Sharpening Mutual Fund Alpha

Transcription

1 Sharpening Mutual Fund Alpha Bing Han 1 Chloe Chunliu Yang 2 Abstract We study whether mutual fund managers intentionally adopt negatively skewed strategies to generate superior performance. Using the fund flow and return data of U.S. actively managed equity funds from 1999 to 2014, we identify a negative correlation between alpha and the third moment (skewness) of the fund return distribution. The average difference of the Carhart four-factor alpha between funds in the lowest and highest skewness decile portfolio is 5.28% per year. Then, we examine whether fund investors pay attention to return skewness when choosing among actively managed mutual funds. Our empirical evidence suggests that fund investors are not sophisticated enough to detect the trade-off between alpha and skewness; many simply invest in mutual funds with superior performance without taking into account the potential downside risk. Consequently, the managerial incentive problem has been raised. Without having to improve their forecasting skills, mutual fund managers can still generate flow-attracting strategies by loading on more downside risk. Specifically, as their compensation is determined by relative performance, fund managers that deliver inferior performance in the first half-year are more likely to increase downside risk in the second half-year than interim winners. This tendency is more prominent among small and growth funds. 1 Bing Han, Rotman School of Management, University of Toronto. bing.han@rotman.utoronto.ca. 2 Chloe Chunliu Yang, Fanhai International School of Finance, Fudan University. chloe_yang@fudan.edu.cn. 1

2 I. Introduction In the hedge fund industry, trading strategies with negative skewness are very popular. Negatively skewed strategies appear to earn positive returns most of the time, but occasionally incur significant losses. As analyzed in Ingersoll et.al. (2007), this type of strategy is popular because it is the best manipulation strategy for maximizing the Sharpe ratio. It involves selling out-of-the-money options that ensure a regular return from writing options, while creating a large exposure to extreme market crash episodes. Options are commonly used in the hedge fund industry, but are rarely used in the mutual fund industry. Hence a natural question arises, does the same type of manipulation exist in the mutual fund industry? If so, are mutual fund investors aware of this manipulation strategy? When would fund managers be more likely to adopt negatively skewed strategies? In this paper, we investigate these questions by analyzing U.S. equity fund data. When selecting among actively managed equity funds, investors tend to favor the ones that generate high risk-adjusted performance (a.k.a. alpha). This preference has been well documented in the existing literature (see, e.g., Chevalier and Ellison, 1997; Sirri and Tufano, 1998). On the other hand, mutual fund managers are compensated according to their relative performance and/or proportionally to the funds total net assets under management (TNA). Hence, they are incentivized to generate superior performance and attract more flows. Knowing that flows chase past performance, fund managers are motivated to maximize alpha. 2

3 They can achieve this goal through various means. For instance, they can try to access superior information or interpret and analyze information more accurately. Alternatively, they can try to improve their stock-picking ability. However, obtaining information and honing stock picking skills require significant effort. If there exists a manipulation strategy which can increase alpha with minimum effort, then the possibility of managerial moral hazard arises. In other words, mutual fund managers may employ such information-free strategies to maximize performance without spending much effort or adding fundamental value to the fund. We first show that there is a negative correlation between return skewness and fund performance. Using the fund flow and return data of U.S. equity funds from 1999 to 2014, we sort funds into decile portfolios according to their return skewness. The value-weighted longshort portfolio which holds funds with low skewness and shorts funds with high skewness generates positive raw return, style-adjusted return, Capital Asset Pricing Model (CAPM) alpha, Fama-French three-factor alpha, and Carhart four-factor alpha at 5% significance level. Specifically, the average difference of Carhart four-factor alpha after deducting expenses between funds in the lowest and highest skewness decile portfolio is 5.28% per year. As a robustness check, we also double sort mutual funds into portfolios according to past fund returns and skewness. We find that there is still a trade-off between alpha and skewness after controlling for past fund returns. For instance, the value-weighted long-short portfolio which holds funds with low skewness and shorts funds with high skewness generates a positive and significant Carhart four-factor alpha of 2.88% per year. In other words, mutual fund portfolios with low and negative skewness are those with high future alphas. This implies that mutual fund managers may be able to adopt information-free strategies by changing the shape of the probability distribution of returns to boost performance. However, the cost of 3

4 this approach is an increased exposure to downside risks, which may lead to catastrophic meltdowns as seen in the case of Long Term Capital Management. If mutual fund investors are not sophisticated enough to identify the trade-off between alpha and skewness, they could be fooled into investing in poorly managed or unskilled mutual funds. When using a portfolio approach, an interesting observation is that the decile portfolio with the lowest skewness attracts the most fund flows. Then, by conducting the Fama- Macbeth cross-sectional regressions, we examine the mutual fund flows response to skewness and find no significant relation. In other words, mutual fund investors may be unaware of the alpha-skewness trade-off and they do not appear to have a specific or monotonic preference for mutual fund returns skewness. However, in the existing asset pricing literature, there is well-documented evidence that investors have a preference for assets with positive skewness (i.e. assets with a very small probability of generating a large payoff). Kumar (2009) demonstrates that individual investors with a high propensity to gamble also excessively invest in lottery-type stocks. Bali, Cakici, and Whitelaw (2011) find that stocks with lottery-like features have low expected returns. If mutual fund investors are also in favor of lottery-like payoffs, then negatively skewed strategy may not be a desirable flow-attracting strategy. Our empirical evidence stated in the previous paragraph eliminates this possibility: fund investors do not appear to prefer funds with higher return skewness. This raises another puzzling question: why do individual stock investors prefer lottery-type stocks while showing no preference for mutual funds with extreme returns? What characteristics of mutual funds contribute to this difference? The reason for this discrepancy may be that lottery-type stocks and mutual funds attract 4

5 distinct socioeconomic clienteles. According to the Investment Company Institute (ICI) Fact Book 2017, most mutual fund investors are married or living with partners, well-educated and earning incomes well above the median. These characteristics are the opposite of those of a gambler. More importantly, for 92% of mutual fund investors, the purpose for investing in mutual funds was saving for retirement. In other words, the gambling preference is unlikely to be the reason for investors to invest in mutual funds. Therefore, given the trade-off between alpha and skewness, a negatively skewed strategy would attract more flows than positively skewed one. Next, we demonstrate that mutual fund managers who underperform in the first half-year are more likely to decrease their return skewness in the second half-year compared to those halfyear winners (the tournament hypothesis). The mutual fund industry can be viewed as a tournament in which fund managers are evaluated based on their performance relative to their peers at the end of each year. Thus, the mid-year losers would bear intensive pressure to boost their performance in the latter part of the year. If they are aware of the trade-off between skewness and alpha, the losing fund managers may be tempted to adapt their investment behavior by shifting the skewness of their portfolio returns. To achieve the goal of shifting return skewness, fund managers may invest more into stocks with negatively skewed returns to construct holding portfolios with overall negatively skewed payoffs, or they may replicate the payoff of options by actively buying and selling stocks. We test the tournament hypothesis using both a portfolio and a regression approach. By sorting mutual funds according to their accumulative half-year performance, we find that more percentage of funds classified as interim losers tend to load on more downside risk than 5

6 those classified as interim winners. This hypothesis holds more for smaller funds and growth funds compared to larger or value funds. Furthermore, this behavioral difference between interim losers and winners has become more pronounced during recent years while the size of mutual fund industry has grown tremendously. In a multivariate regression, the same prediction holds that interim losers are more inclined to load on more downside risk in the second half-year than interim winners. The remainder of this paper is structured as follows: section 2 reviews the related literature, section 3 defines main variables, section 4 describes the data sources and provides some basic summary statistics, section 5 and 6 present the empirical results and section 7 concludes. II. Literature Review During the past two decades, researchers have investigated the relationship between mutual fund flows and past performance and they have found an asymmetric relationship. For instance, a convex flow-performance relationship was first documented by Sirri and Tufano (1998). When looking at past performance, the existing literature only considers alpha and volatility without taking into account the skewness of fund return distributions. This implies that investors only care about the mean and variance of returns. However, this requires normally distributed returns or quadratic utility functions, otherwise individual investors 6

7 would care about the third moment of returns, i.e., skewness. In this paper, we contribute to the mutual fund literature by examining the role of skewness in the flow-performance relationship. Ingersoll et.al. (2007) point out that alpha is prone to severe manipulation. They claim that if a portfolio can be created with any desired leverage, then in theory, the alpha can be made as high as desired. In the mutual fund industry, if the flow-performance relationship is convex, then fund managers have an incentive to change risk levels to enhance their alpha. Brown, Harlow, and Starks (1996) and Chevalier and Ellison (1997) document that mutual fund managers strategically shift risk levels to attract additional fund flows. Huang, Sialm and Zhang (2011) investigate whether risk shifting is harmful to mutual fund investors and they find that mutual funds that shift their risk levels tend to underperform when compared to those with stable risk levels. Our research differs from the existing literature as these authors mainly focus on the second moment of returns, i.e., volatility, whereas this paper puts emphasis on the third moment, i.e., skewness. It has been well-documented in the asset pricing literature that investors have a common preference for positively skewed payoffs. Brunnermeier, Gollier, and Parker (2008) claim that optimistic investors favor stocks with positive skewness. Barberis and Huang (2008) found that a positively skewed security can be overpriced and consequently earn a negative excess return in the future. Kumar (2009) documents that individual investors who heavily invest in lottery-type stocks also exhibit gambling preferences. Bali, Cakici, and Whitelaw (2011) find that stocks with lottery-like features have low expected returns. In most of the previous research, investors preferences can only be indirectly inferred from price and return 7

8 implications. In this paper, we advance prior work by directly testing mutual fund investors reaction to various levels of skewness using fund flows data. This paper also relates to the mutual fund manager tournaments literature. The mutual fund industry can be viewed as a tournament in which the amount of rewards that a fund manager receives depends on his/her performance relative to industry peers. The existing literature documents that mutual fund managers strategically shift risk levels to attract additional flows when losing the tournaments. For instance, Brown, Harlow, and Starks (1996) demonstrate that fund managers with inferior performance in the first half-year excessively increase fund volatility in the latter part of an annual assessment compared to mid-year winners. Huang, Sialm, and Zhang (2011) examine the performance consequences of risk shifting and attribute fund managers risk-shifting behavior to agency issues. While they focus on the second moment of returns (volatility), we consider the third moment of returns (skewness) and find empirical evidence showing that mid-year losers are more likely to change return skewness compared to mid-year winners. III. Variable Definitions In this section, we first define skewness, the main variable of interest, as well as different measures we use to evaluate fund performance. Then, we describe the definitions for other variables such as flows and volatility. 8

9 A. Skewness Skewness is of extreme importance to investing. Most asset returns have either positive or negative skewness, rather than following the standard normal distribution with a skewness of zero. For instance, the existing literature documents that market returns exhibit negative skewness. A negative relation between skewness and expected returns has been established by both theoretical and empirical studies. Arditti (1967), Kraus and Litzenberger (1976) and Kane (1982) extend the mean-variance portfolio theory by introducing investors preference for positive skewness. This extension could generate the implication that an asset with high systematic skewness would have low expected returns. While the existing studies focus on individual stocks, this paper is about mutual funds. Since the median number of mutual funds owned by investors is only 4 and a mutual fund is already a portfolio composed of individual stocks, we consider the total skewness in our analysis. The total skewness (Skewness i,t ) of fund i for month t is calculated using daily fund returns within the previous month: D t Skewness i,t = D 3 t(d t 1) D t (D t 2) (R i,d μ i ), (1) σ i d=1 where D t is the number of trading days in the previous month, R i,d is the return on fund i on day d, μ i is the mean of returns of fund i over the previous month, and σ i is the standard deviation of daily returns of fund i over the previous month. If skewness is less than -1 or greater than 1, the distribution is considered highly skewed. If skewness is between -1 and 1 or between 1 and 1, the distribution is moderately skewed. A 2 2 positively skewed return distribution means that there are frequent small losses and a few 9

10 large gains. In contrast, a negatively skewed return distribution means that there are frequent small gains and a few large losses. B. Performance Measures To examine the relation between skewness and fund performance, we use the following performance measures: raw return, style-adjusted return, Capital Asset Pricing Model (CAPM) alpha, Fama-French three-factor alpha, and Carhart four-factor alpha. All the fund performance measures are net of expenses. Raw fund return is the monthly fund return. Styleadjusted return is calculated by subtracting the value-weighted average return of all funds belonging to the same Lipper investment categories from monthly fund return. To estimate CAPM alpha, we run the following regression: R i,t R f,t = α i + β i,m (R M,t R f,t ) + e i,t, (2) where the dependent variable is the monthly return on portfolio i in month t minus the riskfree return and R M,t is the return of the market portfolio. The intercept of the model, α i is the measure of abnormal performance, i.e., CAPM alpha. To estimate Fama-French three-factor alpha, we run the following regression: R i,t R f,t = α i + β i,m (R M,t R f,t ) + β i,smb SMB t + β i,hml HML t + e i,t, (3) 10

11 where the dependent variable is the monthly return on portfolio i in month t minus the riskfree return, SMB is the return difference between small and large capitalization stocks, HML is the return difference between high and low book-to-market stocks. The intercept of the model, α i is the measure of abnormal performance, i.e., Fama-French three-factor alpha. To estimate Carhart four-factor alpha, we run the following regression: R i,t R f,t = α i + β i,m (R M,t R f,t ) + β i,smb SMB t + β i,hml HML t + β i,mom MOM t + e i,t, (4) where the dependent variable is the monthly return on portfolio i in month t minus the riskfree return and MOM is the return difference between stocks with high and low past returns. The intercept of the model, α i is the measure of abnormal performance, i.e., Carhart fourfactor alpha. C. Other Variable Definitions Using monthly total net asset values from CRSP, we define the monthly net flow into a fund following Huang, Wei and Yan (2007): Flow i,t = TNA i,t TNA i,t 1 (1+R i,t ), (5) TNA i,t 1 (1+R i,t ) where R i,t is the return of fund i during month t, and TNA i,t is fund i s total net asset value at the end of month t. We also winsorize the top and bottom 2.5% tails of the flow data to eliminate outliers. 11

12 The other control variables are defined as follows: Vol, the volatility of the fund s daily returns over the prior month; Fee, the fund s annual expense ratio plus actual 12b-1 fees in the previous calendar year; Cat_flow, the monthly dollar flow divided by the one-month lagged TNA for all funds in the same investment category; LogAge, the log of the fund s age since the fund was first offered; LogSize, the log of the fund s TNA in millions; Turnover, the fund s turnover ratio from the prior calendar year; and Lag_flow, mutual fund flow for the previous month. IV. Data Our primary data are obtained from three comprehensive databases: the Center for Research in Security Prices (CRSP) survivorship bias-free mutual fund database, the Thomson Financial Mutual Fund Holdings, and the CRSP US stock database. Following Kacperczyk, Sialm, and Zheng (2005), only actively managed domestic equity funds are included in the final sample. Specifically, funds classified with the following Lipper investment categories are selected: 1) Large-Cap Core (LCCE), 2) Large-Cap Growth (LCGE), 3) Large-Cap Value (LCVE), 4) Mid-Cap Core (MCCE), 5) Mid-Cap Growth (MCGE), 6) Mid-Cap Value (MCVE), 7) Multi-Cap Core (MLCE), 8) Multi-Cap Growth (MLGE), 9) Multi-Cap Value (MLVE), 10) Small-Cap Core (SCCE), 11) Small-Cap Growth (SCGE), 12) Small-Cap Value (SCVE), 13) Equity Income (EIEI). This selection procedure removes bond, balanced, international, and sector funds. We also exclude index funds as well as funds that are not offered to new investors. A mutual fund s data are included in a particular period if it includes Total Net Assets (TNA) and returns (both daily and monthly). Following Koijen (2014), we merge different share classes of mutual funds to construct a weighted average of returns and expense ratios using the TNA of each share class as the weight. To address the 12

13 incubation bias documented by Evans (2006), we exclude observations prior to the date when the fund was first publicly offered, as well as observations where the fund names are missing in the CRSP database. Fund months are also dropped from the sample for funds with TNA less than USD 5 million. Our sample period spans the years from 1999 to 2014, when daily returns data are available. Table I reports basic summary statistics and correlation structure of the main fund characteristics. Panel A shows the number of mutual funds included in this study, the average TNA, the total fees, and the average fund age at the end of each year. The total number of mutual funds increases from 1018 in 1999 to 1269 in At the same time, the average TNA first decreases and then increases after reaching the lowest point in The total fees, which are measured as the fund s annual expense ratio plus actual 12b-1 fees, have decreased slightly from 1.23% to 1.12% per annum over time. The average age has increased from 15.2 years in 1999 to 20.1 years in Panel B of Table I documents summary statistics for the main fund characteristics. For each variable, we compute a cross-sectional mean in each month and report the time series average of these cross-sectional means. Similar as market returns, the average skewness of actively managed mutual funds is also negative (-0.022). Fund skewness ranges between to 4.374, which shows a significant cross-sectional variation of mutual funds with respect to the skewness of their return distribution. In Panel B of Table I, summary statistics for other fund characteristics are also reported. The average volatility for daily fund returns is 1.144% per month. On average, funds attract positive flows (0.020% per month) and generate positive raw return and positive CAPM alpha after deducting expenses (0.584% and 0.025% per month, respectively). However, the average style-adjusted return, Fama-French three-factor alpha, and Carhart four-factor alpha are negative. Panel C of Table I presents the correlation structure between skewness and other 13

14 fund characteristics. The correlation between skewness and volatility is 6.2%, which suggests that skewness is hardly a proxy for volatility. The correlation between skewness and fund flow is slightly negative (-2.9%). Panel D of Table I reports skewness by fund investment categories. For most of the investment styles (11 out of 13), the mean skewness of fund return distribution is negative. In contrast to the previously documented pattern that skewness is more negative on average for large-cap firms, the two investment styles which have positive mean skewness are Large-Cap Core and Large-Cap Growth. V. The Relation between Skewness and Alpha In this section, we show that there is a trade-off between skewness and alpha using both a portfolio and a regression approach. Then we present empirical evidence showing that flows do not respond to skewness in subsection C. A. Portfolio Evidence A.1. Fund Portfolios Sorted by Skewness At the beginning of each month, we sort all mutual funds into 10 portfolios according to their skewness in the previous month. For each decile portfolio, we compute the equal-weighted and value-weighted average fund performance and fund flows for each month. We also report basic fund characteristics for each decile portfolio. Table II summarizes the results. Fund 14

15 performance is net of expenses, since net-of-expense returns are important for mutual fund investors. Fees charged by funds are also reported in Panel C of Table II. Equal-weighted and value-weighted fund performance and fund flows are summarized in Panel A and B of Table II. The results indicate that the value-weighted (equal-weighted) fund portfolio with the lowest skewness generates a Carhart four-factor alpha of 0.20% (0.15%) per month, while the fund portfolio with the highest skewness generates a Carhart four-factor alpha of -0.24% (-0.16%) per month. The value-weighted (equal-weighted) long-short portfolio which holds funds with the lowest skewness and shorts funds with the highest skewness generates a Carhart four-factor alpha of 0.44% (0.31%) per month, which is statistically significant at 5% (10%) level. Two recent papers (Barber, Huang, and Odean, 2016; Berk and Van Binsbergen, 2016) document that mutual fund investors rely on CAPM alpha when allocating assets across funds. Table II shows that value-weighted (equalweighted) long-short fund portfolio generates a CAPM alpha of 0.47% (0.32%) per month, which is statistically significant at 1% (5%) level. The value-weighted long-short portfolio also generates positive raw return, style-adjusted return, and Fama-French three-factor alpha at 5% significance level. Therefore, the evidence indicates that funds with lower skewness perform better than funds with higher skewness after deducting expenses. Since negative return skewness is associated with high tail risk, a natural question is whether the abnormal returns we uncover are concentrated in a particular period or exhibit a different pattern during good and bad times. Figure 1 shows the cumulative returns for $1 invested in the long-short portfolio in the beginning of the sample period in 1999 with net proceeds at the end of the period reinvested in each subsequent period. $1 invested in the long-short fund 15

16 portfolio generates $2.6 in the end of Figure 1 also shows the cumulative returns for $1 invested in the market portfolio as well as the fund portfolio deciles 1 and 10. $1 invested in the market portfolio increases by 3.3-fold over the entire sample period, while $1 invested in the fund portfolio deciles 1 and 10 generates $5.0 and $1.9, respectively. Although the cumulative return for the long-short portfolio is slightly lower than the cumulative return for the market portfolio, the volatility of the long-short portfolio (2.5%) is almost half of the volatility of the market portfolio (4.5%). The volatility of the fund portfolio decile 1 (4.7%) and 10 (4.6%) is comparable to that of the market portfolio. Over the entire sample period, the market portfolio experienced the largest decline (-17.2%) in October 2008 after Lehman Brother s crash in September Fund portfolio decile 1 and 10 also experienced the largest decline in the same month (-15.7% and -19.7%, respectively), while the long-short portfolio generates a positive return of 4.1%. The long-short portfolio experienced the largest return decline (-12.6%) in April 2000, which is the beginning of the dotcom crash. In the same month, the market portfolio experienced a 5.9% decline in return, while the return for the fund portfolio decile 10 increased slightly by 0.3%. The correlation between the returns of the long-short portfolio and the market portfolio is slightly positive (3.4%). Panel A and B of Table II also present the net fund flows for each fund portfolio decile. In contrast to the gambling preference documented by the previous literature, we find a negative correlation between fund return skewness and flows, i.e., fund flows chase funds with negative or low skewness. The value-weighted (equal-weighted) net fund flows for fund portfolio decile 1 and 10 are 0.22% (0.23%) and -0.06% (-0.08%) per month, respectively. The difference in the value-weighted (equal-weighted) monthly net fund flows between decile 1 and decile 10 equals 0.28% (0.32%) per month, which is statistically significant at 5% 16

17 (1%) level. This suggests that mutual fund investors dislike funds with positive skewness, which is the opposite of the gambling preference. Panel C of Table II reports some basic fund characteristics for fund portfolio deciles sorted according to skewness. The mean skewness of these deciles varies from to 0.46, while the mean volatility remains similar for different deciles. This suggests the return difference among different fund portfolios are hardly explained by volatility. The mean fund size does not vary much. The mean TNA for funds in decile 1 and 10 are relatively smaller. The mean turnover for funds in decile 1 is the highest (89.8%), which suggests the negatively-skewed fund returns may result from fund managers active trading. The expenses charged by funds in decile 1 and 10 are relatively high (1.31% and 1.28%). The funds in decile 1 and 10 are younger funds with a mean age of less than 16 years. A.2. Fund Portfolios Sorted by Skewness and Return In this subsection, we examine the relation between skewness and future fund performance after controlling for past fund return. The previous section shows that fund portfolio deciles with negatively skewed returns would generate high subsequent returns and attract more flows. In the meantime, previous research documents that fund returns are persistent in the short run (see, e.g. Bollen and Busse, 2004) and fund flows chase the most recently realized performance (see, e.g., Chevalier and Ellison, 1997; Sirri and Tufano, 1998). We may wonder whether the pattern shown in the previous subsection could be attributable to fund return persistence rather than a trade-off between skewness and return. To disentangle these two possible explanations, we double sort fund portfolios into 100 portfolios based on both past 17

18 fund returns and skewness. More specifically, we first form decile portfolios ranked based on realized returns in the previous month. Then, within each return decile, we sort mutual funds into decile portfolios ranked based on skewness of fund return distribution over the previous month. Table III presents the subsequent fund performance for these decile portfolios. For brevity, we only report fund performance averaged over the lag-return decile portfolios. In other words, fund performance of 10 equal-weighted (value-weighted) fund portfolios which contain funds with similar levels of lag return are reported in each column of Panel A (B), table III. We find that in the predicting period, portfolios with low skewness earn significantly high alpha. The fund performance measured by raw return, style-adjusted return, CAPM alpha, Fama-French three-factor alpha and Carhart four-factor alpha is significantly positive for both equal-weighted and value-weighted long-short portfolios. For instance, after controlling for lag returns, the value-weighted long-short portfolio which holds funds with the lowest skewness and shorts funds with the highest skewness generates a CAPM alpha of 0.27% per month with a t-statistic of The Carhart four-factor alpha is 0.24% per month for the value-weighted long-short portfolio, which is also statistically and economically significant. Although the magnitude of performance generated by the long-short portfolio from the bivariate sort on return and skewness is smaller than those presented for the univariate sort in Table II, it remains economically large and statistically significant at 5% level for all performance measures. The fund flow attracted by the value-weighted long-short portfolio is 0.15% per month, which remains statistically significant (with a t-statistic of 2.06). Again, this contrasts with the gambling preference hypothesis. The result suggests that the effect of skewness is preserved after controlling for lag return. 18

19 One concern is that bivariate sorts may not sufficiently control for lag returns. Another concern is that other fund characteristics (e.g., volatility and fees) which may also affect future fund performance are not controlled by the bivariate sorts. To address these concerns, in the next section, we perform cross-sectional regressions to investigate the relation between skewness and fund performance in which these variables appear as control variables. B. Multivariate Regression Evidence In this subsection, we further investigate the relation between skewness and fund performance using multivariate regressions. Using this approach allows us to control for mutual fund characteristics that are related to fund performance. For instance, funds with the lowest skewness charge higher fees on average. It might be that funds charge higher fees perform better. Furthermore, the portfolio approach assumes constant factor loadings across time while funds factor loadings may vary over time. In this subsection, we take into account possible time variations in the factor loadings of individual funds by estimating factor loadings using a rolling window estimation procedure. Specifically, we use 3 years of past monthly fund returns to estimate the coefficients of the factor models (3), (4), and (5). Subsequently, we subtract the expected return from the realized fund return to determine the abnormal return of a fund in each month. Next, in each month we run Fama-Macbeth cross-sectional regressions to estimate the correlation of fund performance and skewness, controlling for other fund characteristics that could potentially affect mutual fund performance. Fund performance is measured using raw 19

20 fund return, style-adjusted return, CAPM alpha, Fama-French three-factor alpha, and Carhart four-factor alpha. All the explanatory variables are lagged by 1 month, except for expenses and turnover, which are lagged by 1 year due to data availability. We report the means and t- statistics from the time series of coefficient estimates following Fama and MacBeth (1973). To account for autocorrelation problem, we calculate the Fama-MacBeth t-statistics using the Newey and West (1987) autocorrelation and heteroskedasticity consistent standard errors. The empirical specification is as follows: Alpha i,t = a + b 1 Skewness i,t 1 + b 2 Alpha i,t 1 + controls + ε i,t, (6) where Alpha i,t is the fund i s performance in month t measured as raw returns, style-adjusted returns, CAPM alpha, Fama-French three-factor alpha, and Carhart four-factor alpha, respectively. The coefficient of Skewness is expected to be negative if funds with lower skewness perform better in the future. Similarly to Spiegel and Zhang (2013), the control variables used in the regression are Vol, the volatility of the fund s daily returns over the prior month; Fee, the fund s annual expense ratio plus actual 12b-1 fees in the previous calendar year; Cat_flow, the monthly dollar flow divided by the one-month lagged TNA for all funds in the same investment category; LogAge, the log of the fund s age since the fund was first offered; LogSize, the log of the fund s TNA in millions; Turnover, the fund s turnover ratio from the prior calendar year; and Lag_flow, mutual fund flow for the previous month. We also add lag one-month fund return as a control variable. 20

21 Table III reports the parameter estimates using raw return, style-adjusted return, CAPM alpha, Fama-French three-factor alpha, and Carhart four-factor alpha as dependent variables, respectively. Consistent with our hypothesis, the coefficients for skewness are significantly negative in all regressions. The regression results support the statement that there is a tradeoff between alpha and skewness. The sign and magnitude of the coefficient on Skewness are consistent with the previous analysis using the portfolio approach. Specifically, a decrease in skewness by 0.55 (corresponding approximately to one standard deviation of Skewness) increases the monthly Carhart four-factor alpha by 0.08%, or by approximately 0.99% on an annual basis. This effect is economically and statistically significant. The impact of volatility on subsequent fund performance is insignificant. Fee has a statistically significant negative effect on fund performance when performance is measured by raw fund return, style-adjusted return, and CAPM alpha. The effect of Fee becomes insignificant if fund performance is measured by Fama-French three-factor alpha or Carhart four-factor alpha. Similarly, when fund performance is measured by raw fund return and CAPM alpha, the effect of Size on fund performance is negative and statistically significant. However, it becomes insignificant when fund performance is measured by style-adjusted return, Fama-French three-factor alpha or Carhart four-factor alpha. The coefficient of lag fund flow is positive. This suggests that either mutual fund investors invest more into funds which perform better subsequently, or funds received more cash flows perform better due to price pressure. C. The Relation between Skewness and Flows In this subsection, we investigate whether mutual fund investors are aware of the trade-off between alpha and skewness using a regression approach based on Fama and MacBeth (1973) 21

22 that controls for multiple fund characteristics simultaneously. Specifically, we perform the following regressions: Flow i,t = a + b 1 Skewness i,t 1 + b 2 Alpha i,t 1 + controls + ε i,t, (7) Where Flow i,t is the net fund inflow for fund i in month t and Alpha i,t 1 is the lagged fund performance measured as raw returns, style-adjusted returns, CAPM alpha, Fama-French three-factor alpha, and Carhart four-factor alpha, respectively. The control variables include Vol, the volatility of the fund s daily returns over the prior month; Fee, the fund s annual expense ratio plus actual 12b-1 fees in the previous calendar year; Cat_flow, the monthly dollar flow divided by the one-month lagged TNA for all funds in the same investment category; LogAge, the log of the fund s age since the fund was first offered; LogSize, the log of the fund s TNA in millions; Turnover, the fund s turnover ratio from the prior calendar year; and Lag_flow, mutual fund flow for the previous month. If mutual fund investors are aware of this trade-off, then fund flows should respond to both alpha and skewness. Consequently, mutual fund managers would take both alpha and skewness into consideration when making investment decisions. However, if mutual fund investors are not sophisticated enough to identify the relation between skewness and future fund performance, fund flows would only react to alpha but not skewness. In this case, fund managers could utilize the flow-attracting strategy by decreasing skewness to raise alpha. We conduct Fama-Macbeth cross-sectional regressions to investigate the relation between skewness and flows. Table IV summarizes the regression results. Similarly, time-series 22

23 average coefficients and Newey-West robust standard errors (in parentheses) are reported. Consistent with the existing literature, the regression results suggest that fund flows chase past performance. The coefficients of fund performance are positive and statistically significant at the 1% level in all regressions. However, the coefficients of skewness are negative but insignificant for all regressions, which suggest that mutual fund investors may be ignoring the level of skewness when investing in funds. The effect of volatility on subsequent fund flows is negative and statistically significant for all regressions, implying that fund investors dislike funds with high volatility. Both fund age and turnover ratio are negatively correlated with future fund flows, while fund size has a positive impact on future fund flows. The positive and significant coefficients on lag fund flows and lag style flows suggest that fund flows are persistent, which is consistent with previous research. The regression results show that fund flows do not significantly respond to the skewness of fund returns. Nevertheless, the existing literature documents that stock investors possess a gambling preference. For instance, Bali, Cakici and Whitelaw (2011) identify a negative relation between the maximum daily return over the past one month (MAX) and expected stock returns. They then infer that investors prefer lottery-like assets. An interesting question which is worth further investigating arises: why do investors favor individual stocks with positively-skewed payoffs, while mutual fund investors have no preference or even opposite preference for the fund holding portfolios? One possible explanation is that mutual fund investors are mostly retail investors and mutual fund holding portfolios are too complicated for them to understand. Thus, they simply aim at mutual funds with higher performance without considering the third moment of return distribution. A second possible explanation lies within distinct socioeconomic clienteles for lottery-type stocks and mutual funds. Kumar (2009) documents that lottery-type stocks underperform and attract low-income investors, 23

24 who are more likely to be gamblers. On the contrary, according to the Investment Company Institute (ICI) Fact Book 2017, households with higher annual incomes are more likely to own mutual funds than those with lower annual incomes. In mid-2016, 66 percent of U.S. households with annual income of $50,000 or more owned mutual funds, compared to 17 percent of households with annual income of less than $50,000. Thus, the discrepancy between the investment behavior in mutual funds and in individual stocks could come from the income level difference between mutual fund investors and individual stock investors. Kumar (2009) also suggests that state lotteries and lottery-type stocks attract very similar socioeconomic clienteles. He then argues that investors who prefer lottery-type stocks are those who gamble in the stock market. The typical characteristics of the heaviest lottery players are poor, young, relatively less educated, single men, who live in urban areas and belong to specific minority (African-American and Hispanic) and religious (Catholic) groups. In contrast, most of mutual fund investors possess the opposite characteristics. According to ICI Research Perspective 2016, 73% of individuals that owned mutual funds in mid-2016 were married or living with a partner; half were college graduates; $94,300 is the median household income (the median U.S. household income was $59,039 in 2016). More importantly, for 92% of mutual fund investors, the purpose for investing in mutual funds was saving for retirement. In other words, gambling preferences can hardly be the reason for fund investors to invest in mutual funds. Therefore, given the trade-off between alpha and skewness, the negatively skewed strategy would attract more flows than positively skewed one. This raises the managerial incentive problem. Mutual fund managers could strategically enhance alpha by increasing the downside risk. Having their sole emphasis on alpha, investors may invest into poorly managed or unskilled mutual funds. 24

25 VI. Skewness and Tournaments The mutual fund industry can be viewed as a tournament in which the amount of rewards that a fund manager receives depends on his/her performance relative to industry peers. Mutual funds are regularly ranked according to their relative performance over a certain time period (e.g. a month / quarter / year). Among these rankings, the annual performance ranking is of the most importance, as one year is a common assessment period for fund managers. Also, Ma, Tang, and Gomez (2018) document that performance-based incentives for fund managers are asymmetric: managers are rewarded for outperformance, but are not equally penalized for underperformance. For instance, they cite the description of Victory Value Fund s portfolio manager compensation in 2011 as follows: performance in an upper decile may result in an incentive bonus that is 150% of the target while below-average performance may result in an incentive bonus as low as zero. In other words, fund managers are compensated under a call option-like structure depending on their relative performance. This call option-like compensation scheme may induce fund managers to change their investment strategies before the end of the assessment period. More specifically, given the negative correlation between fund performance and return skewness, fund managers who deliver inferior performance (interim losers ) in the first half-year may be tempted to adopt more negatively skewed strategies to improve their ranking by year end. In comparison, for those who earn superior mid-year returns, they will want to maintain their high rankings and may be reluctant to change their investment strategies in the second half-year. Instead of loading on more downside risk, they may even consider reducing risk to retain their high rankings. In this subsection, we investigate whether fund managers who are more likely to lose the 25

26 competition would adapt their investment behavior and strategically changing the skewness for the return distributions more than those mid-year winners. The existing literature documents that mutual fund managers strategically shift risk levels to attract additional flows when losing the tournaments. For instance, Brown, Harlow, and Starks (1996) demonstrate that fund managers with inferior performance in the first half-year excessively increase fund volatility in the latter part of an annual assessment compared to mid-year winners. Huang, Sialm, and Zhang (2011) examine the performance consequences of risk shifting and attribute fund managers risk-shifting behavior to agency issues. While they focus on the second moment of returns (volatility), we consider the third moment of returns (skewness). If fund managers are aware of the negative relation between skewness and fund performance, those who generate inferior performance in the first half-year may decrease the skewness of the return distribution to boost performance in the second half-year. We measure skewness shifting of a mutual fund i in year t by comparing the skewness of the return distribution in the first half-year Skew i,t,1 with the skewness of the return distribution in the second half-year Skew i,t,2 : Skew i,t = Skew i,t,2 Skew i,t,1. (8) If fund i decreases the skewness of its return distribution in the second half-year of year t, Skew i,t will be negative. 26

27 To assess fund managers mid-year performance, we calculate the cumulative fund performance for each fund i in the first half-year of year t: 6 RTN i,t = (1 + r i,t,j ) 1, (9) j=1 where r i,t,j is the performance of fund i in month j of year t. Similar as the previous sections, we use 5 measures to evaluate fund performance: raw fund return, style-adjusted return, CAPM alpha, Fama-French three-factor alpha, and Carhart four-factor alpha. If the mid-year losers are expected to adopt more negatively skewed strategies compared to mid-year winners, it leads to the following prediction: Skew Loser < Skew Winner. (10) It is worth noting that this prediction is an average tendency rather than a precise relation. Also, it does not forecast whether the return skewness in the second half-year would be higher or lower than the first half-year. The exact skewness adjustment would depend on many factors such as general market conditions, the return gap between the interim losers and the interim winners, and fund investment objective categories. In order to decrease the skewness of their return distributions, fund managers may either load on more stocks with negatively skewed returns or replicate the option-like payoffs by actively buying and selling stocks. In subsections A and B, we use both a portfolio and a regression approach to test prediction (10). 27

28 A. Portfolio Evidence To test equation (10), for each year in the data sample, we divide mutual funds into 4 subgroups according to their mid-year performance (RTN) and skewness changes ( Skew). First, each year we classify funds into two subgroups of interim winners and losers based on their cumulative performance in the first half-year (RTN). Specifically, funds are classified into the winners ( losers ) subgroup if they generate above (below) the median value of RTN in the first half-year. Second, we rank funds according to the change in their return skewness levels from the first half-year to the second half-year ( Skew). Similarly, fund i is classified into the high (low) Skew subgroup if Skew i,t is larger (smaller) than the median value of Skew in year t. Table VI reports the fraction of fund-year observations belonging to each of the four subgroups: high RTN/high Skew, high RTN/low Skew, low RTN/high Skew, and low RTN/low Skew. The null hypothesis is that the classification according to RTN and the classification according to Skew are independent, so that the frequency of the sample observations placed into each of these four subgroups is equal (i.e., 25%). The alternative hypothesis consistent with prediction (10) is that significantly more observations would fall into low RTN/low Skew and high RTN/high Skew subgroups than the other two subgroups. A chi-square test with one degree of freedom is used to establish the statistical significance of these frequencies. Prediction (10) is tested over three time frames: the whole sample period ( ), two eight-year periods, and four subperiods. Panel A of Table VI presents the percentage of 28

29 sample observations belonging to each subgroup and the χ 2 statistics. Consistent with prediction (10), while 26.2% (larger than the expected 25% under the null hypothesis) of interim losers fall into the low Skew category, only 23.8% of interim winners are classified into the low Skew category. This difference is statistically significant at all standard significance levels. While the frequencies listed in Panel A of Table VI are in support of the tournament hypothesis that interim losers tend to load on more downside risks than interim winners for the whole sample period, we may wonder whether this prediction holds for different time periods. As assets under management of U.S. equity funds increased from $ 4 trillion in 1999 to more than $ 8 trillion in 2014, we would expect that the competition among fund managers has become fiercer over the years. Consequently, with an increasingly competitive environment, interim losers may be more inclined to strategically change return skewness in recent years than those in early years of the sample period. In panel B of Table VI, the whole sample period is divided into two eight-year subperiods. During the subperiod, 25.6% interim losers fall into the low Skew category, while 24.4% of interim winners are classified into the low Skew category. This difference is statistically significant with a χ 2 - statistic of 6.5. In comparison, in the more recent subperiod ( ), 26.8% interim losers fall into the low Skew category, while only 23.2% of interim winners are classified into the low Skew category. Consistent with our conjecture, this difference in the more recent subperiod is bigger and more significant with a much higher χ 2 - statistic of Other than the general trend over time, another possible conjecture is that fund managers may be less inclined to increase downside risk after experiencing a dramatic stock market crash. 29