Realized Skewness and Future Stock Returns:

The Role of Information

Youngmin Choi and Suzanne S. Lee1

April 25, 2014

Abstract

This paper examines the relationship between realized daily skewness and future stock returns and

investigates the impact of information releases on that relationship. We find that there exists a negative

relationship between realized daily skewness and subsequent stock returns when there is no high-impact

information release, but that the relationship becomes positive if the realized skewness is associated with

such releases. We show that the profitability of a zero-investment portfolio can be enhanced by

incorporating this positive relationship in the presence of high-impact information into investment

strategies. As the positive relationship mainly results from riskier stocks with volume increase in the

presence of information releases, we offer an explanation for this finding based on the divergence of

investors’ opinion.

JEL classification codes: G14, G17

Key words: realized skewness, return predictability, equity market, high frequency data, investors opinion

1 Both authors are with the Scheller College of Business, Georgia Institute of Technology, 800 West Peachtree

Street NW, Atlanta, GA 30308. We would like to thank seminar participants at Georgia Tech for their comments

and suggestions. All comments are welcome and any errors are ours. Please send any correspondence to Youngmin

Choi at youngmin.choi@scheller.gatech.edu or Suzanne S. Lee at suzanne.lee@scheller.gatech.edu.

1

1. Introduction

Many studies in finance focus on the higher moments of asset return distribution and their

important implications in asset pricing. A large stream of literature has been devoted to investigating the

cross-sectional relationship between higher moments and stock returns. In particular, the skewness that

measures the asymmetry of return distribution has been an interesting topic for research. Several studies

theoretically predict and empirically confirm the negative relationship between skewness and subsequent

stock returns (see Arditti (1967), Kraus and Litzenberger (1976), Mitton and Vorkink (2007), Barberis

and Huang (2008), Zhang (2005), Kelly (2012), Conrad, Dittmar, and Ghysels (2013), and Amaya,

Christoffersen, Jacobs, and Vasquez (2013), among many others).

Despite such intriguing results on the negative relationship, important questions have yet to be

answered in this literature, including: Does this negative relationship hold in every circumstance, and

what determines this relationship? We are motivated to answer these questions because a large body of

literature suggests the importance of information releases on future stock return predictability. For

example, recent studies document the finding that stock returns exhibit momentum when price changes

are accompanied by information releases, while they exhibit return reversal if price changes are not

accompanied by information.2 Given this literature, we investigate the role of high-impact information

releases in explaining this relationship between the realized skewness and future stock returns. We define

high-impact information releases as those firm-level information releases that tend to generate (or be

associated with) unusually large price changes, namely jumps in asset prices. We consider this type of

information releases because it is well documented in the asset pricing literature that the skewness of

return distribution is better captured by asset pricing models that incorporate jumps.3 Hence, we expect

that examining the aforementioned relationship in the presence (or absence) of high-impact information

releases will allow us to discover the answer to our questions.

2 See Savor (2012), Chan (2003), Pritamani and Singal (2001), and Tetlock (2010) for references. These papers

argue that investors under-react to information-related price changes, but overreact to other shocks. 3 See Merton (1976) and Bakshi, Cao, and Chen (1997), among many others.

2

In measuring skewness in stock returns, we apply high-frequency data to estimate the realized

daily skewness, following Amaya, Christoffersen, Jacobs, and Vasquez (2013), who use this method to

present a negative relationship between realized skewness and next week’s stock returns. Another reason

why we use the realized daily skewness of a stock is because we need a daily-level skewness measure to

incorporate the impact of information releases. We consider the relationship between this skewness

measure and subsequent returns over the next one to 20 trading days in relation to high-impact

information releases. To mitigate the concern regarding the impact of microstructure noise in high-

frequency data on skewness inference, we choose our sample period from recent years (January 2005-

December 2010). This is because more recent data have far fewer infrequent trading or illiquidity

problems that may generate unnecessary noise in the high-frequency data. In estimating the effect of high-

impact information releases on subsequent stock price dynamics, we employ the Fama-McBeth (1973)

regression method.

In selecting high-impact information releases, we depend on a recent study by Lee (2012), who

used high-frequency data to identify important information releases that are more likely than others to

generate jumps in prices in individual U.S. stock markets. In particular, we select two highly influential

firm-specific information events such as earnings announcements and analyst recommendation releases.

This choice of high-impact information events is also motivated by the statistical limiting property,

whereby the realized skewness measure based on the sum of cubed returns is likely to capture only the

jump components of return distribution if we use high frequency data for estimation (see Jacod (2012)).

In addition, these two types of information are the well-documented types of information that generate

momentum or drift in stock returns after the announcements.

By including analyst recommendation reports as well as earning announcements in our

information criteria, we are able to provide extensive coverage of firm-related news. While earnings

announcements by a firm provide clear information on the cash flows of the firm, analyst

recommendation reports cover not only cash-related news but also other firm-specific news such as

management changes or unexpected financial issues. Thus, analyst recommendation reports offer

3

additional refined and comprehensive information on the firm. To our knowledge, no study in the current

literature has examined how these high-impact news releases affect the relationship between the realized

skewness capturing jumps in returns and subsequent return patterns.

Using a full sample of firm-day observations, we first examine the unconditional relationship

between realized daily skewness and subsequent stock returns over the next 1, 5, 10, and 20 trading days.

We confirm the existing evidence of a negative relationship between realized daily skewness and future

stock returns, which is consistent with Amaya, Christoffersen, Jacobs, and Vasquez (2013). However, we

find that this negative relationship no longer holds when we consider subsamples accompanied by the

aforementioned high-impact information releases. Specifically, in the subsample with information

releases, all subsequent returns over the next 1, 5, 10, and 20 trading days are positively related to the

realized daily skewness, and this positive relationship is statistically significant at the 1% level for all

cases of selected horizons.

When we examine the other subsamples without high-impact information releases, the well-

documented negative relationship between skewness and subsequent stock returns holds. In other words,

we can interpret this as investors accepting lower future returns from investments with higher positive

skewness and require higher returns from investments with negative skewness in the absence of high-

impact information releases. This is consistent with Arditti (1967), who considers the negative skewness

of a stock as a proxy for the riskiness of that stock. However, when the realized daily skewness of a stock

is associated with high-impact information on the firm, our findings suggest that the interpretation of

skewness as a risk measure turns out not to be valid. This outcome is found after controlling for the usual

informative variables such as size factor, value factor, momentum factor, and trading volume, which are

documented as well-known predictors of cross-sectional stock returns in existing literature (Fama and

French (1993), Jegadeesh and Titman (1993), and Lee and Swaminathan 2000).4

4 We also confirm our finding that different patterns between realized skewness and future stock returns hold

when we alter the frequency of analysis to the weekly level, following Amaya, Christoffersen, Jacobs, and Vasquez (2013).

4

We also examine the relationship between realized daily skewness and subsequent returns using

separate subsamples of positive skewness and negative skewness in relation to the high-impact

information releases. We find that the positive relationship in the presence of information releases is

stronger for the subsample with negative skewness than that for the subsample with positive skewness. In

other words, the momentum patterns appear to be stronger for the stocks with negative skewness

accompanied by high-impact information releases. It is also noteworthy that we observed the existing

negative relationship in the absence of information releases mainly for the stocks with positive skewness.

This evidence is consistent with the prediction by Mitton and Vorkink (2007) and Barberis and Huang

(2008), who demonstrate that assets with greater skewness have lower returns.

As regards implications of our results, we examine the profitability of an investment strategy

using these distinctive findings. First, we sort stocks based on their realized daily skewness and measure

the performance of quintile portfolios over the next 10 and 20 day. To examine the effect of the high-

impact information releases, we separate the full sample into a sample of stocks that experience high-

impact information releases and a sample of stocks that do not experience any such releases. We confirm

that the strong negative relationship between realized daily skewness and future stock returns prevails

mostly in the sample without information releases. We again find stronger positive relationship between

realized daily skewness and future stock returns in the sample with information, and the abnormal return

from a zero-investment strategy that is long the highest quintile portfolio and short the lowest quintile

portfolio, based on the realized skewness and the presence of information, provides statistically

significant returns even when we take into account other important risk factors. Furthermore, we provide

evidence that the profitability of a zero-investment portfolio can be enhanced by incorporating the

presence of high-impact information into investment strategies.

Finally, we offer explanations for the relationship between skewness and subsequent return that

depends on the presence of information releases. Since we expect the release of high-impact information

to influence the opinion of investors in the financial markets, we test how realized skewness of stock

returns is related to measures of divergence of investors’ opinion. Using several measures of divergence

5

of opinion, daily turnover, market-adjusted turnover, unexplained trading volume, or change in trading

volume, we find that realized skewness is negatively related to these measures when there are high-impact

information releases, while it is positively related to divergence measures when there are no such

information releases. In addition, we find that measures of divergence of investors’ opinion increase in

high-impact information sample compared to no-information sample. Consistent with Miller (1977) and

Diether, Malloy, and Scherbina (2002), our findings suggest that riskier stocks with greater divergence in

investors’ opinion around information releases have lower subsequent returns. Investors will not be

rewarded for bearing risk (measured by the negative realized skewness) if there are high-impact

information releases because prices reflect the more optimistic valuation of investors who hold these risky

assets and suffer losses in the subsequent periods.

Overall, this paper contributes to several different stems of literature in finance. Our study is the

first in the literature to document the finding that the existing negative relationship between skewness and

subsequent stock holds only in the absence of high impact information releases, while the relationship

becomes positive in the presence of such information releases. Our finding is unique in that it is based on

realized daily skewness using high-frequency data, which can capture different part of the returns

distribution at the micro level. Moreover, our study contributes to the literature on information and return

predictability by showing that return reversal patterns is stronger for stock with positive skewness in the

absence of information releases, while momentum pattern is stronger for stocks with negative skewness

around information releases. Furthermore, we offer an explanation for the new finding of a positive

relationship in the presence of high-impact information releases. We also contribute to the literature on

divergence in investors’ opinion by providing new evidence that the skewness is negatively related to the

increase in divergence of opinion only around the information releases. We believe that this negative

skewness may have contributed to the evidence of lower returns documented in the related literature, such

as Diether, Malloy, and Scherbina (2002).

6

The remainder of this paper is organized as follows. Section 2 presents the data and sample

construction. Section 3 presents empirical results of estimations, and Section 4 offers a potential

explanation for the findings. Finally, Section 5 concludes.

2. Data and Sample Description

We analyze all stocks listed in the Trade and Quote (TAQ) database. The sample period for our

analysis is from January 3, 2005 to December 31, 2010. We choose to consider this recent sample period

to mitigate concerns regarding the impact of market microstructure noise in high-frequency data on

inference by higher moments as data from recent years have much less infrequency trading and fewer

illiquidity problems that may generate unnecessary noise in the data.5 To calculate higher moments, we

record prices of all stocks in the TAQ database at five minute intervals starting from 09:30 EST until

16:00 EST and construct the five-minute returns as the difference between log prices with five-minute

marks, as in Andersen, Bollerslev, Diebold, and Ebens (2001). To ensure sufficient liquidity and filter out

possible noise in high-frequency data, we require a stock to have at least 80 transactions per day and use

the recorded price close to the five-minute interval time grid. In addition to this requirement, we further

exclude stocks that have a price of less than five dollars.

We also obtain data on market capitalizations and trading volumes from the Center for Research

in Security Prices (CRSP) database. We also use data from the CRSP database to compute several

measures of divergence in investors’ opinion such as daily turnover, market-adjusted turnover, or

unexplained trading volume. Our accounting data, such as book values of individual firms, are obtained

from the COMPUSTAT database. For returns over horizons beyond one trading day, instead of using

high-frequency returns from the TAQ database, we use daily returns from the CRSP database for

corresponding firms and dates and calculate returns over longer horizons. Given all these filtering

5 The robustness of the realized higher moment inference to noise is also verified by simulation in Amaya et al.

(2013).

7

requirements, the total number of companies covered in our sample varies, ranging from 3,443 to 6,387

per year, depending on changes in market conditions over our sample period.

As regards the five-minute price records, we define the five-minute log return as the difference

between log prices observed at five-minute intervals. The the l-th intraday return for the k-th firm on day t

is first constructed by

��,�,� = log��,�,�� � − log��,�,��, (1)

where ��,�,� is the l-th intraday price of the k-th firm observed on day t, and n is the number of intraday

returns observations in a day. Since we record five-minute prices starting from 09:30 EST to 16:00 EST,

for each day, we have � = 78. Following Amaya, Christoffersen, Jacobs, and Vasquez (2013), who

document the negative relationship between realized skewness and the cross-section of equity returns on a

weekly horizon, we apply the similar methodology to construct other realized higher moments such as

realized daily skewness and realized daily kurtosis. That is, we construct realized daily skewness (RDSk,t)

for the k-th firm on day t by

����,� = √�∑ ��,�,������

����,���

, (2)

where the realized daily variance (����,�) for the k-th firm on day t is used to standardize the sum of

cubed intraday 5 minute returns and is calculated with the sum of squared intraday 5-minute returns as in

����,� =���,�,���

���, (3)

following the well-known realized variance literature (Andersen and Bollerslev (1998) and Andersen,

Bollerslev, Diebold and Labys (2003)). A measure of realized daily kurtosis (����,�) for the k-th firm on

day � is computed as

����,� =�∑ ��,�,� ��������,��

. (4)

8

Table 1 presents the time-series summary statistics of means and medians by year for variables

considered in this paper. This table shows that the number of stocks in our sample decreased significantly

during the period of financial crisis. For example, during the year 2006, the number of stocks included is

6,387, while this number is 3,703 in the year 2008, during which our sample selection criterion filters out

noisier data. We also observe much higher average realized daily variance of 0.30% in the year of 2008

when compared to 0.09% in the years 2006 or 2007. The realized daily skewness is negative in general.

The realized daily kurtosis is shown not to vary as much as volatility. Overall, the distribution of asset

returns using high-frequency data shows time-varying variance, negatively skewed tails, and high kurtosis.

The other control variables for our regression analysis, such as the ratio (in percentage) of trading volume

to total shares of outstanding and momentum returns also show some time variation by year, as expected.

We also observe a recent finding in the literature on asset pricing showing the devastating performance of

momentum strategy after the financial crisis.6

To examine first the relational patterns between higher moments and stock returns without

conditioning on the presence of information, we construct portfolios by sorting stocks into deciles based

on realized daily volatility, realized daily skewness, and realized daily kurtosis. The sorting procedure is

repeated every day during our sample period between January 2005 and December 2010. Table 2 shows

the equal-weighted characteristics of these decile portfolios. Panel A, B, and C present time-series

averages for portfolio characteristics sorted by realized daily volatility, skewness, and kurtosis,

respectively. Since we are interested in the relationship between realized moments and subsequent returns,

we report averages for the decile portfolio returns over the subsequent month in next 20-day return. In

particular, Panel B indicates that while contemporaneous return is positively related to realized skewness,

returns over the subsequent month tend to be negatively related to realized skewness, which is consistent

with the findings of Amaya, Christoffersen, Jacobs, and Vasquez (2013). However, we do not observe

any distinct relational pattern between realized kurtosis and subsequent future returns, which is

inconsistent with Amaya, Christoffersen, Jacobs, and Vasquez (2013). Even when we conduct the same

6 See Daniel, Jaganathan, and Kim (2012) and Daniel and Moskowitz (2013).

9

analysis with a weekly sorting frequency, which is identical to the approach of Amaya, Christoffersen,

Jacobs, and Vasquez (2013), the general relational pattern between realized skewness and next week’s

return remains similar.

We confirm existing evidence and find that the negative relational pattern between realized

skewness and subsequent return does not depend on the choice of sample period. As we shall see in

Section 3, the negative relationship between realized daily skewness and future stock returns is

statistically significant when we perform the Fama-MacBeth regressions. Although Table 2 shows the

results with the return calculated over the next month for the purpose of data description, we also confirm

that this negative relationship holds for subsequent returns over several holding periods of one to 20

trading days. We will get back to this result in our main analysis in Section 3.

In selecting high-impact information releases, we depend on a recent study by Lee (2012), who

used high frequency data to identify important information releases that are more likely than others to

generate large intraday price changes (namely jumps in prices) in individual U.S. stock markets. In

particular, we choose to use the two most influential information events documented therein, namely

earnings announcements and analyst recommendation releases. This choice is also motivated by the

statistical limiting property whereby the realized skewness measure (based on the sum of cubed returns) is

likely to capture only the jump component of return distribution if high frequency data are used for

skewness estimation (see Jacod (2012)). The other reason why we select these two types of information is

that these naturally cover most firm-related news about a firm. While earnings announcements provide

valuable information about cash flow, analyst reports offer extensive coverage of a wider array of

information (see Savor (2012)). Thus, by including not only earnings announcements but also analyst

reports on a firm, we expect to consider a comprehensive set of information about the firm.

In order for us to examine how these high-impact news releases affect the relationship between

skewness capturing jumps in prices and the subsequent return dynamic, we create separate subsamples

with and without these influential firm-specific information releases. Since the chosen information events

are firm-specific, we first collect all the firm-date observations for both information events from the

10

International Brokers’ Estimation System (I/B/E/S) from January 2005 to December 2010. Although we

use high-frequency data to calculate realized skewness and other higher moments, our analysis does not

depend on time-stamps at intraday level of these information releases. This is because our study considers

how realized daily skewness accompanied by information releases at the daily level affect returns over the

next one to 20 trading days. Hence, the intraday time-stamp delay concern raised by Bradley, Clarke, Lee,

and Ornthanalai (2014) is not an issue for our study. On the other hand, several studies report that these

information events tend to occur overnight.7 When firm-related events occur during the day, analysts

usually examine the issues during business hours and release their reports on the same day or one day

after the event. In some cases, analysts can release their reports about a firm before the issue is released to

the public in order to offer their expectations. For all of these reasons, when we create our dummy

variable for information release dates, we cover one day before and after information release dates which

are recorded in the I/B/E/S database.

Table 3 present the time-series summary statistics (by year) for all firms in our full sample, firms

with earnings announcements, firms with analyst recommendation releases, firms with both types of

information releases, and firms without the information releases. For each year, we list the total number

of all firm-trading day observations and average firm sizes. Roughly, we have more than four million

firm-date observations in our full sample. We then separately report those statistics for the subsamples

accompanied by earnings announcements and those accompanied by analyst recommendation releases.

Since we are not interested in the separate impact of earnings and analyst recommendation news events

on the relationship between realized skewness and subsequent stock returns, we combine the two

subsamples and call it the “Information” sample, with the rest of the sample becoming the “No-

information” sample. The fact that earnings announcements and analyst recommendation releases can

confound each other is not a concern in this study as we are interested in how these types of influential

information releases affect the subsequent stock return patterns. It is noteworthy that the Information

7 Altınkılıç and Hansen (2009) report that the percentage of overnight recommendation releases is 61%. Bradley,

Clarke, Lee, and Ornthanalai (2014) report that this percentage is over 70% and earnings releases occur overnight in over 80% of cases after the year 2003.

11

sample includes larger firms than the No-information sample, with the average size of firms included in

the Information sample being $8,761.97 million while that for the No-information sample is $5,214.45

million. Although we find this difference in average firm size between the two subsamples, we show later

that the determinant of different relational patterns is not purely due to the size issue.

3. Realized Skewness and Future Returns

3.1. The role of information releases on the relationship between skewness and future

returns

In this section, we assess the cross-sectional relationship between the realized skewness and

future stock returns by conducting various cross-sectional regression analyses with several control

variables. Then, in order to examine how high-impact information releases affect the relationship, we take

two approaches. Using the subsamples (the Information and No-information samples) presented in Table

3, we first conduct the regression analyses separately and examine the differences. The second approach

is to examine the interaction term of daily realized skewness with a dummy variable to identify the

additional impact of the presence of information releases using the full sample. Both approaches offer

consistent results, indicating that the presence of high-impact information matters for the relationship.

Specifically, the regression specification we consider first is as follows:

�"��,��#,��$ = % + '����,� + ()*�,� + +�,��#,��$ , (5)

where �"��,��#,��$ is the cumulative return of the k-th stock over a period starting on day t+i and ending

on day t+j, ����,� is the realized daily skewness of the k-th stock returns on day t, calculated as in

equation (3), *�,� represents a vector of several control variables for the k-th firm observed at the end of

day t, and +�,��#,��$ is an error term. As it is well-documented in the literature that size, book-to-market,

and momentum predict the cross-section of stock returns (Fama and French (1992), Fama and French

(1993) and Jegadeesh and Titman (1993)), we include log size (log(ME)), log book-to-market ratio

(log(BM)), and a cumulative percentage return from previous 12 months to previous 2 months as of day t

12

(Mom) in the set of control variables, *�,�. As other papers (Lee and Swaminathan (2000) and Conrad,

Hameed, and Niden (1994)) present evidence of a relationship between trading volume and future stock

returns, we also include trading volume (vol pct) as a ratio (in percentage) of trading volume relative to

total shares outstanding. By including these control variables in all regressions, we ensure that our

findings are not due to the relationship between stock returns and other firm characteristics. To estimate

the regression equation, we employ the Fama and MacBeth (1973) approach.

Table 4 reports the coefficient estimates for four cross-sectional regressions with different

horizons for subsequent returns calculations. We consider the horizons for subsequent returns of a stock

from one trading day to 20 trading days in order to see whether the effect becomes stronger or weaker

over time. Panel A provides results for all firm-trading day observations. It confirms the negative

relationship between realized skewness and subsequent returns, consistent with the evidence documented

in Amaya, Christoffersen, Jacobs, and Vasquez (2013), who studied weekly subsequent returns with the

realized daily skewness averaged at the weekly frequency. All coefficient estimates for the realized daily

skewness are negative and statistically significant at the 1% level for subsequent returns over the next 5 to

20 trading days. It also indicates that the absolute magnitude of these estimates becomes larger and the

significance stronger over longer horizons. In general, the evidence presented in Panel A is consistent

with Arditti (1967), who identifies total skewness as one of risk measures that explain returns on equity. It

is also consistent with recent studies by Mitton and Vorkink (2007), Barberis and Huang (2008), and

Boyer, Mitton, and Vorkink (2010), who suggest that stocks with high idiosyncratic skewness should

have low expected returns. Kraus and Litzenberger (1976) and Harvey and Siddique (2000) present

similar views, although they consider systematic skewness as a risk measure.

To illustrate the effect of information releases on this relationship, we run the regressions with the

same specification as in equation (5) but separately with the Information and No-information samples,

which we present in Table 3. Panel B and Panel C in Table 4 present the results of these two regression

analyses, respectively. Comparing Panel B and Panel C, we discover that the aforementioned negative

relationship no longer holds when we consider the subsample with the high-impact information releases.

13

Specifically, all the subsequent returns over the next 1, 5, 10, and 20 trading days are positively related to

realized daily skewness, and this positive relationship is statistically significant at the 1% level for all

cases with different horizons.

When we study the other subsample (without the information releases), the negative relationship

continues to hold for all four different horizons. We also observe that Panel C indicates a stronger

negative relationship without information releases when compared to Panel A (with the full sample),

measured both as the absolute magnitudes of coefficient estimates and statistical significance. In other

words, when there are no influential information releases about the firm, investors who invest in stocks

with lower realized skewness are compensated with higher subsequent returns. This finding is consistent

with the traditional risk-return framework.

Overall, our findings in Panel B and Panel C of Table 4 suggest that the negative realized daily

skewness of a stock returns distribution can be considered as a proxy for riskiness of the stock only when

there is no firm-related information release. This view is well supported by a strong and significant

negative relationship between realized skewness and subsequent returns. Contrary to this general

understanding, a positive relationship between realized daily skewness and future stock returns in the

information sample suggests that the conventional view of negative skewness as a risk measure does not

hold when there are influential firm-related information releases. We provide a potential explanation for

this unexpected relationship in the presence of high impact information releases in Section 4.

As a second approach, we examine the effect of information releases on subsequent stock return

dynamics with an alternative regression specification. Given the previous results reported in Table 4, we

expect the presence of information releases to be the key determinant of relationship between the realized

daily skewness and subsequent future returns. Hence, we construct a dummy variable (-�,#�./,�) to be set

equal to one if there are high-impact information releases for the k-th firm on day t or to zero otherwise.

Using this dummy variable, we run the regressions with the following specification:

�"��,��#,��$ = % + '����,� + 0����,� ∗ -�,#�./,�� + ()*�,� ++�,��#,��$, (6)

14

where �"��,��#,��$ is the cumulative return of the k-th stock over a period starting on day t+i and ending

on day t+j, ����,� is the realized daily skewness of the k-th stock returns on day t, calculated as in

equation (3), *�,� represents a vector of several control variables for the k-th firm observed at the end of

day t, and +�,��#,��$ is an error term. The components of *�,� are the same as those used in equation (5).

We add a new interaction term ����,� ∗ -�,#�./,�� to identify the difference in the relationship between

the skewness and future returns depending on the information releases. To estimate this regression, we

employ the regression for the full sample only because the dummy variable expects to capture the effects

of information releases.

We provide the coefficient estimates for this alternative regression specification in Table 5. The

first coefficient of interest in this table is ', which represents the relationship between realized daily

skewness and subsequent returns for no-information cases. The results in Table 5 show that coefficient '

estimates are negative for all horizons under consideration. They are also statistically significant at the 1%

level for the future return horizons over 5 trading days up to 20 trading days. The absolute value of

coefficient estimates increases as we expand the return horizons. For example, for future returns over 5

trading days, the coefficient associated with the realized daily skewness is -3.3814 with a t-statistics of -

4.61, whereas for the 20 trading day horizon, the coefficient is -6.0761 with a t-statistics of -5.01, which is

consistent with the conclusion we obtained from Table 4 using the sample without information release.

Another regression result to which we should pay attention in Table 5 is the sum of the two

coefficients β+γ, which indicates the effect of the information on the relationship, as 0 represents the

difference of the effect due to the presence of information. The 0 coefficient estimates are positive and

statistically significant at the 1% level for all horizons. Furthermore, the coefficients of β+γ are positive

for all horizons. We also note that the absolute value of coefficient estimates increases as we increase the

horizons, suggesting stronger momentum return patterns over longer horizons up to 20 trading days,

which again is consistent with results in Table 4. This finding is also consistent with those of Savor

(2012), who uses analyst recommendation reports as a proxy for publicly available information and

15

observes that major daily price changes with information are followed by drift while those without

information exhibit reversals. All of these findings from our alternative specifications suggest the similar

conclusion.

We consider other specifications for the same hypothesis we study in Tables 4 and 5. For

example, we also take into account the autocorrelation of returns by including the daily returns of the firm

on the corresponding day t as one of the control variables in all of our regression analyses, and find that

the results are consistent with those reported in Tables 4 and 5. We also include (but do not report) the

dummy variable for the presence of other types of information releases in our regression specifications.

However, our main results (documented above) are robust. Other specifications considered (but not

reported here) are for the subsamples with other types of high-impact information releases, such as

Federal Open Market Committee (FOMC) announcements, nonfarm payroll employment reports, jobless

claims, etc. These types of news are also documented as high-impact information news (see Lee (2012),

Lucca and Moench (2011), and Savor and Wilson (2013)), and we included them as additional sources of

high-impact information. However, we confirm that earnings announcements and analyst

recommendation reports, which are fundamentally related to firm-specific news, are main contributors to

our main findings in Tables 4 and 5 and that other information releases do not exhibit the patterns we

observe in Tables 4 and 5. Therefore, we conjecture that the information that matters for our findings

could be related to cash flow news rather than discount rate news.

3.2. Subsample analysis: Positive and negative skewness samples

In this subsection, we disentangle the source of the relationships we documented earlier by

performing additional subsample analysis. We separate the full sample into positive and negative realized

daily skewness subsamples in order to investigate any asymmetric subsequent responses by stock markets.

The basic estimation method is identical to that used in the previous regression analyses.

Table 6 reports the coefficient estimates for the regression analyses for the positive skewness

sample in Panel A and those for the negative skewness sample in Panel B. As our main objective is to

16

investigate the effect of the presence of high-impact information on the relationship between realized

skewness and future stock returns, we further separate the positive skewness sample and the negative

skewness sample into one with information releases and the other one without information release.

Results shown in Table 6 provide evidence that our finding of a negative relationship between realized

skewness and subsequent stock returns comes mainly from the positive skewness sample in the absence

of information releases. This indicates that the skewness (or lottery) preference of investors in individual

stock markets appear to be the main driver of the negative relationship between realized skewness and

future returns rather than compensating investors who take more risk by investing in stocks with negative

skewness. In particular, this finding further suggests that investors show stronger overreaction to

unusually positive jumps in prices without any substantial firm-specific information releases, which

generate lower subsequent returns for positively skewed stocks.

Contrary to the finding of a negative relationship between realized skewness and future stock

returns, the positive relationship between realized skewness and subsequent stock returns is observed

mostly in the negative skewness sample in the presence of influential information releases, as documented

in Table 6. This implies that in general, the skewness of stock returns cannot be regarded as a proxy for

risk when there are news releases. In particular, the overvaluation of the riskier stocks with negative

skewness turns out to be the main driver of the positive relationship. This finding further suggests that

investors show stronger under-reactions to negative jumps in stock prices in the presence of influential

information releases, such that the subsequent returns of negatively skewed stocks tend to be lower later.

Although most existing research on the negative relationship between skewness and stock returns

does not thoroughly examine this asymmetric feature we document in this subsection, our findings allow

us to distinguish the source of the relationships. To our knowledge, ours is the first empirical study using

realized skewness to illustrate that positively skewed stocks are the main driver for the existing evidence

of a negative relationship found in the absence of information releases. Moreover, the over-valuation of

negatively skewed stock in the presence of information releases is also new to the literature.

17

3.3. Implications: Cross-section of stock returns and profitability

The regression analysis in the previous subsection suggests that the presence of high-impact

information leads to different relational patterns between realized daily skewness and future stock returns.

That is, the relationship is negative when there are no high-impact information releases, while it becomes

positive when there are high-impact information releases. In this section, we study the implications of this

finding for practical applications. We first study the distinctive abnormal cross-sectional return patterns

generated from the quintile portfolios of stocks sorted according to realized skewness. Second, we test

whether our findings regarding these distinctive patterns lead to profitable a zero-investment strategy

using the calendar-time portfolio analysis method.

To implement the first sorted portfolio approach, we compute the realized daily skewness for all

stocks in our full sample, assign these stocks into quintiles on the basis of their realized daily skewness

measures, and examine subsequent 10- or 20-trading day returns of these quintile portfolios. We also

conduct the same analysis using the subsample with high-impact information (Information sample) and

the subsample without information (No-information sample). For each subsample and each quintile

portfolio, we estimate raw returns and alphas of the 10-day and 20-day subsequent returns from the

CAPM, Fama and French (1993) three-factor model, and Carhart's (1997) four-factor model. The results

of this analysis are provided in Table 7 along with associated t-statistics. In general, not only raw returns

but also the risk-adjusted returns of quintile portfolios tend to show clear increasing (Panel B) or

decreasing patterns (Panel C) as a function of realized daily skewness. This indicates that the realized

daily skewness of a stock explains the cross-section of stock returns even after incorporating the common

risk factors of market, size, value, and momentum.

A more intriguing finding from Table 7 is the opposite patterns shown in Panel B and Panel C. As

we observed in the previous section, this difference in return patterns between the information sample and

the no-information sample also suggests that the relationship between realized daily skewness and the

subsequent returns of the quintile portfolios becomes opposite depending on the presence of high-impact

information about the firm. Clearly, from Panel C of Table 7, decreasing patterns of alphas for quintile

18

portfolios imply that the negative realized daily skewness of a stock can be considered a risk factor, and

investors are willing to accept lower subsequent returns from positively skewed stocks when there are no

high-impact information releases about the firm.

It is noteworthy from Panel B of Table 7 that the positive and statistically significant alphas of the

long-short portfolio (which buys stocks in the top quintile and shorts stocks in the bottom quintile) are

mostly due to the low alpha of the bottom quintile portfolio. This demonstrates that stocks with lower

realized daily skewness are not compensated with higher subsequent returns if these stocks are

accompanied by high-impact information releases. This is also consistent with our previous finding in

Table 6 that a positive relationship mostly exists in the sample of negative skewness with information

releases. As this finding is further related to our potential explanation on the positive relationship, we will

provide more detailed explanations about this finding in Section 4.

Given the findings on different patterns between realized daily skewness and subsequent returns

depending on the presence of information releases, we might naturally ask whether these statistically

strong relationships could lead to arbitrage opportunities after taking account common risk factors. Thus,

as a second approach to examining the implications, we test whether our finding of distinctive patterns in

the relationship leads to a profitable trading strategy by a calendar time portfolio analysis. In this analysis,

we first assign each stock in the full sample into one of two portfolios on the basis of the sign of realized

daily skewness. That is, at each point in time, one portfolio consists of stocks that experience negative

realized daily skewness, while the other portfolio consists of stocks with positive realized daily skewness.

The return of each portfolio is computed as an equal-weighted average of returns of stocks in the portfolio

over the next 5 days, 10 days, and 20 days. We then construct zero-investment portfolios by taking a long

position on the portfolio with negative skewness and a short position on the portfolio with positive

19

skewness. We also conduct the same analysis using the subsample with high-impact information

(Information portfolio) and the subsample without information (No-information portfolio).8

From this analysis, we expect the no-information portfolio, which takes a long position on stocks

with negative skewness and a short position on stocks with positive skewness, to show positive abnormal

returns. By contrast, the information-based portfolio is expected to show negative abnormal returns since

we documented that stocks with low realized daily skewness obtain lower returns when they experience

high-impact information releases. To test these hypotheses, we estimate the following time-series

regression using the returns for the aforementioned zero-investment portfolios.

��,��$2/3� = %2/3� + ')2/3� *�,��$ + +�,��$2/3� (7)

where ��,��$2/3� is a return of the portfolio from the day of the portfolio construction at day t to day t+j,

%2/3� measures the abnormal return, *�,��$ is a set of common risk factors, including the market excess

returns, the size factor, the value factor, and the momentum factor for the corresponding time period from

day t to t+j, and +�,��$2/3� is an error term.9 By testing whether the intercept (%2/3�) is significantly different

from zero, we can determine whether zero-investment trading strategy would be profitable.

The coefficient estimates from the regression specification (7) for this calendar time portfolio

analysis are provided in Table 8. As a robustness check, we provide the results for the CAPM, Fama and

French (1993) three-factor model, and Carhart's (1997) four-factor model to ensure that the observed

returns are not due to other existing risk factors. Panel A of Table 8 reports the coefficient estimates for

zero-investment based on the sign of the realized daily skewness from the full sample. The coefficient

estimates of alpha (%2/3�) suggest that the zero-investment trading strategy is profitable for 5-, 10-, and

20-trading day horizons. For a 20-trading day investment horizon, the portfolio that takes a long position

on stocks with negative realized daily skewness and a short position on stocks with positive realized daily

skewness earns a positive and statistically significant abnormal return of 11.0971 basis points. This

8 We also conduct a similar calendar time portfolio analysis by sorting stocks according to the daily realized

skewness instead of the signs of realized daily skewness, and we find similar results. The related results are available upon request.

9 All the four factors used are from the Kenneth French’s website.

20

positive and significant abnormal return of the zero-investment portfolio implies that the alpha of this

portfolio mainly results from the negative relationship.

However, when we take into account the presence of high-impact information releases, we are

able to enhance the profitability of zero-investment trading strategy. Panel B provide the abnormal returns

from a combined zero-investment portfolio. This combined portfolio takes a long position of the zero-

investment strategy on the No-information sample and a short position on the Information sample. In

other words, it takes long (short) positions on negatively (positively) skewed stocks from the No-

information sample and positively (negatively) skewed stocks from the Information sample. By taking

into account the presence of high-impact information, the abnormal return for 20-trading day horizon

from the zero-investment portfolio is increased from 11.0971 basis points to 17.2706 basis points. Panels

C and D separately report which zero-investment portfolio generates abnormal returns. We note here that

we use all stocks in the market by categorizing them into positive and negative skewness samples in

creating the zero-investment strategy. Panel C and D suggest that incorporating the signs of skewness into

portfolio formation generates statistically significant abnormal returns only in the No-information sample.

We do not observe significant abnormal returns from the Information sample, although the negative alpha

is consistent with the evidence of positive relationship documented earlier and has contributed to the

enhancement of profitability from the combined portfolio.

As we observe the positive relationship between realized daily skewness and subsequent returns

when there are high-impact information is mostly due to largely negatively skewed stocks (see Table 6

and Panel B of Table 7), we further show that we can enhance the profitability of a zero-investment

strategy if we use extremely skewed stocks. In particular, we sort stocks according to their realized daily

skewness and construct two zero-investment portfolios by taking a long (short) position on stocks in the

top percentile and short a (long) position on stocks in the bottom percentile from the Information (No-

information) sample. The abnormal returns on the zero-investment portfolios using extreme samples in

the Information sample and the No-information sample are provided in Panels E and F of Table 8. While

the magnitudes of abnormal returns from the No-information sample in Panel F remain around the same

21

level, those from the Information sample in Panel E dramatically increase. This increase of abnormal

returns from the Information sample when we use extremely skewed (measured by realized daily

skewness) stocks also demonstrates that the positive relationship between realized daily skewness and

subsequent stock returns in the presence of high-information strongly holds for the stocks with extremely

negative realized daily skewness. The magnitude of abnormal returns from the zero-investment portfolios

using extreme samples increases as the holding period increases. Overall, we prove that we can further

enhance the profitability of the zero-investment trading strategies by taking account the presence of high-

impact information and by using extremely skewed samples.

In this section, we demonstrate an implication of our findings. Specifically, we show that the

positive relationship between realized daily skewness and subsequent returns conditional on the presence

of high-impact information helps explain a cross-section of stock returns and that this anomaly might be

exploited to provide abnormal returns. We also present the evidence of a negative relationship in the

cross-section of stock returns when there is no information release. Furthermore, these distinctive

relational patterns can be exploited to generate abnormal returns from a zero-investment trading strategy,

and the profitability of the zero-investment portfolio can be significantly enhanced if we take into account

the effect of the presence of information on the relational patterns. In addition, as we witness that the

positive relationship comes from largely negatively skewed (measured by realized daily skewness) stocks,

the profitability of the zero-investment strategy can be dramatically increased when we use extremely

skewed stocks in constructing the portfolios.

3.4. Robustness Analysis

In this subsection, we employ additional regression tests to prove that our results are robust. As

the realized daily skewness of stock returns is computed from high-frequency time-series of returns that

may be subject to noise in the data or to information asymmetry, we might suspect that our main findings

are mainly driven by small companies even though we controlled for the firm size in every specification

we employed in this study. Thus, we perform subsample analyses and present our finding that a positive

22

relationship between realized daily skewness and subsequent stock returns (conditional on the presence of

high-impact information release) strongly holds for small firms as well as large firms in Table 9. In this

analysis, we separate our full sample into two subsamples: one with firms having above-median market

capitalization, the other with firms having below-median market capitalization. For these two subsamples,

we employ the regression specification (6) to detect any distinctive pattern between realized skewness and

subsequent returns depending on high-impact information releases.

As we can expect that the relationship is stronger for small firms, the magnitude of coefficient

estimates for interaction term (RDS� ∗ -info) for small firms is larger than that of estimates for large firms.

This result indicates that our finding of a positive relationship in the presence of information appears to be

stronger for smaller firms. This result also supports the explanation for the positive relationship we offer

in Section 4. However, the results of the regressions for large firms shown in Table 9 still present strongly

positive and significant coefficient estimates. This suggests that the positive relationship in the presence

of influential information releases is not driven by noise or information asymmetry as large firm also

presents similarly significant evidence.

Our next robustness check uses data with a weekly horizon. Our main results are based on

samples collected at a daily frequency because of the availability of high-impact information at that

frequency. Although we estimate the realized higher moments using intraday high-frequency data, we

study the changes in the relationship between the realized daily skewness and the returns over the next

several trading days depending on the presence of daily information releases. We can also test the same

hypothesis to see whether this change in the relationship holds for a weekly horizon. Given the evidence

documented by Amaya, Christoffersen, Jacobs, and Vasquez (2013), who report a very strong negative

relationship between the realized skewness aggregated over a week and the subsequent week’s returns,

we also perform a robustness test if the presence of information releases affects the negative relationship

at a weekly frequency.

Table 10 reports the coefficient estimates for the following specifications for each week w:

23

�"��,4� = % + ' ��56�,4 + '���7"8�,4 + '���+���,4 + 0)*�,4 + +�,4� , (8)

where �"��,4� is the weekly return of the k-th firm for the subsequent week w+1, and *�,4 denotes

characteristics of the k-th firm at the end of week 8, as control variables such as firm size, book-to-

market, and number of intraday transactions. For each week w, the three higher moments are computed

from Wednesday to the following Tuesday for each firm as a weekly average over a weekly horizon. We

use this approach following those used in Amaya, Christoffersen, Jacobs, and Vasquez (2013) for

comparison purposes. We estimate the parameters using Fama and MacBeth (1973) cross-sectional

regressions and report the estimates along with t-statistics in parentheses in Table 10.

Using the full sample, we confirm the negative relationship between realized skewness and the

next week’s return. The regression coefficient is statistically significant at the 1% level. Then, we perform

the same analysis with a weekly horizon using the subsamples with and without information releases

during the corresponding week. For the subsample with no information releases during the week, the very

strong negative relationship continues to hold, which is consistent with the findings of Amaya,

Christoffersen, Jacobs, and Vasquez (2013), whereas for the subsample with information releases, we no

longer observe this negative relation. The coefficient estimate '�for the realized skewness does not show

any statistical significance. That is, while the negative relationship continues to hold for times with no

information releases, the significant positive relationship we observed at a daily frequency does not

appear to hold with data aggregated at a weekly frequency. We identify this discrepancy in the results

with daily and weekly frequency because the high-impact information considered in this paper is expected

to influence abnormal returns distribution over the short-term such as within a day in individual stock

markets (possibly generating jumps at intraday level, as shown in Lee (2012)), and hence its impact is

expected to weaken over the longer weekly horizon.

4. Potential Explanation: Divergence in Investors’ Opinion

24

So far, we document the finding that the relationship between realized skewness and future stock

returns is subject to the presence of high-impact information releases and further demonstrate its practical

implications for the profitability of investment strategies. In this section, we explain the underlying reason

for our finding.

The negative relationship between realized skewness and subsequent stock returns when there are

no influential information releases is consistent with both previous empirical findings and theoretical

predictions by many previous studies (see Arditti (1967), Mitton and Vorkink (2007) and Barberis and

Huang (2007) for total skewness including idiosyncratic skewness, and Kraus and Litzenberger (1976)

and Harvey and Siddique (2000) for co-skewness). To explain the negative relationship using positively

skewed stock returns, it has been shown in the literature that some investors have a preference for positive

skewness, which presents lottery-like returns properties. Therefore, they tend to place higher value on

positively skewed stocks and are willing to accept lower future returns from them. On the negative side,

risk-averse investors are in general reluctant to undertake investments with a greater possibility of

extreme losses measured by negative skewness. In this case, they are likely to demand greater

compensation or rewards for such unusual risk. Our contribution to this line of literature is that these

existing explanations cannot support the evidence of the positive relationship we find between the

skewness and future returns when there are high-impact information releases. From our subsample

analysis, we also provide new evidence that this negative relationship tends to be mainly driven by the

skewness preference, as indicated in Panel A of Table 6.

More importantly, in this section, we offer an explanation for the positive relationship between

skewness and future stock returns. Given that we discover that the differentiating factor for this change in

the relationship was the presence of high-impact information releases, we conjecture that the changes in

consensus among investors in response to high-impact information releases may affect temporary changes

in stock returns distribution and subsequent investment behavior. To test our conjecture, we examine

changes in investors’ opinion in the samples with and without information releases as well as their impact

on the realized daily skewness to provide a plausible explanation for our findings.

25

Table 11 shows how the divergence in investors’ opinion changes depending on the presence of

high-impact information releases. As many existing papers document the fact that the trading volume of a

stock is a good proxy for measuring divergence of opinion among investors (see Chen, Hong, and Stein

(2001), Garfinkel and Sokobin (2006), and Garfinkel (2009)), we use five measures of divergence in

investors’ opinion using the trading volume of a stock: daily turnover, market-adjusted turnover, change

in market-adjusted turnover, unexplained (unexpected) trading volume, and change in trading volume.10

Daily turnover for the k-th firm on day t is defined as the ratio of the firm’s daily trading volume on day t

to total number of shares outstanding on day t:11

�9:6;<+��5="��,� =<ℎ"7�ℎ?:�@)A-9:6;��9-:�B=56+@"�<ℎ"7�ℎ?:�@)A�ℎ9�"A5+�A�9�-:�B� (9)

Market-adjusted turnover is defined as the difference between the k-th firm’s daily turnover and daily

market-wide turnover on day t:

CD<E�,� =<�9-:�B=56+@"�,�

�ℎ9�"A5+�A�9�-:�B�,� −<�9-:�B=56+@"FG3�H�,�

�ℎ9�"A5+�A�9�-:�BFG3�H�,� (10)

Change in market-adjusted turnover is the difference in market-adjusted turnover between day t and day t-

1. Finally, we use the standardized unexplained (unexpected) volume, which is a standardized prediction

error from a regression of trading volume on the absolute value of returns of the k-th firm

�I��,� =I��,���,� (11)

I��,� = <�9-:�B=56+@"�,� − JK<�9-:�B=56+@"�,�L (12)

JK<�9-:�B=56+@"�,�L = 9� + M N��,�N� + M�N��,�NO (13)

where ��,� is the standard deviation of the residuals from the regression, calculated over the model’s

estimation period [t-52, t-5], and the plus and minus superscriptions on the absolute valued returns

indicate when returns were positive or negative.

10 Another possible measure of divergence of opinion in investors might be the dispersion of analyst forecasts (see

Diether, Malloy, and Scherbina (2002)).

11 This definition of daily turnover is equivalent to the volume percentage used as one of control variables in

equation (5) and (6). In this section, we follow the related literature on divergence of investors’ opinion to call it daily turnover.

26

Comparing Panels B and C of Table 11, the divergence in investors’ opinion drastically increases

on the days when there are high-impact information releases. We show that this increase is statistically

significant at the 1% level for all the divergence measures under consideration. While the negative

relationship between realized skewness and subsequent stock returns has been explained by the skewness

preference framework, we argue that the positive relationship between realized skewness and future stock

returns can be explained by the prediction of Miller (1977), who suggests that the increase in divergence

in investors’ opinion may lead a stock to be overvalued because the short-sale constraint prevents the

negative opinion of investors from being revealed in the stock markets. Miller further argues that the

riskier class of stocks might have lower expected returns if the riskiest stocks experience greater

divergence in investors’ opinion.

To link our findings to the prediction of Miller (1977) and test how the realized skewness of stock

returns is related to divergence of opinion, we first examine a contemporaneous relationship between our

realized skewness measure and several measures of divergence in investors’ opinion with ordinary least

squares (OLS) regressions. Panels A, B, and C of Table 12 report the estimated coefficients of OLS

regressions of realized skewness on divergence in investors’ opinion measures for full sample, a sample

with information releases, and a sample without information releases, respectively. Since we conjecture

that the divergence in investors’ opinion around information releases is one of the determinants that lead

to different relationships between realized daily skewness and future returns of a stock, we study how

divergence in investors’ opinion is related to realized daily skewness with and without information

releases.

In Panels B and C of Table 12, the results of the regression analysis of realized daily skewness on

the divergence of opinion show the opposite sign of the coefficient estimates for all measures of

divergence of opinion. Specifically, it illustrates that our measure of realized skewness is negatively and

significantly related to all the measures of divergence of opinion when there are high-impact information

releases, while it is positively related to those divergence measures when there are no information releases.

In other words, in the presence of high-impact information releases, the stocks experiencing the increase

27

in divergence in investors’ opinion tend to have more negatively skewed distributions, which make these

stocks riskier to investors. In turn, our findings suggest that those riskier stocks with the greater

divergence in investors’ opinion generate lower future stock returns, which is consistent with the

prediction of (Miller (1977)).

In particular, this provides an explanation for our finding, presented in Table 6, which shows that

the significantly positive relationship between skewness and future return is mainly found in the negative

skewness sample in the presence of information releases. This explanation also supports the evidence

presented in Panel B of Table 7, which shows that the lowest quintile portfolio from the information

sample offers especially low return in the subsequent period. The stocks in the lowest quintile portfolio

with high-impact information releases constitute the riskiest group of stocks (measured by their negative

realized daily skewness) with highly divergent opinion of investors (due to releases of high-impact

information).12

It is noteworthy that the negative relationship is mainly observed with positive skewness and the

positive relationship with negative skewness, both suggesting lower returns in the subsequent period.

Here, notice that both positive and negative skewness is likely to increase the idiosyncratic volatility of

stock returns due to the presence of extreme movements in either direction. In other words, this increased

idiosyncratic volatility is negatively related to subsequent stock returns with or without high impact

information releases. Our unreported analysis also suggests that the increase in the individual stock’s

volatility level is even higher in our Information sample, which only includes the times of firm-specific

information releases. We believe that our new evidence of a positive relationship between realized

skewness and subsequent return (in addition to the negative relationship already documented in the

12 Chen, Hong, and Stein (2001) show that negative skewness over a six-month period is most pronounced in

stocks that experienced an increase in trading volume in relation to trends over the past six months. Although we also consider volume and skewness, our skewness measure is calculated for one day using intraday data, and our evidence in Table 12 shows a daily contemporaneous relationship with or without information releases, while theirs purpose is to forecast skewness for the subsequent half year without taking into account information releases.

28

literature) contributes to the idiosyncratic volatility puzzle documented in Ang, Hodrick, Xing, and Zhang

(2006).

5. Conclusion

The role of skewness in stock returns in asset pricing has been investigated by many researchers.

It is well documented that the skewness of stock returns is considered one of the risk measures for

expected subsequent returns. Using high-frequency data capturing finer market movements up to intraday

level, we show that highly influential firm-specific information releases (which tend to generate extreme

market volatility) can change conventional views of realized skewness as a risk measure.

First, we show that in general, there exists a negative relationship between realized daily

skewness and subsequent returns over 1 to 20 trading days. We then document that this existing

relationship between realized daily skewness and future return is reversed when we take into account the

presence of high-impact information releases about firms. Specifically, by separately analyzing the stocks

experiencing high-impact information releases and those without information, we discover that there

exists a strong positive relationship between realized daily skewness and subsequent returns when high-

impact information releases occur and a strong negative relationship when there are no influential

information releases. In other words, when there are high-impact information releases generating unusual

market reactions, the risk-return compensation framework does not appear to work. More interestingly,

we find the negatively skewed stocks tend to be the significant driver for the positive relationship, while

positively skewed stocks tend to be the significant driver for the negative relationship.

Second, we document how our finding of a distinctive pattern in the relationship between realized

daily skewness and subsequent returns (conditional on the presence of high-impact information) explains

the cross-section of stock returns even after taking into account common risk factors, including market

excess returns, the size factor, the value factor, and the momentum factor. We also show that this anomaly

might be exploited to produce an abnormal return. Interestingly, our evidence suggests that we might be

able to enhance the profitability of the zero-investment trading strategy by taking account the distinctive

29

relational patterns between realized daily skewness and subsequent returns depending on the presence of

information. Consistent with our finding that the positive relationship between realized daily skewness

and subsequent returns results from negatively skewed stocks, we are also able to significantly enhance

the profitability of the zero-investment trading strategy if we use extremely skewed (measured by realized

daily skewness) in constructing the portfolio. The increase of abnormal returns by using extreme samples

is significant and the gains from the information sample dominate those from the no-information sample

as we focus on more extreme samples.

The different patterns in the relationship depending on the presence (or absence) of high-impact

information are not driven by small firms. While we observe a stronger positive relationship for small

firms, the positive relationship in large firm remains statistically significant. Another robustness check is

for a time horizon over which we compute realized skewness using high-frequency data. When we

examine the same issue with realized weekly skewness instead of realized daily skewness (which we used

in this study), we find that the negative relationship in the no-information sample still holds strongly,

while the positive relationship in the information sample disappears. One of the reasons for this change in

the relationship in the information sample is that the high-impact information considered in this paper

includes earnings announcements and analyst recommendation reports, which are generally reflected in

abnormal return distribution soon (within a day) after they are released.

After we document our new finding of a positive relationship between realized daily skewness

and subsequent stock return when there are high-impact information releases, we offer a possible

explanation for this phenomenon using divergence in investors’ opinion around information releases. We

demonstrate that measures of divergence in investors’ opinion used in this paper dramatically increase

when there are information releases. Furthermore, we find that the divergence in opinion is negatively

related to realized daily skewness when it is accompanied by high-impact information releases, while it is

positively related to realized daily skewness when there are no information releases. In other words, we

note that the increase in the measures of divergence in investors’ opinion is associated with more

negatively skewed stocks, which we find are the main source of the positive relationship between

30

skewness and future returns. This implies that these riskier stocks tend to experience greater divergence in

investors’ opinion when there are high-impact information releases and tend to be over-valued (or

associated with lower subsequent returns), which is consistent with the prediction of Miller (1977) that

risky stocks will not be rewarded with high expected returns if they experience divergent investors’

opinion because negative opinions among investors is not revealed due to short-sale constraints.

31

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33

Figure 1. Univariate analysis for realized daily skewness and subsequent stock returns: Effect of high-impact information releases

This figure presents the relationship between realized daily skewness and subsequent stock returns (10-trading day cumulative return, ������,����). The figure is generated using 10,000 random

samples from original data for better presentation. The left panel presents the relationship between realized daily skewness and next 10-trading day returns when high-impact information about the

firm is released. The middle panel shows the relationship no high-impact information is released. The rightmost figure shows the relationship for the full sample.

34

Table 1. Summary statistics of base sample

This table provides time-series summary statistics of means and medians for the sample used in this paper. The first column in the table, Number of stocks, shows the numbers of stocks included in a

full sample of individual stocks, which is extracted from the TAQ database and merged with the CRSP daily stock file. The second column, Daily return, lists average daily returns of stocks computed

from the CRSP daily file. Realized daily variance, Realized daily skewness, and Realized daily kurtosis are computed using 5-minute returns from the TAQ database according to equations (1), (2),

and (3), respectively. ME ($ mil) represents market capitalization calculated using the closing market prices of firms. Vol pct is computed as the percentage of trading volume relative to total shares

outstanding. Mom is the cumulative return over 11 months, from previous 12 month to previous 2 month, as of day t. In 5-minute return and higher moment calculations, stocks with a price lower than

$5 are excluded. To be included in the sample, a stock must have at least 80 transactions within a trading day.

Number of Stocks Daily return Realized daily variance Realized daily skewness Realized daily kurtosis ME ($mil) Vol pct Mom

Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median

2005 6,387 0.08% 0.00% 0.12% 0.03% 0.00 -0.01 8.06 6.22 4,230.40 841.37 1.17% 0.58% 17.22% 11.00%

2006 6,247 0.09% 0.00% 0.09% 0.03% 0.01 0.01 7.45 5.72 5,175.36 1,080.92 1.18% 0.60% 20.86% 12.17%

2007 3,772 0.01% 0.00% 0.09% 0.03% -0.01 -0.03 7.85 5.74 6,969.56 1,581.61 1.82% 0.69% 18.19% 13.96%

2008 3,703 -0.15% -0.15% 0.30% 0.08% -0.05 -0.03 7.96 5.66 5,780.48 1,188.50 2.70% 0.91% -9.32% -11.33%

2009 3,443 0.26% 0.11% 0.21% 0.07% -0.03 -0.03 7.94 5.85 4,704.06 996.44 3.75% 0.91% -20.04% -28.09%

2010 4,153 0.12% 0.06% 0.13% 0.03% -0.01 -0.02 7.68 5.80 5,914.73 1,394.37 2.52% 0.79% 45.48% 27.20%

35

Table 2. Characteristics of decile portfolios sorted by realized higher moments

This table presents the cross-sectional characteristics of portfolios sorted by realized higher moments. All stocks in the sample are ranked by their

higher moments and assigned to deciles. The sorting procedure is repeated for every day from January 2005 to December 2010. Panel A, Panel B,

and Panel C present the results of sorted portfolios based on realized volatility, realized skewness and realized kurtosis for a corresponding day,

respectively. The first row of each panel, Next 20-day return, shows the average returns (in basis points) of sorted portfolios over the next 20 trading

days. The remaining characteristics of decile portfolios are computed for daily sorted portfolios. Size, BE/ME, Price, Intraday transactions, and

Number of stocks are the average market capitalization (in millions of dollars), average book-to-market equity ratio, average price of stocks in each

sorted portfolio, average intraday transactions per day, and average number of stocks included in daily decile portfolios, respectively.

Panel A: Characteristics of portfolios sorted by realized daily volatility

1 (Low) 2 3 4 5 6 7 8 9 10 (High)

Next 20-day return (bp) 48.91 64.83 72.45 76.25 83.74 87.81 95.32 101.09 116.73 148.86

Current day return (bp) 5.28 3.95 3.16 3.11 3.05 3.32 3.97 3.69 5.78 38.28

Realized volatility 0.143 0.196 0.234 0.271 0.309 0.353 0.406 0.480 0.609 1.365

Realized skewness 0.014 0.001 -0.008 -0.010 -0.012 -0.014 -0.013 -0.022 -0.029 -0.039

Realized kurtosis 6.564 6.424 6.680 6.881 7.081 7.357 7.738 8.406 9.457 11.678

Size (mil) 11,000 10,000 8,191 6,505 5,219 4,101 3,171 2,355 1,557 686

BE/ME 2.89 2.71 2.34 1.98 1.75 1.53 1.35 1.21 1.18 1.44

Price 130 97.3 73.4 53.3 40 33.8 29.5 24.8 20.5 11

Intraday transactions 2,621 2,862 2,881 2,943 2,991 3,005 2,943 2,845 2,653 2,195

Number of stocks 298 298 298 298 298 298 298 298 298 298

Panel B: Characteristics of portfolios sorted by realized daily skewness

1 2 3 4 5 6 7 8 9 10

Next 20-day return (bp) 90.88 91.72 97.2 97.15 92.73 89.01 87.81 88 84.35 77.17

Current day return (bp) -179.15 -129.61 -85.45 -47.26 -14.62 19.82 55.07 96.37 147.3 210.92

Realized volatility 0.704 0.536 0.500 0.491 0.490 0.481 0.484 0.492 0.527 0.690

Realized skewness -2.398 -1.084 -0.652 -0.360 -0.120 0.107 0.347 0.635 1.060 2.334

Realized kurtosis 15.786 7.446 5.921 5.315 5.062 5.069 5.281 5.857 7.294 15.260

Size (mil) 3,619 4,830 5,593 5,995 6,189 6,186 6,061 5,817 5,182 4,017

BE/ME 1.73 1.64 1.74 1.87 1.93 1.92 1.95 1.75 1.65 1.73

Price 40.3 58 54.3 53.8 52.5 55.5 57.5 50.5 51.6 39.2

Intraday transactions 2,076 2,597 2,879 3,018 3,132 3,141 3,085 2,989 2,774 2,250

Number of stocks 298 298 298 298 298 298 298 298 298 298

Panel C: Characteristics of portfolios sorted by realized daily kurtosis

1 2 3 4 5 6 7 8 9 10

Next 20-day return (bp) 85.17 84.26 89.26 89.85 88.47 93.57 93.56 94.13 92.27 85.49

Current day return (bp) 7.94 8.8 7.69 7.55 7.45 8.71 6.96 6.34 7.04 5.01

Realized volatility 0.407 0.412 0.435 0.456 0.479 0.508 0.544 0.583 0.642 0.848

Realized skewness 0.004 0.005 0.003 0.001 0.000 -0.002 -0.008 -0.015 -0.023 -0.095

Realized kurtosis 3.135 3.804 4.335 4.891 5.529 6.315 7.363 8.912 11.702 22.290

Size (mil) 9,856 7,690 6,549 5,771 5,124 4,576 4,041 3,562 3,301 3,030

BE/ME 1.91 1.85 1.79 1.79 1.71 1.74 1.70 1.71 1.72 1.97

Price 61.9 57.9 62.4 58 58 48 50.4 45 38.5 33.3

Intraday transactions 4,688 3,915 3,408 3,067 2,755 2,476 2,200 1,958 1,802 1,678

Number of stocks 298 298 298 298 298 298 298 298 298 298

36

Table 3. Time-series distribution of firm-specific information releases

This table describes our firm-date observations with and without firm-specific information releases over our sample period (from 2005 to 2010). The first two columns, Full sample, list the number of

all firm-date observations and average size of firms included in the sample for each year. The next two columns include information about the subsamples that includes firm-date observations

accompanied by two different types of firm-specific information releases. The Earnings announcements column shows the number of firm-date observations accompanied by earnings announcements

for corresponding firms (from the I/B/E/S database). The Analyst recommendations column shows the total number of subsample for all observations accompanied by one or more analyst

recommendation reports on a corresponding firm (from the I/B/E/S database). The two columns in Information sample show the observations accompanied by either earnings announcements or

analyst recommendations for a corresponding firm. No-information sample shows the subsample that includes observations that are not accompanied by the two types of firm-specific information

releases we consider in this study (i.e., earnings announcement and analyst recommendations).

Full sample Earnings announcements Analyst recommendations Information sample No-information sample

Obs Mean firm size (mil) Obs Mean firm size (mil) Obs Mean firm size (mil) Obs Mean firm size (mil) Obs Mean firm size (mil)

2005 980,987 4,230.40 24,462 8,001.39 13,364 4,470.30 36,928 6,710.89 944,059 4,133.38

2006 808,158 5,175.36 20,546 9,560.05 10,613 5,640.93 30,494 8,189.67 777,664 5,057.16

2007 613,696 6,969.56 15,497 12,420.33 7,142 8,450.58 22,116 11,125.15 591,580 6,814.20

2008 616,971 5,780.48 17,443 11,555.97 6,986 7,056.27 23,815 10,173.61 593,156 5,604.10

2009 573,554 4,704.06 16,191 9,065.10 6,641 5,403.07 22,386 7,959.61 551,168 4,571.84

2010 613,290 5,914.73 17,006 11,290.86 7,394 6,704.19 23,843 9,822.00 589,447 5,756.68

Total 4,206,656 5,349.03 111,145 10,121.78 52,140 6,035.86 159,582 8,761.97 4,047,074 5,214.45

37

Table 4. Relationship between realized skewness, subsequent returns, and information releases: Information vs. no-information sample

This table presents the effect of information releases on the relationship between realized daily skewness and subsequent returns by separating all observations into an information sample and a no-

information sample. The table reports coefficient estimates of the following regression: ���,��,��� = + ����,� + ���,� + �,��,���, where �,��,��� is an error term.

Panel A provides results of the regression analysis for all firm-date observations. Panels B and C show the results of the regression analysis for the subsample with at least one of two firm-specific

information releases and the subsample without any of firm-specific information release, respectively. ���,��,��� is the cumulative return of the k-th stock over a period starting on day t+i and

ending on day t+j. ���,� is the realized daily skewness of the k-th stock returns on day � computed using 5-minute returns from the TAQ database. �,� includes several control variables for the k-th

firm on day t, including log size of the firm (log(ME)), log book-to-market ratio (log(BM) computed from COMPUSTAT), the cumulative return over 11 months, from previous 12 month to previous

2 month, as of day t (Mom), and the percentage of trading volume to total shares outstanding (vol pct). All parameters are computed using the Fama-MacBeth cross-sectional regression method and

the numbers in parentheses are t-statistics with robust standard errors. The sample period of analysis is from January 2005 to December 2010.

Panel A: Full sample Panel B: Information sample Panel C: No-information sample

Retk,t+1 Retk,t+1,t+5 Retk,t+1,t+10 Retk,t+1,t+20 Retk,t+1 Retk,t+1,t+5 Retk,t+1,t+10 Retk,t+1,t+20 Retk,t+1 Retk,t+1,t+5 Retk,t+1,t+10 Retk,t+1,t+20

RDSk,t, -0.0884 -2.4246*** -2.9826*** -4.2829*** 2.0382*** 2.8231** 5.1944*** 5.9925*** -0.4047 -3.2724*** -4.3105*** -6.0524***

(-0.24) (-3.43) (-3.56) (-3.73) (3.16) (2.34) (3.45) (2.92) (-1.07) (-4.46) (-4.85) (-4.95)

log(ME) -1.8296*** -6.5333*** -9.8762*** -16.3374*** -2.4584*** -6.1695*** -9.0398*** -15.5479*** -1.9219*** -6.7453*** -10.1733*** -16.7234***

(-3.85) (-5.76) (-6.61) (-6.85) (-3.34) (-4.21) (-4.85) (-5.64) (-3.98) (-5.82) (-6.66) (-6.83)

log(BM) 0.7336 3.2192*** 5.3529*** 9.4700*** 2.3929** 11.5426*** 14.0313*** 16.6171*** 0.6681 2.8179*** 5.0649*** 9.3135***

(1.55) (3.22) (3.84) (4.67) (2.34) (4.79) (4.60) (3.93) (1.42) (2.85) (3.64) (4.60)

Mom -0.0326 -0.2021*** -0.4146*** -0.9084*** 0.0520 -0.1017 -0.2371* -0.7328*** -0.0412 -0.1988** -0.4145*** -0.9060***

(-1.02) (-2.59) (-3.56) (-4.99) (1.19) (-1.06) (-1.82) (-3.73) (-1.31) (-2.56) (-3.54) (-4.95)

vol pct 0.0688 -0.1702 -1.6684* -2.9801** -1.7077** -3.7260*** -2.7976 -6.7375*** 0.5858 0.4642 -1.5892* -2.9980**

(0.20) (-0.26) (-1.96) (-2.58) (-2.07) (-2.69) (-1.59) (-2.85) (1.56) (0.63) (-1.69) (-2.33)

Constant 15.58** 61.14*** 96.25*** 168.80*** 27.67*** 70.10*** 105.85*** 179.47*** 15.37** 61.51*** 96.78*** 169.76***

(2.52) (4.19) (4.90) (5.73) (3.47) (4.22) (4.73) (5.45) (2.47) (4.20) (4.90) (5.72)

N 3,018,830 3,043,864 3,043,867 3,043,867 365,256 366,634 366,634 366,634 2,653,574 2,677,230 2,677,233 2,677,233

R-sq 0.0351 0.0398 0.0404 0.0415 0.0702 0.0834 0.0860 0.0874 0.0393 0.0411 0.0409 0.0421

*, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

38

Table 5. Relationship between realized skewness, subsequent returns, and information releases: Information dummy

This table presents the effect of information releases on the relationship between realized daily skewness and subsequent returns by introducing an

interaction term between realized daily skewness (���,�) and an information dummy variable (�,���,�) set to one if any types of firm-specific

information on the k-th firm are released around day t. The table reports the coefficient estimates of the following regression: ���,��,��� = +

����,� + �����,� ∗ �,���,�� + ���,� + �,��,���, where �,��,��� is an error term.

���,��,��� is the cumulative return of the k-th stock over a period starting on day t+i and ending on day t+j. ���,� is the realized daily skewness of

the k-th stock returns on day � computed using 5-minute returns from the TAQ database. �,� includes several control variables for the k-th firm on

day t, including log size of the firm (log(ME)), log book-to-market ratio (log(BM) computed from COMPUSTAT), the cumulative returns over 11

months, from previous 12 month to previous 2 month, as of day t (Mom), and a percentage of trading volume to total shares outstanding (vol pct). All

parameters are computed using the Fama-MacBeth cross-sectional regression method using the full sample. The numbers in parentheses are t-

statistics with robust standard errors. The sample period of analysis is from January 2005 to December 2010.

Retk,t+1 Retk,t+1,t+5 Retk,t+1,t+10 Retk,t+1,t+20

RDSk,t, -0.4615 -3.3814*** -4.3284*** -6.0761***

(-1.21) (-4.61) (-4.91) (-5.01)

RDSt*d_info 2.8513*** 6.1108*** 8.8353*** 11.9625***

(4.43) (5.47) (5.94) (5.75)

log(ME) -1.8314*** -6.5465*** -9.9077*** -16.3500***

(-3.85) (-5.77) (-6.63) (-6.85)

log(BM) 0.7410 3.2259*** 5.3758*** 9.4990***

(1.56) (3.22) (3.85) (4.69)

Mom -0.0326 -0.2020*** -0.4149*** -0.9087***

(-1.02) (-2.59) (-3.56) (-4.99)

vol pct 0.0651 -0.1543 -1.6697* -2.9664**

(0.19) (-0.23) (-1.96) (-2.57)

Constant 15.60** 61.24*** 96.53*** 168.94***

(2.52) (4.20) (4.91) (5.73)

N 3,018,830 3,043,864 3,043,867 3,043,867

R-sq 0.0363 0.0406 0.0411 0.0421

*, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

39

Table 6. Subsample analysis with positive and negative skewness

This table presents the asymmetric effects of information releases on the relationship between realized daily skewness and subsequent returns by

introducing an interaction term between realized daily skewness (���,�) and an information dummy variable (�,���,�), which is set to one if firm-

specific information on the k-th firm is released around day t. The table reports the coefficient estimates of the following regression for each

subsample of positive skewness and negative skewness: ���,��,��� = + ����,� + ���,� + �,��,���, where �,��,��� is an error term.

���,��,��� is the cumulative return of the k-th stock over a period starting on day t+i and ending on day t+j. ���,� is the realized daily skewness of

the k-th stock returns on day � computed using 5-minute returns from the TAQ database. �,� includes several control variables for the k-th firm on

day t, including log size of the firm (log(ME)), log book-to-market ratio (log(BM) computed from COMPUSTAT), the cumulative return over 11

months, from previous 12 month to previous 2 month, as of day t (Mom), and a percentage of trading volume to total shares outstanding (vol pct). All

parameters are computed using the Fama-MacBeth cross-sectional regression method. The numbers in parentheses are t-statistics with robust

standard errors. The sample period of analysis is from January 2005 to December 2010.

Panel A. Sample with positive skewness only

Positive skewness with information

Positive skewness without information

Retk,t+1 Retk,t+1,t+5 Retk,t+1,t+10 Retk,t+1,t+20

Retk,t+1 Retk,t+1,t+5 Retk,t+1,t+10 Retk,t+1,t+20

RDSk,t, 0.2897 0.5995 2.4168 4.3111

-1.1257** -5.2773*** -4.8106*** -9.0057***

(0.23) (0.25) (0.72) (0.97)

(-2.28) (-4.06) (-3.54) (-4.70)

log(ME) -3.4173*** -6.9742*** -8.4768*** -13.8494***

-2.3129*** -5.8915*** -8.5925*** -15.1784***

(-3.62) (-3.63) (-3.54) (-4.16)

(-4.30) (-4.33) (-5.10) (-5.67)

log(BM) 2.7450* 11.1988*** 12.4249*** 12.9387**

0.1242 3.1717*** 6.0408*** 10.3024***

(1.74) (3.51) (3.17) (2.25)

(0.22) (2.80) (3.93) (4.61)

Mom 0.6447 -6.5659 -22.3778 -77.8314***

-6.2243* -24.3668*** -43.8575*** -92.2194***

(0.12) (-0.58) (-1.47) (-3.38)

(-1.88) (-2.92) (-3.60) (-4.89)

vol pct -11.6731 -116.5551 -13.3895 -150.5628

42.3366 -54.8439 -161.8068 -192.1552

(-0.08) (-0.50) (-0.04) (-0.40)

(0.78) (-0.51) (-1.16) (-1.01)

Constant 34.4040*** 71.4629*** 94.9677*** 156.1853***

18.1128*** 56.4781*** 84.7923*** 160.1379***

(3.49) (3.54) (3.65) (4.26)

(2.77) (3.58) (4.13) (5.16)

N 182,339 182,990 182,990 182,990

1,321,336 1,333,130 1,333,132 1,333,132

R-sq 0.1099 0.1235 0.1246 0.1276

0.0487 0.0490 0.0489 0.0496

40

Panel B. Sample with negative skewness only

Negative skewness with information

Negative skewness without information

Retk,t+1 Retk,t+1,t+5 Retk,t+1,t+10 Retk,t+1,t+20

Retk,t+1 Retk,t+1,t+5 Retk,t+1,t+10 Retk,t+1,t+20

RDSk,t, 4.8441*** 7.6919** 12.4875*** 13.9753***

0.1855 0.6108 0.1847 1.1270

(3.29) (2.52) (3.68) (2.87)

(0.32) (0.55) (0.14) (0.64)

log(ME) -2.1489* -9.7031*** -12.0507*** -21.6782***

-1.9321*** -8.1071*** -12.5272*** -19.1171***

(-1.75) (-3.01) (-4.38) (-4.00)

(-2.72) (-6.47) (-7.08) (-7.26)

log(BM) 2.1494 5.9527* 10.8847*** 12.3486**

0.8220 2.5124** 4.5043*** 9.1008***

(1.46) (1.75) (2.58) (2.06)

(1.57) (2.15) (2.76) (3.89)

Mom 8.4260 -13.2098 -17.9062 -65.6949***

-2.6267 -15.4178** -40.0790*** -86.4128***

(1.58) (-1.17) (-1.17) (-2.96)

(-0.81) (-2.01) (-3.40) (-4.67)

vol pct -269.9864** -382.9253* -275.4256 -916.9064**

146.6851** 224.0433** -163.9463 -454.4214**

(-2.23) (-1.90) (-1.06) (-2.39)

(2.51) (2.01) (-1.15) (-2.23)

Constant 28.9866** 102.6866*** 137.5957*** 242.6597***

14.8312** 73.3473*** 117.0646*** 194.0231***

(2.48) (3.47) (4.82) (4.67)

(2.11) (4.76) (5.55) (6.26)

N 182,917 183,644 183,644 183,644

1,332,238 1,344,100 1,344,101 1,344,101

R-sq 0.1140 0.1237 0.1286 0.1294

0.0481 0.0489 0.0468 0.0488

*, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

41

Table 7. Cross-section of stock returns and realized daily skewness

This table shows the raw returns and alpha of quintile portfolios formed based on realized daily skewness. Raw returns (in bps) are computed for quintile portfolios sorted on realized daily skewness

over 10-trading days and 20-trading days after sorting in the first and the second part of each panel, respectively. The results presented in CAPM, 3-Factor, and 4-Factor are the intercepts from time-

series regressions of the returns on quintile portfolios on market excess returns, three factors (market excess returns, size factor, and value factor), and four factors (market excess returns, size factor,

value factor, and momentum factor), respectively. All factors used in the analysis are drawn from the website of Kenneth French. Panel A shows the results for the full sample, Panel B for the

information sample, and Panel C for the no-information sample. The numbers in parentheses are t-statistics.

Panel A: Full sample Panel B. Information sample Panel C. No-information sample

i) 10-day return i) 10-day return i) 10-day return

1 (Low) 2 3 4 5 (High) H-L 1 (Low) 2 3 4 5 (High) H-L 1 (Low) 2 3 4 5 (High) H-L

Raw return Mean 46.65 49.16 45.71 41.67 38.75 -7.90* 35.09 53.52 49.16 58.52 51.32 16.23** 49.05 48.46 45.27 39.97 36.84 -12.21***

t-stat (3.43) (3.67) (3.47) (3.24) (3.06) (-1.94) (2.33) (3.65) (3.44) (4.21) (3.72) (2.44) (3.64) (3.63) (3.46) (3.12) (2.92) (-2.94)

CAPM Mean 18.28 20.68 17.40 13.85 11.51 -6.77* 5.41 24.09 19.84 29.88 23.00 17.60*** 20.87 20.09 17.10 12.22 9.71 -11.17***

t-stat (3.89) (5.35) (5.06) (4.01) (2.87) (-1.69) (0.85) (4.18) (3.93) (5.88) (4.27) (2.68) (4.39) (5.14) (4.95) (3.50) (2.40) (-2.71)

3-Factor Mean 12.97 15.56 12.36 8.81 6.38 -6.60 -0.47 18.58 14.66 24.31 17.43 17.90*** 15.65 14.98 12.09 7.21 4.68 -10.97***

t-stat (3.10) (4.84) (4.55) (3.21) (1.86) (-1.63) (-0.08) (3.57) (3.25) (5.49) (3.62) (2.75) (3.66) (4.59) (4.40) (2.56) (1.33) (-2.64)

4-Factor Mean 13.93 16.36 13.09 9.49 7.09 -6.84* 0.62 19.28 15.23 24.91 18.16 17.55*** 16.60 15.80 12.83 7.90 5.41 -11.19***

t-stat (3.49) (5.40) (5.17) (3.70) (2.16) (-1.68) (0.11) (3.74) (3.41) (5.68) (3.85) (2.68) (4.07) (5.14) (5.01) (2.99) (1.61) (-2.67)

ii) 20-day return ii) 20-day return ii) 20-day return

1 (Low) 2 3 4 5 (High) H-L 1 (Low) 2 3 4 5 (High) H-L 1 (Low) 2 3 4 5 (High) H-L

Raw return Mean 91.30 97.17 90.87 87.90 80.76 -10.54* 77.51 102.66 99.47 108.19 99.18 21.67** 92.98 96.14 89.30 85.57 77.17 -15.80***

t-stat (4.63) (5.05) (4.82) (4.77) (4.41) (-1.91) (3.63) (4.86) (4.98) (5.42) (5.01) (2.39) (4.74) (5.02) (4.75) (4.65) (4.23) (-2.78)

CAPM Mean 26.68 32.66 26.86 25.02 18.96 -7.72 10.01 35.16 33.63 43.12 34.58 24.57*** 28.70 31.90 25.46 22.83 15.68 -13.03**

t-stat (3.69) (5.44) (5.08) (4.68) (3.00) (-1.44) (1.15) (4.38) (4.98) (5.85) (4.62) (2.75) (3.88) (5.24) (4.76) (4.20) (2.43) (-2.36)

3-Factor Mean 16.42 23.05 17.63 15.74 8.89 -7.54 -0.83 26.53 25.64 33.77 24.93 25.76*** 18.57 22.14 16.19 13.52 5.57 -13.00**

t-stat (2.63) (4.68) (4.23) (3.68) (1.68) (-1.43) (-0.11) (3.64) (4.23) (5.26) (3.75) (2.97) (2.89) (4.43) (3.82) (3.08) (1.02) (-2.39)

4-Factor Mean 19.15 25.34 19.63 17.52 10.79 -8.36 1.72 28.92 27.32 35.55 26.70 24.98*** 21.33 24.45 18.21 15.32 7.50 -13.83**

t-stat (3.34) (5.73) (5.27) (4.46) (2.16) (-1.58) (0.23) (4.10) (4.64) (5.61) (4.11) (2.85) (3.59) (5.44) (4.81) (3.79) (1.45) (-2.52)

*, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

42

Table 8. Calendar-time zero investment portfolios

This table presents the profitability of zero-investment portfolios based on our finding of a relationship between realized daily skewness and subsequent stock returns.

The table reports coefficient estimates for the following regressions: ��,������� = ���� + ��������,��� + ��,���

���� where ��,���

���� is an error term.

The dependent variables in this analysis are the returns of zero-investment portfolios. The explanatory variables, ��,���, include common risk factors, including the market excess return (MKT), the size factor (SMB), the value

factor (HML), and the momentum factor (UMD). Each panel provides the results for the returns over the next 5-, 10-, and 20-trading days of holding periods after forming the portfolios. Panel A provides the result for the

zero-investment strategy that takes long positions on stocks that experienced negative realized daily skewness and short positions on stocks that experienced positive realized daily skewness without taking account of the

presence of information. Panel B provides the results of a zero-investment strategy that take a long position on the No-information sample and a short position on the Information sample. In panel C, the dependent variable is

the return of a zero-investment portfolio that takes long positions on stocks that experienced negative realized daily skewness with high-impact information releases and short positions on stocks that experienced positive

realized daily skewness with high-impact information releases. Panel D provides the results using as the dependent variable the return on the zero-investment strategy that takes long positions on stocks that experienced

negative realized daily skewness and short positions on stocks that experienced positive realized daily skewness without any high-impact information releases. To show the possible profitability, Panel E and F provide results

of zero-investment portfolios using the top and the bottom percentile portfolios sorted on the realized daily skewness and the presence or the absence of high-impact information releases, respectively. The numbers in

parentheses are t-statistics.

Panel A. Portfolio formed regardless of information releases

Panel B. Combined portfolio with Information and No-information samples

Model parameters ���� � !" �# $ �% & �' (

���� � !" �# $ �% & �' (

5-days Est 5.0318** 0.0686*** 7.9144** -0.0107

t-stat (2.35) (4.19) (2.35) (-0.48)

5-days Est 5.0131** 0.0735*** 0.0131 -0.0237 7.5516** -0.0241 0.0707** 0.0203

t-stat (2.37) (3.96) (0.49) (-0.78) (2.25) (-1.06) (2.07) (0.44)

5-days Est 5.0402** 0.0700*** 0.0160 -0.0341 -0.0123 7.5307** -0.0214 0.0685** 0.0283 0.0095

t-stat (2.37) (3.68) (0.58) (-1.21) (-0.83) (2.23) (-0.96) (1.98) (0.63) (0.38)

10-days Est 9.4915*** 0.0581*** 16.1473*** -0.0056

t-stat (3.32) (4.19) (3.92) (-0.30)

10-days Est 9.4384*** 0.0508*** -0.0059 0.0302 16.0680*** -0.0028 0.0155 -0.0181

t-stat (3.28) (3.60) (-0.18) (1.22) (3.92) (-0.14) (0.42) (-0.48)

10-days Est 9.5990*** 0.0414*** -0.0034 0.0083 -0.0277* 16.0778*** -0.0034 0.0156 -0.0195 -0.0017

t-stat (3.31) (3.01) (-0.10) (0.36) (-1.88) (3.89) (-0.17) (0.42) (-0.53) (-0.09)

20-days Est 10.6399*** 0.0615*** 17.3880*** -0.0055

t-stat (2.74) (4.48) (3.03) (-0.36)

20-days Est 10.4671*** 0.0567*** 0.0049 0.0159 17.4269*** 0.0018 0.0117 -0.0385

t-stat (2.77) (3.88) (0.18) (0.73) (3.09) (0.10) (0.31) (-1.14)

20-days Est 11.0971*** 0.0358** 0.0065 -0.0233 -0.0530*** 17.2706*** 0.0070 0.0113 -0.0288 0.0132

t-stat (2.92) (2.47) (0.23) (-1.11) (-3.92) (3.01) (0.39) (0.29) (-0.80) (0.67) *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

43

Table 8. Continued

Panel C. Portfolio formed around information releases

Panel D. Portfolio formed with no information releases

Model parameters ���� � !" �# $ �% & �' (

���� � !" �# $ �% & �' (

5-days Est -1.9577 0.0772*** 5.9568*** 0.0665***

t-stat (-0.53) (3.33) (2.74) (3.95)

5-days Est -1.6471 0.0943*** -0.0512 -0.0418 5.9045*** 0.0702*** 0.0195 -0.0215

t-stat (-0.45) (3.54) (-1.24) (-0.73) (2.74) (3.71) (0.73) (-0.72)

5-days Est -1.6046 0.0886*** -0.0467 -0.0581 -0.0193 5.9262*** 0.0673*** 0.0218 -0.0298 -0.0098

t-stat (-0.44) (3.32) (-1.11) (-1.14) (-0.72) (2.74) (3.49) (0.78) (-1.06) (-0.66)

10-days Est -4.5861 0.0614*** 11.5612*** 0.0559***

t-stat (-1.02) (3.20) (3.92) (3.79)

10-days Est -4.5975 0.0513** -0.0165 0.0462 11.4705*** 0.0485*** -0.0010 0.0280

t-stat (-1.04) (2.42) (-0.42) (1.05) (3.86) (3.20) (-0.03) (1.11)

10-days Est -4.4474 0.0425** -0.0141 0.0257 -0.0259 11.6304*** 0.0391*** 0.0015 0.0062 -0.0276*

t-stat (-1.00) (2.01) (-0.36) (0.62) (-1.15) (3.89) (2.64) (0.04) (0.26) (-1.86)

20-days Est -4.6232 0.0661*** 12.7648*** 0.0605***

t-stat (-0.74) (3.70) (3.18) (4.23)

20-days Est -4.8805 0.0542*** -0.0024 0.0504 12.5464*** 0.0560*** 0.0093 0.0118

t-stat (-0.81) (2.79) (-0.06) (1.31) (3.20) (3.67) (0.32) (0.53)

20-days Est -4.1069 0.0285 -0.0004 0.0021 -0.0651*** 13.1637*** 0.0355** 0.0108 -0.0267 -0.0519***

t-stat (-0.68) (1.49) (-0.01) (0.06) (-2.86) (3.33) (2.33) (0.37) (-1.22) (-3.80)

Panel E. Portfolio formed around information releases (Extreme sample)

Panel F. Portfolio formed with no information releases (Extreme sample)

Model parameters ���� � !" �# $ �% & �' (

���� � !" �# $ �% & �' (

5-days Est -18.7520*** 0.1198*** 7.4980** 0.0961***

t-stat (-2.69) (2.98) (2.12) (3.26)

5-days Est -18.4505*** 0.1539*** -0.0203 -0.1173 7.4717** 0.0966*** 0.0076 -0.0049

t-stat (-2.65) (3.27) (-0.24) (-1.27) (2.12) (2.95) (0.17) (-0.11)

5-days Est -18.4423*** 0.1528*** -0.0195 -0.1204 -0.0037 7.5232** 0.0897*** 0.0130 -0.0247 -0.0234

t-stat (-2.64) (3.25) (-0.22) (-1.37) (-0.08) (2.12) (2.71) (0.28) (-0.59) (-0.99)

10-days Est -31.3445*** 0.1151*** 15.0805*** 0.0781***

t-stat (-3.80) (3.86) (3.20) (3.66)

10-days Est -31.6059*** 0.0886** -0.0120 0.1045 15.0840*** 0.0661*** -0.0218 0.0559

t-stat (-3.85) (2.50) (-0.18) (1.49) (3.17) (2.97) (-0.44) (1.37)

10-days Est -31.3730*** 0.0749** -0.0083 0.0727 -0.0402 15.3037*** 0.0531** -0.0183 0.0259 -0.0379

t-stat (-3.80) (2.11) (-0.12) (1.10) (-1.16) (3.19) (2.46) (-0.37) (0.67) (-1.53)

20-days Est -44.8691*** 0.0839*** 16.7146*** 0.0784***

t-stat (-3.80) (2.72) (2.65) (3.92)

20-days Est -45.9714*** 0.0641* 0.0533 0.0421 16.7487*** 0.0781*** -0.0035 0.0038

t-stat (-3.96) (1.85) (0.73) (0.63) (2.66) (3.78) (-0.08) (0.12)

20-days Est -45.4221*** 0.0459 0.0547 0.0079 -0.0462 17.4896*** 0.0535*** -0.0017 -0.0423 -0.0623***

t-stat (-3.85) (1.33) (0.75) (0.11) (-1.17) (2.75) (2.59) (-0.04) (-1.30) (-2.81)

44

Table 9. Robustness Checks: Firm size

The results show the robustness of the main finding with respect to firm size. The subsamples in this table, which consist of small and large firms,

include all firm-date observations that are above and below the median of market capitalization from the full sample. The classification is performed

for each trading day. This table reports the coefficient estimates of the following regressions in each subsample: ���,��,��� = + ����,� +

�����,� ∗ �,���,�� + ���,� + �,��,���, where �,��,��� is an error term.

���,��,��� is the cumulative return of the k-th stock over a period starting on day t+i and ending on day t+j after day t. ���,� is the realized daily

skewness of the k-th stock returns on day t computed using 5-minute returns from the TAQ database. �,� includes several control variables,

including log size of a firm (log(ME)), log book-to-market ratio (log(BM) computed from COMPUSTAT), the cumulative return over 11 months,

from previous 12 month to previous 2 month, as of day t (Mom), and the ratio of trading volume to total shares outstanding (vol pct). All parameters

are computed using the Fama-MacBeth cross-sectional regression method. The sample period of analysis is from January 2005 to December 2010.

Small firms Large firms

Retk,t+1 Retk,t+1,t+5 Retk,t+1,t+10 Retk,t+1,t+20 Retk,t+1 Retk,t+1,t+5 Retk,t+1,t+10 Retk,t+1,t+20

RDSk,t, -0.0137 -3.2871*** -4.3593*** -5.9170*** -0.6143 -2.3361*** -2.8326*** -4.6918***

(-0.03) (-3.86) (-4.02) (-4.02) (-1.61) (-2.94) (-2.97) (-3.52)

RDSk,t,*d_info 5.7611*** 12.7865*** 14.8333*** 20.1037*** 1.7190*** 2.7519** 5.5204*** 7.2416***

(4.08) (5.38) (5.03) (4.67) (2.83) (2.37) (3.48) (3.38)

log(ME) -6.8639*** -21.9897*** -28.3596*** -39.2187*** -0.7672* -4.0432*** -8.2127*** -16.1804***

(-5.61) (-7.05) (-7.93) (-7.10) (-1.82) (-4.58) (-6.78) (-9.32)

log(BM) 0.5041 3.5039*** 7.3835*** 14.1733*** 0.2876 0.6986 0.3060 0.8600

(0.91) (2.90) (4.29) (5.62) (0.58) (0.75) (0.24) (0.49)

Mom -0.0121 -0.1393* -0.3347*** -0.8133*** -0.0327 -0.1742* -0.3675*** -0.7433***

(-0.42) (-1.94) (-3.00) (-4.51) (-0.84) (-1.96) (-2.90) (-4.07)

vol pct 0.9560** 2.4516*** 2.0923* 1.9365 -0.7412 -2.4549** -6.3235*** -9.7260***

(2.02) (2.62) (1.75) (1.19) (-1.33) (-2.30) (-4.49) (-5.47)

Constant 42.7451*** 142.9961*** 192.3216*** 282.1209*** 8.6643 46.8058*** 92.7699*** 186.9992***

(5.18) (6.50) (6.97) (6.65) (1.55) (3.80) (5.51) (7.75)

N 1,352,391 1,363,671 1,363,674 1,363,674 1,666,439 1,680,193 1,680,193 1,680,193

R-sq 0.0356 0.0371 0.0374 0.0385 0.0609 0.0622 0.0597 0.0584

*, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

45

Table 10. Result with weekly horizon

This table presents the robustness of our main findings to different estimation horizon for higher moments. The table reports the coefficient estimates for the following regression specification:

���,)�� = + ���*+,,) + �-��.�/,) + �0�1�2�,) + ���,) + �,)��, where �,)�� is an error term.

���,)�� is the subsequent weekly return of the k-th stock after investing in week w. �*+,,) , ��.�/,) and �1�2�,) are the realized volatility, realized skewness, and realized kurtosis of the k-th

stock returns over week w. Three higher moments are computed as the average of realized higher moments over a weekly horizon. Each week /, from Wednesday to the following Tuesday, each

variable is computed for each firm using 5-minute return data from the TAQ database. �,) includes several control variables for the k-th firm over week /, including log (Intra-transactions) is the log

of the average number of intraday transactions on each trading day, log(BM) is the log of book-to-market ratio, and log(Size) is the log of market capitalization.. The coefficient estimates are

computed using the Fama-MacBeth cross-sectional regression method. The numbers in parentheses are t-statistics with robust standard errors. The sample period of analysis is from January 2005 to

December 2010.

Panel A. Full sample Panel B. Information sample Panel C. No-information sample

(1) (2) (3) (4) (1) (2) (3) (4) (1) (2) (3) (4)

Realized Volatility 8.8890 14.3442 6.2062 35.4830 9.0145 9.5297

(0.68) (1.08) (0.24) (1.23) (0.72) (0.74)

Realized Skewness -5.2196*** -7.8722*** -3.5304 -1.9704 -6.1628*** -9.2849***

(-2.72) (-3.31) (-0.63) (-0.46) (-3.51) (-3.88)

Realized Kurtosis 0.0093 -0.5756 -0.9584 -1.2985 0.1501 -0.5489

(0.02) (-1.20) (-1.15) (-1.49) (0.41) (-1.08)

log(Size) -7.8548* -6.4688 -7.5330

(-1.72) (-1.57) (-1.59)

log(BM) 2.6206 6.6731 1.7199

(1.06) (1.56) (0.73)

log(Intra transactions) 4.6768 2.8113 3.5712

(1.06) (0.62) (0.80)

Constant 15.8310 23.4565 22.5771 35.0189* 19.3287 28.7356 34.1654 43.4320 14.3722 22.0360 20.0785 41.7769*

(1.12) (1.27) (1.13) (1.67) (1.34) (1.43) (1.60) (1.52) (1.01) (1.22) (1.03) (1.94)

N 975,747 975,691 975,691 683,596 191,906 191,905 191,905 161,200 783,841 783,786 783,786 522,396

R-sq 0.0157 0.0015 0.0023 0.0381 0.0266 0.0048 0.0051 0.0629 0.0166 0.0016 0.0025 0.0399

*, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

46

Table 11. Measures of divergence in investors’ opinion

This table provides the summary statistics for several measures of divergence in investors’ opinion considered in this paper. We report the number of observations (Obs), average (Mean), and standard

deviations (Std.) for the five different measures of divergence in investors’ opinion in the first, second, and third columns of each panel, respectively. In Panel A, the summary statistics for the full

sample are provided. We further separate our sample into a sample with information releases and a sample without information release. Panel B reports the statistics for divergence measures for the

sample with information releases, and Panel C reports those without information release. In Panel D, we further provide the differences in the divergence measures between Panel B and Panel C along

with their statistical significance. Details about the measures of divergence in investors’ opinion are provided in the main text and also in Garfinkel (2009). Daily turnover is computed as the ratio of

the firm’s daily trading volume on day t to total number of shares outstanding on day t. Market-adjusted daily turnover is the difference between a firm’s daily turnover and daily market-wide turnover

on day t (computed from market-wide trading volume and market-wide shares outstanding and adjusted with a 180-day median). Change in market-adjusted turnover is the difference in market-

adjusted turnover between day t and day t-1. Unexpected trading volume is a standardized prediction error from a regression of trading volume on the absolute value of returns of the k-th firm using

the equation (11), (12), and (13). Change in trading volume is the difference in trading volume between day t and day t-1.

Panel A: Full sample

Panel B: Sample with information

Panel C: Sample without information Panel D. (Information) – (No-information)

Variables Obs Mean Std.

Obs Mean Std.

Obs Mean Std. Difference

Daily turnover 2,551,563 0.0107 0.0197

313,654 0.0166 0.0262

2,237,909 0.0099 0.0185 0.0067***

Market-adjusted turnover 2,551,563 0.0009 0.0195

313,654 0.0062 0.0259

2,237,909 0.0001 0.0183 0.0061***

Change in market-adjusted turnover 2,551,563 0.0002 0.0223

313,654 0.0046 0.0259

2,237,909 -0.0004 0.0216 0.0050***

Unexplained trading volume 2,551,562 0.2354 3.5985

313,654 0.9151 4.0476

2,237,908 0.1402 3.5206 0.7749***

Change in trading volume 2,768,719 0.0001 0.0235

338,224 0.0015 0.0291

2,430,495 -0.0001 0.0226 0.0016***

*, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

47

Table 12. Determinants of information-related skewness: Divergence in investors’ opinion

This table presents the relationship between realized daily skewness and the measures of divergence in investors’ opinion. The table reports coefficient estimates for the following ordinary least

squares regression in each subsample: ���,� = + ��34�25�67�,� + �,� where �,� is an error term.

That is, a dependent variable of the regression is a realized daily skewness (���,�) of the k-th firm on day t, and the explanatory variables �34�25�67�,� is selected from the measures of divergence

in investors’ opinion such as daily turnover, market-adjusted daily turnover, change in market-adjusted turnover, unexplained trading volume, and change in trading volume of the k-th firm on day t.

The first four measures of divergence in investors’ opinion divergence are documented in Garfinkel (2009). The realized daily skewness (���,�) for the k-th firm on day t is computed using 5-minute

returns from the TAQ database. Daily turnover is computed as the ratio of the firm’s daily trading volume on day t to total number of shares outstanding on day t. Market-adjusted daily turnover is the

difference between a firm’s daily turnover and daily market-wide turnover on day t (computed from market-wide trading volume and market-wide shares outstanding and adjusted with a 180-day

median). Change in market-adjusted turnover is the difference in market-adjusted turnover between day t and day t-1. Unexpected trading volume is a standardized prediction error from a regression

of trading volume on the absolute value of returns of the k-th firm using the equation (11), (12), and (13). Change in trading volume is the difference in trading volume between day t and day t-1.

Panel A shows the regression results for the full sample and includes all realized daily skewness, Panel B shows the subsample of realized daily skewness accompanied by firm-specific information

releases, and Panel C shows the subsample unaccompanied by any firm-specific information releases. The numbers in parentheses are t-statistics with robust standard errors.

Panel A: Full sample

Panel B: Information sample

Panel C: No-information sample

(1) (2) (3) (4) (5)

(1) (2) (3) (4) (5)

(1) (2) (3) (4) (5)

Daily turnover 0.521***

-0.538***

0.823***

(9.93)

(-4.10)

(11.64)

Market-adj turnover

0.625***

-0.555***

0.961***

(11.12)

(-4.16)

(11.88)

∆ Market-adj turnover

0.574***

-0.412***

0.774***

(10.73)

(-3.22)

(11.28)

Unexplained volume

0.002***

-0.004***

0.003***

(6.57)

(-4.19)

(8.35)

∆ trading volume

0.890***

-0.036

1.105***

(11.09)

(-0.32)

(9.36)

Adj R-sq 0.0001 0.0001 0.0001 0.0001 0.0002

0.0001 0.0001 0.0001 0.0001 0.0001

0.0001 0.0002 0.0002 0.0001 0.0004

N 2,551,503 2,551,503 2,551,507 2,551,503 2,551,506 313,653 313,653 313,653 313,653 313,653 2,237,850 2,237,850 2,237,854 2,237,850 2,237,853

*, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.