Why do option prices predict stock returns? *

Transcription

1 Why do option prices predict stock returns? * Joost Driessen a Tse-Chun Lin b Xiaolong Lu c a Department of Finance, Tilburg University, Tilburg b School of Economics and Finance, The University of Hong Kong, Hong Kong c 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.: ; fax: address: j.j.a.g.driessen@uvt.nl Tel.: ; fax: address: tsechunlin@hku.hk Tel.: ; fax: address: xllu@hku.hk

2 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

3 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

4 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

5 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

6 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

7 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 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: 6

8 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 with the standard deviation being 0.63; the average analyst recommendation change is 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

9 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)) 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: event = β + βoption + β ln size + βbm + βret + βσ + βturnover + ε, (1) it, 0 1 it, 5, t 1 2 it, 5, t 1 3 it, 5, t 1 4 im, 6, m 1 5 im, 1 6 it, 5, t 1 it, where eventit, 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 optionit, 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 spread or it, 5, t 1 skewit, 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 sizeit, 5, t 1, the book to market ratio of the previous week bmit, 5, t 1, the stock return over the past six months ret, the equity return volatility calculated using daily data in the previous month im, 6, m 1 im, 1 σ, and the turnover rate calculated as the stock trading volume over the number of shares outstanding for the previous week turnoverit, 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 spreadit, 5, t 1 and an increase in skewit, 5, t 1. 8

10 [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 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

11 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: High ( ), (5) t Lowt = α + β1 Rmt Rft + SMBt + HMLt + εt [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 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 basis points (t-statistic= -2.85) for the event group, and 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: exretitt,, + 4 = β0 + β1 optionit, 5, t 1 + γcontrolsit, 1 + εit,, (2) 10

12 where exret itt,, + 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 controls are it, 1 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: exret = β + ( β + β dummy ) option + γcontrols + ε, (3) itt,, it, it, 5, t 1 it, 1 it, where dummyit, 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 β 1. When any one of the events occurs, the predictability becomes β1+ β2. Hence, the interacted coefficient β2 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 dummyit, in the previous step by three individual event dummy variables to test the hypothesis for each event type separately: exret = β + ( β + β sue + β recommend + β revision ) option + γcontrols + ε, (4) itt,, it, 3 it, 4 it, it, 5, t 1 it, 1 it, where sueit, equals 1 if an earnings announcement takes place for firm i on day t, and 0 otherwise; recommendit, equals 1 if an analyst recommendation change takes place, and 0 otherwise; revisionit, an analyst forecast revision takes place, and 0 otherwise. By the same argument as in the previous step, the interacted coefficients of β 2, β 3, and β4 help us to 11

13 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%) + ( ) * 5.28% = So the fraction of the predictability that comes from the informed option traders private information about the three events can be calculated as: ( ) * 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 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

14 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 with a t-statistic of After including all control variables, the coefficient estimate on the IV skew becomes with a t-statistic of 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 (t-statistic = -3.48), and the interacted coefficient is (t-statistic = -2.23). After inclusion of all control variables, the IV skew has a statistically significant coefficient of while the interaction term carries a significant coefficient of 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 ). 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: * (1-6.57%) + ( ) * 6.57% = The fraction of the predictability that is associated with informed option traders private information about the events can be measured as: ( ) * 6.57% / = 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

15 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 (t-statistic = -3.83), while the interaction term with the analyst recommendation change dummy carries a significant coefficient of (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 ). 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: exret = β + ( β + β dummy ) optionabove + ( β + β dummy ) optionbelow itt,, it, it, 5, t it, it, 5, t 1 + γcontrols + ε, (6) it, 1 it, where optionaboveit, 5, t 1 takes value of average IV spread or IV skew over the previous week 14

16 if it is above the median, and takes value zero otherwise, and similarly for optionbelowit, 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 (t-statistic = -3.86), and its interaction with the event dummy variable is (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 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): exret = β + ( β + β dummy + β basp * dummy ) option + γcontrols + ε, (7) itt,, it, 3 it, 5, t 1 it, it, 5, t 1 it, 1 it, where the baspit, 5, t 1 is the average bid-ask spread over the previous week. We expect β 3 to have the opposite sign of β 1 and β 2, since we expect lower predictability when options have higher bid-ask spreads. [Table 9 to be inserted here] 15

17 Table 9 reports regression results for equation (7). The triple interaction between event dummies, the option trading measure and bid-ask spread, β 3, equals 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 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: optionit, + 1, t+ 5 = β0 + β1 retit, + β2 optionit, 5, t 1+ β3 retit, 5, t 1 + γcontrolsit, 1 + εit,, (8) where the option it, + 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 spread and it, + 1, t + 5 skew it, + 1, t + 5. The variable ret, it is the stock return on the event-day and the retit, 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 β 1 is zero, there is no change in the IV spread or skew, 16

18 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 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 β 1 for on the event-day stock return is significant and equal to -3.30, and for the earnings announcement subsample, the analyst recommendation subsample, and the analyst forecast revision subsample. After adding all control variables, the β 1 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

19 optionchange, = option, (9), 5, 1 option, 22, 6 it it t it t exret = β + ( β + β dummy ) optionchange + γcontrols + ε, (10) itt,, it, it, it, 1 it, 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 (t-statistic= -4.12) and the interacted term is (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: exret = β + ( β + β dummy ) option + γcontrols + ε, (11) itt,, it, it, 22, t 1 it, 1 it, [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 (t-statistic= -1.98) and the interacted coefficient is (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 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

20 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 A put option is ATM if its moneyness is between 0.95 and 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

21 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

22 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: n it, spread = w ( IV IV ), (12) i i, call i, put it, jt, jt, jt, j= 1 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: OTMP ATMC skew, = IV, IV,, (13) it it it 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 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

23 Reference: Amin, K. I. and C. M. C. LEE, 1997, Option trading, price discovery, and earnings news dissemination, Contemporary Accounting Research, 14(2): 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): Bali, T. G. and Armen Hovakimian, 2009, Volatility spreads and expected stock returns, Management Science, 55(11): Bates, D.S., 1991, The crash of 87: Was it expected? The evidence from option markets, Journal of Finance, 46(3): Black, Fischer, 1975, Fact and fantasy in the use of options, Financial Analysts Journal, 31(4): 36-41, Black, Fischer and Myron Scholes, 1973, The pricing of options and corporate liabilities, Journal of Political Economy, 81(3): 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): 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): Carhart, Mark M., 1997, On persistence in mutual fund performance, Journal of Finance, 52(1): Chakravarty, Sugato, Huseyin Gulen and Stewart Mayhew, 2004, Informed trading in stock and options markets, Journal of Finance, 59(3):

24 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): Doran, J. S., B. C. Tarrant and D. R. Peterson, 2007, Is there information in the volatility skew?, Journal of Futures Markets, 27(10): 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): Fama, E. F. and K. R. French, 1993, Common risk factors in the returns on bonds and stocks, Journal of Financial Economics, 33 (1): 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): Ni, S. X., Jun Pan and A. M. Poteshman, 2008, Volatility information trading in the option market, Journal of Finance, 63(3): Pan, Jun and A. M. Poteshman, 2006, The information in option volume for future stock prices, Review of Financial Studies, 19(3): 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): Petersen, Mitchell, 2009, Estimating standard errors in finance panel data sets: comparing approaches, Review of Financial Studies, 22(1): Roll, Richard, Eduardo Schwartz and Avanidhar Subrahmanyam, 2010, O/S: The relative trading activity in options and stock, Journal of Financial Economics, 96(1): Rubinstein, Mark, 1994, Implied binomial trees, Journal of Finance, 49(3): Stoll, H. R., 1969, The relationship between put and call option prices, Journal of Finance, 24(5):