Does MAX Matter for Mutual Funds? *

Transcription

1 Does MAX Matter for Mutual Funds? * Bradley A. Goldie Miami University Tyler R. Henry Miami University Haim Kassa Miami University, and U.S. Securities and Exchange Commission This Draft: March 19, 2018 *We thank John Bae, Turan Bali, Fan Chen, Ryan Davis, Jared DeLisle, Hui Guo, Scott Murray and participants at the 2016 SFA Conference, the 2017 FMA conference, and the 2017 FMA European conference for helpful comments. Authors are responsible for any errors or omissions. Contact Information: Goldie is an Assistant Professor of Finance, Farmer School of Business, Miami University, Oxford, OH 45056, goldieba@miamioh.edu. Henry is the Frank H. Jellinek, Jr. Assistant Professor of Finance, Farmer School of Business, Miami University, Oxford, OH 45056, henrytr3@miamioh.edu. Kassa is an Assistant Professor of Finance, Farmer School of Business, Miami University, Oxford, OH 45056, kassah@miamioh.edu, and Visiting Scholar at U.S. Securities and Exchange Commission, 100 F Street N.E. Washington D.C The Securities and Exchange Commission disclaims responsibility for any private publication or statement of any SEC employee or Commissioner. This article expresses the author's views and does not necessarily reflect those of the Commission, the Commissioners, or other members of the staff.

2 Does MAX Matter for Mutual Funds? Abstract Extreme returns (MAX) have been shown to impact future expected stock returns. We examine whether this relationship is present in mutual fund returns. We find that high MAX funds, as measured by past extreme daily returns, underperform both in portfolio sorts and cross-sectional tests. We further test possible explanations for why MAX funds underperform. First, we measure mutual fund flows to determine investor response to MAX. Second, we examine the underlying holdings of MAX funds to measure their concentration in MAX stocks. We find evidence that both fund flows and holdings contribute to the MAX effect on mutual fund returns. Keywords: Mutual fund flows and performance, MAX, lottery preferences, skewness. JEL Classification: G11, G23

3 1. Introduction The empirical asset pricing literature demonstrates that stocks with lottery-like payoffs, as measured by a stock s maximum daily return over the month (MAX), have low future returns, yet some investors exhibit a preference for stocks with such characteristics (Bali, Cakici, and Whitelaw (2011)). The mutual fund literature finds that fund investors respond to past performance, documenting a well-known flow-performance relationship (Chevalier and Ellison (1997), Sirri and Tufano (1998)). In this paper, we study whether mutual funds with high MAX characteristics (measured by the fund s maximum daily return over the month) also have low future returns. After documenting that MAX funds underperform in both portfolio sorts and crosssectional tests, we seek possible explanations for this underperformance. We investigate both the underlying holdings of MAX funds and investor flows into these funds as potential sources of underperformance. We find support for both mechanisms as contributors to a MAX effect in mutual fund returns. At the individual stock level, recent evidence indicates that a stock s maximum daily return during the month predicts its performance in the following month (Bali, Cakici, and Whitelaw (2011), Annaert, De Ceuster, and Verstegen (2013), and Walkshäusl (2014)). Specifically, portfolios of high MAX stocks underperform portfolios of low MAX stocks, and this result has been partly attributed to investors preference for stocks with a high likelihood of a lottery-like payoff. However, rather than holding individual stocks, many investors instead choose to invest in managed mutual funds. At year-end 2014, U.S.-registered investment companies managed over $18.2 trillion in assets, the majority of which ($15.8 trillion) were held within mutual funds. 1 Given 1 Investment Company Institute 2015 Annual Fact Book: U.S. mutual funds account for 53% of total worldwide mutual fund and ETF assets. 1

4 the prominence of mutual funds as an investment vehicle, both the determinants of fund performance and the characteristics that attract flows to mutual funds are questions of central importance for fund investors and fund managers alike. The underperformance of high MAX stocks documented by Bali, Cakici, and Whitelaw (2011) applies to characteristic-sorted portfolios of individual stocks formed explicitly based on a stock s MAX measure. A related, but unexplored, question is whether some mutual funds demonstrate similar MAX-like characteristics, despite not being formed specifically based on this characteristic. In particular, we are interested in determining if high MAX mutual funds suffer from poor performance, and whether the preference for lottery-like payoffs (using MAX as a proxy) carries over to the mutual fund space. If high MAX mutual funds display the same underperformance as documented for individual stocks, the mechanism by which this relationship occurs is likely to be different for mutual funds than it is for stocks. The literature suggests that the underperformance of high MAX stocks is due to high investor demand for these stocks, which leads to lower expected returns (Bali, Cakici, and Whitelaw (2011)). Due to the nature of open ended fund flows, this mechanism does not directly translate to mutual funds. We alternatively explore two possible explanations for why MAX funds would underperform. The first is related to fund flows. If investors demonstrate a preference for MAX characteristics in mutual funds, rather than driving the price up, and subsequent expected returns down, as is the case with stocks, investor demand would lead to greater fund inflows and assets under managements. Berk and Green (2004) show how decreasing returns to scale in investment ability can erode the performance of mutual funds as they grow in size. Consistent with the Berk and Green (2004) model, increased flows to mutual funds with MAX characteristics could lead to future underperformance, relative to funds without this characteristic. Second we examine the portfolio holdings of MAX mutual funds. If MAX funds 2

5 concentrate their holdings in MAX stocks, then the underperformance of MAX fund returns can be at least partially attributed to the underperformance of the underlying stocks. 2 We begin by calculating the lottery features of a mutual fund as the average of the five maximum daily fund returns during the month (MAX). 3 We then document a negative relationship between a fund s MAX and its subsequent return. In cross-sectional tests, we find that funds with greater lottery-like characteristics have lower future performance. Specifically, a one percent increase in fund MAX leads to an annualized 2.6 percent reduction in risk-adjusted performance. Controlling for the fund s lagged performance, idiosyncratic volatility, and other fund characteristics do not diminish the influence of fund MAX on future performance. We next confirm that the MAX-performance relationship holds in the time-series by creating portfolios based on monthly sorts of a mutual fund s MAX measure. Results show that funds in the high MAX portfolio have significantly negative risk-adjusted performance of 3.13 percent on an annualized basis, and high MAX funds significantly underperform low MAX funds by an annualized 4.02 percent. The size of this performance difference is economically significant, and in some cases larger in magnitude than the portfolio-based return differential found in other characteristic-based studies of mutual fund performance. 4 Overall, these tests support the notion that lottery-like payoffs affect a fund s subsequent performance; MAX funds underperform both in the cross-section and in time-series sorted portfolios. 2 We note that these two alternative mechanisms are not mutually exclusive. 3 Bali, Brown, Murray, and Tang (2017) similarly proxy for lottery demand using MAX calculated with the average of the five highest daily returns in the month. Bali, Cakici, and Whitelaw (2011, Table 2) show that the MAX-return relationship is robust to calculating MAX using the average of the highest returns over 1, 2, 3, 4, or 5 days. In robustness tests (Section 6), we show that our main results also hold when calculating MAX over these alternate horizons. 4 For some recent examples, see Kacperczyk, Sialm, and Zheng (2005), Cremers and Petajisto (2009), Amihud and Goyenko (2013), and Jordan and Riley (2015). 3

6 Having established a link between a fund s lottery characteristics and future returns, we next investigate whether investors demonstrate a preference for mutual funds with such features. Additionally, we explore this demand separately for retail and institutional investors. Past literature at the individual stock level shows that retail investors have stronger demand for lottery-like payoffs (Kumar (2009), Doran, Jiang and Peterson (2012), Han and Kumar (2013)), so this distinction may also hold for investors in mutual funds. We perform regressions of a fund s flows on the prior month s measurement of lottery-like payoffs (MAX), in addition to other well-known determinants of fund flows, including lagged fund performance and fund risk. Results confirm evidence of a relationship between flows and lottery characteristics, but this outcome is driven by retail investors. Specifically, retail share class funds with higher lottery characteristics in the prior month have significantly higher inflows during the current month. We do not find similar evidence for institutional share class funds, suggesting that institutional investors ignore the lottery features of mutual funds. Together, these results provide evidence of retail, but not institutional, demand for lottery-like mutual funds. Furthermore, the flow results combined with the return results suggest that retail investors chase lottery funds that are likely to suffer from future underperformance. 5 In the context of the Berk and Green (2004) model, these results suggest that at least part of the poor performance of MAX mutual funds may be attributed to investor demand of these funds. 5 In a contemporaneous study, Akbas and Genc (2016) do not detect any relationship between extreme payoffs and future fund performance when using style-adjusted monthly returns over the prior year. Instead, our approach follows the methodology of the empirical asset pricing literature (Bali, Cakici, and Whitelaw (2011), Bali, Brown, Murray, and Tang (2017)) to characterize lottery-like payoffs using maximum daily fund returns over the prior month, and find a negative relationship consistent with results found in other asset classes. Akbas and Genc (2016) do, however, find a positive relationship between extreme returns and fund flows for both retail and institutional investors, though their extreme return measure is uncorrelated with future fund performance. Our finding of only retail demand is more consistent with the predictions of the MAX literature. 4

7 To further understand the potential source of the lottery-like behavior of these funds, we examine the MAX characteristics of the individual stocks held by the mutual funds. Using data on fund holdings, we compute the MAX for each stock held by a given fund, and compare the weighted average of the individual stocks MAX (calculated with individual stock returns) to the mutual fund s MAX (calculated with fund returns). We find that high MAX mutual funds are more likely to hold high MAX stocks, and this effect is especially prominent in the highest quintile of MAX-sorted funds. In other words, lottery funds hold more lottery-like stocks. This result suggests that funds can generate lottery-like payoffs by tilting their portfolio holdings towards high MAX stocks. We also provide evidence of persistence in the lottery characteristics of mutual funds. While lottery funds this month are likely to be lottery funds next month, funds do move into or out of the lottery group, presumably through adjustments to fund holdings. These results suggest that high concentrations of MAX stocks in MAX mutual funds contributes to the underperformance of these funds. Overall, our message is that mutual funds with MAX characteristics underperform. We find that both retail investor preference for such funds, and concentration of MAX stock holdings by these funds contribute to the underperformance of MAX mutual funds. Importantly, our results using mutual fund flows provide a direct test of investor-based demand for lottery-like assets, by confirming a link between MAX and actual trading activity. Our paper makes contributions to three distinct areas of the literature. First, our results that show an effect of MAX on the returns to managed mutual funds extends the existing literature that documents a relationship between MAX and the returns to other asset classes. Past work has shown that MAX is negatively correlated with the returns to U.S. stocks (Bali, Cakici, and Whitelaw (2011)), and European stocks (Annaert, Ceuster, and Verstegen (2013) and Walkshäusl (2014)). 5

8 Other papers show that lottery features affect the returns of other individual assets, such as options (Doran, Jiang and Peterson (2012), Boyer and Vorkink (2014)) and IPO returns (Green and Hwang (2012)). Our finding that the MAX-return relationship carries over to the performance of managed portfolios provides important reinforcement to the findings of these earlier papers. Detecting an effect of MAX on the returns to mutual funds, an asset class unlikely to demonstrate such a result, provides convincing evidence that a lottery-like payoff is an asset characteristic that influences future returns. This contribution is noteworthy because, while diversification levels in mutual funds could potentially eliminate a great deal of the return skewness in fund returns, our results show that some effect of MAX on future returns survives this diversification. Secondly, our results add to the growing literature that examines the fund characteristics that predict mutual fund performance. 6 Specifically, we show that funds with lottery-like features underperform on an absolute basis, and also underperform relative to funds without such characteristics. Such a finding has relevance both for the mutual fund choice faced by fund investors and the portfolio holdings choice faced by fund managers. Lastly, our flow results make a contribution to studies on the determinants of mutual fund flows (Ippolito (1992), Chevalier and Ellison (1997), Sirri and Tufano (1998), Berk and Green (2004)), and how these factors differ for institutional and retail investors (Del Guercio and Reuter (2014), Ivković and Weisbenner (2009)). We add to this literature by showing that retail investor preference for lottery mutual funds is another determinant of fund flows. The absence of an 6 Kacperczyk, Sialm, and Zheng (2005), Kacperczyk, Sialm, and Zheng (2008), Cremers and Petajisto (2009), Amihud and Goyenko (2013), Ferreira, Keswani, Miguel, and Ramos (2013), and Kacperczyk, Van Nieuwerburgh, and Veldkamp (2014) are just a few recent examples from this voluminous literature. 6

9 institutional preference for lottery mutual funds supports existing literature that finds lottery type preferences are stronger among retail investors. Using mutual fund flow data provides the advantage of being able to observe actual trading activity, and therefore directly test retail demand for lottery characteristics. Our finding that lottery preferences are found even among diversified mutual funds validates the inferences from research in other asset classes where the lottery characteristics would be stronger by construction. The remainder of the paper is organized as follows. Section 2 provides the background motivation related to MAX and asset returns, and mutual fund flows and performance. Section 3 describes the data used in the study and our empirical methods. Section 4 investigates the empirical relationship between MAX and mutual fund returns. Section 5 examines the flow-performance relationship, the composition of lottery funds, and the persistence of fund characteristics. We perform robustness tests in Section 6, and offer concluding remarks in Section Background 2.1 Lottery Preferences, MAX, and Stock Returns Various theoretical models provide motivation for an empirical relationship between the lottery characteristics of a stock and its future returns. In general, these models describe a preference for assets with lottery-like payoffs, or skewness, and show that this preference can affect asset prices. Furthermore, this preference can be shown to hold whether investors maximize traditional expected utility functions (Mitton and Vorkink (2007)), or make decisions according to cumulative prospect theory (Barberis and Huang (2008)). Regardless of approach, both models show that skewed securities may become overpriced and earn negative average excess returns in the future. 7

10 Using these theoretical results as motivation, Bali, Cakici, and Whitelaw (2011) construct a variable that captures the lottery-like feature of a stock its highest (positive) daily return within a month, or MAX. Empirically, they demonstrate that MAX has a strong negative correlation with the cross-section of expected stock returns; a portfolio of stocks in the lowest MAX quintile outperforms a portfolio of stocks in the highest MAX quintile by 1% per month. They interpret these results as being consistent with an investor preference for lottery-like payoffs; investors are willing to pay more for high MAX stocks, which reduces future returns. Other papers have found a similar relationship among European stocks (Annaert, Ceuster, and Verstegen (2013), Walkshäusl (2014)) and Australian stocks (Zhong and Gray (2016)). A separate line of work identifies the characteristics of investors who actively seek to hold less-diversified portfolios in order to capture high levels of skewness. For example, Kumar (2009) and Bailey, Kumar and Ng (2011) provide evidence that retail investors have a stronger preference for lottery-like payoff stocks, and that these investors are less likely to invest in mutual funds, which provides nice motivation for the approach in our study. Han and Kumar (2013) find that individual stocks with a high proportion of retail trading have strong lottery features, tend to be overpriced, and earn negative risk adjusted returns. Bali, Brown, Murray, and Tang (2017) also find that lottery demand is driven by individual, and not institutional, investors. Research also examines whether a lottery-like preference exists within other asset classes or across alternate trading venues, and in particular, whether this preference is more pronounced among individual or less-sophisticated investors. Eraker and Ready (2015) provide evidence of lottery preferences in stocks traded over-the-counter. Boyer and Vorkink (2014) find demand for lottery features in the options market, and Doran, Jiang and Peterson (2012) show that this demand is especially prevalent among retail option investors. Green and Hwang (2012) suggest that first- 8

11 day IPO returns reflect a preference for skewness that is driven by individual investors. Autore and DeLisle (2016) argue that SEOs with high expected skewness underperform and institutions who receive shares in the primary market are aware of this skewness-induced overpricing. Despite this active literature that tests for skewness preferences in asset returns, what remains unexamined is whether a lottery-like preference for stock returns carries over to the returns of managed mutual funds. Given the prevalence of mutual funds as the vehicle of choice for many investors, determining whether such a relationship also exists in mutual funds seems to be worthy of investigation. Thus, in this paper, we extend the literature on skewness preferences by studying mutual fund investors preference for lottery-like payoffs. 2.2 Mutual Fund Performance The literature on mutual fund performance has its roots in the works of Sharpe (1966) and Jensen (1968), who conclude that the average active mutual fund manager lacks skill and underperforms a passive benchmark. In a seminal study, Carhart (1997) also finds no evidence of skilled mutual fund managers, and several papers through the years have come to a similar conclusion that the average fund does not outperform net of fees. Fama and French (2010) show that in aggregate, mutual funds underperform various benchmarks by the amount of their expense ratios, and distinguishing skill from luck at the individual fund level is a challenge. More recently, however, several papers find evidence that some managers are skilled, or that some trading strategies implemented by fund managers do lead to outperformance. This branch of the literature does not focus on the performance of mutual funds in aggregate, but rather on subsets of funds that have skill. For example, there is evidence of skill by fund managers that focus on local holdings (Coval and Moskowitz (2001)), concentrate in certain industries 9

12 (Kacperczyk, Sialm, and Zheng (2005)), have a high active share deviation from their benchmark index (Cremers and Petajisto (2009)), have high levels of unobserved actions, or return gap (Kacperczyk, Sialm, and Zheng (2008)), or can stock pick during expansionary periods and market time during recessions (Kacperczyk, Van Nieuwerburgh and Veldkamp (2014)). 7 This latter study in particular emphasizes the importance of identifying skilled managers since only a subset of managers add value. However, just as investors are interested in detecting managers that add value, they may be equally interested in identifying managers that reduce value through their portfolio choices. Given the finding in the literature that high MAX stocks underperform low MAX stocks, we are interested in determining whether high MAX mutual funds similarly underperform low MAX mutual funds. The growing literature that examines the fund characteristics that predict mutual fund performance typically directs its focus on features that lead to outperformance. Conversely, we are interested in detecting fund characteristics that may lead to underperformance, as this information has value for mutual fund investors. After determining whether there is a link between MAX and fund performance, the logical next step is to investigate whether this relationship affects investor flows into mutual funds. 2.3 Fund Flows and Performance Does a mutual fund s exposure to lottery-like characteristics also affect its fund flows? If we can establish a relationship between MAX and fund performance, it is natural to extend this line of inquiry to the role of MAX on the flow-performance relationship. Understanding the determinants of flows into mutual funds has important consequences for fund manager incentives and 7 This represents only a cursory review of the vast literature on fund performance. For a more comprehensive review, see Berk and Van Binsbergen (2015). 10

13 compensation design. Mutual fund fees are typically tied to assets under management, so managers have some incentives to increase flows which will lead to higher revenues for the fund advisor. Several papers have reported a convex flow-performance relationship (Ippolito (1992), Chevalier and Ellison (1997), Sirri and Tufano (1998)), where mutual fund investors increase flows to high past performers but do not withdraw funds from poor past performers with similar intensity. This flow-performance asymmetry incentivizes increased risk-taking, or tournament-like behavior by fund managers (Brown, Harlow, and Starks (1996)). Indeed, Chang, Luo, and Ren (2015) show that mutual fund managers increase fund return skewness in response to poor interim performance. Such a result links the tournament-like behavior of fund managers to preferences for fund return skewness. How does investor sophistication affect mutual fund flows? The literature has provided extensive evidence that institutional investors use more sophisticated performance evaluation measures than retail investors, making institutional fund flows less sensitive to past raw returns than retail fund flows, but more sensitive to risk-adjusted measures of performance (Del Guercio and Tkac (2002), James and Karceski (2006), Huang, Wei and Yan (2012), Evans and Fahlenbrach (2012)). Del Guercio and Reuter (2014) show that the flow-performance relationship varies for different classes of retail investors, providing broker-sold funds with an incentive to increase fund beta in an effort to attract flows. Similarly, we are interested in whether retail (vs. institutional) funds increase their exposure to lottery-like characteristics in order to attract flows. Clifford, Fulkerson, Jame, and Jordan (2016) find that institutional and retail investors respond differently to measures of fund risk, causing a flow differential across the two groups. Given the findings of these past studies, we hypothesize that retail investors are more likely to increase flows into mutual 11

14 funds with lottery-like exposure. In other words, we expect that funds with high MAX will have higher retail flows than non-high MAX funds. 3. Data and Empirical Methods Our sample is comprised of mutual funds from the CRSP Survivor-Bias-Free U.S. Mutual Fund database. We include all U.S. equity mutual funds from January 2000 to December We exclude all mutual funds that CRSP identifies as index funds, ETFs, or variable annuities, and all funds that do not have a CRSP Objective Code indicating a U.S. domestic equity fund. For our tests of mutual fund flows we perform our analysis at the share class level, enabling us to distinguish between flows to retail and institutional share classes. For all other tests, including tests using mutual fund returns, we aggregate multiple share classes of a fund using the CRSP class group variable to identify mutual funds at the fund level. Fund flow for fund i and share class j in month t is calculated as: Flow i, j, t [ TNA ( TNA )(1 r )] i, j, t i, j, t 1 i, j, t, TNA i, j, t 1 where TNAi,j,t is the total net asset value for fund i and share class j in month t, and ri,j,t is the fund and share class total return during the same month. 8 Assets under management is calculated as the sum of assets for all fund share classes. Age and manager tenure are measured as the maximum age and manager tenure for all reporting share classes. Other variables including returns, expense ratio, and turnover ratio are calculated as the weighted average for all share classes of a fund. Averages are weighted by share class assets under management. The load 8 To minimize the effect of outliers, we winsorize the flow variable at the upper and lower 1% level. Our results are robust if we instead delete flow observations that have a value less than -0.5 or greater than 2.0, as in Coval and Stafford (2007). 12

15 variable, which is an indicator for the presence of either a front or back-end load, takes a value of one if any of the share classes have a load and zero otherwise. Our measurement of the MAX variable is calculated as the average return to the fund in the five highest daily returns of the month. 9 When a fund has more than one share class, we calculate the daily fund return by weighting the individual share class after-fee returns by assets under management. 10 We use the CRSP daily return database for our measured daily returns. The fund styles come from the CRSP Objective Code. We group all sector funds into a single style and then separate the other size, growth and income based styles into their unique objective codes. A listing of all used CRSP Objective codes can be found in Table MAX and Mutual Fund Performance Our first objective is to examine whether there is an empirical relationship between a mutual fund s MAX measure and its subsequent performance. While such a result would support existing findings in the literature, it is not clear that this performance relationship should hold for an asset class comprised of, presumably, well diversified portfolios. Evidence of a MAX-performance relationship for mutual funds would be especially convincing of the role of lottery characteristic for asset returns. 4.1 Summary Statistics In anticipation of our performance tests, we first determine whether certain fund styles are more likely to identify as lottery funds. For each fund style, we calculate the percentage of stylemonths that fall into the high MAX quintile, and report these results in Table 1. We find that lottery 9 In section 6, we show that results are similar if we calculate MAX using the single highest return day of the month. 10 The only difference in returns across different share classes of the same fund is due to different fees. Before-fee returns are the same. 13

16 funds are likely to be small cap and micro-cap funds. For small cap fund returns, 36.5 percent of the fund-months fall into the highest MAX quintile. We also observe that sector funds are frequently categorized as lottery funds. The returns to sector funds fall into the high MAX quintile 43.7 percent of the time. Sector funds are likely to be less diversified than funds following other investment styles, which makes it more likely that this idiosyncratic characteristic would flow through to the portfolio return. In Table 2, we report the cross-sectional correlation between a fund s monthly MAX variable and other characteristics of the fund. MAX and the subsequent monthly return are negatively correlated, providing initial motivation for our main tests. MAX is also negatively correlated with fund size, fund family size, fund age, and the load indicator variable. MAX is positively correlated with a fund s turnover ratio and expense ratio. Thus, smaller, younger funds with high turnover and higher expense ratios appear to be more likely to have lottery features. Of all these correlations, however, the correlation between MAX and subsequent returns is the largest in magnitude. Next, we form quintile portfolios based on a fund s monthly MAX measure and report the summary statistics of these MAX portfolios in Table 3. By construction, MAX increases across the five portfolios, with a value of 1 percent for the lowest quintile of funds and a value of 2.26 percent for the highest quintile of funds. For comparison, performing similar sorts on individual stocks instead of mutual funds, Bali, Brown, Murray, and Tang (2017) report an average MAX of percent in the lowest quintile and 6.3 percent in the highest quintile. 11 So, some effect of fund diversification in mitigating average return skewness is evident from our results, especially 11 For comparison to our quintile sorts, this represents the average across the lowest two and highest two deciles, respectively, reported in Table 2 of Bali, Brown, Murray, and Tang (2017). 14

17 in the high MAX quintile. Yet, despite the impact of diversification, the average return across the five highest daily returns in the month still more than doubles moving from the low MAX to the high MAX quintile of mutual funds. Ultimately, we are interested in whether this MAX difference is associated with a difference in future fund returns. Results from Table 3 confirm such an outcome; the fund return in the subsequent month is much lower in the high MAX quintile (0.279 percent) than in the low MAX quintile (0.482 percent), and this return difference is statistically significant. Importantly, this decrease in subsequent fund return across the MAX quintiles is not monotonic. As seen in Figure 1, the subsequent monthly fund return decreases slowly moving from MAX quintile 1 to MAX quintile 4, and then drops drastically from quintile 4 to quintile 5. Thus, any MAX return relationship for mutual funds is likely to be driven by funds in the highest MAX group. This return pattern we document for mutual funds is consistent with the MAX-return relationship shown by Bali, Cakici and Whitelaw (2011). Therefore, the effect of MAX on future returns found in individual stocks does carry over to the mutual fund space. One other notable result in Table 3 is the large increase in fund turnover as we move from MAX quintile 4 to quintile Funds in the highest MAX group trade much more actively than funds in the other groups. 4.2 Does MAX Predict the Cross-Section of Mutual Fund Performance? So far, we have established two related empirical relationships: there is an overall negative correlation between a mutual fund s MAX variable and its return in the following month, and lottery funds in the highest MAX quintile have markedly lower returns than the funds in the lower four MAX quintiles. Now, we turn to more formal tests of the role of lottery features for mutual fund returns. In Tables 4 and 5, we investigate the predictive ability of MAX on the cross-section 12 Because turnover is calculated at the quarterly level, this result reports MAX relative to the prior quarter s turnover. 15

18 of fund returns using both cross-sectional regressions and portfolios sorts. The results from both methods confirm that lottery-like (high MAX) mutual funds underperform non-lottery (low MAX) mutual funds. A. Cross-Sectional Tests: Fund Performance and MAX In Table 4, we test whether fund MAX in the current month predicts fund performance in the following month. Similar to Amihud and Goyenko (2013) and Jordan and Riley (2015), we run Fama-MacBeth (1973) style regressions of risk-adjusted performance on various known predictors of fund performance, but also include our variable of interest, MAX. Specifically we estimate the following model of fund performance: Alpha MAX Alpha FundControls i, t i, t 1 i, t 1 i, t 1 i, t where Alpha i,t is the alpha for fund i in month t, calculated from a Fama-French four-factor model using rolling 60-month observations. We run these regressions for 422,090 fund-month observations. In addition to controlling for the fund s alpha in the prior month, we also control for other fund characteristics that have been shown to predict mutual fund performance, such as idiosyncratic risk, fund size, fund family size, a load indicator variable, fund expense ratio, fund turnover ratio, and fund age. As an initial pass, in column (1) we suppress the fund controls and investigate the relationship between MAX and future mutual fund performance while controlling only for past performance. Similar to prior results in the mutual fund literature, we find that past performance is a significant predictor of future performance. 13 However, we also find a significant 13 For examples, see Huang, Sialm, and Zhang (2011), Amihud and Goyenko (2013), and Doshi, Elkamhi, and Simutin (2015). 16

19 negative coefficient on MAX (t-statistic of -2.08), suggesting that funds with higher MAX have lower future performance. 14 In column (2), we include the fund controls and continue to find a negative relationship between fund MAX and future performance. Economically, a one percent increase in a fund s monthly MAX leads to a 22 basis point reduction in next month s risk-adjusted performance (tstatistic of -2.52). On an annualized basis, this represents underperformance of 2.6 percent. In terms of economic significance, this performance effect is of similar or greater magnitude to those found in other studies of mutual fund performance. For example, Amihud and Goyenko (2013) report that a 0.1 decrease in fund R 2 (a proxy for fund selectivity) leads to a reduction in annualized alpha of percent. Jordan and Riley (2015) find that a one standard deviation increase in lagged fund risk lowers future fund alpha by 0.99 percent per year. Thus, fund MAX appears to be an even stronger predictor of fund performance. Akbas and Genc (2016) also examine the relationship between extreme fund returns and future mutual fund performance. Defining extreme positive returns as the maximum style-adjusted monthly fund return over the past year, they do not detect any relationship between extreme returns and future fund performance. Additionally, the empirical asset pricing literature has documented a well-known negative relationship between idiosyncratic volatility and future stock returns (Ang, Hodrick, Xing, and Zhang (2006, 2009)), but Bali, Cakici and Whitelaw (2011) show that MAX reverses this relation for portfolios of individual stocks. With this result in mind, and to ensure that our results are not driven by idiosyncratic risk, we also control for idiosyncratic volatility in our regressions. In 14 For all tests that have a time-series element, we use Newey-West (1987) standard errors. For cross-sectional regressions we use robust standard errors. 17

20 column (2), we find a positive but insignificant effect of idiosyncratic volatility (calculated with daily mutual fund returns over the month) on future fund performance. We augment these regressions in column (3) by controlling for fund investment style fixed effects in order to more precisely capture the influence of the fund MAX on the individual fund s performance. The results continue to show a statistically significant negative coefficient (t-statistic of -2.33) on MAX, suggesting that this result is not driven by differences in fund style. In this specification, a one percent increase in fund MAX again leads to an annualized risk-adjusted performance of -2.7 percent. We also find that funds with higher expense ratios have lower future performance. The other fund characteristics do not have an economically significant effect on performance. Overall, the results from Table 4 show that mutual fund MAX is associated with lower future performance, consistent with our hypothesis that lottery-like mutual funds underperform relative to non-lottery funds. B. Portfolio Sorts: The Performance of High MAX and Low MAX Mutual Funds The results from Table 4 suggest that high MAX mutual funds underperform, but these tests do not specifically isolate the highest MAX funds. Next, we perform portfolio-based tests to directly measure the performance effect of investing explicitly in lottery-like funds. In Table 5, we report four-factor time-series regression results for MAX-sorted portfolios. Using the prior month s MAX to sort funds into quintiles, we calculate equally weighted portfolio returns by quintile. We also calculate the return to a hedge portfolio as the difference between the returns of the low MAX portfolio and the high MAX portfolio. Next, we regress the excess returns of each of the five MAX-sorted portfolios (and the hedge portfolio) on the Fama-French-Carhart 18

21 (1996, 1997) four factors. We find interesting patterns with respect to both the risk exposures and the risk-adjusted performance of the mutual fund portfolios. With regards to risk exposures, as we move from the low MAX to the high MAX portfolios, we observe monotonic increases in market (MKTRF) betas and size (SMB) betas, and a monotonic decrease in value (HML) betas. Additionally, the difference in beta between the low and high MAX portfolios is significant for all three of these factors. These results imply that high MAX mutual funds have significantly larger exposure to the market risk premium and small stocks than low MAX funds, but significantly lower exposure to value stocks. None of the portfolios display significant exposure to the momentum factor. Overall, these results illustrate the differential risk characteristics of the MAX-sorted portfolios. While the differential risk exposures are informative, ultimately we are interested in the relative risk-adjusted performance of these portfolios. First, we find that alpha decreases monotonically as we move from the low MAX portfolio to the high MAX portfolio. The low MAX portfolio has a positive, but insignificant, alpha. Interestingly, the alphas for the four lowest MAX portfolios, those containing the non-lottery funds, are all insignificantly different from zero. Thus, the risk-adjustment procedure appears to accurately explain the returns to the non-lottery fund portfolios. However, the high MAX portfolio has a statistically significant alpha of percent. On an annualized basis, the portfolio of lottery mutual funds underperforms the benchmark by 3.13 percent. Additionally, the low-minus-high MAX portfolio has a statistically significant and economically large alpha of percent per month, indicating that high MAX funds underperform low MAX funds by 4.02 percent per year. Again, to emphasize the economic significance of this performance differential, we compare our findings to some prior results from the mutual fund performance literature. Kacperczyk, Sialm, and Zheng (2005) find that the alpha 19

22 from a portfolio of mutual funds in the highest quintile of industry concentration exceeds that of the lowest quintile portfolio by 0.39 percent per quarter, while Cremers and Petajisto (2009) report that funds in the highest quintile of active share outperform those in the lowest quintile by 2.98 percent on an annualized basis. So, the risk-adjusted performance differential we document between high and low MAX funds is in line with, or even exceeds, that from previous studies that use different measures to predict mutual fund performance. Additionally, we can get some sense of how effective the diversification benefit of mutual funds is at attenuating the MAX-return relationship that exists for portfolios of individual stocks. Bali, Cakici, and Whitelaw (2011) show that the alpha difference between the highest and lowest decile of MAX-based portfolios is 0.89 percent per month. While our main tests utilize quintile sorts, in unreported results we find that the alpha differential between the highest and lowest decile of MAX-based mutual funds is 0.46 percent per month. Thus, the magnitudes that we document are about one half of the performance differential found in portfolios of individual stocks formed explicitly on MAX. We conclude that the effect of MAX on subsequent asset returns survives the diversification benefit of mutual funds. Overall, the results in Tables 4 and 5 show that high MAX mutual funds underperform, on average. Next we investigate whether investors do in fact respond to such performance differences. 5. MAX Funds: Investor Flows, Composition, and Persistence The results of Section 4 confirm a relationship between MAX and mutual fund performance; high MAX funds significantly underperform on both an absolute and relative basis. These results are consistent with previous studies on the relationship between MAX and stock returns, and provide additional support to the asset pricing literature on the role of MAX for average returns. We now 20

23 try to understand the causes of this performance relationship. In particular, we examine how investors react to lottery funds, how a fund becomes a lottery fund, and whether fund lottery characteristics are persistent. 5.1 Effect of MAX on Fund Flows Several studies have documented investor demand for assets with lottery characteristics. One advantage of using mutual fund data is that we can directly address the question of demand through an investigation of investor flows. Thus, we first test whether mutual fund investors respond to lottery-like characteristics through their fund flows. Additionally, we are interested in whether institutional and retail investors respond differently to a fund s MAX. For individual equities, Han and Kumar (2013) show that stocks with a high proportion of retail trading have strong lottery features. We investigate whether a similar effect holds for mutual funds. In Table 6, we regress a fund s net flows on a fund s MAX from the prior month, and various other characteristics that have been shown to influence fund flows. Given the well-documented relationship between flows and lagged performance, we control for a fund s prior month excess return in these regressions. Additionally, we control for fund volatility as measured by the standard deviation of daily fund returns over the prior twelve months. Other fund controls include fund age, size, family size, expense ratio, turnover ratio, load, and lagged flow. Finally, to control for any inflows that may result from time-varying changes in investor preference for certain fund styles (Greene and Stark (2016)), we control for both fund style and time fixed effects. In these regressions, the dependent variable is the monthly net fund flow at the share class level. Because we are interested in whether there is a different flow response by retail and institutional investors to fund lottery characteristics, we interact lagged fund MAX with an 21

24 indicator variable for share classes that are identified as a retail fund. Additionally, we interact lagged volatility and excess return with the retail fund indicator to allow for different reactions by retail and institutional investors to past fund performance and risk. In column (1), results show that while the coefficient on MAX is insignificantly positive, the coefficient on the interaction between MAX and retail fund is significantly positive, and economically large. Thus, retail investors appear to increase flows for funds with lottery characteristics, while institutional investors do not react to past fund MAX. A one percent increase in fund MAX, equivalent to movement from the lowest to the highest MAX quintile, leads to a percent increase in retail fund flows (relative to total net assets) in the following month. Results from this specification also show that fund flows are significantly positively related to last month s excess return for all investors, yet the interaction shows that this effect is stronger for retail investors. Additionally, fund flows are significantly negatively related to prior fund volatility. The results of this test support a positive flow response of mutual fund investors to lottery like characteristics, but this effect is driven by retail investors. Institutional investors appear to ignore the lottery characteristics of a fund, but do pay attention to prior fund risk and performance. In column (2), we repeat these regressions with the addition of other control variables that have been shown to affect mutual fund flows. These fund controls include fund age, fund size, family size, expense ratio, turnover ratio, load, and lagged fund flow. 15 In column (3) we include the additional fund controls and fund style fixed effects, to ensure that any flow relationship is not driven by the potential style-chasing of retail investors. The main result from column (1) holds 15 Again, for space considerations, we suppress the reporting of the coefficients for these other fund control variables. Full results are available upon request. 22

25 with these additional controls; there exists a positive relationship between fund flows and MAX for retail funds. Furthermore, given that we control for lagged returns in these regressions, the effect of MAX on retail flows holds even after controlling for the well-known flow-performance relationship. Additionally we point out that lagged MAX and lagged volatility have opposite effects on retail fund flows. So, while it may be natural to think that these two variables are capturing similar characteristics of fund returns, we provide evidence that the market clearly views them differently. While investors avoid funds with high total risk, they demonstrate a preference for funds with lottery characteristics. This result adds new context to the literature that examines the relevance of MAX for the behavior of asset prices. Overall, the results of Table 6 provide convincing evidence that retail mutual fund investors chase lottery-like payoffs, while institutions appear to pay less attention to higher MAX funds. Furthermore, this flow behavior should be independent of any potential style-chasing by retail investors. Akbas and Genc (2016) find a positive relationship between extreme fund returns and fund flows for both retail and institutional share classes, though their extreme return measure is uncorrelated with future fund performance. Using MAX, which is negatively correlated with future performance, we document a positive effect on fund flows for retail share classes only, which is consistent with the predictions in the MAX literature. Berk and Green (2004) show that decreasing returns to scale in investment ability erodes the performance of mutual funds as they grow in size. The results in this section document a positive relationship with MAX and subsequent mutual fund flows. In the context of Berk and Green (2004) these results suggest that retail investor preference for MAX could indirectly contribute to the underperformance of MAX mutual funds. 5.2 Composition and Persistence of Lottery Funds 23

26 So far, we have provided evidence that mutual funds with lottery characteristics have lower future performance and retail investors in particular have higher flows into lottery-like funds. We now investigate how a lottery fund can achieve its lottery like characteristics, and whether these characteristics are persistent. Given the diversification benefits of a mutual fund portfolio, we examine the relationship between the lottery characteristics of the individual assets held by a fund, and the lottery-like behavior of the fund itself. To accomplish this task, we first compute the MAX for each stock held by a given fund as the average of the five highest daily returns of that stock during the month. Then, for each fund, we calculate the value-weighted average holding MAX, the equal-weighted average holding MAX, and the median holding MAX. We refer to these measures as holding MAX, to distinguish them from the fund MAX. In Panel A of Table 7, we sort our sample of mutual funds into quintiles according to the fund MAX (calculated with the mutual fund returns), and report the simple average of the various measures of holding MAX (calculated with individual stock returns) for each quintile of fund MAX. The objective is to identify what relationship, if any, exists between fund MAX and the fund s holding MAX. The results show a near monotonic increase in holding MAX across quintiles of fund MAX, for all three measures of holding MAX. For example, the average value-weighted holding MAX is 6.35 percent for the high fund MAX quintile, and 4.58 percent for the low MAX quintile. This difference of 1.77 percent is statistically significant. Figure 2 provides a graphical illustration of the relationship between holding MAX and fund MAX. The figure confirms an increase in holding MAX across the quintiles of fund MAX. While the shape resembles a hockey stick rather than a pure monotonic increase, a prominent jump in holding MAX is evident between the fourth and fifth quintile of fund MAX. Thus, the lottery funds have especially high exposure to high MAX stocks. In Panel B of Table 7, we report results 24