Global Equity Fund Performance, Portfolio Concentration, and the Fundamental Law of Active Management

Global Equity Fund Performance, Portfolio Concentration, and the Fundamental Law of Active Management Joop Huij and Jeroen Derwall * ABSTRACT This paper investigates the relation between portfolio concentration and the performance of global equity funds. Concentrated funds with higher levels of tracking error display better performance than their more broadly diversified counterparts. We show that the observed relation between portfolio concentration and performance is mostly driven by the breadth of the underlying fund strategies; not just by fund managers willingness to take big bets. Our results indicate that when investors strive to select the best performing funds, they should not only consider fund managers tracking error levels. It is of greater importance that they take into account the extent to which fund managers carefully allocate their risk budget across multiple investment strategies and have concentrated holdings in multiple market segments simultaneously. * Derwall is at Maastricht University and Tilburg University. Huij is at Rotterdam School of Management and Robeco Asset Management. Email addresses are: j.derwall@finance.maastrichtuniversity.nl and jhuij@rsm.nl. We thank Martin Martens, seminar participants at Maastricht University and Robeco Asset Management for helpful comments. The views expressed in this paper are not necessarily those of Robeco Asset Management. 1 Electronic copy available at: http://ssrn.com/abstract=1456352

Global Equity Fund Performance, Portfolio Concentration, and the Fundamental Law of Active Management ABSTRACT This paper investigates the relation between portfolio concentration and the performance of global equity funds. Concentrated funds with higher levels of tracking error display better performance than their more broadly diversified counterparts. We show that the observed relation between portfolio concentration and performance is mostly driven by the breadth of the underlying fund strategies; not just by fund managers willingness to take big bets. Our results indicate that when investors strive to select the best performing funds, they should not only consider fund managers tracking error levels. It is of greater importance that they take into account the extent to which fund managers carefully allocate their risk budget across multiple investment strategies and have concentrated holdings in multiple market segments simultaneously. 2 Electronic copy available at: http://ssrn.com/abstract=1456352

1. INTRODUCTION Several studies based on U.S. equity fund data document that active fund managers who take big bets by holding concentrated portfolios display better performance than managers who hold more diversified portfolios. Kacpercyk, Sialm and Zheng (2005) find that managers of funds who concentrate their holdings in specific industries perform better after controlling for risk using various performance measures. In a similar manner, Baks, Busse and Green (2006) use holdings information to consider managers willingness to take big bets in a relatively small number of stocks. They find that focused managers outperform their more broadly diversified counterparts. In a related study, Cremers and Petajisto (2009) look at funds share of portfolio holdings that differ from the benchmark index and report that funds with the highest active share significantly outperform their benchmark indexes, both before and after expenses. Recently, Amihud and Goyenko (2009) propose to measure portfolio concentration using funds R-squared values obtained by regressing fund returns against several benchmark factors. Their study finds that R-squared values have a negative and significant predictive effect on fund performance, which indicates that managers who generate higher tracking error levels and deviate more from their benchmarks generally do better than those who stay close to their benchmarks. This documented relation between fund performance and managers willingness to take big bets is remarkable and seems to be inconsistent with Grinold s (1989) and Grinold and Kahn s (2000) Fundamental Law of Active Management, which states that the performance of an active strategy is driven by fund manager skill in combination with the strategy s breadth (i.e., the number of independent investment decisions), and 3 Electronic copy available at: http://ssrn.com/abstract=1456352

not necessarily by tracking error. 1 The main objective of this study is to get a better understanding of how fund performance, managers willingness to take big bets, and the breadth of the underlying strategies are interrelated. To achieve this objective, we study global equity mutual funds, which have a relatively wide breadth of investment opportunities. 2 To quantify the breadth of the underlying fund strategies we use a definition that is in line with the one used by Grinold and Kahn (2000) and Chincarini and Kim (2006) and take the number of predictive factors to which the funds are exposed. We group factors into three different classes to capture distinctive dimensions of risk, or market segments, which ensures that breadth reflects diversification across independent investment opportunities: styles (i.e., market capitalization and valuation multiples), countries, and sectors. Consistent with the aforementioned studies we find that global equity funds with higher levels of tracking error and more concentrated portfolios display better performance than funds with more diversified portfolios. Interestingly, at the same time we find that funds that are concentrated in both styles, sectors and countries have higher tracking error levels than funds that are only concentrated in one or two of the 1 There are more good reasons why the documented relation between fund performance and managers willingness to take big bets is remarkable: Brown, Harlow and Starks (1996) document that managers with the poorest year-to-date performance typically increase risk to levels that are consistent with their own interest but not with that of their shareholders. Also, Huang, Clemens and Sialm (2009) and Brown and van Harlow (2009) find that funds that increase risk perform worse than funds that keep risk levels stable over time. 2 Global equity mutual funds invest in companies around the world, including U.S. companies. These funds are different from international funds, which mainly invest in companies that are headquartered outside the U.S. 4

market segments. In other words, fund managers willingness to take big bets and the breadth of strategies they follow appears to be positively correlated. But when we double sort funds, first based on their tracking error levels and then on the number of market segments to which they are exposed, it appears that fund performance is mostly driven by the latter. Within groups of funds with different levels of tracking error, we observe a positive relation between the number of segments to which the funds are exposed and their performance. In fact, funds with high tracking-error levels that are exposed to only one or two segments do not display outperformance and might even display underperformance. Moreover, funds with lower tracking-error levels that are exposed to all three segments do not display any differential performance at all. The underperformance in the group of low tracking-error funds can fully be attributed to funds that are exposed to only one, or two, segments. Our findings shed new light on the relation between portfolio concentration and fund performance. It appears that this relation is more complex than documented in earlier studies and that there is an important interaction with the breadth of the underlying fund strategies. The strong positive relation between fund performance and the breadth of the underlying strategies we find is in line with the Fundamental Law of Active Management. The results of our study also have significant implications for mutual fund investors. Investors who strive to select the best performing funds should not only consider fund managers preference for taking big bets. More important is that investors take into account the extent to which fund managers carefully allocate their risk budgets 5

across multiple investment strategies and concentrate portfolio holdings in multiple market segments at the same time. The rest of the paper is organized as follows. In Section 2 we describe the data we use in this study. Section 3 presents our empirical findings. Section 4 provides robustness checks. Section 5 concludes. 2. MUTUAL FUND DATA We obtain return data on global equity funds from the 2007 Morningstar database. The database covers monthly returns for global equity funds up to December 2007. By extending the universe of funds to the global spectrum, we are not only able to investigate portfolio concentration in industries or sectors, but also in countries. This enables us to investigate the interaction between portfolio concentration in these different market segments and fund performance. As we mentioned in the previous section, these interactions turn out to be of great importance when it comes to understanding the relation between portfolio concentration and the performance of global equity funds. Given the small cross-section of global equity funds before the 90s, and given that high-quality data on sector index returns are only available as from 1995, our sample covers the period January 1995 to December 2007. Over this period, our sample holds 555 global equity funds. We exclude 19 funds from our sample that have less than 36 consecutive return observations. This brings our sample to 536 funds. 6

Because our methodology only requires fund return data that are readily available, our sample basically covers all funds that existed during our sample period. Therefore, the effects that selection bias and survivorship bias described in Brown, Goetzmann, Ibbotson and Ross (1992) could have on the results of this study are likely to be insignificant. We conjecture that the holdings-based approach that is sometimes seen in related studies are much more sensitive to survivorship bias. Fund holdings data are compiled from mandatory SEC filings, but also from voluntary disclosures by mutual funds. It could well be the case that holdings disclosures are endogenous in the sense that fund managers are more likely to report holdings after good performance than after poor performance. In that case, there may be a spurious positive relation between portfolio concentration and fund performance, because both funds with good and poor performance by definition have concentrated holdings and only the funds with good performance are included in the analysis (because these are the funds that disclose their holdings). Since our return-based analysis includes all funds that existed during our sample period, our results alleviate concerns that the reported relation between portfolio concentration and fund performance can (partly) be attributed to a form of selection or survivorship bias. We also hasten to comment that a returns-based approach is favorable especially in the context of evaluating global equity funds, because detailed holdings information involving non-u.s. funds is scarce and very difficult to obtain. 7

3. EMPIRICAL RESULTS This section presents our empirical results. We first investigate the performance of concentrated versus diversified funds. Next, we examine the relation between fund performance and the breadth of the underlying strategies. In particular, we investigate if diversifying bets across multiple market segments affects performance. 3.1 The performance of concentrated versus diversified funds We start our empirical analysis by investigating the relation between portfolio concentration and fund performance. Recent empirical studies based on U.S mutual funds suggest that funds with concentrated holdings and hence higher tracking-error levels - deliver superior performance. This observation is consistent with the notion that managers with superior information about specific capital market segments tend to exploit their skill by holding portfolios that have a relatively high concentration in those segments. To see whether a positive relation between portfolio concentration and performance also exists for our sample of global equity mutual funds, we examine if any differential performance can be observed between funds with different levels of trackingerror. Consistent with Cremers and Petajisto (2009) and Amihud and Goyenko (2009), we take the R-squared value from regressing fund returns relative to market returns as a measure of fund managers willingness to take big bets and hold concentrated portfolios: 8

Equation (1): r i, t = α i + β1, i RMRFt + ε i, t where r i, t is the excess return of fund i at month t, and RMRF t is the excess return on the MSCI World index at month t. The one-month T-bill rate from Ibbotson is taken as a measure of the risk-free rate to compute excess returns. The market model in Equation (1) is estimated for each fund using its entire return history. Funds that have a belowmedian R-squared value in this regression are funds with relatively high levels of idiosyncratic risk and are grouped into the HIGH tracking-error group. Funds that have an above-median R-squared value are grouped into the LOW tracking-error group. To evaluate fund performance, we take the intercept from the market model in Equation (1). This intercept, known as Jensen s (1969) alpha, reflects a fund s return that is not due to its sensitivity to returns of the global market portfolio (i.e., beta ). In addition, we measure performance adjusted for residual risk, using the Information Ratio as performance measure. We refer to Goodwin (1998) for a discussion of this measure. The Information Ratio is here defined as the alpha of a fund divided by the standard deviation of the fund s residual returns, which is also obtained using the market model in Equation (1). To ensure that our results are not driven by a few outliers, we normalize and windsordize fund alphas: Equation (2): z _ Alpha i = min 3,max 3, α i µ α σ α 9

where µ α is the average fund alpha obtained from the global market model and σ α is the standard deviation. Information Ratios are standardized in the same way we standardize fund alphas. [INSERT TABLE 1 ABOUT HERE] We now evaluate the standardized alphas and Information Ratios for the HIGH and LOW tracking-error groups. The results are in Panel A of Table 1. It appears that HIGH tracking-error funds have a relatively higher standardized alpha compared to LOW tracking-error funds: 0.22 versus -0.20. Not surprisingly HIGH tracking-error funds have a lower R-squared from the market model regression, compared to LOW tracking-error funds. The conclusions about the relation between concentration and performance remain unaffected when we measure fund performance using the Information Ratio: HIGH tracking-error funds have a superior standardized Information Ratio compared to LOW tracking-error funds: 0.15 versus -0.16. The results are statistically significant using both performance measures. These results are consistent with the findings of Kacpercyk, Sialm and Zheng (2005), Baks, Busse and Green (2006), Cremers and Petajisto (2009) and Ahimud and Goyenko (2009) and support the notion that fund managers who take big bets by holding concentrated portfolios display better performance than passive managers who hold more diversified portfolios. To investigate if the performance differences are concentrated in a specific subperiod, we perform several additional tests. First, we split our sample in half and repeat our analysis for the subperiods January 1995 to December 2001 and January 2002 to December 2007. The results are presented in Panels B and C, respectively, of 10

Table 1. The standardized alphas for the LOW and HIGH tracking-error groups are - 0.18 and 0.24, respectively, for the first subperiod. These figures are -0.24 and 0.26 for the second subperiod. When we consider the groups standardized Information Ratios, we find similar results. The performance differences are statistically highly significant for both subperiods. Additionally, we consider the cumulative return spread between HIGH and LOW tracking-error groups over time. [INSERT FIGURE 1 ABOUT HERE] The result in Figure 1 corroborates our previous finding that the relatively higher returns that HIGH tracking-error funds have earned are not concentrated in specific periods. We conclude that funds with higher levels of tracking error systematically display better performance than funds with lower levels. The results are both economically and statistically significant using various performance measures. 3.2 Tracking error, fund performance, and the breadth of strategies A deeper understanding of the relation between tracking error levels and fund performance involves an examination of the risk dimensions that global equity mutual funds can bet on. Proceeding further, we examine the relation between fund performance and the breadth of the underlying strategies. In the tradition of Grinold (1989) and Grinold and Kahn (2000), we can define the breadth of a strategy as the number of independent investment decisions (return 11

forecasts) a managers makes. The notion of independence is important because many investment decisions are not uncorrelated but instead driven by a common source of information, i.e., such as a common risk factor. Therefore, to approximate the breadth of the underlying fund strategies we use a definition that is in line with the one used by Chincarini and Kim (2006) and take the number of factors in a predictive model to which the funds are exposed. In particular, we investigate if being exposed to multiple factors simultaneously affects performance. We group factors into three different factor models to capture distinctive dimensions of risk, or market segments, which ensures that breadth reflects diversification across investment opportunities that are independent. The models we consider are based on styles (i.e., market capitalization and valuation multiples), countries and sectors. Our decision to explore these three types of models is motivated by previous related studies. Several studies on international equity mutual funds suggests that multiple common factors jointly do a good job of describing the returns on international equity portfolios (such as Gallo and Swanson (1996)), although other studies suggest a single-factor model is useful (e.g., Cumby and Glen (1990)). Global market, style, country, and sector factors are likely important candidates for inclusion in models of global equity fund returns. For example, a large body of empirical literature has demonstrated the importance of country and industry factors in the explanation of security returns, although the relative importance of these factors is still the subject of debate. 3 In a similar manner, studies have uncovered that information about firm size, stocks value characteristics such as low a P/B ratio, and information 3 See, e.g., Beckers, Grinold, Rudd and Stefek (1992), Heston and Rouwenhorst (1994), Griffin and Karolyi (1998), Cavaglia, Brightman and Aked (2000), Cavaglia and Moroz (2002), and Chen, Bennet and Zheng (2006). 12

about past stock return can be used to identify unique style factors in markets around the world, even after controlling for country and industry effects. 4 To measure funds exposures to styles, sectors and industries we take the incremental adjusted R-squared values of three multifactor models. The first multifactor model measures fund exposures to styles: Equation (3): r i, t = α i + β1, i RMRFt + β 2, ismbt + β3, ihmlt + ε i, t where SMB t is the return differential between the MSCI World Small Cap index and the MSCI World index at month t, and HML t is the return differential between the MSCI World Value index and the MSCI World Growth index at month t. The second multifactor model measures fund exposures to sectors: Equation (4) : r i, t α i + β1, i SECTOR j, t + ε i, t j = where SECTOR, is the excess return on sector j at month t for the following MSCI j t World sector indexes: Energy, Materials, Industrials, Consumer Discretionary, Consumer Staples, Health Care, Financials, IT, Telecom and Communication Services and Utilities. Finally, the third multifactor model measures fund exposures to countries: Equation (5): r i, t α i + β1, icountry j, t + ε i, t j = 4 See, e.g., Lakonishok, Schleifer and Vishny (1994), Fama and French (1992, 1997)), Jegadeesh and Titman (1993), Rouwenhorst (1998), Hamelink, Harasty, and Hillion (2001), Nijman, Swinkels and Verbeek (2004), and Scowcroft (2005)) for evidence on the importance of country, industry and style factors. 13

where COUNTRY, is the excess return on country j at month t for the following MSCI j t World country indexes: United States, United kingdom, Japan, Europe excluding the United Kingdom, Canada, Pacific excluding Japan, emerging Asia and emerging Europe. To investigate if the multifactor models have incremental explanatory power for describing global equity fund returns, we first evaluate the distributional characteristics of their adjusted R-squared values. The multifactor models in Equations (3), (4) and (5) are estimated for each fund using its entire return history. [INSERT TABLE 2 ABOUT HERE] The results in Table 2 indicate that style, sector, and country exposures have incremental explanatory power for describing global equity fund returns. For our sample of global equity funds, all three multifactor models produce regression R-squared values that are on average higher and less variable than the R-squared from a global market model. The average (adjusted) R-squared value is roughly 84 percent for all three multifactor models, while this value is 81 percent for the single-factor model. However, it does not appear to be the case that one of the multifactor models dominates the other models in terms of explanatory power. Moreover, it is unclear if the models capture distinct dimensions of risk, which is important for identifying the breadth of strategies. For example, it could be the case that style factors proxy for the same underlying risks as sector or country factors. To investigate this issue more closely, we compute the differences in adjusted R-squared values between the style, sector, and country models for all funds. If all models capture 14

the same dimensions of risk that determine expected returns, then differences in R- squared across models should be near zero. However, the results in Table 2 indicate that the differences in R-squared values can be quite substantial in some cases. For example, the range between the 10 th and 90 th percentiles of differences in R-squared values between the style and country model is 8 percent. The figures for the differences in R-squared values between the style and sector models and the country and sector models are very similar. These results indicate that style, sector, and country exposures capture distinct dimensions of risk. We now continue our empirical analysis by examining the relation between the number of factors to which the funds are exposed and their performance. For this purpose, we allocate each fund to one of following four groups. Group 0 contains funds for which the R-squared value of the market model is higher than the (adjusted) R- squared values of the three multifactor models. This group thus contains mainly broadly diversified global equity funds that have the least concentration in specific styles, countries or sectors. Group 1 contains funds for which one of the three multifactor models produces a higher adjusted R-squared value than the single-factor market model. Group 2 contains funds for which two of the three multifactor models produce higher adjusted R-squared values than the market model. Finally, group 3 contains funds for which all three multifactor models produce higher adjusted R-squared values than the market model. The latter group therefore includes funds that adopt the largest number of distinctive concentrated strategies, i.e., these funds deviate from a global market portfolio by concentrating their holdings in at least three different market segments: styles, countries and sectors. 15

[INSERT TABLE 3 ABOUT HERE] We now evaluate the performance differentials between the four fund groups. The results are presented in Table 3. The key message from Table 3 is that increasing the breadth of fund strategies increases both tracking error and performance. For example, alpha is the highest and statistically significant for funds that belong to Group 3. The positive relation between funds tracking error levels and breadth leads to the question if large concentrated bets or allocations across multiple strategies positively affect the performance of global equity mutual funds. We could hypothesize that the observed relation between portfolio concentration and performance is mostly driven by fund managers being concentrated in multiple market segments at the same time, not just by fund managers willingness to take big bets. To disentangle these effects, we perform a double-sort of all funds based on the funds levels of tracking error and the breadth of the underlying fund strategies. [INSERT TABLE 4 ABOUT HERE] Table 4 provides the results of first sorting funds based on their tracking error levels into HIGH and LOW tracking-error groups and then within each group further sorting funds based on the number of market segments in which they are invested. It appears that within each tracking-error group, fund performance increases as breadth increases, especially in terms of the Information Ratio. The importance of being concentrated in multiple market segments at the same time appears to be much more pronounced than taking large bets as such. In fact, Table 4 makes apparent that HIGH tracking-error funds that have exposure to only one 16

or two segments do not display outperformance and might even display a much stronger underperformance than LOW tracking-error funds that are exposed to all three market segments. LOW tracking-error funds that are concentrated in all three market segments do not display any underperformance at all, compared to the returns predicted by the global market model. Hence, the underperformance of funds in the LOW tracking-error group can fully be attributed to funds that are exposed to only one or two market segments. In a nutshell, HIGH tracking-error funds only outperform when they have a wide breadth of strategies. 4. ROBUSTNESS CHECKS In this section we perform several tests to examine if our results are robust to various choices we made with respect to the design of our research. 4.1 Alternative classifications for concentration in multiple market segments The key insight from the previous section is that the relation between portfolio concentration and fund performance that previous studies have put forward is mostly driven by fund managers being concentrated in multiple market segments at the same time and not by fund managers willingness to take big bets per se. Of course, this conclusion could depend on our definition of concentration in multiple market segments. We measured the breadth of strategies by looking at the incremental adjusted R- 17

squared values of multifactor models for three market segments. A fund was considered to be exposed to a particular market segment if the multifactor model for that market segment delivered a higher adjusted R-squared value than the market model. However, a visual inspection of the R-squared values of the employed models indicates that the incremental explanatory power of the multifactor models is very marginal in a substantial number of cases. One may therefore wonder how sensitive our results are to imposing minimum threshold levels for models incremental explanatory power. For example, how do the results change if we require the adjusted R-squared values of the multifactor models to be a certain percentage higher than the R-squared value of the market model? To investigate this issue, we repeat the analyses we performed in the previous section, but now we require the adjusted R-squared values of the multifactor models to exceed the R-squared value of the market model with 2.5 percent and 5 percent, respectively. [INSERT TABLE 5 ABOUT HERE] The results of these analyses are presented in Panels A and B of Table 5. As expected, the composition of the fund groups significantly changes when we use these alternative definitions. Because the explanatory power of the multifactor models now should be substantially larger than that of the market model, fewer funds end up in the groups 1, 2 and 3. Nonetheless, our conclusions are hardly affected. Irrespective of whether we require the multifactor models to exceed the R-squared value of the market model with 2.5 percent or 5 percent, our results indicate that increasing breadth leads to both 18

higher tracking error and better performance. Moreover, the results corroborate our earlier finding that the importance of breadth is much more pronounced than taking large bets as such. We can therefore safely conclude that our findings are robust to the definition that we use to measure the breadth of strategies. 4.2 Fund performance estimated relative to style, country and sector models We next investigate if the observed relation between fund alphas and exposures to multiple market segments can be attributed to a possible inability of the market model to fully describe returns in these segments. In that case, fund alphas could to a large extent reflect model misspecification rather than managerial skill. We therefore investigate to which extent the fund alphas can be attributed to constant exposures to the three market segments by evaluating their alphas relative to the multifactor models in Equations (3), (4) and (5). The portion of fund return that is left unexplained by these factor models can be attributed to either stock selection or timing skills, and thus measures managerial skill. [INSERT TABLE 6 ABOUT HERE] The results in Table 6 indicate that our conclusions about managerial skill cannot be attributed to model misspecification. Irrespective of whether we use the style, country or sector model to estimate fund alphas, our results show that (i) funds with higher levels of tracking error display better performance than funds with lower levels, and that (ii) HIGH tracking-error funds with limited breadth do not display outperformance and might even experience a much stronger underperformance than LOW tracking-error funds that 19

have the widest possible breadth. These results corroborate our previous finding that HIGH tracking-error funds only outperform when they are exposed to multiple market segments. 5. SUMMARY AND CONCLUDING COMMENTS Recent evidence from U.S. equity mutual funds suggests that fund managers who are willing to take big bets and hold more concentrated portfolios display better performance than managers who hold more broadly diversified portfolios. We argue that the relation between portfolio concentration and performance depends not only on whether fund managers take large bets as such but also on the breadth of the underlying strategies. Our conclusion emerges from an investigation into the returns of global equity mutual funds from the U.S. fund market. Consistent with earlier studies, we find that concentrated funds with higher tracking-error levels show better performance than their more broadly diversified counterparts. However, we then show that there is a positive correlation between the tracking-error level of a fund and breadth of the underlying strategies, measured by the number of independent market segments to which the fund is exposed. Moreover, it appears that fund performance is mostly driven by the latter. There is a positive relation between the number of market segments in which the funds are concentrated and performance, and this relation is independent of whether the fund have high or low tracking-error levels. In fact, funds that have a high tracking-error level but which are concentrated in only one or two market segments underperform diversified funds that are concentrated in multiple market segments. Funds with a high 20

tracking-error level outperform only when they are concentrated in multiple market segments simultaneously. Our findings shed new light on the relation between portfolio concentration and fund performance and have implications for mutual fund investors. Investors who aim for picking best-performing funds should take into account more than just fund managers willingness to take big bets. What crucially matters is the breadth of the underlying fund strategies, i.e., the extent to which fund managers have concentrated holdings in multiple market segments at the same time. At the very least, our results encourage the refinement of measures of active management. It would be worthwhile to make more salient measures that explicitly portray the different dimensions of active risk taking by a global portfolio manager, and their expected consequences for portfolio performance. 21

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TABLE 1. Tracking error and performance Z_Alpha Z_Information ratio Rsq_Market # Coef t-stat p-val Coef t-stat p-val Panel A. Entire sample 1995-2007 LOW 276-0.20-3.57 0.00-0.16-2.76 0.01 0.89 HIGH 260 0.22 3.79 0.00 0.15 2.57 0.01 0.71 Panel B. 1st period 1995-2001 LOW 152-0.18-2.41 0.02-0.21-2.64 0.01 0.84 HIGH 124 0.24 2.84 0.00 0.26 2.92 0.00 0.62 Panel C. 2nd period 2002-2007 LOW 277-0.24-4.29 0.00-0.18-3.16 0.00 0.93 HIGH 260 0.26 4.49 0.00 0.19 3.21 0.00 0.79 We measure portfolio concentration by taking the R-squared values from the funds after regressing their returns on excess market returns based on the equation: r t i i RMRFt i t (1) i, = α + β1, + ε, where r i, t is the excess return of fund i, and RMRF t is the excess return on the MSCI World index. We estimate the market model described by Equation (1) for each fund based on the fund s entire return history. Funds that have a below (above) median R-squared value in this regression are allocated to the HIGH (LOW) bet size fund group. To evaluate the performance of the funds, we take the intercept from the market model in Equation (1), i.e., alpha. In addition, we use the Information Ratio as performance measure, which is defined as alpha divided by the standard deviation of the fund s residual returns as derived from Equation (1). We present normalized alphas and Information Ratios of HIGH and LOW bet size groups, along with respective t-statisctic and p-value, based on the full-sample period a well as subperiods (1995-2001 and 2002-2007). In addition, we report the groups average R-squared from the market model. 25

TABLE 2. Adjusted R-squared values of market model, style model, country model and sector model Market model Style model Country model Sector model Style vs Country model Style vs Sector model Country vs Sector model Average 0.81 0.84 0.84 0.83 0.00 0.01 0.01 Stdev 0.12 0.10 0.10 0.10 0.05 0.04 0.04 Percentile 0% 0.11 0.15 0.35 0.39-0.43-0.26-0.28 10% 0.64 0.71 0.70 0.68-0.05-0.03-0.03 20% 0.73 0.78 0.78 0.75-0.03-0.01-0.01 30% 0.77 0.81 0.82 0.80-0.01 0.00 0.00 40% 0.80 0.83 0.84 0.83-0.01 0.00 0.00 50% 0.83 0.86 0.86 0.85 0.00 0.01 0.01 60% 0.85 0.88 0.88 0.87 0.00 0.01 0.02 70% 0.88 0.89 0.90 0.89 0.01 0.02 0.03 80% 0.90 0.91 0.92 0.92 0.02 0.03 0.04 90% 0.93 0.94 0.94 0.94 0.04 0.05 0.06 100% 1.00 1.00 1.00 0.99 0.13 0.18 0.18 26

TABLE 2 (CONTINUED) Adjusted R-squared values of market model, style model, country model and sector model This table reports the distribution of funds adjusted R-squared values from multifactor style, country and sector models: Equation (3): r i, t = α i + β1, irmrft + β2, ismbt + β3, ihmlt + ε i, t where SMB is the return difference between the MSCI World Small Cap index and the MSCI World index, and t return difference between the MSCI World Value index and the MSCI World Growth index. Equation (4) : r i, t = α i + β1, isector j, t + ε i, t j HMLt is the where SECTOR, is the excess return on sector j based on MSCI World sector indexes: Energy, Materials, Industrials, j t Consumer Discretionary, Consumer Staples, Health Care, Financials, IT, Telecom and Communication Services and Utilities. Equation (5): r i, t = α i + β1, icountry j, t + ε i, t j where COUNTRY j, t is the excess return on country j based on MSCI World country indexes: United States, United kingdom, Japan, Europe excluding the United Kingdom, Canada, Pacific excluding Japan, emerging Asia and emerging Europe. All models are estimated for each fund based on the funds entire return history. 27

TABLE 3. Portfolio concentration in multiple market segments and fund performance Z_Alpha Z_Information ratio Rsq_Market # Coef t-stat p-val Coef t-stat p-val Panel A. Entire sample 1995-2007 0 9-0.34-1.10 0.27-0.18-0.57 0.57 0.93 1 39-0.44-2.94 0.00-0.45-2.93 0.00 0.90 2 157-0.17-2.27 0.02-0.18-2.39 0.02 0.84 3 331 0.15 2.85 0.00 0.13 2.50 0.01 0.78 Panel B. 1st period 1995-2001 0 5-0.96-2.26 0.02-0.92-2.09 0.04 0.87 1 24-0.30-1.54 0.12-0.29-1.42 0.16 0.80 2 97-0.08-0.84 0.40-0.11-1.09 0.28 0.75 3 150 0.15 1.86 0.06 0.15 1.83 0.07 0.72 Panel C. 2nd period 2002-2007 0 6-0.64-1.67 0.09-0.38-0.99 0.32 0.96 1 57-0.36-2.90 0.00-0.32-2.62 0.01 0.89 2 148-0.35-4.58 0.00-0.34-4.37 0.00 0.88 3 326 0.24 4.58 0.00 0.21 4.13 0.00 0.85 We allocate each fund to one of following four breadth groups. Group 0 contains funds for which the R-squared of the market model exceeds the (adjusted) R-squared values of the three multifactor models. Group 1 contains funds for which one of the three multifactor models produces a higher adjusted R-squared value than the single-factor model. Group 2 contains funds for which two multifactor models produce higher adjusted R-squared values than the market model. Group 3 contains funds for which all multifactor models produce higher adjusted R-squared values than the market model. We report normalized fund alphas (Z_Alpha) and Information ratios (Z_Information Ratio) for each group, along with respective t- statistic and p-value, based on the full-sample period a well as subperiods (1995-2001 and 2002-2007). In addition, we report the groups average R-squared from the market model. 28

TABLE 4. Tracking error, concentration in multiple market segments, and fund performance Z_Alpha Z_Information ratio Rsq_Market # Coef t-stat p-val Coef t-stat p-val Panel A. Entire sample 1995-2007 LOW-0 9-0.34-1.11 0.27-0.18-0.58 0.56 0.93 LOW-1 35-0.41-2.60 0.01-0.41-2.54 0.01 0.91 LOW-2 97-0.29-3.13 0.00-0.28-2.90 0.00 0.90 LOW-3 135-0.07-0.88 0.38-0.01-0.08 0.94 0.88 HIGH-0 0 N/A N/A N/A N/A N/A N/A N/A HIGH-1 4-0.73-1.59 0.11-0.79-1.67 0.10 0.81 HIGH-2 60 0.03 0.26 0.79-0.02-0.20 0.84 0.74 HIGH-3 196 0.30 4.48 0.00 0.23 3.34 0.00 0.70 Panel B. 1st period 1995-2001 LOW-0 5-0.96-2.30 0.02-0.92-2.13 0.03 0.87 LOW-1 19-0.21-0.97 0.33-0.27-1.20 0.23 0.85 LOW-2 54-0.34-2.64 0.01-0.37-2.84 0.00 0.84 LOW-3 74-0.02-0.15 0.88-0.03-0.23 0.82 0.82 HIGH-0 0 N/A N/A N/A N/A N/A N/A N/A HIGH-1 5-0.65-1.55 0.12-0.36-0.84 0.40 0.63 HIGH-2 43 0.24 1.67 0.10 0.22 1.50 0.13 0.64 HIGH-3 76 0.30 2.81 0.01 0.32 2.85 0.00 0.61 Panel C. 2nd period 2002-2007 LOW-0 5-0.61-1.51 0.13-0.30-0.74 0.46 0.97 LOW-1 34-0.40-2.55 0.01-0.38-2.42 0.02 0.94 LOW-2 94-0.39-4.12 0.00-0.38-3.99 0.00 0.93 LOW-3 144-0.10-1.35 0.18 0.00 0.02 0.98 0.92 HIGH-0 1-0.77-0.85 0.40-0.73-0.79 0.43 0.87 HIGH-1 23-0.30-1.59 0.11-0.24-1.22 0.22 0.82 HIGH-2 54-0.29-2.37 0.02-0.26-2.06 0.04 0.79 HIGH-3 182 0.51 7.51 0.00 0.38 5.56 0.00 0.79 29

TABLE 4 (CONTINUED). Tracking error, pconcentration in multiple market segments and fund performance We report the results of first sorting funds based on their levels of non-systematic risk measured by equation (1) into HIGH and LOW bet-size groups and then within each group further sorting funds based on the number of segments to which they are exposed ( breadth ). We report normalized fund alphas (Z_Alpha) and Information ratios (Z_Information Ratio) for each group, along with respective t-statistic and p-value, based on the full-sample period a well as subperiods (1995-2001 and 2002-2007). In addition, we report the groups average R-squared from the market model. 30

TABLE 5. Alternative classifications for concentration in multiple market segments Z_Alpha Z_Information ratio Rsq_Market # Coef t-stat p-val Coef t-stat p-val Panel A. Explanatory power above 2.5% 0 200-0.28-4.30 0.00-0.24-3.64 0.00 0.93 1 115-0.18-2.12 0.03-0.18-2.01 0.04 0.90 2 130 0.35 4.42 0.00 0.30 3.60 0.00 0.84 3 91 0.35 3.68 0.00 0.28 2.88 0.00 0.78 LOW-0 175-0.27-3.93 0.00-0.22-3.17 0.00 0.91 LOW-1 55-0.32-2.60 0.01-0.31-2.49 0.01 0.87 LOW-2 31 0.21 1.28 0.20 0.28 1.66 0.10 0.86 LOW-3 7 0.50 1.45 0.15 0.65 1.83 0.07 0.85 HIGH-0 25-0.32-1.76 0.08-0.36-1.92 0.06 0.76 HIGH-1 60-0.05-0.44 0.66-0.05-0.40 0.69 0.75 HIGH-2 99 0.40 4.34 0.00 0.30 3.19 0.00 0.74 HIGH-3 84 0.34 3.41 0.00 0.25 2.47 0.01 0.65 Panel B. Explanatory power above 5% 0 334-0.22-4.32 0.00-0.20-3.99 0.00 0.86 1 114 0.31 3.63 0.00 0.28 3.21 0.00 0.76 2 47 0.49 3.66 0.00 0.39 2.87 0.00 0.68 3 41 0.38 2.67 0.01 0.33 2.26 0.02 0.61 LOW-0 241-0.26-4.36 0.00-0.22-3.66 0.00 0.90 LOW-1 24 0.18 0.95 0.34 0.27 1.42 0.16 0.86 LOW-2 3 0.89 1.68 0.09 1.15 2.13 0.03 0.85 LOW-3 0 N/A N/A N/A N/A N/A N/A N/A HIGH-0 93-0.11-1.17 0.24-0.16-1.66 0.10 0.76 HIGH-1 90 0.34 3.59 0.00 0.28 2.88 0.00 0.74 HIGH-2 44 0.46 3.34 0.00 0.34 2.41 0.02 0.66 HIGH-3 41 0.38 2.67 0.01 0.33 2.25 0.02 0.61 31

TABLE 5 (CONTINUED). Alternative classifications for concentration in multiple market segments We allocate funds to one of the four aforementioned groups based on the number of stategies they pursue, but now we require the adjusted R-squared values of the multifactor models to exceed the R-squared value of the market model by 2.5 percent and 5 percent. Next, we double-sort funds based on their levels of non-systematic risk measured by equation (1) into HIGH and LOW bet-size groups and then within each group further sorting funds based on the number of segments to which they are exposed ( breadth ). We report normalized fund alphas (Z_Alpha) and Information ratios (Z_Information Ratio) over the period 1995-2007 for each group, along with respective t-statistic and p-value. In addition, we report the groups average R-squared from the market model. 32

TABLE 6. Fund performance estimated relative to style, country and sector models Z_Alpha Z_Information ratio Rsq # Coef t-stat p-val Coef t-stat p-val Panel A. Style model LOW 276-0.14-2.45 0.01-0.12-2.12 0.03 0.91 HIGH 260 0.15 2.54 0.01 0.11 1.82 0.07 0.77 0 9-0.21-0.65 0.51-0.06-0.19 0.85 0.93 1 39-0.31-2.04 0.04-0.29-1.87 0.06 0.91 2 157-0.11-1.45 0.15-0.15-1.90 0.06 0.85 3 331 0.10 1.89 0.06 0.09 1.72 0.09 0.82 LOW-0 9-0.21-0.66 0.51-0.06-0.19 0.85 0.93 LOW-1 35-0.27-1.69 0.09-0.24-1.50 0.13 0.92 LOW-2 97-0.25-2.58 0.01-0.27-2.72 0.01 0.91 LOW-3 135-0.02-0.28 0.78 0.01 0.09 0.93 0.90 HIGH-1 4-0.66-1.40 0.16-0.68-1.43 0.15 0.80 HIGH-2 60 0.10 0.85 0.40 0.04 0.30 0.76 0.77 HIGH-3 196 0.18 2.66 0.01 0.14 2.14 0.03 0.77 33

TABLE 6 (CONTINUED). Fund performance estimated relative to style, country and sector models Z_Alpha Z_Information ratio Rsq # Coef t-stat p-val Coef t-stat p-val Panel B. Country model LOW 276-0.03-0.57 0.57-0.16-2.70 0.01 0.91 HIGH 260 0.07 1.17 0.24 0.15 2.50 0.01 0.77 0 9 0.04 0.12 0.90-0.03-0.08 0.94 0.92 1 39-0.12-0.81 0.42-0.29-1.85 0.07 0.90 2 157-0.05-0.64 0.52-0.16-2.04 0.04 0.86 3 331 0.06 1.24 0.21 0.10 1.87 0.06 0.82 LOW-0 9 0.04 0.12 0.90-0.03-0.08 0.94 0.92 LOW-1 35-0.06-0.38 0.71-0.24-1.45 0.15 0.91 LOW-2 97-0.15-1.55 0.12-0.33-3.37 0.00 0.91 LOW-3 135 0.05 0.66 0.51-0.02-0.25 0.80 0.90 HIGH-1 4-0.66-1.41 0.16-0.73-1.53 0.13 0.82 HIGH-2 60 0.10 0.87 0.38 0.11 0.87 0.38 0.79 HIGH-3 196 0.07 1.06 0.29 0.18 2.63 0.01 0.77 34

TABLE 6 (CONTINUED). Fund performance estimated relative to style, country and sector models Z_Alpha Z_Information ratio Rsq # Coef t-stat p-val Coef t-stat p-val Panel C. Sector model LOW 276-0.21-3.55 0.00-0.45-8.23 0.00 0.90 HIGH 260 0.20 3.49 0.00 0.45 8.30 0.00 0.76 0 9-0.51-1.61 0.11-1.26-4.07 0.00 0.92 1 39-0.48-3.18 0.00-0.82-5.51 0.00 0.89 2 157-0.19-2.47 0.01-0.25-3.35 0.00 0.84 3 331 0.16 3.01 0.00 0.25 4.93 0.00 0.82 LOW-0 9-0.51-1.63 0.10-1.26-4.41 0.00 0.92 LOW-1 35-0.40-2.53 0.01-0.83-5.74 0.00 0.91 LOW-2 97-0.34-3.54 0.00-0.61-6.90 0.00 0.90 LOW-3 135-0.03-0.41 0.68-0.17-2.24 0.03 0.90 HIGH-1 4-1.20-2.56 0.01-0.70-1.62 0.10 0.80 HIGH-2 60 0.04 0.37 0.71 0.29 2.71 0.01 0.75 HIGH-3 196 0.28 4.25 0.00 0.52 8.64 0.00 0.76 We report performance evaluation results of sorting funds based on, respectively, tracking error (LOW/HIGH), breadth (0, 1, 2, 3), and tracking error and breadth (LOW-0 to HIGH-3). Panel A reports results based on a Style performance attribution model. Panel B reports results based on the Country Model. Panel C reports results based on the Sector model. We report normalized fund alphas (Z_Alpha) and Information ratios (Z_Information Ratio) for each group, along with respective t- statistic and p-value. In addition, we report the groups average R-squared from the employed performance evaluation model. 35

FIGURE 1. Cumulative return difference between HIGH and LOW bet size funds $1.20 $1.15 $1.10 $1.05 $1.00 $0.95 $0.90 jan-95 jan-96 jan-97 jan-98 jan-99 jan-00 jan-01 jan-02 jan-03 jan-04 jan-05 jan-06 jan-07 36