Implied Volatility Spreads and Future Options Returns

Transcription

1 Implied Volatility Spreads and Future Options Returns Chuang-Chang Chang, Zih-Ying Lin and Yaw-Huei Wang ABSTRACT While numerous studies have documented that call-put implied volatility spreads positively predict future stock returns, the predictive relationship is recently found to be negative for future call option returns. We further investigate whether and how the predictive relationship for options returns is influenced by various information events and conditions. In addition to confirming the existence of the opposite predictive relationships for both call and put returns, our empirical results reveal that the predictive relationships are stronger during periods of earnings announcement and/or high sentiment. In addition, we find that investors learn from informed trading and revise their predictability bias by examining the impacts of information asymmetry, stock liquidity, and options liquidity on the predictive relationships. Keywords: Volatility spreads; Option returns; Earnings announcements; Investor sentiment; Investor Learning. JEL Classification: G14 Chuang-Chang Chang and Zih-Ying Lin are collocated at the Department of Finance, National Central University, Taoyuan, Taiwan, ROC; Yaw-Huei Wang (the corresponding author) is at the Department of Finance, National Taiwan University, Taiwan, ROC. Address for correspondence: Department of Finance, National Taiwan University, No.1 Roosevelt Road, Section 4, Taipei 106, Taiwan, ROC. Tel: ; The authors would like to express their sincere gratitude for the helpful comments provided by Andy Fodor, Yigit Atilgan and Hung-Neng Lai, and would also like to express their appreciation for the financial support provided for this study by the Taiwanese Ministry of Science and Technology (MoST). 1

2 1. INTRODUCTION Strong support is provided in several prior related studies on the importance of derivatives implied information in the prediction of the price dynamics of the underlying asset, with several of these studies demonstrating that call-put implied volatility (CPIV) spreads can positively predict the returns of the underlying stocks. 1 These findings are consistent with the argument that based on the advantages of low transaction and high leverage levels, informed traders may initiate the realization of their privileged information in the options markets. 2 Moreover, Atilgan (2014) and Chan, Ge, and Lin (2015) found that the predictability of stock returns made by the CPIV is stronger during earnings announcement and merger and acquisition (M&A) announcement events, respectively. They indicated that the trading activity of informed traders is an important driver of the CPIV, and hence the predictability of stock returns is more pronounced during major information events. Doran, Fodor and Jiang (2013) recently examined whether the same predictive relationship may exist for options returns, but they found that the CPIV was negatively, 1 Examples include Bali and Hovakimian (2009), Cremers and Weinbaum (2010), Doran and Krieger (2010), and An, Ang, Bali and Cakici (2014). 2 See Manaster and Rendleman (1982), Back (1993), Sheikh and Ronn (1994), Easley, O Hara and Srinivas (1998), Cao (1999) and Pan and Poteshman (2006). Easley et al. (1998) noted that informed traders with private information are more likely to trade in the options market when option liquidity is high, stock liquidity is low and information asymmetry in the stock market is high, whilst Pan and Poteshman (2006) found that stocks with low put-call ratios outperformed stocks with high put-call ratios, with the predictability of stock returns being higher for those stocks with a higher concentration of informed traders. 2

3 rather than positively, related to the future returns of call options, particularly for out-ofthe-money (OTM) contracts; they suggested that this negative relationship was driven by the options demand from the mispricing attributable to individual investors, a finding which is in line with those of Mahani and Poteshman (2008), Goyal and Saretto (2009) and An et al. (2014). However, the role of earnings announcement on the predictive relationship for options returns has not yet been explored. Since the option market is a platform where informed traders are likely to realize their private information, the first objective of this paper is to investigate how earnings announcement affects the predictive relationship between the CPIV and future options returns. Prior studies such as Kandel and Pearson (1995), Amin and Lee (1997), Choy and Wei (2012), and Choy (2015) have provided evidence of more aggressive trading activity or higher trading volume around earnings announcement. However, whether this change represents useful information for prediction or actually is just a reflection of divergent opinions among traders is still debatable in literature. While one stream claims that earnings announcement is an informationally intensive event (Beaver, 1968; Ball and Brown, 1968; Battalio and Mendenhall, 2005; Diavatopoulos, Doran, Fodor and Peterso, 2012), the other one argues that trading around earnings announcement is 3

4 due to differential opinions (Harris and Raviv, 1993; Kim and Verrecchia, 1994). 3 We also investigate whether this predictive relationship is found to be stronger during periods of high investor sentiment, essentially because investors are widely regarded as being more irrational, with a tendency to exhibit much more severe misreaction when market sentiment is high; indeed, it has been suggested in a number of behavioral theories that such investors may form incorrect beliefs leading to the erroneous evaluation of assets. 4 Several studies have suggested that investor sentiment contains a market-wide component which has a direct effect on the prices of both stocks and options, 5 and that investor misreaction is dependent upon investor sentiment. 6 As such, investor sentiment may affect the beliefs of investors, thereby increasing the likelihood of such investors exhibiting misreaction during periods of high sentiment, leading to such investors trading more often and more aggressively. Thus, if the predictive relationship in the 3 In particular, Mahani and Poteshman (2008) found that unsophisticated investors in the options market overreacted to past news on the underlying stocks and tended to believe that the stock prices would move away from their fundamental values on the release of earnings announcement news. 4 See, for example, De Long, Shleifer, Summers and Waldmann (1990), Lee, Shleifer and Thaler (1991) and Kumar and Lee (2006). 5 Baker and Wurgler (2006) provided evidence to show that this market-wide sentiment was related to differences in the characteristics of cross-sectional stock returns. Several studies have further shown that sentiment-driven investors lead to prices deviating from their fundamental value in the options markets (see Figlewski, 1989; Figlewski and Green, 1999; Han, 2008; Lemmon and Ni, 2010; and Ofek, Richardson and Whitelaw, 2004). 6 Yu and Yuan (2011) indicated the existence of a positive mean-variance relationship in low-sentiment periods, whilst Chung, Hung and Yeh (2012) noted that the return predictability of sentiment was more pronounced in an expansion state. Stambaugh, Yu and Yuan (2012) found a broad set of anomalies in cross-sectional stock returns, which they found to be stronger following periods of high investor sentiment levels. 4

5 options market is indeed driven by mispricing, then we would expect to find it becoming stronger during periods of high-sentiment. We subsequently examine whether investors learns from informed trading and then mitigate their predictability bias in the options markets because prior studies such as Daniel, Hirshleifer, and Subrahmanyam (1998), Gervais and Odean (2001), Nicolosi, Peng, and Zhu (2009), and Seru, Shumway, and Stoffman (2010) have documented the existence of investor learning in the financial markets. Specifically, we attempt to investigate whether the predictive relationship is found to be weaker during periods of high information asymmetry, low stock liquidity and high options liquidity, essentially because, as suggested by Easley et al. (1998), these are conditions under which informed investors are more likely to trade in options. If the investors learn from informed traders and adjust their trading behavior, then we would expect to find it becoming weaker during periods when informed investors participate more aggressively in the options market. The empirical findings based on all US listed stocks and options are summarized as follows. Firstly, earnings announcements are found to have significant influences on the predictability of the options returns indicated by the CPIV. The negative (positive) relationship between CPIV and future call (put) options returns is found to be stronger when it coincides with an earnings announcement event, which is 5

6 consistent with the findings of Choy and Wei (2012) and Choy (2015). Secondly, we find that an increase in investor sentiment strengthens the negative (positive) relationship between the CPIV and the future returns of call (put) options, which is consistent with the extant behavioral theories in which it is posited that investors may tend to form incorrect beliefs which can lead to them misevaluating their assets during periods of high investor sentiment. Finally, we find that lower stock liquidity, higher options liquidity and higher information asymmetry in the stock market tend to weaken the negative (positive) relationship between the CPIV and the future returns of call (put) options, which is consistent with the finding of research that investors have learning behavior and hence improve their predictability ability. Doran et al. (2013) is the study most relevant to this study. However, in addition to confirming the existence of the negative predictive relationship between the CPIV and future returns of call options, we additionally contribute to the literature with the investigation on the following several aspects. Firstly, we examine the effect of earnings announcement on the predictive relationship. Secondly, we show how the predictive relationship changes with investor sentiment. Thirdly, we document whether investors learn from informed trading and then adjust the prediction bias. The remainder of this paper is organized as follows. Our hypothesis development is described in Section 2, followed in Section 3 by a description of the data used for 6

7 this study. The empirical methodology adopted for our study is explained in Section 4, with the empirical results subsequently being presented and discussed in Section 5. Finally, the conclusions drawn from this study are presented in Section HYPOTHESIS DEVELOPMENT Whether the trading activity around earnings announcement contains useful information or is a result of divergent opinions is still open question. Amin and Lee (1997) identified a tendency for trading activity within the options market to increase prior to earnings announcements, whereas this was not found to be the case within the market of the underlying stock. As the options market provides a more effective channel for investors to realize their beliefs or privileged information, an interesting question is whether such increase in trading activity is driven by noise traders who believe themselves to be informed, or by actual informed traders. On the other hand, Choy and Wei (2012) found increased participation by individual investors in the options market around earnings announcement periods, with Choy (2015) subsequently providing evidence to show behavior biases amongst individual investors in the options market, with such biases being more pronounced prior to earnings announcement periods. 7 Consequently, individual investors are likely to play 7 Mahani and Poteshman (2008) also found that unsophisticated option investors tended to overreact to prior news on the stock market and believed that the mispriced stock price would move further away from the fundamental value once the scheduled news was released. 7

8 an important role in the options market during such earnings announcement periods. In line with the suggestions of both Manaster and Rendleman (1982) and Sheikh and Ronn (1994) that investors may tend to trade on their information in the options market prior to trading in the market of the underlying stock, Atilgan (2014) found that stocks with higher implied volatility spread (defined as the implied puts minus calls) earned significantly negative stock returns. However, Doran et al. (2013) found that this relationship did not hold in the options market; instead, they documented a negative predictive relationship from the CPIV to call option returns, and therefore posited that the negative relationship was driven by options mispricing by individual investors. In other words, trading by individual investors leads to the mispricing of options, with the options prices subsequently reverting; this is the reason why the CPIV can predict contrary returns for call options. According to the prior studies cited here, whether and how earnings announcement affects the relationship between the CPIV and future options returns have not reached a consensus. We therefore propose our first hypothesis, as follows: Hypothesis 1a: The negative (positive) predictability of call (put) option returns made by the CPIV will be more pronounced around earnings announcement periods. Hypothesis 1b: The negative (positive) predictability of call (put) option returns made by the CPIV will be weaker around earnings announcement 8

9 periods. As noted in several of the prior related studies, misreaction is clearly discernible in the options market; 8 and indeed, as noted by Chang, Hsieh and Wang (2015), such misreaction tends to be even more severe during periods of high investor sentiment. Numerous other prior related studies have further suggested that sentiment-driven investors can cause prices to deviate from their fundamental values, with such investor sentiment affecting asset prices in both the stock and options markets. 9 Doran et al. (2013) suggested that the negative relationship between CPIV and the future returns of call options is caused by mispricing which is attributable to individual investors. However, investors behavior bias is associated with not only their beliefs, but also their sentiment. Mian and Sankaraguruswamy (2012) demonstrate that market-wide investor sentiment affects the sensitivity of stock prices to earnings news, and therefore conclude that the sentiment-driven mispricing of earnings contributes to the general mispricing of stocks due to investor sentiment. We therefore posit that investor sentiment is also an important influence on the relationship between the CPIV and future options returns. In addition, we further examine whether the effect of earnings announcement on the predictive relationship will find to be 8 See Stein (1989), Poteshman (2001), Chao, Li and Yu (2005) and Mahani and Poteshman (2008). 9 The literature on the stock market includes Brown and Cliff (2005), Coval and Shumway (2005), Kumar and Lee (2006), Lemmon and Portniaguina (2006), Baker and Wurgler (2006, 2007), Yu and Yuan (2011) and Stambaugh et al. (2012). See Figlewski (1989), Figlewski and Green (1999), Ofek, Richardson and Whitelaw (2004), Han (2008) and Lemmon and Ni (2010) for an overview of the options market. 9

10 particularly strong during periods of high investor sentiment. We also expect to find that the sentiment effect will be similarly applicable to put options, which leads on to our second hypothesis, as follows: Hypothesis 2a: The negative (positive) predictability of call (put) option returns made by the CPIV will be more pronounced during periods of high investor sentiment. Hypothesis 2b: The impact of earnings announcements on the negative (positive) predictability of call (put) option returns made by the CPIV will be stronger during periods of high investor sentiment. Easley et al. (1998) demonstrated that in those cases where stock liquidity is low, options liquidity is high or there is high information asymmetry in the stock market, informed investors are more likely to try to take advantage of their private information within the options market; therefore, there is a greater likelihood of larger numbers of informed investors trading in the options market when any one of these three condition exists. Furthermore, since Doran et al. (2013) suggested that the negative predictability of call option returns made by the CPIV is driven by the mispricing attributable to the demand of individual investors, we posit that this negative relationship will be weakened under any of the three market conditions. Several studies indicated that trading experience helps improve individual investors predictability ability and hence reduce their behavior bias. As Choy and Wei 10

11 (2012) and Choy (2015) have indicated that greater numbers of individual investors may be found to be trading in the options market during earnings announcement and Battalio and Mendenhall (2005) and Atilgan (2014) suggested that earnings announcement contains information and informed traders will take advantage of private information prior to the announcement, it will be natural to ask whether individual investors learn and adjust their beliefs from informed trading. We are, therefore, also interested in determining whether there is any discernible reduction in the effect of earnings announcement on the predictive relationship when information asymmetry in the stock market is high, stock liquidity is low or options liquidity is high. In other words, we conjecture that individual investors learns from informed trading and thus mitigate the mispricing that results in the predictive relationship. We also expect to find that the effects of these information environments are similarly applicable to put options. Accordingly, we propose our third hypothesis, as follows: Hypothesis 3a: The predictability of call (put) option returns made by the CPIV will be found to be less negative (positive) when information asymmetry in the stock market is high, stock liquidity is low or options liquidity is high. Hypothesis 3b: The effect of earnings announcement on the predictability of call (put) option returns made by the CPIV will be found to be less 11

12 negative (positive) when information asymmetry in the stock market is high, stock liquidity is low or options liquidity is high. 3. DATA The primary dataset used in this study comprises of the daily transaction details of all options and optioned stocks traded in the US exchanges, with our sample period running from January 1996 to December The data on stock options and their underlying stocks are respectively obtained from OptionMetrics and CRSP, whilst accounting information on the firms for our analysis on the impact of earnings announcements was also obtained from Compustat. 11 The total number of earnings announcement events and the total number of corresponding firms are reported in Table 1; both of these totals exhibit an increasing trend over time, for example, the total number of events increased from 93 in 1996 to 812 in <Table 1 is inserted about here> The stock data include daily prices, returns, volume and outstanding shares, whilst the options data include daily closing bid and ask quotes, implied volatilities and deltas. 12 Following Doran et al. (2013), we define moneyness as the strike price over the stock price (K/S) and use the range of 0.95 to 1.05 to group the moneyness of 10 Following the general practice within the extant literature, all financial and utility firms (those with CRSP share codes other than 10 or 11) were excluded from the study sample. 11 In addition to the earnings announcement dates, we also collect the book values of the announcing firms. 12 The stock options traded in the US market are all American-style options. 12

13 options. In specific terms, 0.95 K/S 1.05 is at-the-money (ATM) for both call and put options, K/S >1.05 is OTM for calls and K/S < 0.95 is OTM for puts. As suggested by Atilgan (2014), we exclude any options meeting the following conditions: (i) prices violate the no-arbitrage condition; (ii) the midpoints are less than or equal to 0.125; (iii) maturities are not within days; (iv) implied volatilities are not between 3 and 120 per cent; (v) open interest is non-positive; and (vi) there are missing details on the volume of trading. Transactions are also required for all four option moneyness categories (ATM call/put and OTM call/put) for a stock on any particular day. The implied volatilities of a put option and a call option with the same strike price and expiration date should essentially be equal; therefore, the difference between the implied volatilities of a matched pair of put and call options, which is referred to as the implied volatility spread, can be used to proxy for the price pressure in the options market. 13 Following Cremers and Weinbaum (2010), we compute the weighted average volatility spread for stock i on day t as follows: N CPIV it = it j=1 w jt (IVcall jt IVput jt ) (1) where j represents the j th matched pair of put and call options with the same strike price and expiration date on stock i; Nit represents the number of valid option pairs for stock i on day t; IVcalljt (IVputjt) is the implied volatility of the call (put) option in the j th pair 13 The implied volatilities are adjusted for expected dividends and early exercise. 13

14 of options j; and wjt are the weights which are computed based on the average open interest of the j th pair of call and put options. Two investor sentiment measures are adopted in this study to facilitate our investigation into the influence of investor sentiment on the relationship between the CPIV and future option returns; these measures are the Baker and Wurgler sentiment ( BW sentiment ) index and the University of Michigan consumer sentiment ( UOM sentiment ) index, which are respectively obtained from the Wurgler website and the Federal Reserve Economic Data (FRED) database. As suggested by Easley et al. (1998), the probability of informed trading (PIN) can be used to capture informed trading within the market; we therefore obtain an updated version of the PIN from the Stephen Brown website for use as a proxy for information asymmetry. We also create an information asymmetry measure (ASY index), as proposed by Drobetz et al. (2010). 14 The Amihud illiquidity (2002) and Pastor and Stambaugh (2003) liquidity (PS liquidity) measures are used in this study to assess stock liquidity; these measures are respectively obtained from the Hasbrouck and Stambaugh websites. We follow Atilgan (2014) to measure option liquidity by option volume and option bid-ask spread. The descriptive statistics of the CPIV and the other variables, including the means, medians, 14 See Drobetz et al. (2010) for a more detailed discussion. 14

15 standard deviations and the 10%, 50% and 90% percentiles, are reported in Table 2. <Table 2 is inserted about here> 4. EMPIRICAL METHODOLOGY Two frameworks are adopted in this study for our analysis of the effects of a particular factor on the predictive relationship between CPIV and option returns. Firstly, based on our full sample, we run a regression model with a dummy variable to examine the impacts of earnings announcements, investor sentiment, information asymmetry, stock liquidity and options liquidity on the predictive relationship. Secondly, based on our sample of observations around earnings announcement periods, we go on to run a regression model for various -samples grouped by the levels of investor sentiment, information asymmetry, stock liquidity or options liquidity to examine the joint effects of earnings announcements and any of the other factors on the predictive relationship. 4.1 Full Sample Methodology In order to facilitate our examination of the impacts on the return predictability made by CPIV that are attributable to earnings announcements, investor sentiment, information asymmetry, stock liquidity and options liquidity, we modify the regression model adopted in the Doran et al. (2013) study to run a regression model which is expressed as: 15

16 O R i,t+1 = a 0 + β 1 CPIV i,t + β 2 D i,t + β 3 CPIV i,t (2) D i,t + β 4 IV i,t + β 5 MOM i,t + β 6 BM i,t + β 7 ME i,t + ε i,t O where R i,t+1 is defined as the buy-and-hold option/stock return over period [t, t+1] and Di,t is a dummy variable which takes the value of 1 if time t is the earnings announcement date or if it is classified as a time with high sentiment, high information asymmetry, low stock liquidity or high options liquidity for stock i. We follow Doran et al. (2013) to control for the effects of market equity (ME) in billions, book-to-market equity (BM), momentum (MOM) and implied volatility (IV) on option returns. Specifically, MEi,t is the number of shares outstanding multiplied by the stock price at the end of the month; BMi,t is the book equity at the end of the prior fiscal year over market equity; MOMi,t is defined as the buy and hold stock returns over the past 12-month period; and IVi,t is computed as the moneyness-weighted mean of the implied volatilities of all options on the first day of the month of the CPIV measurement. 4.2 Earnings Announcement Sample Methodology Following Atilgan (2014), we set the earnings announcement date as time 0, whilst CPIV is measured as time 1. We then calculate buy-and-hold option/stock returns for the earnings announcement window over the time period [0, 1]. For our examination of the return predictability made by CPIV during the earnings announcement periods, we drop the dummy variable and its interaction term with CPIV from Equation (2); 16

17 that is, we run a regression model which is expressed as: O R i,t+1 = a 0 + β 1 CPIV i,t + β 4 IV i,t + β 5 MOM i,t + β 6 BM i,t + β 7 ME i,t + ε i,t (3) For our investigation of the ways in which investor sentiment, information asymmetry, stock liquidity or options liquidity affect the role of earnings announcement on the predicative relationship between CPIV and the option/stock returns, we run the regression model for sub-samples grouped by the levels of investor sentiment, information asymmetry, stock liquidity and option liquidity. Specifically, the firms are first of all grouped based on their investor sentiment (information asymmetry, stock liquidity or option liquidity) levels into the three groups of low (<33%), mid (33-67%) and high (>67%); we then run the regression model with panel data for the returns of the stocks or options across various categories of moneyness-maturity. 5. EMPIRICAL RESULTS 5.1 Earnings Announcements Prior to formally testing for the impacts of earnings announcements on the predictability of option returns from CPIV, we use the sample around earnings announcement periods to provide some preliminary evidence on the existence of the relationships between CPIV and option returns documented by Doran et al. (2013). Following Atilgan (2014), we let the earnings announcement date be day 0 and 17

18 then sort the stocks into five quintiles based on CPIV measured on day 1. We subsequently calculate the buy-and-hold option returns for the earnings announcement window over the period [0, 1] for each group of firms across various moneyness categories for call and put options; the same procedure is also applied to the stocks. The CPIV mean levels and the average stock and option returns for all categories are reported in Table 3, from which we can see that the average call option return for the highest CPIV group is found to be significantly lower than that for the lowest CPIV group at the 10 per cent level, whilst the relationship is significant at the 5 per cent level in the opposite direction for put options; these results are not dependent on whether ATM or OTM contracts are being considered. <Table 3 is inserted about here> Furthermore, the average stock return with the highest CPIV is larger than that with the lowest CPIV, although the difference is not found to be statistically significant. Overall, these preliminary results are in line with the findings of Doran et al. (2013) for the options market and Atilgan (2014) for the stock market. The formal tests for the effects of earnings announcements are implemented by running the regression model specified in Equation (2) with t-statistics based on robust standard errors clustered by firm. As shown in Table 4, the positive predictive relationship between CPIV and future stock returns is weakened by earnings 18

19 announcements, whilst the contrary predictive relationship between CPIV and future option returns is strengthened. <Table 4 is inserted about here> In specific terms, for both ATM and OTM calls, the regression coefficients of both CPIV and its interaction term with the event day are found to be negatively significant at the 1 per cent level, whilst for both ATM and OTM puts, the coefficients are found to be positively significant, again at the 1 per cent level. In other words, in addition to being consistent with the contrary predictive relationship documented by Doran et al. (2013), our results also suggest that the contrary predictive relationship becomes even stronger when firms make earnings announcement, which is driven by the mispricing caused by the greater involvement of individual investors during these periods (Choy and Wei, 2012; Choy, 2015). By contrast, the involvement of greater numbers of individual investors around periods of earnings announcement leads to the positive predictive relationship in the stock market becoming negative, since the sum of the coefficient on CPIV and the interaction term is In summary, the results from our preliminary and formal tests jointly provide support for our Hypothesis 1a. The predictability of option returns made by CPIV becomes stronger, essentially because, as suggested by Doran et al. (2013), it is a 19

20 reflection of the mispricing driven by the demand from individual investors, and as suggested by Choy and Wei (2012) and Choy (2015), there is a tendency for greater numbers of individual investors to participate in the markets around earnings announcements periods. In addition, the positive predictability in the stock market is found to disappear during such periods Investor Sentiment Two measures of investor sentiment, BW and UOM, were used for our investigation of the impact of investor sentiment on the predictability of option returns made by CPIV. In order to examine whether the contrary predictive relationship is more pronounced during a regime of high investor sentiment, we run the regression model specified in Equation (2), with the dummy variable taking the value of 1 if the sentiment level is ranked in the top 20 per cent; otherwise 0. The t-statistics are based on robust standard errors clustered by firm. The estimation results of the regression model across various asset and moneyness categories are reported in Table 5. <Table 5 is inserted about here> As shown in Panel A of Table 5, the coefficient on the interaction term of CPIV and BW sentiment is found to be negatively significant at the 10 per cent level for ATM 15 We also run a regression of earnings announcement stock/option returns on CPIV. The dependent variable is the [0, 1] return around the earnings announcement date (day 0). The same control variables (ME, BM, and MOM) are included. We find that the coefficient of CPIV for stocks is insignificantly negative, while it is significantly negative (positive) at the 1 per cent level for call (put) options. 20

21 call options, and at the 5 per cent level for OTM call options. Although the coefficient is found to be statistically insignificant for put options, the signs for both the ATM and OTM contracts are consistent with the expectations of Hypothesis 2a; in other words, when investor sentiment is high, the contrary predictive relationship driven by the demand from individual investors is strengthened, particularly for call options. For stocks, the positive predictive relationship is weakened, although the effect does not have any statistical significance. As shown in Panel B of Table 5, the results based on the UOM sentiment measure are found to be consistent with those based on the BW sentiment measure. Our empirical results on investor sentiment are therefore in line with our Hypothesis 2a. Given that individual investors are more likely to be driven by sentiment, if the contrary predictive relationship arises as a result of their demand, then it should be more clearly discernible during periods of high investor sentiment. Since we demonstrated in the previous sub-section that the contrary predictive relationship between CPIV and future option returns is particularly strong around earnings announcement periods, we focus on these specific periods for our further examination of whether the earnings announcement effect is dependent upon an investor sentiment regime. In specific terms, we run the panel regression model specified in Equation (3) using the earnings announcement returns of options across 21

22 various moneyness categories for the three groups of firms sorted by their investor sentiment levels. The coefficients on CPIV are summarized in Table 6, along with their t-statistics from the regressions with the same control variables; the results reported in Panel A, which are based on the BW sentiment measure, reveal that the CPIV coefficients for both ATM and OTM call options are found to be negatively significant at the 1 per cent level for the high-sentiment group, whereas they are found to be statistically insignificant for the other two sentiment groups. <Table 6 is inserted about here> Furthermore, the CPIV coefficients for both ATM and OTM put options are found to be positively significant at the 5 per cent level for the high- and mid-sentiment groups, with the former having a larger value, whereas they are found to be insignificant for the low-sentiment group. The coefficients for stock returns are found to be insignificant for all sentiment groups. The results based on the UOM sentiment, which are reported in Panel B, are consistent with those based on the BW sentiment measure. In summary, there may be a tendency for investors to be more irrational during periods of high investor sentiment, or indeed, there may be greater numbers of individual (sentiment-driven) investors participating in the options market. As a result, the contrary predictive relationship made by CPIV is found to be more pronounced 22

23 during such periods, even when firms are making their earnings announcement. These results are consistent with our Hypothesis 2b, particularly for call options. 5.3 Individual Investors Learning Effect As suggested by Easley et al. (1998), informed traders are more likely to trade in the options market when there is high (low) information asymmetry (liquidity) in the stock market or high liquidity in the options market. Since the contrary predictive relationship between CPIV and future options returns is caused by the demand from individual investors in the options market, we expect to find that this predictive relationship will be weakened when there is a greater likelihood of informed investors trading in options and thus individual investors can learn from informed trading. In order to facilitate our examination of whether this contrary predictive relationship is affected by the likelihood of informed trading from which individual investors learn to adjust their behavior bias, we re-run the regression model specified in Equation (2) with the inclusion of alternative measures for information asymmetry, stock liquidity and options liquidity, as described in the following sub-sections Information asymmetry The results obtained based on the two alternative information asymmetry measures are reported in Table 7, where the dummy variable takes the value of 1 if the information asymmetry measure is ranked in the top 20 per cent; otherwise 0. As shown in Panel A 23

24 of Table 7, for ATM calls, the regression coefficients on the interaction term of CPIV and the ASY information asymmetry index, as proposed by Drobetz et al. (2010), are found to be significantly positive at the 5 per cent level, whilst those for OTM calls are found to be significantly positive at the 1 per cent level; the regression coefficients for both ATM and OTM puts are found to be significantly negative at the 1 per cent level. <Table 7 is inserted about here> These results indicate that the contrary predictive relationship is weakened when there is high information asymmetry in the stock market, which could provide sufficient motivation for greater numbers of informed investors to trade in the options market. In addition, the positive predictive relationship in the stock market is unaffected by the level of information asymmetry, since the production term of CPIV and the ASY index is statistically insignificant. The results obtained based on the PIN as an alternative information asymmetry measure, as proposed by Easley et al. (1998), are reported in Panel B of Table 7, from which we can see that for all options categories, although the sign of the interaction term is the same as that for CPIV, all of the coefficients are nevertheless found to be statistically insignificant. 16 The results on information asymmetry are consistent with our Hypothesis 3a; in 16 The PIN values were obtained from the Stephen Brown website. 24

25 other words, higher information asymmetry in the stock market gives rise to trading by informed investors in the options market, thereby weakening the contrary predictive relationship between CPIV and future stock returns, essentially because it is driven by the misreaction of individual investors in the options market. After excluding the dummy variable and its interaction term with CPIV, we subsequently went on to run the panel regression model specified in Equation (3) with the earnings announcement returns of options as the dependent variable. The regression was run across various categories of moneyness for the three groups of firms sorted by their information asymmetry levels. The coefficients on CPIV and the t- statistics are reported in Table 8. <Table 8 is inserted about here> As shown in Panel A of Table 8, based on the ASY index, the coefficients on CPIV for the lower information asymmetry groups are found to be significant at the 1 per cent level and more negative (positive) than those on the higher information asymmetry groups for call (put) options, whereas no significant pattern is discernible for the stock market. The coefficients on CPIV are also found to be statistically insignificant for call options when information asymmetry is higher. In other words, if there are more informed investors trading in the options market, the predictive relationship driven by the misreaction attributable to individual investors 25

26 around earnings announcement periods could be significantly weakened. However, as shown in Panel B of Table 8, no clear pattern is discernible when using the PIN value as an alternative measure. These results are in line with our Hypothesis 3b on information asymmetry Stock liquidity A further prediction of the sequential trading model of Easley et al. (1998) is that there is a greater likelihood of informed investors trading in options when the liquidity of the underlying stock is lower. We run the panel regression specified in Equation (2) with the liquidity and illiquidity measures respectively proposed by Pastor and Stambaugh (2003) and Amihud (2002). 17 The dummy variable takes the value of 1 if the liquidity (illiquidity) level is ranked in the bottom (top) 20 per cent; otherwise 0. The regression results are reported in Table 9. <Table 9 is inserted about here> As shown in Panel A of Table 9, under the Pastor and Stambaugh (PS) liquidity measure, the coefficients of the interaction term of CPIV and the dummy variable are positive for all categories of stocks and options, with most of them having statistical insignificance. As shown in Panel B of Table 9, under the Amihud illiquidity measure, 17 The Amihud illiquidity and the Pastor and Stambaugh liquidity measure are respectively obtained from the websites of Hasbrouck and Stambaugh. 26

27 all of the signs on the interaction term of CPIV and the dummy variable for options remain the same as those of CPIV, with most of them exhibiting statistical significance. In summary, we have been unable to find any clear-cut evidence in the present study to show the ways in which stock liquidity affects the predictive relationship, despite the potential for informed investors to trade in more options when stock liquidity is lower. Given that we can find no evidence to support the effect of stock liquidity on the full sample, we go on to run the panel regression model specified in Equation (3) focusing on the earnings announcement returns of options across various categories of moneyness for the three groups of firms sorted by their stock liquidity levels. The results are summarized in Table 10. <Table 10 is inserted about here> If lower stock liquidity does indeed motivate informed investors to trade in more options, we should expect to find the return predictability produced by CPIV being weakened when stock liquidity (illiquidity) is lower (higher). As shown in Panel A of Table 10, under the PS liquidity measure, for both ATM and OTM call options, the CPIV coefficients of the low-liquidity groups are found to be less negative than those of the high-liquidity groups. Similar results are also found in the comparison between the low and high groups under the Amihud illiquidity measure; these results are reported in Panel B of Table

28 In summary, although we are generally unable to identify any clear evidence providing support the impact of stock liquidity on the return predictability produced by the CPIV, we do find that such predictability is weakened when stock liquidity (illiquidity) is lower (higher) around earnings announcement periods, particularly for call options. In other words, our analysis based on earnings announcement events is consistent with our Hypothesis 3b; that is, the likelihood of informed trading motivated by lower stock liquidity results in the predictability around earnings announcement periods becoming less significant Options liquidity Easley et al. (1998) further suggested that informed investors prefer to take advantage of their private information in the options market when trading in the options market is more liquid. Thus, if the contrary return predictability produced by CPIV is driven by the behavioral biases of individual investors, then we would expect to find this predictability being weakened when options liquidity is high, since this tends to attract more informed trading. Following Atilgan (2014), we go on to run the regression model specified in Equation (2) using the option bid-ask spread and option volume to measure option liquidity. The dummy variable takes the value of 1 if the spread (volume) is ranked in the bottom (top) 20 per cent; otherwise 0. The estimation results are shown in Table 28

29 11, where the t-statistics are based on robust standard errors clustered by firm. <Table 11 is inserted about here> As shown in Panel A of Table 11, when the bid-ask spread is used as the measure of liquidity, the coefficients on the product term of CPIV and the dummy variable are found to be significantly positive for both ATM and OTM call options at the 1 per cent level, and significantly negative for both ATM and OTM put options at the 5 per cent level. These results indicate that the more aggressive participation of informed traders in the options market during periods of high liquidity results in the weakening of the predictive relationship between CPIV and future option returns. Furthermore, the positive predictive relationship found in the stock market is found to be strengthened, although it is only significant at the 10 per cent level. As shown in Panel B of Table 11, the results with trading volume as the alternative liquidity measure show a similar pattern, although they are less promising. Overall, these results are consistent with our Hypothesis 3a on options liquidity. To facilitate an additional investigation into whether options liquidity affects the predictive relationship around earnings announcement periods, we drop the dummy variable and its product term with CPIV and then go on to run the panel regression model specified in Equation (3) across various moneyness categories for the three groups of firms sorted by their option liquidity levels. The results of the CPIV 29

30 coefficient are summarized in Table 12. <Table 12 is inserted about here> As shown in both panels, the CPIV coefficients for the higher liquidity groups of call (put) options are found to be more negative (positive) than those of the lower liquidity groups for both moneyness categories. Obviously, these results are inconsistent with our Hypothesis 3b derived from the argument of Easley et al. (1998) that there are likely to be more informed investors trading in the options market when liquidity is higher. These results do, however, appear to be in line with the argument put forward by Choy and Wei (2012) and Choy (2015); both of these studies suggested that options trading around earnings announcement periods tends to be dominated by individual investors. Therefore, the higher liquidity in the options market around earnings announcement periods may be primarily driven by greater numbers of individual investors, as opposed to the presence of informed investors. Although informed investors may generally tend to trade more options during periods of high options liquidity, they may decide not to engage in trading around earnings announcement periods, given their awareness of aggressive participation in the market by individual investors. In summary, we provide clear evidence in support of the effect of options liquidity 30

31 in the predictive relationship between CPIV and future options returns. Specifically, the contrary predictive relationship is weakened when greater numbers of informed investors trade in options during periods of high liquidity. However, this is not the case around earnings announcement periods. 6. CONCLUSIONS Based on the extant literature on the negative predictive relationship between CPIV and future call options returns, we contribute to the literature by examining whether and how earnings announcements, investor sentiment, and informed trading affect the predictive relationship on the returns of both call and put options. In particular, by investigating the relationships under various conditions that are widely in the extant literature to proxy for the extent of involvement of informed traders, we can examine whether individual investors learn from informed traders and adjust their behavior bias. The empirical results reported in this study, which are based on optioned stocks traded in the US market, reveal that earnings announcements and investor sentiment have significant impacts on the predictive relationship. In addition, we provide evidence that individual investors can learn from informed trading and thus mitigate mispricing in the options market. 31

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