Evaluating the style portfolio performance of Spanish equity pension plans

Evaluating the style portfolio performance

of Spanish equity pension plans

*

Evaluación de la rentabilidad basada

en el estilo de los planes de pensiones españoles

que invierten en aciones

Laura Andreu

_.

José Luis Sarto.

Luis Vicente Gimeno.

ABSTRACT This paper fi rstly examines the strategic asset allocations followed by Spanish equity

pension plans from 2001 to 2006. Once the investment style of each portfolio is known, the second aim of the paper is to analyse the performance obtained by these portfolios along with the performance obtained by their investment style to determine the value added by each manager and the suitability of the style chosen. In this sense, the performance evaluation has been conducted by considering diffe-rent performance measures used in fi nancial literature along with an alternative metric proposed to test the consistency of the different metrics. Finally, the study also addresses some robustness analyses to examine the consequences of imposing the portfolio constraint when non-exhaustive models are used and the effects of some well-known biases such as survivorship and look-ahead bias.

KEY WORDS Return-based style analysis; Pension Plans; Performance Measures.

RESUMEN En este artículo se analizan las asignaciones estratégicas de los planes de pensiones

espa-ñoles de renta variable durante el periodo 2001-2006. Una vez conocidos los estilos de gestión de cada cartera, el trabajo se centra en analizar la rentabilidad obtenida por cada plan así como la asociada con las asignaciones estratégicas elegidas, cuyo objetivo es determinar el valor añadido obtenido por los gestores y la idoneidad del estilo elegido. En este sentido, la valoración de la efi ciencia se ha rea-lizado a partir de diferentes medidas recogidas en la literatura fi nanciera así como de una medida alterativa propuesta para medir la congruencia entre los diferentes índices. Finalmente, se llevan a cabo diferentes análisis de robustez para determinar las consecuencias de imponer la restricción de cartera cuando se consideran modelos no exhaustivos así como los efectos del sesgo de supervivencia y del sesgo look-ahead.

PALABRAS CLAVE Análisis de estilos basado en rentabilidades; Medidas de rentabilidad; Planes de

Pensiones.

1. INTRODUCTION

The evaluation of portfolio management is an appealing topic that has aroused the interest of researchers and practitioners through time. The attention paid to this issue has increa-sed as a consequence of the growth of assets under management by collective investment.

* The authors would like to express their thanks to the University of Zaragoza for the award of project 268-159 and to the Foundation UCEIF for their fi nancial support. Any possible errors are the exclusive responsibility of the authors.

** Corresponding author: Laura Andreu. Accounting and Finance Department at the Faculty of Economics and Business Studies, Gran Vía, 2, 50005 Zaragoza, Spain. E-mail: landreu@unizar.es

This phenomenon can be explained given that individual investors can reap the benefi ts of diversifi cation by investing through institutions managed by professional managers. However, the indirect holding of equities by relying on fund managers introduces agency costs in addition to fees due to the need to monitor the actions of fund managers to ensure

compliance with the stated objectives and to evaluate their performance (1)_{. For that}

rea-son, benchmark portfolios are often built to determine the performance and value added by managers.

As mentioned by Lee (1999), it is important to make judgements about the quality of the performance such as how well the fund manager is performing against his peers or against other portfolios with similar objectives. In order to answer these questions, we need to analyse the investment style followed by the different portfolios to identify the benchmark for comparison. Trying to identify a fund manager style is not an easy task and different approaches have been suggested in fi nancial literature. In general, two approaches allow us to enhance our knowledge about the ways performance is achieved. These two fra-meworks are called return-based style analysis (RBSA) and holding-based style analysis (HBSA), respectively.

The fi rst framework was introduced by Sharpe (1992) and it makes the regression of a portfolio return against a set of style benchmarks to determine the combination of indexes that best tracks the manager’s performance. The second approach was introduced by Da-niel et al. (1997) and it examines the stocks actually held in the investment portfolio map-ping them into styles at different points of time. Once a suffi cient history of these holdings is obtained, an estimation of the manager’s average style profi le can be developed and used as benchmark.

Therefore, HBSA requires a detailed analysis of the characteristics of funds’ holdings at each point of time when the evaluation of the manager is going to be analysed. Since portfo-lio holdings are not available with a high frequency and it is very hard to deal with so much information, the vast majority of the studies (see, e.g., recent studies such as Swinkels and Van Der Sluis, 2006 and Karatepe and Gökgöz, 2006) have focused on RBSA to determine the investment style allocated by the portfolio and to evaluate their performance to identify the best-managed portfolios. This analysis only requires the returns of the fund and the indexes for comparison purposes. Therefore, the approach of Sharpe (1992) offers the investor the simplest way to style analysis.

In this sense, the fi rst aim of this paper is to determine the investment style followed by Spanish equity pension plans through the RBSA proposed by Sharpe (1992). Following the approach proposed by Cesari and Panetta (2002), we calculate the RBSA by using gross returns in order to evaluate the managers’ investment strategies since they are the output of the fi nancial management before the consideration of different fees that may distort the performance obtained by active management.

(1) The identifi cation of the investment style is very important due to the problems caused by the wide variety of investment vocations and the use of misleading names. In this sense, some studies such as Brown and Goetzmann (1997) and DiBartolomeo and Witkowski (1997) document misclassifi cation problems. As a consequence, investors have respon-ded to the proliferation of investment portfolios by more closely scrutinizing of manager's investment style.

cles in its conventional form. The traditional RBSA model, named as «strong style analy-sis» by De Roon et al. (2004), constrains the style weights not allowing neither short nor leverage positions. This makes perfect sense in the case of mutual funds but not in other investment vehicles like hedge funds, where the manager can take short positions or can be leveraged in some asset classes (see, e.g., Fung and Hsieh, 1997; Agarwal and Naik, 2000 and Ben Dor et al., 2003).

As a consequence, fi nancial literature has improved the traditional methodology to fi t it to different investment portfolios and to different market conditions (less developed markets) in which the fi nancial activity is carried out. In this sense, this paper contributes to the lite-rature examining the consequences of imposing the portfolio constraint to the style weights when non-exhaustive models are used to avoid the multicollinearity problems existing bet-ween the benchmarks.

Therefore, our fi rst hypothesis is focused on testing if the investment style of each pension plan explains appropriately the return achieved by the portfolio. Subsequently, we aim at measuring the performance achieved by each portfolio as well as the performance obtai-ned by the investment style chosen. The underlying hypothesis of this analysis is to exami-ne whether the managers are adding value to the mere tracking of the benchmarks. In this sense, we support the view of market effi ciency with costly information and therefore, we expect that pension plans can beat the market before expenses but not after management fees and turnover costs, as shown in Cesari and Panetta (2002).

This analysis of performance is carried out considering different metrics proposed in fi nan-cial literature along with an alternative metric proposed. The use of the different metrics is justifi ed since they provide us different perspectives as we will discuss later and, they allow us to check their consistency.

In relation with the performance evaluation, De Roon et al. (2004) report the performance obtained by different actively managed funds and their corresponding mimicking portfolios by using Sharpe and Jensen ratios as performance measures. These authors also include

in the traditional style model the intercept β₀ that represents the value added by active

management.

Other pieces of research that have studied the performance, in an internationally context, are those conducted by Graham and Harvey (1996, 1997). They propose two new perfor-mance measures in order to identify investment consultants that give superior advice by examining the performance obtained by a sample of asset-allocation strategies. As these authors mention, these measures are designed to evaluate a wide variety of scenarios and investment vehicles. Specifi cally, the fi rst measure (GH1) proposed by Graham and Har-vey (1997) calculates the difference between the newsletter return and the return on the volatility-matched portfolio whereas the second measure (GH2) calculates the difference between the return that the newsletter could obtain assuming the same volatility of the benchmark portfolio and the actual return. Therefore, both measures provide different perspectives, GH1 draws an effi cient frontier and checks whether the newsletter lies above or below this frontier while GH2 compares all funds with a common level of volatility.

In this sense, in spite of the fact that the fi rst studies analysing the effi ciency of managed portfolios are conducted with US data, other papers have analysed the effi ciency in Euro-pean markets. Results using UK data on mutual and pension funds provide, in general, similar conclusions than those obtained in the US market. They fi nd evidence of economi-cally and statistieconomi-cally signifi cant underperformance.

Specifi cally, Blake and Timmermann (1998) examine the gross returns on 2,300 UK open-ended mutual funds from 1972 to 1995 fi nding statistically signifi cant underperformance. A year later, Blake et al. (1999) examine the asset allocations of a sample of 364 UK occu-pational pension funds that retained the same fund manager over the period 1986-1994. Their results suggest that total return is dominated by asset allocation, with a negative average return from stock selection and very negative average return to market timing. Afterwards, Thomas and Tonks (2001) in a large sample of pension funds, fi nd little evi-dence of any abnormal performance. The authors also report that pension funds seem to follow very similar investment strategies, so that identifying outperformance is a diffi cult task. Therefore, the above-mentioned studies seem to conclude that fund managers have no private information.

In relation to the Spanish market, we can highlight the studies of Rubio (1992, 1993 and 1995), Mayorga and Marcos (1996), Freixas et al. (1997), and Ferrando and Lassala (1998) due to their analysis of Spanish funds performance considering different perspectives. Mo-re Mo-recently, other papers focus on performance evaluation and performance measuMo-res have appeared. Specifi cally, Ferruz and Sarto (2004) and Gómez-Bezares et al. (2004) pro-vides a survey about the traditional performance measures along with the introduction of some alternative ones in order to solve some criticisms detected in the traditional metrics. On the other hand, Ferruz and Vicente (2006) also evaluate the results of domestic equity funds considering both gross and net returns.

Finally, we also conduct an additional analysis to test the robustness of our results to the

presence of survivorship bias and look-ahead bias (2)_{. The infl uence of pension plan size is}

also checked by analysing asset-weighted portfolios.

In this respect, our research is motivated, primarily, by the large ongoing studies that analyse this topic considering investment funds compared to the lack of conclusions about the investment style and performance added by personal pension plan managers, espe-cially in the Spanish market. In this context, Matallín and Fernández (2000) and Fernán-dez and Matallín (1999) analyse the performance of Spanish investment funds during the period from 1992 to 1996 using the traditional model including six different benchmarks.

Some years later, Ferruz and Vicente (2005_a and 2005_b) also determine the investment

style of Spanish funds stressing the importance of analysing the multicollinearity between benchmarks. This feature is especially important in less developed markets as the Spanish industry where there are not many indices that fulfi l the initial hypothesis required by Sharpe (1992). These requirements are the exclusivity, exhaustivity and independence of the benchmarks.

(2) The infl uence of these biases on other topics like performance persistence and investor behaviour has been widely analysed. However, little is known about the infl uence of these biases on asset allocation.

unexplored but important sample. Moreover, the study presents original features since it includes the robustness analysis of the results controlling for different biases and it inclu-des both an individual RBSA for each pension plan included in our sample and an aggre-gated analysis making up different portfolios.

The paper demonstrates the importance of selecting the right benchmarks and the in-terest of relaxing the portfolio constraint imposed in the original version of the RBSA when non-exhaustive models are used. Furthermore, our robustness tests show that the biases analysed do not affect signifi cantly to the fi ndings obtained. This fact could be explained given that there are not many differences in the composition of the portfolios. A scarce number of pension plans disappear during the time period analysed or have information for less than 36 months.

The performance results obtained by using gross returns also highlight the quality of the management of at least one out of three Spanish equity pension plans regardless of the performance measure used. Specifi cally, the average annual value added by the active ma-nagement is 1.1700% and 0.0044% for Spanish pension plans investing in World and Euro Zone equities. However, it is important to note that the value added by active management is not statistically different from zero. This fi nding indicates that pension plans’ returns are comparable to that of the chosen benchmarks, so that managers are compensated for their information gathering according to the defi nition of market effi ciency with costly in-formation (see, e.g. Cesari and Panetta, 2002). The similar results found by using different performance measures leads us to examine the correlation coeffi cients between them, obtaining high values of correlation and therefore, similar performance rankings.

The paper is organised as follows. Section 2 includes an explanation of the database used and the methodology applied. Section 3 gathers the return-based style analysis as well as the performance evaluation analysis. Section 4 provides additional analyses about the in-vestment style of Spanish pension plans. Finally, the conclusions are drawn in Section 5.

2. DATA AND METHODOLOGY

Our study is focused on Spanish personal pension plans due to their importance in the Spanish pension market, where they represent more than 80% of the investors and about 60% of the money managed. Moreover, these portfolios are very interesting due to their social importance to provide coverage to some important contingencies like retirement and disability, among others. Nevertheless, the Spanish pension market is not as developed as it is in other European countries such as UK and the Netherlands and it deserves great attention.

The fi rst Spanish private pension plans appear in 1988 but it is at the end of the 20th cen-tury when the development of the industry takes off. Consequently, the time period analy-sed in the study (2001-2006) covers the most important years. At the end of the sample

period, private pension plans managed about €81,200 million of over 9 million investors

through more than 3,000 pension plans belonging to 88 different fi nancial groups. The heterogeneity of the Spanish pension market due to the existence of a vast majority of

small plans along with a scarce number of large plans is also an important feature to bear in mind.

The focus of our analyses are those equity pension plans investing in World and Euro Zone equities given that the number of Spanish portfolios investing in domestic equities is very confi ned. This leaves us a fi nal sample of 63 and 69 pension plans, respectively. Specifi cally, we analyse the monthly gross returns of plans investing in World and Euro Zone equities from January 2001 to December 2006 (see Appendix 1, where some descriptive statistics of our sample are reported) through the RBSA methodology proposed by Sharpe (1992). In this sense, the returns provided by the Spanish Association of Collective Investment and Pension Funds (Inverco) are net of the management and custodial fees charged by the portfolios. To evaluate the portfolio management and therefore, the value added by pension managers before the charges of different fees and commercial costs, we calculate gross returns as follows:

(1 + NR_pt) = (1 + GR_pt)(1 – f_pt) (1)

where NR_pt is the net return obtained by portfolio p in month t, GR_pt is the gross return

obtained by portfolio p in month t and f_pt is the percentage of management and custodial

fees charged by portfolio p in month t (3)_.

In order to determine the asset allocation of each pension plan, the primary aspect to be considered is the defi nition of the asset classes representative of the different assets held by the portfolio. In this sense, the offi cial investment criteria provided by the Spanish Asso-ciation of Collective Investment and Pension Funds (Inverco) establish that Spanish equity personal pension plans must invest more than 75% of their portfolios in stocks.

Therefore, we have collected information about the monthly returns of several

bench-marks given the global vocation of one of our samples of pension plans (4)_{. Specifi cally, we}

have collected information of different stock markets like Spain, UK, Euro Zone, World, US and Japan along with information about different benchmarks representative of public and corporate fi xed-income assets. With this broad set of benchmarks we make sure that we have considered all basic asset types existing in the portfolio holdings of Spanish equity pension plans.

Therefore, the next step is to examine the multicollinearity between the benchmarks (5) _due

to the important consequences of this phenomenon as pointed out by Ben Dor et al. (2003),

among others (6)_{. This analysis allows us to ensure that the proposed models, including a}

benchmark representative of the equity holding (World or Euro Zone equities) along with a benchmark representative of the long-term debt and of cash investment, will not generate

(3) The information about the fees charged has been provided by the General Authority of Insurance and Pension Funds (DGSFP).

(4) This information has been provided by Morgan Stanley Capital International, (MSCI) Bank of Spain and International Financial Analysts (AFI).

(5) These results are available upon request to the authors.

(6) Note that empirical research has shown that performance evaluation is sensitive to the choice of the benchmark, see e.g. Lehmann and Modest (1987) and Grinblatt and Titman (1994).

pension plan managers.

Although the investment vocation of the Spanish pension plans analysed indicates that the equity holding is focused on Euro Zone and World equities, it is probable that Spanish equities also play an important role in the portfolios. Therefore, it is very interesting to analyse the correlation between the national index and the benchmarks representative of

the respective investment vocation (7)_.

We fi nd no signifi cant multicollinearity problems in the models proposed in Expression 2. These models include the benchmark representative of the equity holdings of the respec-tive vocations (MSCI World index and MSCI Emu index), an index of Spanish long-term fi xed-income assets (Spanish 5-year fi xed-income index) and an index related to cash (1-day Repos of Spanish Treasury Bills). Thus, the return for a given pension plan is described

by the following expression (8)_:

World: R_pt = β₀ + β₁R_MSCIWorld,t + β₂R_FI,t + β₃R_Cash,t + e_pt

}

Euro Zone: R_pt = β₀ + β₁R_MSCIEmu,t + β₂R_FI,t + β₃R_Cash,t + e_pt

where R_pt is the return obtained by portfolio p in month t, R_MSCIEmu,t and R_MSCIWorld,r are the

re-turns of the equity benchmarks whereas R_FI,t and R_Cash,t are the returns of the fi xed-income

and liquidity benchmarks, β_k are the style allocations of the different asset classes and e_pt is

the return of portfolio p in month t not explained by the model.

In this sense, the best explanation of the return achieved by a portfolio is given by the style

allocations (β_p) that minimise the residual variance of the model considering two constraints:

the estimated style factors sum to one and must be non-negative (9)_.

T T

Min

Σ

pt = Min

Σ

[

]

2

t = 1 t = 1

k

}

Subject to

Σ

j = 1

Remember that the benchmarks included in the model must be exclusive, exhaustive and independent. Otherwise, the separation of the individual explanatory effect of each bench-mark from the overall return obtained by the portfolio is not possible.

De Roon et al. (2004) provide evidence that the «strong style analysis» shown in Expres-sion 3 leads to the most accurate estimates of the style weights if the portfolios analysed fulfi l these constraints (short sales are not allowed and therefore, the investment in the different asset classes can not exceed one hundred per cent of the portfolio budget).

(7) We reject the possibility of including the domestic equity index (MSCI Spain index) for two important reasons: the high correlation observed between the national benchmark and the equity benchmarks of each investment vocation (MSCI World index and MSCI Emu) and the lack of exclusiveness between these benchmarks.

(8) Following the approach of De Roon et al. (2004), the estimated model includes a constant β0 in order to obtain the return added by active management to the mere passive tracking of the style portfolio.

ver, it is well documented that these constraints may provoke biased results in some cases. The special features of hedge funds lead to Fung and Hsieh (1997), Agarwal and Naik (2000) and Ben Dor et al. (2003), among others, to relax the positivity constraint.

Similarly, we propose the relaxation of the portfolio constraint (10) _{when non-exhaustive}

mo-dels are considered to avoid the multicollinearity problems reported in fi nancial literature (see e.g. Lobosco and DiBartolomeo, 1997; Buetow et al., 2000, and Ben Dor et al., 2003) since not all the potential strategic assets are included in the model. Note that, models pro-posed in Expression 2 are well specifi ed although they are non-exhaustive including only an equity benchmark representative of the investment vocation, a long-term fi xed-income benchmark and a cash index representing the liquidity that these investment portfolios have to hold in order to face the withdraws.

3.

RBSA RESULTS AND PERFORMANCE EVALUATION

The style allocation results of Spanish equity pension plans investing in World and Euro Zone equities are reported in Tables 1 and 2, respectively. Note, however, that these tables show the results of the strong style analysis as well as the results of the alternative model proposed relaxing the portfolio constraint.

From these tables we can confi rm the validity of the models proposed given the high

ad-justed R2 _{coeffi cients and the fi nding that the sum of the beta parameters in the alternative}

model is very close to one in the vast majority of the pension plans analysed. This latter fi nding provides evidence that our models show robust results to explain the strategic style allocated by pension plan managers. This individual analysis is quite interesting and it is in line with the national literature (see e.g. Fernández and Matallín, 1999). However, it must be complemented by reporting aggregate results as shown in Section 4.

Then, we focus our attention on the evaluation of the portfolio performance by compa-ring the effi ciency obtained by the different Spanish equity personal pension plans and their style portfolios to detect the best-managed pension plans. In this sense, different approaches to measure the performance are tackled in the paper in order to consider different perspectives and to test the consistency of the different metrics.

Following the paper of De Roon et al. (2004), the fi rst metric considered to evaluate the

portfolio performance is the intercept β₀. This parameter can be seen as a performance

measure (11) _{since it gathers the return that the portfolio has achieved above or below to its}

style portfolio (or investment style).

We must highlight that a positive (negative) value of β₀ only implies that portfolio active

management obtains higher (lower) returns in comparison to the style portfolio when the

style model shows a residual variance close to zero. Due to the high R2 _{obtained in our}

mo-dels, this requirement is fulfi lled and, therefore, we can use this metric as a performance measure.

(10) It will be referred as the alternative model from hereafter.

T ABLE 1 S TYLE A LLOCA TIONS OF S P ANISH PENSION PLANS INVESTING IN W ORLD E QUITIES *

The table is divided in two parts. The left part includes the style allocations considering the

strong version

of the style model and the right part gathers the results relaxing

the portfolio constraint.

β0 β1 β2 β3 Adj. R 2 β0 β1 β2 β3 Σ β Adj. R 2 1 -0.0004 (-0.019;0.018) 0.8389 (0.739;0.938) 0.0000 (-0.000;+0.000) 0.1611 (-8.867;9.189) 85.25% -0.0004 (-0.019;0.018) 0.8389 (0.726;0.952) 0.0000 (-0.503;0.503) 0.1611 (-8.881;9.203) 1.000 85.25% 2 -0.0020 (-0.011;0.007) 1.0000 (0.925;1.075) 0.0000 (-0.391;0.391) 0.0000 (-3.646;3.646) 94.15% -0.0020 (-0.011;0.007) 1.0000 (0.925;1.075) 0.0000 (-0.391;0.391) 0.0000 (-3.646;3.646) 1.000 94.15% 3 0.0030 (-0.016;0.022) 0.9867 (0.851;1.122) 0.0133 (-0.454;0.481) 0.0000 (-9.908;9.908) 84.79% 0.0030 (-0.016;0.022) 0.9867 (0.851;1.122) 0.0133 (-0.454;0.481) 0.0000 (-9.908;9.908) 1.000 84.79% 4 -0.0016 (-0.013;0.010) 0.8744 (0.777;0.972) 0.0526 (-0.455;0.560) 0.0730 (-4.656;4.802) 86.95% -0.0013 (-0.013;0.010) 0.8716 (0.774;0.969) 0.0335 (-0.474;0.541) 0.0000 (-4.727;4.727) 0.905 86.95% 5 0.0001 (-0.022;0.023) 0.8267 (0.677;0.977) 0.0000 (-0.538;0.538) 0.1733 (-11.179;11.526) 75.22% 0.0001 (-0.022;0.023) 0.8267 (0.677;0.977) 0.0000 (-0.538;0.538) 0.1733 (-11.179;11.526) 1.000 75.22% 6 -0.0039 (-0.030;0.022) 0.8705 (0.685;1.056) 0.0000 (-0.000;+0.000) 0.1295 (-10.564;10.823) 57.99% -0.0036 (-0.030;0.022) 0.8694 (0.649;1.090) 0.0000 (-1.156;1.156) 0.0000 (-10.711;10.711) 0.869 57.99% 7 -0.0009 (-0.008;0.006) 0.9994 (0.942;1.057) 0.0006 (-0.298;0.300) 0.0000 (-2.786;2.786) 96.24% -0.0009 (-0.008;0.006) 0.9994 (0.942;1.057) 0.0006 (-0.298;0.300) 0.0000 (-2.786;2.786) 1.000 96.24% 8 -0.0017 (-0.009;0.005) 1.0000 (0.941;1.059) 0.0000 (-0.309;0.309) 0.0000 (-2.880;2.880) 96.03% -0.0017 (-0.009;0.005) 1.0000 (0.941;1.059) 0.0000 (-0.309;0.309) 0.0000 (-2.880;2.880) 1.000 96.03% 9 -0.0029 (-0.010;0.004) 1.0000 (0.942;1.058) 0.0000 (-0.302;0.302) 0.0000 (-2.811;2.811) 96.24% -0.0029 (-0.010;0.004) 1.0000 (0.942;1.058) 0.0000 (-0.302;0.302) 0.0000 (-2.811;2.811) 1.000 96.24% 10 -0.0001 (-0.010;0.010) 0.9749 (0.893;1.057) 0.0000 (-0.425;0.425) 0.0251 (-3.938;3.988) 92.27% 0.0000 (-0.010;0.010) 0.9747 (0.893;1.056) 0.0000 (-0.425;0.425) 0.0000 (-3.963;3.963) 0.975 92.27% 11 0.0062 (-0.001;0.013) 0.9109 (0.744;1.078) 0.0891 (-0.774;0.952) 0.0000 (-0.000;+0.000) 71.46% 0.0062 (-0.015;0.027) 0.9109 (0.741;1.081) 0.0891 (-0.774;0.953) 0.0000 (-8.653;8.653) 1.000 71.46% 12 0.0031 (-0.021;0.027) 0.6953 (0.498;0.893) 0.0000 (-0.687;0.687) 0.3047 (-11.629;12.238) 58.77% 0.0031 (-0.021;0.027) 0.6953 (0.498;0.893) 0.0000 (-0.687;0.687) 0.3047 (-11.629;12.238) 1.000 58.77% 13 -0.0009 (-0.006;0.004) 0.8964 (0.774;1.019) 0.1036 (-0.545;0.753) 0.0000 (-0.000;+0.000) 81.21% -0.0009 (-0.006;0.004) 0.8964 (0.774;1.019) 0.1036 (-0.545;0.753) 0.0000 (-0.000;+0.000) 1.000 81.21% 14 0.0007 (-0.024;0.026) 1.0000 (0.789;1.211) 0.0000 (-0.733;0.733) 0.0000 (-12.812;12.812) 71.38% 0.0007 (-0.024;0.026) 1.0000 (0.789;1.211) 0.0000 (-0.733;0.733) 0.0000 (-12.812;12.812) 1.000 71.38%

β0 β1 β2 β3 Adj. R 2 β0 β1 β2 β3 Σ β Adj. R 2 15 0.0024 (-0.021;0.026) 0.6523 (0.477;0.828) 0.1105 (-0.769;0.990) 0.2371 (-9.716;10.191) 54.85% 0.0031 (-0.020;0.026) 0.6466 (0.471;0.822) 0.0747 (-0.804;0.954) 0.0000 (-9.947;9.947) 0.721 54.85% 16 0.0019 (-0.002;0.006) 0.9047 (0.806;1.003) 0.0953 (-0.428;0.618) 0.0000 (-0.000;+0.000) 87.05% 0.0019 (-0.010;0.014) 0.9047 (0.804;1.005) 0.0953 (-0.428;0.619) 0.0000 (-4.876;4.876) 1.000 87.05% 17 0.0064 (-0.007;0.020) 0.4619 (0.346;0.578) 0.1312 (-0.475;0.737) 0.4070 (-5.237;6.051) 54.69% 0.0064 (-0.007;0.020) 0.4619 (0.346;0.578) 0.1312 (-0.475;0.737) 0.4070 (-5.237;6.051) 1.000 54.69% 18 0.0072 (-0.007;0.022) 0.8011 (0.679;0.924) 0.1585 (-0.480;0.797) 0.0403 (-5.909;5.990) 77.34% 0.0072 (-0.007;0.022) 0.8011 (0.679;0.924) 0.1585 (-0.480;0.797) 0.0403 (-5.909;5.990) 1.000 77.34% 19 0.0026 (-0.019;0.024) 0.9197 (0.797;1.042) 0.0355 (-0.544;0.615) 0.0448 (-10.599;10.689) 86.88% 0.0026 (-0.019;0.024) 0.9197 (0.797;1.042) 0.0355 (-0.544;0.615) 0.0448 (-10.599;10.689) 1.000 86.88% 20 0.0002 0.6669 0.0000 0.3331 57.39% 0.0002 0.6669 0.0000 0.3331 1.000 57.39% (-0.029;0.029) (0.485;0.849) (-0.722;0.722) (-14.287;14.953) (-0.029;0.029) (0.485;0.849) (-0.722;0.722) (-14.287;14.953) 21 -0.0004 (-0.014;0.013) 1.0000 (0.889;1.111) 0.0000 (-0.380;0.380) 0.0000 (-6.711;6.711) 91.05% -0.0004 (-0.014;0.013) 1.0000 (0.889;1.111) 0.0000 (-0.380;0.380) 0.0000 (-6.711;6.711) 1.000 91.05% 22 0.0028 (-0.019;0.025) 0.9202 (0.796;1.044) 0.0467 (-0.535;0.628) 0.0331 (-10.799;10.865) 86.98% 0.0028 (-0.019;0.025) 0.9203 (0.796;1.044) 0.0476 (-0.534;0.629) 0.0321 (-10.800;10.864) 1.000 86.98% 23 -0.0016 (-0.013;0.010) 0.8763 (0.780;0.973) 0.0672 (-0.435;0.570) 0.0564 (-4.623;4.736) 87.16% -0.0014 (-0.013;0.010) 0.8734 (0.777;0.970) 0.0467 (-0.455;0.549) 0.0000 (-4.678;4.678) 0.920 87.16% 24 0.0122 (-0.023;0.047) 1.0000 (0.779;1.221) 0.0000 (-1.034;1.034) 0.0000 (-16.456;16.456) 76.40% 0.0122 (-0.023;0.047) 1.0000 (0.779;1.221) 0.0000 (-1.034;1.034) 0.0000 (-16.456;16.456) 1.000 76.40% 25 -0.0008 (-0.018;0.016) 1.0000 (0.894;1.106) 0.0000 (-0.487;0.487) 0.0000 (-7.848;7.848) 90.53% -0.0008 (-0.018;0.016) 1.0000 (0.894;1.106) 0.0000 (-0.487;0.487) 0.0000 (-7.848;7.848) 1.000 90.53% 26 -0.0017 (-0.008;0.004) 0.8949 (0.843;0.947) 0.0580 (-0.211;0.327) 0.0471 (-2.464;2.558) 96.14% -0.0015 (-0.008;0.005) 0.8913 (0.840;0.943) 0.0316 (-0.238;0.301) 0.0000 (-2.508;2.508) 0.923 96.14% 27 -0.0011 (-0.010;0.008) 0.9936 (0.919;1.068) 0.0064 (-0.380;0.393) 0.0000 (-3.599;3.599) 93.84% -0.0011 (-0.010;0.008) 0.9936 (0.919;1.068) 0.0064 (-0.380;0.393) 0.0000 (-3.599;3.599) 1.000 93.84% 28 0.0042 (-0.021;0.030) 0.5814 (0.421;0.741) 0.4186 (-0.330;1.168) 0.0000 (-11.919;11.919) 54.49% 0.0042 (-0.021;0.030) 0.5791 (0.419;0.739) 0.4032 (-0.346;1.152) 0.0000 (-11.918;11.918) 0.982 54.49%

(Continúa pág. sig.)

T ABLE 1 (cont.) S TYLE A LLOCA TIONS OF S P ANISH PENSION PLANS INVESTING IN W ORLD E QUITIES *

The table is divided in two parts. The left part includes the style allocations considering the

strong version

of the style model and the right part gathers the results relaxing

β0 β1 β2 β3 Adj. R 2 β0 β1 β2 β3 Σ β Adj. R 2 29 0.0051 (-0.013;0.023) 0.8244 (0.697;0.951) 0.0000 (-0.000;+0.000) 0.1756 (-7.134;7.485) 71.29% 0.0055 (-0.012;0.023) 0.8234 (0.673;0.974) 0.0000 (-0.785;0.785) 0.0000 (-7.316;7.316) 0.823 71.29% 30 -0.0037 (-0.037;0.029) 1.0000 (0.723;1.277) 0.0000 (-1.446;1.446) 0.0000 (-13.468;13.468) 67.95% -0.0037 (-0.037;0.029) 1.0000 (0.723;1.277) 0.0000 (-1.446;1.446) 0.0000 (-13.468;13.468) 1.000 67.95% 31 0.0001 (-0.014;0.014) 0.7730 (0.654;0.892) 0.2270 (-0.423;0.877) 0.0000 (-5.432;5.432) 84.04% 0.0001 (-0.014;0.014) 0.7730 (0.654;0.892) 0.2270 (-0.423;0.877) 0.0000 (-5.432;5.432) 1.000 84.04% 32 0.0022 (-0.008;0.013) 0.6159 (0.528;0.704) 0.0000 (-0.459;0.459) 0.3841 (-3.895;4.663) 80.16% 0.0031 (-0.007;0.014) 0.6140 (0.526;0.702) 0.0000 (-0.459;0.459) 0.0000 (-4.275;4.275) 0.614 80.27% 33 0.0017 (-0.020;0.023) 1.0000 (0.821;1.179) 0.0000 (-0.624;0.624) 0.0000 (-10.852;10.852) 82.39% 0.0017 (-0.020;0.023) 1.0000 (0.821;1.179) 0.0000 (-0.624;0.624) 0.0000 (-10.852;10.852) 1.000 82.39% 34 0.0018 (-0.020;0.023) 1.0000 (0.821;1.179) 0.0000 (-0.624;0.624) 0.0000 (-10.854;10.854) 82.39% 0.0018 (-0.020;0.023) 1.0000 (0.821;1.179) 0.0000 (-0.624;0.624) 0.0000 (-10.854;10.854) 1.000 82.39% 35 -0.0017 (-0.005;0.001) 0.9007 (0.828;0.974) 0.0993 (-0.288;0.486) 0.0000 (-0.000;+0.000) 92.38% -0.0017 (-0.011;0.007) 0.9007 (0.826;0.975) 0.0993 (-0.288;0.486) 0.0000 (-3.608;3.608) 1.000 92.38% 36 0.0034 (-0.008;0.015) 0.8866 (0.793;0.980) 0.1134 (-0.367;0.594) 0.0000 (-4.765;4.765) 88.51% 0.0034 (-0.008;0.015) 0.8865 (0.793;0.980) 0.1135 (-0.367;0.594) 0.0000 (-4.765;4.765) 1.000 88.51% 37 -0.0040 (-0.014;0.006) 0.8583 (0.776;0.941) 0.0000 (-0.431;0.431) 0.1417 (-3.870;4.154) 90.08% -0.0040 (-0.014;0.006) 0.8583 (0.776;0.941) 0.0000 (-0.431;0.431) 0.1417 (-3.870;4.154) 1.000 90.08% 38 -0.0013 (-0.010;0.007) 1.0000 (0.929;1.071) 0.0000 (-0.371;0.371) 0.0000 (-3.454;3.454) 94.47% -0.0013 (-0.010;0.007) 1.0000 (0.929;1.071) 0.0000 (-0.371;0.371) 0.0000 (-3.454;3.454) 1.000 94.47% 39 0.0008 (-0.009;0.010) 0.6345 (0.405;0.864) 0.3655 (-0.851;1.582) 0.0000 (-0.000;+0.000) 35.89% 0.0008 (-0.027;0.029) 0.6345 (0.401;0.868) 0.3655 (-0.852;1.583) 0.0000 (-11.346;11.346) 1.000 35.89% 40 -0.0031 (-0.021;0.015) 0.6786 (0.528;0.829) 0.1441 (-0.638;0.926) 0.1772 (-7.110;7.465) 61.37% -0.0023 (-0.020;0.016) 0.6665 (0.517;0.816) 0.0552 (-0.726;0.836) 0.0000 (-7.275;7.275) 0.722 61.58% 41 0.0010 (-0.019;0.021) 0.8985 (0.728;1.069) 0.0888 (-0.799;0.977) 0.0127 (-8.258;8.283) 69.20% 0.0014 (-0.019;0.022) 0.8883 (0.718;1.059) 0.0092 (-0.878;0.897) 0.0000 (-8.268;8.268) 0.898 69.20% 42 0.0065 (-0.007;0.020) 0.4633 (0.347;0.580) 0.1360 (-0.471;0.743) 0.4007 (-5.257;6.059) 54.69% 0.0065 (-0.007;0.020) 0.4633 (0.347;0.580) 0.1360 (-0.471;0.743) 0.4007 (-5.257;6.059) 1.000 54.69%

(Continúa pág. sig.)

T ABLE 1 (cont.) S TYLE A LLOCA TIONS OF S P ANISH PENSION PLANS INVESTING IN W ORLD E QUITIES *

The table is divided in two parts. The left part includes the style allocations considering the

strong version

of the style model and the right part gathers the results relaxing

β0 β1 β2 β3 Adj. R 2 β0 β1 β2 β3 Σ β Adj. R 2 43 -0.0022 (-0.009;0.005) 0.9926 (0.932;1.054) 0.0074 (-0.311;0.325) 0.0000 (-2.962;2.962) 95.72% -0.0022 (-0.009;0.005) 0.9926 (0.932;1.054) 0.0074 (-0.311;0.325) 0.0000 (-2.962;2.962) 1.000 95.72% 44 -0.0024 (-0.010;0.005) 1.0000 (0.937;1.063) 0.0000 (-0.330;0.330) 0.0000 (-3.073;3.073) 95.51% -0.0024 (-0.010;0.005) 1.0000 (0.937;1.063) 0.0000 (-0.330;0.330) 0.0000 (-3.073;3.073) 1.000 95.51% 45 0.0027 (-0.018;0.023) 0.9218 (0.783;1.060) 0.0782 (-0.418;0.574) 0.0000 (-10.467;10.467) 82.38% 0.0027 (-0.018;0.023) 0.9218 (0.783;1.060) 0.0782 (-0.418;0.574) 0.0000 (-10.467;10.467) 1.000 82.38% 46 0.0023 (-0.015;0.020) 0.9162 (0.806;1.026) 0.0838 (-0.446;0.613) 0.0000 (-8.187;8.187) 87.03% 0.0023 (-0.015;0.020) 0.9161 (0.806;1.026) 0.0839 (-0.446;0.613) 0.0000 (-8.187;8.187) 1.000 87.03% 47 0.0013 (-0.018;0.021) 0.8314 (0.667;0.996) 0.0000 (-0.858;0.858) 0.1686 (-7.827;8.164) 67.84% 0.0013 (-0.018;0.021) 0.8314 (0.667;0.996) 0.0000 (-0.858;0.858) 0.1686 (-7.827;8.164) 1.000 67.84% 48 0.0027 (-0.007;0.012) 0.6670 (0.589;0.746) 0.0405 (-0.368;0.449) 0.2925 (-3.517;4.102) 85.70% 0.0027 (-0.007;0.012) 0.6670 (0.589;0.746) 0.0405 (-0.368;0.449) 0.2925 (-3.517;4.102) 1.000 85.70% *

The numbers in bold are identifi

cation numbers allocated randomly

. The names of the portfolios are available upon request to

the authors. The results reported in the table correspond to those pension plans with at least 36 obser

vations during the time

period analysed

(Januar

y 2001-December 2006). The numbers in parentheses show the confi

dence inter

vals at 5%.

T ABLE 1 (cont.) S TYLE A LLOCA TIONS OF S P ANISH PENSION PLANS INVESTING IN W ORLD E QUITIES *

The table is divided in two parts. The left part includes the style allocations considering the

strong version

of the style model and the right part gathers the results relaxing

T ABLE 2 S TYLE A LLOCA TIONS OF S P ANISH PENSION PLANS INVESTING IN E URO Z ONE E QUITIES β0 β1 β2 β3 Adj. R 2 β0 β1 β2 β3 Σ β Adj. R 2 1 -0.0028 (-0.007;0.001) 0.9128 (0.844;0.981) 0.0872 (-0.370;0.545) 0.0000 (-0.000;+0.000) 93.21% -0.0028 (-0.014;0.008) 0.9128 (0.842;0.983) 0.0872 (-0.371;0.545) 0.0000 (-4.370;4.370) 1.000 93.21% 2 -0.0020 (-0.029;0.025) 0.9112 (0.716;1.107) 0.0888 (-0.703;0.881) 0.0000 (-13.778;13.778) 72.07% -0.0020 (-0.029;0.025) 0.9112 (0.716;1.107) 0.0888 (-0.703;0.881) 0.0000 (-13.778;13.778) 1.000 72.07% 3 -0.0010 (-0.058;0.056) 0.6118 (0.442;0.782) 0.0000 (-0.830;0.830) 0.3882 (-31.803;32.579) 61.26% -0.0003 (-0.058;0.057) 0.6110 (0.441;0.781) 0.0000 (-0.829;0.829) 0.0000 (-32.167;32.167) 0.611 61.26% 4 -0.0005 (-0.028;0.027) 0.7902 (0.657;0.923) 0.0000 (-0.806;0.806) 0.2098 (-12.721;13.141) 77.68% 0.0000 (-0.028;0.028) 0.7892 (0.656;0.922) 0.0000 (-0.805;0.805) 0.0000 (-12.925;12.925) 0.789 77.68% 5 -0.0008 (-0.019;0.017) 0.7712 (0.655;0.887) 0.0000 (-0.755;0.755) 0.2288 (-6.978;7.435) 78.28% -0.0003 (-0.018;0.018) 0.7701 (0.654;0.886) 0.0000 (-0.755;0.755) 0.0000 (-7.205;7.205) 0.770 78.28% 6 -0.0006 (-0.019;0.018) 0.8027 (0.685;0.921) 0.0215 (-0.748;0.791) 0.1758 (-7.163;7.515) 78.91% -0.0006 (-0.019;0.018) 0.8027 (0.685;0.921) 0.0215 (-0.748;0.791) 0.1758 (-7.163;7.515) 1.000 78.91% 7 0.0052 (-0.009;0.019) 0.5149 (0.423;0.607) 0.0000 (-0.597;0.597) 0.4851 (-5.214;6.185) 71.70% 0.0064 (-0.008;0.020) 0.5127 (0.421;0.604) 0.0000 (-0.596;0.596) 0.0000 (-5.691;5.691) 0.513 71.81% 8 0.0010 (-0.008;0.010) 0.7350 (0.677;0.793) 0.0000 (-0.380;0.380) 0.2650 (-3.360;3.890) 92.90% 0.0010 (-0.008;0.010) 0.7350 (0.677;0.793) 0.0000 (-0.380;0.380) 0.2650 (-3.360;3.890) 1.000 92.90% 9 0.0014 (-0.009;0.012) 0.6768 (0.606;0.747) 0.0646 (-0.394;0.523) 0.2586 (-4.115;4.633) 88.20% 0.0014 (-0.009;0.012) 0.6768 (0.606;0.747) 0.0646 (-0.394;0.523) 0.2586 (-4.115;4.633) 1.000 88.20% 10 -0.0004 (-0.016;0.015) 0.9462 (0.847;1.046) 0.0538 (-0.595;0.702) 0.0000 (-6.186;6.186) 87.99% -0.0004 (-0.016;0.015) 0.9462 (0.847;1.046) 0.0538 (-0.595;0.702) 0.0000 (-6.186;6.186) 1.000 87.99% 11 -0.0007 (-0.019;0.018) 0.7167 (0.631;0.803) 0.0000 (-0.537;0.537) 0.2833 (-8.515;9.082) 87.66% -0.0001 (-0.019;0.018) 0.7158 (0.630;0.802) 0.0000 (-0.536;0.536) 0.0000 (-8.792;8.792) 0.716 87.66% 12 -0.0007 (-0.019;0.018) 0.7169 (0.631;0.803) 0.0000 (-0.535;0.535) 0.2831 (-8.486;9.052) 87.77% -0.0001 (-0.019;0.018) 0.7159 (0.630;0.802) 0.0000 (-0.535;0.535) 0.0000 (-8.762;8.762) 0.716 87.77% 13 -0.0013 (-0.019;0.017) 0.7357 (0.648;0.823) 0.0254 (-0.521;0.572) 0.2389 (-8.015;8.493) 87.99% -0.0007 (-0.019;0.017) 0.7324 (0.645;0.820) 0.0000 (-0.545;0.545) 0.0000 (-8.242;8.242) 0.732 87.99% 14 -0.0009 (-0.019;0.017) 0.7944 (0.678;0.911) 0.0000 (-0.757;0.757) 0.2056 (-7.015;7.426) 79.22% -0.0009 (-0.019;0.017) 0.7944 (0.678;0.911) 0.0000 (-0.757;0.757) 0.2056 (-7.015;7.426) 1.000 79.22% 15 -0.0056 (-0.020;0.008) 0.8662 (0.608;1.124) 0.1338 (-1.587;1.854) 0.0000 (-0.000;+0.000) 46.02% -0.0056 (-0.046;0.035) 0.8662 (0.602;1.131) 0.1338 (-1.588;1.855) 0.0000 (-16.427;16.427) 1.000 46.02%

β0 β1 β2 β3 Adj. R 2 β0 β1 β2 β3 Σ β Adj. R 2 16 0.0022 (-0.016;0.020) 0.6626 (0.569;0.756) 0.1590 (-0.279;0.597) 0.1784 (-9.044;9.401) 82.59% 0.0022 (-0.016;0.020) 0.6626 (0.569;0.756) 0.1590 (-0.279;0.597) 0.1784 (-9.044;9.401) 1.000 82.59% 17 -0.0025 (-0.016;0.011) 0.6261 (0.538;0.714) 0.3739 (-0.205;0.953) 0.0000 (-5.536;5.536) 79.90% -0.0025 (-0.016;0.011) 0.6261 (0.538;0.714) 0.3739 (-0.205;0.953) 0.0000 (-5.536;5.536) 1.000 79.90% 18 -0.0009 (-0.015;0.014) 0.7559 (0.662;0.850) 0.0000 (-0.611;0.611) 0.2441 (-5.589;6.078) 84.13% -0.0009 (-0.015;0.014) 0.7559 (0.662;0.850) 0.0000 (-0.611;0.611) 0.2441 (-5.589;6.078) 1.000 84.13% 19 0.0002 (-0.011;0.012) 0.6880 (0.614;0.762) 0.1740 (-0.309;0.657) 0.1380 (-4.470;4.746) 87.16% 0.0002 (-0.011;0.012) 0.6880 (0.614;0.762) 0.1741 (-0.309;0.657) 0.1379 (-4.470;4.746) 1.000 87.16% 20 -0.0004 (-0.018;0.018) 0.7955 (0.679;0.912) 0.0000 (-0.760;0.760) 0.2045 (-7.042;7.451) 79.12% -0.0004 (-0.018;0.018) 0.7955 (0.679;0.912) 0.0000 (-0.760;0.760) 0.2045 (-7.042;7.451) 1.000 79.12% 21 -0.0012 (-0.029;0.027) 0.9085 (0.705;1.112) 0.0915 (-0.740;0.923) 0.0000 (-14.181;14.181) 71.78% -0.0012 (-0.029;0.027) 0.9081 (0.705;1.111) 0.0919 (-0.739;0.923) 0.0000 (-14.181;14.181) 1.000 71.78% 22 -0.0005 (-0.028;0.027) 0.8894 (0.694;1.085) 0.1106 (-0.681;0.902) 0.0000 (-13.772;13.772) 71.85% -0.0005 (-0.028;0.027) 0.8894 (0.694;1.085) 0.1106 (-0.681;0.902) 0.0000 (-13.772;13.772) 1.000 71.85% 23 -0.0004 (-0.018;0.018) 0.7961 (0.679;0.913) 0.0000 (-0.763;0.763) 0.2039 (-7.078;7.486) 79.01% -0.0004 (-0.018;0.018) 0.7961 (0.679;0.913) 0.0000 (-0.763;0.763) 0.2039 (-7.078;7.486) 1.000 79.01% 24 -0.0006 (-0.015;0.014) 0.7297 (0.650;0.810) 0.0351 (-0.476;0.546) 0.2352 (-6.242;6.712) 88.05% 0.0000 (-0.015;0.015) 0.7270 (0.647;0.807) 0.0158 (-0.495;0.526) 0.0000 (-6.469;6.469) 0.743 88.05% 25 -0.0001 (-0.017;0.017) 0.7080 (0.597;0.819) 0.1345 (-0.588;0.857) 0.1575 (-6.733;7.048) 76.30% 0.0003 (-0.017;0.017) 0.7067 (0.596;0.818) 0.1275 (-0.595;0.850) 0.0000 (-6.890;6.890) 0.834 76.30% 26 0.0023 (-0.023;0.028) 0.5623 (0.439;0.686) 0.2878 (-0.461;1.037) 0.1498 (-11.515;11.814) 64.77% 0.0027 (-0.023;0.028) 0.5601 (0.437;0.683) 0.2698 (-0.479;1.019) 0.0000 (-11.661;11.661) 0.830 64.77% 27 0.0000 (-0.018;0.018) 0.7980 (0.682;0.914) 0.0305 (-0.727;0.788) 0.1715 (-7.053;7.396) 79.22% 0.0000 (-0.018;0.018) 0.7980 (0.682;0.914) 0.0305 (-0.727;0.788) 0.1715 (-7.053;7.396) 1.000 79.22% 28 -0.0006 (-0.010;0.009) 0.7955 (0.733;0.858) 0.0000 (-0.409;0.409) 0.2045 (-3.699;4.108) 92.90% -0.0001 (-0.010;0.010) 0.7945 (0.732;0.857) 0.0000 (-0.409;0.409) 0.0000 (-3.900;3.900) 0.794 92.90% 29 -0.0042 (-0.032;0.023) 0.5652 (0.452;0.679) 0.0000 (-0.000;+0.000) 0.4348 (-12.508;13.377) 64.49% -0.0033 (-0.031;0.024) 0.5638 (0.432;0.695) 0.0000 (-0.811;0.811) 0.0000 (-12.936;12.936) 0.564 64.60% 30 -0.0019 (-0.035;0.031) 0.7648 (0.627;0.902) 0.0000 (-0.000;+0.000) 0.2352 (-15.444;15.914) 69.55% -0.0014 (-0.035;0.032) 0.7636 (0.604;0.923) 0.0000 (-0.983;0.983) 0.0000 (-15.672;15.672) 0.764 69.66%

(Continúa pág. sig.)

T ABLE 2 (cont.) S TYLE A LLOCA TIONS OF S P ANISH PENSION PLANS INVESTING IN E URO Z ONE E QUITIES

β0 β1 β2 β3 Adj. R 2 β0 β1 β2 β3 Σ β Adj. R 2 31 0.0085 (-0.025;0.042) 0.5896 (0.450;0.729) 0.0000 (-0.000;+0.000) 0.4104 (-15.512;16.333) 56.49% 0.0085 (-0.026;0.043) 0.5896 (0.428;0.752) 0.0000 (-0.999;0.999) 0.4104 (-15.513;16.334) 1.000 56.49% 32 -0.0024 (-0.024;0.019) 0.9550 (0.799;1.111) 0.0000 (-0.631;0.631) 0.0450 (-10.934;11.024) 81.24% -0.0024 (-0.024;0.019) 0.9550 (0.799;1.111) 0.0000 (-0.631;0.631) 0.0450 (-10.934;11.024) 1.000 81.24% 33 -0.0016 (-0.012;0.009) 0.9890 (0.941;1.037) 0.0110 (-0.281;0.303) 0.0000 (-4.683;4.683) 97.68% -0.0016 (-0.012;0.009) 0.9890 (0.941;1.037) 0.0110 (-0.281;0.303) 0.0000 (-4.683;4.683) 1.000 97.68% 34 0.0061 (-0.014;0.026) 1.0000 (0.871;1.129) 0.0000 (-0.837;0.837) 0.0000 (-7.987;7.987) 83.61% 0.0061 (-0.014;0.026) 1.0000 (0.871;1.129) 0.0000 (-0.837;0.837) 0.0000 (-7.987;7.987) 1.000 83.61% 35 0.0001 (-0.020;0.021) 0.4632 (0.365;0.561) 0.0000 (-0.591;0.591) 0.5368 (-8.954;10.027) 68.63% 0.0012 (-0.019;0.022) 0.4614 (0.364;0.559) 0.0000 (-0.590;0.590) 0.0000 (-9.475;9.475) 0.461 68.74% 36 -0.0009 (-0.008;0.006) 0.8469 (0.712;0.982) 0.1531 (-0.746;1.052) 0.0000 (-0.000;+0.000) 74.94% -0.0009 (-0.022;0.020) 0.8469 (0.709;0.985) 0.1531 (-0.746;1.052) 0.0000 (-8.581;8.581) 1.000 74.94% 37 -0.0008 (-0.012;0.010) 0.7278 (0.655;0.801) 0.0413 (-0.435;0.518) 0.2309 (-4.316;4.778) 88.93% -0.0002 (-0.011;0.011) 0.7241 (0.651;0.797) 0.0122 (-0.464;0.488) 0.0000 (-4.539;4.539) 0.736 88.93% 38 -0.0003 (-0.018;0.017) 0.7914 (0.675;0.908) 0.0000 (-0.756;0.756) 0.2086 (-7.008;7.425) 79.12% -0.0003 (-0.018;0.017) 0.7914 (0.675;0.908) 0.0000 (-0.756;0.756) 0.2086 (-7.008;7.425) 1.000 79.12% 39 -0.0029 (-0.017;0.011) 0.7466 (0.669;0.825) 0.0000 (-0.000;+0.000) 0.2534 (-5.384;5.891) 84.65% -0.0023 (-0.016;0.012) 0.7450 (0.654;0.836) 0.0000 (-0.590;0.590) 0.0000 (-5.631;5.631) 0.745 84.65% 40 0.0005 (-0.017;0.018) 0.6889 (0.577;0.800) 0.0000 (-0.726;0.726) 0.3111 (-6.614;7.236) 75.57% 0.0013 (-0.016;0.018) 0.6874 (0.576;0.799) 0.0000 (-0.725;0.725) 0.0000 (-6.922;6.922) 0.687 75.57% 41 -0.0030 (-0.032;0.026) 1.0000 (0.811;1.189) 0.0000 (-1.233;1.233) 0.0000 (-11.764;11.764) 70.87% -0.0030 (-0.032;0.026) 1.0000 (0.811;1.189) 0.0000 (-1.233;1.233) 0.0000 (-11.764;11.764) 1.000 70.87% 42 0.0086 (-0.022;0.040) 0.5760 (0.402;0.750) 0.1198 (-0.993;1.232) 0.3042 (-13.303;13.912) 47.72% 0.0086 (-0.022;0.040) 0.5760 (0.402;0.750) 0.1198 (-0.993;1.232) 0.3042 (-13.303;13.912) 1.000 47.72% 43 -0.0029 (-0.016;0.011) 0.7498 (0.673;0.826) 0.0000 (-0.000;+0.000) 0.2502 (-5.283;5.783) 85.28% -0.0023 (-0.016;0.011) 0.7482 (0.659;0.837) 0.0000 (-0.579;0.579) 0.0000 (-5.527;5.527) 0.748 85.28% 44 -0.0023 (-0.015;0.011) 0.7024 (0.618;0.787) 0.0000 (-0.552;0.552) 0.2976 (-4.965;5.560) 84.86% -0.0016 (-0.015;0.011) 0.7005 (0.616;0.785) 0.0000 (-0.550;0.550) 0.0000 (-5.249;5.249) 0.701 84.96% 45 0.0042 (-0.004;0.012) 0.7685 (0.619;0.918) 0.2315 (-0.767;1.230) 0.0000 (-0.000;+0.000) 67.01% 0.0042 (-0.019;0.028) 0.7685 (0.615;0.922) 0.2315 (-0.768;1.231) 0.0000 (-9.534;9.534) 1.000 67.01% 46 0.0053 (-0.001;0.012) 0.8100 (0.688;0.932) 0.1900 (-0.623;1.003) 0.0000 (-0.000;+0.000) 76.93% 0.0053 (-0.014;0.025) 0.8100 (0.685;0.935) 0.1900 (-0.623;1.003) 0.0000 (-7.762;7.762) 1.000 76.93%

(Continúa pág. sig.)

T ABLE 2 (cont.) S TYLE A LLOCA TIONS OF S P ANISH PENSION PLANS INVESTING IN E URO Z ONE E QUITIES

β0

β1

β2 β3

Adj. R

2

β0 β1

β2

β3

Σ

β

Adj. R

2

47

-0.0002

(-0.023;0.023)

0.7858

(0.661;0.910)

0.0678

(-0.728;0.864)

0.1463

(-9.944;10.237)

77.67%

-0.0002

(-0.023;0.023)

0.7858

(0.661;0.910)

0.0678

(-0.728;0.864)

0.1463

(-9.944;10.237)

1.000

77.67%

48

0.0027

(-0.014;0.020)

0.6995

(0.604;0.795)

0.0000

(-0.000;+0.000)

0.3005

(-6.578;7.178)

76.40%

0.0034

(-0.014;0.020)

0.6982

(0.587;0.809)

0.0000

(-0.721;0.721)

0.0000

(-6.880;6.880)

0.698

76.40%

49

-0.0011

(-0.029;0.027)

0.7867

(0.653;0.921)

0.0000

(-0.826;0.826)

0.2133

(-12.958;13.385)

77.56%

-0.0006

(-0.029;0.028)

0.7855

(0.652;0.919)

0.0000

(-0.825;0.825)

0.0000

(-13.162;13.162)

0.786

77.56%

50

-0.0015

(-0.010;0.007)

0.8016

(0.744;0.859)

0.0000

(-0.374;0.374)

0.1984

(-3.367;3.764)

94.15%

-0.0011

(-0.010;0.008)

0.8003

(0.743;0.858)

0.0000

(-0.373;0.373)

0.0000

(-3.556;3.556)

0.800

94.15%

51

0.0020

(-0.002;0.006)

0.7910

(0.717;0.865)

0.2090

(-0.287;0.705)

0.0000

(-0.000;+0.000)

89.56%

0.0020

(-0.010;0.014)

0.7910

(0.715;0.867)

0.2090

(-0.287;0.705)

0.0000

(-4.736;4.736)

1.000

89.56%

*

The numbers in bold are identifi

cation numbers allocated randomly

. The names of the portfolios are available upon request to

the authors. The results reported in the table correspond to those pension plans with at least 36 obser

vations during the time

period analysed

(Januar

y 2001-December 2006). The numbers in parentheses show the confi

dence inter

vals at 5%.

T

ABLE

2 (cont.)

S

TYLE

A

LLOCA

TIONS

OF

S

P

ANISH

PENSION

PLANS

INVESTING

IN

E

URO

Z

ONE

E

plans, respectively. This fi gure shows that there are a considerable number of pension plans with extreme results as well as a high number of managers adding value. Moreover, slightly better results are observed when analysing pension plans that invest in World equities.

FIGURE 1

HISTOGRAMOFTHEPERFORMANCEASSOCIATEDWITHTHEACTIVEMANAGEMENT

This fi gure exhibits the histogram of the performance added or subtracted by active management of the portfolio according to the estimation of Equation 3 for each pension plan included in the different samples of Spanish equity pension plans. The left side of the fi gure shows the histogram for pension plans investing in World equities whereas the histogram of the portfolios investing in Euro Zone equities is displayed in the right side of the fi gure.

Noting that the value of β₀ might be biased when considering the model without the

por-tfolio constraint is important. Since β₀ represents the difference between the actual return

and the style return, whether we let the sum of betas be less than one, the style return

tends to decrease and therefore, the value of β₀ presents an upward bias. For that reason,

and given that the «strong style model» and the alternative one report high adjusted R2_{, we}

think that results of the traditional model fi t better to the performance evaluation purpose. Hence, from hereafter, the performance analysis is based on the results.

Apart from using the intercept β₀, the Sharpe ratio is also employed to evaluate the

per-formance of Spanish equity pension plans. In this sense, De Roon et al. (2004) suggests that this traditional measure could also be a good performance indicator since it does not depend on the estimations of the style model.

E(R_p) – R_f

S_P = —————— (4)

σ(R_p)

where E(R_p) is the average return on portfolio p; R_f is the return of the risk-free asset and

σ (R_p) is the standard deviation in the return on portfolio p.

It is important to note that we calculate three different Sharpe ratios to evaluate the

performance of each portfolio and of each investment style. Firstly, the Sharpe ratio (S_p)

of the actual return and risk assumed by Spanish equity pension plans is calculated.

Secondly, we examine the Sharpe ratio of the style portfolio (S_pstyle) from the return and

risk associated to the strategic allocations (β₁, β₂, β₃) obtained from the RBSA (see

Global: R_Stylep,t = β₁R_MSCIWorld,t + β₂R_FI,t + β₃R_Cash,t

}

Euro Zone: R_Stylep,t = β₁R_MSCIEmu,t + β₂R_FI,t + β₃R_Cash,t

T _[R

Stylep,t – E(RStylep,t)] 2

σ_{Style p} =

[

Σ

]

1/2

(6)

t = 1 T

where T represents the number of months analysed in the period January 2001-December 2006 (T = 72).

The comparison of these two ratios allows us to use the indicator proposed by Sharpe

(1992) (12)_{, which represents the relative effi ciency gained (or lost) by each pension plan.}

PS = S_p – S_pstyle (7)

Therefore, this measure shows the average monthly performance that active management

adds to the mere passive tracking of the style portfolio. Thus, the intercept β₀ and the PS

ratio allow us to evaluate the performance of the active management of Spanish pension plans.

Finally, the Sharpe ratio that could be obtained whether the portfolio had followed an

opti-mum style allocation (S_pstyle*_{) is examined. Considering a similar approach to that proposed}

by Graham and Harvey (1997) in GH1, we suggest an alternative performance measure which is referred to as «return difference». The goal pursued with this measure is to de-termine the average monthly performance that pension managers are losing with respect to the best strategic style that each plan could have followed in terms of the risk-return trade-off.

Hence, we calculate the optimum asset allocation combination (β₁*_{, β}

2

*_{, β}

3

*_{) that provides}

the maximum Sharpe ratio, imposing as previously the positivity and portfolio constraints as well as the investment restriction that requires that more than 75% of the portfolio must

be invested in equities according to Inverco. Therefore, this ratio (S_pstyle*_{) can be obtained}

as follows:

[β*

1 · E(RMSCI) + β

*

2 · E(RFI) + β

*

3 · E(RCash)] – Rf

MaxS_pStyle* _{= ———————————————————————}

σ* Style

}

3

Subject to

_Σ

j= 1 0 ≤β

*

j≤1 β1≥ 0.75

j = 1

Once the optimum effi ciency is calculated, we compute the return associated to this

op-timum effi ciency (S_pStyle*_{) considering the level of risk really assumed by the portfolio as}

follows:

E(R*

p) = SpStyle * _{· σ(R}

p) + Rf (9)

taking into account the level of risk assumed by the portfolio. Therefore, the «return diffe-rence» can be expressed as follows:

Return difference = E(R*

p) – E(Rp) (10)

This metric indicates the performance lost by Spanish pension plans with respect to the

return that could be obtained according to S_pStyle*_{. The interpretation of this measure is}

displayed in Figure 2.

FIGURE 2

DIFFERENCESBETWEENTHEOBJECTIVEANDTHEACTUALRETURN

This fi gure exhibits the graphical interpretation of the «return difference», the new performance metric proposed in this study. Note that R_A (R_B) are the actual return of Portfolio A (B) whereas R*

A (R

*

B) indicates the target return

associate to its level of risk. The slope of the function is indicated in Equation 9.

Tables 3 and 4 show the performance measures examined in each dataset. It can be seen that more than 24% of the Spanish Euro Zone equity pension plans present positive values

of β₀ and PS along with return differences of zero, indicating that their active management

has added value achieving effi cient risk-return trade-offs. This percentage is up to more than 40% in the case of World equity pension plans.

However, in spite of the positive values of the β₀ coeffi cient, these parameters do not tend

to be statistically different from zero. Therefore, the investment in a Spanish pension plan or the construction of our own portfolio makes no difference from a fi nancial perspective. However, other perspectives like the fi scal are important, especially in the case of Spanish pension plans given that these collective investment products have important tax benefi ts.

Furthermore, the rankings provided by the different performance metrics are examined in Table 5. A quick look at this table shows their strong similarity. Hence, the levels of corre-lation between these metrics have been analysed through Pearson’s correcorre-lation coeffi cient. These results are reported in Table 6.

TABLE 3

PERFORMANCE EVALUATIONOF SPANISHPLANSINVESTINGIN WORLD EQUITIES *

β0 Sp SpStyle SpStyle* PS Return Difference

1 -0.00040 0.19776 0.22627 0.25833 -0.02851 0.00199

2 -0.00199 N/A 0.01502 0.04823 N/A 0.00358

3 0.00304 0.54116 0.48263 0.54116 0.05853 0.00000

4 -0.00155 N/A 0.02535 0.04823 N/A 0.00254

5 0.00014 0.35198 0.39603 0.42845 -0.04404 0.00200

6 -0.00388 N/A N/A 0.01892 N/A 0.00506

7 -0.00090 N/A 0.01508 0.04823 N/A 0.00238

8 -0.00170 N/A 0.01502 0.04823 N/A 0.00214

9 -0.00288 N/A 0.01502 0.04823 N/A 0.00439

10 -0.00005 0.01464 0.01640 0.04823 -0.00176 0.00148

11 0.00622 0.17042 0.04024 0.17042 0.13018 0.00000

12 0.00315 0.57510 0.52809 0.57510 0.04701 0.00000

13 -0.00091 0.00243 0.02628 0.02968 -0.02385 0.00117

14 0.00074 0.42182 0.46259 0.50559 -0.04076 0.00217

15 0.00239 0.12191 0.07527 0.12191 0.04664 0.00000

16 0.00185 0.06797 0.02528 0.06797 0.04269 0.00000

17 0.00639 0.31670 0.09204 0.31670 0.22467 0.00000

18 0.00723 0.22057 0.03723 0.22057 0.18334 0.00000

19 0.00256 0.11341 0.05400 0.11341 0.05941 0.00000

20 0.00016 0.25355 0.32035 0.33490 -0.06680 0.00222

21 -0.00036 0.44277 0.49633 0.54214 -0.05356 0.00236

22 0.00281 0.11088 0.04523 0.11088 0.06564 0.00000

23 -0.00158 N/A 0.02595 0.04823 N/A 0.00254

24 0.01223 0.26712 0.06406 0.26712 0.20306 0.00000

25 -0.00083 0.04541 0.06841 0.10251 -0.02299 0.00241

26 -0.00172 N/A 0.02414 0.04823 N/A 0.00269

27 -0.00109 N/A 0.01564 0.04823 N/A 0.00257

28 0.00416 0.25194 0.14348 0.25194 0.10846 0.00000

29 0.00509 0.14354 0.02643 0.14354 0.11711 0.00000

30 -0.00366 N/A 0.01502 0.04823 N/A 0.00654

31 0.00013 N/A N/A N/A N/A N/A

32 0.00224 0.11939 0.04848 0.11939 0.07090 0.00000

33 0.00168 0.46023 0.49024 0.53252 -0.03001 0.00197

β0 Sp SpStyle SpStyle* PS Return Difference

34 0.00176 0.46314 0.49024 0.53252 -0.02710 0.00189

35 -0.00171 N/A 0.02576 0.04823 N/A 0.00265

36 0.00340 0.10083 0.01795 0.10083 0.08288 0.00000

37 -0.00398 N/A 0.02386 0.04823 N/A 0.00498

38 -0.00127 N/A 0.01502 0.04823 N/A 0.00279

39 0.00083 0.06291 0.07377 0.07377 -0.01087 0.00047

40 -0.00310 N/A 0.05026 0.04823 N/A 0.00340

41 0.00103 0.04377 0.02540 0.04823 0.01837 0.00020

42 0.00651 0.32053 0.09215 0.32053 0.22838 0.00000

43 -0.00218 N/A 0.01574 0.04823 N/A 0.00362

44 -0.00241 N/A 0.01502 0.04823 N/A 0.00391

45 0.00268 0.44240 0.39350 0.44240 0.04890 0.00000

46 0.00227 0.14168 0.09101 0.14168 0.05068 0.00000

47 0.00128 0.05095 0.02588 0.05095 0.02507 0.00000

48 0.00270 0.12852 0.04458 0.12852 0.08394 0.00000

* This table shows some Spanish pension plans without a value of Sharpe ratio due to the existence of negative return premium. Some studies in fi nancial literature like Ferruz and Sarto (2004) have documented that in these cases it is not possible to use this ratio because of the inconsistent results provided.

TABLE 4

PERFORMANCE EVALUATIONOF SPANISHPLANSINVESTINGIN EURO ZONE EQUITIES *

β0 Sp SpStyle SpStyle* PS Return Difference

1 -0.00278 N/A 0.02481 0.03329 N/A 0.00326

2 -0.00197 0.41647 0.57946 0.59247 -0.16299 0.00488

3 -0.00097 0.28091 0.39076 0.41420 -0.10985 0.00392

4 -0.00047 0.08263 0.10449 0.11784 -0.02186 0.00102

5 -0.00080 0.00230 0.02150 0.03329 -0.01920 0.00146

6 -0.00059 0.00788 0.02242 0.03329 -0.01454 0.00124

7 0.00523 0.17801 0.02155 0.17801 0.15646 0.00000

8 0.00098 0.04442 0.02151 0.04442 0.02291 0.00000

9 0.00136 0.05845 0.02484 0.05845 0.03361 0.00000

10 -0.00043 0.01421 0.02345 0.03329 -0.00924 0.00104

11 -0.00070 0.08155 0.10521 0.12060 -0.02367 0.00157

12 -0.00069 0.08167 0.10521 0.12060 -0.02354 0.00156

(Continúa pág. sig.)

β0 Sp SpStyle SpStyle* PS Return Difference

13 -0.00130 0.03887 0.07439 0.08696 -0.03552 0.00201

14 -0.00085 0.00161 0.02150 0.02284 -0.01989 0.00103

15 -0.00561 N/A 0.02688 0.03329 N/A 0.00663

16 0.00216 0.46103 0.41263 0.46103 0.04840 0.00000

17 -0.00246 N/A 0.02097 0.02097 N/A 0.00216

18 -0.00091 N/A 0.02150 0.03329 N/A 0.00152

19 0.00017 0.03288 0.03041 0.03329 0.00246 0.00002

20 -0.00037 0.01151 0.02150 0.03329 -0.00999 0.00106

21 -0.00124 0.41525 0.55562 0.56732 -0.14038 0.00431

22 -0.00050 0.46108 0.58104 0.59247 -0.11996 0.00363

23 -0.00040 0.01102 0.02150 0.03329 -0.01047 0.00108

24 -0.00060 0.03937 0.05689 0.06848 -0.01753 0.00122

25 -0.00008 0.02303 0.02817 0.03329 -0.00514 0.00044

26 0.00226 0.17953 0.13944 0.17953 0.04009 0.00000

27 0.00002 0.02089 0.02282 0.03329 -0.00194 0.00060

28 -0.00060 0.00751 0.02150 0.03329 -0.01399 0.00116

29 -0.00419 N/A 0.09574 0.11004 N/A 0.00534

30 -0.00186 0.04173 0.09561 0.11004 -0.05388 0.00324

31 0.00854 0.28497 0.09572 0.28497 0.18925 0.00000

32 -0.00237 0.43369 0.57354 0.57668 -0.13985 0.00386

33 -0.00155 0.07375 0.10485 0.11784 -0.03110 0.00230

34 0.00615 0.12134 0.02148 0.12134 0.09987 0.00000

35 0.00010 0.09149 0.10474 0.11784 -0.01325 0.00076

36 -0.00088 0.00745 0.02782 0.03329 -0.02037 0.00136

37 -0.00084 0.00210 0.02348 0.03329 -0.02138 0.00130

38 -0.00034 0.01217 0.02150 0.03329 -0.00932 0.00102

39 -0.00287 N/A 0.02151 0.03329 N/A 0.00345

40 0.00053 0.03131 0.02151 0.03329 0.00980 0.00008

41 -0.00302 N/A 0.02148 0.03329 N/A 0.00407

42 0.00864 0.23346 0.05173 0.23346 0.18173 0.00000

43 -0.00287 N/A 0.02150 0.03329 N/A 0.00345

44 -0.00229 N/A 0.02151 0.03329 N/A 0.00284

45 0.00425 0.10966 0.03213 0.10966 0.07753 0.00000

(Continúa pág. sig.)

TABLE 4 (cont.)

β0 Sp SpStyle SpStyle* PS Return Difference

46 0.00534 0.13398 0.02974 0.13398 0.10425 0.00000

47 -0.00022 0.04716 0.05840 0.06848 -0.01124 0.00102

48 0.00269 0.08083 0.02151 0.08083 0.05932 0.00000

49 -0.00109 0.06136 0.09561 0.11004 -0.03424 0.00226

50 -0.00152 N/A 0.02150 0.03329 N/A 0.00208

51 0.00200 0.07368 0.03079 0.07368 0.04289 0.00000

* This table shows some Spanish pension plans without a value of Sharpe ratio due to the existence of negative premium. Some studies in fi nancial literature like Ferruz and Sarto (2004) have documented that in these cases it is not possible to use this ratio because of the inconsistent results provided.

TABLE 5

PERFORMANCERANKINGS

PANEL A: WORLD EQUITY PANEL B: EURO ZONE EQUITY

β0 PS Return Difference β0 PS Return Difference

24 0.01223 42 0.22838 3 0.00000 42 0.00864 31 0.18925 7 0.00000

18 0.00723 17 0.22467 11 0.00000 31 0.00854 42 0.18173 8 0.00000

42 0.00651 24 0.20306 12 0.00000 34 0.00615 7 0.15646 9 0.00000

17 0.00639 18 0.18334 15 0.00000 46 0.00534 46 0.10425 16 0.00000

11 0.00622 11 0.13018 16 0.00000 7 0.00523 34 0.09987 26 0.00000

29 0.00509 29 0.11711 17 0.00000 45 0.00425 45 0.07753 31 0.00000

28 0.00416 28 0.10846 18 0.00000 48 0.00269 48 0.05932 34 0.00000

36 0.0034 48 0.08394 19 0.00000 26 0.00226 16 0.0484 42 0.00000

12 0.00315 36 0.08288 22 0.00000 16 0.00216 51 0.04289 45 0.00000

3 0.00304 32 0.0709 24 0.00000 51 0.002 26 0.04009 46 0.00000

22 0.00281 22 0.06564 28 0.00000 9 0.00136 9 0.03361 48 0.00000

48 0.0027 19 0.05941 29 0.00000 8 0.00098 8 0.02291 51 0.00000

45 0.00268 3 0.05853 32 0.00000 40 0.00053 40 0.0098 19 0.00002

19 0.00256 46 0.05068 36 0.00000 19 0.00017 19 0.00246 40 0.00008

15 0.00239 45 0.0489 42 0.00000 35 0.0001 27 -0.00194 25 0.00044

46 0.00227 12 0.04701 45 0.00000 27 0.00002 25 -0.00514 27 0.0006

32 0.00224 15 0.04664 46 0.00000 25 -0.00008 10 -0.00924 35 0.00076

16 0.00185 16 0.04269 47 0.00000 47 -0.00022 38 -0.00932 4 0.00102

34 0.00176 47 0.02507 48 0.00000 38 -0.00034 20 -0.00999 38 0.00102

33 0.00168 41 0.01837 41 0.0002 20 -0.00037 23 -0.01047 47 0.00102

47 0.00128 10 -0.00176 39 0.00047 23 -0.0004 47 -0.01124 14 0.00103

(Continúa pág. sig.) PERFORMANCE EVALUATIONOF SPANISHPLANSINVESTINGIN EURO ZONE EQUITIES *

PANEL A: WORLD EQUITY PANEL B: EURO ZONE EQUITY

β0 PS Return Difference β0 PS Return Difference

41 0.00103 39 -0.01087 13 0.00117 10 -0.00043 35 -0.01325 10 0.00104

39 0.00083 25 -0.02299 10 0.00148 4 -0.00047 28 -0.01399 20 0.00106

14 0.00074 13 -0.02385 34 0.00189 22 -0.0005 6 -0.01454 23 0.00108

20 0.00016 34 -0.0271 33 0.00197 6 -0.00059 24 -0.01753 28 0.00116

5 0.00014 1 -0.02851 1 0.00199 24 -0.0006 5 -0.0192 24 0.00122

31 0.00013 33 -0.03001 5 0.002 28 -0.0006 14 -0.01989 6 0.00124

10 -0.00005 14 -0.04076 8 0.00214 12 -0.00069 36 -0.02037 37 0.0013

21 -0.00036 5 -0.04404 14 0.00217 11 -0.0007 37 -0.02138 36 0.00136

1 -0.0004 21 -0.05356 20 0.00222 5 -0.0008 4 -0.02186 5 0.00146

25 -0.00083 20 -0.0668 21 0.00236 37 -0.00084 12 -0.02354 18 0.00152

7 -0.0009 2 N/A 7 0.00238 14 -0.00085 11 -0.02367 12 0.00156

13 -0.00091 4 N/A 25 0.00241 36 -0.00088 33 -0.0311 11 0.00157

27 -0.00109 6 N/A 4 0.00254 18 -0.00091 49 -0.03424 13 0.00201

38 -0.00127 7 N/A 23 0.00254 3 -0.00097 13 -0.03552 50 0.00208

4 -0.00155 8 N/A 27 0.00257 49 -0.00109 30 -0.05388 17 0.00216

23 -0.00158 9 N/A 35 0.00265 21 -0.00124 3 -0.10985 49 0.00226

8 -0.0017 23 N/A 26 0.00269 13 -0.0013 22 -0.11996 33 0.0023

35 -0.00171 26 N/A 38 0.00279 50 -0.00152 32 -0.13985 44 0.00284

26 -0.00172 27 N/A 40 0.0034 33 -0.00155 21 -0.14038 30 0.00324

2 -0.00199 30 N/A 2 0.00358 30 -0.00186 2 -0.16299 1 0.00326

43 -0.00218 31 N/A 43 0.00362 2 -0.00197 1 N/A 39 0.00345

44 -0.00241 35 N/A 44 0.00391 44 -0.00229 15 N/A 43 0.00345

9 -0.00288 37 N/A 9 0.00439 32 -0.00237 17 N/A 22 0.00363

40 -0.0031 38 N/A 37 0.00498 17 -0.00246 18 N/A 32 0.00386

30 -0.00366 40 N/A 6 0.00506 1 -0.00278 29 N/A 3 0.00392

6 -0.00388 43 N/A 30 0.00654 39 -0.00287 39 N/A 41 0.00407

37 -0.00398 44 N/A 31 N/A 43 -0.00287 41 N/A 21 0.00431

41 -0.00302 43 N/A 2 0.00488

29 -0.00419 44 N/A 29 0.00534

15 -0.00561 50 N/A 15 0.00663

As expected, positive and high correlation can be observed between the intercept β₀ and

the PS measure because both metrics evaluate the performance added or subtracted by the active management of the portfolio. Furthermore, a negative and high correlation bet-ween the abovementioned measures and the return difference is observed due to the spe-cifi cation of the variable (the best management will be associated with the highest values of

TABLE 5 (cont.)