pension funds in mexico and chile: a risk-reward hans ... · pension funds in mexico and chile: a...

Hans SchlechterBernardo K. PagnoncelliArturo Cifuentes

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Pension Funds in Mexico and Chile: A Risk-Reward Comparison

Documento de Trabajo Nº 55

Pension Funds in Mexico and Chile: A Risk-Reward Comparison

Hans Schlechter1, Bernardo K. Pagnoncelli

⇤2, and Arturo Cifuentes

3

1CLAPES UC, Santiago, CHILE

2Universidad Adolfo Ibanez, Santiago, CHILE

3CLAPES UC, Santiago, CHILE, and, Columbia University, New York, USA

March 2019

Abstract

Mexico and Chile have Defined Contributions (DC) pension systems. In both cases a�liates areo↵ered several investment funds with, allegedly, di↵erent risk-return profiles. Analyzing actual returndata for the April 2008-March 2018 period, and using a number of risk—and return—related metrics,we reach quite di↵erent conclusions in relation to such funds. In the case of Mexico, the funds deliveredreturns according to their intended risk profile, and they are consistently ranked correctly in terms ofabsolute risk, risk-adjusted returns, and cumulative returns. Chilean funds, on the other hand, exhibitederratic risk-return patterns, with the most conservative fund outperforming the riskiest fund in terms ofcumulative returns. Overall our analysis is an indictment on the idea of using asset allocation limits tocontrol portfolio risk (Chile), and supports the view that risk is much better controlled using an overallportfolio-level risk metric (Mexico). Since most pension funds still rely heavily on asset-class limits tomanage risk, our results should serve as a serious warning against the danger of relying on this practice.

Keywords— Pension Funds; Defined Contribution; Rank-order Metrics

JEL classification— H55;G17;G11

1 Introduction

Mexico and Chile can be considered, arguably and with some caveats, two successful emerging market stories inLatin America. Both countries started to implement market-oriented reforms in the 80s, based loosely on whatlater became known as the Washington consensus. In short, they carried out several privatizations of governmententerprises, adopted a more flexible position on international trade and foreign investments, embraced fiscal disciplinealong with a floating exchange rate, and pushed for deregulation on many fronts, among other things. Perhapsmore important, both countries enjoy the benefits of having independent central banks run by highly capable, andinternationally respected, professionals. Additionally, Mexico and Chile are the only Latin countries that belong tothe Organization for Economic Cooperation and Development (OECD). Mexico was accepted in 1994, Chile in 2010.And today, their GDPs per capita (at PPP) are among the highest in Latin America—approximately $25, 900 in thecase of Chile, and $20, 600 in the case of Mexico (International Monetary Fund, 2018).

Within this context, both countries have also innovated. Chile introduced in 1980 a radical modification to itssocial security system; it was based on the adoption of a privately-managed defined contribution (DC) scheme, inwhich, essentially, the workers are directly responsible for their retirement (Edwards, 1998). The Chilean concept alsoserved as a blueprint for pension-related reforms that were carried out by many emerging economies e.g. Mexico, ElSalvador, Peru, Poland, Bulgaria, Costa Rica, Hungary and Lithuania. Mexico, on the other hand, which can boastof having the most developed and biggest fixed income market in Latin America, pioneered in the early 2000 a setof very original collective-action clauses that were adopted by many emerging countries in relation to the issuance ofsovereign debt (Gelpern, 2003).

⇤This work was supported by Fondecyt project number 1170178.

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The Chilean pension system started its transformation in 1980 when the government introduced a mandatory DCscheme; and it entered what we can describe as its mature phase in 2002, when the regulator implemented five di↵erentinvestment funds (A, B, C, D and E). The idea behind this modification was to o↵er the a�liates di↵erent risk-returnoptions. The A fund (the riskiest fund) is supposed to appeal to younger workers, and ideally, deliver higher returns.The E fund, the most conservative, is aimed at meeting the needs of older workers, close to the retirement age. Broadlyspeaking, the a�liates are expected to move gradually from the A to E fund as they approach their retirement age,in what is known as the life-cycle investment strategy (Viceira, 2008). There are, however, some restrictions basedon the age of the worker, as well as a “default” strategy for those workers who do not explicitly make a choice. Thefunds are managed by private institutions known as AFPs (based on their Spanish acronym), which are exclusivelydedicated to manage pension funds (thus, cannot engage in any other activity), and are supervised by a dedicatedregulator known as Superintendencia de Pensiones (SP). Chilean workers are mandated to contribute 10% of theirsalaries (this obligation stops when the salary reaches a limit of roughly $ 3,200 per month as of 2019). The AFPsmanage approximately US$ 210 billion, representing 72% of GDP (OECD, 2018). A more comprehensive descriptionof the Chilean pension system can be found in Superintendencia de Pensiones de Chile (2003, Chapter 4), InternationalCenter for Pension Management (2018), OECD (2017a), Fernandez (2013), and Edwards (1998).

Mexico started the transformation of its pension system a bit later, in 1997, when it also introduced a DC schemeinspired in large measure by the Chilean architecture. In Mexico the funds are managed by institutions known asAFORES (again, based on their Spanish acronym). Initially, like their Chilean counterparties, they o↵ered only oneinvestment choice. However, the system was progressively modified and this evolution culminated in 2008 with theintroduction of five funds (known as SIEFORES 1 through 5, or more commonly SB1,. . . , SB5), which are analogousto the five Chilean funds, except that the order is reversed: the SB1 fund is the most conservative (for workers olderthan 60), and the SB5 fund the riskiest (for workers younger than 27). Later, in 2013, the system was reorganizedaround four SBs (the SB4 fund and the SB5 fund were collapsed in one fund). Unlike the case of Chile, Mexicanworkers contribute only 6.5% of their monthly salaries, and not all workers are a�liated with the SAR (the name bywhich the previously described DC system is known). All private-sector employees who joined the workforce after July1997, as well as most public sector workers who joined after April 2007, are enrolled in the SAR system. However,there are still many workers covered by other state and federal programs, or some special systems available for certainpublic and state university employees. In fact, this is probably the reason (in addition to the 6.5% contributioncompared to the 10% in Chile) that the AFORES manage only US$ 200 billion (approximately 15% of GDP), a figurecomparatively lower than their Chilean counterparties. AFORES, as the AFPs in Chile, are regulated by a dedicatedsupervisor known as CONSAR. A more complete description of the Mexican pension system can be found in OECD(2016a), OECD (2016b), Comision Nacional del Sistema de Ahorro para el Retiro (2017a) and Alonso, Hoyo, andTuesta (2015).

The Mexican and Chilean pension systems, partly perhaps due to the increasing global shift from defined benefits(DB) pension schemes to DC schemes, have received a fair amount of attention, mostly from the public policyviewpoint. The chief concerns are related to how to improve coverage, the fees associated with managing the fundsand whether there is enough competition in the sector. Moreover, there is a permanent debate on what shouldthe contribution rate needed to achieve an acceptable replacement rate, as well as discussions on the appropriateretirement age and whether di↵erent mortality tables should be applied to men and women (see Comision Nacionaldel Sistema de Ahorro para el Retiro (2017b), Alonso et al. (2015), Willmore (2014), Aguila, Mejia, Perez-Arce, andRivera (2013), Comision Asesora Presidencial sobre el Sistema de Pensiones (2015), Krasnokutskaya, Li, and Todd(2018) and Lopez Garcıa and Otero (2017) for more details). Fuentes, Garcıa-Herrero, and Escriva (2010) provide agood summary of many pending challenges from the public policy viewpoint.

Analysis of these pension systems from a financial vantage point is a subject that has received much less attention.We cite a few exceptions. Fernandez (2013) concluded that the Chilean asset managers exhibited significant herdbehavior and their returns, once adjusted for risk, were not better than those of index-based alternatives. Pagnoncelli,Cifuentes, and Denis (2017) introduced a hybrid (active-passive) investment strategy for pension funds and testedit with the Chilean system. The authors found that in most cases the managers had not done better than passivealternatives, and they hinted that some of the investment constraints imposed by the regulator had had a negativeimpact on returns. In relation to the Mexican system, Santillan-Salgado, Martınez-Preece, and Lopez-Herrera (2016)looked at all the funds returns and concluded that their volatilities showed significant variation over time and thatthe returns showed autocorrelation (memory) e↵ects, a topic they considered crucial for risk management purposes.In De la Torre, Galeana, and Aguilasocho (2018) the authors suggest a benchmark that could be useful to assess theperformance of such funds.

With that as background, we stress that the ultimate goal of the regulators when they created di↵erent investmentfunds (SB1,. . . , SB4 in Mexico; A,. . . , E in Chile) was to o↵er options with distinguishable risk-return profiles. To

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put it di↵erently, the idea was that the A and SB4 funds should deliver, in the long-term (granted, a somewhatsubjective term), higher returns than the E and SB1 funds, respectively. We believe it is then appropriate—enoughtime has elapsed since they were created—to assess if the returns of these funds have been commensurate with theirintended risk profiles. We think this is important for two reasons, the most obvious is that such analysis has not beenundertaken, and thus, this study would fill an important void. The second consideration is that Mexico and Chilehave adopted a somewhat di↵erent approach to manage the risk of their pension funds (a topic we discuss in moredetail later), and thus, there are important lessons to be learned from this divergence.

In summary, the purpose of this study is to look at the performance of the Mexican and Chilean pension fundsfrom a portfolio management perspective, based on di↵erent risk-return metrics. And more specifically, to examine ifthe regulators were successful in creating funds with di↵erent risk-return profiles.

2 Investment Regulations in Mexico and Chile

Before we compare the investment regulation of both countries, it is important to put the matter into a broadercontext: managing a pension fund is really a portfolio management problem subject to risk constraints. In thelast seventy years there has been important progress in portfolio and financial risk management. However, generallyspeaking, the pension fund industry has been somewhat slow to adapt. Markowitz’s seminal work established formallythat there was a trade-o↵ between risk and return in portfolio management and proposed to use the standard deviationas a tool to measure risk (Markowitz, 1952; Rubinstein, 2002). Notwithstanding the big conceptual innovation behindthis thought, the shortcomings of the standard deviation (e.g. it penalizes both losses as well as gains) were quicklyrecognized. In due course market practitioners suggested improvements, such as the Value-at-Risk (VaR) (Linsmeier& Pearson, 2000), and more recently the Conditional-Value-at-Risk or CVaR (Rockafellar & Uryasev, 2000, 2002).Moreover, in the context of pensions, it has also been recognized that short-term volatility (referred to as the volatilityof journey in Smith, 2011) is irrelevant, and shortfalls (or downside risk) over long periods is what really matters (QSInvestors Research Group, 2010).

All these improvements have been gradually incorporated into the standard practices of portfolio and risk man-agement. In fact, Solvency II and Basel III—the insurance and banking regulations adopted after the painful lessonsof the subprime (2008) crisis—have incorporated these concepts. Pension fund regulators, however, seems to be stuckon the idea of controlling risk via asset class limits, rather than relying on suitable metrics. In fact, an OECDreport informs that only two OECD countries (Mexico and Denmark), have investment guidelines that incorporatequantitative risk metrics. All other countries (Chile included) still rely on old fashion asset class limits (Antolın etal., 2009). Another report by the World Bank also focuses on the fact that the pension industry has been slow toadopt the practices already embraced by the banking and insurance sector (Brunner, Hinz, & Rocha, 2008). A morerecent report (PricewaterHouseCoopers, 2016) indicates that most pension funds are still subject to guidelines basedon asset allocation limits. Berstein and Chumacero (2003) have gone a bit further and outright suggest that, in thecase of Chile, asset allocation limits have negatively impacted the returns (a suggestion that seems to agree withPagnoncelli et al., 2017). And finally, a 2014 report by Schroders (Schroder Investment Management, 2014), o↵ereda rather pessimistic view of current practices, stating that “... the impact of investments risks and returns on DCportfolios are often misunderstood.”

In Mexico and Chile the regulators have imposed limits by asset class, but with one crucial di↵erence: in the caseof Mexico the regulator relies also on a portfolio-level risk-metric, whereas the Chilean system does not employ suchconcept. Hence, these two countries can be considered a natural experiment that can be useful to explore the e↵ectsof di↵erent regulations. In what follows we describe briefly the investment guidelines prevailing in Mexico and Chileduring the 2008-2018 period, the time-frame considered in this study.

2.1 Mexico

The Mexican regulation is based on two key ideas: an upper limit by asset class for each (SB) fund, as well as aVaR-based limit, introduced by the regulator in 2004, at the global portfolio level.

In terms of the asset class limits, the SB4 fund has the highest upper limit for equities (45%), while the SB1 fundhas the lowest (10%). The limits for structured products, REITs and commodities are also higher for the SB4 fundand lower for the SB1 fund. There are no lower-bound limits (except in relation to the SB1 fund, which must keepat least 51% of its holdings invested in inflation-protected securities). In essence, the regulator does not force theSBs to maintain a minimum exposure to any asset class. In terms of the VaR, there is a limit that increases fromthe SB1 fund (0.70%) to the SB4 fund (2.10%). It refers to the maximum amount (expressed as percentage of the

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current portfolio market value) that the portfolio could lose in one day, with a 95% confidence. Its calculation relieson market data from the previous 1,000 trading days.

In order to control the leverage of more volatile instruments, in October 2012, the regulator introduced anadditional metric, the Conditional Value-at-Risk (�CVaR). Each AFORE needs to report, for each fund, the di↵erencein CVaR between the complete portfolio and the portfolio excluding derivatives.

Table 1: Mexican pension regulation: Key points

Item Description

Market and liquidity risks Defines maximum limits for risk parameters of each SB. The VaRranges from 0.70% for the SB1 fund to 2.10% for the SB4 fund,and the liquidity coverage ratio corresponds to 80% of the highlyliquid assets.

Risk by issuer and/orcounterparty

Defines maximum limits for instruments according to theirmedium- and long-term credit ratings, distinguishing between do-mestic and international issuers. It also limits the holdings of asingle issuance for all funds to a 35% of the assets by the samefund manager.

Asset class limits Defines maximum limits by asset classes, allowing more exposureto variable income instruments as the intended risk-profile of thefund increases (from SB1 to SB4).

Conflicts of interest Limits the maximum exposure of the funds to related companies(15% for all funds), as well to companies related to the fund man-ager (5%).

Investment vehicles andderivatives

The regulation allows all funds to use investment vehicles such asmutual funds and derivatives.

Source: Investment Regime of the SIEFORES, CONSAR.

2.2 Chile

In Chile the regulation has two main elements, upper and lower asset-class limits combined with a penalty forunderperforming with respect to its peers. In terms of the asset-class limits, similarly to the Mexican case, they arecommensurate with the intended risk profile of each fund, although the actual figures are di↵erent. The A fund, forexample, can hold up to 80% of its assets in equities, while the limit for the E fund is zero. Unlike the Mexican case,however, the regulator imposes minimums by asset class. Thus, for instance, the D fund must have at least 5% ofits holdings in equities. Additionally, the regulator imposes a “minimum” yield test: the performance of each fund(that is, by fund class) is compared to its peers (industry average) based on the returns of the last 36 months. Amanager whose fund underperforms must compensate the a�liates. To this end, the managers (AFPs) must maintaina special reserve fund equivalent to 1% of the market value of such fund. This regulation has been considered themain cause behind the herd behavior (similar portfolios) that has been detected in relation to the Chilean managers(Chant West, 2014). Table 2 shows a summary of the regulation (a complete summary can be found in Appendix B).

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Table 2: Chilean pension regulation: Key points

Item Description

Minimum yield test Fund managers are responsible for ensuring that the annualizedreal yield (RY) for each fund during the previous 36 months mustsatisfy the following condition. Let X be the real annualized yieldfor all the funds of the same type for the previous 36 months. Andlet Y = X � 1

2 |X|. Then, the A and B funds must satisfy: RYmust be greater or equal than min(X � 4%, Y ). In the case of theC, D and E funds the condition is: RY must be greater or equalthan min(X � 2%, Y ).

Risk by issuer and/orsectors

Defines upper and lower bounds for instruments issued by a singleissuer. There are also di↵erent limits by economic sectors, such asthe financial sector, the external sector, investment vehicles andmutual funds, and state-owned companies. Additionally, there arelimits within certain sectors.

Asset class limits Each fund must comply with a minimum and maximum limit byasset class (maximum 80% and minimum 40% on variable incomefor the A fund to 20% and 5% for the E fund). Additionally, thereis an upper limit for certain types of instruments.

Conflicts of interest Imposes limits for investment in instruments issued by companiesrelated to the fund manager, as well as the obligation to invest re-sources from the manager’s obligatory reserve provision in sharesof the fund that it manages.

Investment vehicles andderivatives

The regulation allows operations involving derivatives for hedgingand investment, as well as investments in mutual funds (with someconstrains) and a limited exposure to alternative assets.

Source: Superintendencia de Pensiones de Chile.

3 The Data

The study is based on the actual—as opposed to nominal—monthly returns of each fund during the period April2008-March 2018. In the case of Mexico, the data were downloaded from the open-data platform of the Mexicangovernment and corrected using the UDI, inflation-adjusted Mexican peso (Comision Nacional del Sistema de Ahorropara el Retiro, 2018; Banco Central de Mexico, 2018). In the case of Chile the data were downloaded from thewebsite of the Chilean regulator and also corrected using the UF, inflation-adjusted Chilean peso (Superintendenciade Pensiones, 2018). Therefore, the returns presented in this work correspond to real returns. In the case of Mexicowe considered the four basic funds (SB1, SB2, SB3 and SB4) managed by the four leading managers (based onassets under management): XXI Banorte, Banamex, Sura and Profuturo GNP. In the Chilean case, we consideredthe five funds (A, B, C, D and E), managed by all six managers: Cuprum, Habitat, Planvital, Provida, Capital andModelo. Tables 3 and 4 present some key statistics regarding the Mexican and Chilean system monthly returns forthe 2008-2018 period.

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Table 3: Mexican funds: monthly returns and descriptive statistics, expressed in percentage (%), April 2008- March 2018

Fund Manager Mean St.Dev. Min Max

SB1

XXI Banorte 0.13 1.33 -4.52 4.25Banamex 0.13 1.37 -3.59 4.98SURA 0.15 1.43 -4.27 4.22Profuturo GNP 0.11 1.45 -4.66 3.03

SB2


SB3


SB4


4 Results

It is important to note that the actual pension of the future retiree is determined—when all is said and done—bythe accumulated balance at the moment of retirement. Hence, what really matters is the cumulative return over theworking life. Average monthly returns, and to some extent, monthly fluctuations of returns, are not as relevant aslong-term returns. Nevertheless, the statistics shown in Tables 3 and 4 suggest some interesting trends. Generallyspeaking, Mexican funds have generated, on average, absolute returns in line with their intended risk profiles (the SB4funds outperforming the SB1 funds). A visual inspection of the Chilean funds, however, suggest a rather di↵erenttrend (or more precisely, lack of trend), as all funds (from A through E) delivered strikingly similar results (a pointwe will revisit later). This is the first sign that Mexican and Chilean funds have behaved in a very di↵erent fashion.

4.1 Cumulative Returns and Risk

Figures 1 (Mexico) and 2 (Chile) compare the 5-year cumulative returns of all funds, for each manager, consideringall possible 5-year (60-month) periods between April 2008 and March 2018. Each point in the graph represents thecumulative return a worker would have obtained for an investment in a specific fund, made 5-year prior to the dateindicated on the horizontal axis, assuming the worker maintained the position during the entire 5-year period. Forexample, the left-most points in the graphs (which correspond to March 2013) reflect the returns associated with theApril 2008-March 2013 time-window.

These two graphs reveal some extraordinary findings. In the Mexican case, regardless of the manager, all funds(SBs) exhibit markedly di↵erent returns; and in all cases the returns are in line with the expected risk profile of eachfund. Take Sura for example (Figure 1), the SB4 fund shows always returns superior to those of the SB3 fund; andthe SB3 fund, in turn, outperforms the SB2 fund, and so on. Thus, the funds are ranked, in terms of their cumulativereturns, for all 5-year periods, in the “correct” order. The same holds for the other three managers. In the Chileancase, it is equally clear that in many cases the funds are ranked in a sequence which is the opposite of what it wasexpected. To be precise, in many instances the A fund cumulative returns are lower than those of the B fund; andthose of the B fund, below the C fund; and so forth. Worse yet, in many periods the A fund return is below the Efund return! This disturbing pattern occurs in 39% of the cases (that is, 24 out of the 61 time-windows considered).

Figure 3a depicts the 5-year cumulative returns for each of the four Mexican funds (SBs), for each fund manager.Again, each point in the graph represents the cumulative return obtained during the 5-year period ending on themonth indicated on the horizontal axis. As in Figures 1 and 2, we considered all possible 60-month periods, movingone month at a time, starting with April 2008. Analogously, Figure 3b shows the cumulative returns for all five funds,for each Chilean manager.

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Table 4: Chilean funds: monthly returns and descriptive statistics, expressed in percentage (%), April 2008- March 2018

Fund Manager Mean St.Dev. Min Max

A

Cuprum 0.33 3.91 -22.44 9.13Habitat 0.36 3.84 -20.46 9.62Planvital 0.34 3.86 -20.46 10.23Provida 0.30 3.88 -21.65 9.53Capital 0.28 3.81 -20.14 9.64Modelo 0.34 2.74 -6.23 6.53

B


C


D


E


The message conveyed by the images is clear: while in the Mexican case there is an obvious performance di↵er-ence by manager, in the case of Chile such di↵erence is almost negligible. All managers exhibit virtually identicalperformance for their respective funds. An exception, in the Mexican case, are the SB1 funds: the discrepancies aremild among all the managers, which is to be expected, as these portfolios are forced to be invested in highly ratedand liquid securities, which o↵er more stable and similar returns across all choices. In short, Figure 3b reinforces theview that Chilean managers are characterized by strong herd behavior, as indicated before, and therefore selectingthe “appropriate” manager is less important than in the Mexican pension market. More precisely, the following cal-culation stresses the point: the A fund average cumulative 5-year return, (considering the 61 time-windows permittedby our data), for each of the Chilean managers are (according to the same order shown in Figure 2 and omittingModelo to avoid distorsions): 29.5%, 30.3%, 28.6%, 26.8%, and 26.4%. The corresponding mean value is 28.3% witha standard deviation equal to 2.1%. By the same token, the corresponding figures for the four Mexican managersand considering the the SB4 fund returns (“equivalent” to the Chilean A fund) are: 21.2%, 27.6%, 32.0%, and 29.9%.And the corresponding mean value is 27.7% with a standard deviation equal to 5.4%. This calculation validates theimpression conveyed by Figure 3b—Chilean managers show a remarkably similar performance. Therefore, in whatfollows, the Chilean results will be presented at the industry (aggregated) level as the di↵erences in performanceamong managers are virtually negligible.

Figures 4a and 4b display another curious trend. These graphs show the average cumulative return, for several

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Figure 1: Mexico: Cumulative returns by asset manager, for each fund type, for all 5-year windows, as afunction of the last month in each 5-year window (March 2013 - March 2018).

holding periods (starting with one-month and up to 60-months), for all fund managers. In Figure 4a, we see thatthe Mexican funds exhibit a clearly distinguishable pattern as the periods gets longer: their returns become moredivergent. In other words, the di↵erence in performance among the four funds, for all managers, grows as the holdingperiod gets longer. That is not the case (Figure 4b) with the Chilean funds. The funds o↵er remarkably similarreturns. In fact, four of the five funds show returns that tend to converge over time. Considering the industry averagein Mexico for a 60-month holding period, the di↵erence in cumulative return between the riskiest funds (the SB4s)and the most conservative funds (the SB1s) is 16.8%, The corresponding di↵erence in the case of Chile (i.e. betweenthe A fund and the E fund) is only a mere 3.7% (for the intermediate funds lie in between). This is rather unsettlingas it questions the benefits of actually o↵ering these five funds.

Figures 5a and 5b show the Sharpe ratios (SRs) for all funds and all managers. (For convenience, the SRs ratioswere calculated assuming that the risk-free rate was zero.) The SR reflects the return adjusted by risk (i.e. normalizedby units of risk). Hence, one could argue that in theory, after adjusting for risk, all funds should exhibit similar SRs.In the Mexican case, broadly speaking, the SB2, SB3 and SB4 funds do show this trend. The exception is Profuturo,which, as of March 2015, shows a noticeable di↵erence among the SRs of these three funds. That said, what it isinteresting to notice, is that notwithstanding the similar values, the SB4 funds tend to show slightly higher SRs thanthe SB2 and SB3 funds. We can say that in general investors in the SB4 funds were paid a small premium for therisk they took. The lowest SRs associated with the SB1 funds are somehow to be expected, due, in part, to themoney market and inflation-linked securities the SB1 funds are forced to maintain. This, clearly, puts a brake on thepotential yield of the SB1 funds.

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Figure 2: Chile: Cumulative returns by asset manager, for each fund, for all 5-year windows, as a functionof the last month in each 5-year window (March 2013 - March 2018).

Figure 5b shows, again, another unsettling outcome in relation to the Chilean funds: investors in most fundssimply took a lot of risk while they were not compensated for it. For instance, the SR for the E fund is on average1.6 times that of the C fund, and about 2.7 times that of the A fund. This suggests that the riskiest funds (A and B)delivered, consistently, risk-adjusted returns that were inferiors, i.e. not in line with their risk profiles.

In terms of looking at the risk of the di↵erent funds, to avoid the shortcomings related to the use of the standarddeviation as a risk metric, we considered two alternative metrics commonly used in risk management and financialengineering: the Value-at-Risk (VaR) and the Conditional Value-at-Risk (CVaR). The VaR is the maximum loss that

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(a) Mexico

(b) Chile

Figure 3: Mexico and Chile: Cumulative returns by fund type, for each manager, for all 5-year windows, asa function of the last month in each 5-year window (March 2013 - March 2018)

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(a) Mexico

(b) Chile

Figure 4: Mexico and Chile: Cumulative returns by fund type, for each manager, for holding periods ofdi↵erent lengths, (March 20013 - March 2018).

a portfolio can su↵er in a specific period of time, estimated with a given (normally very high) level of confidence(Linsmeier & Pearson, 2000). If the VaR is estimated with a confidence 1�↵, it follows that the probability of havinglosses exceeding the VaR is ↵. More formally, the VaR of a random variable X with cumulative distribution function(cdf) F (·) and with a confidence level ↵ 2 [0, 1] is defined as

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(a) Mexico

(b) Chile

Figure 5: Mexico and Chile: Sharpe ratio by asset manager, for each fund type, for all 5-year windows, as afunction of the last month in each 5-year window (March 2013 - March 2018).

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VaR↵[X] := min{t|F (t) � ↵} = min{t|P (X t) � ↵}.

The CVaR, which is an alternative risk metric to the VaR, considers only those losses that exceed the VaR(Rockafellar & Uryasev, 2000). The CVaR of a random variable X with cdf F (·) and with confidence level ↵ 2 [0, 1]is defined as

CVaR↵[X] :=1

1� ↵

Z 1

↵

VaR� [X]d�.

In short, the CVaR (also known as expected shortfall) is the expected value of the losses that exceed the VaR.When X is a discrete random variable with support points z1 < z2 < . . . < zN and associated probabilities p1, . . . , pN ,it follows from (Rockafellar & Uryasev, 2002) that

CVaR↵[X] :=1

1� ↵

" k↵X

k=1

pk � ↵

!zk↵ +

NX

k=k↵+1

pkzk

#,

where ↵ 2 (0, 1) and k↵ is such thatPk↵

k=1pk � ↵ >

Pk↵�1

k=1pk.

In this study we focused on the CVaR of the funds’ returns. Relying solely on the VaR somehow limits the scopeof the analysis, since the VaR does not fully capture the tail end of the distribution associated with lower returns.The CVaR, which focuses on the values exceeding the VaR, does. Additionally, another shortcoming of the VaR isthat it violates the so-called subadditivity condition. The CVaR, a coherent risk metric (Artzner, Delbaen, Eber, &Heath, 1999), does not have this limitation. In the context of pension funds we consider a fund to be riskier if itsCVaR becomes more negative.

Figures 6a and 6b show the CVaR (90% confidence), for the Mexican and Chilean system, (again, using 5-yearshifting windows), for all fund managers. Generally speaking, in all cases the di↵erent funds exhibit risk levels inagreement with the regulators’ intentions. An interesting trend is that in Chile, the risk associated with the D and Efunds, in recent years, seems to converge. The 90%-CVaR in the case of Chilean funds show no major trends and aweak cyclical e↵ect; the expected loss for the A fund settles around -4.6% (conditional on incurring in losses), whileit is around -1.3% for the E fund. As for the Mexican funds, the 90%-CVaRs, present a positive trend with almost nocyclical behavior. However, it should be noted that on average, the CVaR of the SB1 funds is around -2.6%, whichmeans that these funds are riskier—according to this metric—than the Chilean E funds, which show an average CVaRof -1.29%. Additionally, the average CVaR of the SB4 funds is -3.9%, higher than its Chilean-counterparty (the Afund is around -5.12%), meaning that in case of incurring in loses, the SB4 funds are likely to lose less money thanthe Chilean A funds.

4.2 Rank-Order Metrics

Having considered di↵erent criteria to evaluate risk and return, we now examine the rank order imply by these criteria.To this end, we focus on the two most relevant parameters, the CVaR (a more encompassing metric than the VaR)and the 5-year cumulative return. An adequate performance of the system would mean that in terms of risk andreturn the Mexican funds should displayed decreasing risk and return levels when moving from SB4 to SB1. By thesame token, the Chilean funds should also exhibit decreasing risk and returns when moving from A to E. In short, ifnot always, at least most of the time the SB4, SB3, SB2 and SB1 funds should be rank-ordered as 1, 2, 3, 4 (Mexico);and the A, B, C , D and E funds should be ranked as 1, 2, 3, 4, 5 (Chile).

For this purpose, we consider three di↵erent rank-order metrics. Each addresses a di↵erent aspect of the departurefrom the correct (desired) rank order.

(i) Hamming distance. This metric assigns a value of 0 if a fund is in the correct position and 1 otherwise (seeHamming, 1950). Thus, the maximum possible value is 5, corresponding to a situation in which all the fundsare in the “wrong” position. For example, the sequence (1, 2, 3, 4, 5) obviously results in a value equal to zero.However, the sequences (5, 3, 4, 2, 1) and (3, 4, 1, 5, 2) are assigned a value of 5, while (1, 2, 3, 5, 4) wouldget a 2. Let us note that the sequence (5, 4, 3, 2, 1), which in our case represents the worst-case scenario, isassigned a value of 4, explained by the correct position of Fund C. A shortcoming of this metric is that onlyfocusses on whether a fund is in the correct position, but not the distance to its “correct” position.

13

(a) Mexico

(b) Chile

Figure 6: Mexico and Chile: CVaR based on monthly returns by asset manager, for each fund type, for all5-year windows, as a function of the last month in each 5-year window (March 2013 - March 2018).

14

(ii) Spearman footrule. This metric considers the absolute di↵erence between the position in which a fund is,and the position it should have, and adds all five numerical values (see Diaconis & Graham, 1977). In short, itattempts to capture the magnitude of the deviation from the correct rank order as well. For example (3, 4, 1,5, 2) results in a value equal to |3� 1|+ |4� 2|+ |1� 3|+ |5� 4|+ |2� 5| = 10. If the funds are rank-orderedin exactly the reverse sequence, i.e. (5, 4, 3, 2, 1), something we can describe as the worst possible situation,the value is 12, which is indeed the maximum possible value this metric can have.

(iii) Kendall Tau rank distance. This metric counts the number of pairwise discrepancies between the correctrank order and the actual rank order (see Kendall, 1938, 1955). Since we have five funds, the possible pairwisecomparisons are ten (1 with 2, 3, 4, and 5, and then 2 with 3, 4 and 5, and so on), and hence the maximumpossible value is 10. The following example clarifies the calculation. Suppose the funds have been rank-orderedin the following sequence: (3, 4, 1, 2, 5). In this case the Kendall Tau is 4 because the pairs (3, 1), (3, 2), (4,1) and (4, 2) represent pairwise disagreements with respect to the desired sequence (1, 2, 3, 4, 5).

In all three metrics, higher values are associated with higher levels of discrepancy in terms of the rank order. Tofacilitate the comparisons, we normalized all metrics by their maximum value. Thus, a value of 0 reflects a perfectrank order, that is, (1, 2, 3, 4) in the case of Mexico and (1, 2, 3, 4, 5) in the case of Chile; whereas a value of 1indicates the maximum discrepancy with respect to the desired benchmark.

Figures 7a and 7b show the normalized values of the three metrics applied to the CVaR, in the Mexican andChilean cases, as a function of time, again, using 5-year moving windows. Table 5 reports the average values. Fromthe plots, as well as from the tables, we can conclude that the Mexican funds are correctly rank-ordered by riskfor almost all the periods observed (with exception of Profuturo GNP), while the Chilean funds are not. Whenconsidering a 5-year time-window, the average Hamming distance is 3.3% in the case of the Mexican funds and 22.0%for the Chilean funds. The average Spearman distances are 1.8% and 9.0%, respectively; and the average Kendall Taudistances are 1.0% and 5%, again, respectively. A similar tendency is detected when considering 4-year and 6-yeartime-windows. The evidence indicates that the Mexican regulation was more e↵ective than the Chilean regulation interms of producing funds that are, in terms of their risk, rank-ordered correctly.

Figures 8a and 8b show the normalized values of the three metrics applied to the 5-year cumulative returns, in theMexican and Chilean cases, as a function of time, using 5-year moving windows. Table 6 reports the average values.The evidence is compelling. While the Mexican funds maintain very low rank-order metrics (an average Hammingdistance of 2.0%, and Spearman and Kendall Tau distances of 1.0% each for a 5-year time-window), their Chileancounterparties present a Hamming distance of 46%, a Spearman distance of 49%, and a Kendall Tau distance of44%. These figures suggest that the Chilean funds were in disarray for almost half of the time-period considered.The Mexican funds, on the contrary, were ranked correctly for virtually the entire period studied (the exception isProfuturo, which showed some anomalies starting in 2016).

5 Concluding Remarks

Mexico and Chile have structured their pension systems based on a common goal: o↵ering future retirees severalinvestment options, that is, funds, which in theory, should have di↵erent risk-reward profiles. These countries di↵er,however, in the type of investment regulation they enacted to achieve this goal. Mexico structured its investment reg-ulation around two simple concepts: maximum limits by asset classes combined with a portfolio-level risk restriction.Obviously, the restrictions vary according to the intended risk profile of the fund. Chile, on the other hand, optedfor maximum and minimum limits by asset class, with limits dictated by the desired risk profile of each fund. Chiledoes not employ any portfolio-level risk metric to control risk (such as VaR or CVaR), but it does enforce a minimumyield test based on the industry average.

Our analysis, based on a number of risk—and return—related metrics applied to actual fund returns during theApril 2008—March 2018 period is unequivocal: while the Mexican funds exhibited returns very much in line withthe desired risk-reward profile intended for such funds, their Chilean counterparties were characterized by an erraticbehavior, at odds with the regulator desire. To be precise: the Mexican funds exhibited, consistently, cumulativereturns in agreement with their risk profile (highest for the SB4 funds, lowest for the SB1 funds), for all 5-yearwindows tested within our dataset (longer and shorter time windows yielded similar findings). Additionally, theMexican funds, in terms of risk (CVaR), were, again, in almost all cases ranked as expected (the SB4 funds on top,the SB1 funds at the low end). Finally, all Mexican funds (when analyzed by asset manager) exhibited similar Sharperatios (risk-adjusted returns). The exception were the SB1 funds that showed lower SRs due to their high percentageof (mandatory) holdings in highly-rated, but low-yielding, securities.

15

(a) Mexico

(b) Chile

Figure 7: Rank-order performance metrics based on the 90%-CVaR, and a rolling 5-year time-window, March2013-March 2018.

The Chilean funds, however—leaving aside that all managers delivered, for the same type of fund, essentiallyidentical returns as it has been reported in Section 4.1—displayed some disturbing risk-reward patterns. First, 39%of the cumulative 5-year return windows examined resulted in the A fund ranked at the bottom (in terms of returns)while the E fund was on top, and all the other funds (B, C and D), in between, but in a sequence that was exactlythe opposite of what it was intended by the regulator. Second, in terms of risk (CVaR), the Chilean funds were,again, unsatisfactorily ordered in about half of the cases. And third, and perhaps more troubling, the Chilean fundsexhibited consistently Sharpe ratios that were not only notoriously dissimilar among all funds, but incredibly, revealedthat the riskier funds had delivered inferior risk-adjusted returns compared to the most conservative funds. In essence,the more risk Chilean investors took, the less they were compensated for it.

It might be argued that perhaps our findings related to the Chilean funds are an artifact of the period considered(April 2008-March 2008). The reason to consider this period is that Mexico implemented its multi-funds systemonly in 2008. However, extending our analyses to the beginning of the Chilean multi-fund system (October 2002),reinforces our findings, i.e., the Chilean funds keep on showing the same all undesirable patterns already identified

16

Table 5: Average rank-order metrics, based on the 90%-CVaR (March 2013 - March 2018), for di↵erent-sizetime-windows.

Window-size in yearsManager Distance 4 5 6

XXI BanorteHamming 0.00 0.00 0.00Spearman 0.00 0.00 0.00Kendall Tau 0.00 0.00 0.00

BanamexHamming 0.00 0.00 0.02Spearman 0.00 0.00 0.01Kendall Tau 0.00 0.00 0.01

SURAHamming 0.00 0.00 0.00Spearman 0.00 0.00 0.00Kendall Tau 0.00 0.00 0.00

Profuturo GNPHamming 0.17 0.13 0.06Spearman 0.09 0.07 0.03Kendall Tau 0.06 0.04 0.02

(a) Mexico


Industry averageHamming 0.20 0.22 0.23Spearman 0.08 0.09 0.10Kendall Tau 0.05 0.05 0.06

(b) Chile

in the April 2008-March 2008 time-window. To this distressing picture, we need to add two more elements: Chileanmanagers (as it has been reported before) revealed a manifest herd behavior, and, for longer time periods, all Chileanfunds (from B to E) seem to converge to identical returns.

Being mindful that correlation does not imply causation, we need to be cautious before deriving sweeping conclu-sions. Nevertheless, one factor is salient: Mexico employs a portfolio-level risk-controlling feature, while Chile doesnot. Granted, we might argue that perhaps the rationale behind a rolling daily VaR for a long-term investment vehicle(such as a pension fund) is unwarranted. But it is certainly better than no portfolio-level risk-restriction at all. Afterall, the Chilean approach (controlling risk by asset class limits) has no theoretical or empirical basis. In essence, thisform of indirect risk control is based on the notion that market conditions do not change as a function of time—apatently false assumption.

Moreover, we suspect that in the Chilean case, another element that has amplified the deficiencies of not havinga portfolio-level risk constraint is that the regulator forces the funds to maintain minimum positions in all assets(we assume, in the spirit of promoting diversification). Such constraints clearly limit the ability of asset managers tocontrol risk properly. In short, Chilean asset managers have also been victims of the regulation.

In summary, two things are clear. First, while the Mexicans funds behaved as intended, the Chilean funds behavedin a manner completely at odds with their goal. And second, both countries approached the objective of creatingfunds with di↵erent risk-reward profiles by means of quite di↵erent investment regulations. These two facts, takentogether, should be considered a serious warning for the many pension funds that still keep on using asset-class limitsas the preferred tool to control risk. Furthermore, the fact that the period considered included the subprime crisismakes this situation even more alarming: a good investment policy is supposed to protect investors precisely againstthe things that happen when the markets are not operating under a “normal” regime.

Finally, a potential criticism to our analyses is that the time period considered is not long enough to derivestatistically significant conclusions. To this observation we might be able to respond noting that the data consideredto analyze the Chilean system was not a sample from a much bigger universe; it was the universe (all the data points

17

(a) Mexico

(b) Chile

Figure 8: Average rank-order metrics, based on the cumulative return (March 2013 - March 2018), fordi↵erent-size time-windows.

since the system was implemented). However, a more relevant consideration can be drawn from an entirely di↵erentdiscipline that has also an important e↵ect of society’s welfare: earthquake engineering.

When there is a quake many buildings fail. What civil engineers do then is to analyze those which fail, and seewhat lessons they can derive from these failures. And then they incorporate the new insights into building codes andconstruction practices. One thing civil engineers do not do after a quake, is to wait many years until a su�cientlyhigh numbers of building fail in order to derive “statistically significant” conclusions, or, have a “su�ciently longobservation period.” The empirical evidence is on their side: controlling by risk (i.e. magnitude of the earthquakes),building failures have decreased over time. Had engineers waited one-hundred years to derive statistically significantobservations, earthquake engineering probably would still be in its infancy. By the same token, waiting one-hundred

18

Table 6: Average rank-order metrics, based on the cumulative returns (March 2013 - March 2018), fordi↵erent-size time-windows.


XXI BanorteHamming 0.07 0.03 0.00Spearman 0.04 0.02 0.00Kendall Tau 0.03 0.02 0.00

BanamexHamming 0.06 0.05 0.02Spearman 0.04 0.02 0.01Kendall Tau 0.03 0.02 0.01

SURAHamming 0.02 0.00 0.00Spearman 0.01 0.00 0.00Kendall Tau 0.01 0.00 0.00

Profuturo GNPHamming 0.01 0.00 0.00Spearman 0.00 0.00 0.00Kendall Tau 0.00 0.00 0.00

(a) Mexico


Industry averageHamming 0.52 0.46 0.48Spearman 0.54 0.49 0.55Kendall Tau 0.48 0.44 0.51

(b) Chile

years to enjoy the benefits of a long fund-returns database—while damaging the pension prospects of several genera-tions in the meantime—does not seem like a prudent proposition. When danger is imminent, and the consequencesare grave, one must often act with whatever information is available. And what we have observed regarding theChilean pension system calls for an urgent need to re-evaluate its investing regulation regime.

19

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A Mexican Investment Regime

Table 7: Summary of limits contained in the Investment Regime applicable to each fund type.

Item DescriptionLimits by fund type

SB1 SB2 SB3 SB4

Market andliquidity risks

Value at Risk 0.70% 1.10% 1.40% 2.10%Di↵. of the Conditional Value Risk 0.30% 0.45% 0.70% 1.00%Liquidity coverage ratio 80% 80% 80% 80%

Risk by issuerand/orcounterparty

Debt issued or endorsed by the FederalGovernment

100% 100% 100% 10%

SPE debt from mxBBB to mxAAA orint’l currencies BB to AAA

10% 10% 10% 10%

Debt from mxBBB to mxAAA or int’lcurrencies BB to AAA

5% 5% 5% 5%

Subordinated debt mxBB+ to mxBBB-or int’l currencies B+ to BB-

1% 1% 1% 1%

Hybrid debt from mxBBB+ to mxBBBor int’l currencies BB+ to BB

2% 2% 2% 2%

Foreign securities from BBB- to AAAfrom one issuer or counterparty

5% 5% 5% 5%

Holdings of a single issuance Maximum 35%, $300mdp

Asset class limits

Foreign securities 20% 20% 20% 20%Equity 10% 30% 35% 45%Foreign currency 30% 30% 30% 30%Securitizations 10% 15% 20% 30%Structured securities 10% 15% 20% 20%Mexican REITs and REITs 5% 10% 10% 10%Inflation protected securities Yes No No NoCommodities 0% 5% 10% 10%

Conflicts of interestSecurities by related entities 15% 15% 15% 15%Securities by entities with patrimoniala�liation with the manager

5% 5% 5% 5%

Investment vehiclesand derivatives

Investment mandates Yes Yes Yes YesDerivatives Yes Yes Yes Yes

Source: Investment Regime applicable to SIEFOREs pension funds, CONSAR.

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B Chilean Investment Regime

Table 8: Limits on structural investments (as percentage of the value of the fund)

Min. Max. Min. Max. Min. Max. Min. Max. Min. Max.Issued by the General Treasury of the Republic, Central Bank of Chile, Ministry of Housing, Recognition bonds and other government securities.

30% 40% 30% 40% 35% 50% 40% 70% 50% 80%

Shared Limit: Foreign instruments and indirect investment abroad through investment and mutual fundsLimit per fund: Foreign instruments and indirect investment abroad through investment and mutual funds

45% 100% 40% 90% 30% 75% 20% 45% 15% 35%

Investment in foreign currency without exchange rate coverageRestricted securities: Restricted ACC + [ACC+CFI+PFI] low liquidity + [CFI+CFM+CME+CIE] non-approved CCR + [DEB+BCA+ACC+ECO+OAC] less than three years + [FIN + LHF + DEB + BCA + ECO + EXT + OAC] less than BBB and N-3 or with less than 2 ratings.

10% 20% 10% 20% 10% 20% 10% 20% - -

Variable income (minimum limit)Alternative assets: Real estate assets, private capital, private debt, infrastructure and other asset traded in private markets + investment vehicles of foreign private capital and debt and foreign co-investment + indirect investment in alternative assets + national investment funds investing mainly in alternative assets

5% 15% 5% 15% 5% 15% 5% 15% 5% 15%

Instrument

Minimum: 30% of VF (A+B+C+D+E); Maximum: 30% of VF (A+B+C+D+E)

50% of investment

50% of investment

50% of investment

50% of investment

50% of investment

A fund B fund C fund D fund E fund

Variable income (maximum limit): [National securities + foreign securities] if they are capital + other public-offering instruments that are capital instruments under the supervision of the regulator.

Fund A > Fund B > Fund C > Fund D > Fund E

40% 25% 15% 5% -

80% 60% 40% 20% 5%

Source: Investment Regime applicable to Chilean pension funds since November 2017, Superintendecia de Pensiones.

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Table 9: Maximum limits on investments by instrument and group of instruments (as percentage of the valueof the fund)

A fund B fund C fund D fund E fundMax. limit Max. limit Max. limit Max. limit Max. limit

National and foreign exchangeable public and private company bonds

30% 30% 10% 10% 3%

Operations or contracts for loans or mutuum of financial letter (national)

15% of national portfolio





Instruments on Loan (foreign)1/3 foreign

investment A1/3 foreign

investment B1/3 foreign

investment C1/3 foreign

investment D1/3 foreign

investment E

Restricted ACC + [ACC+CFI] low liquidity + [CFI+CFM+CME+CIE] non-approved CCR + [FIN+LHF+DEB+BCA+ECO+EXT+OAC] less than BBB and N-3 or less than two risk ratings

20% 20% 20% 20% -

Contributions from promises of suscription and payment of investment fund shares

2% 2% 2% 2% 2%

Total resources delivered as margins in hedge fund transactions.

2% national and 2% foreign





Transactions with derivatives. Includes net buyer position of foreign currency through derivatives.

3% 3% 3% 3% 3%

Overnight + Time deposit 2% 2% 2% 2% 2%Investment in foreign currency 5% 5% 5% 5% 5%Foreign private capital investment vehicles + co-investment in private capital + future commited contributions to foreign private capital investment vehicles and foreign co-investment of private capital. Includes indirect foreign investment through national investment funds and their contracts of promise.

7% 6% 4% 3% 2%

Instrument

Source: Investment Regime applicable to Chilean pension funds since November 2017, Superintendecia de Pensiones.

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