Chapter 26 return based style analysis applied to spanish balanced pension plans

Return-Based Style Analysis Applied to Spanish Balanced Pension Plans Laura Andreu, Cristina Ortiz, José Luis Sarto, and Luis Vicente CONTENTS 26.4.1 Defi nition of the Basic Asset C

Return-Based Style

Analysis Applied to

Spanish Balanced

Pension Plans

Laura Andreu, Cristina Ortiz, José Luis Sarto, and Luis Vicente

CONTENTS

26.4.1 Defi nition of the Basic Asset Classes and Study

26.4.2 Importance of Asset Allocation on the

26.4.3 Importance of Asset Allocation on the

26.4.4 Importance of Asset Allocation on

This ch a pter i dentifi es t he investment style carried out by Spanish

balanced pension plans during the period 2000–2007 For this reason,

we analyze the multicollinearity between diff erent benchmarks in order to choose the best style model

Once we have selected the best model to explain the returns obtained

by e ach ba lanced plan, we de termine t he i mportance of t hese st rategic allocations to explain the diff erences on the performance of portfolios In this sense, we try to determine how much of the variability of returns over time is explained by asset allocation, how much of the variation in returns among plans is explained by the diff erences in the strategic policies, and the proportion of return that is explained by asset allocation Moreover,

we carry out some additional analyses to test the incidence of some well-known biases such as survivorship bias and look-ahead bias on the impor-tance of the strategic asset allocation

Consistent w ith p revious l iterature, w e fi nd t hat st rategic po licy explains, on average, about 90% of t he va riability of returns over t ime, more than 40% of the variation in returns among plans, and about 100%

of the total return obtained

26.1 INTRODUCTION

Investors have a wide variety of portfolios and investment vocations to choose from when it comes to deciding the appropriate pension plan to invest in Th is chapter tries to shed some light for investors to make this important decision while focusing on the analysis of the investment styles of each portfolio Given that some previous papers* have documented misclassifi cation problems and even the names of some portfolios could be misleading, the analysis of the style allocations of these portfolios becomes of particular interest In this sense, studies such as Brown and Goetzmann (1997) show that up to 40% of mutual funds is misclassifi ed

Chan et al (2002) highlight that the increasing attention to the portfolio investment style is justifi ed since it provides a clear evidence of manager skills and portfolio risks In this study, we estimate the style allocations of Spanish balanced pension plans and the infl uence of these assignments on the performance of each portfolio

In this context, although fi nancial l iterature ha s u sually focused on equity po rtfolios, t his st udy a nalyzes ba lanced p lans g iven t hat t his

* See G ruber (1996), Brown a nd G oetzmann (1997), D iBartolomeo a nd Wit kowski (1997), Chan et al (2002), and Swinkels and Van der Sluis (2006), among others.

category presents a broader leeway to managers.* Furthermore, this vocation is very relevant i n t he Spanish pension i ndustry, where t here were 197 equity balanced pension plans with a market value of more than

€7400 billion, and 1.2 million investors at the end of 2007

In general, fi nancial literature has emphasized the importance of the asset allocation analysis on the portfolio performance However, we fi nd some disagreement over the exact relationship since the seminal papers of Brinson et al (1986, 1991) Th ese authors state that more than 90% of the variability of the returns obtained over time is determined by the variation

of the strategic policy However, these fi ndings have oft en been misinter-preted by academics and professional investors, causing a controversy that stems from using the same results to answer diff erent questions In this sense, the study of Ibbotson and Kaplan (2000) clarifi es this controversy, addressing diff erent questions and providing evidence that asset alloca-tion explains about 90% of the variability of U.S mutual fund returns over time, more than 40% of the variation of returns among funds, and almost 100% of the total return obtained by the portfolios

In this study, we apply the so-called return-based style analysis (RBSA) introduced by Sharpe (1988, 1992) Th is methodology compares the return

of a po rtfolio w ith t he per formance of a fa mily of st yle benchmarks to determine the combination of indexes that best track the vocation of the portfolio, a nd ha s be en u sed, t raditionally, t o cla ssify a nd e valuate t he performance of equity mutual funds (see, e.g., Sharpe, 1992; Lobosco and DiBartolomeo, 1997; Otten and Bams, 2001) More recently, other pieces

of research have appeared, focusing on the analysis of hedge funds due to their special characteristics (see, e.g., Fung and Hsieh, 1997; Agarwal and Naik, 2000; Ben Dor et al., 2003; Harri and Brorsen, 2004)

Very little investigation has been devoted to st yle analysis applied to Spanish portfolios as these works have been primarily dedicated to invest-ment funds Fernández and Matallín (1999) analyzed the performance of Spanish funds during the period from 1992 to 1996, using the traditional model including six diff erent benchmarks Ferruz and Vicente (2005) also analyzed the style of Spanish investment funds, highlighting the potential multicollinearity problems between benchmarks

Th e rest of the study is organized as follows Section 26.2 describes the data, Section 26 3 ex plains t he m ethodology, Section 26 4 p resents t he

* Spanish balanced pension plans have to invest in equity assets between 30% and 75% of their portfolios.

empirical results of the research carried out, and Section 26.5 summarizes and concludes

26.2 DATA

Two pension plan datasets have been created from data provided by the

Spanish Association of Collective Investment and Pension Funds (Inverco)

from April 2000 to December 2007 Both samples are free of survivorship and look-ahead biases, and collect monthly returns and total net assets (TNAs) of 115 and 77 Spanish balanced pension plans investing in Euro zone and global equities, respectively

Information o btained f rom t he ma nagement co mpanies ha s be en decisive t o cla ssify t he portfolios according t o t heir i nvestment

voca-tions because Inverco distinguishes only basic categories such as fi

xed-income, equity, ba lanced, a nd g uaranteed plans Once t he i nvestment goal of each portfolio is identifi ed, we fi nd that the number of domestic plans is low, while Euro zone and world equities represent the principal vocations of Spanish balanced pension plans (around 70% of the entire dataset)

Table 26.1 presents some basic descriptive statistics of both databases

A sharp increase in the total assets managed by Spanish balanced pension plans can be observed A signifi cant rise in the number of investors is also

TABLE 26.1 Descriptive Statistics of the Spanish Pension Plan Samples

April 2000 December 2007 April 2000 December 2007

Number of pension

Total net assets

(million euros) 1.040 3.948 225 2.053 Number of investors 215.101 707.524 70.572 398.339 Average assets by

pension plan

(million euros)

15.29 44.86 20.45 39.48

Average number

of investors by

pension plan

3.163 8.04 6.416 7.66

Notes: Th is table reports the fi gures of Spanish balanced plans Specifi cally, the left part

reports the statistics of those pension plans investing in Euro zone and the right part reports t he st atistics of t hose plans investing in w orld markets Th e table contains the number of listed pension plans on the dates indicated, the net assets managed, the number of investors, the average assets by portfolio, and the average number of investors by plan Th es e fi gures are referred to the beginning and the end of the sample period (April 2000 and December 2007).

seen for both the investment aims On t he contrary, the number of pen-sion plans has remained stable over time

Using data from international and national associations such as Morgan

Stanley Capital International, Bank of Spain, and International Financial Analysts,* we collected information about the monthly returns of a set of

benchmarks that represent the main investment objectives of the pension plan portfolios

As one of the subcategories analyzed gathers portfolios that invest

in world eq uities, we co llected i nformation of se veral eq uity bench-marks from different stock markets such as the United Kingdom, the Euro z one, t he w orld, t he U nited S tates, a nd J apan a long w ith se v-eral S panish an d E uropean G overnment f ixed-income b enchmarks,

a p rivate deb t i ndex, a nd a ben chmark r epresentative o f c ash W ith this broad set of benchmarks, we make sure that we have considered all the basic asset types existing in the portfolio holdings of Spanish balanced pension plans Specifically, we gather information about 12 benchmarks An ex haustive description of t hese indexes is shown in Appendix 26.A.1

26.3 METHODOLOGY

In this section, we describe the basic model used to determine the stra-tegic asset allocations Th e model proposed by Sharpe (1992) focused on obtaining the portfolio assignments on a number of major asset classes, estimating t he ex posures of portfolio returns t o t hese relevant bench-marks Th is RBSA can be described as follows:

0 1 1

R = β +βR + +β R + +β R + ε (26.1) where

R pt (R jt ) is the return of pension plan p (basic asset type j) in month t

βj is the style weight of the basic asset class j

β0 is the added va lue of active management above the merely passive tracking of the style portfolio†

εpt is the residual return not explained by the model

* See http://www.mscibarra.com/ for equity benchmark information and http://www.bde.es/ and http://www.afi es for fi xed-income and cash indexes.

† Th e parameter β0 has been included in the model following the approach of De Roon et al (2004) and Harri and Brorsen (2004).

In order to obtain robust estimations, the benchmarks must be mutu-ally exclusive (not including any securities that already form part of any other ben chmark co nsidered), ex haustive (as ma ny st rategic a ssets a s possible should be included in the model), and they must have returns that d iff er f rom e ach o ther (the co rrelation be tween t he ben chmarks should be low) Hence, the model requires a balance between the level of precision and the number of explanatory benchmarks because an appro-priate selection of styles is crucial to obtain a suitable style model In this sense, Lobosco and DiBartolomeo (1997) show that the accuracy of the model does not necessarily i mprove when considering f urther bench-marks Buetow et a l (2000) and Ben Dor et a l (2003) a lso state some concerns about possible distorted fi ndings because of linearity problems

of the benchmarks

Following t he st yle analysis proposed by Sharpe (1992), t he model is solved by obtaining a se t of st yle weights βj that minimize the residual variance when considering t wo restrictions: t he estimated st yle weights sum to one and they must be nonnegative

= =

0 1 1

1 1

subject to ∑k j=1β =j 1, 0≤ β ≤j 1, j=1,2, ,…k

Th e portfolios analyzed in this study comply with both features, which enable us to state that this restricted model leads to the most accurate style estimates In some cases, these constraints may cause biased results, such

as when hedge funds are analyzed A circumstance that has led to relax the positivity constraint to some authors.*

Finally, it is relevant to note that these models are typically evaluated

in terms of their ability to explain the returns of the portfolio Th er efore, the coeffi cient of determination can be interpreted as the percentage of

the variability of the return of portfolio p due to the portfolio style deci-sion In this sense, high values of R2 coeffi cients provide evidence of the accuracy of the model applied and, furthermore, imply that the results obtained from the parameter β0 refl ect properly the added value reached

by the active management of the portfolio analyzed as stressed by

De Roon et al (2004)

* See Fung and Hsieh (1997), Agarwal and Naik (2000), Ben Dor et al (2003), among others.

26.4 EMPIRICAL RESULTS

26.4.1 Defi nition of the Basic Asset Classes and Study

of the Multicollinearity

Given the investment vocation of the database analyzed, we have to con-sider d iff erent eq uity i ndexes a s w ell a s d iff erent fi xed-income bench-marks representing the wide variety of assets that can be included in these portfolios Moreover, an exhaustive analysis of multicollinearity between the benchmarks has to be carried out to ensure that the proposed models will not generate results that fail to refl ect appropriately the actual invest-ment styles In this sense, as we have previously invest-mentioned, a total of

12 benchmarks have been considered, being the correlation results shown

in Appendix 26.A.2

High positive and statistically signifi cant correlation is observed between

the fi ve eq uity be nchmarks ( MSCI Emu in dex, World i ndex, U.S i ndex,

Japan index, and U.K index), as well as between the diff erent fi xed-income

benchmarks, regardless of the maturity of the assets included in each index Hence, Appendix 26.A.2 demonstrates the importance of selecting the right style indexes, as some authors like Ben Dor et a l (2003) and Ferruz and Vicente (2005) have stressed Specially, when t he a nalysis is tackled on a less developed market such the Spanish industry where it is diffi cult to fi nd benchmarks that fulfi ll the requirements established by Sharpe (1992) Bearing in mind the results provided by the multicollinearity analysis, the style models proposed for each sample are as follows:

= β + β0 1 MSCIEmut+ β2 5yPublicdebt, + β3 Repos + ε

Global R pt = β + β0 1 MSCIWorldtR + β2 5yPublicdebt,R t+ β3 ReposR t + εpt (26.4)

Th erefore, the models proposed include an equity benchmark that is rep-resentative of the investment vocation (MSCI Emu index or MSCI World index), a l ong-term fi xed-income benchmark (5 year public debt) and a cash index (1 day treasury bill repos) representing the liquidity that these investment portfolios have to hold in order to face the withdraws

26.4.2 Importance of Asset Allocation on the Variability

of Returns over Time

Th e variability of returns over time explained by the asset allocation policy

is obtained by regressing the performance obtained by each pension plan (total return) against the performance obtained by the asset allocation policy

(policy return), reporting the R2 coeffi cient In this sense, the policy return

of a pension plan p in the period t, PR pt, is calculated by the mere tracking of the strategic weights of the basic assets allocated by the pension plan:

= β1 MSCIt+ β2 5yPublicdebt, + β3 Repos

where

PRpt is the policy return of pension plan p in month t

R jt is the return of the benchmark of the basic asset type j in month t

βj is the style factor or policy weight of the basic asset type j

In order to present comparable results, Table 26.2 shows the R2 coeffi cients obtained from the style analysis for the equally weighted portfolios consid-ering all surviving pension plans with at least 36 o bservations in the two samples analyzed In this sense, our results confi rm the evidence previously found in fi nancial literature, with 90% of the variability of Spanish balanced pension plan returns over time explained by the variability of policy returns

Th is fi nding is similar in the two samples considered and indicates the high degree of tracking of the strategic policy by pension plan managers

As we have previously mentioned, an original contribution of this research is the evaluation of the incidence of several well-known biases in

fi nancial literature, such a s survivorship bias and look-ahead bias along with the infl uence of portfolio size In this case, this analysis is applied in the most controversial question: the importance of asset allocation in the variability of returns over time

To reach this aim, we have built three diff erent equally weighted portfo-lios: fi rst, an unbiased portfolio gathering all Spanish pension plans exist-ing i n e ach per iod regardless of t he number of observations; second, a survivorship bias portfolio that encompasses only those plans that survive

at the end of the sample period (December 2007); and third, a look-ahead

TABLE 26.2 Results of Time-Series Regression in Financial Literature

Sample Average R2 (%)

Brinson et al (1986) U.S pension funds 93.60 Brinson et al (1991) U.S pension funds 91.50 Ibbotson and Kaplan (2000) U.S mutual funds 81.40

U.S pension funds 88.00 Drobetz and Köhler (2002) German–Swiss mutual funds 82.90 Spanish balanced pension plans Euro zone equity 89.06

bias portfolio gathering only those pension plans with at least 36 o bser-vations Moreover, we have computed an asset-weighted portfolio for the unbiased dataset Th us, a total of four portfolios have been examined Th e results are shown in Table 26.3

A similar incidence of look-ahead bias is observed in both datasets Th e

consideration of a minimum period of time leads to a higher R2 coeffi cient, thereby, increasing the importance attributed to asset allocation to explain the variability of returns over time In contrast, the impact of survivorship bias is not so clear since diff erent patterns are revealed by pension plans

that invest in Euro zone and world equities Finally, the higher R2

coef-fi cient reached i n a sset-weighted portfolios se ems to i ndicate t hat a sset allocation is more important in large pension plans

26.4.3 Importance of Asset Allocation on the Variability

in Returns among Plans

Following the study of Ibbotson and Kaplan (2000), we try to determine how much of t he va riation i n returns a mong plans is ex plained by t he diff erences i n t he po rtfolio st rategic po licies Th is a pproach i mplies a cross-sectional regression of compound monthly total returns (TRp) on compound monthly policy returns (PRp) for the entire period, being these

compound rates of return for each plan p calculated as follows:

,1 ,2 ,

TRp =T(1 TR )(1 TR ) (1 TR ) 1+ p + p … + p T − (26.6)

,1 ,2 ,

PRp =T(1 PR )(1 PR ) (1 PR ) 1+ p + p … + p T − (26.7)

TABLE 26.3 Portfolio Results of Time-Series Regression

Euro Zone Equities World Equities

R2 % Gap% R2 % Gap%

Portfolio with survivorship bias 89.14 −0.15 91.23 0.80 Portfolio with look-ahead bias 89.40 0.11 90.61 0.18 Unbiased asset-weighted portfolio 92.76 3.47 90.89 0.46

Notes: Th e det ermination co effi cient r esults o f fi ve diff erent p ortfolios a re

shown in o rder to detect the infl uence of some biases on the impor-tance of asset allocation on the variability of returns over time Besides, the table provides information about the diff erence (gap) between the determination coeffi cients of the diff erent portfolios in comparison to the unbiased equally weighted portfolio.

TRp (PRp ) is the compound monthly total (policy) return on plan p over

the entire period of analysis

TRp,t (PRp,t ) is the total (policy) return of plan p in month t

T is the number of monthly returns, t = 1, 2,…, T

Th e cross-sectional R2 coeffi cient of this analysis reports the variability

of returns among Spanish balanced pension plans explained by the diff er-ent strategic policies allocated In this sense, if all portfolios perfectly fol-lowed the same passive asset allocation policy, there would be no variation among plans In contrast, if all pension plans were invested passively with a wide range of asset allocation policies, all the variations in returns would be attributable to strategic policy Accordingly, the two factors that drive the

cross-sectional R2 are the diff erences between the pension plan’s asset allo-cation policies and the diff erences in the degree of active management.*

Table 26.4 shows the R2 coeffi cients obtained from the cross-sectional regressions carried out in our samples as well as t he fi ndings shown in prior research

Th e R2 coeffi cients goes f rom 4 2.39% to 55.66%, wh ich i mplies t hat asset allocation explains, on average, more than 40% of the variation of returns across pension plans It is important to note that Spanish

bal-anced plans i nvesting i n Euro zone equities ex hibit a h igher R2 coeffi -cient than those investing in world equities Th us, the results reveal that

* Ibbotson and Kaplan (2000) show how the degree of a ctive management aff ects the

cross-sectional R2

TABLE 26.4 Portfolio Results of Cross-Section Regressions a

Sample Average R2 %

Brinson et al (1986) U.S pension funds —

Brinson et al (1991) U.S pension funds —

Ibbotson and Kaplan (2000) U.S mutual funds 35

U.S pension funds 40 Drobetz and Köhler (2002) German–Swiss mutual funds 65

Spanish balanced pension plans Euro zone equity 55.66

a Our results are free of survivorship bias but they present look-ahead bias in order to obtain statistically signifi cant results, whereas prior studies present both biases Due to the existence of look-ahead bias in the sample, the assess-ment of the incidence of the biases is not appropriate in this cross-sectional analysis.