Institutional Skewness Preferences and the Idiosyncratic Skewness Premium

Transcription

1 Institutional Skewness Preferences and the Idiosyncratic Skewness Premium Alok Kumar University of Notre Dame Mendoza College of Business August 15, 2005 Alok Kumar is at the Mendoza College of Business, University of Notre Dame (Phone: ; I would like to thank Robert Battalio, Sudheer Chava, and George Korniotis for helpful discussions and valuable comments. In addition, I would like to thank Hang Li for excellent research assistance. I am responsible for all remaining errors and omissions.

2 Institutional Skewness Preferences and the Idiosyncratic Skewness Premium ABSTRACT This study examines whether idiosyncratic skewness preferences of institutional investors influence stock returns. On aggregate, institutions exhibit an aversion for idiosyncratic skewness but prefer systematic skewness, and in the cross-section, larger (smaller) and more (less) diversified institutions exhibit stronger (weaker) aversion for idiosyncratic skewness. The aggregate institutional preferences generate an annual, risk-adjusted idiosyncratic skewness premium of 3.17%. However, in the cross-section, the premium is strongly negative (positive) when institutional ownership is lower (higher). These pricing effects are further amplified when arbitrage costs are higher. Idiosyncratic skewness preferences of institutions are partially reflected in the size factor (SMB). A factor which captures those preferences can explain about 14% of the variation in SMB. Collectively, the evidence indicates that institutional idiosyncratic skewness preferences get impounded into stock prices. IN AN ECONOMY WHERE INVESTORS HOLD CONCAVE PREFERENCES and like positive skewness (e.g., Arditti (1967), Kane (1982)), everything else equal, stocks that decrease the skewness of a portfolio earn higher expected returns (e.g., Kraus and Litzenberger (1976), Lim (1989)). In this economy, idiosyncratic skewness is irrelevant at the margin and is unlikely to influence expected stock returns. Consistent with these theoretical predictions, Harvey and Siddique (2000) find that stocks with lower systematic skewness (i.e., coskewness) outperform stocks with higher coskewness by about 3.60% per year. 1 In other words, a positive and economically significant coskewness premium exists. This evidence suggests that marginal, price-setting investors prefer stocks with higher coskewness and their preferences get impounded into stock prices. 1 Following Harvey and Siddique (2000), I decompose total skewness into systematic and idiosyncratic components. Idiosyncratic skewness of a stock is defined as the skewness of the residual from a regression where the excess (over the riskfree rate) stock returns are regressed on excess market returns and squared excess market returns. The systematic skewness (or coskewness) is the coefficient estimate of the squared excess market return variable. See Harvey and Siddique (2000) for other related coskewness measures. 1

3 In an alternative economic setting, even idiosyncratic skewness may be priced along with coskewness. Specifically, Barberis and Huang (2005, hereafter BH) argue that idiosyncratic skewness would earn a negative premium in an economy where investors hold cumulative prospect-theoretic (CPT) preferences (Tversky and Kahneman (1992)). Investors with CPT preferences overweight the tail probabilities and prefer to hold securities with higher skewness because these securities can generate an asymmetric wealth distribution. Given their appetite for positive idiosyncratic skewness, all else equal, CPT investors would be willing to accept lower mean returns for securities with higher idiosyncratic skewness. 2 Consequently, in an economy where idiosyncratic skewness loving investors are the marginal investors, everything else equal, securities with higher idiosyncratic skewness would earn lower returns. 3 The BH model also predicts that the return differential between the extreme idiosyncratic skewness portfolios would be larger when arbitrage costs are higher. Of course, not all types of investors exhibit a preference for idiosyncratic skewness. For instance, Kumar (2005) finds that, all else equal, retail investors prefer total skewness, while surprisingly, institutional investors exhibit an aversion for total skewness. In this study, decomposing total skewness into idiosyncratic and systematic components, I find that institutions prefer systematic skewness but dislike idiosyncratic skewness. Moreover, certain subsets of institutions (larger and more diversified institutions) exhibit stronger aversion for idiosyncratic skewness while smaller and less diversified institutions prefer idiosyncratic skewness. 4 The heterogeneity in investors preferences for skewness suggests that skewness is likely to impact returns differentially in the cross-section. Specifically, idiosyncratic skewness premium would be positive when institutional ownership is higher, particularly when arbitrage costs are higher. In contrast, consistent with the theoretical predictions of the Barberis and Huang (2005) model, idiosyncratic skewness premium would be negative when stocks have lower institutional ownership. 2 The BH model predicts a nonlinear relation between skewness and expected returns, where only securities with very high skewness earn lower expected returns. 3 CPT preferences are not necessary to generate a preference for skewness. For instance, Brunnermeier and Parker (2005) show that anticipatory utility (e.g., dream utility) can generate a preference for skewness in portfolio choices. Also, see Polkovnichenko (2005). 4 Similar to retail investors (e.g., Goetzmann and Kumar (2004), Mitton and Vorkink (2004)), less diversified institutions may trade expected returns for skewness. Also, see Simkowitz and Beedles (1978) and Conine and Tamarkin (1981). 2

4 I empirically test these theoretical predictions in this paper. Specifically, I examine the skewness preferences of institutional investors and investigate whether the heterogeneity in idiosyncratic skewness preferences of investors has differential impact on stock returns in the cross-section. Prior studies have examined institutional preferences (e.g., Badrinath, Kale, and Ryan (1996), DelGuercio (1996), Falkenstein (1996), Gompers and Metrick (2001), Bennett, Sias, and Starks (2003), Grinstein and Michaely (2005), Frieder and Subrahmanyam (2005)) but those studies do not examine institutional skewness preferences. Furthermore, as discussed earlier, previous studies (e.g., Kraus and Litzenberger (1976), Lim (1989), Harvey and Siddique (2000)) have examined whether systematic skewness is priced but the aggregate pricing effects of idiosyncratic skewness have not been investigated before. The paper is divided into two distinct parts. In the first part of the paper, I examine the aggregate institutional preferences for idiosyncratic and systematic skewness. I also investigate whether institutional skewness preferences vary in the cross-section. In particular, I examine whether smaller and relatively less diversified institutions exhibit weaker skewness aversion (or even prefer skewness) while larger and more diversified institutions exhibit stronger skewness aversion. 5 My results indicate that, at an aggregate level, institutions exhibit a preference for systematic skewness (i.e., coskewness) but disklike idiosyncratic skewness. 6 Even in the crosssection, all institutional types (banks, insurance companies, investment companies, independent advisors, and others) exhibit an aversion for idiosyncratic skewness. However, when I categorize institutions based on their total asset holdings and degree of diversification, I find that smaller and relatively less diversified investors prefer idiosyncratic skewness while their coskewness preferences are ambiguous. This evidence indicates that the skewness preferences of smaller and less diversified institutions are similar to the preferences of retail investors (Kumar (2005)). Consequently, the pricing effects of institutional skewness preferences are likely to vary in the cross-section of stocks. 5 In a related study, Kumar (2005) shows that institutions dislike total skewness but does not distinguish between systematic skewness and idiosyncratic skewness. Furthermore, unlike my study, he does not examine the cross-sectional variation in institutional skewness preferences. Most importantly, the focus of my study is on examining the pricing effects of institutional skewness preferences while Kumar (2005) focuses on the relation between investor demographics and stock preferences of retail investors. The institutional stock preferences are presented for robustness. 6 The results on institutional preferences for coskewness are consistent with the evidence in Harvey and Siddique (2000), who show that stocks with higher coskewness earn lower average returns. 3

5 In the second part of the paper, I directly investigate whether the idiosyncratic skewness preferences of institutions are reflected in stock returns. First, I examine whether, on aggregate, the idiosyncratic skewness aversion of institutions translate into a positive idiosyncratic skewness premium. Next, I examine whether the idiosyncratic skewness premium varies in the cross-section with the level of institutional ownership and arbitrage costs. This analysis is motivated by one of the key theoretical predictions of the BH model, which posits that securities with sufficiently large idiosyncratic skewness earn negative average excess returns due to investors strong appetite for idiosyncratic skewness. Lastly, I examine whether the commonly used risk factors (i.e., the Fama-French factors and the momentum factor) partially reflect the pricing effects of institutional skewness preferences rather than compensation for risk. The results indicate that both total skewness and idiosyncratic skewness earns a positive and economically significant premium. During the 1962 to 2004 period, the aggregate idiosyncratic (total) skewness premium is 3.17% (2.94%) annually on a risk-adjusted basis. These estimates are robust to concerns about microstructure issues, liquidity, and industry concentration. However, in the cross-section, I find that the annual, risk-adjusted idiosyncratic skewness premium is strongly negative ( 8.21%) when institutional ownership is lower. 7 The evidence strongly supports the theoretical predictions of the Barberis and Huang (2005) model. Furthermore, consistent with the predictions of the BH model, I find that the pricing effects of skewness are exacerbated when idiosyncratic volatility (an arbitrage cost proxy) is higher. This amplification results from the combined effects of institutional aversion to idiosyncratic volatility and higher arbitrage costs among stocks that have higher idiosyncratic volatility (Wurgler and Zhuravskaya (2002)). To examine whether the commonly used risk factors partially reflect institutional skewness preferences, I construct an idiosyncratic skewness factor (ISKEW). The factor represents the spread of a zero-cost portfolio which takes a long (short) position in stocks with the highest (lowest) idiosyncratic skewness. I find that the idiosyncratic skewness factor can explain about 14% of the variation in the size factor (SMB). The correlations between the 7 These stocks would have a greater concentration of retail investors who prefer skewness (Goetzmann and Kumar (2004), Mitton and Vorkink (2004), Kumar (2005)). Note that the institutional holdings data are available from Therefore, when conditioning on institutional ownership, I can only compute the skewness premium for the 1980 to 2004 period. 4

6 idiosyncratic factor and the other two Fama-French factors are moderate while the momentum factor is virtually uncorrelated with the skewness factor. These results indicate that the SMB factor partially reflects the pricing effects of institutional idiosyncratic skewness preferences rather than compensation for risk. Collectively, the results from the asset pricing tests indicate that institutional skewness preferences get impounded into stock prices. The rest of the paper is organized as follows: in the next section, I briefly describe the data and define the skewness measures. In Section II, I examine the institutional preferences for systematic skewness and idiosyncratic skewness. In Section III, I provide estimates of aggregate idiosyncratic skewness premium and examine whether the premium varies in the cross-section with the level of institutional ownership. In Section IV, I construct an idiosyncratic skewness factor and examine the relation between this factor and the commonly used risk factors. Finally, I conclude in Section V with a summary of the main results and a very brief discussion. I. Data and Methodology A. Institutional Investor Data The primary data for my study consist of quarterly institutional holdings from Thomson Financial for the 1980 to 2004 period. The data contain the end of quarter stock holdings of all institutions that file form 13F with the Securities and Exchange Commission (SEC). Institutions with more than $100 million under management are required to file form 13F with the SEC and common stock positions of more than 10,000 shares or more than $200,000 in value must be reported on the form. A typical institution in the sample holds a 155-stock portfolio (median is 80) worth $133 million (median = $25 million). There is also considerable heterogeneity in the size of institutions in the sample. More than 10% of institutions hold stock portfolios with market capitalization of under $64 million and about 19% of institutions hold stock portfolios worth $1 billion or more. The level of institutional ownership in stocks has grown steadily during the last 25 years. For instance, in the year 1980, about 47% of stocks had zero institutional ownership, but in 5

7 recent years, only less than 5% of stocks have zero institutional ownership. 8 Furthermore, during the eighties, the mean institutional ownership in a typical stock was about 12%, but in recent years (2000 to 2004), the mean institutional ownership in stocks has increased to about 31%. 9 Collectively, the evidence suggests that institutions are likely to be the marginal, price-setting investors in an increasing number of stocks. 10 Several other standard datasets are used in this study. For the July 1962 to December 2004 period, I obtain monthly prices, returns, shares outstanding, and monthly volume turnover data from the Center for Research on Security Prices (CRSP) and quarterly book value of common equity data from COMPUSTAT. The exchange code and the share code for all stocks are also obtained from CRSP. Lastly, the monthly time-series of the three Fama-French factors and the momentum factor from Ken French s data library. I only consider common stocks (CRSP share code 10 and 11) in my empirical analysis. During the 1962 to 2004 sample period, there are 25,262 securities in the CRSP database and 21,363 securities from this set can be classified as common stocks. This subset includes 4,356 NYSE, 14,281 NASDAQ, and 2,726 AMEX stocks. In any given month, there are between 1,943 and 7,418 common stocks in the sample, where the mean (median) is 4,791 (5,041). B. Skewness Measures: Summary Statistics Following recent studies (e.g., Pástor and Stambaugh (2003), Ang, Hodrick, Xing, and Zhang (2005)), I use daily returns instead of monthly returns to obtain measures of skewness at a given point in time. At the end of each month, for each stock, I compute three different measures of skewness. The skewness measures for a stock are computed only when there are at least 15 daily return observations for that stock during the month under consideration. 11 The total skewness measure of a stock is the third moment of its returns. Specifically, 8 These estimates are biased upwards because smaller institutions and small stock positions are excluded from the sample. 9 Note that these are equal-weighted averages, which do not reflect the institutional presence in the market in dollar terms. When measured in dollar terms, the total institutional ownership was about 20% in 1980 and about 57% in December See Gompers and Metrick (2001) or Bennett, Sias, and Starks (2003) for further details on the institutional ownership data. 11 My results are insensitive to the choice of this cutoff. The skewness estimates are very similar when I use a 13-day or a 17-day cutoff. 6

8 the total skewness of stock i in a given month is computed as follows: Total Skew i = Dt t=1 (R it µ i ) σ 3 i. Here, D t isthenumberofdaysinagivenmonth,µ i is the mean return of stock i in that month, and σ i is the standard deviation of returns of stock i in that month. To decompose the total skewness into idiosyncratic and systematic components, I adopt the Harvey and Siddique (2000) methodology. I estimate the following regression: R it R ft = α i + β i RMRF t + γ i RMRF 2 t + ε it, (1) where R it istherateofreturnonstocki on day t, R ft is the riskfree rate of return on day t, RMRF t is the market return in excess of the riskfree rate on day t, andε it is the residual stock return on day t. The regression model is estimated for each stock at the end of each month. The idiosyncratic skewness of stock i in a given month is defined as the skewness of the residual ε it and the systematic skewness (or coskewness) of stock i in that month is the coefficient estimate γ i in the regression above. Table I presents the summary statistics for the three skewness measures for the full sample period (1962 to 2004) and two sub periods (1962 to 1979 and 1980 to 2004). The full sample results indicate that, on average, stocks have positive total and idiosyncratic skewness measures but a negative coskewness measure. Furthermore, the sub sample results indicate that the skewness distributions are quite stable over time. The evidence of mean negative coskewness is consistent with previous studies (e.g., Simkowitz and Beedles (1978)), which finds that portfolio skewness decreases almost monotonically as the number of stocks in the portfolio increases. There is considerable degree of heterogeneity in the three skewness measures. Even though the mean total skewness and the mean idiosyncratic skewness measures are positive, over 10% of stocks have negative total skewness and negative idiosyncratic skewness. Similarly, while the mean coskewness measure is negative, more than 25% of stocks have positive coskewness. 7

9 C. Properties of Skewness Sorted Portfolios To examine the characteristics of stocks that have higher skewness, I obtain the factor exposure estimates and other stock characteristics (stock price, market capitalization, and mean institutional ownership) for skewness sorted portfolios. 12 To define idiosyncratic skewness portfolios, each month, I measure the idiosyncratic skewness of the entire universe of stocks for which returns data are available from CRSP. Next, each month, I sort stocks using their idiosyncratic skewness measures and form idiosyncratic skewness quintile portfolios. Portfolio 1 consists of stocks with the lowest idiosyncratic skewness while portfolio 5 contains stocks with the highest idiosyncratic skewness. Lastly, for each idiosyncratic skewness portfolio, I compute the monthly portfolio return as value-weighted average of all stocks in the portfolio and construct a monthly portfolio return time-series. In an analogous manner, I define total skewness quintile portfolios. Table II reports the factor exposures and other stocks characteristics of skewness sorted portfolios. Panel A (Panel B) reports the characteristics of idiosyncratic (total) skewness sorted portfolios. One of the key differences between the extreme (low and high) skewness portfolios is along the size dimension. The highest skewness quintile portfolio has a disproportionate representation from small-cap stocks while the lowest skewness quintile portfolio does not exhibit a significant size tilt. Higher skewness stocks also have slightly lower prices and slightly lower mean institutional ownership. Nevertheless, there is considerable institutional presence even among higher skewness stocks. This evidence suggests that institutional preferences are likely to be an important determinant of the return generating process of higher skewness stocks. Along other dimensions, the differences between extreme skewness portfolios are mixed and no clear pattern emerges. For instance, examining the total skewness sorted portfolios, I find that the highest quintile portfolio is tilted toward growth and low momentum stocks. However, idiosyncratic skewness sorted portfolios do not exhibit significant differences along these two dimensions. Overall, the evidence indicates that the risk characteristics of skewness sorted portfolios do not differ significantly. Therefore, the raw and risk-adjusted return 12 I obtain the factor exposure estimates by regressing the skewness portfolio returns on the three Fama- French factors (excess market return or RMRF, small-minus-big or SMB, and high-minus-low or HML) and the momentum factor (up-minus-down or UMD). 8

10 differentials between extreme skewness portfolios are likely to be similar. 13 II. Institutional Preferences for Systematic and Idiosyncratic Skewness The extant literature on institutional preferences (e.g., Badrinath, Kale, and Ryan (1996), DelGuercio (1996), Falkenstein (1996), Gompers and Metrick (2001), Bennett, Sias, and Starks (2003), Grinstein and Michaely (2005), Frieder and Subrahmanyam (2005)) provides a rich characterization of the types of stocks institutions like. For instance, institutions prefer larger, higher priced, higher beta, and more mature stocks. In contrast, institutions dislike high dividend yield stocks and stocks with higher total volatility. Institutional preferences also change over time. In particular, Bennett, Sias, and Starks (2003) show that, in more recent years, institutional preferences have shifted toward smaller and riskier (higher variance) stocks. While Bennett, Sias, and Starks (2003) provide convincing evidence of changing institutional preferences, it is not immediately clear whether institutions exhibit an increasing preference for volatility or skewness because skewness and variance are strongly correlated. In the context of horse race betting, contrary to the widely held belief, Golec and Tamarkin (1998) show that bettors prefer skewness rather than risk. In a similar vein, it is possible that institutions prefer skewness and do not necessarily exhibit a recent tilt towards risk-seeking behavior. By employing measures of volatility and skewness simultaneously, the institutional volatility and skewness preferences can be identified more precisely. 14 To characterize the skewness preferences of institutional investors, first, I examine whether, at an aggregate level, institutions exhibit an incremental preference (or aversion) for skewness, after controlling for the known determinants of institutional preferences. The analysis on skewness preferences also allows me to identify the volatility preferences of institutions more accurately. Unlike previous studies, I differentiate between idiosyncratic and systematic measures of volatility and skewness. Because institutions are relatively more sophisticated, 13 For robustness, I also examine whether the Pástor and Stambaugh (2003) liquidity betas differ across skewness sorted portfolios. I find that the liquidity betas have mixed signs and are statistically insignificant. This evidence indicates that skewness portfolios do not differ significantly along the liquidity dimension. For brevity, liquidity beta estimates are not reported. 14 It is also likely that volatility and skewness measures using daily rather than monthly returns provide a more accurate characterization of institutional preferences. 9

11 they may prefer stocks with higher systematic risk and higher systematic skewness. Stocks with higher systematic risk yield higher returns and stocks with higher skewness have the desirable feature that they increase portfolio skewness. In contrast, institutions may shun stocks with higher idiosyncratic volatility and higher idiosyncratic skewness because they are known to yield lower mean returns (e.g., Ang, Hodrick, Xing, and Zhang (2005)). I also investigate whether skewness preferences vary in the cross-section of institutions. It is conceivable that constraints faced by institutions such as the prudent man rules (DelGuercio (1996)) vary with institutional size. If skewness preferences of institutions are induced by these constraints, skewness preferences would vary with institutional size. Furthermore, it is possible that, similar to retail investors, smaller and relatively less diversified institutions prefer stocks with lottery-type characteristics. 15 variation in institutional skewness preferences. A. Aggregate Institutional Preferences Again, this would lead to cross-sectional To examine institutional skewness preferences, first, I construct an aggregate institutional portfolio by combining the stock holdings of all institutions. Next, I estimate a panel regression specification with fixed quarter effects. 16 In the regression model, the excess weight assigned to a stock in the aggregate institutional portfolio is the dependent variable and systematic and idiosyncratic skewness measures are used as the primary independent variables. 17 My methodology for characterizing institutional preferences is slightly different from the one adopted in the previous literature (e.g., Gompers and Metrick (2001), Bennett, Sias, and Starks (2003)), where the total institutional ownership in a stock is used as the dependent variable. The stock-level institutional ownership measure includes both expected and unex- 15 Stocks with higher idiosyncratic volatility, positive skewness, and lower prices are defined as lottery-type stocks. See Kumar (2005) for further details. 16 For several reasons, I use a panel regression specification instead of estimating a series of cross-sectional regressions at the end of each quarter. Most importantly, because the coefficient estimates in the quarterly cross-sectional regressions are not independent, standard tests for significance of coefficient estimates cannot be employed. In contrast, the panel regression framework allows me to correct for potential auto-correlation in errors (which leads to non-independent coefficient estimates in cross-sectional regressions) using the Newey and West (1987) approach. 17 The excess portfolio weight allocated to stock i in month t is given by: EW ipt = wipt wimt w imt 100, where w ipt is the actual weight assigned to stock i in group portfolio p in month t and w imt is the weight of stock i in the aggregate market portfolio in month t. 10

12 pected components of institutional allocation choices. The expected institutional allocation to a stock is the level of allocation in the stock when institutions randomly allocate resources to different stocks. This component does not reflect institutional preferences. In contrast, the unexpected institutional allocation to a stock (actual allocation expected allocation) is likely to reflect institutional preferences more accurately. The excess portfolio weight assigned to a stock in the aggregate group portfolio captures the unexpected institutional allocation to that stock. In the panel regression model, I use the following additional independent variables to control for the known determinants of institutional preferences: (i) idiosyncratic volatility, which is the variance of the residual obtained by fitting a four-factor model to the daily stock returns series in the previous month, (ii) market beta, which is estimated using the daily stock returns series in the previous month, (iii) firm size, (iv) book-to-market ratio, (v) short-term momentum (past one-month stock return), (vi) longer-term momentum (past twelve-month stock return), (vii) monthly volume turnover, and (viii) an S&P500 dummy which is set to one if the stock belongs to the S&P500 index. All stock characteristics are measured at the end of each quarter. The panel regression estimates are reported in Table III. 18 First, I present the estimates for the aggregate institutional portfolio where I combine the holdings of all institutions in the sample (see column (1)). I find that, at an aggregate level, institutions prefer systematic skewness (coefficient estimate = 0.019, t-statistic = 2.065) but dislike idiosyncratic skewness (coefficient estimate = 0.012, t-statistic = 6.105). The evidence on systematic skewness preference of institutions is consistent with the findings in Harvey and Siddique (2000). Their study appropriately assumes that investors would exhibit a preference for systematic skewness (i.e., coskewness), and consistent with this assumption, they show that stocks with lower systematic skewness earn higher returns. My evidence provides direct support for the main assumption in the Harvey and Siddique (2000) study. Furthermore, the institutional aversion for idiosyncratic skewness is also consistent with our priors. It is reasonable to conjecture that, all else equal, relatively sophisticated and well-diversified institutions would 18 The independent variables have been standardized to facilitate comparisons among coefficient estimates within a regression specification and also across specifications. I also check that multi-collinearity is not contaminating my results. 11

13 exhibit an aversion for stocks that do not increase the overall skewness of their portfolios. The coefficient estimates from the panel regression are easy to interpret in economic terms. For instance, the idiosyncratic skewness coefficient estimate indicates that one standard deviation decrease in the idiosyncratic skewness of a stock corresponds to an excess aggregate institutional holding of about $385 million ( = $ million). 19 Similarly, the systematic skewness coefficient estimates indicates that one standard deviation increase in the systematic skewness of a stock corresponds to an excess aggregate institutional holding of about $610 million. Overall, the panel regression estimates indicate that skewness preferences of institutions have economically significant impact on their aggregate stock holdings. The coefficient estimates for the control variables are broadly consistent with the extant evidence on institutional preferences. Similar to previous studies, I find that, on a marginal basis, institutions invest disproportionately more in larger, higher beta, and higher priced stocks. Additionally, institutions prefer stocks that belong to the S&P 500 index. In contrast, institutions invest disproportionately less in stocks with higher idiosyncratic volatility, higher lagged returns, and higher turnover. At a first glance, the negative coefficient estimate on the lagged return variables appear puzzling. However, as Bennett, Sias, and Starks (2003) discuss, this evidence indicates that institutions do not exhibit an incremental preference for high momentum stocks, after controlling for their preferences for firm size and stock price level. Institutions may still engage in positive feedback trading. Similarly, the negative sign on the monthly turnover variable indicates that institutions do not exhibit an incremental preference for high turnover stocks, after controlling for institutional preferences for other firm characteristics. B. Cross-Sectional Variation in Institutional Preferences How do institutional preferences vary in the cross-section? As discussed earlier, institutional size and institutional diversification preferences may influence their skewness preferences. 19 The aggregate institutional portfolio is worth $0.250 trillion in January 1980, $7.51 trillion in June 2002, and $9.53 trillion in December The average size of the aggregate institutional portfolio during the 1980 to 2004 period is $3.21 trillion. The economic interpretation of the coefficient estimates are based on the average size of the aggregate institutional portfolio. 12

14 For instance, institutions who hold under-diversified portfolios may do so intentionally because they like skewness. Furthermore, a variety of institutional constraints may induce them to hold conservative stocks (e.g., DelGuercio (1996)). For instance, banks are known to have more conservative stock preferences. This suggests that their preference (aversion) for systematic (idiosyncratic) skewness is likely to be the strongest. Overall, consistent with the evidence of preference heterogeneity presented in Bennett, Sias, and Starks (2003), the magnitudes of institutional skewness preferences may vary across different types of institutions (banks, insurance companies, investment companies, independent investment advisors, and unclassified). The panel regression estimates for institutional categories based on institutional size and diversification choices are reported in Table III (Panel A, columns (2)-(5)) and the estimates for the five institutional types are presented in Panel B (columns (1)-(5)). To categorize institutions based on size, I sort all institutions into deciles based on their average portfolio holdings during the period they are active. The institutions in lowest (highest) decile are identified as small (large) institutions. In an analogous manner, by sorting institutions using a crude diversification measure (the number of stocks in the portfolio) of their portfolios, I am able to identify institutions with low and high diversification preferences. The panel regression estimates for small institutions are presented in Panel A, column (2). Small institutions have an average stock holding of less than $64 million while large institutions hold stock portfolios worth $1.33 billion or more. The coefficient estimates indicate that small institutions exhibit a preference for idiosyncratic skewness while their systematic skewness preferences are ambiguous. They also prefer stocks with higher idiosyncratic volatility. Furthermore, small institutions exhibit significantly weaker preference for larger stocks, and unlike other institutional groups, they exhibit an aversion for stocks in the S&P 500 index. Overall, the skewness and volatility preferences of small institutions have many similarities with the stock preferences of retail investors identified in Kumar (2005). Examining the preferences of large institutions (see column (3)), I find that they exhibit marginally stronger preference (aversion) for systematic (idiosyncratic) skewness. They also exhibit a strong preference for value stocks (i.e., high B/M stocks) and stocks in the S&P 500 index. Examining the preferences of diversification based institutional groups, I find 13

15 that the skewness preferences of less diversified investors (mean number of stock holdings is 22) resemble those of smaller institutions (see Panel A, column (4)) while the preferences of more diversified investors (mean number of stock holdings is 332) are more aligned with the preferences of large institutions. To get another perspective on the heterogeneity in the skewness preferences of institutions, I examine the preferences of five institutional types. Consistent with the evidence on institutional stock preferences from previous studies (e.g., Bennett, Sias, and Starks (2003)), I find that the skewness preferences across institutional types are very similar. All institutions dislike idiosyncratic skewness and they either prefer or exhibit indifference for systematic skewness. Consistent with the known preferences of different types of institutions, I also find some heterogeneity in their skewness preferences, where the magnitudes of the coefficient estimates on skewness variables vary across institutional types. In particular, I find that banks exhibit the strongest aversion (preference) for idiosyncratic (systematic) skewness. This result is consistent with the evidence from previous studies that indicates that banks exhibit the most conservative preferences (e.g., DelGuercio (1996), Gompers and Metrick (2001), Bennett, Sias, and Starks (2003)). My new evidence on skewness preferences of banks further reinforces the notion that banks hold the most conservative set of stock preferences. C. Institutional Preference Estimates: Robustness Checks For robustness, I re-estimate the panel regression for two sub samples, where I consider the portfolios of all institutions. In the first robustness test, I only consider stocks that have a minimum price of $5. Because I estimate idiosyncratic volatility, beta, and skewness using daily returns, there might be a concern that my results are strongly influenced by microstructure effects such as abnormally large bid-ask spreads, infrequent trading, etc. In the second robustness test, I only consider stocks with positive institutional ownership. This test is designed to capture institutional preferences once they decide to invest in a particular stock. These estimation results are also reported in Table III (Panel B, columns (6) and (7)). I find that the estimation results for the two sub samples are very similar to the full sample 14

16 results. In particular, the skewness preferences of institutions identified using the full sample (see Panel A, column (1)) and the two sub samples are very similar. For instance, the coefficient estimate of idiosyncratic skewness in the two sub samples are and 0.015, respectively. In comparison, the coefficient estimate of idiosyncratic skewness in the full sample is The systematic skewness estimates in the sub samples are also very similar to the full sample estimates. Taken together, the results from the robustness tests indicate that microstructure effects are not contaminating my coefficient estimates. Furthermore, the conditional institutional skewness preferences are similar to their unconditional preferences. Collectively, the evidence from the set of panel regressions conveys one strong and consistent message. When other stock characteristics are held constant, institutional investors dislike idiosyncratic skewness. In the remaining part of the paper, I examine whether the idiosyncratic skewness preferences of institutional investors have pricing effects, both at an aggregate level and in the cross-section of stocks. III. Unconditional and Conditional Skewness Premium Estimates Due to the steadily growing institutional presence in the stock market (see Section I), institutional investors are likely to be the marginal investors for a large segment of the market. Particularly, the aggregate institutional skewness preferences is likely to determine whether an idiosyncratic skewness premium exists at the aggregate level. Furthermore, in the crosssection of stocks, institutional skewness preferences and level of institutional ownership is likely to determine the variation in the magnitude of the idiosyncratic skewness premium jointly. Additionally, if returns are influenced by the systematic demand shocks generated by changing institutional preferences, the magnitude of arbitrage costs would be a critical determinant of the magnitude of any preference induced pricing effects. Given these three potential sources of influence on stock returns, I examine how the level of institutional ownership, the magnitude of institutional idiosyncratic skewness preferences, and the magnitude of arbitrage costs jointly determine the cross-sectional variation in the idiosyncratic skewness premium. 15

17 A. Unconditional Skewness Premium To set the stage, I estimate the idiosyncratic skewness premium at the aggregate level. Using the procedure described in Section I.C, I define idiosyncratic skewness and total skewness quintile portfolios. The time-series averages of skewness sorted portfolio returns are reported in Table IV. In this table, I also report the CAPM and the four-factor alphas of idiosyncratic skewness quintile portfolios. The CAPM alpha is the intercept from the market model regression and the four factor alpha measure is the intercept from the four-factor model. 20 Irrespective of the performance measure employed, I find that portfolio performance increases with idiosyncratic skewness. The increase in performance is not monotonic but the highest idiosyncratic skewness quintile portfolio outperforms the lowest idiosyncratic skewness quintile portfolio. Focusing on idiosyncratic skewness portfolios, I find that the return differential between the two extreme quintile portfolios (high idiosyncratic skewness low idiosyncratic skewness) is 0.263% monthly. This translates into an annual idiosyncratic skewness premium of 3.156% and risk adjustment does not significantly affect the magnitude of the estimated premium. When I examine the performance differential between the extreme quintile portfolios using the four-factor (CAPM) alpha, the annual, risk-adjusted skewness premium is 3.168% (2.964%). For robustness, I also obtain the total skewness premium estimates. The total skewness premium estimates are slightly lower (2.940% annually on a risk-adjusted basis) than the idiosyncratic skewness premium, but nevertheless, they are significant both in statistical and economic terms. To examine whether the magnitude of the aggregate skewness premium varies with time, I estimate the premium for six-year, non-overlapping sub periods starting in The annualized, risk-adjusted idiosyncratic skewness premium estimates are presented in Figure 1. The premium has been significantly positive in five out of the seven sub periods, positive but economically small in one sub period (1993 to 1998), and significantly negative in another sub period (1969 to 1974). The sub period analysis indicates that the skewness premium estimates are stable through time, especially following 1975 since when the institutional 20 In the four-factor time-series model, portfolio returns is the dependent variable and the four commonly used risk factors (RMRF, SMB, HML, and UMD) are employed as independent variables. 16

18 presence in the stock market has increased steadily. Overall, the aggregate level idiosyncratic skewness premium estimates are consistent with the aggregate institutional skewness preferences documented earlier. Specifically, my evidence is consistent with the hypothesis that stocks with higher idiosyncratic skewness earn higher returns because institutions dislike idiosyncratic skewness and demand higher compensation for holding stocks that have higher idiosyncratic skewness. B. Unconditional Skewness Premium Estimates: Robustness Checks I employ several additional tests to establish the robustness of the idiosyncratic skewness premium estimates. My focus is on the idiosyncratic premium estimates, but for robustness, I continue to report total skewness estimates. The results from the robustness tests are summarized in Table IV, Panel B. In the first test, to ensure microstructure effects are not driving the skewness premium estimates, each month, I exclude all stocks which are priced below $5. For this sub sample, I find that the monthly idiosyncratic premium estimate is greater (0.309%) than the original estimate of 0.264% (see row (1)). This finding is not surprising because institutional ownership is higher in stocks with higher prices. If the skewness premium is influenced by institutional preferences, the magnitude of the premium would be greater in the segments of the market where institutional ownership is higher. In other words, if higher priced stocks are the natural habitat of institutional investors, the systematic demand shocks generated by their changing preferences would have stronger influence on the returns of stocks in their habitat (Barberis, Shleifer, and Wurgler (2005)). 21 In the second test, I exclude all NASDAQ and AMEX stocks and only consider NYSE stocks. Even though I use the four-factor model to obtain risk-adjusted estimates of the skewness premium, there may be concerns that the premium is simply another manifestation of the size anomaly. Additionally, one might believe that the idiosyncratic skewness premium primarily reflects the premium for holding micro-cap stocks. The skewness premium estimates for the NYSE sub sample (see row (2)) indicate that contrary to such beliefs, 21 This argument ignores the effect of arbitrage costs, which is likely to be an important determinant of the premium. I examine the sensitivity of skewness premium estimates to arbitrage costs in Section III.D. 17

19 the monthly premium is again higher (0.286%) than the baseline estimates. This evidence is also consistent with the main hypothesis entertained in the paper, which posits that institutional skewness preferences influence the skewness premium. Because retail investors exhibit an incremental preference for relatively smaller NASDAQ stocks (Goetzmann and Kumar (2004)) and institutional concentration is greater in NYSE stocks, institutional preferences should impact the returns on NYSE stocks more strongly. The evidence from the second robustenss test is consistent with this assertion. In the third robustness test, I re-estimate the skewness premium for the 1980 to 2004 sub sample. These sub sample skewness premium estimates serve as benchmarks for the conditional skewness estimates, where in some instances I can only use the 1980 to 2004 sub period because institutional data are available only for this sub period. The results (see row (3)) indicate that the idiosyncratic premium estimates are positive and economically significant (3.324% annually on a risk-adjusted basis) for the 1980 to 2004 sub period. Again, the sub sample estimates are marginally higher than the full sample estimates. In the remaining two tests, I re-estimate the full sample risk-adjusted skewness premium estimates after employing controls for liquidity and industry exposures. To control for liquidity, I use the Pástor and Stambaugh (2003) liquidity factor and to control for industry exposures, I follow the Pástor and Stambaugh (2002) methodology. 22 I define three industry factors which represent the three principal components of the four-factor residuals of the 48 Fama-French industry portfolios. The new factors are used as additional controls in a multi-factor model specification to obtain risk-adjusted estimates of the skewness premium. I find that with the additional set of controls, the skewness premium estimates are slightly higher (lower) when I control for liquidity (industry exposures). And as before, the annual risk-adjusted skewness premium estimates of 3.468% and 3.060% are economically significant. C. Institutional Ownership and the Skewness Premium So far, the investigation has focused on the aggregate and unconditional estimates of the skewness premium. In this section, I change gears and shift the focus to cross-sectional 22 I thank Ľuboš Pástor for providing the liquidity factor data. 18

20 estimates of the skewness premium. This analysis is motivated by one of the key theoretical predictions of the Barberis and Huang (2005) model, which posits that in an economy where investors exhibit a preference for idiosyncratic skewness, securities with sufficiently large skewness would earn negative average excess returns. Given the evidence on institutional skewness preferences, the theory implies that idiosyncratic skewness premium would be negative (strongly positive) when stocks have lower (higher) institutional ownership. To test the theoretical predictions of the BH model, first, at the end of each quarter, I perform independent double sorts using the institutional ownership (IO) and skewness measures. 23 Next, I compute the value-weighted monthly returns for each of the 25 skewness-io quintile portfolios and obtain both raw and risk-adjusted performance measures for those portfolios. Lastly, I obtain the institutional-ownership conditional skewness premium estimates for each institutional ownership quintile portfolio. This premium is the performance differential between the high (top quintile) and low (bottom quintile) skewness portfolios, holding institutional ownership fixed. The conditional skewness premium estimates are reported in Table V, Panel A. I find that idiosyncratic skewness premium estimates are strongly negative when the institutional ownership is low (IO 3.48%) and those estimates are significantly higher than the unconditional estimates when the institutional ownership is high (IO 45.10%). For instance, the monthly four-factor alpha is 0.684% (0.432%) when institutional ownership is low (high). The other two performance measures (the mean monthly return and the CAPM alpha) yield similar estimates. These results strongly support the theoretical predictions of the BH model. Consistent with the theory, I find that the return generating process is strongly influenced by institutional preferences in the habitat of institutions. In contrast, when retail concentration is higher, returns on skewness sorted portfolios are predominantly determined by the skewness preferences of retail investors. To better understand the mechanism that generates the skewness premium, I report the performance measures of five idiosyncratic skewness quintile portfolios for low (Panel B) and high (Panel C) institutional ownership categories. The results indicate that when institutional ownership is low (IO 3.48%), idiosyncratic skewness portfolios earn either 23 Each skewness and IO sorted portfolio contains at least 126 stocks. 19

21 insignificantly positive or significantly negative returns. In particular, the highest skewness quintile portfolio exhibits severe under-performance. This evidence indicates that skewness loving retail investors are willing to accept significantly lower returns in exchange for higher skewness. In contrast, when institutional ownership is high (IO 45.10%), portfolio performance increases almost monotonically with idiosyncratic skewness. For instance, the lowest idiosyncratic skewness quintile portfolio earns an average monthly return of 0.994% while the highest idiosyncratic skewness quintile portfolio earns an average monthly return of 1.420%. The evidence indicates that skewness averse institutional investors demand a premium when idiosyncratic skewness is high and they are willing to accept lower mean returns when the idiosyncratic skewness is low. D. Institutional Ownership and the Skewness Premium Estimates: Robustness Checks As mentioned earlier, the institutional ownership data are available only from 1980 onwards. To examine whether the differential impact of institutional skewness preferences in the crosssection of stocks extends to the full sample (1962 to 2004), I use stock price as a proxy for institutional ownership. Because institutional investors tilt their portfolios toward higher priced stocks (see Table III), price is an appropriate proxy for institutional ownership. 24 The price conditional skewness premium estimates (Panel A) and disaggregated skewness portfolio performance measures for low and high price categories (Panels B and C) are reported in Table VI. The full sample estimates with an institutional ownership proxy is similar to the estimates reported in Table V. When stock price is low (P $3.79), portfolio returns decrease (almost monotonically) with skewness. However, when stock price is high (P $24.41), the pattern completely reverses and portfolio returns increase with skewness. This mechanism yields a significantly positive (negative) idiosyncratic skewness premium when stock price is high (low). For additional robustness, I examine whether the positive idiosyncratic skewness pre- 24 I also experimented with firm size as an institutional ownership proxy. The results are very similar to the reported results, though somewhat weaker. 20