The Mismatch between Mutual Fund Scale and Skill

Transcription

1 The Mismatch between Mutual Fund Scale and Skill Yang Song November 4, 2017 Click here for the latest version Abstract I demonstrate that skill and scale are mismatched among actively managed equity mutual funds. Many mutual fund investors behave as though they rely on the Capital Asset Pricing Model. They confuse the effects of fund exposures to other common factors with managerial skill. Actively managed mutual funds with positive factor-related past returns thus accumulate assets to the point that they significantly underperform. I also show that the negative aggregate benchmark-adjusted performance of all actively managed equity mutual funds is caused mainly by the poor performance of this small subset of oversized funds. My model predicts that less skilled active fund managers tilt their portfolios toward common factors in order to gather more flows and collect more fees. I find empirical evidence consistent with the model s predictions. Graduate School of Business, Stanford University. songy@stanford.edu. I am deeply indebted to my advisors, Darrell Duffie and Hanno Lustig, for their continuous support and guidance. I am also grateful to Ken Singleton and Svetlana Bryzgalova for detailed suggestions and serving on my dissertation committee. I would like to thank Juliane Begenau, Jonathan Berk, Shai Bernstein, John Cochrane, Will Gornall, Steven Grenadier, David Hirshleifer, Ben Hébert, Peter Koudijs, Arvind Krishnamurthy, Charles Lee, Jiacui Li, Jiasun Li, Terrance Odean, Paul Pfleiderer, Monika Piazzesi, Jonathan Wallen, Mike Schwert, Amit Seru, Victoria Vanasco, Yao Zeng, Mindy Zhang Xiaolan, Rebecca Zhang, Qingyuan Zhao, and Jeffrey Zwiebel for helpful comments and discussions. 1

2 I. Introduction Mutual fund investors place hundreds of billions of dollars in actively managed equity mutual funds. The extent to which an actively managed mutual fund can add value for investors depends not only on the portfolio manager s skills in discovering superior investment opportunities but also on the scale of the fund. As pointed out by Berk and Green (2004), actively managed mutual funds face decreasing returns to scale. 1 That is, the more assets that an active fund manages, the worse is the fund s return performance, due, for example, to larger price impacts and higher execution costs. In this paper, I demonstrate that skill and scale are mismatched among actively managed equity mutual funds. In particular, because mutual fund flows respond positively to fund past returns arising from exposures to factors other than the market factor, actively managed funds with positive prior factor-related returns (the sum of the return components due to exposures to factors other than the aggregate market), accumulate assets to the point that they significantly underperform various benchmarks. 2 In this sense, these mutual funds garner more assets than can be justified by their managerial skill. I also show that the negative aggregate benchmark-adjusted performance of actively managed mutual funds documented by Malkiel (1995), Gruber (1996), Wermers (2000), and Fama and French (2010) is driven mainly by the poor performance of the small set of funds that have significantly positive prior factor-related average returns. My model and empirical analyses suggest that the oversized underperforming active funds have less skilled managers who tilt their portfolios toward factors that are expected to be compensated with positive premia, in order to gather more flows and thereby collect more fees. My analysis is inspired by the observation of Berk and van Binsbergen (2016) and Barber, Huang, and Odean (2016) that mutual fund flows are better predicted by the CAPM alphas than those of other performance evaluation models, such as the Fama-French-Carhart (FFC) four-factor alphas (Carhart (1997)) and fund returns in excess of the market return (the no model benchmark). 3 In other words, many mutual fund investors appear to confuse the cause for returns associated with fund exposures to common factors (beyond the aggregate market) with managerial skill. In a fully rational world, mutual fund investors would distinguish return components that are due to managerial skill, such as processing private information and discovering mispriced stocks, 1 For supporting evidence, see, for example, Chen, Hong, Huang, and Kubik (2004), Lewis (2015), and Harvey and Liu (2017). Due to methodological differences, Pástor, Stambaugh, and Taylor (2015) find insignificant fund-level decreasing returns to scale, but significant industry-level decreasing returns to scale. See Harvey and Liu (2017) for more discussion. 2 The set of benchmarks that I use includes the Capital Asset Pricing Model (CAPM), the Fama-French-Carhart (FFC) four-factor model (Carhart (1997)), and a seven-factor model that augments the FFC four factors with the three industry factors of Pástor and Stambaugh (2002b) (Barber, Huang, and Odean (2016)). I also use the Vanguard benchmark of Berk and van Binsbergen (2015) and a variant of the Fama-French (FF) three-factor model proposed by Cremers, Petajisto, and Zitzewitz (2013), both of which are constructed by investable indices for mutual fund investors. 3 Those performance evaluation models also include the Fama-French three-factor model (Fama and French (1993)) and several multi-factor models that augment the FFC four factors with the industry factors of Pástor and Stambaugh (2002b) or with the profitability and investment factors of Fama and French (2015). Berk and van Binsbergen (2016) also use some dynamic equilibrium models. 2

3 from components that are due to factor exposures. 4 Because of actual investor behavior, however, actively managed mutual funds with positive factor-related past returns are likely to accumulate so much assets that they have negative expected return performance in the future, because increases in fund size lead to a deterioration in performance. This relationship could be due to the effect of larger trade sizes on price impacts and on other execution costs. 5 My empirical study relies on the CRSP mutual fund database. I focus on actively managed equity mutual funds from 1984 through To estimate a fund s factor-related return, I use the FFC four-factor model. The factor-related return is calculated as the sum of the return components that are traced to size, value, and momentum (not including the market factor). In a companion paper, Song and Zhao (2017) propose an alternative statistical confounding factor approach, which strips out the components of fund returns that can be traced to exposures to factors beyond those of Carhart (1997), without forcing any particular ex-ante specification of the factors. I also estimate the factor-related returns of funds using this confounding factor approach and obtain even sharper results. I start with an analysis of how fund flows respond to factor-related returns. Controlling for factor-adjusted expected returns ( real alpha), I find that fund flows are positively correlated with past factor-related returns, regardless of whether flows are measured in absolute dollars or as a proportion of fund s total assets under management (AUM). For example, funds whose factorrelated average returns over the previous four years are in the top tercile of the sample distribution receive twice as much flows per quarter, on average, as other funds with the same factor-adjusted expected returns. Together with the observation that fund flows also respond positively to factoradjusted expected returns, this evidence is consistent with the findings of Berk and van Binsbergen (2016) and Barber, Huang, and Odean (2016) that fund flows are better explained by the past CAPM alphas than those of some multi-factor models. 6 Because returns of actively managed mutual funds depend critically on fund size (Berk and Green (2004)), I proceed by studying how past factor-related returns are correlated with future return performance. In particular, I find a significantly negative relationship between a fund s past factor-related average returns and its future returns. For example, active mutual funds in the top decile by factor-related average returns over the previous four years, on average, underperform the bottom decile of funds by 450 to 550 basis points (bps) over the subsequent year. (The particular excess return depends on the benchmark.) I also find that controlling for factor-adjusted expected 4 As observed by Pástor and Stambaugh (2002a), Alpha is often interpreted as skill displayed by the fund s manager in selecting mispriced securities, but a nonzero alpha need not reflect skill if some passive assets can also have nonzero alphas. In that scenario, a manager could achieve a positive alpha in the absence of any skill simply by starting a new fund that invests in nonbenchmark passive assets with historically positive alphas. To address such concerns, one can expand the set of benchmarks to include more passive assets, even to the point of including all assets available to the manager. 5 With a sufficiently large fund, a manager may also spread his or her information-gathering activities too thin. See Section IV for more discussion of decreasing returns to scale. 6 This is because one can decompose a fund s CAPM alpha as the sum of its factor-related average return and its factor-adjusted expected return. (See Section II.B.) Barber, Huang, and Odean (2016) also show that factor-related returns are significant predictors of fund flows. 3

4 returns ( real alpha), or controlling for fund size, or controlling for the dollar-value-added measure proposed by Berk and van Binsbergen (2015), funds with positive prior factor-related average returns have significantly negative future return performance and underperform other funds. show that these findings are not explained by mean reversion in factor exposures. 7 I also provide a comprehensive set of robustness checks. This behavior is consistent with a market in which active funds with positive prior factor-related returns accumulate so much assets that they subsequently have significantly negative performance through the effect of diminishing returns to scale. Malkiel (1995), Gruber (1996), Wermers (2000), and Fama and French (2010) document that the aggregate actively managed equity mutual fund portfolio has significantly negative benchmarkadjusted returns after fees. 8 In fact, I find that this negative aggregate performance is caused mainly by the poor performance of the top third of funds in the sample by prior factor-related average returns. These funds with positive prior factor-related returns have significantly negative average benchmark-adjusted net returns over the subsequent year, ranging from 190 to 260 bps depending on benchmark. (Gross of fees, the future annual benchmark-adjusted returns of these funds average from 90 to 160 bps.) In contrast, the other two-thirds of funds have near zero benchmark-adjusted returns over the subsequent year, net of fees, and significantly positive benchmark-adjusted returns gross of fees. I provide evidence that this sharp difference in fund performance can be explained by fund flows associated with positive prior factor-related returns through the scale effect. Previous work, for example, Chen, Hong, Huang, and Kubik (2004), Yan (2008), Pollet and Wilson (2008), and Edelen, Evans, and Kadlec (2009), identifies execution costs and other liquidity constraints as important causes of diminishing returns to scale for actively managed mutual funds. By exploring crosssectional variation in execution and trading costs of active mutual funds, I demonstrate that the negative performance of active funds with positive prior factor-related returns is more significant among those funds that have higher execution and trading costs. This is consistent with the hypothesized scale effect. In this sense, these flows into funds with positive prior factor-related returns are more than can be justified by the managerial skill of the fund managers. Given the finding that fund flows respond positively to past factor-related returns, it is natural to ask how fund managers with different levels of active management skill choose their factor exposures differently. I answer this question with both theoretical and empirical analyses. My theoretical model endogenizes the decreasing returns to scale of active asset management. The model assumes that mutual fund flows treat fund returns that are actually attributable to common factors other than the market factor (such as momentum or value) as signals of managerial skill. Under the model assumptions, active fund managers with lower managerial skill tilt their portfolios toward common factors that are expected to be compensated with positive premia in order to gather more flows. These less skilled active managers, would otherwise, collect lower management fees, so are 7 Barber, Huang, and Odean (2016) show that the factor exposures of actively managed equity mutual funds are mean reverting. 8 Fama and French (2010) also document that the aggregate portfolio has near zero benchmark-adjusted returns gross of fees. I 4

5 less averse to the reputational risk of loss resulting from factor exposures. I find empirical evidence consistent with these theoretical predictions. In summary, I analyze the joint dynamics of several key variables: fund flows, factor-related past returns, and factor-adjusted expected returns. For this purpose, I also estimate a structural panel vector autoregressive (PVAR) model. The structural PVAR model captures the economic relationships among these three variables as follows. Positive shocks to both factor-related average returns and factor-adjusted expected returns are associated with increased investment flows into a mutual fund. Growth in a fund s size is associated with an erosion in future performance. As a result, past factor-related returns are negatively correlated with future factor-adjusted expected returns. This paper contributes to the extensive mutual fund literature in several ways. First, the results in this paper have implications for aggregate mutual fund performance and for a long-running debate over whether managerial skill exists. 9 Malkiel (1995), Gruber (1996), Wermers (2000), and Fama and French (2010) document that the aggregate actively managed equity mutual fund portfolio has significantly negative benchmark-adjusted returns after fees, and has near zero average benchmarkadjusted returns before fees. This fact has been used to argue for a lack of managerial skill for equity fund managers. I show instead that the negative aggregate return performance is caused mainly by the poor performance of the small set of active funds with significantly positive factor-related past returns. The majority of mutual fund managers have significant positive benchmark-adjusted returns before fees, indicating they are sufficiently skilled to outperform benchmarks. Second, this paper fits into the literature that examines the relationship between mutual fund performance and investment flows into mutual funds. 10 Berk and van Binsbergen (2016) and Barber, Huang, and Odean (2016) show that mutual fund flows are better explained by the CAPM model than by some other performance evaluation models. This paper goes further by demonstrating that the flows from investors based on factor-related past returns lead to a significant mismatch between scale and skill among actively managed mutual funds. On average, active mutual funds with positive factor-related past returns accumulate so much assets that they have significantly negative expected future performance. The data are consistent with a model, which I provide, in which mutual fund managers have incentives to garner more flows and thereby collect more fees by loading on factors other than the aggregate market. These incentives are greater for lesser skilled 9 On the one hand, Jensen (1968), Malkiel (1995), Gruber (1996), Carhart (1997), Wermers (2000), Bollen and Busse (2001), French (2008), and Fama and French (2010), among others, argue that mutual fund managers lack skills. On the other hand, empirical work finds evidence of managerial skill includes Grinblatt and Titman (1989), Grinblatt and Titman (1993), Daniel, Grinblatt, Titman, and Wermers (1997), Chevalier and Ellison (1999), Moskowitz (2000), Kacperczyk, Sialm, and Zheng (2005), Kosowski, Timmermann, Wermers, and White (2006), Kacperczyk and Seru (2007), Cohen, Frazzini, and Malloy (2008), Kacperczyk, Sialm, and Zheng (2008), Cremers and Petajisto (2009), Glode (2011), Del Guercio and Reuter (2013), Kacperczyk, Van Nieuwerburgh, and Veldkamp (2014), Berk and van Binsbergen (2015), and Kempf, Manconi, and Spalt (2017). Berk and Green (2004), taking a theoretical perspective, explain why mutual fund performance does not persist even if fund managers are skilled. Berk and van Binsbergen (2015) also summarize this debate. 10 Early work includes Ippolito (1992), Chevalier and Ellison (1997), Sirri and Tufano (1998), Lynch and Musto (2003), Frazzini and Lamont (2008), Pástor and Stambaugh (2012), and Pástor, Stambaugh, and Taylor (2015), among many others. See Barber, Huang, and Odean (2016) for a more comprehensive review. 5

6 Log number of funds CRSP Code: ED CRSP Code: EF ED funds AUM Fraction of AUM Log AUM % 75% 50% 25% 5% Year Year Figure 1: Number of funds & fund size distribution. The first graph displays the logarithm of the number of actively managed equity mutual funds that invest at least 75% of their assets in the domestic equity market (CRSP Code starting with ED ) and the logarithm of the number of actively managed equity mutual funds that invest at least 25% of their assets in the international equity market (CRSP Code starting with EF ) that are included in the sample. The first graph also displays the total assets under management (AUM) of CRSP ED funds as a fraction of the aggregate AUM of all funds in the sample. The second graph displays the evolution of the distribution of the logarithm of AUM of all funds in millions of dollars by plotting the 5th, 25th, 50th, 75th, and 95th percentiles of the distribution in each year. active fund managers. The rest of the paper is organized as follows. Section II introduces the dataset and the econometric models used in this paper, including the confounding-factor model of Song and Zhao (2017). Section III analyzes how mutual fund flows respond to fund returns that are related to common factors other than the aggregate market, and how mutual funds that have experienced different factor-related returns perform differently in the future. Section IV offers both theoretical and empirical analyses of the choices by a fund manager of factor exposures when assuming that fund flows chase positive factor-related returns. Section V estimates a structural panel vector autoregressive model that describes the joint dynamics of fund flows, factor-adjusted returns, and factor-related returns. Section VI provides concluding remarks. Proofs and robustness checks are found in appendices. II. Data and Factor Models In this section, I describe the mutual fund dataset and how I estimate factor-related average returns, factor-adjusted expected returns, and fund flows, the three key variables whose relationships are explored in this paper. 6

7 A. Data I use the standard CRSP survivorship-bias-free mutual fund database, spanning from 1984 to I focus on actively managed equity mutual funds that invest at least 75% of their assets in the domestic equity market (CRSP Objective Code starting with ED ). Appendix C.A provides similar results when including actively managed equity mutual funds that invest at least 25% of assets in the international equity market (CRSP Objective Code starting with EF ). For this analysis, I eliminate index funds, balanced funds, sector funds, and ETFs. Mutual funds often market different share classes of the same portfolio to different types of clients. The key difference across these subclasses is, in most cases, the fee structure. I aggregate all subclasses into a single fund. I include only those funds whose monthly returns are fully available for at least four years. 11 I then exclude funds which never managed more than $5 million in total assets. Figure 1 shows the resulting number of equity mutual funds in each year, along with summary statistics regarding assets under management (AUM). The figure shows a significant rising trend in the number of funds. In total, the resulting sample includes more than 5000 distinct mutual funds. B. Estimation of factor-related returns and factor-adjusted returns A mutual fund s expected return can be decomposed, through linear factor models, into the fund s factor-adjusted expected return and the mean return components arising from exposures to the specified set of factors. For this decomposition, I use the four factors of the Fama-French- Carhart (FFC) model (Carhart (1997)). I estimate the following time-series regression of prior monthly excess returns for each individual fund i. For some number m of months prior to a given time t, r i,τ r f,τ = αi,t ffc + b i,t (MKT τ r f,τ ) + s i,t SMB τ + h i,t HML τ { +p i,t UMD τ + ν i,τ, τ t m 12,..., t 1 }, (1) 12 where r i,τ is the mutual fund return net of fees in month τ; r f,τ is the risk-free interest rate; 12 MKT is the return on the value-weighted market portfolio; SMB, HML, and UMD are the returns on the three factor portfolios in Fama and French (1993) and Carhart (1997) adjusted by the market 11 My sample misses a small group of actively managed equity mutual funds in the CRSP database, which are terminated within a relatively short period (less than four years) after their appearance in the database. In the survival analysis in Appendix G, I find that factor-related average past returns and factor-adjusted expected returns have similar effects on fund termination. Thus, my later analysis (Section III) of the influence of factor-related average past returns on fund flows and fund future return performance, controlling for factor-adjusted expected returns, is unlikely to be affected by this survival bias. 12 The risk-free interest rate here is the one-month Treasury bill rate. I download the interest rate series together with the factor returns from Kenneth French s website ( data_library.html). As a robustness check, I also use one-month overnight index swap (OIS) rate. The OIS rate is the fixed rate on an overnight index swap, which pays a predetermined fixed rate in exchange for receiving the compounded daily federal funds rate over the term of the contract. The results are similar and are provided upon request. 7

8 return. 13 The parameter αi,t ffc is the factor-adjusted expected return (the FFC four-factor alpha), while b i,t, s i,t, h i,t, and p i,t are the fund exposures to the market, size, value, and momentum, respectively. The noise term ν i,t is assumed to have a zero mean and satisfy the standard assumptions of ordinary least squares (OLS). 14 Using the fund-by-fund OLS estimators ŝ i,t, ĥi,t, and ˆp i,t for the corresponding coefficients in equation (1), the factor-related average return for fund i over the prior m months from time t is i,t = 1 m t 1/12 τ=t m/12 (ŝ i,t SMB τ + ĥi,thml τ + ˆp i,t UMD τ ). (2) That is, the factor-related average return i,t is the estimated sum of mean return components that are due to exposures to size, value, and momentum, over the previous m months. This factorrelated average past return does not incorporate the effect of exposure to the market factor MKT, because the market-factor-related returns are found to be mostly irrelevant for fund flows (Berk and van Binsbergen (2016) and Barber, Huang, and Odean (2016)). I also estimate, using OLS, the CAPM alpha, denoted α capm i,t, for each fund i over the same prior m months from the regression { r i,τ r f,τ = α capm i,t + β i,t (MKT τ r f,τ ) + η i,τ, τ t m 12,..., t 1 }, (3) 12 where β i,t is the market beta, and the noise term η i,τ is assumed to satisfy the standard OLS assumptions. Because the other three factors in (1) have been adjusted for market exposures, so are orthogonal to the market factor, the CAPM alpha α capm i,t can be decomposed as ˆα capm i,t = ˆα ffc i,t + i,t. (4) C. A confounding-factor approach There could be other factors beyond the FFC factors that explain cross-sectional variation in mutual fund returns. By accounting for the effects of those other factors on fund returns, one could better distinguish between return components that are due to managerial skill ( real alpha) from components that are due to exposures to factors that many other funds are also exposed to. To this end, Song and Zhao (2017) develop a novel statistical confounding factor approach, which strips out the components of fund returns that can be traced to exposures to factors beyond those of Carhart (1997), without forcing any particular ex-ante specification of the factors. 13 That is, I orthogonalize the return of each of the three factors to the market return. 14 See Page 52 of Greene (2010) for standard OLS assumptions. 8

9 The associated model of returns of fund i at time t for a lagging month τ, is r i,τ r f,τ = αi,t cf + γi,t(mkt m τ r f,τ ) + γi,tsmb s τ + γi,thml h τ + γi,tumd u τ w { + γ j i,t Zj τ,t + ζ i,τ, τ t m 12,..., t 1 }. (5) 12 j=1 where Z 1,..., Z w are the most significant w confounding factors, after controlling for the FFC four factors that explain cross-sectional variation in mutual fund returns. The confounding factors Z 1,..., Z w are not specified in advance. Instead, they are estimated from mutual fund returns. The parameter αi,τ cf is the factor-adjusted expected return based on this confounding-factor approach. The noise term ζ i,τ is assumed to satisfy the standard OLS assumptions. Song and Zhao (2017) develop a statistical procedure that estimates model (5) consistently and efficiently. Details of the estimation procedure are provided in Appendix A. I use three confounding factors (w = 3) when estimating this confounding-factor model. 15 The factor-related average return for fund i over the prior m months of time t, based on this alternative, is calculated as cf i,t = 1 m t 1/12 τ=t m/12 ˆγ s i,tsmb τ + ˆγ h i,thml τ + ˆγ u i,tumd τ + 3 j=1 ˆγ j i,t Zj τ,t, (6) where γi,t s, ˆγh i,t, ˆγu i,t and {ˆγj i,t, j = 1, 2, 3} are the estimates of the corresponding coefficients in model (5). This confounding-factor approach can better estimate mutual fund returns that are traced to fund exposures to common factors than the FFC four-factor model. It also improves the identification of the underperforming funds (Section III.D). More results based on this approach are deferred to Appendix A. D. Estimation of fund flows Before 1992, most mutual funds reported their assets under management (AUM) only quarterly. Thus, I calculate investment flows into each fund on a quarterly basis. Following prior research on fund flows, for example, Chevalier and Ellison (1997) and Berk and van Binsbergen (2016), the investment flow into fund i in the quarter that ends at time t is estimated as Flow i,t = AUM i,t where AUM i,t is fund i s total assets under management at time t. 2 ( ) 1 + ri,t j/12 AUMi,t 1/4, (7) j=0 15 Owen and Wang (2016) provide criteria to determine the optimal number of confounding factors by crossvalidation. The choice of w = 3 is based on Owen and Wang (2016). Results with other numbers of confounding factors are similar and are provided upon request. 9

10 III. Factor exposures, flows, and future performance In this section, I analyze how mutual fund flows respond to past factor-related returns. 16 I also estimate the influence of the past factor-related returns of a mutual fund on its future returns. I find that (i) controlling for factor-adjusted expected returns ( real alpha), mutual fund flows are positively correlated with past factor-related returns, (ii) controlling for factor-adjusted expected returns, funds with positive prior factor-related average returns have significantly negative return performance and underperform other funds in the future, (iii) controlling for fund size, funds with positive prior factor-related average returns have significantly negative future performance and underperform other funds, (iv) a fund s future return performance is decreasing in its prior factor-related average returns, and (v) the negative aggregate performance of actively managed mutual funds is driven mainly by the poor performance of the small set of funds with significantly positive prior factor-related average returns. I also provide evidence that the negative performance of this small set of funds can be explained by flows into these funds associated with positive prior factor-related returns through the effect of diminishing returns to scale. In this sense, these flows are excessive and erode fund performance through the effect of larger trade sizes on price impacts and on other components of execution costs. A. Mutual fund flows and factor-related returns I first examine how mutual fund flows respond to prior factor-related returns. I take a rollingwindow approach, as follows. For each calendar year of data, I sort all mutual funds into decile portfolios based on a fund s factor-adjusted expected return in (1), as estimated using monthly returns in the prior four years. 17 For example, the top decile portfolio is the set of mutual funds with the highest FFC four-factor alpha over the prior four-year estimation period. I then split each decile portfolio into three subgroups based on the sample distribution of factor-related average returns in (2) of all mutual funds, as estimated over the same four-year period. That is, the first group within each decile consists of those funds whose estimated factor-related average past fouryear returns are in the top third of all funds by that measure (not just the set of funds included in that decile). The middle and bottom groups consist of those funds whose estimated factor-related average past four-year returns are in the middle and bottom thirds of all funds by that measure, respectively. 18 I then calculate average quarterly fund flows for all fund portfolios over the same 16 As I have defined in Section II.B, a fund s factor-related return refers to the sum of the return components that are due to exposures to a set of common factors other than the aggregate market. 17 Kamstra, Kramer, Levi, and Wermers (2017) find that the flows of investment from other fund categories, for example, money market and bond mutual funds, into equity mutual funds are more likely to happen in the spring. To account for this seasonality in asset allocation, each of the four-year estimation windows ends in March of a given year. I also use a three-year estimation window. The results are similar and are provided upon request. 18 The factor-adjusted expected returns and the factor-related average returns are correlated cross-sectionally. (See Section IV for a discussion.) Dividing each FFC-alpha decile this way allows an analysis of how fund flows respond to similar factor-related average returns across different FFC-alpha deciles. As a result, the three groups within a given decile do not necessarily consist of equal numbers of funds. 10

11 four-year period. 19 I compare flows of funds into each of the three groups of funds within a given FFC-alpha decile. Because funds in the same decile have similar past factor-adjusted expected returns, this allows an analysis of how mutual fund flows respond to factor-related returns, while controlling for factoradjusted expected returns. The same analysis is done based on the confounding-factor model (5). The conclusions for this alternative approach are similar and presented in Appendix A. Table I reports the time-series average of fund flows and the time-series average of factor-related average returns for all fund portfolios. As one can see, the first group of funds in each FFC-alpha decile has positive average factor-related returns (ranging from 3.4% to 4.5% per year). These funds, on average, attract more flows than the two lower factor-related return groups of the same FFC-alpha decile. The middle group in each decile has average factor-related returns that are near 0%, and average flows that are higher than those of the bottom group, which has negative average factor-related returns. Due to these differences in fund flows, the higher factor-related return group in each FFC-alpha decile, on average, has a larger AUM at the end of a given four-year estimation period than the two lower factor-related return groups within the same decile. By comparing the ten rows in columns (3), (8), or (13) of Table I, one can see that fund flows also respond positively to factor-adjusted expected returns. The last column of Table I shows the results of tests of a positive difference in average fund flows between the top and bottom groups within a given factor-adjusted return decile. To estimate the standard errors for the flow differences, I bootstrap the entire sample 10,000 times, and I repeat the same exercise described in this section for each bootstrap sample. 20 The standard errors are estimated as the sample standard deviations of the corresponding flow differences across all bootstrap samples. As one can see, all of the test statistics are significant at conventional confidence levels (the p-values based on the bootstrap sample distribution are below 3%), implying a rejection of the null hypothesis of identical mean flows into the top and bottom groups of each of the factor-adjusted return deciles. For example, consider the ninth factor-adjusted expected-return decile in Table I. Averaging across four-year time windows, the first group of funds (those with top-tercile prior factor-related average returns) attracts $35.1 million of investment flows per quarter and has an AUM that grows from $728.7 million to $ million. The bottom group of this decile (those funds with bottomtercile prior factor-related average returns) receives only about a third as much flows and has an AUM that, on average, grows from $801.4 million to only $984.5 million over four-year estimation periods. The middle group receives an average of $26.7 million inflows per quarter during these four-year time windows. In summary, Table I shows that higher past factor-related average returns are associated with 19 Because investors might not respond immediately to recent returns, I also calculate quarterly fund flows for all fund portfolios over the last three years, or two years, or one year of each four-year estimation window. I reach the same conclusion, and the results are provided upon request. 20 To get one bootstrap sample, I resample the funds identities with replacement, and I use the entire history of each resampled fund. For details of the bootstrap algorithm, see Appendix E. 11

12 Table I Response of fund flows to factor-related average returns. For each calendar year of data, mutual funds are sorted into decile portfolios based on the FFC four-factor alpha over the prior 48 months. Each FFC-alpha decile portfolio is then divided into three subgroups depending on the sample distribution of factor-related average returns in (2) of all funds, as estimated over the same four-year period. The top, middle, and bottom groups within a given decile consist of funds whose estimated factor-related average past four-year returns are in the top, middle, and bottom thirds of all funds by that measure, respectively. AUMt 4 and AUMt (in millions) are the time-series average of cross-sectional mean of assets under management for a given fund portfolio at the beginning and the end of each four-year estimation period, respectively. Flow (in millions) is the time-series average of cross-sectional mean of average quarterly flows over each four-year estimation period. α capm and (in %) are the time-series average of cross-sectional mean of CAPM alpha and factor-related average return, respectively. P (Flow) is the p-value of test of a positive difference in average fund flows between the top and bottom groups within a given decile. AUMt 4 AUMt Flow α capm AUMt 4 AUMt Flow α capm AUMt 4 AUMt Flow α capm P (Flow) top-tercile middle-tercile bottom-tercile (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) 1 (L) % % % % % % % % % 10 (H) % 12

13 larger fund flows for actively managed equity mutual funds, controlling for factor-adjusted expected returns. Together with the observation that fund flows also respond positively to factor-adjusted expected returns, this evidence is consistent with the findings of Berk and van Binsbergen (2016) and Barber, Huang, and Odean (2016) that fund flows are better predicted by the CAPM alphas than the FFC four-factor alphas (decomposition (4)). Given that fund flows reveal the preferences of mutual fund investors, this result is consistent with an economy in which many mutual fund investors treat return components that are actually attributable to size, value, and momentum as though they are signals of active management skill, and in which these investors respond by investing more in funds with higher prior factor-related returns. 21 B. Fund flows and fund future performance Given the finding that factor-related past returns are positively correlated with mutual fund flows, I now estimate the influence of a fund s prior factor-related returns on its future returns. B.1. Controlling for factor-adjusted expected returns As pointed out by Berk and Green (2004) and as empirically supported by, for example, Chen, Hong, Huang, and Kubik (2004), Lewis (2015), and Harvey and Liu (2017), mutual fund performance depends critically on fund size. That is, the more assets that an active fund manages, the worse is the fund s return performance, controlling for other determinants of performance. 22 I call this the scale effect. I have shown that funds with positive past factor-related returns garner higher flows and have larger AUM than other funds, controlling for prior factor-adjusted expected returns ( real alpha). These funds with positive prior factor-related returns are thus expected to underperform in the future due to the scale effect. To verify that the scale effect applies in my setting, I follow the same rolling-window sorting procedure 23 described in Section III.A. I am interested in the future return performance of the first group of funds in each FFC-alpha decile. For each calendar year of data, this first group consists of those funds with top-tercile factor-related average returns over the previous four years. As shown in Table I, these top-tercile funds receive twice as much flows per quarter, on average across the entire sample period, as other funds with the same prior factor-adjusted expected returns. 21 Relying on cross-sectional variation in investor sophistication and time-series variation in market sentiment, Barber, Huang, and Odean (2016) provide evidence supporting the argument that many mutual fund investors confuse the effects of fund exposures to those common factors with managerial skill. Berk and van Binsbergen (2016) interpret this result as indicating that those factors other than the aggregate market do not help explain how investors measure risk. For a more detailed discussion, see Barber, Huang, and Odean (2016). 22 This relationship could be due to larger price impacts and higher trading and execution costs, among other reasons. For example, fund managers are likely to pay larger bid-ask spreads for larger trades, which diminish the returns available to pay out to fund investors. 23 That is, for each calendar year of data, I first sort all mutual funds into decile portfolios based on the prior factor-adjusted expected returns, as estimated by monthly returns in the past four years. I then split each decile into subgroups depending on the sample distribution of factor-related average returns of all funds, as estimated over the same four-year period. 13

14 CAPM alpha (%) FFC alpha (%) MF alpha (%) decile (a) Group 1: CAPM alpha decile (b) Group 1: FFC alpha decile (c) Group 1: MF alpha CAPM alpha (%) FFC alpha (%) MF alpha (%) decile (d) Group 2: CAPM alpha decile (e) Group 2: FFC alpha decile (f) Group 2: MF alpha Figure 2: Out-of-sample return performance after fees: control for the FFC four-factor alpha. For each calendar year of data, mutual funds are sorted into decile portfolios based on the FFC four-factor alpha, as estimated over the prior 48 months. Each decile portfolio is then divided into two groups, depending on whether a fund s average factor-related return in (2) over the same four-year period is in the top third of all funds by that measure. Group 1 in each decile consists of those funds with top-tercile factor-related average past four-year returns. I then compute the monthly AUM-weighted net returns in the next 12 months for each fund portfolio. The time series of monthly AUM-weighted returns over the entire sample period is regressed on the market return, the FFC four factors, and the BHO seven factors to obtain the out-of-sample benchmark-adjusted returns for a given fund portfolio. The dashed lines denote the 95% confidence intervals. To measure future return performance, after sorting mutual funds into factor-adjusted expectedreturn deciles for each calendar year of data, I compute the monthly AUM-weighted returns in the next one year for the first group of funds in each decile. For comparison, I also calculate the monthly AUM-weighted returns of the remaining funds in each decile (those with lower prior factorrelated average returns). The time series of the monthly AUM-weighted returns over the entire sample period for a given fund portfolio is then benchmarked to the CAPM model, the FFC fourfactor model, and the seven-factor model of Barber, Huang, and Odean (2016). The seven-factor BHO model augments the FFC four-factor model with the three industry factors 24 of Pástor and Stambaugh (2002b). I report the results in Figure 2 and Table II. 24 The industry factors are the first three principal components of the residuals in multiple regressions of the Fama- French 49 industry returns on the MKT, SMB, HML, and UMD factors. Thus, the industry factors capture common industry returns orthogonal to the other four factors. I use this seven-factor model to evaluate fund performance because Song and Zhao (2017) find that the industry factors explain cross-sectional variation in mutual fund returns. 14

15 Table II Out-of-sample return performance after fees: control for the FFC four-factor alpha. For each calendar year of data, mutual funds are sorted into decile portfolios based on the FFC four-factor alpha, as estimated over the prior 48 months. Each decile portfolio is then divided into two groups, depending on whether a fund s average factor-related return in (2) over the same four-year period is in the top third of all funds by that measure. Group 1 in each decile consists of those funds with top-tercile factor-related average past four-year returns. I then compute the monthly AUM-weighted net returns in the next 12 months for each fund portfolio. The time series of monthly AUM-weighted returns over the entire sample period is regressed on the market return, the FFC four factors, and the BHO seven factors to obtain the out-of-sample benchmark-adjusted returns for a given fund portfolio. ***,**,and * denote statistical significance at 1%, 5%, and 10% level, respectively. Ret(%) α capm (%) α ffc (%) α mf (%) Group 2 Group 1 Diff Group 2 Group 1 Diff Group 2 Group 1 Diff Group 2 Group 1 Diff (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) 1 (L) * ** *** 2.08 (1.34) (1.54) (1.69) (1.29) (1.53) (1.74) (1.25) (1.48) (1.80) *** 2.07* *** 2.23* *** 2.33* (0.77) (1.07) (1.24) (0.73) (1.05) (1.30) (0.82) (1.03) (1.36) *** 2.08* *** 2.44** *** 2.50** (0.67) (0.94) (1.16) (0.65) (0.92) (1.18) (0.61) (0.92) (1.21) * *** 2.67** *** 2.69* (0.82) (0.90) (1.30) (0.81) (0.89) (1.34) (0.76) (0.86) (1.40) ** 2.23* ** 2.24* (0.68) (0.97) (1.30) (0.69) (0.93) (1.32) (0.65) (0.91) (1.34) ** ** 1.48 (0.73) (0.86) (1.08) (0.69) (0.82) (1.08) (0.61) (0.77) (1.11) * 2.22* ** 2.19* ** 2.12* (0.60) (0.89) (1.22) (0.61) (0.89) (1.25) (0.59) (0.88) (1.30) * ** 2.45** ** 2.50** (0.52) (0.85) (0.99) (0.53) (0.83) (0.99) (0.50) (0.80) (1.04) ** 2.73** ** 2.92** ** 3.16** (0.69) (1.10) (1.31) (0.69) (1.13) (1.35) (0.66) (1.08) (1.40) 10 (H) * ** 3.08** ** 3.06* (1.10) (1.70) (1.55) (0.95) (1.71) (1.53) (0.92) (1.65) (1.60) All ** 1.92* *** 2.41** *** 2.47** (0.55) (0.82) (1.08) (0.54) (0.81) (1.10) (0.55) (0.79) (1.10) 15

16 Some striking patterns emerge. On the one hand, funds with top-tercile past factor-related returns, on average, have significantly negative net returns of 191 bps, 238 bps, and 258 bps over the subsequent year, when adjusted by the aggregate market return, by the FFC four factors, and by the BHO seven factors, respectively. For example, the FFC four-factor adjusted net future returns of the top-tercile funds range from 191 bps to 350 bps across the various deciles. On the other hand, the remaining funds in each factor-adjusted expected-return decile have net-offees future returns that are not statistically different from zero, under all three benchmarks. 25 Their average net returns over the subsequent year are 1 bps, 3 bps, and 11 bps under the three benchmarks, respectively. When using the confounding-factor approach described in Section II.C to estimate the factor-related and factor-adjusted returns of mutual funds, I get even sharper results, which are presented in Appendix A. A superficially plausible alternative story is that the negative future performance of funds with positive factor-related past returns is caused by mean reversion in factor exposures. This alternative story does not explain the evidence, however, because I measure future performance relative to the FFC four-factor model and the seven-factor model, which already strip out the impact of mean reversion in factor exposures. 26 B.2. Controlling for fund-level AUM In Sections III.A and III.B.1, I showed that, controlling for factor-adjusted expected returns, funds with positive prior factor-related returns garner larger flows and underperform benchmarks and other funds in the future. To put it differently, imagine two mutual funds that have the same assets under management at a given point of time. Fund A has reached its current size because of positive prior factor-related returns. Fund B has negligible prior factor-related returns and has attracted flows instead by relying on investor recognition of its factor-adjusted expected returns. Fund A would then be expected to have worse future return performance than fund B. To further my analysis of this phenomenon, I follow the rolling-window approach of Section III.B.1, except that I sort all mutual funds into decile portfolios based on fund AUM at the end of each four-year estimation window. As in Section III.B.1, funds in the first group of each AUM decile have top-tercile past-four-year factor-related average returns, as estimated from (2), that are significantly positive (around 4% on an annual basis). I then measure future performance for all fund portfolios relative to the CAPM model, the FFC four-factor model, and the BHO seven-factor model as in Section III.B.1. I present the results in Figure 3 and Table III. As one can see, controlling for AUM, funds with top-tercile prior factor-related average returns significantly underperform other funds. For example, when benchmarked to the FFC four-factor model, funds with top-tercile prior factor-related average returns have future annual returns net of fees that are significantly lower than those of other funds with the same AUM. The differences 25 These tests are based on the linear regressions of the returns of a fund portfolio on a given set of factors. 26 I analyze mean reversion in factor exposures of actively managed equity mutual funds in Appendix F. This mean reversion actually helps to explain the negative future CAPM alpha. See Appendix F for more discussions. 16

17 CAPM alpha (%) FFC alpha (%) MF alpha (%) decile (a) Group 1: CAPM alpha decile (b) Group 1: FFC alpha decile (c) Group 1: MF alpha CAPM alpha (%) FFC alpha (%) MF alpha (%) decile (d) Group 2: CAPM alpha decile (e) Group 2: FFC alpha decile (f) Group 2: MF alpha Figure 3: Out-of-sample return performance after fees: control for fund AUM. For each calendar year of data, mutual funds are sorted into decile portfolios based on fund AUM at the year-end. Each decile is divided into two groups, depending on whether a fund s average factor-related return in (2), as estimated over the prior four years, is in the top third of all funds by that measure. Group 1 in each AUM decile consists of those funds with top-tercile factor-related average past four-year returns. I compute the monthly AUM-weighted net returns in the next 12 months for each fund portfolio. The time series of monthly AUMweighted returns over the entire sample period is regressed on the market return, the FFC four factors, and the BHO seven factors to obtain the out-of-sample benchmark-adjusted returns for a given fund portfolio. The dashed lines denote the 95% confidence intervals. range from 207 bps to 340 bps per year across the various AUM deciles. On an absolute basis, while the top-tercile funds in each AUM decile have significantly negative future performance under all three benchmarks, the remaining funds across the various AUM deciles have benchmark-adjusted future net returns that are not statistically different from zero. In Appendix C, I also compare future fund returns by controlling for the prior dollar-value-added measure proposed by Berk and van Binsbergen (2015). This measure is, approximately, the AUM multiplied by the prior factor-adjusted expected return gross of fees. Berk and van Binsbergen (2015) argue that the dollar value added by a mutual fund is a reflection of its managerial skill. When controlling for dollar value added, I still find that funds with positive prior factor-related returns underperform other funds. The results in Section III.A, Section III.B, and Appendix C are all consistent with a market in which mutual funds with positive prior factor-related returns accumulate so much assets that they have significantly negative future return performance caused by diminishing returns to scale. In 17