Institutional Skewness Preferences and

the Idiosyncratic Skewness Premium∗

Alok KumarUniversity of Notre Dame

Mendoza College of Business

August 15, 2005

∗Alok Kumar is at the Mendoza College of Business, University of Notre Dame (Phone: 574-631-0354;

email: akumar@nd.edu). 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.

Institutional Skewness Preferences and

the Idiosyncratic Skewness Premium

ABSTRACT

This study examines whether idiosyncratic skewness preferences of institutional investors in-

fluence 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) diver-

sified 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 insti-

tutional 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 de-

crease 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., coskew-

ness) 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.

1Following Harvey and Siddique (2000), I decompose total skewness into systematic and idiosyncraticcomponents. Idiosyncratic skewness of a stock is defined as the skewness of the residual from a regressionwhere the excess (over the riskfree rate) stock returns are regressed on excess market returns and squaredexcess market returns. The systematic skewness (or coskewness) is the coefficient estimate of the squaredexcess market return variable. See Harvey and Siddique (2000) for other related coskewness measures.

1

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 pre-

mium 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.

2The BH model predicts a nonlinear relation between skewness and expected returns, where only securitieswith very high skewness earn lower expected returns.

3CPT preferences are not necessary to generate a preference for skewness. For instance, Brunnermeierand Parker (2005) show that anticipatory utility (e.g., dream utility) can generate a preference for skewnessin portfolio choices. Also, see Polkovnichenko (2005).

4Similar to retail investors (e.g., Goetzmann and Kumar (2004), Mitton and Vorkink (2004)), less diver-sified institutions may trade expected returns for skewness. Also, see Simkowitz and Beedles (1978) andConine and Tamarkin (1981).

2

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 in-

vestigate whether institutional skewness preferences vary in the cross-section. In particular,

I examine whether smaller and relatively less diversified institutions exhibit weaker skew-

ness 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 sys-

tematic skewness (i.e., coskewness) but disklike idiosyncratic skewness.6 Even in the cross-

section, all institutional types (banks, insurance companies, investment companies, indepen-

dent 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.

5In a related study, Kumar (2005) shows that institutions dislike total skewness but does not distinguishbetween systematic skewness and idiosyncratic skewness. Furthermore, unlike my study, he does not examinethe cross-sectional variation in institutional skewness preferences. Most importantly, the focus of my studyis on examining the pricing effects of institutional skewness preferences while Kumar (2005) focuses on therelation between investor demographics and stock preferences of retail investors. The institutional stockpreferences are presented for robustness.

6The results on institutional preferences for coskewness are consistent with the evidence in Harvey andSiddique (2000), who show that stocks with higher coskewness earn lower average returns.

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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 aggre-

gate, 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 secu-

rities with sufficiently large idiosyncratic skewness earn negative average excess returns due

to investors’ strong appetite for idiosyncratic skewness. Lastly, I examine whether the com-

monly 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 posi-

tive 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 indus-

try concentration. However, in the cross-section, I find that the annual, risk-adjusted id-

iosyncratic 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 skew-

ness preferences, I construct an idiosyncratic skewness factor (ISKEW ). The factor repre-

sents 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

7These stocks would have a greater concentration of retail investors who prefer skewness (Goetzmannand Kumar (2004), Mitton and Vorkink (2004), Kumar (2005)). Note that the institutional holdings dataare available from 1980. Therefore, when conditioning on institutional ownership, I can only compute theskewness premium for the 1980 to 2004 period.

4

idiosyncratic factor and the other two Fama-French factors are moderate while the momen-

tum 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

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., Pastor 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,

8These estimates are biased upwards because smaller institutions and small stock positions are excludedfrom the sample.

9Note that these are equal-weighted averages, which do not reflect the institutional presence in the marketin dollar terms. When measured in dollar terms, the total institutional ownership was about 20% in 1980and about 57% in December 2004.

10See Gompers and Metrick (2001) or Bennett, Sias, and Starks (2003) for further details on the institu-tional ownership data.

11My results are insensitive to the choice of this cutoff. The skewness estimates are very similar when Iuse a 13-day or a 17-day cutoff.

6

the total skewness of stock i in a given month is computed as follows:

Total Skewi =

∑Dtt=1(Rit − µi)

σ3i

.

Here, Dt is the number of days in a given month, µi is the mean return of stock i in that

month, and σi 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:

Rit −Rft = αi + βiRMRF t + γiRMRF 2t + εit, (1)

where Rit is the rate of return on stock i on day t, Rft is the riskfree rate of return on day

t, RMRF t is the market return in excess of the riskfree rate on day t, and εit 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 εit and the systematic skewness (or coskewness) of stock i in that month is the

coefficient estimate γi 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. Simi-

larly, while the mean coskewness measure is negative, more than 25% of stocks have positive

coskewness.

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C. Properties of Skewness Sorted Portfolios

To examine the characteristics of stocks that have higher skewness, I obtain the factor expo-

sure 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. Portfo-

lio 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) skew-

ness 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 consider-

able 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

12I 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

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 pref-

erences 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 insti-

tutional 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 skew-

ness, 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,

13For robustness, I also examine whether the Pastor and Stambaugh (2003) liquidity betas differ acrossskewness 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. Forbrevity, liquidity beta estimates are not reported.

14It is also likely that volatility and skewness measures using daily rather than monthly returns provide amore accurate characterization of institutional preferences.

9

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 (DelGuer-

cio (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 Again, this would lead to cross-sectional

variation in institutional skewness preferences.

A. Aggregate Institutional Preferences

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 re-

gression 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 vari-

ables.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-

15Stocks with higher idiosyncratic volatility, positive skewness, and lower prices are defined as lottery-typestocks. See Kumar (2005) for further details.

16For several reasons, I use a panel regression specification instead of estimating a series of cross-sectionalregressions at the end of each quarter. Most importantly, because the coefficient estimates in the quarterlycross-sectional regressions are not independent, standard tests for significance of coefficient estimates cannotbe employed. In contrast, the panel regression framework allows me to correct for potential auto-correlationin errors (which leads to non-independent coefficient estimates in cross-sectional regressions) using the Neweyand West (1987) approach.

17The excess portfolio weight allocated to stock i in month t is given by: EW ipt = wipt−wimt

wimt× 100, where

wipt is the actual weight assigned to stock i in group portfolio p in month t and wimt is the weight of stocki in the aggregate market portfolio in month t.

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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

18The independent variables have been standardized to facilitate comparisons among coefficient estimateswithin a regression specification and also across specifications. I also check that multi-collinearity is notcontaminating my results.

11

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 stan-

dard deviation decrease in the idiosyncratic skewness of a stock corresponds to an excess

aggregate institutional holding of about $385 million (0.012100

×3.21×106 = $385.20 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 institu-

tional 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.

19The aggregate institutional portfolio is worth $0.250 trillion in January 1980, $7.51 trillion in June 2002,and $9.53 trillion in December 2004. The average size of the aggregate institutional portfolio during the1980 to 2004 period is $3.21 trillion. The economic interpretation of the coefficient estimates are based onthe average size of the aggregate institutional portfolio.

12

For instance, institutions who hold under-diversified portfolios may do so intentionally be-

cause 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 institu-

tions (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 insti-

tutions hold stock portfolios worth $1.33 billion or more. The coefficient estimates indicate

that small institutions exhibit a preference for idiosyncratic skewness while their system-

atic 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

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 institu-

tions, 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 institu-

tions, 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 prefer-

ences 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

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 −0.011 and −0.015,

respectively. In comparison, the coefficient estimate of idiosyncratic skewness in the full

sample is −0.012. 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 con-

sistent 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), in-

stitutional 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 cross-

section 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 own-

ership, 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

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 idiosyn-

cratic 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 Ir-

respective of the performance measure employed, I find that portfolio performance increases

with idiosyncratic skewness. The increase in performance is not monotonic but the high-

est 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 skew-

ness) 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 port-

folios 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 1963. 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

20In the four-factor time-series model, portfolio returns is the dependent variable and the four commonlyused risk factors (RMRF, SMB, HML, and UMD) are employed as independent variables.

16

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 orig-

inal 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 manifesta-

tion of the size anomaly. Additionally, one might believe that the idiosyncratic skewness

premium primarily reflects the premium for holding micro-cap stocks. The skewness pre-

mium estimates for the NYSE sub sample (see row (2)) indicate that contrary to such beliefs,

21This argument ignores the effect of arbitrage costs, which is likely to be an important determinant ofthe premium. I examine the sensitivity of skewness premium estimates to arbitrage costs in Section III.D.

17

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 institu-

tional 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 liq-

uidity, I use the Pastor and Stambaugh (2003) liquidity factor and to control for industry

exposures, I follow the Pastor and Stambaugh (2002) methodology.22 I define three indus-

try 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 pre-

mium. 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

22I thank Lubos Pastor for providing the liquidity factor data.

18

estimates of the skewness premium. This analysis is motivated by one of the key theoreti-

cal 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 institu-

tional 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 mea-

sures.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 esti-

mates 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 uncon-

ditional 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 concen-

tration 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

23Each skewness and IO sorted portfolio contains at least 126 stocks.

19

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 id-

iosyncratic 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 cross-

section 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-

24I also experimented with firm size as an institutional ownership proxy. The results are very similar tothe reported results, though somewhat weaker.

20

mium in the high institutional ownership category varies with the level of coskewness. In

particular, I investigate whether the idiosyncratic skewness premium is positive even when

coskewness is low. The results indicate that the idiosyncratic skewness premium is positive

in all three coskewness categories (low, medium, and high), where the premium is highest

for the medium coskewness category. Holding institutional ownership fixed (high or top

quintile), the raw monthly idiosyncratic skewness premium (i.e., the mean monthly return)

for the low, medium, and high coskewness categories are 0.309%, 0.505%, and 0.405%, re-

spectively. The corresponding risk-adjusted monthly idiosyncratic skewness premium (i.e.,

the four-factor alpha) are 0.379%, 0.580%, and 0.409%, respectively. All these estimates are

statistically significant at the 5% level. Overall, the evidence indicates that the idiosyncratic

skewness premium is distinct from the coskewness premium identified in the Harvey and

Siddique (2000) study.

E. Arbitrage Costs and the Skewness Premium

In this section, I investigate the role of the third key determinant of the idiosyncratic skew-

ness premium, namely, arbitrage costs. The Barberis and Huang (2005) model posits that

arbitrage costs would be an important determinant of the idiosyncratic skewness premium.

In particular, when arbitrage costs are low (high), the magnitudes of the skewness premium

are predicted to be low (high).

To examine the impact of arbitrage costs on the idiosyncratic skewness premium, follow-

ing Wurgler and Zhuravskaya (2002), I use idiosyncratic volatility (variance of the residual

from a CAPM regression) as a proxy for arbitrage costs. Holding institutional ownership

fixed (low and high), I examine the variation in the idiosyncratic skewness premium as

arbitrage costs increase. The results are summarized in Figure 2.

Consistent with the theoretical predictions, I find that, when the institutional ownership

is in the lower two quintiles (IO ≤ 12.17%) and the mean arbitrage costs are low (lowest

quintile), the idiosyncratic skewness premium is insignificantly different from zero.25 How-

25I consider the bottom two and the top two quintiles instead of the extreme quintiles alone because thenumber of stocks per portfolio is very low in the latter instance. For a similar reason, I perform a nested sortrather than an independent sort along the arbitrage cost dimension. Several portfolios have zero membershipwhen I perform independent sorts using institutional ownership, skewness, and arbitrage cost measures.

21

ever, when the mean arbitrage costs are in the highest quintile, the idiosyncratic skewness

premium is significantly negative. Similarly, when the institutional ownership is in the higher

two quintiles (IO ≤ 25.37%) and the mean arbitrage costs are low (lowest quintile), the id-

iosyncratic skewness premium is insignificantly different from zero. However, when the mean

arbitrage costs are in the highest quintile, the idiosyncratic skewness premium is significantly

positive. Collectively, the evidence is consistent with the theory and indicates that arbitrage

costs are an important determinant of the idiosyncratic skewness premium.

F. Institutional Preferences and Returns: Additional Evidence

To further demonstrate that institutional preferences influence returns, I examine the preference-

return relation in another related setting. The earlier evidence on institutional preferences

indicates that, in addition to idiosyncratic skewness, institutions dislike idiosyncratic volatil-

ity (see Table III). If institutional preferences do indeed matter for returns, institutional

idiosyncratic volatility preferences would be an important determinant of the idiosyncratic

volatility premium.

Ang, Hodrick, Xing, and Zhang (2005) report the puzzling finding of negative returns in

higher idiosyncratic volatility stocks. I examine whether the degree of under-performance

within the high idiosyncratic volatility portfolio varies with the level of institutional owner-

ship. If institutional volatility preferences influence returns, holding idiosyncratic volatility

fixed at the high level, stocks with higher (lower) institutional ownership is expected to earn

relatively higher (lower) returns. In other words, the degree of under-performance would

decrease with institutional ownership.

I obtain unconditional and conditional under-performance estimates for the highest id-

iosyncratic volatility quintile portfolio for the 1980 to 2004 period. When I do not condition

on institutional ownership, the mean monthly under-performance for the highest idiosyn-

cratic volatility quintile portfolio is 0.282% per month. This evidence is consistent with

the under-performance estimates reported in Ang, Hodrick, Xing, and Zhang (2005). More

importantly, when I condition on institutional ownership, the degree of under-performance

decreases (almost monotonically) as institutional ownership increases (see Figure 3). When

institutional ownership is low, the high idiosyncratic volatility portfolio earns a mean monthly

22

return of −1.295%. But when institutional ownership is high, the mean under-performance

is only 0.087%.26 Taken together, this evidence from a different setting further indicates that

institutional preferences influence stock returns.

IV. Are Institutional Preferences Reflected in Common Risk Factors?

My evidence so far indicates that institutional skewness preferences are systematic, and

therefore, those preferences get impounded into asset prices. In this section, I examine

whether the common risk factors, i.e., the three Fama-French factors (Fama and French

(1993)) and the momentum factor (e.g., Jegadeesh and Titman (1993), Carhart (1997)), at

least partially reflect the pricing effects of institutional skewness preferences. Harvey and

Siddique (2000) have already shown that the SMB (small-minus-big or size), HML (high-

minus-low or value), and UMD (up-minus-down or momentum) factors partially capture

the information contained in coskewness measures. In this section, I examine whether those

factors also reflect the pricing effects of idiosyncratic skewness preferences of institutions.

A. Skewness Factor and the Common Risk Factors

To examine the relation between institutional skewness preferences and the common risk

factors, I construct an idiosyncratic skewness factor (ISKEW ). The factor represents the

spread of a zero-cost portfolio that takes a long (short) position in stocks with the highest

(lowest) idiosyncratic skewness. The composition of the zero-cost portfolio is updated at

the end of each month. Using the ISKEW factor, I estimate several time-series regression

specifications. The dependent variable in these regression models is one of the four common

risk factors and the primary independent variables are the lagged and contemporaneous

measures of the ISKEW factor. To control for potential auto-correlation in the factor

returns, I use lagged factor returns as additional independent variables.

The time-series regression coefficient estimates along with White (1980) and Newey and

West (1987) adjusted t-values of coefficient estimates are reported in Table VII. The esti-

mates indicate that small stocks earn positive returns when high (low) idiosyncratic skewness

26This pattern is identical when I exclude stocks priced below $5.

23

portfolio earns higher (lower) returns. The coefficient estimate for ISKEWt in the SMB re-

gression is significantly positive (estimate = 0.559, t-statistic = 8.330) and the idiosyncratic

skewness factor alone can explain about 14% of the variation in SMB. The contempora-

neous correlations between the idiosyncratic factor and the other two Fama-French factors

are moderate while the momentum factor is virtually uncorrelated with the skewness factor.

Overall, these estimates indicate that the SMB factor partially reflects the pricing effects

of idiosyncratic skewness preferences of institutions rather than compensation for risk.

B. Factor Model Estimation Results for Size and B/M Sorted Portfolios

To further quantify the effects of institutional skewness preferences on returns, I examine

the explanatory power of the ISKEW factor using a time-series factor model estimation

framework. I consider value-weighted returns for size and B/M decile portfolios.27 For each

of these twenty portfolios, I estimate the factor model twice, once with the ISKEW factor

alone, and again with the ISKEW factor along with the four commonly used risk factors.

The factor model estimation results are presented in Table VIII. The factor model esti-

mates indicate that the ISKEW factor alone can explain about 8% of the variation in size

decile 1 portfolio returns. This evidence further reinforces the assertion that idiosyncratic

skewness preferences of investors influence returns. As expected, the explanatory power of

the ISKEW factor decreases monotonically as one moves to higher size decile portfolios,

where for the highest size decile portfolio, the ISKEW factor has no explanatory power

(the adjusted R2 is negative). In unreported results, I find that when the SMB factor is

included in the factor model, the ISKEW coefficient estimates are mostly insignificant.

This evidence indicates that the ISKEW factor does not have any incremental explanatory

power over the four risk factors.

When I consider B/M decile portfolios, the explanatory power of the ISKEW factor

is very low (less than 2%). However, in relative terms, the explanatory power is higher

for the extreme (the highest and the lowest deciles) B/M portfolios. Taken together, the

factor model estimates further indicate that investors’ idiosyncratic skewness preferences get

impounded into stock prices.

27The portfolio returns are obtained from Ken French’s data library.

24

V. Summary and Conclusions

This study examines the relation between idiosyncratic skewness preferences of institu-

tional investors and stock returns. In an economy where investors hold concave preferences

and like positive skewness, everything else equal, stocks that decrease the skewness of a port-

folio earn higher expected returns (e.g., Kraus and Litzenberger (1976), Lim (1989), Harvey

and Siddique (2000)). At the margin, idiosyncratic skewness is irrelevant in this economy

and is unlikely to influence expected stock returns. However, in an alternative economic set-

ting, idiosyncratic skewness may be priced along with coskewness. Specifically, Barberis and

Huang (2005) present a model with skewness loving investors where idiosyncratic skewness

earns a negative premium. The Barberis and Huang (2005) model also predicts that the

magnitude of the idiosyncratic skewness premium would be larger when arbitrage costs are

higher. I test these theoretical predictions in this paper.

In the first part of the paper, I examine the aggregate institutional preferences for id-

iosyncratic and systematic skewness. I find that, at an aggregate level, institutions exhibit

a preference for coskewness but disklike idiosyncratic skewness. This evidence suggests that

skewness is likely to impact returns differentially in the cross-section. Specifically, idiosyn-

cratic skewness premium would be positive when institutional ownership is higher, particu-

larly 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.

In the second part of the paper, I directly investigate whether the idiosyncratic skewness

preferences of institutions are reflected in stock returns. I find 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. Furthermore, in the cross-section, I find that the

annual, risk-adjusted idiosyncratic skewness premium is strongly negative (−8.21%) when

institutional ownership is lower. 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.

25

I also examine whether the commonly used risk factors (the Fama-French factors and the

momentum factor) partially reflect the pricing effects of institutional idiosyncratic skewness

preferences rather than compensation for risk. I construct an idiosyncratic skewness factor

that 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). This evidence indicates that

the SMB factor partially reflects the pricing effects of institutional idiosyncratic skewness

preferences rather than compensation for risk. The correlations between the idiosyncratic

factor and the other two Fama-French factors are moderate while the momentum factor is

virtually uncorrelated with the skewness factor.

In sum, my results indicate that institutions exhibit distinct skewness preferences and

those preferences influence stock returns. The cross-sectional evidence on skewness premium

also suggests that interesting cross-sectional patterns in stock returns may be masked in

an aggregate level analysis. An asset pricing framework that recognizes the importance of

institutional ownership, institutional preferences, and arbitrage costs may be more successful

in explaining the cross-sectional variation in stock returns. In broader terms, my results

suggest that institutional preferences may play an important role in the return generating

process in other related settings. It would be interesting to identify those instances and

examine the conditional patterns in stock returns.

26

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29

Table ISkewness Measures: Summary Statistics

This table reports the summary statistics for three skewness measures for the full sample period (1962 to2004) and two sub periods (1962 to 1979 and 1980 to 2004). The total skewness measure of a stock is the

third moment of its returns: Total Skewi =∑Dt

t=1(Rit−µi)

σ3i

. Here, Dt is the number of days in a given month,µi is the mean return of stock i in that month, and σi is the standard deviation of returns of stock i inthat month. To decompose the total skewness into idiosyncratic and systematic components, I estimate thefollowing regression: Rit −Rft = αi +βiRMRF t + γiRMRF2

t + εit, where Rit is the rate of return on stocki on day t, Rft is the riskfree rate of return on day t, RMRF t is the market return in excess of the riskfreerate on day t, and εit is the residual stock return on day t. The regression model is estimated for each stockat the end of each month. The idiosyncratic skewness of stock i in a given month is defined as the skewnessof the residual εit and the systematic skewness (or coskewness) of stock i in that month is the coefficientestimate γi in the regression above.

1962-2004 1962-1979 1980-2004

Statistic Total Idio Sys Total Idio Sys Total Idio Sys

Mean 0.210 0.189 −0.078 0.207 0.172 −0.065 0.221 0.201 −0.079

Median 0.234 0.207 −0.056 0.249 0.210 −0.052 0.233 0.208 −0.053

Std Dev 0.351 0.279 0.636 0.449 0.361 0.923 0.344 0.272 0.472

10th Pctl −0.054 −0.050 −0.460 −0.152 −0.143 −0.443 −0.037 −0.035 −0.445

25th Pctl 0.116 0.097 −0.206 0.096 0.069 −0.208 0.119 0.101 −0.199

75th Pctl 0.355 0.315 0.055 0.385 0.329 0.078 0.355 0.320 0.051

90th Pctl 0.487 0.433 0.258 0.529 0.450 0.287 0.499 0.447 0.234

30

Table IIProperties of Skewness Sorted Portfolios

This table reports the properties of skewness sorted portfolios for the 1962 to 2004 period. Panel A (Panel B)reports the characteristics of idiosyncratic (total) skewness sorted portfolios. To define idiosyncratic skewnessportfolios, each month, I measure the idiosyncratic skewness of the entire universe of stocks for which returnsdata are available from CRSP. Next, each month, I sort stocks using their idiosyncratic skewness measuresand form idiosyncratic skewness quintile portfolios. Quintile portfolio 1 consists of stocks with the lowestidiosyncratic skewness while quintile portfolio 5 contains stocks with the highest idiosyncratic skewness.Lastly, for each idiosyncratic skewness portfolio, I compute the monthly portfolio return as value-weightedaverage of all stocks in the portfolio and construct a monthly portfolio return time-series. In an analogousmanner, I identify the returns of total skewness quintile portfolios. I obtain the factor exposure estimates byregressing 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 orUMD). The sample period means of stock price, market capitalization, and institutional ownership are alsoreported. Due to data limitations, the institutional ownership measures are computed for the 1980 to 2004period. The institutional investor data are from Thomson Financial for the period 1980 to 2004. *, **, and*** denote significance at the 10%, 5%, and 1% levels, respectively.

Panel A: Total Skewness Portfolios

Skew Quintile RMRF SMB HML UMD Mkt Cap Price Insti Own

Low (−3.87 to −0.38) 0.976∗∗∗ −0.005 0.081∗∗∗ 0.003 $666.36 $21.25 18.85%

Q2 (−0.38 to −0.06) 0.988∗∗∗ −0.006 −0.008 0.034∗∗∗ $806.01 $22.17 20.38%

Q3 (0.06 to 0.40) 1.027∗∗∗ −0.010 −0.023 0.005 $780.88 $21.38 19.61%

Q4 (0.40 to 0.89) 1.023∗∗∗ −0.002 −0.010 −0.037∗∗∗ $712.18 $21.51 20.04%

High (0.89 to 4.03) 0.996∗∗∗ 0.155∗∗∗ 0.004 −0.051∗∗∗ $443.12 $19.66 17.16%

Q5−Q1 0.020 0.160∗∗∗ −0.077∗∗ −0.054∗∗ −$218.24∗∗∗ −$1.59∗∗ −1.69%∗∗∗

Panel B: Idiosyncratic Skewness Portfolios

Skew Quintile RMRF SMB HML UMD Mkt Cap Price Insti Own

Low (−3.69 to −0.40) 0.998∗∗∗ −0.038∗∗ 0.051∗∗ −0.022∗ $693.59 $20.02 18.46%

Q2 (−0.40 to 0.03) 0.993∗∗∗ −0.000 −0.023 −0.006 $761.39 $22.66 20.26%

Q3 (0.03 to 0.37) 1.004∗∗∗ −0.025∗∗ 0.008 0.020∗∗ $750.92 $21.89 19.73%

Q4 (0.37 to 0.85) 1.017∗∗∗ −0.010 −0.060∗∗∗ −0.023∗∗ $691.72 $20.65 19.72%

High (0.85 to 3.85) 0.996∗∗∗ 0.184∗∗∗ 0.036∗ −0.007 $480.71 $19.97 16.91%

Q5−Q1 −0.002 0.222∗∗∗ −0.015 0.015 −$212.88∗∗∗ −$0.05 −1.55%∗∗∗

31

Table IIIInstitutional Preferences for Systematic and Idiosyncratic Skewness:

Panel Regression Estimates

This table reports the panel regression (with fixed quarter effects) estimates where the excess weight assignedto a stock in the institutional group portfolio is the dependent variable. The excess portfolio weight allocatedto stock i in month t is defined as: EW ipt = wipt−wimt

wimt× 100, where, wipt is the actual weight assigned to

stock i in group portfolio p in month t and wimt is the weight of stock i in the aggregate market portfolioin month t. The systematic and idiosyncratic skewness measures are used as the primary independentvariables. To define idiosyncratic and systematic components of skewness, I estimate the following regression:Rit − Rft = αi + βiRMRF t + γiRMRF 2

t + εit, where Rit is the rate of return on stock i on day t, Rft isthe riskfree rate of return on day t, RMRF t is the market return in excess of the riskfree rate on day t,and εit is the residual stock return on day t. The regression model is estimated for each stock at the endof each month. The idiosyncratic skewness of stock i in a given month is defined as the skewness of theresidual εit and the systematic skewness (or coskewness) of stock i in that month is the coefficient estimateγi in the regression above. Additionally, I use the following additional independent variables to controlfor the known determinants of institutional preferences: (i) idiosyncratic volatility, which is the variance ofthe 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) firmsize, (iv) book-to-market ratio, (v) short-term momentum (past one-month stock return), (vi) longer-termmomentum (past twelve-month stock return), (vii) stock price, (viii) monthly volume turnover, and (ix) anS&P500 dummy which is set to one if the stock belongs to the S&P500 index. All stock characteristics aremeasured at the end of each quarter. In Panel A, the aggregate portfolios for the following investor groupsare considered: (i) all institutions, (ii) small institutions (average portfolio size ≤ $64 million), (iii) largeinstitutions (average portfolio size ≥ $1.33 billion), (iv) relatively less diversified institutions (mean numberof stocks in the portfolio is 22), and (v) relatively more diversified institutions (mean number of stocks in theportfolio is 332). In Panel B, the aggregate portfolios of the following five institutional types are considered:(i) banks, (ii) insurance companies, (iii) investment companies (mutual funds), (iv) independent investmentadvisors, and (v) others or unclassified. Additionally, I estimate the panel regression for two sub samples:(i) only stocks with a price of $5 or above are considered, and (ii) only stocks with positive institutionalownership (IO) is considered. The White (1980) and Newey and West (1987) adjusted t-values of coefficientestimates are reported in parentheses below the estimates. The institutional investor data are from ThomsonFinancial for the period 1980 to 2004.

32

Table III(Continued)

Institutional Preferences for Systematic and Idiosyncratic Skewness:Panel Regression Estimates

Panel A: Estimates for All Institutions and Subsets based on Size and Diversification Level

Dependent variable: Excess portfolio weight (in percent) in stock i in the group portfolio.

Institutional Size Institutional Diversification

Variable (1):All Institutions (2):Small (3):Large (4):Low (5):High

Skewness

Idiosyncratic Skewness −0.012 0.003 −0.012 0.004 −0.013

(−6.105) (1.965) (−6.659) (1.872) (−6.772)

Systematic Skewness 0.019 −0.002 0.024 −0.001 0.009

(2.065) (−0.645) (1.925) (−1.074) (1.994)

Other Stock Characteristics

Idiosyncratic Volatility −0.021 0.014 −0.015 0.007 −0.018

(−6.828) (2.526) (−3.561) (3.494) (−4.109)

Market Beta 0.070 0.004 0.077 −0.003 0.078

(10.496) (2.185) (11.256) (−1.896) (11.869)

Log(Firm Size) 0.358 0.025 0.399 0.030 0.388

(18.357) (6.705) (33.419) (12.970) (31.569)

Book-To-Market 0.014 0.015 0.040 −0.011 0.010

(1.326) (0.712) (13.419) (−1.169) (0.910)

Past 1-Month Return −0.019 −0.002 −0.022 −0.001 −0.023

(−5.070) (−0.145) (−5.836) (−0.124) (−5.797)

Past 12-Month Return −0.041 −0.001 −0.051 −0.020 −0.049

(−6.623) (−0.159) (−8.325) (−5.303) (−8.069)

Stock Price 0.027 −0.002 0.025 0.010 0.027

(3.032) (−1.290) (2.921) (3.183) (2.691)

Monthly Turnover −0.014 −0.002 −0.006 0.004 −0.003

(−2.492) (−1.264) (−0.941) (1.714) (−0.868)

S&P500 Dummy 0.011 −0.004 0.025 0.003 0.019

(5.883) (−3.804) (12.093) (2.235) (10.149)

Mean Number of Stocks 4,229 4,229 4,229 4,229 4,229

Mean Adjusted R2 26.99% 12.25% 28.65% 10.11% 27.61%

33

Table III(Continued)

Institutional Preferences for Systematic and Idiosyncratic Skewness:Panel Regression Estimates

Panel B: Estimates for Subsets of Institutions and Subsets of Stocks

Type of Institution

Variable (1):Banks (2):Ins (3):Invest (4):Indep (5):Others (6):Min $5 (7):PosIO

Skewness

Idiosync Skewness −0.015 −0.006 −0.011 −0.009 −0.006 −0.011 −0.015

(−7.543) (−3.281) (−4.446) (−4.936) (−2.832) (−5.770) (−7.421)

Systematic Skewness 0.037 0.031 0.001 0.001 0.001 0.016 0.020

(2.356) (2.707) (0.606) (0.597) (0.834) (2.715) (2.704)

Other Stock Characteristics

Idiosyncratic Volatility −0.001 0.009 −0.007 −0.034 0.005 −0.089 −0.029

(−0.464) (2.218) (−2.200) (−9.105) (1.270) (−5.351) (−5.490)

Market Beta −0.022 0.030 0.063 0.103 0.038 0.137 0.072

(−5.438) (9.598) (14.530) (13.927) (11.711) (10.675) (7.755)

Log(Firm Size) 0.369 0.255 0.296 0.291 0.237 0.239 0.423

(33.063) (28.215) (33.607) (21.533) (21.187) (16.326) (17.840)

Book-To-Market 0.012 −0.005 0.024 0.074 0.034 −0.012 0.556

(0.215) (−0.036) (2.571) (0.532) (2.106) (−0.969) (2.702)

Past 1-Month Return −0.019 −0.015 −0.020 −0.018 −0.008 −0.018 −0.031

(−7.157) (−6.878) (−5.221) (−4.828) (−3.923) (−3.984) (−7.737)

Past 12-Month Return −0.055 −0.054 0.001 −0.018 −0.076 −0.052 −0.041

(−11.833) (−10.882) (0.150) (−2.847) (−13.062) (−5.621) (−6.708)

Stock Price 0.022 0.008 0.014 0.026 0.012 0.021 0.010

(3.252) (1.494) (2.150) (2.910) (3.687) (2.688) (1.474)

Monthly Turnover −0.046 −0.009 −0.009 0.007 −0.012 −0.004 −0.005

(−12.910) (−1.965) (−3.545) (0.760) (−5.505) (−0.741) (−0.715)

S&P500 Dummy 0.046 0.008 0.002 −0.019 0.049 0.010 0.030

(20.934) (5.371) (1.034) (−10.081) (13.643) (5.633) (11.563)

Mean Number of Stocks 4,229 4,229 4,229 4,229 4,229 3, 050 3, 220

Mean Adjusted R2 20.98% 10.70% 12.69% 16.16% 13.96% 18.28% 37.87%

34

Table IVUnconditional Skewness Premium Estimates

This table reports unconditional estimates of skewness premium. The skewness premium is the returndifferential between the two extreme (the highest and the lowest quintiles) skewness quintile portfolios. Todefine idiosyncratic skewness portfolios, each month, I measure the idiosyncratic skewness of the entireuniverse of stocks for which returns data are available from CRSP. Next, each month, I sort stocks usingtheir idiosyncratic skewness measures and form idiosyncratic skewness quintile portfolios. Quintile portfolio1 consists of stocks with the lowest idiosyncratic skewness while quintile portfolio 5 contains stocks withthe highest idiosyncratic skewness. Lastly, for each idiosyncratic skewness portfolio, I compute the monthlyportfolio return as value-weighted average of all stocks in the portfolio and construct a monthly portfolioreturn time-series. In an analogous manner, I identify the returns of total skewness quintile portfolios. Thetotal skewness is the third moment of returns and the idiosyncratic skewness is the third moment of theresidual from the following regression: Rit −Rft = αi + βiRMRF t + γiRMRF2

t + εit, where Rit is the rateof return on stock i on day t, Rft is the riskfree rate of return on day t, RMRF t is the market return inexcess of the riskfree rate on day t, and εit is the residual stock return on day t. The mean monthly returnspread and risk-adjusted performance measures (CAPM and four-factor alphas) are reported in the table.The CAPM alpha is the intercept from the market model regression and the four factor alpha measure isthe intercept from the four-factor model, where portfolio returns is the dependent variable and the fourcommonly used risk factors (RMRF, SMB, HML, and UMD) are employed as dependent variables. PanelA reports the full sample (1962 to 2004) estimates while Panel B reports the estimates from the followingfive robustness tests: (i) only stocks with a minimum price of $5 are considered, (ii) only NYSE stocks areconsidered, (iii) 1980 to 2004 sub sample is considered, (iv) an additional liquidity control is employed tomeasure the risk-adjusted performance, and (v) additional industry controls are employed to measure therisk-adjusted performance. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

Panel A: Full Sample (1962 to 2004) Skewness Premium Estimates

Monthly Return CAPM Alpha Four-Factor Alpha

Skewness Quintile Total Idio Total Idio Total Idio

Q1 (Low) 0.792 0.746 −0.145∗∗ −0.204∗∗∗ −0.118∗∗ −0.169∗∗∗

Q2 0.946 0.957 −0.005 0.001 0.025 0.051

Q3 0.997 1.031 0.026 0.073∗ 0.083∗ 0.102∗∗

Q4 0.984 1.029 0.039 0.056 0.107∗ 0.101∗∗

Q5 (High) 1.028 1.008 0.063∗ 0.043∗ 0.127∗∗ 0.095∗

Q5−Q1 0.236∗∗ 0.263∗∗ 0.209∗∗ 0.247∗∗ 0.245∗∗ 0.264∗∗

Panel B: Skewness Premium Estimates from Robustness Tests

Monthly Return CAPM Alpha Four/Multi-Factor Alpha

Robustness Test Total Idio Total Idio Total Idio

Only Stocks with Price ≥ $5 0.238∗∗ 0.285∗∗ 0.215∗∗ 0.262∗∗ 0.281∗∗ 0.309∗∗∗

Only NYSE Stocks 0.223∗∗ 0.240∗∗ 0.208∗ 0.216∗∗ 0.277∗∗ 0.286∗∗

1980-2004 sub sample 0.233∗∗ 0.309∗∗∗ 0.182∗ 0.274∗∗ 0.340∗∗∗ 0.277∗∗

Control for Liquidity 0.319∗∗∗ 0.289∗∗

Control for Industry 0.293∗∗ 0.255∗∗

35

Table VInstitutional Ownership and the Idiosyncratic Skewness Premium Estimates

This table reports estimates of idiosyncratic skewness premium for the period 1980 to 2004, conditional onthe level of institutional ownership. To measure the conditional skewness premium, I proceed as follows:At the end of each quarter, I perform independent double sorts using the institutional ownership (IO)and idiosyncratic skewness measures. Next, I compute the value-weighted monthly returns for each ofthe 25 skewness-IO quintile portfolios and obtain both raw and risk-adjusted performance measures forthose portfolios. Lastly, I obtain the institutional ownership conditional idiosyncratic skewness premiumestimates for each institutional ownership quintile portfolio. The conditional idiosyncratic skewness premiumis the performance differential between the high (top quintile) and low (bottom quintile) skewness portfolios,holding institutional ownership fixed. The idiosyncratic skewness is the third moment of the residual fromthe following regression: Rit − Rft = αi + βiRMRF t + γiRMRF2

t + εit, where Rit is the rate of return onstock i on day t, Rft is the riskfree rate of return on day t, RMRF t is the market return in excess of theriskfree rate on day t, and εit is the residual stock return on day t. The mean monthly return spread and risk-adjusted performance measures (CAPM and four-factor alphas) are reported in the table. The CAPM alphais the intercept from the market model regression and the four factor alpha measure is the intercept from thefour-factor model, where portfolio returns is the dependent variable and the four commonly used risk factors(RMRF, SMB, HML, and UMD) are employed as dependent variables. Panel A reports the idiosyncraticskewness premium estimates, Panel B reports the performance measures of idiosyncratic skewness quintileportfolios when institutional ownership is low (IO ≤ 3.48%), and Panel C reports the performance measuresof idiosyncratic skewness quintile portfolios when institutional ownership is high (IO ≥ 45.10%). Theinstitutional investor data are from Thomson Financial for the period 1980 to 2004. *, **, and *** denotesignificance at the 10%, 5%, and 1% levels, respectively.

36

Table V(Continued)

Institutional Ownership and the Idiosyncratic Skewness Premium Estimates

Panel A: Institutional Ownership and Skewness Premium Estimates (1980 - 2004 Period)

Insti Own Monthly Return CAPM Alpha Four-Factor Alpha

Quintile Total Idio Total Idio Total Idio

Low (IO ≤ 3.48%) −0.117∗ −0.628∗∗∗ −0.210∗∗ −0.732∗∗∗ −0.098∗ −0.684∗∗∗

Q2 (3.48%-12.17%) 0.119 0.173 0.059 0.069 0.087 0.067

Q3 (12.17%-25.37%) −0.100 −0.186 −0.171 −0.245 −0.012 −0.231

Q4 (25.37%-45.10%) 0.107 0.247∗ 0.115∗ 0.277∗∗ 0.106 0.256∗∗

High (IO > 45.10%) 0.426∗∗∗ 0.385∗∗∗ 0.427∗∗∗ 0.369∗∗∗ 0.667∗∗∗ 0.432∗∗∗

Panel B: Skewness Portfolio Performance when Institutional Ownership is Low

Skewness Monthly Return CAPM Alpha Four-Factor Alpha

Quintile Total Idio Total Idio Total Idio

Low 0.703 0.967 −0.359 −0.086 −0.307 0.011

Q2 1.142 0.880 0.082 −0.238 −0.048 −0.374

Q3 1.259 0.807 0.131 −0.193 0.153 −0.163

Q4 0.950 1.162 −0.221 0.030 −0.259 0.120

High 0.586 0.339 −0.569∗∗ −0.818∗∗ −0.405∗ −0.673∗∗

Panel C: Skewness Portfolio Performance when Institutional Ownership is High

Skewness Monthly Return CAPM Alpha Four-Factor Alpha

Quintile Total Idio Total Idio Total Idio

Low 0.994 0.918 −0.148 −0.219∗∗ −0.297∗∗ −0.240∗∗

Q2 1.057 1.167 −0.075 0.014 −0.051 0.015

Q3 1.289 1.269 0.134∗ 0.124 0.221∗∗ 0.152∗

Q4 1.258 1.288 0.076 0.115 0.166∗∗ 0.220∗∗

High 1.420 1.303 0.279∗∗ 0.150∗∗ 0.370∗∗ 0.192∗∗

37

Table VIStock Price and the Idiosyncratic Skewness Premium

This table reports estimates of idiosyncratic skewness premium for the period 1962 to 2004, conditionalon stock price. To measure the conditional skewness premium, I proceed as follows: At the end of eachquarter, I perform independent double sorts using the stock price and idiosyncratic skewness measures.Next, I compute the value-weighted monthly returns for each of the 25 skewness-price quintile portfoliosand obtain both raw and risk-adjusted performance measures for those portfolios. Lastly, I obtain the priceconditional idiosyncratic skewness premium estimates for each institutional ownership quintile portfolio. Theconditional idiosyncratic skewness premium is the performance differential between the high (top quintile)and low (bottom quintile) skewness portfolios, holding stock price fixed. The idiosyncratic skewness is thethird moment of the residual from the following regression: Rit −Rft = αi + βiRMRF t + γiRMRF 2

t + εit,where Rit is the rate of return on stock i on day t, Rft is the riskfree rate of return on day t, RMRF t is themarket return in excess of the riskfree rate on day t, and εit is the residual stock return on day t. The meanmonthly return spread and risk-adjusted performance measures (CAPM and four-factor alphas) are reportedin the table. The CAPM alpha is the intercept from the market model regression and the four factor alphameasure is the intercept from the four-factor model, where portfolio returns is the dependent variable andthe four commonly used risk factors (RMRF, SMB, HML, and UMD) are employed as dependent variables.Panel A reports the idiosyncratic skewness premium estimates, Panel B reports the performance measuresof idiosyncratic skewness quintile portfolios when stock price is low (P ≤ $3.79), and Panel C reports theperformance measures of idiosyncratic skewness quintile portfolios when stock price is high (P ≥ $24.41). *,**, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

38

Table VI(Continued)

Stock Price and the Idiosyncratic Skewness Premium

Panel A: Stock Price and Skewness Premium Estimates (1962 - 2004 Period)

Price Monthly Return CAPM Alpha Four-Factor Alpha

Quintile Total Idio Total Idio Total Idio

Low (P ≤ $3.79) −1.582∗∗∗ −1.527∗∗∗ −1.630∗∗∗ −1.573∗∗∗ −1.672∗∗∗ −1.698∗∗∗

Q2 ($3.79− $8.79) −0.925∗∗∗ −0.779∗∗∗ −0.996∗∗∗ −0.827∗∗∗ −1.136∗∗∗ −0.951∗∗∗

Q3 ($8.79− $15.22) −0.410∗∗ −0.236∗ −0.458∗∗ −0.275∗ −0.563∗∗∗ −0.485∗∗∗

Q4 ($15.22− $24.41) 0.087 0.029 0.064 0.015 0.106∗ −0.084

High (P > $24.41) 0.297∗∗ 0.333∗∗ 0.274∗∗ 0.318∗∗∗ 0.376∗∗ 0.294∗∗

Panel B: Skewness Portfolio Performance when Price is Low

Skewness Monthly Return CAPM Alpha Four-Factor Alpha

Quintile Total Idio Total Idio Total Idio

Low 1.792 1.719 0.698∗∗ 0.639∗∗ 0.980∗∗ 1.025∗∗

Q2 1.769 1.742 0.633∗ 0.592∗ 0.942∗∗ 0.849∗∗

Q3 1.409 1.278 0.247 0.124 0.556∗ 0.441∗

Q4 0.738 0.961 −0.443∗∗ −0.228∗∗ −0.095∗ 0.053

High 0.209 0.191 −0.932∗∗ −0.935∗∗ −0.693∗∗ −0.672∗∗

Panel C: Skewness Portfolio Performance when Price is High

Skewness Monthly Return CAPM Alpha Four-Factor Alpha

Quintile Total Idio Total Idio Total Idio

Low 0.733 0.716 −0.184∗∗ −0.215∗∗ −0.246∗∗ −0.212∗∗

Q2 0.926 0.921 −0.009 −0.022 −0.010 −0.003

Q3 0.989 1.060 0.033 0.123∗ 0.050 0.105∗

Q4 0.985 0.988 0.032 0.038 0.090∗ 0.105∗

High 1.030 1.049 0.090∗ 0.103∗ 0.129∗ 0.083∗

39

Table VIIInstitutional Skewness Preferences and Common Risk Factors:

Time Series Estimation Results

This table reports the monthly time-series regression estimates for the 1962 to 2004 period, where thedependent variable is one of the four common risk factors (RMRF, SMB, HML, or UMD) and the primaryindependent variables are the lagged and contemporaneous measures of the ISKEW factor. To controlfor potential auto-correlation in the factor returns, I use lagged factor returns as additional independentvariables. The ISKEW factor represents the spread of a zero-cost portfolio that takes a long (short)position in stocks with the highest (lowest) idiosyncratic skewness. The composition of the zero-cost portfoliois updated at the end of each month. The idiosyncratic skewness is the third moment of the residual fromthe following regression: Rit − Rft = αi + βiRMRF t + γiRMRF 2

t + εit, where Rit is the rate of returnon stock i on day t, Rft is the riskfree rate of return on day t, RMRF t is the market return in excess ofthe riskfree rate on day t, and εit is the residual stock return on day t. The White (1980) and Newey andWest (1987) adjusted t-values of coefficient estimates are reported in the parentheses below the coefficientestimates.

Dependent variable is:

Independent Var RMRF RMRF SMB SMB HML HML UMD UMD

Constant 0.364 0.368 0.079 0.068 0.468 0.387 0.905 0.968

(1.760) (1.767) (0.561) (0.481) (3.407) (2.794) (4.784) (4.911)

Skewness Factor

ISKEW t−2 0.103 0.100 −0.086 −0.154 0.076 0.091 −0.126 −0.069

(1.038) (0.998) (−1.267) (−2.132) (1.154) (1.376) (−1.390) (−1.523)

ISKEW t−1 0.031 0.040 0.083 0.095 −0.009 −0.011 −0.125 −0.007

(0.318) (0.406) (1.230) (1.317) (−0.133) (−0.167) (−1.385) (−0.157)

ISKEWt 0.257 0.251 0.563 0.559 −0.153 −0.169 0.054 −0.132

(2.601) (2.535) (8.352) (8.330) (−2.329) (−2.593) (0.602) (−1.457)

Control Variables

Factort−2 −0.051 −0.003 0.045 −0.123

(−1.123) (−0.059) (0.997) (−1.355)

Factort−1 0.044 0.119 0.139 0.068

(0.977) (2.609) (3.051) (0.750)

Number of Months 502 502 502 502 502 502 502 502

Adjusted R2 1.53% 1.96% 13.73% 14.94% 1.51% 3.79% 0.81% 1.29%

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Table VIIITime-Series Factor Model Estimates for Size and B/M Sorted Portfolios

This table reports the factor model estimates for size and B/M decile portfolios. The decile portfolios areformed at the end of each year in December using NYSE size break-points and then held fixed throughoutthe following year. The following time-series factor model is estimated:

Rpt − Rft = αp + β1pISKEW t + εpt, t = 1, 2, . . . , T.

Here, Rpt is the rate of return on the size or B/M decile portfolio, Rft is the riskfree rate of return,ISKEW t is idiosyncratic skewness factor, and εpt is the residual return on the portfolio. ISKEW representsthe spread of a zero-cost portfolio that takes a long (short) position in stocks with the highest (lowest)idiosyncratic skewness. The composition of the zero-cost portfolio is updated at the end of each month.The idiosyncratic skewness is the third moment of the residual from the following regression: Rit − Rft =αi + βiRMRF t + γiRMRF 2

t + εit, where Rit is the rate of return on stock i on day t, Rft is the riskfreerate of return on day t, RMRF t is the market return in excess of the riskfree rate on day t, and εit is theresidual stock return on day t. The White (1980) and Newey and West (1987) adjusted t-values of coefficientestimates are reported in the parentheses below the coefficient estimates.

Decile Size Sorted Portfolios B/M Sorted Portfolios

Portfolio Constant ISKEW Adj R2 Constant ISKEW Adj R2

D1 (Low) 0.602 0.939 0.298 0.282

(2.133) (6.547) 7.86% (1.243) (2.317) 1.38%

D2 0.555 0.890 0.475 0.171

(1.996) (6.307) 7.32% (2.165) (1.530) 0.27%

D3 0.577 0.779 0.473 0.194

(2.168) (5.766) 6.16% (2.184) (1.767) 0.43%

D4 0.528 0.768 0.474 0.160

(2.058) (5.888) 6.42% (2.206) (1.462) 0.23%

D5 0.584 0.692 0.488 0.159

(2.368) (5.530) 5.68% (2.439) (1.562) 0.29%

D6 0.488 0.541 0.583 0.250

(2.071) (4.519) 3.81% (2.928) (2.470) 1.03%

D7 0.557 0.441 0.676 0.180

(2.401) (3.745) 2.58% (3.417) (1.794) 0.45%

D8 0.519 0.432 0.694 0.221

(2.297) (3.766) 2.61% (3.532) (2.208) 0.78%

D9 0.470 0.284 0.721 0.274

(2.262) (2.690) 1.26% (3.389) (2.533) 1.09%

D10 (High) 0.405 0.085 0.859 0.356

(2.062) (0.857) −0.05% (3.499) (2.853) 1.43%

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1963−1968 1969−1974 1975−1980 1981−1986 1987−1992 1993−1998 1999−2004−6

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Figure 1. Idiosyncratic skewness premium for six-year non-overlapping sub-periods. This figureshows the annualized idiosyncratic skewness premium for six-year sub-periods for the period 1963 to 2004.The idiosyncratic skewness premium is the return differential between the two extreme (the highest andthe lowest quintiles) idiosyncratic skewness quintile portfolios. To define idiosyncratic skewness portfolios,each month, I measure the idiosyncratic skewness of the entire universe of stocks for which returns data areavailable from CRSP. Next, each month, I sort stocks using their idiosyncratic skewness measures and formidiosyncratic skewness quintile portfolios. Quintile portfolio 1 consists of stocks with the lowest idiosyncraticskewness while quintile portfolio 5 contains stocks with the highest idiosyncratic skewness. Lastly, for eachidiosyncratic skewness portfolio, I compute the monthly portfolio return as value-weighted average of allstocks in the portfolio and construct a monthly portfolio return time-series. The idiosyncratic skewness isthe third moment of the residual from the following regression: Rit−Rft = αi+βiRMRF t+γiRMRF 2

t +εit,where Rit is the rate of return on stock i on day t, Rft is the riskfree rate of return on day t, RMRF t is themarket return in excess of the riskfree rate on day t, and εit is the residual stock return on day t.

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Mean Monthly Return CAPM Alpha Four−Factor Alpha−2

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Panel A: Stocks with Lower (Quintiles 1 and 2) Institutional Ownership

Mean Monthly Return CAPM Alpha Four−Factor Alpha−0.5

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Panel B: Stocks with Higher (Quintiles 4 and 5) Institutional Ownership

LowArb

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Figure 2. Institutional ownership, arbitrage costs, and idiosyncratic skewness premium. Forlow (quintiles 1 and 2; Panel A) and high (quintiles 3 and 4; Panel B) institutional ownership categories,this figure shows the raw (mean monthly return) and risk-adjusted (the CAPM alpha and the four-factoralpha) idiosyncratic skewness premium estimates, as arbitrage costs vary. Idiosyncratic volatility (varianceof the residual from a CAPM regression) is used as a proxy for arbitrage costs. The idiosyncraticskewness premium is the return differential between the two extreme (the highest and the lowest quintiles)idiosyncratic skewness quintile portfolios. The idiosyncratic skewness is the third moment of the residualfrom the following regression: Rit−Rft = αi +βiRMRF t + γiRMRF 2

t + εit, where Rit is the rate of returnon stock i on day t, Rft is the riskfree rate of return on day t, RMRF t is the market return in excess ofthe riskfree rate on day t, and εit is the residual stock return on day t. The sample period is 1980 to 2004.The institutional investor data are from Thomson Financial for the period 1980 to 2004.

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All Institutions Low Q2 Q3 Q4 High0

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Institutional Ownership

Highest Idiosyncratic Volatility Portfolio (Top Quintile)

Figure 3. Institutional ownership and under-performance of the highest idiosyncratic volatilityportfolio. This figure shows the mean monthly under-performance (negative of mean monthly return) ofinstitutional ownership portfolios within the highest (top quintile) idiosyncratic volatility (variance of theresidual from a CAPM regression) portfolio. The mean number of stocks in the portfolios are shown abovethe bars. The institutional investor data are from Thomson Financial for the period 1980 to 2004.

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