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Return dispersion, mutual fund activeness
and performance in Europe
Studentnr: 2401762 Name: Cas Bonsema Study Program: MSc Finance
Supervisor: dr. A. Plantinga
Field Key Words: Cross-sectional volatility, European mutual fund performance, active management, stock selection, fund activeness, return dispersion
Special Research Project: Active management and cross-sectional volatility
Abstract
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1. Introduction
Early studies on active equity mutual funds find that they on average underperform low cost index funds.1 Passive index funds and ETFs have been on the rise for the past decade at the expense of active management. However, Cremers and Petajisto (2009)’s seminal study on Active Share sparked renewed interest in active management as they found that more active funds do outperform their benchmarks. Active equity management aims to outperform a benchmark index, e.g. MSCI France, by selecting winner stocks and avoiding or underweighting loser stocks.
Yet, little thought is given to the notion that the performance of active management depends on the payoffs to selecting stocks. Return dispersion measures the stock selection opportunities available in the market. It is the cross-sectional standard deviation of stock returns in a single period, e.g. a month. When return dispersion is high — so when there is a large difference between the returns of winner and loser stocks — overweighting winner stocks has a greater impact on (relative) performance. On the other hand, if there is no return dispersion, all stocks earn the same return in the cross-section and overweighting winner stocks is useless. Moreover, funds who engage in more stock selection should benefit more from increased return dispersion in the market, assuming the managers have skill.
Petajisto (2013) finds that the most active stock pickers outperform their benchmark. Furthermore, cross-sectional volatility predicts the performance of stock pickers. Von Reibnitz (2015) reports that the most active US mutual funds earn higher risk-adjusted returns in times of high return dispersion. The research on return dispersion focuses on US mutual funds. Yet the findings for US funds are not necessarily representative of European mutual funds. In Europe, the average mutual fund is smaller and there are a larger number of funds active in the fund industry;
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see Otten and Bams (2002). Therefore, the research question this paper aims to answer is: Do European active managers benefit from increased stock selection opportunities during periods of high return dispersion?
I contribute to the literature by examining the relationship between return dispersion, fund activeness and performance for European active mutual funds. I find that low to medium levels of return dispersion earn the most active European funds the highest excess returns. In contrast, Von Reibnitz (2015) finds that in the US, periods of high return dispersion lead to the highest excess returns (for the most active funds). Overall, return dispersion in the market seems to have a fundamentally different impact on performance when comparing European mutual funds with US funds.
This study examines the effects of return dispersion and activeness on fund performance by creating five portfolios sorted on fund activeness and defining different return dispersion environments. 2
R measures fund activeness, where the 2
R is from a multifactor benchmark regression. Mutual funds that are more active have a lower 2
R because of higher idiosyncratic risk relative to a passive benchmark. Return dispersion captures the opportunity set available to active managers. The return dispersion measure uses STOXX 600 index constituents to capture a broad selection of stocks available to active managers in Europe. Finally, the intercept from a multifactor benchmark model, alpha, measures performance of the mutual fund portfolios.
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dispersion, there is no outperformance for any fund portfolio. Over the full sample period, the most active fund portfolios outperform, but low to medium levels of return dispersion are driving the outperformance. Thus, European active managers benefit only partially from increased stock selection opportunities during periods of increased return dispersion.
A potential explanation for why high levels of dispersion are not associated with outperformance is that active managers may aim to lower their tracking error by reducing active portfolio weights. It is also possible that the diversity of European stocks already provides active managers with high stock selection payoffs, which lowers the impact of increasing return dispersion. Overall, the most active funds do not outperform in every return dispersion environment, which indicates investors should consider the dispersion environment present in the market.
The paper consist of the following structure: Section 2 discusses the literature, Section 3 describes the methodology and Section 4 discusses data sources and descriptive statistics. Section 5 presents the main results, Section 6 contains robustness checks and additional analyses and Section 7 concludes.
2. Literature review
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However, these studies do not account for the level of return dispersion in the market, i.e. the potential payoffs to stock selection. In Grinold (1989)’s fundamental law of active management, alpha depends on a managers’ skill but also breadth, which is the number of independent investment opportunities. High return dispersion corresponds to stock returns moving more independently, thereby increasing the potential for alpha. Gorman, Sapra, and Weigand (2010a) derive an analytical framework in which they relate cross-sectional return dispersion with Grinold (1989)’s fundamental law of active management. They find that periods of higher return dispersion represent opportunities for active managers to earn higher returns but their information ratios, or skill levels, are expected to stay the same. Therefore, for a given level of skill, if there is no return dispersion in the market, active management does not add value since all stocks earn the same return. Conversely, as return dispersion increases, the potential for active management to add value also increases.
Based on US data, De Silva, Sapra and Thorley (2001) find that return dispersion has increased substantially over the past decade. Ankrim and Ding (2002) find the same result for equity markets in the US, Canada, Japan and the UK. Gorman, Sapra, and Weigand (2010b) find that return dispersion accurately forecasts the dispersion in mutual fund alphas over three-month and one-year horizons, which suggests that the potential gains from active investing have increased along with return dispersion.
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active fund managers perform best in times of high cross-sectional return dispersion. Caquineau and Möttölä (2016) examine a sample of active European large cap mutual funds and find a positive relationship between Active Share and fund performance; though, the performance gap has decreased near the end of the sample period.
Similarly, Miller (2007) constructs active expense ratios and active alphas for a sample of mutual funds using 1 R 2, which is the active component of a funds’ returns. Amihud and
Goyenko (2013) use 1 R 2
as a measure of fund activeness, where a multifactor benchmark model, such as Fama and French (1993), determines R2. A high R2 corresponds to low activeness because
fund returns do not deviate much from (passive) benchmark returns. They find that a portfolio of funds, sorted on lowest lagged 2
R and highest lagged alpha, produces significant excess returns of 3.8% per annum.
Finally, Von Reibnitz (2015) combines research on cross-sectional volatility and fund activeness. Funds with the most active strategies generate superior risk-adjusted returns in the months with high cross-sectional volatility. Additionally, in lower dispersion environments, there is generally no significant outperformance of the most relative to the least active funds. Smith (2014) finds similar results for US equity hedge funds; performance is strongest in times of elevated cross-sectional volatility.
3. Research methods
3.1. Cross-sectional volatility measure,
CSVCross-sectional volatility, or return dispersion, measures the stock selection opportunities available to active managers. Cross-sectional volatility in month t is calculated using an equally weighted
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2 1 1 1 n t it mt i CSV r r n
(1)where r is the return of STOXX 600 index constituent it i for month t , r is the equally weighted mt
average return of all STOXX 600 index constituents in month t and n is the number of STOXX 600 index constituents in month t . The STOXX 600 index represents a broad cross-section of the available opportunities for active managers including small, mid and large cap companies across Europe.
Following Von Reibnitz (2015), five different return dispersion environments are defined. Months are ranked according to their level of cross-sectional volatility at the end of the month. The result is five quintiles of cross-sectional volatility, ranging from Q1 (low CSV ) to Q5 (high t
t
CSV ), where each quintile contains 20% of the total number of months. Forming quintiles allows
for non-linearity in the relationship between the level of cross-sectional volatility and fund performance. The results are robust to sorting months into three dispersion environments (low, middle and high).
3.2. Mutual fund activeness measure, Selectivity
The “Selectivity” measure from Amihud and Goyenko (2013) is used to determine the level of fund activeness: 2 2 2 2 2 2 1 IR IR Selectivity R TotalRisk SystematicRisk IR (2)
where IR is the variance of the error term, i.e. idiosyncratic or non-systematic risk. 2 TotalRisk2
is the (total) variance and SystematicRisk is the part of the variance which is explained by a 2
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benchmark, resulting in a lower R and thus a higher level of “Selectivity”. 2
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R is estimated using 36-month rolling regressions of the Fama and French (1993) three-factor
model with the addition of momentum following Carhart (1997), from now on referred to as FFC:
it ft it it mt ft it t it t it t it
r r r r s SMB h HML m MOM (3) where r is the net return of mutual fund it i in month t , rft is the European risk-free rate in month
t , and r is the return on a European or country-specific market portfolio in month mt t . SMB , t
t
HML , MOM are the month t t returns on, respectively, the size, book-to-market, and momentum
factor-mimicking portfolios.
In each month t , funds are sorted into portfolios based on their Rt21, where Rt21 is estimated according to Eq. (3). over the 36 months prior to month t . The sorting generates five selectivity portfolios, each containing 20% of the funds in a given month, ranging from low selectivity (S1) to high selectivity (S5). Rt21 is used instead of Rt2 because Rt21 is available to investors ex ante.
Lastly, using Rt21 implies that the level of activeness is constant over time, at least for the next month. This is not necessarily true, even though funds are not likely to alter their activeness substantially from one month to the next. Additionally, 2
1
t
R updates the level of activeness slowly because of the rolling regressions. For example, a fund that is more active over the past 12 months, relative to the first 24 months, will have a 2
1
t
R that is too high. Sorting funds into portfolios mitigates this problem somewhat, but not completely. Overall, 2
1
t
R is an imperfect measure of fund activeness, which is potentially biasing the results.
3.3. Fund performance measurement
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portfolios. After sorting months into five dispersion quintiles, the average excess returns of each fund portfolio are regressed on the FFC factor returns over the months in the dispersion quintile.2 Performing FFC regressions within each quintile allows for factor betas specific to the dispersion environment. These time-varying factor betas are important because active mutual funds might alter their exposure to a factor depending on its return, e.g. reducing the exposure to the market when market returns are low. Strivers and Sun (2010) find a positive relationship between return dispersion in the market and the subsequent value premium, and a negative relationship between dispersion and the momentum premium. For example, in times of low dispersion, when the value premium is low and the momentum premium is high, (skilled) active managers might decrease their exposure to value stocks and increase their exposure to stocks with high momentum.
4. Data
4.1. Mutual fund data
Thomson Reuters’ Datastream provides mutual fund data, which it sources from the Lipper funds database. Funds that, according to Lipper classifications, focus on Equity and have at least 50% of their assets invested in countries in Europe, the Eurozone or Scandinavia are included. In line with other studies on European mutual funds, funds domiciled in two “offshore” countries, Ireland and Luxembourg, are excluded. I also remove Guaranteed and Protected funds because they likely hold substantial fixed income holdings, despite Lipper classifying them as Equity funds. Furthermore, since the focus is on active mutual funds, all funds with “Index”, “Idx”, “Passive” or “Tracker” in their name, as well as other acronyms, are excluded. The final sample consists of 2,551 active European domiciled equity mutual funds.
2 It is equivalent to estimating a dummy variable FFC regression with 25 cross-terms (five dummies and five factors), including
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Datastream reports multiple share classes for a mutual fund. For this reason, the return of a mutual fund is the equally weighted average of the individual share classes’ returns. The returns are net returns, so they include reinvested dividends and are net of fees and expenses. Lastly, Datastream does not list “dead” mutual funds, so the sample includes only funds who are “alive” at the end of January 2016. Hence, survivorship bias is a concern.
Almost two thirds of the sample consists of funds based in France and the United Kingdom, with 37.5% of funds based in other, mainly developed, European countries. These 37.5% feature a broad selection of countries, which increases the representativeness of my sample of mutual funds. See Table A1 in Appendix A for summary statistics on the country of domicile. Overall, the sample consists of a relatively broad selection of domicile countries. The currency composition reflects the composition of the country of domicile as close to 61% of the sample is denominated in euros. The British pound, Swiss franc and Swedish krona account for 29%, 6.4% and 3.6% of the sample, respectively. For the remainder of the paper, all returns are in euros.
Table 1. Geographical focus of mutual funds
Geographical focus Number of funds % of total funds
Europe 785 30.8% United Kingdom 575 22.5% Euro Zone 412 16.2% France 202 7.9% Switzerland 164 6.4% Europe ex. UK 127 5.0% Sweden 93 3.6% Germany 60 2.4% Spain 57 2.2% Eastern Europe 43 1.7% Finland 33 1.3% Total 2,551 100.0% Total Europe 1,367 52.0%
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Table 1 reports the geographical focus of the investments of the mutual funds. More than half of the funds invest the majority of their assets in Europe or the Eurozone. The remaining funds mainly invest in the UK, France and Switzerland. Overall, almost all the funds in the sample invest in developed (European) countries.
Table 2. Descriptive statistics annualized net mutual fund returns in euros per country of domicile
Average Median Standard Deviation Kurtosis Skewness N Austria 4.02% 7.88% 18.87% 3.58 -0.40 10,097 Belgium 5.92% 12.75% 19.22% 4.44 -0.62 9,719 Bulgaria -2.50% 0.61% 18.80% 2.06 -0.84 111 Switzerland 9.71% 14.56% 15.46% 12.10 -0.98 18,725 Germany 6.40% 11.41% 18.36% 2.59 -0.41 28,315 Denmark 4.61% 11.41% 19.27% 1.81 -0.58 379 Estonia 1.10% 7.57% 23.49% 12.87 -2.03 726 Spain 3.49% 8.39% 17.73% 1.26 -0.35 17,862 Finland 8.09% 11.15% 18.79% 9.94 -0.48 8,399 France 6.15% 12.25% 17.54% 4.71 -0.36 116,352 UK 8.74% 15.39% 16.27% 2.67 -0.40 105,170 Greece 0.68% 5.52% 16.03% 1.77 -0.65 721 Hungary 4.57% 10.81% 19.66% 2.49 -0.47 328 Isle of Man 4.27% 13.89% 19.04% 3.09 -1.09 396 Italy 4.98% 11.11% 15.44% 2.58 -0.12 6,077 Liechtenstein 6.87% 11.02% 15.89% 5.91 -0.28 3,332 Latvia -3.98% -1.20% 15.87% 1.15 0.65 42 Malta -4.28% 0.00% 15.09% 14.52 -2.02 65 Netherlands 6.62% 12.07% 19.83% 21.20 -1.54 4,338 Poland -1.05% 6.79% 19.40% 2.05 -0.39 288 Portugal 2.54% 9.19% 17.20% 2.42 -0.43 3,467 Sweden 11.04% 11.89% 20.90% 2.07 -0.01 9,686 Slovenia 4.83% 9.04% 16.03% 4.64 -0.87 753 Slovakia 0.27% 8.90% 16.57% 0.92 -0.43 181 Full Sample 7.03% 12.95% 17.36% 4.54 -0.44 345,503
The table reports descriptive statistics for net mutual fund returns, annualized from monthly returns and denominated in euros. The net returns are the returns calculated from Datastream’s Total Return Index, which includes reinvested dividends and is net of fees and expenses. Standard deviation is annualized from monthly standard deviations according to: 𝑎𝑛𝑛𝑢𝑎𝑙 𝜎𝑖= 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝜎𝑖∗ √12.
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Finally, Table 2 reports the net mutual fund returns for each country of domicile in euros. Overall, the means, medians and standard deviations are quite similar. Some of the smaller/less-developed countries have low or negative returns, e.g. Bulgaria or Latvia. For every country, except Latvia, the median return is higher than the average return indicating occasional large losses. Furthermore, nearly all countries have large kurtosis indicating peaked distributions. In general, funds domiciled in developed countries have higher returns, possibly due to experience and/or skill of the managers.
4.2. Benchmark model variables
The benchmark FFC model measures fund activeness and alpha. The excess market return rmrf
is the return on MSCI Europe minus the European risk-free rate. SMB , HML, MOM are the
returns on, respectively, the size, book-to-market, and momentum factor-mimicking portfolios. Kenneth French’s database provides the monthly European factor returns of SMB , HML and
WML , see Fama and French (2012) for details on the methodology.3 The factor returns are
denominated in US dollars while the mutual fund returns are in euros. Hence, the factor returns are converted into euros using the following formula:
1 $
1 $ (
1factor Euro factor US
Return FFC Return FFC ReturnUS Euro (4)
Datastream provides the risk-free rate, exchange rates and market index data.
The MSCI Europe index proxies the European market portfolio for funds with a focus on Europe and the Euro Zone. MSCI Europe is a good proxy with coverage of 85% of the free-float market capitalization in developed Europe. For comparison, I regressed the returns of alternative indices, the STOXX 600 and S&P Europe 350, on the returns of MSCI Europe. Both regressions feature betas close to one and 2
R of over 0.98. Country-specific MSCI indices proxy the market
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portfolio for mutual funds investing in the UK, France, Switzerland, and Sweden. For the remaining countries (7.6% of the sample), MSCI Europe is the benchmark regardless of the fund’s geographical focus.
Lastly, the risk-free rate is the Frankfurt one-month Money Market Rate before 1999 and the one-month EURIBOR from 1999 onwards. The correlation between both rates is 0.9999. I use interbank rates instead of rates from government securities because their prices are artificially high due to quantitative easing, causing their yields to be too low. Interbank rates like EURIBOR do contain some credit risk; nonetheless, it is a good proxy for the risk-free rate.
4.3. Selectivity data
The FFC model measures the level of fund activeness, 2 1 t R . Funds with 2 1 t R estimates in the 0.5% tails of the distribution are removed each month, following Amihud and Goyenko (2013). The top 0.5% of funds are essentially closet indexers while the bottom 0.5% are not representative of the population of active mutual funds or are more likely the result of estimation error. The final sample contains 2,551 distinct mutual funds over the period November 1993 to January 2016, with 263,081 fund-month observations.
Fig. 1 shows the distributional properties of the percentage of mutual fund returns explained by the FFC model. For the average fund, a combination of passive (factor) benchmarks explains over 83% of the variation in fund returns. However, there is wide variation in the estimates with a minimum close to 0.10 and a maximum of essentially one. There is a long tail with very active mutual funds, so after accounting for skewness, a combination of passive benchmarks explains 87% of the variation in fund returns for a representative European active mutual fund. It is not entirely clear if this is quite passive or not, because Rt21 can also indicate highly diversified active
strategies, which have a high 2 1
t
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undiversified portfolios resulting in a low Rt21 even though they are not active. Nevertheless, on average, it likely indicates funds are not very active.
Figure 1. Descriptive statistics and histogram Rt21 estimates
Mean Median Standard deviation Minimum Maximum N
2 1
t
R 0.831 0.872 0.139 0.084 0.997 263,081
The figure reports descriptive statistics of the 𝑅𝑡−12 estimates, where 𝑅2𝑡−1 is obtained by regressing the fund’s monthly excess
returns (over 1-month EURIBOR) on the FFC factor returns over a 36 month period, using the Fama and French (1993) and Carhart (1997) factor model. Each month, the top and bottom 0.5% of 𝑅2
𝑡−1 estimates are removed, in line with Amihud and Goyenko
(2013). N is the number of fund/month observations. Frequency is the number of observations for each 𝑅𝑡−12 bin.
4.4. Cross-sectional volatility data
Cross-sectional volatility is calculated using constituents from the STOXX 600 index, downloaded from Thompson Reuters’ Datastream. So-called Total Return Index data is used for computing constituent member’s returns. Total Return Index data includes reinvested dividends and is net of fees and expenses. Datastream’s default STOXX 600 constituent list gives the most current constituents. These constituents are currently “alive”; however, at the beginning of the sample period only 260 constituents are “alive”. Hence, in order to have a broad number of firms in the
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CSV calculations at all times, constituent lists from five-year intervals are used. The earliest available constituent list is from August 1999, causing the number of firms in the CSV calculation to be less than 500 only in the beginning of the sample period for a total of 18 months. Overall, the cross-sectional volatility measure is representative of the opportunities available to active managers during the full sample period.
Figure 2. Monthly cross-sectional volatility based on STOXX 600 index constituents
The figure plots the equally weighted cross-sectional volatility measure using the constituents of the STOXX 600 index. CSV is calculated at the end of each month, starting on 30-11-1993 and ending on 29-01-2016.
Fig. 2 plots the level of cross-sectional volatility from November 1993 to January 2016. Most of the time return dispersion ranges between 5% and 15%, but there are spikes corresponding to the tech bubble in 2000, the financial crisis in 2008/2009 and the European debt crisis in 2011/2012. For the last couple of years return dispersion is stable in the 5% to 10% range.
Table 3 reports descriptive statistics of the return dispersion quintiles as well as for the full sample. The highest quintile has an average CSV of 12.22%, which is 3% higher than the average of quintile four. Furthermore, quintile five also has a standard deviation almost five times higher
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than quintile four. The mean CSV rises in increments of about 1% when moving from Q1 to Q4, while the standard deviation is more variable. Overall, the quintiles represent a broad selection of dispersion environments, with distinct differences between quintiles.
Table 3. Descriptive statistics cross-sectional volatility quintiles
Q1-Q5 Q1 (low) Q2 Q3 Q4 Q5 (high) Mean 8.22% 5.64% 6.64% 7.68% 9.02% 12.22% Median 7.67% 5.72% 6.64% 7.67% 8.96% 11.91% Standard Deviation 2.49% 0.39% 0.23% 0.32% 0.44% 2.07% Kurtosis 2.10 -0.54 -0.81 -1.22 -0.22 1.42 Skewness 1.33 -0.63 -0.03 -0.07 0.42 1.28 Minimum 18.85% 6.18% 7.06% 8.21% 10.00% 18.85% Maximum 4.69% 4.69% 6.22% 7.10% 8.23% 10.05% Count 267 55 53 53 53 53
The table reports the descriptive statistics of monthly cross-sectional volatility (CSV) for the full sample, Q1-Q5 and for the five different quintiles of CSV. Quintiles are formed by ranking months according to their level of cross-sectional volatility at the end of the month. Each quintile contains 20% of the total number of months. Two remaining months are allocated to Q1 to ensure an even number of months for the other quintiles.
5. Results
Table 4 reports annualized alphas estimated from the in-quintile FFC regressions following Eq. (3). The bottom row (All) shows that, over the full sample period, the average alpha is insignificant for all funds combined. The three least active fund portfolios (S1-S3) earn insignificant excess returns, whereas the two most active fund portfolios (S4 and S5) earn significant and positive excess returns of 1.91% and 3.29%, respectively. However, the performance of the selectivity portfolios varies substantially across the return dispersion environments.
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only significant at the 10% level. In the higher dispersion quintiles, the excess returns are insignificant. For the middle selectivity portfolio (S3), excess returns are negative in quintile one, but the underperformance disappears when return dispersion increases.
Table 4. FFC alphas: selectivity portfolios and return dispersion quintiles
S1 (low) S2 S3 S4 S5 (high) S5-S1 All Q1 (low) -2.50%*** -2.22%** -2.21%** -1.47% 0.64% 3.21%* -1.55% (-2.74) (-2.34) (-2.29) (-1.26) (0.38) (1.79) (-1.65) Q2 -3.92%** -2.27%* -0.37% 0.92% 4.53%** 8.76%*** -0.25% (-2.51) (-1.68) (-0.25) (0.57) (2.41) (3.77) (-0.20) Q3 2.73% 2.81%* 1.22% 4.66%** 7.30%*** 4.46% 3.70%*** (1.37) (1.79) (0.88) (2.49) (3.73) (1.45) (2.99) Q4 -1.37% -0.71% -0.28% 3.71% 2.60% 4.02% 0.77% (-0.91) (-0.45) (-0.14) (1.35) (0.72) (1.13) (0.41) Q5 (high) 1.37% 0.84% 2.12% 3.54%* 3.31% 1.91% 2.20% (0.90) (0.51) (1.25) (1.69) (0.90) (0.52) (1.43) All -0.45% 0.10% 0.21% 1.91%** 3.29%** 3.76%*** 1.00% (-0.73) (0.18) (0.34) (2.30) (2.53) (2.85) (1.63)
The table reports the annualized portfolio alpha. Every test month 𝑡, funds are sorted into portfolios based on 𝑅2
𝑡−1. 𝑅2𝑡−1 is
obtained from a 36-month estimation period at time 𝑡 − 1, by regressing the fund’s monthly excess returns (over 1-month EURIBOR) on the factor returns, using the FFC (Fama and French 1993 and Carhart 1997) factor model. Monthly equal weighted average excess returns for the portfolios are calculated for each test month 𝑡. This process is repeated by shifting the test month 𝑡 forward one month at a time. Then, months are sorted in quintiles based on 𝐶𝑆𝑉𝑡, where 𝐶𝑆𝑉𝑡 is calculated following Eq. (1).
S5-S1 is the cross-sectional difference in average returns between the highest and lowest selectivity portfolio. Alpha for each selectivity portfolio is then estimated by regressing the monthly portfolio returns on the factor returns of the FFC model for each dispersion quintile. The regression intercept, alpha, is reported along with its 𝑡-statistic, using Heteroskedasticity and Autocorrelation Consistent (HAC) standard errors (Newey and West 1987). ***, **, * denote significance at the 1%, 5% and 10% level, respectively.
The two least active fund portfolios have (relatively) low idiosyncratic risk, so they likely make few active bets. The combination of relatively few stock bets and low payoffs to selecting winner stocks, leads to gross fund returns that are close to the benchmark. Hence, after expenses are subtracted, they underperform. In the higher dispersion quintiles, the high payoffs to stock selection enable less active funds to earn returns in line with the benchmark.
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earns significant excess returns in quintiles two and three of 4.53% and 7.30% per annum, respectively. Again, alpha is insignificant in the other return dispersion environments. Quintiles two and three appear to be driving the outperformance in the full sample period. Fig. 3, which plots the alphas from Table 4, shows the patterns graphically.
Figure 3. FFC alphas: selectivity portfolios and return dispersion quintiles
The figure reports the annualized portfolio alpha. Every test month 𝑡, funds are sorted into portfolios based on 𝑅2
𝑡−1. 𝑅2𝑡−1 is
obtained from a 36-month estimation period at time 𝑡 − 1, by regressing the fund’s monthly excess returns (over 1-month EURIBOR) on the factor returns, using the FFC (Fama and French 1993 and Carhart 1997) factor model. Monthly equal weighted average excess returns for the portfolios are calculated for each test month 𝑡. This process is repeated by shifting the test month 𝑡 forward one month at a time. Then, months are sorted in quintiles based on 𝐶𝑆𝑉𝑡, where 𝐶𝑆𝑉𝑡 is calculated following Eq. (1). S5-S1 is the cross-sectional difference in average returns between the highest and lowest selectivity portfolio. Alpha for each selectivity portfolio is then estimated by regressing the monthly portfolio returns on the factor returns of the FFC model for each dispersion quintile. The regression intercept, alpha, is reported. ***, **, * denote significance at the 1%, 5% and 10% level, respectively.
The two most active fund portfolios seem to benefit substantially from increased payoffs to stock selection, as evidenced by the large positive alphas. Furthermore, S5 benefits the most from increased return dispersion since the outperformance already shows in quintile two, whereas S4 outperforms only in quintile three. This pattern is consistent with a higher number of stock bets for funds with high levels of activeness.
-6% -4% -2% 0% 2% 4% 6% 8% Q1 (low) Q2 Q3 Q4 Q5 (high) A n n u ali ze d F F C alp h as
Return dispersion quintile
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Overall, for low to medium levels of return dispersion (Q1 to Q3), there is a positive relationship between dispersion and fund performance. Additionally, this relationship is stronger for funds that are more active. However, the relationships weaken substantially in higher dispersion environments. In high dispersion environments (Q4 and Q5), there are no significant excess returns for any fund portfolio, not even for the most relative to the least active fund portfolio. Over the full sample period, the more active funds outperform significantly. Still, selecting the most active funds without taking into account the dispersion environment can lead to disappointing returns. For example, in long periods of high return dispersion (Q4 and Q5), there is no significant outperformance for the most active portfolio of funds, neither on a standalone basis nor relative to the least active funds.
A potential explanation of why higher levels of return dispersion (Q4 and Q5) do not lead to better performance, especially for the most active funds, is because of the existence of risk limits and/or tracking error constraints imposed on active managers. In the framework of Gorman, Sapra and Weigand (2010a), active managers reduce tracking error as return dispersion increases. Hence, in periods with low to medium return dispersion, the level of tracking error is acceptable. High return dispersion, however, leads to unacceptable levels of tracking error. Consequently, active managers may aim to lower their tracking error by reducing active portfolio weights.
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6. Robustness checks
6.1. CAPM model
The Capital Asset Pricing Model (CAPM) is an alternative benchmark to measure excess returns, but it also mitigates concerns of multicollinearity.4 The correlations between SMB , HML and
WML over the full sample period are between 0.27 and 0.54, which is relatively high. However,
the correlations are lower for higher levels of return dispersion. For example, in quintile one, they are around 0.80 while in quintile five only two correlations are relatively high at 0.47 and 0.29. Nonetheless, multicollinearity is potentially biasing the results of the lower quintiles.
Table 5 reports annualized alphas from the CAPM regressions. The overall results are similar, except for higher levels of return dispersion (Q3 and Q4).
Table 5. CAPM alphas: selectivity portfolios and return dispersion quintiles
S1 (low) S2 S3 S4 S5 (high) S5-S1 All Q1 (low) -2.32%** -2.00%* -2.33%* -1.89% -0.02% 2.34% -1.71% (-2.17) (-1.69) (-1.77) (-1.27) (-0.01) (1.17) (-1.38) Q2 -1.98% -0.85% 1.23% 3.11%* 4.08%** 6.17%** 1.10% (-1.42) (-0.75) (0.94) (1.90) (2.14) (2.61) (0.96) Q3 1.36% 1.41% 0.19% 1.40% 3.45% 2.07% 1.53% (0.86) (0.97) (0.13) (0.58) (1.26) (0.73) (0.95) Q4 -3.34%** -2.96%* -3.04% -2.33% -0.88% 2.54% -2.51% (-2.39) (-1.89) (-1.51) (-0.81) (-0.27) (0.86) (-1.30) Q5 (high) 0.81% 0.76% 1.08% 2.73% 3.00% 2.17% 1.64% (0.47) (0.39) (0.39) (0.67) (0.61) (0.48) (0.62) All -0.94%* -0.63% -0.54% 0.60% 1.96% 2.92%* 0.08% (-1.78) (-1.20) (-0.68) (0.53) (1.24) (1.90) (0.10)
The table reports the annualized portfolio alpha. Every test month 𝑡, funds are sorted into portfolios based on 𝑅2
𝑡−1. 𝑅2𝑡−1 is obtained from a 36-month estimation period at time 𝑡 − 1 by regressing the fund’s monthly excess returns (over 1-month EURIBOR) on the factor returns, using the FFC (Fama and French 1993 and Carhart 1997) factor model. Monthly average excess returns for the portfolios are calculated for each test month 𝑡. This process is repeated by shifting the test month 𝑡 forward one month at a time. Then, months are sorted in quintiles based on 𝐶𝑆𝑉𝑡−1, where 𝐶𝑆𝑉𝑡−1 is calculated following Eq. (1). S5-S1 is the cross-sectional difference in average returns between the highest and lowest selectivity portfolio. Alpha for each selectivity portfolio is then estimated by regressing the monthly portfolio returns on the CAPM factor return for each dispersion quintile. The regression intercept, alpha, is reported along with its 𝑡-statistic, using Heteroskedasticity and Autocorrelation Consistent (HAC) standard errors (Newey and West 1987). ***, **, * denote significance at the 1%, 5% and 10% level respectively.
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The divergence of the CAPM with the FFC model in these quintiles might be because funds have large factor loadings on FFC factors and/or the factor returns are high. However, in quintiles three and four, the correlations between factors are not as high as the bottom two quintiles, so the CAPM is likely understating these alphas. Overall, multicollinearity is not an important issue since it is concentrated in the lower return dispersion quintiles, whose results are largely unaffected by eliminating the collinear variables.
6.2. Market timing model
The alphas from the main analysis contain excess returns from stock picking and from timing the market. Hence, market timing ability is potentially affecting the alphas and inferences. Treynor and Mazuy (1966)’s market timing specification separates market timing ability from stock selection ability:
2it ft it it mt ft it mt ft it
r r r r MT r r (5)
where r is the net return of mutual fund it i in month t , rft is the European risk-free rate in month
t and r is the return on MSCI Europe in month mt t . MT is the market timing coefficient, if it
0 it
MT the manager has market timing ability. is the excess return due to stock picking ability it
and is the exposure to the market index. it
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Table 6. Stock selection and market timing coefficients: selectivity portfolios and return dispersion quintiles
Panel A: Stock selection alphas
S1 (low) S2 S3 S4 S5 (high) S5-S1 All Q1 (low) -3.28%** -3.24%** -2.99%* -2.29% 0.12% 3.50%* -2.35% (-2.46) (-2.24) (-1.77) (-1.24) (0.05) (1.83) (-1.48) Q2 -1.85% -0.48% 0.77% 3.17% 3.94%* 5.89%** 1.09% (-1.04) (-0.34) (0.48) (1.59) (1.75) (2.01) (0.78) Q3 2.00% 2.36% 1.62% 2.91% 4.88% 2.82% 2.73% (1.27) (1.62) (0.81) (0.94) (1.24) (0.69) (1.33) Q4 -3.33%* -2.05% -0.06% 0.88% 5.34% 8.94%** 0.12% (-1.88) (-0.95) (-0.02) (0.23) (1.36) (2.47) (0.05) Q5 (high) 3.64% 3.93% 3.58% 6.67% 8.73% 4.92% 5.27% (1.50) (1.26) (0.97) (1.26) (1.40) (0.91) (1.44) All -0.56% 0.07% 0.42% 1.85% 4.35%** 4.93%*** 1.21% (-0.80) (0.09) (0.44) (1.38) (2.58) (3.04) (1.30)
Panel B: Market timing coefficient estimates
Q1 (low) 1.28 1.65* 0.88 0.53 -0.18 -1.47 0.85 (1.54) (1.82) (0.86) (0.46) (-0.10) (-0.83) (0.85) Q2 -0.11 -0.31 0.39 -0.05 0.11 0.22 0.01 (-0.11) (-0.38) (0.59) (-0.06) (0.12) (0.20) (0.02) Q3 -0.33 -0.49 -0.75 -0.78 -0.73 -0.39 -0.62 (-0.36) (-0.55) (-1.20) (-0.64) (-0.62) (-0.38) (-0.70) Q4 0.00 -0.28 -0.91*** -0.97* -1.83*** -1.83*** -0.80** (-0.01) (-0.66) (-2.68) (-1.79) (-4.03) (-3.34) (-2.39) Q5 (high) -0.48* -0.53 -0.42 -0.65 -0.93 -0.46 -0.60 (-1.68) (-1.08) (-0.76) (-0.84) (-1.02) (-0.62) (-1.07) All -0.15 -0.27 -0.36 -0.47 -0.88 -0.73 -0.43 (-0.90) (-1.09) (-1.18) (-1.05) (-1.61) (-1.39) (-1.42)
The table reports the annualized stock selection alpha and the market timing coefficient of Treynor and Mazuy (1966). Every test month 𝑡, funds are sorted into portfolios based on 𝑅2
𝑡−1. 𝑅2𝑡−1 is obtained from a 36-month estimation period at time 𝑡 − 1 by
regressing the fund’s monthly excess returns (over 1-month EURIBOR) on the factor returns, using the FFC (Fama and French 1993 and Carhart 1997) factor model. Monthly average excess returns for the portfolios are calculated for each test month 𝑡. This process is repeated by shifting the test month 𝑡 forward one month at a time. Then, months are sorted in quintiles based on 𝐶𝑆𝑉𝑡−1,
where 𝐶𝑆𝑉𝑡−1 is calculated following Eq. (1). S5-S1 is the cross-sectional difference in average returns between the highest and
lowest selectivity portfolio. Alpha for each selectivity portfolio is then estimated by regressing the monthly portfolio returns on the CAPM factor return for each dispersion quintile. The regression intercept, alpha, and the market timing coefficient are reported along with their 𝑡-statistics, using Heteroskedasticity and Autocorrelation Consistent (HAC) standard errors (Newey and West 1987). ***, **, * denote significance at the 1%, 5% and 10% level respectively.
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average market return is somewhat lower in quintile four than in other quintiles, which is potentially driving the “negative” market timing ability. Stock selection alphas are much more positive in higher dispersion quintiles even though they are not significantly different from zero. Nonetheless, higher return dispersion does seem to lead to higher stock selection payoffs. Finally, over the full sample period (row All), the most active fund portfolio generates significant stock selection alpha of 4.35% per annum. Furthermore, the most relative to the least active fund portfolio generates alpha of 4.93%. This outperformance indicates only the most active managers are skilled in selecting (winner) stocks.
Overall, Treynor and Mazuy (1966)’s test provides only limited new insights into stock selection and market timing ability of active mutual funds. Stock selection alphas seem to increase when return dispersion increases, even though they are not significant. Over the full sample period, there is no significant market timing ability present. Overall, the evidence indicates market timing ability is not the main driver of the results.
Lastly, there are several limitations to the market timing specification. First, it ignores other factors affecting the returns of mutual funds, namely the size, value and momentum factors. These factors might affect the market timing coefficients or the stock selection alphas. Second, investors receive the returns from both stock selection and market timing. Hence, while it is useful to see whether funds possess market timing ability, an investor cannot do much with this information.
6.3. Alternative return dispersion environments
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Table 7. FFC alphas alternative dispersion environments: selectivity portfolios and return dispersion quintiles
S1 (low) S2 S3 S4 S5 (high) S5-S1 All Low -3.10%*** -2.13%*** -1.61%** -0.71% 2.47%* 5.74%*** -1.02% (-4.35) (-3.20) (-2.07) (-0.75) (1.70) (3.52) (-1.44) Mid 1.71% 1.77% 1.31% 5.04%*** 6.22%*** 4.43%* 3.17%*** (1.03) (1.46) (1.21) (3.57) (4.19) (1.91) (3.36) High -0.29% -0.10% 1.10% 2.84% 2.56% 2.87% 1.20% (-0.27) (-0.09) (0.75) (1.46) (0.81) (0.98) (0.84) All -0.45% 0.10% 0.21% 1.91%** 3.29%** 3.76%*** 1.00% (-0.73) (0.18) (0.34) (2.30) (2.53) (2.85) (1.63)
The table reports the annualized portfolio alpha. Every test month 𝑡, funds are sorted into portfolios based on 𝑅2
𝑡−1. 𝑅2𝑡−1 is
obtained from a 36-month estimation period at time 𝑡 − 1, by regressing the fund’s monthly excess returns (over 1-month EURIBOR) on the factor returns, using the FFC (Fama and French 1993 and Carhart 1997) factor model. Monthly equal weighted average excess returns for the portfolios are calculated for each test month 𝑡. This process is repeated by shifting the test month 𝑡 forward one month at a time. Then, months are sorted in quintiles based on 𝐶𝑆𝑉𝑡, where 𝐶𝑆𝑉𝑡 is calculated following Eq. (1).
S5-S1 is the cross-sectional difference in average returns between the highest and lowest selectivity portfolio. Alpha for each selectivity portfolio is then estimated by regressing the monthly portfolio returns on the factor returns of the FFC model for each dispersion quintile. The regression intercept, alpha, is reported along with its 𝑡-statistic, using Heteroskedasticity and Autocorrelation Consistent (HAC) standard errors (Newey and West 1987). ***, **, * denote significance at the 1%, 5% and 10% level respectively.
Table 7 reports the annualized alphas for the alternative dispersion environments. The results confirm the conclusions drawn from the main analysis with quintiles. Low return dispersion is detrimental to the performance of funds with low to medium levels of activeness, while the most active fund portfolio generates significant alpha, but only at the 10% level. Furthermore, medium levels of dispersion allow the two most active fund portfolios to generate statistically significant alphas of 5.04% and 6.22% per annum, respectively. In a high dispersion environment, there is no out or underperformance, which is in line with the results in Section 5. Overall, the results are robust to using three return dispersion environments instead of five quintiles.
7. Conclusion
25
dispersion leads to poor performance for the least active funds. Low and medium dispersion periods are driving the outperformance, over the entire sample period, of the most active funds. Additionally, active European equity mutual funds benefit only partially from increased stock selection opportunities during higher levels of return dispersion. Overall, the dispersion environment significantly influences the returns an investor receives.
The results for European mutual funds contrast the results of Von Reibnitz (2015) for US funds. She reports that only high levels of return dispersion earn the most active funds substantial excess returns, while I find that low to medium levels of dispersion generate the largest excess returns. Furthermore, the results partially contradict Cremers and Petajisto (2009)’s study on Active Share since activeness does not lead to outperformance in every dispersion environment. However, they do support the earlier studies, which report that active management, on average, does not add value. I suspect that because funds in Europe are generally smaller than in the US, they behave quite differently, which might explain the different results. For example, there might still be economies of scale present, which provides an additional incentive to grow the assets under management. Consequently, European managers might care more about keeping their tracking error (or even activeness) at reasonable levels in order to attract new capital. Nevertheless, without more research on the relationship between return dispersion and mutual fund performance in Europe, this is just speculation.
26
market, do not outperform in the highest two dispersion quintiles. Additionally, performance is likely to be worse for the less active funds.
Second, the analysis does not explicitly control for fund level characteristics such as expense ratios, total net assets, fund age and manager tenure. For example, Amihud and Goyenko (2013) find a positive and concave relation between 2
1
t
R and fund size, while Otten and Bams (2002) find a positive relation between fund size and performance.5 They suspect European funds still have economies of scale available. Hence, it is possible that the most active funds are small(er) funds so part of the outperformance is actually due to fund size rather than activeness. Similarly, the least active funds are potentially the largest funds, which likely understates the performance by not controlling for size. The other fund characteristics are likely to average out somewhat when forming portfolios, so their impact is smaller.
Lastly, the question arises if it can be expected that 40% of funds outperform over the full sample period, since, in the aggregate, for every winner there must be a loser. However, individual (retail) investors can also be on the losing side. Furthermore, since my sample contains only the surviving funds, it is possible that the mutual funds who “died” were on the losing side as well. Hence, the observed outperformance is reasonable.
There is great potential for future research on return dispersion. Especially in Europe, this topic is under researched, along with the mutual fund industry as a whole. For example, it would be interesting to see how fund size, manager tenure or a proxy for skill are related to the ability of a fund to capture alpha opportunity in the market. Measuring the performance persistence of funds over time, and across dispersion environments, can reflect a managers skill in capturing alpha.
27
Appendix A
Table A1. Mutual fund sample composition: country of domicile
Country of domicile Number of funds % of total funds
France 856 33.6% UK 738 28.9% Germany 185 7.3% Switzerland 170 6.7% Spain 154 6.0% Sweden 94 3.7% Finland 77 3.0% Belgium 69 2.7% Austria 60 2.4% Italy 35 1.4% Liechtenstein 33 1.3% Netherlands 31 1.2% Portugal 19 0.7% Estonia 6 0.2% Greece 5 0.2% Slovenia 4 0.2% Hungary 3 0.1% Isle of Man 3 0.1% Denmark 2 0.1% Malta 2 0.1% Poland 2 0.1% Slovakia 1 0.0% Bulgaria 1 0.0% Latvia 1 0.0% Total 2,551 100.0%
Total ex. France 1,695 66.4%
Total ex. UK 1,813 71.1%
Total ex. France/UK 957 37.5%
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Appendix B
B.1 Dummy variable regression
The methodology using within-quintile FFC regressions might seem unorthodox. However, performing dummy FFC regressions yields the exact same coefficient estimates. There are five dummy variables, one for each dispersion quintile. For example, the dummy DV(Q1) takes the value of 1 if a month is in quintile one, and 0 otherwise. The full specification has 25 (5 5 ) cross-terms, e.g. DV (Q1) *SMB . There are five dummies and five explanatory variables, the intercept
alpha, rmrf , SMB, HML, and WML . Hence, the dummy FFC regression essentially runs five
separate FFC regressions, one for each dispersion quintile. Dummy regressions also allow for tests on the factor loadings, such as if they are significantly different in different dispersion environments.
Table B1 reports the results. There is some evidence of time-varying factor loadings for the most active fund portfolio. The market factor loading in quintile three, 0.75, is significantly different from the factor loadings in quintiles one and two, but not for quintiles four and five. The same is true for the value factor loading of 0.00 in quintile three. The other fund portfolios generally have factor loadings quite close to each other. Overall, mutual funds do not alter their factor exposures significantly over time.
Lastly, the t -statistics are slightly different because of HAC standard errors (Newey and West
1987), which correct for heteroskedasticity and autocorrelation. The autocorrelation is what is causing the t -statistics to be different. However, the main results and conclusions are unaffected
29
Table B1. Dummy variable regression coefficients: portfolios sorted on activeness and return dispersion S1 (low) S2 S3 S4 S5 (high) S5-S1
1 * DV Q alpha -2.50%*** -2.22%** -2.21%** -1.47% 0.64% 3.21%*
2 * DV Q alpha -3.92%** -2.27% -0.37% 0.92% 4.53%** 8.76%***
3 * DV Q alpha 2.73% 2.81%* 1.22% 4.66%** 7.30%*** 4.46%
4 * DV Q alpha -1.37% -0.71% -0.28% 3.71% 2.60% 4.02%
5 * DV Q alpha 1.37% 0.84% 2.12% 3.54%* 3.31% 1.91%
1 * m f DV Q R R 1.05*** 1.04*** 1.07*** 1.06*** 1.02*** -0.03
2 * m f DV Q R R 1.07*** 1.04*** 1.03*** 1.01*** 0.88*** -0.19***
3 * m f DV Q R R 1.00*** 1.00*** 1.02*** 0.95*** 0.75*** -0.25***
4 * m f DV Q R R 0.96*** 0.98*** 1.00*** 0.96*** 0.85*** -0.11**
5 * m f DV Q R R 0.94*** 0.94*** 0.97*** 0.96*** 0.81*** -0.14**
1 * DV Q SMB 0.07 0.10* 0.26*** 0.41*** 0.52*** 0.46***
2 * DV Q SMB 0.09 0.17*** 0.30*** 0.42*** 0.39*** 0.30***
3 * DV Q SMB 0.11* 0.18*** 0.20*** 0.41*** 0.41*** 0.31***
4 * DV Q SMB 0.09** 0.17*** 0.25*** 0.41*** 0.32*** 0.22***
5 * DV Q SMB 0.06** 0.17*** 0.28*** 0.45*** 0.43*** 0.37***
1 * DV Q HML -0.12* -0.15*** -0.24*** -0.30*** -0.39*** -0.27***
2 * DV Q HML -0.19** -0.13** -0.14** -0.24*** -0.13 0.07
3 * DV Q HML -0.05 -0.07 -0.08 -0.11* 0.00 0.06
4 * DV Q HML -0.02 -0.05 -0.12** -0.23*** -0.13* -0.11*
5 * DV Q HML -0.07** -0.06 -0.21*** -0.26*** -0.20** -0.12*
1 * DV Q WML 0.05 0.06 0.02 -0.01 -0.04 -0.09
2 * DV Q WML 0.05 -0.01 -0.07 -0.12** -0.26*** -0.31***
3 * DV Q WML -0.08* -0.06 -0.04 -0.13*** -0.12*** -0.05
4 * DV Q WML -0.08*** -0.08*** -0.07** -0.15*** -0.09** -0.02
5 * DV Q WML -0.03 -0.07*** -0.06** -0.08*** -0.12*** -0.09**The table reports the coefficients from the dummy variable specification, where the alphas have been annualized using monthly returns. Every test month 𝑡, funds are sorted into quintiles based on 𝑅2
𝑡−1. 𝑅2𝑡−1 is obtained from a 36-month estimation period
30
are sorted in quintiles based on 𝐶𝑆𝑉𝑡−1, where 𝐶𝑆𝑉𝑡−1 is calculated following Eq. (1). S5-S1 is the cross-sectional difference in
average returns between the highest and lowest selectivity portfolio. Alpha for each selectivity portfolio is then estimated by regressing the monthly portfolio returns on the factor returns of the FFC model for each dispersion quintile. The regression intercept, alpha, is reported while 𝑡-statistics, using Heteroskedasticity and Autocorrelation Consistent (HAC) standard errors (Newey and West 1987) are omitted for brevity. ***, **, * denote significance at the 1%, 5% and 10% level respectively.
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