.1

6%

Ste

rlin

gC

orp

Fina

ncia

lsIn

dex

0.34

0.01

−0.0

3−0

.37

−0.0

2−0

.72

−3.6

90.

500.

480.

28−0

.85

−1.5

9−0

.29

−1.7

1−2

.14

5.28

38.6

4%

Ste

rlin

gC

orp

Ban

king

−0.1

70.

020.

01−0

.32

−0.0

9−0

.55

−3.4

90.

55−0

.26

0.40

−0.1

4−1

.62

−0.6

8−1

.25

−2.0

85.

5538

.17%

Ste

rlin

gC

orp

Bro

kera

ge0.

01−0

.01

−0.0

5−0

.08

−0.0

4−1

.85

−0.4

50.

420.

01−0

.12

−1.1

0−0

.26

−0.2

5−4

.64

−0.1

64.

1525

.62%

Ste

rlin

gC

orp

Fina

nce

&In

vest

men

t1.

75−0

.01

−0.1

0−0

.36

0.38

−1.8

2−0

.88

0.40

1.14

−0.2

3−2

.11

−0.9

61.

72−2

.34

−0.3

13.

7627

.26%

Ste

rlin

gC

orp

Insu

ranc

e2.

870.

01−0

.06

−0.3

9−0

.09

−0.2

0−1

1.92

0.52

1.54

0.11

−0.7

7−0

.71

−0.3

6−0

.26

−2.3

72.

7321

.95%

Ste

rlin

gC

orp

Indu

stri

als

Inde

x1.

14−0

.04

−0.0

6−0

.51

0.16

−0.6

5−5

.54

0.46

1.13

−1.0

0−1

.21

−1.5

50.

51−1

.78

−2.2

53.

3242

.50%

Ste

rlin

gC

orp

Bas

icIn

dust

ry3.

05−0

.14

−0.1

5−0

.07

−0.1

7−1

.42

−3.1

40.

201.

85−1

.52

−1.9

2−0

.17

−0.4

6−2

.69

−0.9

20.

9724

.38%

Ste

rlin

gC

orp

Con

sum

erC

ycli

cals

0.61

−0.0

2−0

.07

−0.3

30.

11−0

.63

−5.6

50.

500.

49−0

.57

−1.2

0−1

.06

0.32

−2.0

1−2

.10

3.80

39.5

0%

Ste

rlin

gC

orp

Cap

ital

Goo

ds3.

11−0

.06

−0.0

9−1

.36

0.19

−1.7

9−8

.15

0.26

1.23

−0.8

2−1

.23

−2.0

20.

48−1

.69

−1.8

50.

9933

.27%



Tabl

e1

Con

tinu

ed.

Pane

lB

:T

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eter

min

ants

ofO

ptio

nA

djus

ted

Cre

dit

Spre

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hang

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KB

ond

Inde

xes

alfa

5ysp

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seal

lft

seiv

smb

lead

ussw

sp10

t(al

fa)

t(5y

)t(

sp5y

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ftse

all)

t(ft

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smb)

t(le

adus

)t(

swsp

10)

R2

Ste

rlin

gC

orp

Con

sum

erN

on-C

ycli

cals

0.69

0.01

0.01

−0.3

30.

07−0

.41

−5.0

50.

560.

760.

340.

18−1

.15

0.22

−1.0

4−2

.17

4.12

41.6

3%

Ste

rlin

gC

orp

Ene

rgy

0.09

0.02

−0.0

1−0

.23

0.17

−1.0

0−0

.92

0.51

0.13

0.56

−0.3

6−0

.85

0.72

−2.9

8−0

.43

3.76

31.5

1%S

terl

ing

Cor

pM

edia

1.82

−0.1

4−0

.05

−0.9

20.

17−1

.20

−6.3

30.

471.

00−1

.15

−0.4

6−2

.18

0.34

−1.7

9−1

.06

2.05

32.0

0%S

terl

ing

Cor

pR

eal

Est

ate

1.75

0.01

−0.0

20.

030.

03−0

.52

−7.0

40.

481.

450.

01−0

.58

0.09

0.04

−1.1

3−2

.51

3.43

20.1

7%

Ste

rlin

gC

orp

Ser

vice

sC

ycli

cal

0.84

−0.0

5−0

.08

−0.3

10.

17−0

.33

−5.0

30.

460.

57−0

.71

−1.0

4−0

.89

0.50

−0.5

8−1

.52

2.33

21.2

4%

Ste

rlin

gC

orp

Ser

vice

sN

on-C

ycli

cal

−3.2

00.

08−0

.19

−0.5

30.

210.

01−3

.71

−0.0

9−1

.33

0.86

−2.0

8−0

.99

0.48

0.01

−0.6

9−0

.20

6.83

%

Ste

rlin

gC

orp

Tele

com

mun

icat

ions

0.57

−0.0

4−0

.12

−1.0

60.

31−0

.50

−6.2

80.

490.

21−0

.55

−1.6

1−2

.02

0.67

−0.6

9−1

.39

2.73

23.0

6%

Ste

rlin

gC

orp

Uti

liti

esIn

dex

0.42

0.02

0.01

−0.4

90.

11−0

.65

−2.3

70.

620.

320.

470.

19−1

.53

0.36

−1.4

0−0

.79

3.59

29.1

6%

Ste

rlin

gC

orp

All

Sto

cks

(inc

lude

not-

rate

d)

0.84

0.01

−0.0

3−0

.28

0.07

−0.6

1−3

.26

0.51

1.00

0.06

−0.7

7−1

.13

0.23

−1.6

4−1

.66

5.02

36.2

1%

Ste

rlin

gA

llS

tock

sU

.K.I

ssue

rs0.

760.

01−0

.02

−0.2

70.

06−0

.49

−3.3

70.

540.

870.

34−0

.50

−1.0

90.

16−1

.17

−1.7

34.

9333

.58%

Ste

rlin

gA

llS

tock

sN

on-U

.K.I

ssue

rs1.

02−0

.02

−0.0

4−0

.34

0.10

−0.9

2−3

.78

0.42

1.13

−0.4

7−1

.17

−1.2

70.

36−2

.63

−1.7

45.

1039

.07%

Ste

rlin

gL

arge

Cap

Cor

pIn

dex

0.58

0.01

−0.0

3−0

.43

−0.0

2−0

.65

−4.3

00.

570.

720.

03−0

.73

−1.6

2−0

.18

−1.5

0−1

.98

5.30

45.1

1%

Ste

rlin

gH

igh

Yie

ldIn

dex

5.38

−0.3

8−0

.19

−6.0

41.

99−4

.17

−14.

991.

030.

83−1

.67

−0.6

4−3

.72

1.59

−1.6

2−0

.87

1.48

44.4

4%

Ste

rlin

gH

igh

Yie

ldB

B−5

.05

−0.5

6−0

.50

−4.8

52.

51−2

.97

12.9

90.

40−1

.01

−2.6

9−1

.61

−3.3

12.

46−1

.06

0.75

0.56

38.7

9%S

terl

ing

Hig

hY

ield

B8.

90−0

.28

−0.0

6−6

.16

1.96

−6.6

6−1

0.65

0.46

0.82

−0.8

0−0

.16

−2.8

71.

24−1

.92

−0.4

60.

4324

.10%

Ste

rlin

gH

igh

Yie

ldC

CC

-C3.

04−1

.08

0.49

−1.4

1−1

.96

1.90

−100

.11

1.35

0.19

−1.1

70.

53−0

.28

−0.3

40.

20−1

.92

0.44

3.25

%



Pane

lC

:T

heD

eter

min

ants

ofO

ptio

nA

djus

ted

Cre

dit

Spre

adC

hang

esfo

rE

UB

ond

Inde

xes

alfa

5ysp

5yeu

stox

daxi

vsm

ble

adus

swsp

5t(

alfa

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5y)

t(sp

5y)

t(eu

stox

)t(

daxi

v)t(

smb)

t(le

adus

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swsp

5)R

2

EM

UC

orpo

rate

Inde

x0.

15−0

.03

−0.1

0−0

.23

0.17

−0.1

2−5

.35

0.37

0.18

−1.0

5−2

.46

−0.9

11.

37−0

.23

−2.5

82.

6750

.62%

EM

UC

orp

AA

A−0

.23

−0.0

2−0

.01

−0.0

70.

00−0

.23

−1.0

20.

24−0

.53

−1.0

9−0

.96

−1.4

7−0

.27

−1.1

8−1

.60

3.64

33.8

7%E

MU

Cor

pA

A−0

.27

−0.0

2−0

.03

−0.1

0−0

.04

−0.2

5−1

.32

0.30

−0.5

9−0

.86

−2.0

2−1

.38

−0.8

9−1

.19

−1.9

85.

0544

.91%

EM

UC

orp

A−0

.12

−0.0

2−0

.14

−0.0

60.

100.

21−7

.09

0.39

−0.1

4−0

.55

−2.5

2−0

.19

0.75

0.34

−2.4

82.

5243

.61%

EM

UC

orp

BB

B2.

80−0

.03

−0.2

0−1

.01

0.46

−0.3

4−1

9.69

0.31

0.99

−0.3

4−1

.58

−1.4

01.

08−0

.22

−2.6

80.

6941

.75%

EM

UC

orp

1-3

Yr

0.37

−0.0

2−0

.15

−0.0

80.

250.

18−5

.38

0.31

0.28

−0.4

4−1

.80

−0.2

21.

500.

24−1

.73

1.35

25.7

1%E

MU

Cor

p3-

5Y

r0.

89−0

.05

−0.1

1−0

.39

0.25

−0.3

6−6

.62

0.37

0.83

−1.2

4−2

.22

−1.2

81.

55−0

.55

−2.4

91.

8450

.76%

EM

UC

orp

5-7

Yr

−0.1

1−0

.04

−0.1

0−0

.25

0.14

−0.2

1−4

.38

0.35

−0.1

5−1

.35

−2.9

4−1

.32

1.40

−0.4

7−2

.59

2.50

54.4

8%E

MU

Cor

p7-

10Y

r−0

.25

−0.0

3−0

.05

−0.2

30.

03−0

.31

−3.7

60.

34−0

.41

−1.1

4−2

.15

−1.5

70.

27−0

.87

−2.7

54.

2151

.99%

EM

UC

orp

10+

Yr

−1.5

6−0

.01

−0.0

2−0

.10

−0.0

80.

12−3

.01

0.43

−1.7

3−0

.35

−0.6

6−0

.57

−0.7

70.

33−2

.01

1.81

25.8

8%

EM

UC

orpo

rate

Lar

geC

apIn

dex

−0.0

3−0

.02

−0.1

2−0

.30

0.19

−0.2

1−6

.07

0.38

−0.0

3−0

.58

−2.6

3−1

.11

1.30

−0.3

6−2

.57

2.52

51.6

4%

EM

UFi

nanc

ial

Cor

pora

teIn

dex

−0.3

5−0

.01

−0.0

7−0

.03

−0.0

10.

01−2

.49

0.35

−0.4

9−0

.50

−1.7

7−0

.18

−0.0

40.

01−1

.52

3.40

30.1

7%

Ban

king

−0.4

0−0

.02

−0.0

2−0

.08

−0.0

3−0

.17

−1.6

10.

28−0

.83

−1.0

1−1

.25

−1.0

4−0

.74

−0.8

8−2

.55

4.18

43.4

1%B

roke

rage

−1.2

0−0

.04

−0.1

1−0

.08

0.19

−0.4

0−3

.02

0.39

−1.6

3−1

.42

−2.8

8−0

.53

1.55

−1.1

8−1

.63

2.72

42.4

1%Fi

nanc

e&

Inve

stm

ent

−1.1

40.

01−0

.35

0.11

0.22

0.66

−5.1

50.

60−0

.47

0.07

−1.6

90.

140.

910.

45−0

.69

1.53

12.9

1%In

sura

nce

−0.4

60.

01−0

.04

−0.2

80.

04−0

.08

−6.1

50.

20−0

.87

0.10

−1.2

7−1

.40

0.33

−0.1

7−3

.59

1.41

39.4

5%

EM

UC

orpo

rate

sN

on-F

inan

cial

Inde

x1.

22−0

.04

−0.1

5−0

.52

0.35

−0.3

3−9

.82

0.35

0.86

−0.8

7−2

.38

−1.3

81.

53−0

.39

−2.8

61.

4750

.03%

EM

UC

orpo

rate

sIn

dust

rial

sIn

dex

1.51

−0.0

4−0

.16

−0.6

20.

38−0

.35

−11.

380.

340.

97−0

.70

−2.2

7−1

.40

1.47

−0.3

6−2

.88

1.29

49.2

3%



Tabl

e1

Con

tinu

ed.

Pane

lC

:T

heD

eter

min

ants

ofO

ptio

nA

djus

ted

Cre

dit

Spre

adC

hang

esfo

rE

UB

ond

Inde

xes

alfa

5ysp

5yeu

stox

daxi

vsm

ble

adus

swsp

5t(

alfa

)t(

5y)

t(sp

5y)

t(eu

stox

)t(

daxi

v)t(

smb)

t(le

adus

)t(

swsp

5)R

2

Aut

oG

roup

−0.5

2−0

.09

−0.3

6−0

.10

0.35

0.46

−6.7

20.

45−0

.32

−1.0

3−3

.04

−0.1

31.

560.

31−1

.15

1.20

29.3

2%B

asic

Indu

stry

1.71

−0.0

6−0

.07

−0.4

00.

26−0

.56

−9.1

40.

061.

39−1

.44

−1.2

4−1

.02

1.45

−0.7

5−2

.28

0.22

36.8

2%C

onsu

mer

Cyc

lica

ls0.

14−0

.13

−0.2

50.

160.

280.

71−6

.31

0.48

0.10

−2.1

9−3

.23

0.36

1.30

0.65

−1.7

31.

4730

.53%

Cap

ital

Goo

ds2.

43−0

.05

−0.1

7−0

.49

−0.1

0−0

.53

−9.5

40.

441.

46−0

.70

−1.9

8−0

.85

−0.4

0−0

.47

−1.8

81.

5833

.45%

Con

sum

erN

on-C

ycli

cals

1.70

−0.0

40.

01−0

.25

0.11

0.02

−10.

13−0

.26

0.84

−0.7

7−0

.08

−0.7

10.

670.

02−1

.80

−0.4

98.

55%

Ene

rgy

0.25

−0.1

1−0

.22

−0.5

10.

16−0

.68

6.90

0.63

0.13

−1.0

4−2

.14

−1.7

10.

58−1

.70

1.31

1.40

20.9

7%M

edia

−0.5

6−0

.08

−0.2

1−0

.70

0.22

−0.5

4−0

.48

0.56

−0.2

7−0

.60

−2.0

1−1

.72

0.82

−0.5

4−0

.10

1.44

22.3

5%R

eal

Est

ate

−0.9

8−0

.13

−0.1

30.

13−0

.07

−0.6

0−0

.09

0.24

−0.7

2−2

.48

−2.2

70.

65−0

.25

−0.9

8−0

.03

1.27

12.3

6%S

ervi

ces

Cyc

lica

l3.

380.

05−0

.46

0.38

0.64

0.93

−17.

450.

550.

950.

38−1

.27

0.28

1.26

0.33

−1.4

20.

825.

42%

Ser

vice

sN

on-C

ycli

cal

−1.8

30.

03−0

.01

−0.0

70.

030.

37−7

.30

0.06

−1.8

40.

58−0

.33

−0.5

50.

121.

11−3

.23

0.45

21.6

0%Te

leco

mm

unic

atio

ns−0

.38

0.04

−0.1

3−1

.14

0.58

−0.6

3−1

7.22

0.61

−0.1

40.

29−1

.23

−1.8

81.

14−0

.70

−1.9

61.

9434

.62%

Tech

nolo

gy&

Ele

ctro

nics

16.0

7−0

.25

−0.2

4−1

.97

1.39

−1.7

5−1

6.11

0.80

2.00

−1.1

1−1

.44

−1.4

61.

27−0

.57

−2.0

70.

6418

.28%

EM

UC

orpo

rate

sU

tili

ties

Inde

x−0

.52

−0.0

1−0

.05

−0.2

60.

08−0

.23

−2.1

30.

28−0

.85

−0.4

0−2

.08

−2.2

30.

91−0

.89

−1.8

22.

6739

.41%

Eur

oH

igh

Yie

ldIn

dex

15.2

7−0

.11

−0.6

8−7

.36

3.69

−11.

37−2

2.89

2.27

0.97

−0.2

8−1

.02

−2.8

62.

21−1

.79

−0.9

01.

5340

.64%

Eur

oH

YB

B4.

57−0

.97

−1.1

0−6

.11

2.96

−15.

63−3

.73

1.86

0.54

−2.9

0−1

.63

−4.0

62.

47−4

.34

−0.3

01.

6061

.76%

Eur

oH

YB

12.4

1−0

.05

−0.4

4−5

.63

3.23

−7.3

1−3

0.64

1.42

0.70

−0.1

1−0

.81

−1.9

51.

72−1

.00

−1.0

40.

9225

.13%

Eur

oH

YC

CC

-C64

.63

2.01

0.25

−16.

769.

59−2

4.08

−107

.40

5.48

1.18

1.20

0.12

−1.6

91.

61−1

.07

−1.0

81.

2214

.86%



Stock returns (russ2) are statistically significant along the rating curve, with theexception of the AAA-rated and AA-rated corporates. This result confirms that riskierbonds are more dependent on stock returns.48 Among macroindustries, the coefficientis the highest for industrials; among single industries, it is highest among cyclical onessuch as auto, telecom, and tech industries. As expected, the coefficient magnitude ishigher for consumer cyclicals and services cyclicals with respect to the correspondingnoncyclicals sectors.

Stock market implicit volatility (riv) has a stronger impact on riskier bond indexes,confirming their relatively higher dependence on stock market variability expectations.49

The Small-Minus-Big risk factor has significant effects that increase along the ratingcurve, reducing the credit spread by up to 10 bps for a 1% variation in the regressor.The variable is also significant for industry-specific indexes, with the exception of thebanking and telecommunication index.50

The Conference Board Leading Indicator (lead) becomes weakly significant in thepresence of all other regressors. We must consider, though, that it is a composite indicatorof different variables, some of them present in the estimates. As expected, its impact ishigher on cyclical than on noncyclical industries.

The change in swap spreads (swsp5) is statistically significant with an effect that isinversely related to the rating curve.51 The impact of a change of the same magnitudein the regressor is quite stable across IG industries, widening credit spreads by around3–4 bps on financials, industrials, and utilities.

Regressors measuring purchases and sales of high-yield bonds from institutionalinvestors are highly significant. A $100 million52 purchase (sale), for example, reduces(increases) credit spreads by around 2 bps on the aggregate IG index. This result confirmsthat institutional trading activity signals to the market information not already capturedby other controls included in the estimates. In particular, this variable could link to avariation of risk perception or could be a proxy for supply/demand shocks influencingthe market (Collin-Dufresne et al., 2001). Results from a US regression show thatregressors explain a significant part of credit-spread variability. The main determinantsare interest rate changes, stock returns and volatility, SMB factor, swap spreads, andflows of institutional investors. In particular, results confirm the expected exposure ofHY bonds to stock variables (returns, implied volatility, and SMB factor). Moreover,although industrial bonds seem very exposed to stock market factors, the same cannotbe said for financial and utility bonds.

48 For a 10% positive return on the Russell 2000, we observe a reduction of spreads rangingfrom 3 bps for the A-rated index, to 24 bps for the B-rated, to 42 for the CCC-C-rated index.49 Coefficient magnitudes show that a 1% increase in implicit volatility widens spreads byalmost one basis point for the BBB index and up to 6 bps for the CCC-C index. The mostsensitive macroindustry (industry) is industrials (telecom). The high-yield telecom bondindex exhibits the highest reaction to a 1% change in implicit volatility, with an increase inthe spread of almost 10 bps. Results for US high-yield sectors are available upon request.50 An interpretation of this result is that these two indexes are composed of larger companiesand therefore are less subject to small-size risk.51 A 10 bps increase in swap spreads increases the dependent variable by 2 bps in the AAAindex, 8 bps in the BB index, and up to 26 bps in the CCC-C index.52 Data on buy or sell flows (Table 1A) are in billions of dollars.



4.2. Empirical findings on the final selected specification for the UK area

For the UK area we choose the following specification:

DCSt = α + β1�(5y)t + β2�(sp5y)t + β3(ftse all)t + β4�(ftse iv)t

+ β5(smb)t + β6�(lead us)t + β7�(swsp10)t + εt

(1.2)

where 5y is the five-year UK Treasury yield, sp 5y is the spread between the five-yearUS and UK government bonds, ftse all is the return on the FTSE All Share index, ftse ivis the implicit volatility of options on the FTSE 100, smb is the Fama-French Small-Minus-Big factor, lead us is the Leading Indicator of the US Conference Board, andswsp10 is the spread between the swap rate and the 10-year government bond yield.53

The results, presented in Table 1B, show that goodness of fit is lower than in the USestimate. R2 are around 40% and 44%, respectively, for the aggregate investment-gradeand high-yield indexes. The highest R2R is 49% for the IG five- to seven-year index.Differently from the US specification, not all the selected variables, which were highlysignificant in the specific estimates, maintain their significance when jointly includedin the regression. Interest rate variables, such as the five-year level and the spread withthe US Treasury bond, are seldom significant. Furthermore, the FTSE stock return issignificant for the aggregate HY index54 but not for the aggregate IG index.55 Theimplicit volatility is also not significant, with the exception of the HY BB index, wherea 1% increase in the variable generates a 2.5 bps increase in the spreads. The SMBfactor is strongly significant for some indexes and weakly significant for others56 TheUS leading indicator, a proxy of the US business cycle’s impact on the UK market, hasstrong influence on industrials and, within industrials, on capital goods. Its impact alsodecreases as credit ratings decrease. Changes in the swap spreads are significant for IGindexes, but not for HY indexes. Their impact is quite stable across different ratings andmacroindustries.57

The UK regressors explain a good part of credit spread changes, but to a lesser degreethan in the USA The main finding in this area is that the US business cycle, proxied bythe Leading indicator, affects UK credit spreads.

4.3. Empirical findings on the final selected specification for the Eurozone

For the Eurozone we choose the following specification:

DCSt = α + β1�(5y)t + β2�(sp5y)t + β3(eustox)t + β4�(dax iv)t

+ β5(smb)t + β6�(lead us)t + β7�(swsp10)t + εt

(1.3)

where 5y is the yield on the five-year German government bond, sp 5y is the spreadbetween the five-year US and German government bonds, eustox is the return on the

53 The 10-year replaces the five-year swap spread in the UK area for lack of data.54 A 10% positive stock return lowers the high-yield credit spread by 60 bps.55 The CCC-C index makes an exception with nonsignificant regressors (except for theLeading Indicator) and a very low R-square. Consider though that the index is made ofonly four bonds on average and is therefore highly illiquid and hardly representative. As acomparison, the corresponding US index is composed of 208 bonds.56 The stronger impact is on the B index, where a 1% increase in the variable generates a 6.5bps increase in the spreads.57 Roughly a 0.5 bp increase in the spread for a positive change of 1 bp.



Eurostoxx index, dax iv is the implicit volatility of the options on the DAX, smb isthe Fama-French Small-Minus-Big factor, lead us is the Leading Indicator of the USConference Board, and swsp5 is the spread between the swap rate and the five-yearGerman government bond yield.

Empirical findings are in Table 1C. R2 varies according to the selected dependentvariable, ranging from 50.62% for the aggregate IG index to 40.64% for the aggregateHY index and reaching its peak (61.76%) for the HY BB index. The change ingovernment bond yields is significant only in a few cases, but the spread with USTreasury bonds has higher explanatory power for IG indexes.58 Stock market variablesare significant for HY indexes but not for IG indexes.59

The US Conference Board Leading Indicator (lead us) has significant effects oninvestment-grade indexes.60 For example, the swap spread is significant for IG corporateindexes up to the A rating. The impact is almost constant along the yield and ratingcurves and across macroindustries.

Results from EMU regression also show that our variables do a good job of explainingcredit-spread variability. The significance of the estimates is closer to the US results,in this sense, and all the main determinants are confirmed. Moreover, it is worth notingthe influence that the USA. economy has on the Eurozone, proxied by the interest ratespread between the two economic areas and the US Leading indicator.

4.4. Comparisons of findings across the three markets and with the recent literature

For a more direct comparison of results across macroareas, we estimate again the model(Table 2) for the same time interval starting in January 1999 (i.e., the first date forwhich information on Eurozone markets is available). Limits in this comparison are thatindexes in different macroareas do not have the same degree of representativeness, andregressors are obviously not perfectly correlated (i.e., stock indexes may have differentscope and coverage).

A comparative inspection of estimates shows that goodness of fit is higher in the USA(and in the Eurozone) than in the UK. The difference in representativeness61 betweenthe two indexes may affect the result.

58 Its highest impact is on industrials, where a rise of the US-German spread of 10 bpsgenerates a 1.5 bps increase in credit spreads. Among individual industries, cyclical industriesare the most sensitive to this variable.59 A 10% positive stock return on the Eurostoxx index generates a credit spread reductionof around 6 bps for the BB index and of 16 bps for the CCC-C index. A 1% increase inthe implicit volatility on the DAX (daxiv) widens credit spreads by 3 bps for the BB indexand by around 10 bps for the CCC-C index. On the other hand, a positive 1% change of theSmall-Minus-Big factor reduces credit spreads on the HY index by around 11 bps.60 A one-point increase in the indicator decreases the quality of credit rating, ranging from1 bp for AAA to around 20 bps for BBB. The impact on macroindustries is higher onindustrials (around 10 bps) and, as expected, lower on financials (2.5 bps) and utilities(2 bps). The telecommunications and technology & electronics industries are most sensitiveto this variable (respectively, 17 and 16 bps).61 Index representativeness is highly heterogeneous across different markets. The IG indexincludes 3,789; 1,159; and 478 bonds respectively in the USA, Eurozone, and UK. Theequivalent numbers for the HY index are 1,270; 94; and 31.



Tabl

e2

The

dete

rmin

ants

ofop

tion

adju

sted

cred

itsp

read

chan

ges

for

US

,UK

,and

Eur

oar

eabo

ndin

dexe

s

Thi

sta

ble

repo

rts

find

ings

for

the

US

,U

Kan

dE

uro

area

mar

kets

for

a(r

estr

icte

d)sa

mpl

epe

riod

rang

ing

from

1/19

99to

11/2

003.

The

spec

ific

atio

nsan

dth

eva

riab

les

are

the

sam

eus

edin

Pane

lA-P

anel

Cof

Tabl

e1.

Stoc

kst

ands

for

the

rele

vant

equi

tyin

dex

retu

rn,i

vfo

rth

ere

leva

nteq

uity

inde

xim

plic

itvo

lati

lity

,sw

spfo

rth

esp

read

betw

een

the

swap

rate

and

5-ye

ars

(10

year

s)go

vern

men

tbo

ndyi

eld

for

US

and

Eur

oar

ea(U

K).

Inte

rcep

tsar

eno

tsh

own.

5ysp

5yst

ock

ivsm

ble

adsw

sphy

bhy

st(

5y)

t(sp

5y)

t(st

ock)

t(iv

)t(

smb)

t(le

ad)

t(sw

sp)

t(hy

b)t(

hys)

R2

US

Cor

pora

te−0

.1−0

.37

0.53

−1.0

1−4

.55

0.4

−17.

521

.2−2

.39

−2.0

62.

23−2

.48

−1.5

14.

1−2

.51

3.35

56.6

4%S

terl

ing

Cor

pora

te0.

02−0

.01

−0.3

70.

01−0

.91

−2.7

30.

440.

83−0

.4−1

.24

0.03

−2.6

2−1

.36

3.23

28.1

8%E

MU

Cor

pora

te−0

.03

−0.1

−0.2

30.

17−0

.12

−5.3

50.

37−1

.05

−2.4

6−0

.91

1.37

−0.2

3−2

.58

2.67

50.6

2%

US

Cor

pA

AA

−0.0

7−0

.18

0.18

−0.0

20.

780.

22−8

.06

7.88

−2.4

8−1

.27

1.03

−0.1

0.33

3.68

−2.6

72.

8444

.85%

Ste

rlin

gC

orp

AA

A0.

030.

020.

090.

05−0

.6−0

.82

0.39

0.93

0.86

0.37

0.3

−1.9

5−0

.55

4.57

19.7

9%E

MU

Cor

pA

AA

−0.0

2−0

.01

−0.0

70

−0.2

3−1

.02

0.24

−1.0

9−0

.96

−1.4

7−0

.3−1

.18

−1.6

3.64

33.8

7%

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The effect of a change in the level of interest rates (and spread against the USA for theUK and Eurozone area) of 10 bps generates a change in credit spreads of around 1 bp forIG indexes and around 7–8 bps for high-yield US and Eurozone indexes. The effect isnot statistically significant for the UK. An interesting and comparable result, however, isthe effects of stock returns. A 10% change in the stock index is significant on IG indexesonly in the USA, where it reduces spreads by around 4 bps.62 The interesting point isthat the effect of stock returns on HY indexes is significant in any of the three areas,but the magnitude is widely diversified (22 bps in the USA, 45 bps in the UK, and 73bps in the Eurozone). We argue that this finding cannot be solely explained in terms ofheterogeneity in variables measured across different markets, because the comparisonsof other effects (such as the implicit volatility on stock index options on HY indexes)are substantially equivalent in the three areas. Hence, differences in bankruptcy codesmay matter.

In this respect, the higher OAS reaction in the Eurozone vis-a-vis the UK appearsfully consistent with recent findings of Davydenko and Franks (2008), who comparebankruptcy codes in the UK, Germany, and France. The authors find that creditorrights and recovery rates in bankruptcy are highest in the UK, lowest in France, andintermediate in Germany. The findings depend on, among other things, the fact thatreorganisation plans do not require creditors’ approval in France, and state and employeeclaims come before those of creditors. The ranking of the three countries is consistentwith La Porta et al.’s (2002) scores for creditors’ rights and not in contrast with ourfindings.

Furthermore, the fact that the magnitude of the stock returns on the US HY indexis even smaller than in the UK is in turn consistent with the fact that ‘reorganisationsystems like Chapter 11 may act as a safe haven for distressed firms during adversemacroeconomic conditions, enabling some of them to recover and perhaps be acquired,thus attenuating the impact of macroeconomic instability on bankruptcy hazard’(Bhattacharjee et al., 2004). To sum up, financial distress is less likely to lead tobankruptcy in the USA, but when it does occur, UK legislation backs bondholders’interests more German or French legislation does.

A 1% increase in implicit volatility enlarges the credit spreads for BB-rated indexesby 2.7, 2.5, and 3 basis points in the USA, UK, and Eurozone areas, respectively.63

Cremers et al. (2008) use implied volatility levels and the volatility skew, starting withindividual stock option data, to check the importance of volatility and jump risk oncorporate spreads. In a comparison with CGM (2001), they find that aggregate (stockindex) implied volatility and skew has less economic impact than individual data. Ourresults confirm that general stock market volatility has a limited (but still significant)effect on credit spreads. On the other hand, jump risk (i.e., the risk of jumping to defaultor near-default), measured by volatility skew, is a variable that by definition is morelinked to an individual issuer than to the general market. It is not so unreasonable,therefore, that our estimates did not find a significant relationship between volatilityskew and index credit spreads.

62 UK and Eurozone estimates have coefficients of the same magnitude, but the t-stats arenot significant.63 Implicit volatility is significant also for IG US indexes, where a 1% increase widensspreads by 0.5 bps.



A 1% change in the SMB factor reduces the BBB index credit spread by 1.7 bps in theUSA and 1.3 in the UK64 The effect of the US Leading Indicator (the same variable forall markets) is also comparable in all areas, generating increasing reductions in creditspreads along the credit curve of IG indexes. This confirms the sensitivity of UK andEurozone financial markets to the US business cycle.

Swap spreads (on the five-year maturity for the USA and Eurozone, and on the 10-year maturity for the UK)65 have a comparable effect in the three areas: a 10 bps increasein the swap spread widens credit spreads by around 4 bps in the three markets.

Comparing our results with those in the recent literature, we can highlight some morepoints. Boss and Scheicher (2002) use two Euro indexes, industrial and financial, withthree years of weekly data66 and swap data. They find that interest rate variables primarilyexplain spread changes, and, to a lesser extent, stock market variables. Their analysisdoes not distinguish between IG and HY, or between sectors and ratings. Moreover, theyhave a very limited set of explanatory variables (for example, they omit institutionalinvestor data and implied volatility data). This paucity of data (especially the lack ofHY data) may be one reason stock market variables are not as strongly significant inthe Eurozone regressions.67

Ericsson et al. (2009), using CDS premia, find that leverage, volatility, and interestrates are important determinants of CDS premia but explain only 23% of the variabilityin spread changes. Their nonsynchronous database may contribute to the low correlation.

Avramov et al. (2007) analyse US corporate bonds, using aggregate and firm-levelvariables as regressors. Their data set include IG, HY, and unrated firms, classifiedby spreads. They find that individual volatility and price-to-book ratio play a role inexplaining credit spreads on corporate bonds, especially for low-rated firms; moreover,Fed monetary policy is significant only for high-grade bonds. Their analysis, however,is limited to US bonds, does not break out by sector, and, importantly, does not consideroptions embedded in the bonds.68 Our analysis is, instead, based on indexes. Thisapproach on one hand excludes some variables (for instance, firm-level variables suchstock or volatility), causing the expected explained variation to decrease; on the otherhand, however, the approach helps disentangle some important relationships regarding‘clusters’ of credit ratings and sectors.

Using credit indexes has another important consequence: with monthly rebalancing,every index has a ‘constant quality’ in terms of rating and maturity. In this way, we canlimit the ‘roll down’ effect for the maturity (credit spreads tend to shrink as maturity

64 It is significant for the HY Eurozone index, with a coefficient of 11 bps.65 The 10-year replaces the five-year swap spread in the UK area due to lack of data.66 Notably, using weekly data they introduce in this way a change-of-month bias (compositionof indexes changes at the end of every month).67 They do not analyse any direct relationship between European and US markets, but theyonly statically compare their results with an estimate on a US industrial credit index and donot determine if US data can be a significant factor for Euro markets.68 Our dataset is based on option-adjusted spreads that account for options (typically calloptions) embedded in the bonds. Option value, which is the issuer’s right but not obligationto call the bonds, changes over time, both when monetary policy changes (via interestrate levels) and when the issuer’s creditworthiness improves. Credit spreads shrink as aconsequence. Not taking the options into account can distort results. Moreover, classifyingunrated bonds by spread, especially when there are embedded options, can be much moreproblematic for the analysis.



approaches) and rating migration for the dependent variables; both these effects couldintroduce some bias in the analysis. Moreover, our dataset includes some variables, suchas institutional investor trading activity, that play a role in explaining corporate spreads.

Finally, the analysis outlines a result (completely) new to the empirical literature oncorporate spreads: the presence of common determinants of credit spread changes inthe USA and the Eurozone. Regarding interest rates, European medium- and long-termyields tend to covariate with US bonds; thus, by using the spread between the twoareas as a regressor, we insulate the effect in the analysis. Even if ECB did not changerates in this period, interest-rate term structure is a function, among other things, ofexpected growth and inflation, and the US business cycle seems to have a great impacton the Eurozone. The results regarding US leading indicators, which exert an importantinfluence on European credit spreads, confirm this.

5. Robustness check

To check robustness, we perform Chow tests to control for structural breaks, reestimatethe model with higher frequency data, include lagged variables, and conduct principal-component analysis.

We first divide the sample in each of the three areas into two subperiods69 and performa Chow test to check the model’s structural stability.70 The absence of structural breaksis rejected at the 5% significance level for six indexes in the US estimates71 (US Corp.AAA 15+ Yrs, US Industrial Corp. AAA, US HY Containers, US HY Restaurants,US HY Textiles/Apparel, HY US B 10+ Yrs), for one index in the Eurozone estimates(European Currency High-Yield BB-Rated), and for no indexes in the UK estimates.

Given the high number of indexes considered,72 the number of cases in which the nullis rejected is extremely low: less than 3% in the USA, 1% for the Eurozone, and nil forthe UK. This emphasises the substantial stability of parameters in our estimates.

We perform the second robustness check by repeating our estimate on higher-frequency series (weekly instead of monthly data). We calculate weekly changes usingWednesday data in order to avoid end-of-week distortions generated by low volumes orinsufficient liquidity.73

The choice of using higher frequency data has some costs. The first is that, in a limitednumber of cases, an index with the same constituents does not measure the change. Thisis the case when two adjoining Wednesdays fall in two different months.

The other problem is the loss of all those regressors that cannot be measured onweekly basis. We therefore cannot use the Conference Board indicator, for example, orthe Fama and French risk factor, volumes of HY sales, or purchases from institutionalinvestors. For this reason, we reintroduce other regressors not considered in our finalestimates. These are the slope of the yield curve and interest rate volatility. Furthermore,

69 Subperiod estimates are omitted for space and are available from the authors upon request.70 We use sample halves as breakpoints in each geographical market. Consequently, the lastmonth of the first subsample is May 2000 for the USA, November 2000 for the UK, andJune 2000 for the Eurozone.71 Huang and Kong (2003) reject the null of no structural break for two (AA-AAA 15+ Yrs)out of nine considered indexes.72 207 USA, 125 UK, and 118 EU indexes.73 When Wednesday is a holiday, we measure the change using Thursday data.



we do not have implicit volatility of options on the Russell 2000, on the Bund future,and on the Gilt. We replace them respectively with the implicit volatility of the optionson the Standard & Poor’s 100, with swap options on 10-year Euro, and with sterling.

Estimated results74 on US data show that R2 is smaller and some t-stats less significant(with respect to monthly frequency estimates) as expected given the loss of importantregressors75 and, presumably, the use of OAS changes across the end-of-month indexrebalancing. Nonetheless, our R2’s range from 24% of the total IG index to 44% of thetotal HY index. Interest rate levels, stock returns, swap spreads, and implicit volatilityon rates for HY bonds are all significant, and their coefficients are of magnitudescomparable with those obtained in monthly estimates,76 confirming the robustness ofour estimates to changes in frequency.

Results for UK estimates77 show R2 ranging from 20% to 29% for the overall IGand HY indexes, respectively. Interest rates, stock returns, implicit volatility, and swapspreads are statistically significant. Their coefficient magnitude is comparable with thatof monthly data, confirming the robustness of monthly data results.

Finally, the results78 for the Eurozone show that our R2’s range from 0.41 on theIG index to 0.19 on the HY index. Interest rate level and spread, stock returns, stockvolatility, and swap spread are statistically significant and have coefficients that arecomparable with those from our monthly estimates.

As mentioned, we also added lagged variables for the regressors and found the resultsrobust to their inclusion; coefficients are low, and moreover they are not statisticallysignificant. The fact that data are mainly constructed as variations and have monthlyfrequency can explain this. Given that financial markets tend to react quickly and adjust

74 The final specification of the determinant of OAS on a weekly basis for the USA usesthe five-year Treasury yield, the spread between the 10- and two-year Treasury yield, theimplicit volatility of 10-year Treasury bond futures, the return on the Russell 2000, theimplicit volatility of the Standard & Poor’s 100, and the spread between the swap rate andthe five-year government bond yield. Results are available upon request.75 These are sales and purchases of HY bonds for institutional investors, the Leading indicator,and implicit volatility on Russell 2000, which was more significant than the S&P 100’simplicit volatility in monthly estimates. This last evidence links to the fact that the Russell2000 represents more closely the investment universe in corporate bonds, both IG and HY,given that it comprehends small- and medium-size companies. In fact, the Russell 2000Index is composed of the smallest 2,000 companies in the Russell 3,000 (general) index.76 As an example, estimates of the impact on the overall IG US index of interest rate levels,stock return, and swap spread exhibit coefficients respectively of −0.10, −0.43, and 0.33 inmonthly estimates and of −0.10, −0.32, and 0.29 in weekly estimates.77 The specification of the determinant of OASs in the UK market on weekly data usesthe five-year UK Treasury yield, the spread between the five-year US and UK governmentbond, the spread between 10- and two-year UK Treasury yield, the implicit volatility of swapoptions on the 10-year rate, the return of the FTSE Small Cap index, the implicit volatilityof the FTSE 100, and the spread between the swap rate and the 10-year government bondyield. Results are available upon request.78 The specification of the determinant of OASs in the Eurozone market with weekly datauses the five-year Bund, the spread between the five-year US and German governmentbond, the spread between 10-year and two-year German bonds, the implicit volatility ofswap options on the 10-year rate, the return of the Eurostoxx index, the implicit volatilityof options on the DAX index, and the spread between the swap rate and the yield on thefive-year government bond. Results are available upon request.



to new information, this could be evidence of market efficiency, and it seems quiteplausible.79

Finally, in order to compare the parsimonious specifications in the estimation withall the available variables in our database, we perform a principal-component analysis(PCA) on the estimation errors of the regressions. Our aim is to determine whether thetime-series regression residuals in the covariance matrix have an unidentified commonfactor that explains a significant portion of the variation of the errors. We cannot usethe regression errors of all the indexes, given that we would have the same bond in moreindexes (say, in rating A index and financial index for a bond of these characteristics).Along the lines of Collin-Dufresne et al. (2001), we separate different dimensions toorder the indexes for the analysis and avoid double-counting constituent bonds. For thethree areas, we take indexes each distinct by rating and maturity.80 In this way, we have24 indexes available for the USA and UK, and 19 indexes for the Eurozone.81

The results, reported in Table 3A, show that for the three areas the first componentaccounts for 40%–43% of the unexplained variance; between 13% and 16% of thevariation is instead due to the second component. The first principal component hasdiverse weights in all the three analyses, and negative weights in the UK and the Eurozonealso appear. Collin-Dufresne et al. (2001) report a first principal component explaining75% of the variation in their regression errors, with similar weights in the eigenvector,resulting in an equal-weighted portfolio along bond groups; they conclude that this isevidence of a large systematic factor not captured by the regressors. In contrast, thisanalysis shows that in our case the first component explains a much lower variationcompared to Collin-Dufresne et al. (2001), and has diverse weights in the eigenvectors.The PCA seems therefore to support the idea that no clear, systematic component existsin the regression residuals.

79 The use of all contemporaneous variables could leave the door open to the eventual problemof endogeneity. None of the empirical works in this area tackles this issue, and empiricaldeterminants of credit spreads, using either levels or variations, are used at the same timeintervals as bonds. Given the kind of analysis and the huge database under investigation,in fact, the use of techniques such as systems of equations or an instrumental variableapproach are quite hard to implement. The relative bigger dimensions of risk-free marketsand equity markets compared to corporate bond markets could be an argument in which onecould suppose a limited (if any) problem of this type. Moreover, the use of weekly data canalso be a simple robustness test in this direction, given that eventual endogeneity problemsexacerbated by data frequency should be at least less influenced in this case, and sign andsignificance of coefficients are confirmed in weekly estimates.80 Collin-Dufresne et al. (2001), in order to do a principal-component analysis usingcorporate bonds, construct 15 different bins of regression residuals, distinct by rating andmaturity or by leverage and maturity; afterward, they take the average residual for each binand extract the principal components of the covariance matrix. Ericsson et al. (2004) usePCA on regression residuals of both levels and differences regressions on CDS, analysing thecorrelation matrix of the errors. Given the particular structure of their data, they concentratefirst on the 15 companies with the highest numbers of observations and then order the dataalong leverage in five bins.81 The US and UK indexes are separated into six maturity groups (1-3, 3-5, 5-7, 7-10, 10-15,15+) and four ratings groups (AAA, AA, A, BBB), for a total of 24 indexes. In the Eurozone,there are instead five maturity groups (1-3, 3-5, 5-7, 7-10, 10+), and the index BBB, 10+is not available; therefore we have 19 indexes.


Option-Adjusted Delta Credit Spreads 213Ta

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To double-check our results, we undertake a principal-component analysis on deltacredit spreads to evaluate by comparison how much of the variation the regressorsexplain. The results, reported in Table 3B, show that the first principal componentaccounts for 73–75% of the variation in all the areas, whereas the second componentexplains between 9% and 15%. Moreover, the weights of the first eigenvectors are sim-ilar, resulting in an equally weighted portfolio and no negative weights. By comparisonwith the PCA conducted on the residuals, we can see that the regressors used in theanalysis capture a large part of the variation.

The analysis seems to show that the significance of the determinants of delta creditspreads is quite robust to changes in data frequency, sample period, and inclusion oflagged variables. Moreover, principal-component analysis shows no evidence of clearsystematic factors left in the residuals but does show that regressors capture a large partof the variation.

6. Conclusions

We analyse the determinants of the variation in option-adjusted credit spreads (OASs)with a database covering corporate bond indexes at very detailed levels in the USA,UK, and the Eurozone. We also use new variables (institutional investor flows, monthlydowngrades, and default frequencies). Our results explain a higher portion of credit-spread variability82 than the recent literature’s empirical findings, which focus on theUS market.83

The variables that are more significant are the same across the three markets.84 Thesignificance of one variable that never considered in the literature (purchases and salesof HY from institutional investors) seems to confirm that institutional investors bringthe market information that is not captured in standard regressors such as stock marketperformance, implicit volatility, and others considered in the estimates. This signals apotential variation of risk perception or a proxy of liquidity risk – a variable close tosupply/demand shocks (Collin-Dufresne et al., 2001). This result confirms in some waythe importance of omitted risk factors not considered in the standard structural modelsof credit risk. A relevant cross-market result is the US leading indicator’s effect on UKand Eurozone OAS and the spread between US Treasury and Gilt or Bund, signalling thesensitivity of the two European corporate bond markets to the US business cycle. Ourresults confirm, as expected, that HY indexes and cyclical industries (such as automotive,consumer cyclicals, services cyclicals, and high tech) are much more sensitive to stockmarket and business cycle variables than, respectively, IG indexes and noncyclical-industry indexes. Moreover, comparability across different markets shows that DCSs

82 Adjusted R squared up to 61% for the USA and for the Eurozone, but less than 50% forthe UK.83 For example, Collin-Dufresne et al. (2001) explain between 20% and 30% of credit-spreadvariability of US industrial bonds between July 1988 and December 1997, and up to 40%when they use lagged variables in levels. Elton et al. (2001) explain up to 30% of the spreadunexplained by default premium and tax distortions with a three-factor Fama and French(1995) model for industrial bonds, concluding that a large part of the risk is systematic,exactly as in the stock market.84 They are changes in interest rates, changes in the swap spread, stock market returns,implicit volatility of stock index, leading indicators of the business cycle, and purchases andsales of HY by institutional investors in the US market.



determinants have effects quite similar in magnitude in the three areas. A relevantexception is the largely higher significance of stock returns on HY bonds in the Eurozonethan in the US area. We suggest that differences in bankruptcy regulation across differentmarkets may affect this result. Finally, the lack of significance of Moody’s monthlydefault rates and downgrades suggests that these data do not add, on average, significantinformation to that already incorporated in the credit spreads.85

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option-adjusted delta credit spreads: a cross-country analysis

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