Omitted Risks or Crowded Strategies: Why Mutual Fund Comovement Predicts Future Performance

Omitted Risks or Crowded Strategies: Why Mutual Fund Comovement Predicts Future Performance Timothy K. Chue December 2015 I wish to thank John Campbell, Tarun Chordia, Gang Hu, Byoung Kang, Charles Lee, Alexander Ljungqvist, Mujtaba Mian, Sergei Sarkissian, Avanidhar Subrahmanyam, Qinghai Wang, and Jing Xie for helpful comments, Manhong Chan for able research assistance, and the Hong Kong Polytechnic University and the Research Grants Council of the Hong Kong Special Administrative Region, China for research support. School of Accounting and Finance, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong. E-mail: Timothy.Chue@polyu.edu.hk. Tel: +852-2766-4995. Fax: +852-2330-9845. 1

Omitted Risks or Crowded Strategies: Why Mutual Fund Comovement Predicts Future Performance Abstract Mutual funds return comovement with past winners (losers) identifies an exposure to transitory good (poor) performance making the past alpha of funds with such exposure an overestimate (underestimate) of their true alpha. This identification is robust to the inclusion of active share, benchmark 2 return gap, style tilts, and other fund characteristics as controls. Among mutual funds with similar past alphas, those that had comoved with past losers have future alphas that exceed those that had comoved with past winners by 0.249% per month. Among past winners, the subgroup that did not comove with other winners has an expected alpha of 0.342% per month. This finding is consistent with Stein s (2009) crowded strategy hypothesis, but inconsistent with fund comovement being driven by risk exposure. JEL Classification Numbers: G11, G23. Keywords: Mutual funds; Comovement; Performance persistence; Crowded strategy; Risk exposure. 2

1 Introduction A long literature examines the persistence of mutual fund performance. 1 Many authors use the persistent component of funds benchmark-adjusted returns as a measure of managerial skill. To mutual fund investors, knowing which past winners will continue to outperform and which past losers will keep on losing clearly has practical value. Notwithstanding such popular demand, and companies like Lipper and Morningstar regularly producing rankings of mutual funds based on their track records, it is well-known that past performance by itself is a noisy predictor of future performance. For example, Carhart (1997) shows that, after controlling for momentum, past alphas only help identify funds that will underperform, but not funds that will outperform. Phrased in terms of Morningstar s ranking system, there is a good chance for a one-star fund to remain one-star, but not for a five-star fund to maintain its five-star status. In this study, we show that mutual funds return comovement with other past winners or past losers can be used to sharpen the identification of future winners or losers. When we examine a fund s track record, not only do we pay attention to how many stars it has earned but also to how it has earned them. Some five-star funds attain their five-star status by pursuing strategies similar to other five-star funds as indicated by their degree of return comovement with each other while some other five-star funds achieve their five-star status quite independently. At the other end of the spectrum, there are also one-star funds who comove strongly with other one-star funds and there are one-star funds whose poor performance is largely idiosyncratic. It is not aprioriobvious how a fund s comovement with other winners/losers would affect its future performance. On the one hand, such comovement could arise from funds exposure to a risk factor omitted by Carhart s (1997) four-factor model. If the comovement among the co-winners (those winner funds that had the strongest return comovement with 1 Contributors to this literature include Grinblatt and Titman (1992), Hendricks, Patel, and Zeckhauser (1993), Goetzmann and Ibbotson (1994), Brown and Goetzmann (1995), Malkiel (1995), Elton, Gruber, and Blake (1996), Carhart (1997), Carpenter and Lynch (1999), Zheng (1999), Berk and Green (2004), Bollen and Busse (2004), Busse and Irvine (2006), Busse and Tong (2012), and Berk and van Binsbergen (2015). 3

other winners) captures a positive exposure to this omitted risk factor, the co-winners will be expected to earn a positive risk premium. At the same time, if the comovement among the co-losers (those loser funds that had the strongest return comovement with other losers) captures a negative exposure to this factor, these funds provide a hedge against the omitted risks and are expected to earn a negative alpha going forward. This omitted risk hypothesis has received considerable attention in recent mutual fund research. It is the basic rationale behind the explanation advanced by Moskowitz (2000), Glode (2011), and Kosowski (2011) for why investors are willing to hold funds with negative unconditional alphas but positive conditional alphas during recessions as the business cycle risks that investors care about (and enter their true pricing kernel) are not fully accounted for by Carhart s four factors. Savov (2014) also shows that actively-managed mutual funds tend to pay off when non-traded income declines, thereby providing a hedge to investors with outside income and justifying the unconditional underperformance (i.e. negative alphas) of active funds. On the other hand, comovement could proxy for the crowdedness of a fund s strategy. If a winner s outperformance is associated with strong comovement with other winners, its strategy is more likely to belong to the overcrowded category and its outperformance is less likely to last. By contrast, if a winner attains its outperformance without having much comovement with other winners, overcrowding is less of a concern and its strategy is more likely to remain profitable. Under this crowded strategy hypothesis, it is the idiosyncratic winners (those winner funds who exhibit the lowest comovement with other winners), rather than the co-winners, who are expected to have superior future performance. Stein (2009) discusses the crowded strategy problem in detail. One empirical challenge in examining this problem is that, fund strategies are not disclosed and there is virtually no limit to the possible strategies a fund can follow. But even if the investment strategy being followed were known, another challenge is the difficulty in inferring the degree of crowdedness in the strategy. The fact that the abnormal return on a strategy (e.g. buying low-accrual stocks) is high in a given time period can be due to the strategy being effective (i.e. low-accrual stockswereunder-valued),butitcanalsobeduetoawaveofentrybyotherarbitrageurs 4

into the same strategy during the time period pushing up the price of low-accrual stocks. Our analysis attempts to address these challenges using a fund s comovement with other winners as a measure of crowdedness without having to specify the actual strategy the fund is following. Using U.S. mutual fund data obtained from CRSP and Thomson Reuters over the period 1984 to 2010, we find support for the crowded strategy hypothesis it is the idiosyncratic winners who significantly outperform the co-winners going forward. Quantitatively, the idiosyncratic winners have an after-fee, expected four-factor alpha of 0.342% per month, but the future alpha of the co-winners is insignificantly different from zero. Among past losers, we also find that it is the idiosyncratic losers, rather than co-losers, whose past performance will persist. There are good reasons for why the comovement with co-losers tends to identify transitory (rather than persistent) poor performance. Since the poor returns of the co-losers are correlated, their underperformance is likely driven by their common strategies. As long as these funds, as a group, arenotexpectedtoconsistently pick the wrong strategy, they are also not expected to persistently underperform. Instead, it is more likely for persistent underperformance to come from fund-specific inefficiencies or agency problems which tend not to be correlated across funds. Indeed, the idiosyncratic losers are found to have an after-fee, expected four-factor alpha of -0.290% per month, whereas the co-losers future alpha is insignificantly different from zero. This result suggests that the correlated underperformance of the co-losers during the ranking period is transitory in nature inconsistent with the comovement being driven by a negative exposure to an omitted risk factor but consistent with the co-losers having pursued correlated strategies that did not work out. While such collective poor judgment of the co-losers tends not to last, the underperformance of the idiosyncratic losers is found to persist. After constructing a good-minus-poor (or GMP) factor, which is a portfolio that goes long on past winners and short on past losers, we measure a fund s comovement with past winners/losers by its GMP factor loading over a 12-month rolling window. To forecast future performance, we not only condition on a fund s past performance (how many stars a fund 5

has), but also on the fund s GMP beta (how the fund obtains those stars). By conditioning on past alpha alone, we confirm the well-known finding that the outperformance of past winners does not persist. But by conditioning on GMP beta as well, we identify a segment within the group of past winners those five-star funds who did not comove with other five-star funds who can deliver future outperformance. On the other hand, although previous research documents strong persistence in the poor future performance of past losers, their GMP betas can be used to identify a subgroup one-star funds that display the strongest comovement with other one-star funds whose underperformance is not expected to continue. But comovement does not only matter for funds with extreme past performance (i.e. the one-star or five-star funds). GMP betas can help predict future performance even among funds in the middle three quintiles. For example, conditional on funds being in the fourth quintile of a pre-ranking alpha sort, the subgroup with the lowest (most negative) GMP beta has an after-fee, expected four-factor alpha of 0.170% per month which is statistically significant and higher than the expected alphas of most past winners. By contrast, among median funds (i.e. funds in the third quintile and are thus far from being considered losers ), those with the highest GMP betas are found to have significantly negative future alphas. In Morningstar terminology, we identify a subgroup of four-star funds who will outperform most five-star funds going forward and a subgroup of three-star funds who are expected to have significantly negative benchmark-adjusted returns. Thekeytoourprocedureisthatcomovementwithpastwinners/losersidentifies a transitory component in mutual fund performance. Positive GMP betas indicate exposure to transitory good performance during the pre-ranking period making the pre-ranking alpha of funds with such exposure an overestimate of their true alpha. On the other hand, funds with negative GMP betas had suffered from transitory poor performance making their preranking alpha an underestimate of their true alpha. By first conditioning on past alpha and then sorting on funds GMP betas, our procedure controls for the transitory component of past alpha and obtains a more accurate measure of true skill. A number of comovement-related variables have been shown by previous studies to have 6

predictive power for future fund performance. We show that our findings are distinct from these previous studies. While Cremers and Petajisto (2009) and Amihud and Goyenko (2013) study the effects of active portfolio management by comparing a mutual fund s holdings and returns with those of its benchmark portfolios, we focus on a fund s comovement(or the lack thereof) with other winner/loser funds. 2 Cremers and Petajisto (2009) and Amihud and Goyenko (2013) show that comoving more strongly with a fund s benchmark is bad news for its future performance. 3 By contrast, we find that comovement is not always bad for future performance the question of comovement with whom matters. Consider two funds with the same benchmark-adjusted past performance the one that had comoved with past losers is expected to outperform the one that had comoved with past winners going forward. Kacperczyk, Sialm, and Zheng (2008) show that a fund s return gap, the difference between the fund s actual return and return imputed from its disclosed holdings, is persistent and can be used to predict future performance. Chen, Hong, Huang, and Kubik (2004) and Pollet and Wilson (2008) show that a larger fund size is associated with lower fund returns. Kacperczyk, Van Nieuwerburgh, and Veldkamp (2014) identify skilled managers by their stock-picking skills in booms and market-timing skills in recessions. The authors go on to show that this time-varying measure of managerial skill displays strong predictive power for future performance. To show that our results are distinct from these earlier findings, we use a multivariate regression framework to simultaneously control for the effects of these and other fund attributes. Among the other fund attributes that we control for are a fund s size, value, and momentum tilts, as well as its value-weighted market beta all computed based on the fund s portfolio holdings. The inclusion of the holdings-based style tilt measures follow Kacperczyk, Sialm, and Zheng (2005, 2008) and Kacperczyk, Van Nieuwerburgh, and Veldkamp (2014). 2 Cremers and Petajisto (2009) show that mutual funds with a high active share, the share of a fund s portfolio holdings that differs from its benchmark holdings, significantly outperform. Amihud and Goyenko (2013) use a mutual fund s 2 on a multifactor benchmark model as a measure of active management, and find that fund performance is positively related to active management the lower a fund s 2 the higher its future returns. 3 Among hedge funds, Sun, Wang, and Zheng (2012) also findthat,itisthosefundswhosereturnsare least correlated with other funds in the same style that are expected to have the highest future returns. 7

The use of a holdings-based beta measure as an additional control is motivated by Frazzini and Pedersen (2014), who find that assets with a low market beta tend to earn higher risk-adjusted returns than high-beta assets. In simple correlation analyses, we find that none of the correlation coefficients between these control variables and GMP beta exceed 0.1. In multivariate analyses, we show that the effect of GMP beta on future fund alpha remains significant even after controlling for all these variables. In other words, even among funds with similar active share, benchmark 2 return gap, fund size, picking/timing skills, style tilts, market beta, and similar values for other control variables, comovement with past winners/losers remains a significant predictor of future performance. The remainder of the paper is organized as follows. Section 2 discusses the construction of our data and presents summary statistics. Section 3 introduces our comovement measure. Section 4 investigates the predictive power of a fund s comovement with other past winners/losers for its future performance first in 1x5, one-dimensional sorts and then in 5x5, two-dimensional sorts with monthly, quarterly, and annual rebalancing. Section 5 further examines this predictive power in multivariate regressions controlling for other variables that can also affect future fund performance. Section 6 conducts a number of robustness checks on our main results. Section 7 concludes. 2 Data Our sample covers the time period between January 1984 and June 2010. We obtain information on fund returns, age, total net assets (TNA), expenses, turnover, investment objectives, and other fund characteristics from the Center for Research in Security Prices (CRSP) Mutual Fund Database. We also obtain fund holdings data from the Thomson-Reuters (TR) Mutual Fund Ownership Database. 4 To merge the returns data in the CRSP Mutual Fund Database with the holdings data in the TR Database, we use the MFLINKS product offered 4 These holdings data are collected from both the mutual funds mandatory filings with the SEC and their own voluntary disclosure. 8

by the Wharton Research Data Services (WRDS). 96.3% of the fund-month observations in the merged sample have holdings data available in the previous six months. We exclude those fund-month observations for which no holdings data have been reported for the previous 12 months. 5 Finally, we link the holdings reported in the TR Database to the CRSP US Stock Database. We follow the methodology discussed in a WRDS research note to identify domestic equity mutual funds from the CRSP and TR databases. 6 from that of Kacperczyk, Sialm, and Zheng (2008). This methodology is modified The modifications are necessitated by the move by CRSP to use Lipper (rather than Standard & Poor s Fund Services and Morningstar) as its source of mutual fund data. To begin, we first exclude funds in TR that have the following Investment Objective Codes: International, Municipal Bonds, Bond and Preferred, and Balanced. We then eliminate index funds from our sample. 7 We also exclude all funds in CRSP with a policy variable in C & I, Bal, Bonds, Pfd, B & P, GS, MM and TFM. After the policy screen, we include funds with Lipper Class (if available) equal toeiei,g,lcce,lcge,lcve,mcce,mcge,mcve,mlce,mlge,mlve,scce, SCGE, and SCVE. If Lipper Class is unavailable, we include funds with Strategic Insight Objective Code in AGG, GMC, GRI, GRO, ING, and SCG. If neither Lipper nor Strategic Insight Objective Codes are available, we turn to the Wiesenberger Fund Type Code and include funds with the following objectives: G, G-I, AGG, GCI, GRI, GRO, LTG, MCG, and SCG. If none of the Lipper, Strategic Insight, nor Wiesenberger Codes are available, but the fund has a CS policy (i.e. common stocks are the main securities held by the fund) as classified by CRSP, then the fund is included. If even the policy variable is not available from CRSP, we include funds that, on average, hold between 80% and 105% in common stocks over their life. To address Evan s (2010) concern on incubation bias, we exclude observations that are 5 Such observations make up 0.92% of all fund-month observations in the merged sample. 6 This document, written by Glushkov and Moussawi (2010), can be found at the website: https://wrdsweb.wharton.upenn.edu/wrds/research/applications/ownership/returngap/. 7 WeexcludefundsbasedontheirnamesinCRSP,andthenusealistfromBloombergtoscreenoutany index funds that remain. 9

recorded prior to a fund s starting year (as reported by CRSP) as well as observations for which fund names or starting years are missing. Since incubated funds tend to be smaller, we also exclude those observations for which funds have asset under management (AUM) of less than $5 million (2006 US dollars) or are holding fewer than 10 stocks, as of the end of thepreviousmonth. This exercise identifies 3,141 distinct mutual funds, with 382,830 fund-month observations over our sample period of January 1984 to June 2010 (318 months). 8 The number of funds range from 269 (January 1984) to 1,982 (February 2004). Table 1 reports the summary statistics of our sample. Some of the variables listed are used as explanatory variables of fund performance in subsequent analyses. 3 Comovement with Winner/Loser Funds We rank funds by their benchmark-adjusted performance. Thoseinthetopquintileare labelled winner funds and those in the bottom quintile are labelled loser funds. We examine the extent to which a fund comoves with these winner and loser funds and whether such comovement has predictive power for the fund s future performance. To measure benchmark-adjusted performance, we use Carhart s (1997) four-factor model, as given by: = + 1 + 2 + 3 + 4 + (1) where is the return of fund in excess of the one-month Treasury bill rate in month ; is the excess return on the market; (small minus big) is the return difference between the small capitalization and large capitalization portfolios; (high minus low) is the return difference between the high and low book-to-market portfolios; and (momentum) is the return difference between the winner stock and loser stock portfolios. 8 The research note in WRDS (Glushkov and Moussawi 2010), discussed above, identifies 3,181 unique domestic U.S. equity funds in the period between January 1980 and December 2008. 10

At the end of month, we estimate equation (1) by running a 12-month regression for each fund usingdatafrommonth 11 to Using these parameters, we rank funds based on their benchmark-adjusted performance: 1 2 3 4 Those in the top 20% of this ranking are the winners and those in the bottom 20% are the losers. To examine the extent to which a mutual fund comoves with winner/loser funds, we first form a good-minus-poor (or GMP) factor, which is a portfolio that goes long on past winner funds and short on past loser funds. We then measure fund s comovement with past winner/loser funds by its GMP beta ( ) the loading of fund s excess return on the GMP factor in a five-factor model: = + 1 + 2 + 3 + 4 + + (2) To appreciate how this varies across funds, we carry out a two-dimensional, dependent sort. We firstsortfundsintofive quintiles based on their four-factor, benchmarkadjusted performance in the ranking month. Within each of these quintiles, we further sort funds based on their This two-dimensional sort groups all funds into 25 cells. For each cell in each time period, we compute an equal-weighted average. We then take a time-series average of the for each cell over all ranking months. Table 2 reports these results, with -statistics based on White (1980) standard errors in square brackets. Funds with different benchmark-adjusted performance in the ranking month are sorted into different columns (first-round sort). Within each column, funds in the same benchmark-adjusted performance quintile are further sorted by their (secondround sort). Thus, the northeast corner of the table is populated by those 20% of winner funds that have the lowest while the southwest corner of the table is populated by those 20% of loser funds that have the highest (least negative) We see that even funds with similar past performance do not necessarily comove with each other. Among winner funds, their range from -0.012 to 1.29. We label those 20% of winner funds with the lowest (-0.012) as idiosyncratic winners who tend not 11

to comove with other winner funds. We label those 20% of winner funds with the highest (1.29) as co-winners as they tend to comove strongly with other winner funds. There is also a similar spread among loser funds. Their range from -1.316 for the co-losers (those 20% of loser funds with the most negative ) to 0.018 for the idiosyncratic losers (those 20% of loser funds with the most positive ) Thelastrowofthetablereportsthe spread within each performance quintile. At about 1.3, the spread is most pronounced among winner and loser funds. But it is important to note that, even for funds in the middle three quintiles, their spread is still sizable (at around 0.6) and highly significant. For example, among funds in the fourth quintile (i.e. funds that are at the 60-80 percentile of the benchmark-adjusted performance rank), some comove with loser funds (with a as low as 0 171) while others comove with winner funds (with a as high as 0 447) 4 Comovement and Subsequent Performance Knowing that there are significant variations across funds in their comovement with other winners/losers, we go on to investigate if such differences in comovement have implications for future performance. Comovement could be the result of common exposure to a risk factor one that has not been fully captured by the four-factor model. In fact, this is the basic rationale behind the explanation proposed by Moskowitz (2000), Glode (2011), and Kosowski (2011) for why investors are willing to hold funds with negative unconditional (four-factor) alphas but positive conditional alphas during recessions as the business cycle risks that investors care about (and enter their true pricing kernel) are not fully accounted for by the four-factor model. Savov (2014) also shows that actively-managed mutual funds tend to pay off when non-traded income declines, thereby providing a hedge to investors with outside income and justifying the unconditional underperformance (negative alphas) of active funds. Suppose the comovement among co-winners really reflects exposure to risk factors that are 12

not captured by standard benchmarks. Then this risk exposure can explain why co-winners were winners in the past and will continue to outperform in the future relative to a misspecified benchmark. At the same time, the comovement among co-losers could be a hedge against the systematic risks not captured by conventional factors, and would suggest that their low returns will continue going forward. In sum, if risk exposure were the reason, we would expect persistent, benchmark-adjusted outperformance (underperformance) by the cowinners (co-losers) reflecting their positive (negative) exposure to systematic risks caused by the failure of the four-factor model to fully capture the true pricing kernel. But it could also be the idiosyncratic winners (losers) who exhibit persistent outperformance (underperformance). If the crowded strategy problem discussed by Stein (2009) is a serious one, we expect that it is the strategy of the co-winners whose outperformance is associated with strong comovement with other winners that is more likely to belong to the overcrowded category and their outperformance will not last. By contrast, it is the idiosyncratic winners for whom overcrowding is less of a concern whose strategies are more likely to remain profitable. For losers, since the underperformance among co-losers is correlated, it is likely to be strategy-driven. If these funds, as a group, are not expected to consistently pick the wrong strategy, their underperformance will tend not to persist. By contrast, if the poor performance of the idiosyncratic losers reflects their fund-specific inefficiencies or agency problems and that such problems are long-lasting their underperformance will continue. Whether mutual fund comovement with other winners/losers picks up a transitory or persistent component in performance is thus an empirical question one that we address in analyses below. 4.1 One-Month Horizon For each fund that enters into our ranking in month we calculate its benchmark-adjusted post-ranking performance for month +1 as +1 1 +1 2 +1 3 +1 4 +1 wherethebetasusedarethoseweobtainbyestimatingequation(1)inmonth 13

For each post-ranking month +1 we calculate an equal-weighted average of the benchmarkadjusted returns for all funds in the same cell. We first consider an unconditional test of the risk exposure hypothesis. In a one-dimensional sort of funds by their past we compare the future alphas of funds with different past. If captures risk exposure, high funds will tend to outperform low funds going forward. Yet, if the comovement with past winners/losers is driven by transitory performance, we expect to see no difference in the future alphas of high and low funds. Table 3 reports the time-series average of the benchmark-adjusted post-ranking performance for each cell. Panel A reports the results for net returns (after expenses) and Panel B reports the results for gross returns (before expenses), with -statistics based on White (1980) standard errors in square brackets. Table 3 shows that there is no significant difference in the post-ranking returns (both before and after expenses) across funds with different pre-ranking offering no support for the risk exposure hypothesis. Yet, even though has no unconditional predictive power for future fund alphas, it might still help identify persistent fund performance when used conditionally. Instead of ranking funds by their only, we carry out a dependent, two-dimensional sort first by funds pre-ranking alphas and then by their pre-ranking. The first sort separate funds into winners/losers. The second sort separate winners into idiosyncratic winners/co-winners, and losers into idiosyncratic losers/co-losers. Conditional on funds having similar past alphas, we examine if their GMP betas help identify differences in their future alphas. We report the results of this analysis in Table 4. By examining Table 4, Panel A, we see that it is the idiosyncratic winners (rather than co-winners) who will continue to outperform and the idiosyncratic losers (rather than co-losers) who will continue to underperform going forward. These results are inconsistent with the hypothesis that GMP betas measure risk loadings, but rather, show that comovement with past winners/losers identifies a transitory componentinfundperformance. Thefactthatitistheidiosyncraticwinnersandidiosyncratic losers who tend to have persistent performance supports the idea that the idiosyncratic winners (losers ) past performance were due to their unique, fund-specific managerial skills 14

(inefficiencies). The last row of the panel reports the post-ranking performance spreads among funds within the same pre-ranking performance quintile. Except for the quintile of loser funds, the post-ranking performance spreads are all significant even for the middle three quintiles, whose spreads (see the last row of Table 2) are smaller. The last row of the column All in Table 4 reports the average post-ranking performance spread over the five preranking performance quintiles. The estimate of -0.249 here suggests that, conditional on funds coming from the same pre-ranking performance quintile, those 20% of funds with the lowest is expected to outperform those 20% of funds with the highest by 0.249% per month which is both statistically and economically significant. Turning to Table 4, Panel B, which reports gross returns, we see that the results we obtain from Table 4, Panel A are not driven by the difference in expense across different groups of funds. By comparing the last rows of the two panels, we see that the post-ranking performance spreads are very similar regardless of whether we measure performance using gross or net returns. The second-round, sort does not only matter at the extremes. It allows us to identify future winner and loser funds from the third and fourth pre-ranking performance quintiles. From a one-dimensional sort based on past performance alone, we can see from Table 5 that the benchmark-adjusted post-ranking net returns of the third and fourth quintiles are not significant. The sort enables us to identify the hidden gems funds that will have significant outperformance going forward from among funds in the fourth quintile. The gems being identified arethose20%offourthquintilefundsthathavethe lowest in the pre-ranking period. From Table 2, we see that their is in fact significantly negative, with an estimated value of -0.171 (Row 1, Column 4 in Table 2). This estimate suggests that some of the strategies followed by these funds in the ranking period are similar to those of the co-losers, hurting their performance. If these are really funds that have skill (true alpha being positive) but only happen to have taken an unlucky bet during the ranking period, they are expected to outperform going forward. Our findings are 15

consistent with this interpretation. Those fourth quintile funds with the lowest pre-ranking have a post-ranking net alpha of 0.170% per month (Row 1, Column 4 in Table 4, Panel A). Conditional on, we can also identify funds that will have significantly negative future performance from among the third quintile funds even though unconditionally, the future benchmark-adjusted performance of this quintile as a whole is not significantly different from zero (Table 5, Column 3). Here, we focus on the 20% of third quintile funds that have the highest in the pre-ranking period. From Table 2, we see that their is significantly positive, with an estimated value of 0.291 (Row 5, Column 3 in Table 2). This estimate suggests that some of the strategies followed by this group of funds are similar to those of the co-winners during the ranking period, improving their performance. But note that even after benefitting from the superior performance of such strategies, these funds still only manage to be in the third quintile in the ranking period suggesting that their true alpha (net of fees) may be negative. Consistent with this interpretation, the net alpha of these funds is found to be -0.120% per month going forward (Row 5, Column 3 in Table 4, Panel A). The key to this sharper identification of future alpha is to see that positive GMP betas indicate exposure to transitory good performance during the pre-ranking period making the pre-ranking alpha of funds with such exposure an overestimate of their true alpha. On the other hand, funds with negative GMP betas had suffered from transitory poor performance making their pre-ranking alpha an underestimate of their true alpha. To show that the pattern of post-ranking performance that we observe is not just inherited from the pattern of pre-ranking performance, we report funds benchmark-adjusted performance for the ranking month on Table 6. Among winner funds, it is the co-winners who tend to outperform the idiosyncratic winners in the pre-ranking period. Among losers, it is the co-losers who tend to underperform the idiosyncratic losers in the pre-ranking period. These patterns are reversed in the post-ranking period. Specifically, the last row of Table 6 shows that the pre-ranking performance spreads between high and low funds 16

are always positive, whereas the last row of Table 4, Panel A shows that the post-ranking performancespreadsarealwaysnegative. 4.2 Quarterly and Annual Horizons We next examine horizons longer than one month. For the quarterly horizon, we rank funds at the end of every quarter and hold the same funds in a portfolio for three months before rebalancing. Funds are ranked by their average monthly benchmark-adjusted return in the ranking quarter, and post-ranking performance is measured by a fund s average monthly benchmark-adjusted return in the post-ranking quarter. The post-ranking returns so obtained remain non-overlapping and we continue to use -statistics based on White (1980) standard errors for inferences. For the annual horizon, we rank funds at the end of every month in our sample and hold the same funds in a portfolio for 12 months before rebalancing. Ranking funds at a monthly frequency avoids a significant drop in sample size but the post-ranking returns become overlapping. To ensure that our inferences are robust to the serial correlation so induced, we use Newey-West (1987) standard errors. We rank funds based on their average benchmark-adjusted returns over the 12-month ranking period, and measure performance by the funds average monthly benchmark-adjusted returns in the 12-month post-ranking period. As in the monthly analysis, we first report results based on one-dimensional sorts. At the quarterly horizon, Table 7 shows that there is no significant difference in both the post-ranking net and gross returns across funds with different pre-ranking Table 8 displays the same results for the annual horizon. These results show that there is no support for the risk exposure hypothesis at both the quarterly and annual horizons. Next, we carry out a dependent, two-dimensional sort first by funds pre-ranking alphas and then by their pre-ranking.weconfirm that all our findings reported above carry over to the quarterly and annual horizons. To conserve space, we only report the post-ranking benchmark-adjusted net returns (to be compared with Table 4, Panel A for the monthly 17

horizon) of the two-dimensional sort. Tables 9 and 10 report results for the quarterly and annual horizons, respectively. As the rebalancing interval lengthens, it is not surprising that the pattern we see from Table 4 becomes quantitatively weaker. But the qualitative pattern that it is the idiosyncratic winners (losers) who tend to have persistent outperformance (underperformance) remains even at the annual horizon. For example, if we focus on the benchmark-adjusted return of the idiosyncratic winners, we see that it goes from 0.342% in the post-ranking month (monthly rebalancing), to 0.243% per month in the post-ranking quarter (quarterly rebalancing), and 0.163% per month in the post-ranking year (annual rebalancing). Turning to the last row of the column All, which reports the average post-ranking performance spread over the five pre-ranking performance quintiles, we see that it goes from 0.249% in the post-ranking month (monthly rebalancing), to 0.230% per month in the post-ranking quarter (quarterly rebalancing), and 0.147% per month in the post-ranking year (annual rebalancing). All these post-ranking benchmarkadjusted return spreads are statistically and economically significant. 5 Multivariate Analysis Our analysis thus far has shown that a fund s is associated with its future performance. The goal of the remainder of our paper is to show that this predictive power is not simply due to being correlated with other variables that have already been found to forecast fund returns. To control for the influence of potentially confounding variables, we use a multivariate framework that regresses future benchmark-adjusted performance (net of expenses) on current, current benchmark-adjusted performance, and control variables: P +1 = 1 + 2 + + +1 (3) As before, the benchmark-adjusted performance +1 for fund in month +1 is calculated as +1 1 +1 2 +1 3 +1 4 +1 where the betas ( 1 4 ) are obtained by estimating the Carhart s (1997) four-factor model in month 18 =1

using a rolling 12-month window. 9 The fund-level control variables are discussed below. We estimate equation (3) using a panel regression approach with time-fixed effects, and report -statistics based on standard errors that are clustered along both the fund and time dimensions (as proposed by Thompson 2011) to alleviate concerns that the regression errors are correlated across funds and over time. 5.1 Control Variables Since is a variable constructed based on a fund s comovement with other funds, we begin by controlling for variables that are also comovement related. First, we control for a fund s active share. Cremers and Petajisto (2009) show that mutual funds with a high active share, the share of a fund s portfolio holdings that differs from its benchmark holdings, tend to significantly outperform going forward. Second, instead of active share, we use a mutual fund s 2 on a multifactor benchmark model as a measure of active management. Using this alternative measure of a fund s activeness, Amihud and Goyenko (2013) find that fund performance is positively related to active management the lower a fund s 2 the higher its future benchmark-adjusted returns. By controlling for active share (or 2 )in a multivariate analysis, we address the following question: among funds with similar degrees of active management, do their comovement with other winners or losers in the past still convey additional information for their future performance? is conceptually different from active share or benchmark 2. These two measures of active management pick up a fund s degree of comovement with its benchmark. By contrast, measures the extent to which a fund comoves with other winners or losers. Cremers and Petajisto (2009) and Amihud and Goyenko (2013) find that having a high correlation with its benchmark is bad news for a fund s future performance. Our two-dimensional sorts above show that comovement could be good or bad for future performance the question of comovement with whom matters. For two funds with similar benchmark-adjusted past performance, it is the one that had comoved with past winners that is found to have worse 9 Section 6.2 below reports results that use a rolling 24-month window to estimate the four-factor betas. 19

future performance than the one that had comoved with past losers. Fund style can also induce comovement across funds. Although we already include the market,, and factors in our benchmark model which are return-based measures of fund style, we further control for a fund s size, value, and momentum tilts using the fund s portfolio holdings. 10 The inclusion of these style tilt measures follow Kacperczyk, Sialm, and Zheng (2005, 2008) and Kacperczyk, Van Nieuwerburgh, and Veldkamp (2014). We also include the value-weighted market beta of a fund s portfolio holdings as an additional control motivated by Frazzini and Pedersen s (2014) finding that assets with a low market beta tend to earn higher risk-adjusted returns than high-beta assets. Aside from these comovement-related variables, we also include other controls that recent studies have found to predict future fund performance. First, we control for a fund s return gap, the difference between the fund s actual return and return imputed from its disclosed holdings. Kacperczyk, Sialm, and Zheng (2008) show that a fund s return gap is persistent and can be used to predict future performance. Second, we control for the correlation (over a 12-month window) between a fund s actual return and the return imputed from its disclosed holdings, a measure Kacperczyk, Sialm, and Zheng (2008) use to proxy for the transparency of a fund s investment strategy. Third, we control for fund size. Chen, Hong, Huang, and Kubik (2004) and Pollet and Wilson (2008) show that a larger fund size is associated with lower fund returns. Fourth, we include a dummy variable TOP, which identifies a group of funds with superior stock-picking skills in expansions. Kacperczyk, Van Nieuwerburgh, and Veldkamp (2014) show that these same funds also have superior markettiming skills in recessions and go on to show that TOP displays strong predictive power for future performance. Other variables that we control for include fund age, turnover ratio, and expense ratio. Since both fund size and fund age are skewed to the right, we measure these 10 For each fund, we compute its size score as the value-weighted average of its stock holdings size quintile scores, ranging from one (small cap) to five (large cap), according to NYSE size quintile breakpoints. Similarly, each fund s value score is calculated as the value-weighted average of its stock holdings book-to-market (B/M) quintile scores, ranging from one (the stock s B/M being in the lowest quintile) to five (the stock s B/M being in the highest quintile). Finally, a fund s momentum score is calculated as the value-weighted average of its stock holdings momentum quintile scores, ranging from one (the stock s past 12-month return being in the lowest quintile) to five (the stock s past 12-month return being in the highest quintile). 20

variables in logs. To capture the (potentially nonlinear) effects of fund flows, we include a fund s new money growth ( ) the growth rate of the fund s TNA after adjusting for the return on its existing assets and 2 as additional controls. 5.2 Results As in the two-dimensional sorts that we study above, we investigate the relationship between and future fund performance for post-ranking time periods of one, three, and twelve months. Results for these three intervals are reported on Tables 12, 13, and 14, respectively. For post-ranking intervals of three (twelve) months, the dependent variable is the average monthly benchmark-adjusted return over the three-month (twelve-month) period. The active share variable is downloaded from Antti Petajisto s website. Petajisto (2013) provides further information on the construction of the variable. We perform our multivariate analysis on those fund-month observations for which the active share variable is available, and construct the rest of the control variables using data from CRSP and TR. At the onemonth horizon, a fund s return in CRSP has to be non-missing in the post-ranking month for it to be included in our sample. At the three-month (twelve-month) horizon, a fund needs to have at least one non-missing return in the post-ranking quarter (year) for it to be included. In such cases, we use the average non-missing return as a fund s return over the post-ranking period. 11 Before reporting multivariate regression results, we first examine the correlation matrix for and the control variables. All variables have been cross-sectionally demeaned before the correlation coefficients are computed. In Table 11, above-diagonal entries report the Pearson correlation coefficients and below-diagonal entries report the Spearman correlation coefficients. Not surprisingly, and pre-ranking alpha are highly correlated funds that comove strongly with winners (losers) during the pre-ranking period also tend to have 11 Since it is possible for a fund to have missing return in month +1 but non-missing returns in month +2 and beyond, a fund-month observation can be excluded from our monthly rebalancing sample but included in our annual rebalancing sample. This is the reason why the number of observations in our annual rebalancing sample (with overlapping monthly data), as reported on Table 14, is slightly higher than that of our monthly rebalancing sample, as reported on Table 12. 21

high (low) pre-ranking alphas. But the correlation coefficients (both Pearson and Spearman) between and the rest of the control variables are all below 0.1 alleviating the concern thatthepredictivepowerof for post-ranking alpha is simply driven by being correlated with other variables that can forecast fund returns. From the rest of the correlation matrix, we also see a positive and sizable correlation (in the 0.3 to 0.4 range) between Active Share and 1 2 as both variables are designed to measure a fund s degree of active management relative to its own benchmark. We then report the multivariate regression results. From Column 1 of Tables 12-14, we see that, controlling for past benchmark-adjusted performance (four-factor alpha), funds with a higher tend to have worse future performance. These results are consistent with those we obtain from the two-dimensional sorts in Table 4 (for the one-month horizon), Table 9 (for the three-month horizon), and Table 10 (for the 12-month horizon). To evaluate the economic significance of the coefficient on, we calculate the average spread (the average difference in between the highest and lowest quintiles across different pre-ranking benchmark-adjusted performance) for each horizon. At the one-month horizon, the average spread is 0.889 (last row under Column All in Table 2). Multiplying this by the coefficient of -0.434, we conclude that going from high to low predicts a higher future benchmark-adjusted return of 0.386% per month. At the three-month horizon, we find that the average spread is equal to 1.280 (untabulated). Since the coefficient on is found to be -0.278, going from high to low predicts a higher future benchmarkadjusted return of 0.356% per month. At the 12-month horizon, the coefficient is -0.059 and the average spread is found to be 2.615 (untabulated). Together, they predicts a higher future benchmark-adjusted return of 0.154% per month. 12 Moving to the other columns of Tables 12-14, we see that the effect of on future fund performance remains both statistically and economically significant even after controlling 12 The reason why the spread increases with horizon is due to the fact that we always use a rolling 12-month window to calculate but the definition of winners and losers for an -month horizon is based on benchmark-adjusted performance over the past months. As a result, the strongest comovement and thus the largest spreads are obtained for the 12-month horizon as this is the horizon where the same windowlengthisusedtobothdefine winners/losers and estimate. 22

for other variables. The control variables have the expected signs. In particular, active share, 1 2 return gap, and TOP all have positive predictive power whereas the expense ratio has negative predictive power for future performance. 13 Finally, to explore further if fund flows in the post-ranking period can account for the poor performance of the idiosyncratic losers, we include post-ranking and 2 as additional explanatory variables and run the above multivariate regressions for past losers only. In untabulated results, we find that idiosyncratic losers do suffer from the most serious fund outflow among all funds in the post-ranking period. However, even after controlling for post-ranking and 2,thecoefficient on declines only slightly and remains highly significant in explaining the post-ranking performance difference between the co-losers and idiosyncratic losers. 6 Robustness Checks We conduct four robustness checks on our results. First, in the 5x5 two-dimensional sort, we estimate the post-ranking four-factor betas at the portfolio (rather than fund) level. Second, in the multivariate regression analysis, we obtain the post-ranking four-factor betas using rolling windows of 24 months (instead of 12 months). Third, we examine if the can still forecast future performance when we augment the four-factor model with an active peer benchmark (APB), as proposed by Hunter, Kandel, Kandel, and Wermers (2014). Fourth, Cohen, Coval, and Pástor (2005) show that the similarity of a fund s stock holdings with other funds contains information about the fund s future returns. We examine if this information in holdings can explain the predictive power of for future fund performance. 6.1 Portfolio-Level Betas Our analysis above measures post-ranking performance using beta estimates at the fund level. While this approach has the advantage of allowing betas to vary across funds and over 13 Since post-ranking alphas are measured in monthly % and the expense ratio in annual %, a coefficient of -0.08 translates into, approximately, a one-for-one impact of expenses on after-fee alphas. 23