Why do option prices predict stock returns ?
Joost Driessen
a
b
c
a†
Tse-Chun Lin
b‡
Xiaolong Lu
*
c§
Department of Finance, Tilburg University, Tilburg
School of Economics and Finance, The University of Hong Kong, Hong Kong
School of Economics and Finance, The University of Hong Kong, Hong Kong
Abstract
This paper provides a new perspective on the informational leading role of the option
market relative to the stock market. We study the extent to which the predictive power of
option implied volatilities (IVs) on stock returns lies in earnings-related or/and analyst-related
corporate news. We find that our two proxies for option trading (IV skew and IV spread)
significantly predict earnings surprises, analyst recommendation changes, and analyst forecast
changes. Next, we find that the IV skew and spread predict stock returns, and that the degree
of predictability more than doubles around earnings-related or analyst-related events.
Additionally, we show that informed traders choose to use the option market particularly
because of short-sale constraints on the underlying stock. We also find that the predictability
of option IVs increases with the liquidity of the options.
JEL Classification: G12, G14, G17.
Keywords: Informed traders; corporate events; implied volatility spread; implied volatility
skew; option liquidity.
*
The authors are grateful to Avanidhar Subrahmanyam, Gurdip Bakshi and Mark Grinblatt for valuable
comments and suggestions. We also thank seminar participants at National Chengchi University and National
Taiwan University, the Faculty of Business and Economics at the University of Hong Kong and the Research
Grants Council of the Hong Kong SAR government for the research support. Any remaining errors are our
responsibility alone.
†
Tel.: +31-13-4662324; fax: +31-13-4662875. E-mail address: [email protected]
‡
Tel.: +852-2857-8503; fax: +852-2548-1152. E-mail address: [email protected]
§
Tel.: +852-6685-0628; fax: +852-2548-1152. E-mail address: [email protected]
1. Introduction
Previous research has shown that informed traders take advantage of the high leverage in the
option market to capitalize on their private information (Black (1975) and Back (1993)). One
seminal study by Easley, O’Hara, and Srinivas (1998) argues that options would be preferred by
informed traders when the implicit leverage is high and the option market is liquid. In addition,
options can be used to trade on negative information in case of short-sale constraints on the
underlying stocks. A stream of recent empirical papers finds that proxies for option trading
predict stock returns. For example, Cremers and Weinbaum (2010) find that the deviations from
put-call parity reflects information about future stock price changes, while Xing, Zhang, and
Zhao (2010) show that the firm-level option volatility skew can predict future cross-sectional
equity returns. However, little attention has been paid to the source of these predictability
patterns.
In this paper, we bridge the gap by investigating what type of information the informed
option traders have such that their trading activities in the option market can predict future stock
returns. Following the empirical set up in Boehmer, Jones, and Zhang (2010) who study the
sources of short sellers’ information advantages, we explore the sources of the private
information held by informed option traders regarding the following corporate events: earnings
announcements, the earnings forecast provided by the company (“managerial guidance”),
earnings restatements, analyst recommendation changes, and analyst forecast revisions.
We contribute to the literature by testing two main hypotheses. First, can proxies for option
trading predict earnings-related or analyst-related news? Second, can proxies for option trading
predict underlying stock returns, and, to what extent does the predictability come from days with
earnings-related or analyst-related corporate events? We thus extend existing research by
decomposing the predictability of option trading on stock returns with respect to the specified
corporate events. In addition, we analyze whether informed investors use options because of
leverage or because of short-sales constraints on the stock.
Based on the previous studies, we employ two proxies for informed option trading: the
implied volatility (IV) spread (Cremers and Weinbaum (2010)) and the IV skew (Xing, Zhang,
1
and Zhao (2010)). The IV spread, which is the difference in IVs between matched pairs of call
and put options with identical strike prices and maturities, has been demonstrated to be a
positive predictor of equity returns. 1 On the other hand, the IV skew defined as the difference
between IVs of out-of-the-money (OTM) put options and at-the-money (ATM) call options is
proved to be negatively associated with future stock returns. 2 Intuitively, if informed traders
anticipate a drop in the stock price, they are more likely to buy put options to capitalize on their
private information, especially OTM puts. This will lead to a price increase in those put options,
resulting in a decrease of the IV spread and an increase of the IV skew.
Using option pricing data and corporate news data from January 1999 to December 2010,
our first key finding is that our proxies for option trading have economically large and
statistically significant predictive power on future earnings-related or analyst-related events.
Firms with a lower IV spread or higher IV skew in the pre-event week have lower standardized
unexpected earnings (SUE), more negative analyst recommendation changes, and worse analyst
forecast revisions.
Next we perform regressions of stock returns on each option trading proxy. Consistent with
previous studies, we document that the IV spread (IV skew) carries significantly positive
(negative) information for future excess returns. Firms with a lower (higher) IV spreads (IV
skews) experience lower stock returns in the following week. We then add interaction terms
with dummy variables indicating the days with earnings-related or analyst-related events, and
we calculate the proportion of the predictability of option trading on future excess returns that is
associated with the events. Our second key finding is that 12.2% (12.4%) of the predictability of
the IV spread (IV skew) comes from the days with corporate events including earnings
announcements, analyst recommendation changes and analyst forecast revisions. Since the event
days constitute only 5.3% (6.6%) of the IV spread (IV skew) sample, the predictive power of the
IV spread and skew is twice as large on news days compared with no-news days. Hence, a
substantial proportion of the predictability of option trading on excess returns comes from
1
See for example Ofek, Richardson, and Whitelaw (2004), Bali and Hovakimian (2009), Cremers and Weinbaum
(2010), Atilgan (2010), Chan, Li, and Lin (2012), and Chan, Ge, and Lin (2012).
2
See for example Bates (1991), Bollen and Whaley (2004), Xing, Zhang, and Zhao (2010), Van Buskirk (2011)
and Jin, Livnat, and Zhang (2011).
2
information about earnings-related or analyst-related events. Still, a large part of the
predictability is obtained on other days, which shows that option traders have information that
goes beyond the corporate events that we study.
In addition, we investigate whether the presence of short-sale constraints on the stock or the
option leverage is the main reason for informed traders to choose the option market to capitalize
on their private information. Using piece-wise linear regressions, we analyze whether the
predictability comes from cases where the IV spread (skew) is below (above) its median level,
which would be expected if short-sale constraints is the main driving force. This is what we find
empirically: when the earnings-related or analyst-related events take place, only the
below-median IV spread and above-median IV skew gain stronger predictability on excess
returns. The results point directly towards the short-sale constraint argument.
We also examine the effects of option market liquidity on our main results. Easley, O’Hara,
and Srinivas (1998) argue that liquidity plays an important role in whether the option market is
more attractive to informed traders compared with the stock market. Consistent with their
argument, we find that the proportion of the stock return predictability by option trading that is
associated with the events increases with the option market liquidity. Our findings indicate that
informed investors choose the option market to capitalize on their private information about the
upcoming corporate news when the liquidity of option market is higher.
Lastly, we study the IV spread and skew during the post-event weeks. If informed option
traders believe that the market has not fully incorporated the event news into the stock prices,
one would expect that the IV spread and skew remain at their pre-event level. On the contrary, if
traders think the market has fully reacted to the event news, they would close their option
positions and the IV spread and skew revert to their normal levels. Our results are consistent
with the latter effect.
This study is most related to Boehmer, Jones, and Zhang (2010) who document the
relationship between the predictability of stock returns from shorting activities and the
earnings-related or analyst-related events. Applying a similar empirical framework to the option
market, we find strong evidence that a significant proportion of the predictability of option
trading on excess stock returns lies in similar events.
3
Our paper is also related to the strand of literature that documents the informational leading
role of the option market relative to the stock market (e.g., Chakravarty, Gulen, and Mayhew
(2004), Lakonishok, Lee, Pearson, and Poteshman (2007), Ni, Pan, and Poteshman (2008), Roll,
Schwartz, and Subrahmanyam (2010), and Johnson and So (2011)). We complement the existing
literature by investigating how and when option trading predicts stock returns.
The remainder of the paper is organized as follows. Section 2 briefly reviews the related
literature. Section 3 describes the data and provides summary statistics for the informed option
trading measures and the event measures. Section 4 discusses empirical results for the two main
hypotheses. Section 5 presents three additional tests for the role of the short-sale constraints, the
effects of option market liquidity and the option traders’ post-event trading strategies. Section 6
shows various robustness checks. Section 7 concludes the paper.
2. Related literature
There has been a large and growing body of literature studying the information discovery in the
option market. Option trading has been demonstrated to possess predictive power for the
underlying stock returns (e.g., Chakravarty, Gulen, and Mayhew (2004), Pan and Poteshman
(2006), and Doran, Tarrant, and Peterson (2007)). Two frequently used informed trading
measures constructed from the option market in this stream of research are the IV spread and the
IV skew.
The IV spread measures the deviations from put-call parity. Stoll (1969) shows that a pair
of European style call and put options on the same underlying asset with identical strike price
and expiration date should have equal IVs. For American options which can be exercised early,
the deviation from put-call parity does not necessarily mean an arbitrage opportunity. In addition,
in case of transaction costs, there is a range of call and put prices that preclude arbitrage even for
European options. Then, in a market where options are not perfectly liquid, buy or sell pressure
may lead to deviations from put-call parity that do not reflect an arbitrage opportunity, but rather
(informed) trading. In case of positive information, call buying pressure may push call IVs up,
above put IVs. In case of negative information, the opposite may happen. If informed traders
prefer the option market, the IV spread may then predict future stock returns. Bali and
4
Hovakimian (2009) indeed find that the firm-level IV spread positively predicts stock returns.
Cremers and Weinbaum (2010) show that the IV spread is positively related to future stock
returns, and the predictability cannot be explained by short sale constraints. Atilgan (2010) finds
that stocks with a larger IV spread earn higher abnormal returns during a two-day earnings
announcement window.
The IV skew is the difference between the IVs of OTM put options and ATM call options
on the same security. In the option pricing model of Black and Scholes (1973), IVs of all options
on a given stock should be independent of the strike prices. But in reality, the distribution of the
IV presents the shape of a smile or smirk when plotted against strike prices, implying OTM put
options are more expensive than ATM options (Rubinstein (1994)). The IV skew, which
measures the left-shape of the IV function, is found to contain negative predictive information
for future stock returns. The intuition is that informed traders buy OTM put options to express
their negative information. Note that OTM options provide higher leverage than ATM or
in-the-money (ITM) options. For example, Xing, Zhang, and Zhao (2010) sort stocks on their IV
skew and find that stocks with high IV skews have lower subsequent returns. Van Buskirk (2011)
concludes that an increase in the IV skew suggests a higher probability of the firm experiencing
crashes during short-window earnings announcement periods. Atilgan, Bali, and Demirtas (2011)
find a negative correlation between the IV skew calculated from the S&P 500 index options and
the expected market return. 3
While numerous papers have shown the predictability of option trading on stock returns,
little is known about what drives the predictive power. There are studies investigating the
correlation between option trading and various informational events, for example, earnings
announcements (Patell and Wolfson (1981) and Amin and Lee (1997)), upcoming takeovers
(Cao, Chen, and Griffin (2005)), tail risk of extreme negative events (Van Buskirk (2009)),
future stock splits (Chan, Li, and Lin (2012)), and merger and acquisitions (Chan, Ge, and Lin
(2012)). But no work has been done to link the two streams of studies.
3
Note that the implied volatility skew may also reflect a risk premium for jump risk. This would imply a positive
relation between the IV skew and subsequent stock returns. Existing work does not find an important role for such
an effect.
5
We contribute to the existing literature by combining the two lines of research and
exploring whether the predictive power of option trading on future stock returns comes from
informed traders’ private information related to upcoming corporate events.
3. Data description and summary statistics
We use option data from OptionMetrics, a comprehensive database providing end-of-day bid
and ask quotes, open interests, trading volumes and other relevant information for all options on
US exchange listed equities. The event data of the earnings announcements, the earnings
restatements, the analyst recommendation changes and the analyst forecast revisions are
extracted from the Institutional Brokers' Estimate System (I/B/E/S). The managerial guidance
data are from the First Call Historical Database (FCHD). Since I/B/E/S reports accurate earnings
announcement time only after January 1999, our sample period covers from January 1999 to
December 2010. 4 The stock trading data are from the Center for Research in Security Prices
(CRSP). The general accounting data are provided by the Compustat.
Numeric values are assigned to each type of the earnings-related or analyst-related events
to measure their direction and magnitude. The earnings announcement news is measured by the
value of the standardized unexpected earnings (SUE) calculated as the announced earnings per
share (EPS) less the corresponding analyst consensus forecast scaled by the standard deviation
of the quarterly earnings estimates; the managerial guidance (the earnings forecast of the
company) is measured as the forecast issued by the company less the corresponding analyst
consensus forecast; the earnings restatement equals the newly stated quarterly EPS less the
previously stated one; the analyst recommendation change is the total number of notches
changed, where an analyst recommendation equals a number from 5 to 1 indicating strong buy,
buy, hold, underperform, and sell respectively; the analyst forecast revision is measured as the
new analyst consensus less the old one.
[Table 1 to be inserted here]
Table 1 provides summary statistics on the five types of events. In our sample, the analyst
4
See variables descriptions from I/B/E/S: http://wrds-web.wharton.upenn.edu/wrds/ds/ibes/act/index_doc.cfm.
6
forecast revision occurs most frequently, while the earnings restatement is the most infrequent
one. All five types of events are quite volatile across the sample. The SUE has a mean of -0.19%
and a standard deviation of 3%; the managerial guidance has a mean of 0.04 and a standard
deviation of 0.22; the average earnings restatement is -0.11 with the standard deviation being
0.63; the average analyst recommendation change is -0.17 while its standard deviation is 1.60;
the analyst forecast revision has a mean of 0.67% and its standard deviation is 4%.
The IV spread is calculated as the open-interest weighted average of the differences in IVs
between matched pairs of call and put options on the same underlying with identical strike
prices and expiration dates (Cremers and Weinbaum (2010)). The IV skew is defined to be the
difference between IVs of the out-of-the-money (OTM) put option and the at-the-money (ATM)
call option on the same stock (Xing, Zhang, and Zhao (2010)). Detailed construction of the two
variables is in Appendix.
[Table 2 to be inserted here]
Table 2 reports time series descriptive statistics for each of the informed option trading
measure. For the full sample period of January 1999 to December 2010, we have 7,200,862 IV
spreads calculated for 6,303 distinct firms, and 2,919,955 IV skews for 5,447 firms. Consistent
with previous studies, the IV spread is on average negative while the IV skew is on average
positive. The average daily cross-sectional mean of the IV spread is -1.2%, indicating put
options are in general more expensive than the matched call options with the same strike prices
and maturities. For the IV skew, the average daily cross-sectional mean is 5.7%, suggesting
OTM put options on average more expensive than ATM call options. Both the IV spread and the
IV skew exhibit substantial variations. The average daily cross-sectional standard deviation of
the IV spread is 6%, and 6.3% for the IV skew.
4. Main hypotheses and empirical results
In this section, we test our two main hypotheses. First, can option trading predict the direction
and magnitude of upcoming earnings-related or analyst-related corporate events? Second, does
option trading have predictive power on future excess returns, and, to what extent does the
7
predictability come from the earnings-related or analyst-related corporate events? The detailed
empirical setup is outlined in each of the following subsections. All estimated standard errors are
clustered by firm and calendar quarter to adjust for the cross-sectional and serial correlations in
the pooled regression residuals (Petersen (2009)).
4.1. Predictability of option trading on upcoming events
To test the first hypothesis, we perform pooled OLS regressions of the earnings-related or
analyst-related events on each option trading measure:
β 0 + β 1 optioni ,t −5,t −1 + β 2 ln sizei ,t −5,t −1 + β3bmi ,t −5,t −1 + β 4 reti ,m −6,m −1 + β5σ i ,m −1 + β 6turnoveri ,t −5,t −1 + ε i ,t ,
eventi ,t =
(1)
where eventi ,t indicates the variable capturing the earnings-related or analyst-related events
described in Section 3. To alleviate the influence of extreme values, all event measures are
winsorized at 0.5% level in each tail. The variable optioni ,t −5,t −1 refers to the informed trading
measures constructed from the option market five trading days before the event. It can take the
value of spreadi ,t −5,t −1 or skewi ,t −5,t −1 (the average IV spread and average IV skew over the
pre-event week).
Other explanatory variables controlling for different firm characteristics include: the
natural logarithm of the firm market capitalization for the previous week ln sizei ,t −5,t −1 , the book
to market ratio of the previous week bmi ,t −5,t −1 , the stock return over the past six months
reti ,m −6,m −1 , the equity return volatility calculated using daily data in the previous month σ i ,m −1 ,
and the turnover rate calculated as the stock trading volume over the number of shares
outstanding for the previous week turnoveri ,t −5,t −1 .
We expect to find a negative (positive) relation between the IV spread (IV skew) and
earnings surprises, managerial guidance statements, earnings restatements, analyst changes, and
analyst forecast revisions. If informed traders anticipate bad news to be announced, they are
more likely to buy the put options to capitalize on their private information, especially the OTM
puts, leading to a decrease in spreadi ,t −5,t −1 and an increase in skewi ,t −5,t −1 .
8
[Table 3 to be inserted here]
Table 3 reports the regression results for the IV spread. When only the IV spread is in the
regressions, it significantly predicts earnings announcement surprises, earnings restatements,
analyst recommendation changes, and analyst forecast revisions, all with the expected positive
sign.
With inclusion of all control variables, the predictability of the IV spread remains
statistically significant for the earnings announcement surprise and the analyst recommendation
change, with t-statistics of 3.6 and -6.3, respectively. The economic magnitude of the
predictability is especially large for the earnings announcements. A one standard deviation
increase in the IV spread is associated with an increase in the SUE by 2.59 standard deviations.
[Table 4 to be inserted here]
Table 4 reports regression results for the IV skew. When only the IV skew is in the
regressions, it has significant predictive power for future earnings announcements, managerial
guidance, analyst recommendation changes and analyst forecast revisions. Only for earnings
restatements we do not find significant results.
Including all control variables does not take away the predictive power of the IV skew.
Except for the earnings restatements, all corporate events are still predicted by the IV skew.
Similar to the IV spread regressions, the economic magnitude of the predictability of the IV
skew is particularly large for future earnings announcements. A one standard deviation increase
in the IV skew is accompanied with a one standard deviation decrease in the SUE.
In sum, our findings suggest that our proxies for option trading indeed possess
economically large and statistically significant predictive power for future earnings-related or
analyst-related events.
4.2. Decomposition of the predictability of option trading on future stock returns
Our second hypothesis contributes to existing literature by decomposing the predictability of
option trading on stock returns regarding specified corporate events. In this subsection, we focus
on the three types of events on which the option trading has been demonstrated to have the most
9
predictive power in the first hypothesis, namely the earnings announcements, the analyst
recommendation changes and the analyst forecast revisions. For these events we also have the
most observations.
Before running pooled regressions in the same way as above, we look at the performance of
the long/short portfolios formed on the two option trading proxies. We divide our sample into an
event group and no-event group based on occurrences of the earnings announcement, the analyst
recommendation change or the analyst forecast change. For each sub-sample, stocks are sorted
into deciles every trading day based on the average IV spread or IV skew over the previous
week. Abnormal returns during the post-formation week are calculated for the long/short
portfolio, which longs stocks in the highest decile and shorts stocks in the lowest decile, with
respect to the four Fama-French (1993) and Carhart (1997) factors:
Hight − Lowt =
α + β1 ( Rmt − Rft ) + SMBt + HMLt + ε t ,
(5)
[Table 5 to be inserted here]
Table 5 presents abnormal returns for the long/short portfolios in both sub-groups. In the
value-weighted case, the IV spread hedge portfolio gains a positive daily abnormal return of
10.55 basis points (t-statistic= 3.01) in the post-formation week on event days, and 5.57 basis
points (t-statistic= 4.19) on no-event days. Hence, stocks with high IV spreads outperform
stocks with low IV spreads, and more so around event days. The IV skew hedge portfolio earns
a negative daily abnormal return of -8.34 basis points (t-statistic= -2.85) for the event group, and
-4.10 basis points (t-statistic= -2.89) for the no-event group. As expected, high IV-skew stocks
thus earn lower returns than low IV-skew stocks, again more so around event days. The
equal-weighted results give qualitatively similar patterns.
[Table 6 to be inserted here]
The empirical regression tests are conducted in three steps. In the first step, excess returns are
regressed on each option trading measure and the control variables:
exreti ,t ,t + 4 =
β 0 + β1optioni ,t −5,t −1 + γ controlsi ,t −1 + ε i ,t ,
10
(2)
where exreti ,t ,t + 4 is the daily excess stock return calculated as the stock return in excess of the
S&P 500 return as the market proxy, averaged over day t to day t + 4 . The controlsi ,t −1 are
the lagged control variables described in the previous subsection. Based on previous studies, we
expect the IV spread to be positively correlated with future excess returns, and the IV skew to be
negatively correlated with future excess returns.
In the second step, we add an interaction term between the option trading measures and a
dummy variable indicating the occurrence of any of the three events into the previous
regressions:
exreti ,t ,t + 4 = β 0 + ( β1 + β 2 dummyi ,t )optioni ,t −5,t −1 + γ controlsi ,t −1 + ε i ,t ,
(3)
where dummyi ,t takes the value of 1 if any one of the three events takes place for firm i on day
t , and 0 otherwise. Therefore, when none of the three informational events takes place, the
predictability of option trading on future excess returns is measured as β1 . When any one of the
events occurs, the predictability becomes β1 + β 2 . Hence, the interacted coefficient β 2
indicates the predictability from the event-day such that we can calculate the proportion of the
predictability that is attributed to informed option traders’ private information about the
upcoming three types of events.
In the last step, we replace the dummyi ,t in the previous step by three individual event
dummy variables to test the hypothesis for each event type separately:
exreti ,t ,t + 4 = β 0 + ( β1 + β 2 suei ,t + β3 recommendi ,t + β 4 revisioni ,t )optioni ,t −5,t −1 + γ controlsi ,t −1 + ε i ,t ,
(4)
where suei ,t equals 1 if an earnings announcement takes place for firm i on day t , and 0
otherwise; recommendi ,t equals 1 if an analyst recommendation change takes place, and 0
otherwise; revisioni ,t an analyst forecast revision takes place, and 0 otherwise. By the same
argument as in the previous step, the interacted coefficients of β 2 , β3 , and β 4 help us to
11
gauge the portion of the predictability that comes from informed option traders’ private
information for each event.
Table 6 presents the regression results on the second hypothesis for the IV spread. The first
two columns are for regressions in the first step. As expected, the IV spread is positively related
to future excess returns, with a t-statistic of 6.30 without controls and 5.3 with control variables.
The results indicate that a one standard deviation increase in the IV spread would raise the
average daily excess return in the following week by 3.3 basis points. 5 Our results are in line
with previous studies, but we provide more precise t-statistics by employing the double
clustering procedure for the estimated standard errors.
The third and fourth columns of Table 6 report regression results for the second step. When
we only include the IV spread and its interaction term, the IV spread itself carries a significant
coefficient of 0.55 (t-statistic = 6.51), and the interaction term has a significant coefficient of
0.77 (t-statistic = 2.68). In the fourth column, with inclusion of all the control variables, the
coefficient estimate on the IV spread becomes 0.52 (t-statistic = 5.48), and the coefficient
estimate on the interaction term is still 0.77 (t-statistic = 2.38). Hence, the predictability of the
IV spread over excess returns on event days is more than double of that on non-event days (1.29
vs. 0.52).
To further compute the exact percentages of the predictability that come from the events,
we can follow the analysis in Boehmer, Jones, and Zhang (2010): since event days constitute
5.28% of the whole IV spread sample, the overall predictive power of the IV spread can be
measured as: 0.52 * (1 - 5.28%) + (0.52 + 0.77) * 5.28% = 0.56. So the fraction of the
predictability that comes from the informed option traders’ private information about the three
events can be calculated as: (0.52 + 0.77) * 5.28% / 0.56 = 12.15%.
The last two columns of Table 6 report results for the last step. As presented in the last
column, event after controlling for different firm characteristics, the IV spread carries a
significant coefficient of 0.52. The coefficient estimates on the interacted terms are 0.66, 0.70,
and 0.86 for the earnings announcement dummy, the analyst recommendation change dummy,
5
Boehmer, Jones and Zhang (2010) report that one standard deviation increase in short interest would reduce the
average daily return in excess of riskfree rate in the following week by 3.12 basis points.
12
and the analyst forecast revision dummy respectively, and all are statistically significant.
Following similar calculations as in the previous step, since the earnings announcement days,
the analyst recommendation change days, and the analyst forecast revision days make 1.31%,
1.57%, and 2.84% of the whole IV spread sample, approximately 2.92%, 3.62% and 7.18% of
the predictability of the IV spread on excess returns can be attributed informed option traders’
private information about each corporate event.
[Table 7 to be inserted here]
We then turn to the IV skew, and perform a similar analysis. Table 7 presents the results.
The first two columns report regressions in step one. The relation between the IV skew and
future stock returns is significantly negative. When only including the IV skew, the coefficient
estimate on it is -0.22 with a t-statistic of -3.58. After including all control variables, the
coefficient estimate on the IV skew becomes -0.24 with a t-statistic of -3.98. A one standard
deviation increase in the IV skew would decrease the average daily excess return in the
following week by 2 basis points. Similarly as in the IV spread regressions, our results are
consistent with previous studies, but we have more precise t-statistics due to the double
clustering procedure.
The third and fourth columns of Table 7 provide results for step two. When only including
the IV skew and its interaction term with the event dummy variable, the coefficient estimate on
the IV skew is -0.20 (t-statistic = -3.48), and the interacted coefficient is -0.27 (t-statistic =
-2.23). After inclusion of all control variables, the IV skew has a statistically significant
coefficient of -0.23 while the interaction term carries a significant coefficient of -0.23. The
results imply that the predictability of the IV skew for stock returns on event days is twice as
large as the predictability on non-event days (-0.46 vs. -0.23). If we take into account that the
event days make 6.57% of the whole IV skew sample, the overall predictive power can be
calculated as: -0.23 * (1 - 6.57%) + (-0.23 - 0.23) * 6.57% = -0.25. The fraction of the
predictability that is associated with informed option traders’ private information about the
events can be measured as: (-0.23 - 0.23) * 6.57% / -0.25 = 12.4%.
The last two columns in Table 7 present results distinguishing between the different types
of corporate events. The interacted coefficient is found to be significantly negative for the event
13
of analyst recommendation change even after controlling for the firm characteristics. As
presented in the last column, the IV skew has a significant coefficient of -0.23 (t-statistic =
-3.83), while the interaction term with the analyst recommendation change dummy carries a
significant coefficient of -0.70 (t-statistic = -4.73). Therefore, the predictability of the IV skew
for stock returns on analyst recommendation change days is three times larger than on other
days (-0.93 vs. -0.23). Following similar calculations as in the previous step, as 1.95% of the
days in the IV skew sample are with analyst recommendation changes, 7.54% of the
predictability of the IV skew on future excess returns is associated with the event of the analyst
recommendation change.
To sum up, consistent with previous studies, our paper shows that option trading has
significant predictive power over future excess returns. What is more important is that we
decompose the predictabilities and provide direct evidence that the predictability of option
trading on future excess returns is substantially related to informed investors’ private
information about the future earnings announcements, analyst recommendation changes, and
analyst forecast revisions.
5. Additional tests
5.1. Predictability of stock returns and short-sale constraints
Informed traders may go to the option market because of the leverage provided by options
and/or to get around short-sales constraints on the underlying stock. In the latter case, options
would only be used to exploit negative private information. We thus test which explanation is
most important by looking at whether a larger portion of the option trading predictability on
excess returns comes from the cases with bad news. Empirically, we run piece-wise regressions
with the median of the option trading proxy as the kink point. For both the IV spread and IV
skew, two independent variables take the place of the original one in the regression model:
exreti ,t ,t + 4 = β 0 + ( β1 + β 2 dummyi ,t )optionabovei ,t −5,t −1 + ( β 3 + β 4 dummyi ,t )optionbelowi ,t −5,t −1
+ γ controlsi ,t −1 + ε i ,t ,
(6)
where optionabovei ,t −5,t −1 takes value of average IV spread or IV skew over the previous week
14
if it is above the median, and takes value zero otherwise, and similarly for optionbelowi ,t −5,t −1 .
[Table 8 to be inserted here]
Table 8 presents results for the piece-wise regressions. Among the four interacted terms
with the event dummy variable, only the below-median IV spread and the above-median IV
skew have significant interacted coefficients. The below-median IV spread carries a positive
coefficient of 0.53 (t-statistic = 5.24) and its interaction with the event dummy variable equals
1.08 (t-statistic = 2.80). The coefficient on the above-median IV skew is -0.23 (t-statistic =
-3.86), and its interaction with the event dummy variable is -0.27 (t-statistic = -2.19). The results
suggest that upon the occurrences of the three main corporate events, for both IV spread and IV
skew only the negative news cases imply stronger predictive power over excess returns. This is
in line with the argument that short-sale constraints play an important role for informed option
investors.
5.2. Predictability of stock returns and option market liquidity
Easley, O’Hara, and Srinivas (1998) suggest that the option market would be preferred by
informed traders compared to the stock market when the option liquidity is relatively higher. It is
thus a natural extension to examine whether our results derived in previous two hypotheses
would be stronger when the option market is more liquid. To test this conjecture, we use the
option bid-ask spread, which is calculated as the best ask price less the best bid price scaled by
the midpoint, as a proxy for the option market illiquidity.
We add interaction terms of the bid-ask spread, each informed option trading measure and
the event dummy variable into equation (3):
exreti ,t ,t + 4 = β 0 + ( β1 + β 2 dummyi ,t + β3baspi ,t −5,t −1 * dummyi ,t )optioni ,t −5,t −1 + γ controlsi ,t −1 + ε i ,t ,
(7)
where the baspi ,t −5,t −1 is the average bid-ask spread over the previous week. We expect β3 to
have the opposite sign of β1 and β 2 , since we expect lower predictability when options have
higher bid-ask spreads.
[Table 9 to be inserted here]
15
Table 9 reports regression results for equation (7). The triple interaction between event
dummies, the option trading measure and bid-ask spread, β3 , equals -1.23 for the IV spread
(t-statistic = -2.30) and 0.30 for the IV skew (t-statistic = 1.89). The results imply that the
predictability of the option trading on future excess returns becomes less related to informed
traders’ private information about the three events when the option market liquidity is lower.
Overall, consistent with Easley, O’Hara, and Srinivas (1998), we find that our main results
are weaker when the option market is more illiquid. It suggests that less informed investors to
choose the option market to capitalize on their private information about future earnings-related
or analyst-related events when the option market liquidity decreases.
5.3. Option trading measures in the post-event period
Lastly, we examine the trading strategies of option traders after the announcements of the
corporate events. If option traders believe that the market has not fully incorporated the news into
stock prices, they would continue to hold their option positions and the IV spread and skew are
expected to remain at their pre-event levels for some time. Alternatively, they will choose to
liquidate their options, in which case one would expect the IV spread and skew to revert to their
normal levels. The post-event period option trading is thus investigated as follows:
optioni ,t +1,t +5 =+
β 0 β1reti ,t + β 2 optioni ,t −5,t −1 + β3 reti ,t −5,t −1 + γ Controlsi ,t −1 + ε i ,t ,
(8)
where the optioni ,t +1,t +5 is the average of the daily informed option trading measures over day
t+1 to day t+5. It can take the value of spreadi ,t +1,t +5 and skewi ,t +1,t +5 . The variable reti ,t is the
stock return on the event-day and the reti ,t −5,t −1 is the average stock return over the previous
week.
The coefficient of β1 describes the option trading measure following the stock price
changes. A negative (positive) β1 for the IV spread (IV skew) suggests that informed traders
reduce (or even reverse) their positions after the event days. In other words, they believe that the
market has incorporated the news. If β1 is zero, there is no change in the IV spread or skew,
16
consistent with the view that informed traders maintain their option positions as they believe that
the news has not been fully incorporated in the stock price. Finally, a positive (negative) β1 for
the IV spread (IV skew) suggests that informed traders increase their option positions, perhaps
because they believe that most of the news still has to be incorporated into the stock price.
[Table 10 to be inserted here]
Table 10 provides the regression results for the IV spread. In the first set of regressions
without controlling for different firm characteristics, the coefficient of β1 on the event-day
stock return is significant and equal to -3.30, -3.07 and -3.80 for the earnings announcement
subsample, the analyst recommendation subsample, and the analyst forecast revision subsample.
After adding all control variables, the β1 s still show statistical significance with similar
coefficient estimates. The results suggest that option traders quickly reduce their option
positions after the corporate events, and that the IV spread returns to its normal level.
[Table 11 to be inserted here]
Table 11 shows the regression results using the IV skew as the informed option measure.
Here we find positive and mostly significant coefficients, which show that after a positive
(negative) stock return the IV skew increases (decreases). Hence, also for the IV skew we find
that the IV skew returns to its normal level quickly, in line with the notion that option traders
reduce their option positions after the event.
In summary, our findings provide empirical evidence that option traders reduce their option
positions during the week after the corporate events.
6. Robustness checks
6.1. Alternative option trading measures
Following Cremers and Weinbaum (2010), we use the change in the IV spread (skew) instead of
the level of these variables. We calculate the IV spread (skew) change as the average level over
the previous week less the average level over the previous month (excluding the last week), and
perform similar regressions as before,
17
optionchange
optioni ,t −5,t −1 − optioni ,t − 22,t −6 ,
=
i ,t
exreti ,t ,t + 4 = β 0 + ( β1 + β 2 dummyi ,t )optionchangei ,t + γ controlsi ,t −1 + ε i ,t ,
(9)
(10)
As presented in Table 12, in regression (10) the IV spread change carries a coefficient of 0.56
(t-statistic= 5.12), and its interacted coefficient with the event dummy variable is 0.75
(t-statistic= 2.77). The coefficient on the IV skew change is -0.23 (t-statistic= -4.12) and the
interacted term is -0.25 (t-statistic= -1.66). Following the same calculation as in the main
hypotheses, 10.92% (12.06%) of the predictability of the IV spread (IV skew) change is
correlated with informed investors’ private information about the occurrences of the three main
events.
Another robustness check is on the period over which we measure the IV skew and spread.
In the benchmark analysis, we use the average over the previous week. Now, we use the average
over the previous month:
exreti ,t ,t + 4 = β 0 + ( β1 + β 2 dummyi ,t )optioni ,t − 22,t −1 + γ controlsi ,t −1 + ε i ,t ,
(11)
[Table 12 to be inserted here]
Table 12 shows that this does not affect results much: in regression (11) with average option
trading proxies over the previous month, the coefficient on the IV spread is 0.40 (t-statistic=
3.88) and its interacted term with the event dummy variable is 0.69 (t-statistic= 1.82). The IV
skew coefficient is -0.18 (t-statistic= -1.98) and the interacted coefficient is -0.22 (t-statistic=
-1.71). By the same calculation, 12.49% (12.71%) of the predictability of the prior one-month
IV spread (IV skew) is related to future corporate events.
In sum, we find similar results using IV spread (IV skew) changes and the prior one-month
averages.
6.2. Other proxies
We also consider various other option trading proxies. Specifically, we consider the “left IV
spread”, the “right IV spread”, the “left IV skew” and the “right IV skew”. The left IV spread is
defined to be the open-interest weighted average of the differences in IVs between matched
18
pairs of OTM put options and ITM call options with the same strike price and expiration date.
The right IV spread is the open-interest weighted average of the differences in IVs between
matched OTM call options and ITM put options. 6 The left IV skew is the difference between
the IVs of the OTM put option and the ATM put option, and the right IV skew is the difference
between the IVs of the OTM call option and the ATM call option. 7 We should anticipate the left
IV spread and the left IV skew to predict negative corporate events and excess returns, and the
right IV spread and the right IV skew to predict positive events and returns. We get expected
results (non-tabulated) for the two new IV spreads and the left IV skew. The right IV skew has
little predictive power, suggesting that using negative information is more important in the
option market.
7. Conclusion
Existing work has demonstrated that several measures of option trading have predictive power
for stock returns, consistent with the view that informed traders take advantage of the high
leverage in the option market and/or get around short-sales constraints on the underlying stock
to capitalize on their private information. However, the information sources that lie beneath
these predictive patterns have never been studied in previous research. This is where our paper
contributes to the literature. Using both the IV spread and the IV skew as informed option
trading measures, we document economically large and statistically significant predictive power
of option trading measures on future earnings-related or analyst-related events, namely the
earnings announcements, the analyst recommendation changes and the analyst forecast revisions.
In addition, we decompose the predictability of option trading on stock returns. We find that
12.2% of the predictive power of the IV spread and 12.4% of the predictive power of the IV
skew come from informed option traders’ private information associated with the upcoming
earnings-related or analyst-related events. Furthermore, we show that the short-sale constraint
6
A call option is ITM if its moneyness (strike price to stock price) is between 0.8 and 0.95, and is OTM if its
moneyness is between 1.05 and 1.2. A put option is ITM if the moneyness is between 1.05 and 1.2.
7
A put option is ATM if its moneyness is between 0.95 and 1.05. For each stock each day, we choose the ATM put/
call option with moneyness closest to 1, the OTM put option with moneyness closest to 0.95, and the OTM call
option with moneyness closest to 1.05.
19
plays an important role when informed investors choose the option market to capitalize their
private information. We find that our results are more pronounced when the option market is
more liquid. We also present evidence that option traders quickly reduce their positions during
the week following the events.
20
Appendix: Measures of informed option trading
A.1. IV spread
Following Cremers and Weinbaum (2010), for stock i on day t which has n pairs of
matched call and put options with identical strike prices and expiration dates, the IV spread is
calculated to be the open-interest weighted average of the differences in IVs between the
matched call and put options:
=
spreadi ,t
ni ,t
∑w
j =1
i
j ,t
( IV ji,,tcall − IV ji,,tput ),
(12)
We employ the same filters as in Cremers and Weinbaum (2010): i. the open-interest is
positive; ii. the best bid price is positive.
A.2. IV skew
We construct the measure of the IV skew after Xing, Zhang and Zhao (2010) as the difference
between the IVs of the OTM put option and the ATM call option:
skew
=
IVi ,OTMP
− IVi ,ATMC
,
i ,t
t
t
(13)
A put option with the moneyness of the strike price to stock price ratio between 0.80 and
0.95 is defined to be OTM. A call option is defined to be ATM if the strike price to stock price
ratio is between 0.95 and 1.05. In case of more than one record of OTM put or ATM call options
for one stock on one day, we choose the put option with the moneyness closest to 0.95 and the
call option with the moneyness closest to 1.
Same filters as in Xing, Zhang and Zhao (2010) are employed to reduce the effects of
illiquid options and outliers include: i. the volume of the underlying stock is positive; ii. the
price of the underlying stock is above $5; iii. the IV of the option is between 0.03 and 2; iv. the
mean of the best bid and best ask prices of the option is above $0.125; v. the open interest of the
option is positive; vi. the trading volume of the option is not missing; vii. the time to maturity of
the option is within 10 to 60 days.
21
Reference:
Amin, K. I. and C. M. C. LEE, 1997, Option trading, price discovery, and earnings news
dissemination, Contemporary Accounting Research, 14(2): 153–192.
Atilgan, Yigit, 2010, Deviations from put-call parity and earnings announcement returns,
Working paper.
Atilgan, Yigit, T. G. Bali and K. O. Demirtas, 2011, Implied volatility spreads, skewness and
expected market returns, Working paper.
Back, Kerry, 1993, Asymmetric information and options, Review of Financial Studies, 6(4):
435-472.
Bali, T. G. and Armen Hovakimian, 2009, Volatility spreads and expected stock returns,
Management Science, 55(11): 1797-1812.
Bates, D.S., 1991, The crash of ’87: Was it expected? The evidence from option markets,
Journal of Finance, 46(3): 1009-1044.
Black, Fischer, 1975, Fact and fantasy in the use of options, Financial Analysts Journal, 31(4):
36-41, 61-72.
Black, Fischer and Myron Scholes, 1973, The pricing of options and corporate liabilities,
Journal of Political Economy, 81(3): 637-654.
Boehmer, Ekkehart, C. M. Jones and Xiaoyan Zhang, 2010, What do short sellers know?,
Working paper.
Bollen, N. P. B. and R. E. Whaley, 2004, Does net buying pressure affect the shape of implied
volatility functions?, Journal of Finance, 59(2): 711-753.
Van Buskirk, A., 2009, Implied volatility skew and firm-level tail risk, Working paper.
Van Buskirk, A., 2011, Volatility skew, earnings announcements and the predictability of crashes,
Working paper.
Cao, Charles, Zhiwu Chen and J. M. Griffin, 2005, Informational content of option volume prior
to takeovers, Journal of Business, 78(3): 1073-1109.
Carhart, Mark M., 1997, On persistence in mutual fund performance, Journal of Finance, 52(1):
57-82.
Chakravarty, Sugato, Huseyin Gulen and Stewart Mayhew, 2004, Informed trading in stock and
options markets, Journal of Finance, 59(3): 1235-1258.
22
Chan, Konan, Li Ge and T. C. Lin, 2012, Informational content of option trading on acquirer
announcement return, Working paper.
Chan, Konan, Fengfei Li and T. C. Lin, 2012, Informed trading and stock splits, Working paper.
Cremers, Martijn and David Weinbaum, 2010, Deviations from put-call parity and stock return
predictability, Journal of Financial and Quantitative Analysis, 45(2): 335-367.
Doran, J. S., B. C. Tarrant and D. R. Peterson, 2007, Is there information in the volatility skew?,
Journal of Futures Markets, 27(10): 921-960.
Easley, David, Maureen O'Hara and P. S. Srinivas, 1998, Option volume and stock prices:
evidence on where informed traders trade, Journal of Finance, 53(2): 431-465.
Fama, E. F. and K. R. French, 1993, Common risk factors in the returns on bonds and stocks,
Journal of Financial Economics, 33 (1): 3-53.
Jin, Wen, Joshua Livnat and Yuan Zhang, 2011, Option prices leading equity prices: superior
information discovery or superior information processing?, Journal of Accounting Research,
forthcoming.
Johnson, T. L. and E. C. So, 2011, The option to stock volume ratio and future returns, Journal
of Financial Economics, forthcoming.
Lakonishok, Josef, Inmoo Lee, N. D. Pearson and A. M. Poteshman, 2007, Option market
activity, Review of Financial Studies, 20(3): 813–857.
Ni, S. X., Jun Pan and A. M. Poteshman, 2008, Volatility information trading in the option
market, Journal of Finance, 63(3): 1059–1091.
Pan, Jun and A. M. Poteshman, 2006, The information in option volume for future stock prices,
Review of Financial Studies, 19(3): 871-908.
Patell, J. M. and M. A. Wolfson, 1981, The ex ante and ex post price effects of quarterly
earnings announcements reflected in option and stock prices, Journal of Accounting Research,
19(2): 434-458.
Petersen, Mitchell, 2009, Estimating standard errors in finance panel data sets: comparing
approaches, Review of Financial Studies, 22(1): 435-480.
Roll, Richard, Eduardo Schwartz and Avanidhar Subrahmanyam, 2010, O/S: The relative
trading activity in options and stock, Journal of Financial Economics, 96(1): 1-17.
Rubinstein, Mark, 1994, Implied binomial trees, Journal of Finance, 49(3): 771-818.
Stoll, H. R., 1969, The relationship between put and call option prices, Journal of Finance,
24(5): 801-824.
23
Whitelaw, R. F., Eli Ofek and Matthew Richardson, 2004, Limited arbitrage and short sales
restrictions: evidence from the options markets, Journal of Financial Economics, 74(2):
305-342.
Xing, Yuhang, Xiaoyang Zhang and Rui Zhao, 2010, What does the individual option volatility
smirk tell us about future equity returns?, Journal of Financial and Quantitative Analysis, 45(3):
641-662.
24
Table 1: Earnings-related or analyst-related events
Table 1 reports descriptive statistics on the numerical measures of the earnings-related or analyst-related
events. Data are obtained from the First Call Historical Database (for the managerial guidance) and the
I/B/E/S (for other events). The full sample period is January 1999 to December 2010. Earnings
announcement is measured by the SUE which is the announced quarterly EPS less the corresponding
analyst consensus forecast scaled by the standard deviation of the quarterly earnings estimates.
Managerial guidance is the value of the guidance issued by the company less the corresponding analyst
consensus forecast. Earnings restatement is the newly stated quarterly EPS less the previously stated one.
Recommendation change is the total number of notches changed, where an analyst recommendation
equals a number from 5 to 1 indicating strong buy, buy, hold, underperform, and sell respectively.
Forecast revision is the new analyst consensus less the old one. Firm is the number of firms included.
Day is the number of event days. Std is the standard deviation across observations. N is the number of
observations.
Earning announcement
Managerial guidance
Earnings restatement
Recommendation change
Forecast revision
Firm
Day
25%
50%
75%
8,700
2,509
706
9,415
8,406
3,014
2,587
667
3,714
3,809
-0.07%
-0.03
-0.07
1
-0.25%
0.04%
-0.005
-0.02
1
0.13%
0.23%
0.06
0.02
-1
0.75%
25
Mean
Std
N
-0.19% 3% 152,240
0.04
0.22 10,123
879
-0.11 0.63
-0.17 1.60 161,272
0.67% 4% 274,523
Table 2: Time-series descriptive statistics for informed option trading measures
This table provides descriptive statistics for the IV spread and the IV skew by calendar year. Data are
obtained from the OptionMetrics. The full sample period is January 1999 to December 2010. IV spread is
the difference in IVs between matched pairs of call and put options on the same security with identical
strike prices and maturities. IV skew is the difference between IVs of the OTM put option and the ATM
call option on the same stock. Cross-sectional statistics for each day are calculated first, and then we take
average of the daily time series. Firm is the number of firms included. Std is the standard deviation
across observations.
Year
Firm
Panel A: IV spread
1999
2,952
2000
2,872
2001
2,554
2002
2,457
2003
2,351
2004
2,548
2005
2,723
2006
2,988
2007
3,309
2008
3,355
2009
3,303
2010
3,366
All
6,303
25%
50%
75%
95%
Mean
Std
-0.037
-0.043
-0.030
-0.023
-0.018
-0.018
-0.020
-0.019
-0.022
-0.041
-0.038
-0.029
-0.028
-0.009
-0.012
-0.007
-0.007
-0.005
-0.007
-0.008
-0.007
-0.007
-0.013
-0.012
-0.008
-0.009
0.018
0.017
0.011
0.007
0.007
0.003
0.001
0.003
0.005
0.010
0.009
0.010
0.008
0.097
0.101
0.067
0.050
0.040
0.030
0.027
0.026
0.034
0.067
0.068
0.056
0.055
-0.009
-0.014
-0.011
-0.009
-0.006
-0.009
-0.013
-0.012
-0.012
-0.023
-0.018
-0.013
-0.012
0.077
0.095
0.065
0.050
0.036
0.034
0.050
0.041
0.049
0.084
0.077
0.068
0.060
Panel B: IV skew
1999
2,425
2000
2,330
2001
2,032
2002
1,955
2003
1,838
2004
2,041
2005
2,115
2006
2,369
2007
2,692
2008
2,638
2009
2,461
2010
2,628
All
5,447
0.003
0.001
0.022
0.040
0.037
0.027
0.025
0.023
0.023
0.030
0.035
0.030
0.025
0.030
0.029
0.048
0.064
0.056
0.044
0.042
0.039
0.041
0.057
0.058
0.050
0.047
0.066
0.066
0.082
0.097
0.083
0.066
0.067
0.063
0.067
0.093
0.088
0.076
0.076
0.164
0.168
0.167
0.173
0.156
0.131
0.162
0.150
0.144
0.194
0.159
0.146
0.160
0.041
0.039
0.058
0.073
0.066
0.052
0.056
0.052
0.052
0.068
0.065
0.058
0.057
0.072
0.083
0.065
0.058
0.053
0.048
0.066
0.061
0.059
0.076
0.060
0.061
0.063
26
Table 3: Predicting corporate events using the IV spread
This table presents pooled OLS regression results from regressing the five event measures on the IV spread, with estimated standard errors clustered by firm and
calendar quarter. Earnings announcement is measured by the SUE which is the announced quarterly EPS less the corresponding analyst consensus forecast scaled
by the standard deviation of the quarterly earnings estimates, expressed in percentages. Managerial guidance is the value of the guidance issued by the company
less the corresponding analyst consensus forecast. Earnings restatement is the newly stated quarterly EPS less the previously stated one. Recommendation change
is the total number of notches changed, where an analyst recommendation equals a number from 5 to 1 indicating strong buy, buy, hold, underperform, and sell
respectively. Forecast revision is the new analyst consensus less the old one. IV spread is the average IV spread over the pre-event week. Size is the natural
logarithm of firm market capitalization. B/M is the book to market ratio. Momentum is the stock return over the previous six months. Volatility is the daily equity
return volatility for the previous month. Turnover is the stock trading volume over the number of shares outstanding. ***, **, and * indicate that the coefficient
estimate is significant at 1%, 5% and 10% level respectively.
Intercept
IV spread
Size
B/M
Momentum
Volatility
Turnover
N
R Square (%)
Earnings announcement
-0.0051
0.1329***
(-0.3256)
(3.8299)
1.4821*** 1.2940***
(3.0577)
(3.5793)
0.0313***
(4.9122)
-0.0067
(-0.5338)
0.1877***
(5.6176)
-4.6369***
(-3.8119)
-1.8581*
(-1.8313)
86,433
83,531
0.27
1.75
Dependent variable: Measures of events
Managerial guidance
Earnings restatement
Recommendation change
0.0431***
0.0620***
-0.0423***
-0.0186
-0.1097***
-0.0427
(5.4683)
(5.1834)
(-2.8449)
(-0.7032)
(-2.7870)
-(0.8171)
0.0289
0.0265
1.2198*
1.7541
0.9974***
0.9867***
(0.3346)
(0.3010)
(1.9457)
(1.5495)
(6.9482)
(6.3314)
0.0127***
0.0011
0.0255***
(3.0255)
(0.1368)
(3.3367)
-0.0033
-0.0816*
0.0023*
(-0.2186)
(-1.7606)
(1.9243)
0.0757***
-0.0107
0.1457***
(4.7550)
(-0.1739)
(3.8963)
-1.0452***
0.7816
-2.1144*
(-3.9416)
(0.9176)
(-1.9069)
0.2312
1.0236
-0.7338
(0.6446)
(1.1254)
(-1.1461)
7,827
7,161
489
452
109,603
100,102
0.00
4.69
2.96
5.28
0.08
0.57
27
Forecast revision
-0.0045*** -0.0026***
(-7.4959)
(-4.5275)
0.0163***
0.0050
(3.5044)
(1.3368)
0.0009***
(6.6663)
-0.0005**
(-2.1814)
0.0069***
(8.4655)
-0.0805***
(-6.2702)
-0.0317**
(-2.1093)
194,365
180,663
0.07
3.37
Table 4: Predicting corporate events using the IV skew
This table reports pooled OLS regressions of the five event measures on the IV skew. Estimated standard errors are clustered by firm and calendar quarter.
Earnings announcement is measured by the SUE which is the announced quarterly EPS less the corresponding analyst consensus forecast scaled by the standard
deviation of the quarterly earnings estimates, expressed in percentages. Managerial guidance is the value of the guidance issued by the company less the
corresponding analyst consensus forecast. Earnings restatement is the newly stated quarterly EPS less the previously stated one. Recommendation change is the
total number of notches changed, where an analyst recommendation equals a number from 5 to 1 indicating strong buy, buy, hold, underperform, and sell
respectively. Forecast revision is the new analyst consensus less the old one. IV skew is the average IV skew over the pre-event week. Size is the natural
logarithm of firm market capitalization. B/M is the book to market ratio. Momentum is the stock return over the previous six months. Volatility is the daily equity
return volatility for the previous month. Turnover is the stock trading volume over the number of shares outstanding. ***, **, and * indicate that the coefficient
estimate is significant at 1%, 5% and 10% level respectively.
Intercept
IV skew
Size
B/M
Momentum
Volatility
Turnover
N
R Square (%)
Earnings announcement
0.0896*** 0.1514***
(12.0034)
(5.4930)
-0.5865*** -0.4983***
(-3.2533)
(-3.2277)
-0.0085**
(-2.1740)
-0.0068
(-0.5519)
0.0827***
(3.6162)
-1.8813***
(-2.8319)
-0.7358
(-1.0638)
50,075
48,762
0.23
0.71
Dependent variable: Measures of events
Managerial guidance
Earnings restatement
Recommendation change
0.0797***
0.0902***
-0.0463**
-0.0266
-0.0326
-0.0302
(6.6985)
(4.7959)
(-2.1800)
(-0.5670)
(-0.9174)
(-0.5234)
-0.1715***
-0.0601
-0.0265
-0.2064
-1.3240*** -1.0784***
(-2.8116)
(-1.2383)
(-0.1659)
(-1.3698)
(-5.4873)
(-4.5153)
0.0073
-0.0070
0.0277***
(1.3956)
(-0.5535)
(3.3081)
0.0233
-0.0081
0.0023
(0.7359)
(-0.1630)
(1.6080)
0.1006***
0.0304
0.0989***
(4.9965)
(0.4877)
(2.6446)
-1.4447***
0.8639
-1.2040
(-3.5385)
(0.7964)
(-0.9411)
-0.1159
0.1861
-0.7752
(-0.2622)
(0.1707)
(-1.3396)
4,982
4,602
286
268
71,424
66,622
0.20
4.19
0.00
0.84
0.26
0.46
28
Forecast revision
-0.0023***
-0.0004
(-4.9499)
(-0.5700)
-0.0231*** -0.0073***
(-4.7773)
(-2.7367)
0.0004**
(2.6070)
-0.0005
(-1.3309)
0.0066***
(7.7561)
-0.1074***
(-8.5544)
-0.0382**
(-2.3338)
135,249
128,152
0.25
3.06
Table 5: Four-factor analysis on long/short portfolios
This table displays the four-factor abnormal returns for long/short portfolios formed by sorting on IV
spread and IV skew. We divide the whole sample into an event group and a no-event group based on
occurrences of earnings announcements, analyst recommendation changes or analyst forecast changes.
For each sub-sample, stocks are sorted into deciles every trading day based on the average IV spread
or IV skew over the previous week. Abnormal returns during the post-formation week with regard to
the four Fama-French (1993) and Carhart (1997) factors are calculated for the long/short portfolios,
which long stocks in the highest decile and short stocks in the lowest decile. Panel A contains results
for the value-weighted portfolios, and Panel B is for equal-weighted portfolios. The Newey-West
t-statistics are computed to adjust for the autocorrelations. ***, **, and * indicate that the coefficient
estimate is significant at 1%, 5% and 10% level respectively.
Dependent variable: High - low
IV spread
IV skew
Event
No-event
Event
No-event
Panel A: Value-weighted portfolios
Alpha
Rm - Rf
SMB
HML
Momentum
0.1055***
(3.0108)
-0.0389*
(-1.7048)
-0.0568
(-1.1691)
-0.0343
(-0.7119)
-0.0611*
(-1.8999)
0.0557***
(4.1880)
-0.0028
(-0.3479)
-0.0301
(-1.6110)
0.0242
(1.5070)
-0.0408***
(-3.1892)
-0.0834***
(-2.8538)
-0.0451*
(-1.8270)
0.0871
(1.5065)
0.0749
(1.5285)
-0.1266***
(-3.7289)
-0.0410***
(-2.8922)
-0.0075
(-0.9102)
0.0255
(1.4269)
0.0861***
(4.6138)
-0.0772***
(-6.2128)
0.0975***
(11.0192)
0.0066
(1.3195)
-0.0071
(-0.5896)
-0.0139
(-1.3707)
-0.0270***
(-3.5859)
-0.0785***
(-2.8764)
-0.0351
(-1.5471)
0.0115
(0.2400)
0.0721
(1.6276)
-0.1230***
(-4.2008)
-0.0495***
(-4.3464)
0.0095
(1.3103)
0.0329**
(2.3360)
0.1098***
(7.5380)
-0.0476***
(-5.2610)
Panel B: Equal-weighted portfolios
Alpha
Rm - Rf
SMB
HML
Momentum
0.1623***
(5.5628)
-0.0483**
(-2.1943)
0.0090
(0.2238)
0.0070
(0.1535)
-0.0758***
(-2.6855)
29
Table 6: When does the IV spread predict stock returns?
The table below shows pooled daily regressions of excess returns on the IV spread and its interaction
terms with the event dummy variables. Estimated standard errors are clustered by firm and calendar
quarter. Excess return is the stock return in excess of the market return averaged over day t to day t+4,
expressed in percentages. IV spread is the average IV spread over the previous week. Event is a
dummy variable which equals one if at least one of the earnings announcement, the analyst
recommendation change, and the analyst forecast revision takes place on day t. SUE, Recommend and
Forecast are dummy variables indicating the occurrence for each event respectively. Size is the natural
logarithm of the firm market capitalization. B/M is the book to market ratio. Momentum is the stock
return for the previous six months. Volatility is the daily equity return volatility in the previous month.
Turnover is the stock trading volume over the number of shares outstanding. ***, **, and * indicate
that the coefficient estimate is significant at 1%, 5% and 10% level respectively.
Intercept
IV spread
Event*IV spread
SUE*IV spread
Recommend*IV spread
Forecast*IV spread
Size
B/M
Momentum
Volatility
Turnover
N
R Square (%)
Dependent variable: Excess return
0.0302***
0.0092
0.0303***
0.0091
0.0303***
0.0091
(2.5903)
(0.4106)
(2.6011)
(0.4047)
(2.6028)
(0.4036)
0.5784*** 0.5495*** 0.5520*** 0.5221*** 0.5505*** 0.5204***
(6.2962)
(5.2688)
(6.5145)
(5.4844)
(6.4733)
(5.4331)
0.7708*** 0.7742**
(2.6833)
(2.3766)
0.6305*** 0.6607***
(2.7424)
(2.7924)
0.7528** 0.7047**
(2.4241)
(2.0192)
0.8247** 0.8574**
(2.3582)
(2.0789)
-0.0030
-0.0029
-0.0029
(-0.7762)
(-0.7458)
(-0.7424)
0.0005***
0.0005***
0.0005***
(2.6430)
(2.6320)
(2.6282)
0.0032
0.0031
0.0031
(0.1533)
(0.1495)
(0.1486)
0.8780
0.8834
0.8844
(0.9473)
(0.9528)
(0.9541)
-0.3406*
-0.3361*
-0.3351*
(-1.8669)
(-1.8461)
(-1.8388)
7,181,236 6,376,168 7,181,236 6,376,168 7,181,236 6,376,168
0.05
0.05
0.05
0.06
0.05
0.06
30
Table 7: When does the IV skew predict stock returns?
This table provides pooled daily regressions of excess stock returns on the IV skew and its interactions
with the event dummy variables. Estimated standard errors are clustered by firm and calendar quarter.
Excess return is the stock return in excess of the market return averaged over day t to day t+4,
expressed in percentages. IV skew is the average IV skew over the previous week. Event is a dummy
variable which equals one if at least one of the earnings announcement, the analyst recommendation
change, and the analyst forecast revision takes place on day t. SUE, Recommend and Forecast are
dummy variables indicating the occurrence for each event respectively. Size is the natural logarithm of
the firm market capitalization. B/M is the book to market ratio. Momentum is the stock return for the
previous six months. Volatility is the daily equity return volatility in the previous month. Turnover is
the stock trading volume over the number of shares outstanding. ***, **, and * indicate that the
coefficient estimate is significant at 1%, 5% and 10% level respectively.
Intercept
IV skew
Event*IV skew
SUE*IV skew
Recommend*IV skew
Forecast*IV skew
Size
B/M
Momentum
Volatility
Turnover
N
R Square (%)
Dependent variable: Excess return
0.0291***
0.0484**
0.0293***
0.0481**
0.0294***
(3.0140)
(2.0516)
(3.0345)
(2.0357)
(3.0449)
-0.2166*** -0.2420*** -0.2044*** -0.2299*** -0.2019***
(-3.5796)
(-3.9802)
(-3.4804)
(-3.9104)
(-3.4329)
-0.2724**
-0.2329*
(-2.2300)
(-1.8924)
0.0814
(0.5183)
-0.7035***
(-4.4305)
-0.2526
(-1.3995)
-0.0051
-0.0049
(-1.3432)
(-1.2890)
0.0003***
0.0003***
(2.7132)
(2.6948)
0.0034
0.0033
(0.1583)
(0.1515)
-0.3004
-0.2942
(-0.3259)
(-0.3188)
-0.3666**
-0.3619**
(-2.4495)
(-2.4310)
3,855,794
3,416,210
3,855,794
3,416,210
3,855,794
0.01
0.02
0.01
0.02
0.02
31
0.0478**
(2.0249)
-0.2263***
(-3.8275)
0.0633
(0.3938)
-0.7014***
(-4.7255)
-0.1963
(-1.1029)
-0.0048
(-1.2644)
0.0003***
(2.6830)
0.0032
(0.1470)
-0.2884
(-0.3126)
-0.3570**
(-2.4079)
3,416,210
0.03
Table 8: Predictability of stock returns and short-sale constraints
As in Tables 6 and 7, this table reports results of pooled daily regressions of excess stock returns on
the IV skew and its interactions with the event dummy variables, but here the IV skew and spread are
split up into two variables, separately capturing the impact of the IV spread (skew) above and below
their median value. Regressions are conducted for the IV spread and IV skew separately. Standard
errors are clustered by firm and calendar quarter. The excess return is the stock return in excess of the
market return averaged over day t to day t+4, expressed in percentages. Option Above equals the
average IV spread (skew) of the previous week if it is above the median and zero otherwise. Option
Below equals the average IV spread (skew) of the previous week if it is below the median and zero
otherwise. Event is a dummy variable which equals one if at least one of the earnings announcement,
the analyst recommendation change, and the analyst forecast revision takes place on day t. Size is the
natural logarithm of firm market capitalization. B/M is the book to market ratio. Momentum is the
stock return over the previous six months. Volatility is the daily equity return volatility for the previous
month. Turnover is the stock trading volume over the number of shares outstanding. ***, **, and *
indicate that the coefficient estimate is significant at 1%, 5% and 10% level respectively.
Intercept
Option Above
Event*Option Above
Option Below
Event*Option Below
Size
B/M
Momentum
Volatility
Turnover
N
R Square (%)
Dependent variable: Excess return
IV spread
IV skew
0.0304***
0.0092
0.0291***
0.0483*
-3.0387
-0.4061
-2.8179
-1.9543
0.5790***
0.5155***
-0.2024***
-0.2278***
-2.7102
-3.1462
(-3.4576)
(-3.8582)
-0.2798
-0.2362
-0.3129**
-0.2739**
(-1.0873)
(-1.1239)
(-2.5237)
(-2.1917)
0.5436***
0.5281***
-0.205
-0.2708**
-4.7933
-5.2376
(-1.2599)
(-2.0150)
1.0636***
1.0769***
0.0955
0.1367
-3.0935
-2.7969
-0.3982
-0.5756
-0.003
-0.0049
(-0.7540)
(-1.3632)
0.0005***
0.0033
-2.6363
-2.1278
0.0029
0.0033
-0.1406
-0.151
0.9006
-0.2964
-0.9749
(-0.3160)
-0.3331*
-0.3618**
(-1.8566)
(-2.4397)
7181236
6376168
3855794
3416210
0.05
0.06
0.01
0.02
32
Table 9: Option market liquidity and decomposition of option trading predictability
This table shows pooled daily regressions of excess returns on each informed option trading measure
and its interaction with the event dummy variable and the option bid-ask spread. Standard errors are
clustered by firm and calendar quarter. Excess return is the stock return in excess of the market return
averaged over day t to day t+4, expressed in percentages. Option refers to the IV spread and the IV
skew respectively. IV spread is the average IV spread over the previous week. IV skew is the average
IV skew over the previous week. Event is a dummy variable which equals one if at least one of the
earnings announcement, the analyst recommendation change, and the analyst forecast revision takes
place on day t. BASP is the option bid-ask spread calculated as the best offer less the best bid price
scaled by the midpoint, averaged over the previous week. Size is the natural logarithm of the firm
market capitalization. B/M is the book to market ratio. Momentum is the stock return over the past six
months. Volatility is the daily equity return volatility for the previous month. Turnover is the stock
trading volume over the number of shares outstanding. ***, **, and * indicate that the coefficient
estimate is significant at 1%, 5% and 10% level respectively.
Intercept
Option
Event*Option
Event*Option*BASP
Size
B/M
Momentum
Volatility
Turnover
N
R Square (%)
Dependent variable: Excess return
IV spread
IV skew
0.0304***
0.0091
0.0298***
0.0481**
(2.6101)
(0.4046)
(3.0825)
(2.0325)
0.5524***
0.5226***
-0.2076***
-0.2321***
(6.5101)
(5.4818)
(-3.5085)
(-3.9142)
1.1643**
1.2333**
-0.4964***
-0.3889**
(2.4578)
(2.4148)
(-2.6417)
(-2.1023)
-1.0741**
-1.2337**
0.4333***
0.2983*
(-2.0988)
(-2.3017)
(2.6362)
(1.8922)
-0.0029
-0.0048
(-0.7315)
(-1.2477)
0.0005***
0.0003**
(2.6221)
(2.6921)
0.0031
0.0032
(0.1505)
(0.1471)
0.8847
-0.2874
(0.9540)
(-0.3112)
-0.3324*
-0.3587**
(-1.8266)
(-2.4210)
7,181,236
6,376,168
3,855,794
3,416,210
0.05
0.06
0.01
0.02
33
Table 10: IV spread in post-event period
The table below provides pooled OLS regressions of the post-event IV spread on the event-day stock
return. Regressions are conducted for sub-samples of three types of events separately. Standard errors
clustered by firm and calendar quarter. Post-spread is the average IV spread over the post-event week.
Pre-spread is the average IV spread over the pre-event week. Values of the IV spread are expressed in
percentage form. Ret 0 is the stock return on the event-day. Pre-ret is the average stock return over the
pre-event week. Size is the natural logarithm of the firm market capitalization. B/M is the book to
market ratio. Momentum is the stock return over the previous six months. Volatility is the daily equity
return volatility for the previous month. Turnover is the stock trading volume over the number of
shares outstanding. ***, **, and * indicate that the coefficient is significant at 1%, 5% and 10% level
respectively.
Intercept
Ret 0
Pre-spread
Pre-ret
Size
B/M
Momentum
Volatility
Turnover
N
R Square (%)
Dependent variable: Post-spread
Earnings announcement
Recommendation change
Forecast revision
-0.3788***
-0.1307**
-0.3499***
-0.1199
-0.3083***
-0.1069*
(-8.7916)
(-2.1273)
(-11.1464)
(-1.4267)
(-6.6316)
(-1.8173)
-3.2931*** -3.3124*** -3.0685*** -3.1772*** -3.8065*** -3.4543***
(-11.6325)
(-12.2406)
(-7.2174)
(-7.9597)
(-14.3774)
(-12.5615)
0.6090***
0.5930***
0.6693***
0.6360***
0.7058***
0.6673***
(24.7252)
(21.8321)
(24.4643)
(19.3913)
(31.3544)
(27.9039)
1.9225*
2.3101**
0.4548
0.4543
2.0150**
2.0495**
(1.7696)
(2.1374)
(0.5801)
(0.5258)
(1.9909)
(2.0403)
-0.0021
-0.0063
0.0071
(-0.1333)
(-0.4905)
(0.6033)
0.0204*
0.0036*
0.0004
(1.6640)
(1.6785)
(0.0423)
-0.0288
-0.0843
-0.0074
(-0.5914)
(-1.5165)
(-0.1892)
-5.3740***
-5.3112*
-6.2635**
(-3.2610)
(-1.8749)
(-2.4004)
-8.6733***
-3.8034***
-3.6283***
(-4.1690)
(-2.9957)
(-3.1677)
85,151
82,722
107,540
99,497
191,161
179,902
36.52
35.60
42.40
39.78
48.31
45.10
34
Table 11: IV skew in post-event period
This table displays pooled OLS regressions of the post-event IV skew on the event-day stock return.
Regressions are conducted for sub-samples of three types of events separately. Standard errors are
clustered by firm and calendar quarter. Post-skew is the average IV skew over the post-event week.
Pre-skew is the average IV skew during the pre-event week. Values of the IV skew are converted into
percentages. Ret 0 is the stock return on the event-day. Pre-ret is the stock return over the pre-event
week. Size is the natural logarithm of the firm market capitalization. B/M is the book to market ratio.
Momentum is the stock return over the previous six months. Volatility is the daily equity return
volatility for the previous month. Turnover is the stock trading volume over the number of shares
outstanding. ***, **, and * indicate that the coefficient is significant at 1%, 5% and 10% level
respectively.
Intercept
Ret 0
Pre-skew
Pre-ret
Size
B/M
Momentum
Volatility
Turnover
N
R Square (%)
Dependent variable: Post-skew
Earnings announcement
Recommendation change
3.4255*** 4.0236*** 2.7693*** 3.1152***
(23.2089)
(19.5914)
(24.5834)
(21.7163)
1.6324***
0.8053*
1.6544***
1.0694**
(3.7265)
(1.7403)
(3.5403)
(2.2961)
0.4449*** 0.4076*** 0.5363*** 0.5032***
(23.9731)
(23.8373)
(35.5060)
(29.5101)
-1.3635
-1.8457**
-0.9724
-1.8641*
(-1.5746)
(-1.9821)
(-0.8787)
(-1.8410)
-0.4239***
-0.3192***
(-10.2285)
(-10.7557)
0.1401**
0.0101**
(2.1155)
(2.2401)
-0.5570***
-0.5554***
(-4.4042)
(-4.5705)
6.4452
14.8235*
(0.7558)
(1.9332)
-5.9789**
-6.6104**
(-1.9631)
(-2.3802)
42,644
41,550
62,731
58,733
22.10
22.15
26.94
27.87
35
Forecast revision
2.3729***
2.7635***
(13.1392)
(23.4283)
0.0375
-0.3478
(0.0785)
(-0.7116)
0.5623***
0.5133***
(33.2091)
(20.6175)
-3.7178***
-3.6405***
(-3.5106)
(-3.7995)
-0.3230***
(-12.0790)
0.0665*
(1.6404)
-0.5551***
(-4.8964)
23.0553***
(2.7854)
-11.3300***
(-3.6767)
122,671
116,558
29.00
30.21
Table 12: Alternative option trading proxies
This table presents robustness checks using alternative option trading proxies. Pooled OLS regressions
are conducted for the IV spread and IV skew separately. Standard errors are clustered by firm and
calendar quarter. Excess return is the stock return in excess of the market return averaged over day t to
day t+4, expressed in percentages. Option Change is the change in the IV spread (skew) defined as the
average level over the previous week less the average level over the previous month (excluding the last
week). Option Premonth is the average level of the IV spread (skew) over the previous month. Event is
a dummy variable which equals one if at least one of the earnings announcement, the analyst
recommendation change, and the analyst forecast revision takes place on day t. Size is the natural
logarithm of firm market capitalization. B/M is the book to market ratio. Momentum is the stock return
over the previous six months. Volatility is the daily equity return volatility for the previous month.
Turnover is the stock trading volume over the number of shares outstanding. ***, **, and * indicate
that the coefficient estimate is significant at 1%, 5% and 10% level respectively.
Intercept
Option Change
Event*Option Change
Option Premonth
Event* Premonth
Size
B/M
Momentum
Volatility
Turnover
N
R Square (%)
Dependent variable: Excess return
IV spread
IV skew
0.0043
0.0086
0.0324
0.0443*
(0.1907)
(0.3858)
(1.3124)
(1.9126)
0.5550***
-0.2322***
(5.1185)
(-4.1226)
0.7460***
-0.2548*
(2.7744)
(-1.6552)
0.3998***
-0.1829**
(3.8848)
(-1.9776)
0.6907*
-0.2246*
(1.8161)
(-1.7087)
-0.0028
-0.0029
-0.0033
-0.0044
(-0.7189)
(-0.7532)
(-0.8644)
(-1.1620)
0.0005***
0.0005***
0.0003*
0.0003**
(2.7547)
(2.6450)
(1.8935)
(2.1104)
0.0024
0.0025
0.0058
0.0038
(0.1164)
(0.1206)
(0.2670)
(0.1753)
0.8504
0.8539
-0.3474
-0.2968
(0.9144)
(0.9219)
(-0.3791)
(-0.3216)
-0.3882**
-0.3423*
-0.3524**
-0.3513**
(-2.1708)
(-1.8766)
(-2.2984)
(-2.3785)
6,343,175
6,376,168
3,251,369
3,416,210
0.04
0.03
0.02
0.01
36