Lottery Mutual Funds *

Transcription

1 Lottery Mutual Funds * Bradley A. Goldie Miami University Tyler R. Henry Miami University Haim Kassa Miami University This Draft: November 18, 2016 *We thank Turan Bali, Ryan Davis, Jared DeLisle, Hui Guo, Scott Murray and participants at the 2016 SFA 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.

2 Lottery Mutual Funds Abstract We examine the lottery characteristics of mutual funds. We find that funds with lottery-like features, as measured by MAX, underperform both in portfolio sorts and cross-sectional regression tests. Using fund flows, we show evidence of strong retail, but not institutional, demand for lottery-like investments. We also find that funds with a greater retail investor base are more likely to have lottery characteristics. These results indicate that retail investors chase lottery-like funds, and fund managers may use lottery characteristics to attract retail investment at the expense of fund performance. We conclude that mutual fund investors would benefit from avoiding lottery funds. Keywords: Mutual fund flows and performance, lottery preferences, skewness, MAX. JEL Classification: G11, G23 1

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, 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 lottery characteristics underperform, and whether investor preference for lottery mutual funds is evident through fund flows. Additionally, we investigate whether the demand for lottery mutual funds differs among retail and institutional investors. Despite decades of active research, the question of whether mutual fund managers possess skill seems to be an open question. Naturally, investors have strong incentives to identify managers that add value through their portfolio holdings or trading strategies. While the mutual fund literature typically directs its attention to strategies that outperform, investors have an equally strong incentive to avoid managers that underperform. Recent evidence in the asset pricing literature indicates that a stock s maximum daily return (MAX) 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 1

4 over $18.2 trillion in assets, the majority of which ($15.8 trillion) were held within mutual funds. 1 Given 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 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 whether the preference for lottery-like payoffs carries over to the mutual fund space, and consequently, whether lottery mutual funds also suffer from poor performance. 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). 2 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 1 Investment Company Institute 2015 Annual Fact Book: U.S. mutual funds account for 53% of total worldwide mutual fund and ETF assets. 2 Bali, Brown, Murray, and Tang (2016) 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. 2

5 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. 3 Overall, these tests support the notion that lottery-like payoffs affect a fund s subsequent performance; lottery funds underperform both in the cross-section and in time-series sorted portfolios. 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. 3 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 Next, we investigate whether funds with a greater retail investor base are more likely to have lottery characteristics. We run probit and logit regressions to predict the likelihood that a lottery mutual fund has a higher percentage of its assets under management held by retail share class investors. The predictive regressions confirm that funds in the highest MAX quintile are more likely to be held by retail investors in the prior month. Lottery funds are also more likely to be younger funds with higher expense ratios and greater turnover. The risk characteristics of lottery funds also differ from non-lottery funds, as they have greater exposure to the market risk factor and the size factor, and greater exposure to growth stocks. To further understand the potential source of the lottery-like behavior of these funds, we examine the lottery 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 fund managers can generate lottery-like payoffs for the fund 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. There is recent evidence in the literature showing that fund managers make portfolio allocation decisions with lottery characteristics in mind, and that managers may cater to investors preferences. For example, Chang, Luo, and Ren (2015) show that fund managers 4

7 increase their holdings in stocks with high expected coskewness in an effort to increase fund skewness after periods of interim underperformance. Avramov, Cheng, and Hameed (2016) find evidence that fund managers actively cater to investors preferences, and suggest that less skilled managers target investors with lottery-like preferences through higher marketing expenses. Greene and Stark (2016) show that fund sponsors offer demand-motivated funds to attract inflows based on investor preference for a particular style or strategy, even when there is no expectation of future outperformance. Our results placed in the context of these recent findings are supportive of a story where unskilled managers are catering to the lottery preferences of investors, and retail investors in particular. Overall, our message is that lottery funds underperform, retail investors exhibit a preference for lottery funds, and a fund s retail ownership predicts the likelihood that it is a lottery fund. Importantly, our results using mutual fund flows provide a direct test of investorbased demand for lottery-like assets, by confirming a link between MAX and actual trading activity. We conclude that mutual fund managers may use lottery characteristics to attract retail investment at the expense of fund performance. 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. Bali, Cakici, and Whitelaw (2011) show that MAX has a strong negative correlation with the crosssection of expected stock returns in the U.S. stock market. Annaert, Ceuster, and Verstegen (2013) and Walkshäusl (2014) document a similar relationship among European stocks. 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 5

8 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 should eliminate a great deal of the return skewness in fund returns, our results show that the 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. 4 While most of this literature focuses its attention on fund characteristics that lead to outperformance, we document a fund characteristic that leads to underperformance. 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 institutional preference for lottery mutual funds supports existing literature that finds lottery 4 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 type preferences are stronger among retail investors. Also, mutual funds as portfolios represent a market where we would not expect to find evidence of lottery-seeking behavior. 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 flowperformance 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 (MAX) 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)). 7

10 The theoretical literature on investors preference for lottery-like payoff stocks extends the mean-variance optimization problem into a mean-variance-skewness problem. The motivation for including skewness in the optimization problem relies on the observation that the empirical distribution of realized stock returns is not symmetric (Duffee (1995)). Since a positively (negatively) skewed distribution has a higher chance of an extreme positive (negative) outcome, investors have a preference for positively skewed securities. In equilibrium, positively skewed securities have a higher price, which results in a negative relation between skewness and expected return (Kraus and Litzenberger (1976), Conine and Tamarkin (1981), Harvey and Siddique (2000)). More recently, the literature has identified heterogeneity among investors preference for skewness or lottery-like payoff stocks. Mitton and Vorkink (2007) develop a model with two groups of investors, where the preference for mean and variance is the same across the two groups, but only one group has a positive preference for skewness. They show that, in equilibrium, investors with greater demand for skewness hold less-diversified portfolios than investors with less demand for skewness. Using a different modeling approach, Barberis and Huang (2008) show that when investors with homogeneous preferences make decisions according to the cumulative prospect theory of Tversky and Kahneman (1992), overweighting the probability of extreme returns captures a preference for a lottery-like, or positively skewed, return distribution. Thus, skewed securities may become overpriced and earn negative average excess returns in the future. With the results of these papers 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 8

11 correlation with the cross-section of expected stock returns. Specifically, they show that 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. Annaert, Ceuster, and Verstegen (2013) and Walkshäusl (2014) document a similar relationship among European stocks. Zhong and Gray (2016) show that the MAX effect holds in Australian equities, and provide evidence that this effect results from mispricing rather than underlying economic risk. 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) shows that retail investors have a stronger preference for lottery-like payoff stocks. Further, he reports that among retail investors, the poor, young, less educated, single men who live in urban areas, are non-professional workers, and belong to minority groups tend to show an even stronger preference for lottery-like payoff stocks. Bailey, Kumar, and Ng (2011) show that some individual investors have substantial behavioral biases, most notably, a penchant for lottery-like stocks. They also report that individual investors with a strong preference for lottery stocks 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 (2016) 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 9

12 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-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 predominance 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. 10

13 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 (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)). 5 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, and avoiding, 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. 5 This represents only a cursory review of the vast literature on fund performance. For a more comprehensive review, see Berk and Van Binsbergen (2015). 11

14 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 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. There is a robust literature that examines the relationship between a mutual fund s past performance and its fund flows. Ippolito (1992) shows that mutual fund investors react to prior performance and noticed that the flow response may be non-linear. Later papers reported what is now a well-documented convex flow-performance relationship (Chevalier and Ellison (1997), Sirri and Tufano (1998)). On average, 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? There are many reasons to believe the flow-performance relationship may be different for institutional and retail investors in mutual funds. Del Guercio and Tkac (2002) show that pension funds have a different flow- 12

15 performance relation than retail mutual funds. Namely, pension funds punish poor performers and do not chase winners, which they attribute to the reduced risk-shifting incentives of pension fund managers. Institutional investors often use more sophisticated performance evaluation measures than retail investors. For example, James and Karceski (2006) report that institutional fund flows are less sensitive to past raw returns than retail fund flows, but more sensitive to riskadjusted measures of performance. Huang, Wei and Yan (2012) argue that flows into institutional funds are more sophisticated due to the incorporation of additional information such as volatility and fund age in the investment decision. Evans and Fahlenbrach (2012) confirm the superior monitoring ability of institutional investors in mutual funds, showing that institutional flows are more sensitive to high fees and poor risk-adjusted performance than retail flows. Thus, there is rampant evidence that institutional flows into mutual funds differ from retail flows due to varying levels of investor sophistication. Del Guercio and Reuter (2014) show that the flow-performance relationship varies for different classes of retail investors, and this difference affects the managerial incentives of the various fund segments. Specifically, investors of broker-sold funds chase raw performance, whereas investors in direct-sold funds are more likely to respond to risk-adjusted performance (alpha). The varied incentives across fund segments leads to both differences in risk (beta) and performance (alpha). While they show that broker-sold funds have an incentive to increase fund beta in an effort to attract flows, we are interested in whether retail (vs. institutional) funds increase their exposure to lottery-like characteristics in order to attract flows. In a contemporaneous paper, Clifford, Fulkerson, Jame, and Jordan (2016) also examine differences in fund flows among institutional and retail mutual fund investors. Using a different data set, they focus on the relationship between fund flows and risk. They find that mutual fund 13

16 inflows are greater for funds with higher idiosyncratic risk, but show that this result is stronger among retail investors. Given the findings of these past studies, we hypothesize that retail investors are more likely to increase flows into mutual 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. 6 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 6 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). 14

17 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 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. 7 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. 8 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 MAXperformance relationship for mutual funds would be especially convincing of the role of lottery characteristic for asset returns. 4.1 Summary Statistics 7 In section 6, we show that results are similar if we calculate MAX using the single highest return day of the month. 8 The only difference in returns across different share classes of the same fund is due to different fees. Before-fee returns are the same. 15

18 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 style-months that fall into the high MAX quintile, and report these results in Table 1. We find that lottery 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 (2016) report an 16

19 average MAX of percent in the lowest quintile and 6.3 percent in the highest quintile. 9 So, some effect of fund diversification in mitigating average return skewness is evident from our results, especially 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 9 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 (2016). 10 Because turnover is calculated at the quarterly level, this result reports MAX relative to the prior quarter s turnover. 17

20 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 of fund returns using both cross-sectional regressions and portfolios sorts. The results from both methods confirm that lottery (high MAX) mutual funds underperform nonlottery (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 it, it, 1 it, 1 it, 1 it, where, is the alpha for fund in month, 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 18

21 performance is a significant predictor of future performance. 11 However, we also find a significant negative coefficient on MAX (t-statistic of -2.08), suggesting that funds with higher MAX have lower future performance. 12 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. 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 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. 11 For examples, see Huang, Sialm, and Zhang (2011), Amihud and Goyenko (2013), and Doshi, Elkamhi, and Simutin (2015). 12 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. 19

22 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 (tstatistic 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 riskadjusted 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 leads to a drag on future fund performance, consistent with our hypothesis that lottery 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 mutual 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 (1996, 1997) four factors the market, size, value, and momentum factors. We find interesting patterns with respect to both the risk exposures and the risk-adjusted performance of the mutual fund portfolios. 20

23 First, high MAX portfolios have greater exposure to the market risk factor. The regression coefficient on the market premium increases monotonically as we move from the low MAX portfolio to the high MAX portfolio. Additionally the exposure on the hedge portfolio is statistically significant. This result confirms that high MAX funds have different market risk characteristics than low MAX funds. Second, the regression coefficients on HML are monotonically decreasing as we move from low MAX portfolios to high MAX portfolios and the exposure on the low-minus-high MAX portfolio is negative and statistically significant. These betas indicate that high MAX funds have significant exposure to growth stocks, and low MAX funds have exposure to value stocks. Third, the regression coefficients on SMB are monotonically increasing as we move from low MAX to high MAX portfolios, with a negative and statistically significant coefficient on the low-minus-high MAX portfolio, suggesting that high MAX funds are portfolios of small stocks with high exposure to the SMB factor. 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 relationship between fund MAX and the portfolio 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 nonlottery 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 21

24 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 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. While mutual fund investors typically focus their efforts on identifying funds that outperform, they should be equally concerned about underperforming funds. Our results indicate 22

25 that fund investors would benefit from avoiding mutual funds with lottery-like characteristics. Next we investigate whether investors do in fact respond to such performance differences. 5. Lottery Funds: Investor Flows, Ownership, and Composition 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 try to understand the implications of this performance relationship. In particular, we examine how investors react to lottery funds, whether lottery funds have a different ownership mix than non-lottery funds, and how a fund becomes a lottery fund. 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 23

26 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 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 24

27 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. 13 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 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 have 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. Sirri and Tufano (1998) suggest that differential search costs across high and low performing funds could drive the convex flow-performance relationship. High performing funds 13 Again, for space considerations, we suppress the reporting of the coefficients for these other fund control variables. Full results are available upon request. 25