Idiosyncratic Volatility Shocks, Behavior Bias, and Cross-Sectional Stock Returns. First version: December 2009 This version: January 2017

Transcription

1 Idiosyncratic Volatily Shocks, Behavior Bias, and Cross-Sectional Stock Returns First version: December 2009 This version: January

2 Abstract This paper examines the impact of idiosyncratic volatily shock on cross-section stock value. The results indicate that stocks wh posive (negative) idiosyncratic volatily shocks subsequently underperform (outperform). Unlike the cross-section ranked idiosyncratic volatily method, the shocks identified in this paper are better served to capture the very moment when firm specific information arrives or is fully absorbed. Therefore, the performance divergence of stocks of high and low shocks reflects how investors interpret the new information. We document that cognive bias, such as the disposion effect, overconfidence, and gambler s fallacy could explain the abnormal returns. However, lottery preference, which is a firm specific characteristic, does not explain the effect. JEL Classification: G11, G14 Keywords: Idiosyncratic volatily shocks, disposion effect, investor overconfidence, gambler s fallacy 2

3 1. Introduction The major goal of this paper is to investigate and interpret the relation between idiosyncratic volatily (IV) shocks and future stock returns. This paper differs from previous studies such as, Ang, Hodrick, Xing, and Zhang (AHXZ, 2006), Huang, Liu, Rhee, Zhang (2011), Fu (2009), Chua, Goh, and Zhang (2010), and Hou and Loh (2016) by investigating the inter-temporal role of idiosyncratic volatily in predicting price changes. Specifically, we follow the spir of Gervais, Kaniel, and Mingelgrin (2001) by comparing the idiosyncratic volatily of an individual stock in the portfolio formation month against s own idiosyncratic volatilies in the months prior to formation. A stock s idiosyncratic volatily is estimated for the formation month and for each prior month. These estimates are then ranked from the highest to the lowest for each stock. If the idiosyncratic volatily in the formation month is in the highest (lowest) decile, the stock is said to have a posive (negative) idiosyncratic volatily shock. This ranking method differs from the cross-sectional based ranking method used in all previous studies in this field. Our ranking method provides ranks based on the relative idiosyncratic volatily (IV). The tradional cross-sectional based ranking of IV is an absolute measure, which generally could correlate wh stock static characteristics. For instance, a small size stock typically shows higher IV ranks comparing to a wellestablished blue chip whout any significant new information involved. Higher level of IV rank stocks may also show higher skewness and coskewness. The time series measure we adopt here asks whether the currently observed IV is unusually high (or low) for this stock. There are a few advantages of our method. First, the time-series method generates a much broader cross-section of stocks. Therefore, the 3

4 rank is less likely to be a proxy for particular stock characteristics, such as size. Due to autocorrelation in IV, the portfolio generated by cross-section level ranks could also be consisted of a somewhat stable set of smaller stocks. Second, has a very different economic interpretation than the usual IV rankings. Rather than focusing on stocks wh high or low absolute IV, the time-series ranking identifies when stocks have unusually high or low IV relative to themselves. Under this framework, when new firm specific information arrives, triggers the process of price revision. As the news is incorporated into the price, results in higher IV, higher information uncertainty, and higher trading volume. On the oppose, the low IV shock indicates an unusually quiet period for the stock, wh less firm specific information being revealed, less information uncertainty, and lower trading volume. In other word, we can think of the quiet period as the moment when almost all firm specific news has been fully absorbed by the market. Therefore, the stock performance essentially mimics the market, leading to unusually low IV period. This economic interpretation is strikingly different than the tradional cross section high IV/low IV dichotomy in which high IV could be a firm characteristic (e.g., a stock wh a large number of growth options or lottery preference), rather than a state every stock passes through at some point. We find that individual stocks wh posive (negative) idiosyncratic volatily shocks tend to experience low (high) returns over subsequent months. The strategy of buying stocks wh negative idiosyncratic volatily shocks and selling stocks wh posive idiosyncratic volatily shocks yields a significant risk-adjusted return of 0.891% per month on an equal-weighted basis and 0.488% per month on a value-weighted basis in the month following formation. Further, the significantly abnormal returns can be 4

5 found up to 12 month after the formation month. Therefore, the results are less likely caused by short-term return reversal suggested by Fu (2009). To rule out the possibily of these abnormal returns may be associated wh any specific model, tests also have been conducted based on Carhart 4 factors, Fama-French 5 factors, the new 4 factor model suggested by Hou, Xue, and Zhang (2015), and Fama-French 3 factor plus short-term reversal and liquidy factor, respectively. The abnormal returns still exist for each model and their economic sizes are comparable. The remaining question is what might cause the out- (under-) performance of the stocks wh low (high) IV shock. To answer this question, we first examine the stock performance and trading characteristics surrounding the portfolio formation month. Several important empirical facts are revealed. First, we find that the stocks of high (low) IV shocks under- (out-) perform prior to the portfolio formation month at risk adjusted basis. However, the risk adjusted stock performance is reversed during the formation month. Second, after the portfolio formation month, stocks of high (low) IV shocks under- (out-) perform again, although at lower economic significance. Finally, we examine the trading volume for each portfolio, both before and after the formation month. We find that stocks wh high IV shocks not only reveal high returns, but also high volume shocks in the formation month. The oppose is true for stocks wh negative IV shocks. Interesting, we do not notice any significantly trading volume pattern prior or after the portfolio formation month. Many existing paper already provide some evidence to explain why high IV shock stocks might underperform based on short sale constraints and high level of difference of opinion, such as Bali, Scherbina, and Tang (2011), or lottery preferences of investors and 5

6 market frictions (e.g., Hou and Loh (2016)). These explanations may be reasonable in explaining the underperformance of high IV stocks. However, to our best knowledge, no research intends to explain why stocks of low IV shocks outperform. Our paper intends to close this gap. We argue that the disposion effect provides an explanation of the performance and trading pattern of the stocks of low IV shocks. Disposion effect refers to the phenomenon that investors tend to sell winners too early and ride losers too long (Shefrin and Statman (1985)). The disposion effect could be driven by a combination of prospect theory and mental accounting (e.g. Frazzini (2006), Barberis and Xiong (2009)). For low IV shock stocks, appear that they are on average receiving good news prior to the formation month, given that they are outperformed consistently during this period. As the stocks gain more value, the pressure of disposion effect gets stronger, even though these stocks continue to gain value as the market continue to absorb the news. Finally, the stock reaches at the moment when the news has been fully absorbed from investor perspective this could be indicated by the abnormally low IV shock, or an unusually quiet period. It is also the time when the built-up disposion effect reaches avalanche moment. Investors rush to sell to realize paper gain. Stock price is lowered below fair value to absorb the selling pressure. As most of the news having been incorporated already prior to the formation month, is not surprise to observe that the lower price movement is accompanied by relatively lower trading volume during the formation month. Post the avalanche moment, stock value gains back as the disposion trading pressure has already been released. Therefore, these stocks appear to be outperform again, although at less economic magnude. 6

7 As the disposion effect might explain the performance of low IV shock stocks, the interpretation of stocks of high IV shocks is different. For these stocks, they tend to have had abnormal lower returns over the previous months. However, during the portfolio formation month, their value, IV ranks, and trading volumes gain significantly. Apparently, appears that some kind of firm specific information, generally being perceived posively, arrives during this month. Finally, after the inial h, these stocks return to s usual underperformance wh less economic significance and normal trading volumes again. Given these empirical facts revealed by stocks of high IV shocks, we suggest these patterns might be linked to investor s behavior biases, such as gambler s fallacy and overconfidence bias. The gambler s fallacy refers to the investor s behavior bias as to believe that outcomes in a random sequences to exhib systemic reversal (e.g. Rabin and Vayanos (2010)). As the stocks experience losing streaks, new information leads to higher IV, higher trading volumes, and higher values as investors fall under the spell of gambler s fallacy and overbid the stock. The stocks subsequently underperform. The gambler s fallacy does not rule out the explanation based on overconfidence. Scheinkman and Xiong (2003) present a theoretic model based on heterogeneous beliefs generated by agents overconfidence. By directly incorporating agent s overconfidence, their model generates an option value, dynamic of trading, and speculative component in prices. They also show that price, volume, and volatily increase together as the degree of overconfidence rises. This result fs our observations of the coexistence of high prices, high trading volumes, and high price volatily que well. 7

8 Following the theoretic framework of Scheinkamn and Xiong (2003), we believe the overconfidence bias can also partially explain the underperformance of high IV shock stocks. When new information arrives, investors are divided into two groups. One group could be relatively more optimistic than the other group. Both groups of investors not only differ in the interpretation of the signals but also overestimate s relevance. Second, when evaluating a stock, investors consider both their own views of fundamentals and the fact that the owners of the stock have an option to sell to the other group. Therefore, investors who are more optimistic inially pay prices that exceed their own valuation of fundamentals because they believe that in the future they will find a buyer willing to pay even more. The addional option value, which could be considered as the speculative component, will cause the stock price to rise higher than what is justified by the fundamentals. At the same time, the fluctuations in the value of this option contribute an extra component to price volatily, which is consistent wh the observed posive IV shocks. Finally, as investors learn more about the informativeness of the signals, the inially relative more optimistic investors revise the option value down, and price falls. This leads to subsequent underperformance by these stocks. To conduct direct empirical tests for investor biases on stock price is challenging. We propose a few indirect tests of our hypotheses. The first test is based on the premise that high information uncertainty causes stronger psychological biases, such as the disposion effect (e.g. Hirshleifer (2001), Zhang (2006a, b)). Using analyst dispersion as a proxy measure of information uncertainty, not only low IV shock stocks reveal stronger disposion effect when analyst dispersion is high, the IV effect of high IV shock stocks is also stronger. A second test is based on the premise that investor overconfidence is 8

9 stronger in up markets and weaker in down markets 1.Therefore, if investor bias caused by overconfidence attributes to the abnormal returns of IV shocks, we should expect stronger results in up markets and weaker results in down markets. Our results support this view as significant abnormal returns only exist in up markets. A third indirect test of investor s bias argument is based on results after controlling for instutional ownership. Previous lerature has documented that, in comparing against instutional investors, retail investors are evidenced more cognive bias, such as disposion effect, gambler s fallacy, and overconfidence. As instutional investors are believed to be more rational than average retail investor, we hypothesize that the patterns documented based on IV shock should be weaker for stocks of high instutional ownership, while stronger for stocks of low instutional ownership. Our tests support the view as instutional ownership significantly reduces the IV effect. Finally, this paper also tests whether stock lottery preference could partially explain the IV effect, as suggested by Hou and Loh (2016) and Boyer, Mton, and Vorkink (2010). We find that the lottery preference reduces the IV effect oppose to their findings. Furthermore, the IV shock reduces the influence of the lottery preference impact on stock value. We argue that this difference is caused by the different IV ranking methods between this paper and others. Since lottery preference represents a firm specific static characteristic, s influence on stock price should be weaker when new firm specific information arrives or disappears. That is the very moment when stocks experience high or low IV shocks. 1 E.g., Griffin, Nardari, and Stulz (2007), Chuang and Lee (2006), Statman, Thorley, and Vorkink (2006), Cooper, Gutierrez, Hameed (2004), and Daniel, Hirshleifer, and Subrahmanyam (1998). 9

10 The rest of the paper is organized as the follows. Section 2 provides a brief lerature review. Section 3 describes data and discusses the methodology in estimating idiosyncratic volatily and idiosyncratic volatily shocks. Section 4 first reports the base results of the strategy of buying (selling) stocks wh abnormally low (high) idiosyncratic volatily shocks. Further tests are performed to show that the return-reversal of small size stocks and liquidy factor cannot explain the negative relation between idiosyncratic volatily shocks and future returns. Section 5 presents the main characteristics of the portfolio formed by IV shocks. Based on the characteristics, section 6 provides possible explanations of the IV effect. Section 7 conducts several indirect tests on the validy of the hypotheses. Section 8 summarizes and concludes. 2. Related Lerature The results of this paper relate to the lerature of the idiosyncratic risk and stock returns. Similar studies have drawn strong attention in recent years. Much of the empirical research has documented that a significant number of individual investors are unable to diversify risks. Even instutional investors, such as style fund managers, are found to allocate funds not at the asset level or according to risk, but at the style level [e.g., Chan, Chen and Lakonishok (2002), Chow, Denning, and Huang (2008)]. Therefore, in contrast to the capal asset pricing model (CAPM), idiosyncratic risk may be priced because investors do not hold fully diversified portfolios eher because of transaction costs, incomplete information, instutional constraints, or behavior bias. Prior studies, such as Merton (1987), Barberies and Huang (2001), Malkiel and Xu (2002), and Jones 10

11 and Rhodes-Kropf (2003), use economic theories to argue that stocks wh larger idiosyncratic risk should compensate investors for holding them. Whether idiosyncratic risk and stock returns are posively or negatively related is a hotly debated question. The finding of this paper, that stocks wh substantially increased idiosyncratic volatily (posive shocks) underperform stocks wh substantially decreased idiosyncratic volatily (negative shocks), sheds addional lights on this debate. While the theoretical work referenced above suggests that idiosyncratic volatily should be posively related to expected returns, AHXZ (2006) find the oppose. They show that stocks wh high idiosyncratic volatily in month t have low average returns in month t+1. In their more recent paper, AHXZ (2009) find that this negative relation holds for 23 developed markets. They call the negative relation documented in AHXZ (2006, 2009) a substantive puzzle. AHXZ (2006) attribute the difference between their results and the results of past studies to the use of a different measure of idiosyncratic volatily. Previous studies, such as Goyal and Santa-Clara (2003), Malkiel and Xu (2002) and Tinic and West (1986), do not measure idiosyncratic volatily at the firm level, while AHXZ (2006) do. Several papers have attempted to solve this puzzle. Both Bali and Cakici (2008) and Huang, Liu, Rhee, and Zhang (2011) find that the negative relation documented in AHXZ (2006) is not robust. Most notably, the negative relation between idiosyncratic volatily and expected returns only exists in value-weighted portfolio returns. In addion, even on a value-weighted basis, Huang et al. (2011) find that the negative relation disappears if one month is skipped between the portfolio formation and holding period. They attribute the significant negative relation between idiosyncratic volatily and 11

12 expected return to short-term return reversals of winner and loser stocks wh high idiosyncratic volatily. Fu (2009) argues that the one-month lagged idiosyncratic volatilies used in AHXZ (2006) are noisy proxies for expected idiosyncratic volatilies. They argue that an exponential GARCH model should be used to estimate expected idiosyncratic volatilies. Based upon this model, the paper finds a significant posive relation between the estimated condional idiosyncratic volatilies and expected returns. Again, the paper attributes the results of AHXZ (2006) to return-reversal of a subset of small stocks wh high idiosyncratic volatilies. 2 Stambaugh, Yu, and Yuan (2014) attribute the negative relation documented by AHXZ (2006) to arbrage asymmetry depending on stocks are overpriced or underpriced. When stocks are overpriced, the effect of idiosyncratic risk on expected returns is negative since investors are reluctant to take short posions. When stocks are underpriced, the effect is posive since investors are more likely to take long posions. Bali, Scherbina, and Tang (2014) attribute the negative abnormal returns to unusual news events. They argue that unusual news events increase the level of differences of opinion among investors, which is then posively linked to stock idiosyncratic volatily. Combined wh the constraints on short-sales, this means that stocks will be bid up by optimistic investors while pessimistic investors s on the sidelines. Therefore, a posive relation between volatily shocks and contemporaneous stock returns is observed. In the future, the stock price declines as the level of investor disagreement and return volatily decrease. 2 However, Huang, Liu, Rhee, and Zhang (2010) show that the posive relationship documented in Fu (2009) is caused by an omted variable bias when the previous month return is not explicly controlled for. Guo, Kassa, and Furguson (2014) and Fink, Fink, and He (2012) also cricize Fu s (2009) results, 12

13 3. Data and Methodology The data for this study is obtained from the Center for Research in Secury Prices (CRSP) which includes NYSE, AMEX, and NASDAQ stock daily and monthly returns from July 1963 to December Daily and monthly Fama-French factors are obtained from French s webse. Following AHXZ (2006), idiosyncratic volatily is measured relative to the Fama-French three-factor model r i i i i i i t a mkt MKTt smbsmb t hmlhmlt t (1) where i rt is the excess daily returns of stock i, MKT t is the daily market excess return, and SMB t and HML t represent daily size and book-to-market effects, respectively. i Idiosyncratic volatily is measured as the standard deviation of daily residuals t in month t. For each month, a stock has to have at least 15 trading days in order to have s idiosyncratic volatily estimated. This paper examines the intertemporal role of idiosyncratic risk in predicting future stock returns. This differentiates our paper from previous studies that use a crosssectional ranking method to investigate the relation between idiosyncratic volatily and stock return. Specifically, we follow the method of Gervais, Kaniel, and Mingelgrin (2001) in defining high idiosyncratic volatily shocks by comparing a stock s idiosyncratic volatily in month t against s own idiosyncratic volatily estimated in the previous 19 months. A stock is said to have an abnormally high (low) idiosyncratic volatily shock if s idiosyncratic volatily in month t is among the top (bottom) decile 13

14 of the 20 idiosyncratic volatilies. 3 As we have mentioned previously, our ranking method is more likely to capture the very moment when new firm specific information arrives or dying out. The rank is less likely to be a proxy for particular stock characteristics, such as size. After defining the abnormally high (low) idiosyncratic volatily shock, we design trading strategies based on these classifications by long stocks of highest IV shock and shorting stocks of lowest IV shock following AHXZ (2006). Both equal-weighted and value-weighted portfolio returns are reported. In calculating the value-weighted returns, we use the market capalization as of January of the calendar year for each stock. To remove the impact of low-priced stocks and micro-cap stocks, we exclude any stocks whose prices fall below $3 in the portfolio formation month. 4. Idiosyncratic Volatily Shocks and Stock Returns a. The main results In this section, we present both the mean returns and risk-adjusted abnormal returns of portfolios sorted by an intertemporal comparison of stock idiosyncratic volatily estimated by the Fama-French 3-factor model. The results are displayed in Table 1. Table 1 reports the abnormal returns of each decile portfolio sorted by idiosyncratic volatily shocks. Portfolio 1 (10) is formed by stocks wh negative (posive) idiosyncratic volatily shocks as defined in section 3. The first two columns report the equally weighted abnormal returns and t-stats. The following two columns 3 Tests also have been done by comparing a stock s idiosyncratic volatily in month t against 29 idiosyncratic volatilies estimated during the previous 29 months. Patterns are found to be similar and somewhat more significant than those based on the 20 idiosyncratic volatilies. 14

15 report the value weighted abnormal returns. While the abnormal returns do not decline in a strictly monotonic way for equally weighted method, a generally declining pattern is clearly evidenced on both equal- and value-weighted basis. In addion, the results reveal a clear idiosyncratic effect (hereby IV effect). The difference between portfolio 1 and 10 is 0.891% and 0.488% per month on an equal- and value-weighted basis, respectively. Both differences are highly significant. Table 1 also shows that the IV effect does not only rely on the severe underperformance of portfolio 10. The IV effects are also partially attributed to the significant outperformance of stocks wh lowest IV ranks. For instance, the one month equal-weighted alpha for portfolio 1 is 0.267% per month and highly statistically significant. Meanwhile, the corresponding alpha for portfolio 10 is % and also highly statistically significant. Therefore, explanations have to be developed for both IV1 s outperformance and IV10 s underperformance. b. Do they capture the same information sets: the tradional IV measures and inter-temporary IV shocks? Although we argue that the inter-temporary IV shock measure is better served to capture firm specific news as naturally describes a state that every stock passes through at some point, is still interesting to provide a study to see how they might be related. To do so, we first sort the stocks into deciles based on their corresponding intertemporary IV ranks. Whin each decile, we then follow AHXZ (2006) to sort the stocks into quintile based on the cross-sectional IV level. The following one month abnormal value-weighted returns are then reported in Table 2 for each portfolio. The results suggest 15

16 that the strategy of longing low IV and shorting high IV stocks based on AHXA(2006) still yields significantly abnormal returns in most circumstances, except for the two lowest deciles based on inter-temporary measured IV shocks. This implies that both ranks may capture different information sets. However, the two information sets are also related as the AHXA(2006) abnormal returns seem to be stronger along wh the ranks of IV shocks based on the inter-temporary IV ranks. For instance, in addion to the lack of significance IV effects for decile 1 and 2, the abnormal return is 1.419% for decile 10, which is substantially higher than 0.429% for decile 3. c. Controlling for short-term return-reversal Huang et al. (2011) and Fu (2009) suggest that the idiosyncratic volatily puzzle could be driven by the return reversal of stocks that have the highest idiosyncratic volatilies. Intuively, high idiosyncratic volatilies are contemporaneous wh high returns, which tend to reverse in the following month. Therefore, as documented in AHXZ (2006), the stocks wh the highest idiosyncratic volatilies underperform in the following month, yet stocks wh the lowest idiosyncratic volatilies do not outperform. In this section, we test whether the negative relation between idiosyncratic volatily (IV) shocks and subsequent stock returns is affected by the short-term returnreversal. Specifically, we extend the holding period from one month to 12 months. If the results are driven by the short-term reversal, we should expect the abnormal returns disappear relatively quick as the holding period extended. Table 3 reports the results of longer holding period. The results clearly show that the abnormal returns are not a short-term phenomenon. Even as the holding period is extended to 12 months, the abnormal returns still are statistically significant, on both 16

17 equal-and value-weighted basis. Importantly, we also observe that the abnormal returns do not only rely on the underperformance of decile 10 stocks (highest IV shocks). The stocks of lowest IV shocks yield posive abnormal returns whin the 12 month measurement period. d. Controlling for size Fu (2009) suggests that the IV effect could be potentially driven by stocks small in size and negligible relative to total market capalization. In contrast, note that we have already excluded any stocks whose prices fall below $3 in the portfolio formation month. In this section, we provide further evidence that our results reported in Table 1 are not driven by small cap stocks. To this end, we first sort stocks into large-, medium-, and small-sized groups, based on their market capalization in the portfolio formation month, and then in each group form eher equal- or value-weighted decile portfolios. The results based on the three groups are reported in Table 4. Panel A of Table 4 presents the mean returns for portfolios 1 to 10 and the strategy of 1-10, while panel B presents the FF-3 alphas. In examining Table 4, the negative relation between idiosyncratic volatily shocks and subsequent stock returns clearly exist on all stock size. The last two columns of Table 2 show that, even for large-size stocks, the strategy of long portfolio 1 and short portfolio 10 yields a significant abnormal return of 0.466% (0.388%) per month on an equal- (value-) weighted basis. This pattern is consistent across all size groups and indicates that the phenomenon is not purely driven by the stocks of small size. 17

18 Another interesting fact worth mentioning is that the strength of idiosyncratic volatily shock monotonically increases as stock size declines. The small-size stocks have the largest 1-10 difference in both raw and abnormal returns at 1.331% and 1.356% per month on an equal-weighted and value-weighted basis, respectively. This particular pattern is not a surprise. Many other studies of anomalies have documented a similar pattern. For example, Gervais, Kaniel, and Minglegrin (2001) and Huang and Heian (2010) both find similar patterns in the anomaly of the high volume premium. Blume, Easley, and O Hara (1994) also argues that trading volume is more informative the smaller the size of the stock. e. Robustness check: abnormal returns based on different asset pricing models and addional factors To rule out the possibily that the abnormal returns identified so far only exist for a particular asset pricing model, a series of robustness checks have been performed based on different asset pricing model beyond the basic FF three-factor model. Table 5 reports the regression results. The first model we use is the Carhart four-factor model (Carhart (1997)). After including the momentum factor, the abnormal return alpha is still at 0.57% per month and statistically significant. The second model is based on the Fama-French five-factor model. Again, the abnormal return alpha is 0.62% per month. Hou, Xue, and Zhang (2015) (hereby HXZ four-factor model) propose a new four-factor model consisting of the market factor, a size factor, an investment factor, and a profabily factor. They find that this new factor model explains large amount of anomalies. We therefore also run the 18

19 returns based on their four-factor model. According to Hou, Xue, and Zhang (2015), variables RME, RIA, and ROE in Table 5 represent a size factor, an investment factor, and a profabily factor, respectively. Based on this new model, the abnormal return is still statistically significant at 0.49% per month. The last two regressions are based on models of Fama-French three-factor plus a short-term reversal factor or Pastor- Stambaugh liquidy factor, respectively. It is interesting to note that short-term reversal and liquidy factor does not contribute in explaining the idiosyncratic volatily puzzle. Both coefficients are not statistically significant. 5. Portfolio Characteristics: Average Returns and Trading Volume Prior, During, and After Portfolio Formation Month Up to this point, we have detailed the IV shocks and the subsequent portfolio returns. To identify any potential explanation of these findings, will be beneficial to examine the characteristics of the portfolios formed by IV shocks. One of the most interesting information is to investigate what happens to the portfolio returns before, during, and after the formation month. Table 6 presents the abnormal returns from month -4 to 4 for each portfolio formed in the formation month (or month 0 in the table). Several important empirical facts are identified. First, the abnormal returns for portfolio 1 (10) in the months prior to formation (month 0) are the highest (lowest) among all 10 portfolios. For instance, at month -1, abnormal return is 1.546% per month for RIV1 and % for RIV10, respectively. Second, not only portfolio 1 outperforms portfolio 10 significantly, Table 6 also shows that speed of value gain (loss) for portfolio 1 (10) is accelerated as the time gets closer to 19

20 month 0. At month -4, portfolio 1 and 10 yield an abnormal return of 0.893% and %, respectively. The difference is 0.898%. By the time of month -1, the difference increases to 1.803%. The performance divergence of portfolios 1 to 10 implies that stocks in portfolio 1 are favored by investors prior to month 0 they on average gain value significantly and the gain seems to be accelerated. Meanwhile, investors lose interest in portfolio 10 they on average lose value significantly and the loss seems to be accelerated. However, Table 6 also tells us that the fortune of portfolio 1 (10) is reversed in month 0 the point when we identify IV shocks. In this formation month, portfolio 1 s performance suddenly drops s abnormal return is reduced from a highest posive 1.546% in prior month to a lowest negative abnormal return of %. Portfolio 10 experiences the oppose s abnormal return increases from the lowest abnormal return of % in prior month to the highest posive abnormal return of 1.943%. Therefore, portfolio 1 underperforms portfolio 10 by %, which is a shock difference comparing to the 1.793% outperformance just one month before 0. Our finding that portfolio 1 underperform 10 in month 0 is similar to others, such as Bali, Scherbina, and Tang (2011) and Fu (2009). Finally, after month 0, portfolio 1 starts to yield a higher abnormal return than portfolio 10 again. The performance of portfolio 1 (10) yields an abnormal return of 0.219% (-0.273%), which is the highest (lowest). Compared to the abnormal return patterns revealed prior to month 0, however, the differences are weaker both statistically and economically. For instance, portfolio 1 (10) yields a difference return of 0.259% at month 4, which is materially smaller than the 0.898% difference at month

21 Since trading volumes and returns are closely related, the trading volumes of each portfolio surrounding the formation month are also examined. To compare the relative strength of the trading activies, we follow the method used in Section 3 in ranking the idiosyncratic volatily for each stock. Specifically, we compare a stock s monthly trading volume in month t against s own trading volumes in the previous 19 months. We rank the trading volumes into deciles. Figure 1 presents the average trading volume ranks for portfolios 1 to 10 before, during, and after the formation month 0. The graph shows that the trading volume of the stocks wh the highest (lowest) IV shocks increases (decreases) during the formation month. It subsequently reverts to s normal range in the following 2 to 4 months. Prior to month 0, there is no material difference in trading volumes among the 10 portfolios. 6. Interpretation of the results: Investor behavior bias and the IV effects a. The disposion effect and the performance of negative IV shock stocks Prior explanations based on higher difference of opinion (Bali, Scherbina, and Tang (2011)), or lottery preference (e.g., Boyer, Mton, and Vorkink (2010) and Hou and Loh (2016)), or arbrage asymmetry (Stambaugh, Yu, and Yuan (2014)) can be reasonable in explaining the outperformance of portfolio 10 at month 0 and s subsequent underperformance. For instance, both Boyer, Mton, and Vorkink (2010) and Hou and Loh (2016) suggests that lottery-seeking retail investors are attracted to the stocks of high IVs, which lead to higher performance of portfolio 10 at month 0. It subsequently yields abnormally lower returns. Bali, Scherbina, and Tang (2011) suggest that the value of stocks of higher IV shock gains due to higher difference opinion and short sale 21

22 constraints. Its value then declines as the market participants converge to a consensus. Stambaugh, Yu, and Yuan (2014) suggest that stocks of higher IV bear higher arbrage risk and therefore, are the most overpriced. As investors eventually arbrage away the mispriced portion, high IV overvalued stocks subsequently underperform. All the above explanations focus on explaining the price behavior of high IV stocks. To our best knowledge, no explanation has been provided to address the performance of stocks of lowest IV shocks (portfolio RIV1). To identify potential explanations of the IV effects, we first need to understand what low (high) idiosyncratic volatily really represents. Based on how we calculate the idiosyncratic volatily (IV), a stock exhibs unusually low idiosyncratic volatily and low trading volumes implies that the stock moves along wh the market. In other words, no firm specific news exists or firm specific news is simply fully absorbed by the market. On the contrary, a stock exhibs unusually high idiosyncratic volatily and high trading volumes could imply that firm specific news arrives and the investors generally interpret the news differently. Why do stocks of lowest IV shocks inially outperform prior to month 0, then suddenly underperform whout any apparent news at month 0? We argue a disposion effect might provide a good explanation. Shefrin and Statman (1985) call the investor s behavior of selling winners too early and riding losers too long as the disposion effect. Barberis and Xiong (2009) suggest that the disposion effect has been documented widely based on the trading of individual investors and has been linked to price drift, such as post-earnings announcement and momentum. Based on trading activies of 10,000 households, Odean (1998) finds that investor exhibs a greater propensy to sell 22

23 shares of a stock that has risen in value since purchase rather than of one that has fallen in value. Following the disposion effect argument and empirical facts reported in Table 6 and Figure 1, for IV1 stocks, their value gain prior to month 0, perhaps due to some good news inially. As the good news being incorporated in the market price, their value gain even more. During this process, some investors may already sell early due to the disposion effect. But more investors are attracted to these stocks, which explain the continuation of price gain. As the investors conviction of the stocks and good news gets stronger, stocks gain even more value. Along the process, the pressure of disposion effect also built up. This process, however, will not last forever. At month 0, all firm specific news finally having been fully incorporated into the price. These stocks now simply drift along wh the overall market, which explains the usually low IV. The unusual quiet period of the stock following significant value gain finally provide a signal of an avalanche moment for the disposion effect to be fully released. Investors rush to sell the stocks to book the gains. These trades push down the stock price, which explain why portfolio 1 suddenly underperforms at month 0. Unlike a typical suation where a sudden and large price shift may accompany higher trading volumes, we document usually lower trading volumes as well. The reason is due to the fact that no specific firm news exists anymore for these stocks to attract new investors. Although the stocks drop value suddenly, more of the trades proportionally could be attributable to the investors who wish to book profs due to disposion effect, rather than informed trading. The lacking of new buyers and trading volume further explains the severy of the underperformance in month 0. 23

24 Finally, due to the strong strength of disposion effect triggered by usually quiet period of the stocks, these stock values are artificially depressed. Therefore, is naturally to observe that, after month 0, the stock value bounces back again. However, since the firm specific information has arguably fully been incorporated, the economic size of the outperformance should be reduced after the inial reversal at month 1. This can explain why the abnormal returns post month 1, although posive, are much smaller than those before month 0. b. Overconfidence, gambler s fallacy, and performance of high IV shock stocks Now, we turn our focus to stocks of highest IV shock. We provide two alternative explanations based on cognive biases to explain the performance of these stocks. The first alternative explanation is based on investor s behavior bias caused by overconfidence. The overconfidence bias can lead to the empirical performance of high IV shock stocks. Specifically, Scheinkman and Xiong (2003) present a theoretic model based on heterogeneous beliefs generated by agents overconfidence. In this model, an agent s overconfidence is modeled as the explic cause for disagreement. In equilibrium, they show that price, volume, and volatily increase together as the degree of overconfidence rises. Following the theoretic framework of Scheinkamn and Xiong (2003), the crosssectional price, trading volumes, price volatily, and the subsequent negative abnormal returns may be explained as follows. When new information arrives during the formation month, investors not only differ in the interpretation of the signal but also overestimate s significance. Differences in the interpretation of the signal increase trading volume as 24

25 documented in Figure 1. On the other hand, when evaluating a stock, investors consider both their own views of the fundamentals and the fact that the owner of the stock has an option to sell to others. Therefore, investors who are more optimistic inially pay prices that exceed their own valuation of fundamentals because they believe that in the future they will find a buyer willing to pay even more. The addional option value, which could be considered as a speculative component, will cause the stock price to rise higher than what is justified by the fundamentals. At the same time, the fluctuations in the value of this option contribute an extra component to price volatily, which leads to the observed posive IV shocks. Finally, as investors learn more about the value of the signals, the inially optimistic investors revise the option value down, and price falls. This leads to the subsequent underperformance by these stocks. The second alternative explanation to explain the performance of high IV stocks is based on the gambler s fallacy bias. The gambler s fallacy refers to the investor s behavior bias as to believe that outcomes in a random sequences to exhib systemic reversal (e.g. Rabin and Vayanos (2010)). For instance, one might mistakenly think the chance of observing a head should be higher after observing tail for several times when flipping a coin, although the odds do not change. In Table 6, we first observe the stocks of high IV shock experience several months of losing streaks. As the stocks shed even more value, the influence of gambler s fallacy bias gets stronger. But the pressure is not fully revealed until there is a trigger offered by the market. The trigger at here is when some specific firm news arrives which is indicated by posive IV shock. The news could be good or bad in true nature but the investors on average will interpret the news as good due to gambler s fallacy bias. 25

26 The new firm specific news drives the IV higher. It also leads to higher trading volumes. The investors, meanwhile, rush to buy more, under the influence of belief that the losing streaks should more likely end. As more shares being bought, these stocks are inially overvalued at month 0. Subsequently, as the investors finally learn the true nature of the news, these stocks shed the inial gain, or in other words, underperform again. 7. Tests of Investor behavior bias and the IV effects Disposion effect, investor overconfidence bias, and gambler s fallacy seem to offer good explanations of the empirical IV effects so far. However, to conduct direct empirical tests for investor biases on stock price is challenging if whout some proprietary database. In this section, we propose a few indirect empirical tests of the validy of our hypotheses. a. Information uncertainty and investor behavior bias The first test is based on the premise that high information uncertainty causes stronger psychological biases, such as the disposion effect (e.g. Hirshleifer (2001), Zhang (2006a, b)). Based on this premise, we argue that if one faces more information uncertainty, a risk-averse investor intends to sell more quick to book the gain. In other words, the disposion effect of portfolio 1 should be stronger if these stocks also have higher information uncertainty. In addion, higher information uncertainty also posively influences investor s overconfidence bias and gambler s fallacy. For instance, investors are more intend to believe the reversal of fortune if firm specific news is more ambiguous. Therefore, we should expect the IV effect stronger when there is more information uncertainty. 26

27 We use analyst dispersion as a proxy measure of information uncertainty. All stocks are sorted into three groups according to their analyst dispersion measures in the portfolio formation month. We then report the abnormal returns based on IV shocks in Table 7. As consistent as our prediction, the abnormal returns of stocks of highest analyst dispersion yields 1.051% (0.821%) per month on equal- (value-) weighted basis. The value declines significantly as we move to lower analysis dispersion stocks. For those stocks of lowest analysis dispersion, the IV effect totally disappears. Although Table 7 provides some evidence to show IV effect links to investor s behavior bias, the results also f argument based on the difference opinion and short sale constrain of prior lerature. In order to link the disposion effect, overconfidence, and gambler s fallacy more directly wh the IV effect, we further examine performance of stocks of highest (lowest) IV shocks by showing how the level of information uncertainty influence the performance before, during, and after formation month. Table 8 presents the abnormal returns of stocks of unusually low (high) IV shocks from month -4 to +4 by separating stocks based on analyst dispersion. Table 8 first reports the abnormal returns of stocks of lowest IV shocks (RIV1). These stocks are sorted into three subgroups based on information uncertainty, which is measured by the analyst dispersion. The disposion effect of the subgroup wh the high information uncertainty is substantially higher than that of the lowest analyst dispersion. The relative change in abnormal return between month -1 and 0 is 3.366% as changes from 2.775% at month -1 to % at month 0. This change is substantially large than the relative change of 1.739% for stocks of low information uncertainty as the abnormal returns move from 1.973% at month -1 to 0.234% at month 0. After month 0, stocks of 27

28 low information uncertainty bounce back and yield posive statistically significant abnormal again. However, for stocks of high information uncertainty, not only the economic magnude of the disposion effect is stronger, also lasts longer. The continuation of negative abnormal returns indicates the disposion effect does not disappear entirely after the avalanche moment. Risk-averse investors appear to continue to book prof for these stocks, push down stock value further. The second panel of Table 8 reports the abnormal returns of highest IV shock stocks (RIV10), classified according to the level of information uncertainty. Consistent wh our predictions, we do not find clear evidence of investor bias for stocks of low information uncertainty. As the firm specific information arrives at month 0, appears that investors correctly interpret the information. After a few month of relatively low returns (compared to RIV1 stocks), the stock values bounce back at month 0 wh abnormal return of 0.956%. As the market absorbs the information further, the stocks continue outperform at least up to month 2. In addion, we do not observe the reversal of stock value. However, for stocks of high information uncertainty, they clearly experience a few months of losing streaks prior to month 0 as their abnormal returns are substantially negative. When the new information arrive, the stock values gain substantially as the abnormal returns swch from % at month -1 to 1.925% at month 0. However, the stocks are clearly overbought during this period as their performance reversed subsequently. The performance of these stocks provides further support of our argument that IV effect could be attributable to investor behavior bias, such as overconfidence and gambler s fallacy. 28

29 b. Alternative tests of overconfidence and gambler s fallacy If overconfidence is a possible explanation for the abnormal returns, we hypothesize that the IV shock effects would be stronger (weaker) following an increase (decrease) in overconfidence. Prior empirical findings by Statman, Thorley, and Vorkink (2006), Gervais and Odean (2001), and Daniel, Hirshleifer, and Subrahmanyam (1998), show that investors tend to have stronger (weaker) overconfidence in up (down) markets. Therefore, we expect that the IV shock effect should be weaker in down markets and stronger in up markets. To test this hypothesis, we utilize two measures to define up and down market states. The first definion is based on economic status of the economy. The market is defined as a down market if the economy is in recession. If not, is an up-market. The second definion follows the method proposed by Cooper, Gutierrez, and Hameed (2004). If the cumulative return during the last 12 months prior to the formation month is nonnegative, is defined as an up market; if negative, a down market. 4 Table 9 presents the results. Panels A and B report the results based on economic status and cumulative stock return, respectively. The results show that consistently significant abnormal returns only exist in the up market. In contrast, no significant abnormal returns can be observed in the down market states. After examining the difference of IV effect based on market states, we provide further test based on instutional ownership information of stocks. It is well established that instutional investors are often viewed as more rational and subject to less cognive 4 Alternatively, we also use the market sentiment data based on Baker and Wurgler (2006) to perform the test. We found results are generally comparable. Similar results are also obtained if we define up- and down- market states based on 24-month cumulative returns. 29