Price Shocks, News Disclosures, and Asymmetric Drifts. January 8, 2011

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1 Price Shocks, News Disclosures, and Asymmetric Drifts HAI LU, KEVIN Q. WANG, and XIAOLU WANG January 8, 2011 Hai Lu, an assistant professor of accounting, and Kevin Q. Wang, an associate professor of finance, are at University of Toronto. Xiaolu Wang is an assistant professor of finance at Iowa State University. s: (Hai Lu); (Kevin Wang); (Xiaolu Wang). We are grateful to Qiang Cheng, Siu Kai Choy, Esther Eiling, Raymond Kan, Dongmei Li, Jeffrey Ng, Lars Norden, Lukasz Pomorski, Gord Richardson, Hollis Skaife, Lakshmanan Shivakumar, Kevin Veenstra, Rodrigo Verdi, Ross Watts, Jason Wei, Franco Wong, Liyan Yang, and seminar participants at McGill University, MIT, University of Toronto, University of Wisconsin-Madison, China International Conference in Finance, and the Northern Finance Association conference for helpful comments and suggestions. We thank Social Sciences and Humanities Research Council of Canada for financial support.

2 Price Shocks, News Disclosures, and Asymmetric Drifts ABSTRACT Motivated by investor disagreement and corporate disclosure literatures, we examine how stock price shocks in the absence of public announcement of firm specific newsaffect future stock returns. We find that both large short term price drops and hikes are followed by negative abnormal returns over the subsequent twelve months. The asymmetric drifts, return continuation for negative price shocks versus return reversal for positive ones, are in sharp contrast to the general findings of symmetric drifts in corporate event studies. Moreover, price shocks associated with public news events are followed by significantly weaker downward drifts, suggesting that reduction of information asymmetry/uncertainty from the disclosures mitigates disagreement-induced overpricing. Our findings give rise to a revised momentum strategy with an annualized abnormal return of 21%, suggesting that optimistic investors have suffered substantial losses. Robustness tests indicate that our findings are inconsistent with other potential explanations such as changes in risk, speculative preferences of retail investors, idiosyncratic volatility and its change.

3 1. Introduction All too often large and sudden idiosyncratic stock price changes occur at times when there are no corporate news releases. While they are clearly visible, price shocks without accompanying corporate information releases are difficult to interpret. Are such no-news price shocks noises to investors or do they have an impact on subsequent stock returns? Are market reactions to these shocks significantly different from those to shocks generated by corporate disclosures such as earnings announcements? In disclosures-oriented studies, is it important to separate price-shock effects from disclosure-generated effects? While there exists an extensive literature on corporate information disclosures (e.g., Ball and Brown [1968], Fama [1998], Kothari [2001]), sudden price movements without news announcements are largely overlooked. Price shocks without accompanying news, however, deserve particular attention. First, no-news price shocks are likely to be linked to private information. Understanding how stock prices impound private information not only helps investors for making investment decisions but also benefits regulators for monitoring market manipulation. On the other hand, private information is not the only possible cause for price shocks. Liquidity trades or manipulations, for example, are potential alternatives. The uncertainty about the cause and the existence of noise trades (Black [1986]) prevent investors from effectively inferring the information content of large sudden price changes without accompanying corporate news. These unique features of price shocks provide a natural setting to examine effects of investor disagreement on asset pricing. Motivated by the disagreement literature (e.g., Miller [1977], Harrison and Kreps [1978], Kim and Verrecchia [1994], Scheinkman and Xiong [2003], Hong and Stein [2007]) and the disclosure literature (e.g., Ball and Brown [1968], Bernard and Thomas [1990], Fama [1998], Verrecchia [2001]), we investigate effects of price shocks on future returns. 1 1 Price shocks are defined as the maximum/minimum three-day abnormal return (relative to the market) in a given month. 1

4 Specifically, we contrast price shocks without accompanying news disclosures to those accompanied by public news events. The disagreement literature predicts that in the presence of short-sales constraints, opinion divergence generates a bubble component in asset prices. We hypothesize that the price shocks increase opinion divergence among investors which declines gradually over a post-shock period, but the disagreement effect is mitigated by news events due to the reduction of information uncertainty (e.g., Berkman et al. [2009]). 2 As a result, we expect that both positive and negative price shocks are followed by downward drifts in stock prices and the drifts are stronger for the shocks without accompanying news events. We carry out an extensive set of tests and the results support these predictions. First, we seek evidence that price shocks generate investor disagreement. We examine whether idiosyncratic volatility and trading-based measures (turnover and unexpected volume) exhibit significant variations that are associated with price shocks. These measures are common proxies for opinion divergence despite their limitations (Garfinkel [2009]). We find that these measures increase around the time of a price shock and decline gradually over next twelve months. Second, using the entire cross-section of stocks, we observe an asymmetric pattern of abnormal returns after positive and negative price shocks and the asymmetric drifts are stronger for the shocks without accompanying news events. The corporate news events included in our tests are analyst earnings forecasts, conference calls, earnings announcements, seasoned equity offerings, mergers and acquisitions, management earnings forecasts, analyst recommendations, and dividend declarations. Third, we show that the post-shock abnormal return drifts are more salient among stocks with strong short-sales constraints, which are stocks with low mutual fund breadth or low institutional ownership. This result is consistent with the assumption of disagreement models that 2 Some studies suggest that public news events can increase disagreement in the short run (e.g., Kandel and Pearson [1995], Bamber, Barron, and Stober [1997], Hong and Stein [2007]), while some other studies reach the opposite conclusion (e.g., Berkman et al [2009]). Rogers, Skinner, and Van Buskirk [2009] discuss the short and long term effects of news events on uncertainty with the setting of regular and sporadic management forecasts. The argument that news disclosure reduces information asymmetry and opinion divergence in the long run is consistent with the ultimate purpose of accounting disclosures. 2

5 short-sales constraints are an essential condition for generating an asset bubble. We investigate other potential explanations for the asymmetric drifts but do not find supportive evidence. In particular, the results show that the asymmetric drifts are not a manifestation of the post-earnings announcement drifts (Ball and Brown [1968]), 3 changes in risk (Brown, Harlow, and Tinic [1988, 1993]), idiosyncratic volatility and its change (Ang et al. [2006, 2009], Bali, Scherbina, and Tang [2010]), and the speculative preferences of retail investors (Kumar [2009], Bali, Cakici, and Whitelaw [2010]). Moreover, we do not find significant negative returns around subsequent earnings announcements in the twelvemonth holding period for stocks with extreme positive and negative price shocks. This evidence is inconsistent with the argument that stock prices reflect expectations of future bad news when investors interpret no disclosures as withholding negative information (e.g., Dye [1985], Diamond and Verrecchia [1987], Lev and Penman [1990]). Our study contributes to the literature in multiple ways. First, our focus on no-news price shocks is novel, and the results are surprising. The literature started by Ball and Brown [1968] and Beaver [1968] has been focused on firms experiencing certain types of explicit public news disclosures, even though Cutler, Poterba, and Summers [1989] and Roll [1988] show that a large portion of the variance of the aggregate stock market return cannot be explained by public news on fundamentals. So, why do researchers ignore nonews price shocks in cross-sectional studies over such a long time period? It is likely due to an implicit hypothesis that no-news shocks have no clear informational content such that they should be noises to investors. In other words, such shocks have no implications for future returns and thus they are not important. Broadly and generally speaking, the most novel contribution of our paper is that we show that no-news price shocks are important. Such shocks are followed by significant and long-lasting abnormal returns. Second, no-news price shocks are easily observable but highly intangible signals. The huge uncertainty associated with the shocks has led us to hypothesize that such shocks 3 Post-earnings announcement drifts exist in our sample (see Section 5.1). The asymmetric drift pattern that we uncover is mainly from those price shocks that are not associated with earnings announcement. 3

6 provide a good playing-ground for testing investor disagreement theory. The asymmetric downward drifts following both positive and negative no-news price shocks are indeed consistent with disagreement theory. The role of opinion divergence in this setting suggests an interesting explanation of the price shock effects. 4 Third, a subtle but important implication from the finding of the drifts is that if the no-news price shocks (i.e., price shocks per se) are important, the effects of price shocks and news in general should be treated differently. In other words, we should control for the price shock effects when examining the role of disclosures. Tests of disclosure effects in the literature are, however, unconditional, as they do not differentiate these two effects. In contrast, we have a conditional testing design. Among stocks having price shocks, we compare stocks having news events with those having no news events, so that we can check news-generated effects while controlling for price-shocks-generated effects. 5 The separation, though still being a rough first effort, differentiates our study from other tests in the literatures on corporate disclosures and opinion divergence (e.g., Kandel and Pearson [1995], Garfinkel and Sokobin [2006], Bali, Scherbina, and Tang [2010]). We find evidence that news events mitigate disagreement effects, which is otherwise difficult to demonstrate. The evidence is consistent with the role of disclosures in reducing information asymmetry (e.g., emphasized by Diamond and Verrecchia [1991] and Kim and Verrecchia [1994]) and the ultimate objective of corporate disclosures. Finally, the asymmetric drift pattern is significant in terms of the economic magnitude, which we show through a set of tests conditional on the momentum effect (Jegadeesh and Titman [1993]). The results suggest that the drifts can be exploited in portfolio strategies, leading to significant investment profits. Specifically, one could enhance the profitability of the regular momentum strategy by modifying the winner portfolios to include only the winner stocks that have price shocks associated with explicit corporate 4 This is a counter-argument to that of Bali, Cakici, and Whitelaw [2010], which is discussed in the literature review in Section 2.1 and the related test results are reported in Section We also test for unconditional effects in cross-sectional regressions. 4

7 news disclosures and modifying the loser portfolio to be composed of the loser stocks that have no-news price shocks. We show that the difference in the monthly Fama-French three-factor alphas between the modified winner and loser deciles is equivalent to an annualized abnormal return of 21%. This result suggests that optimistic investors due to information asymmetry may suffer substantial losses while news disclosures partially mitigate the wealth transfer. Overall, the pattern of asymmetric drifts uncovered by our study generates interesting implications for portfolio and trading strategies. 6 Section 2 reviews the literature and discusses the predictions and research design. Section 3 describes data and portfolio characteristics. Sections 4 and 5 present the long lasting post-shock effects and explore other potential explanations. Section 6 shows the economic significance of the asymmetric drifts. Section 7 concludes. 2. Literature Review and Predictions 2.1 LITERATURE REVIEW Following the seminal work of Miller [1977] and Harrison and Kreps [1978], there has been a growing literature on investor disagreement (e.g., Harris and Raviv [1993], Kim and Verrecchia [1994], Chen, Hong and Stein [2002], Scheinkman and Xiong [2003], and Banerjee, Kaniel, and Kremer [2009]). Disagreement models have attracted attention due to their interesting features and realistic assumptions. The main prediction of Miller s model is that prices consist of an optimistic bias when differences of opinion exist and pessimistic investors cannot take adequate short positions. Harrison and Kreps extend Miller s model, which is a static one, to a dynamic setting. They show that in the presence of short-sale constraints and different prior beliefs among investors, the stock price exceeds the fundamental value by the value of a resale option, which is positive on 6 Our findings and the message to avoid buying "stocks that shock" were highlighted in Academic Research Digest published by Citigroup Global Markets (22 June, 2009) when the magazine reviewed an early version of our paper. 5

8 average. The presence of short-sales constraints per se, however, does not lead to Miller s prediction. Tirole [1982], Milgrom and Stokey [1982], and Diamond and Verrecchia [1987] show that the resale options suggested by Harrison and Kreps do not arise in asset prices in models with asymmetric information but identical priors, even if short-sale constraints are imposed. Thus, a key condition for a price bubble is that heterogeneous priors exist. As long as investors agree to disagree and there are short-sales constraints, the resale option has positive value on average. Extending the model of Harrison and Kreps, Scheinkman and Xiong [2003] use overconfidence as the source of heterogeneous beliefs and assume that behavioral limitations lead investors to continue to disagree (which is also emphasized by Hong and Stein [2007]). In our study, we assume the existence of both heterogeneous priors and short-sales constraints. The accounting literature on disagreement is centered on earnings announcements. There are several theoretical studies, but the predictions are mixed. Kandel and Pearson [1995] build a model in which agents use different likelihood functions to interpret the public announcements. Kim and Verrecchia [1994, 1997] construct models in which agents have different information processing abilities so that some of the agents can process the announcements into private or informed judgement, creating opinion divergence. 7 These theoretical analyses predict that earnings announcements increase disagreement. In the model of Kim and Verrecchia [1991], however, investors are diversely informed and differ in the precision of their private prior information; earnings announcements may remove informational disadvantage of some investors, so that there may be a decrease in opinion divergence. Sharing the same view on this point, Diamond and Verrecchia [1991] and Kim and Verrecchia [1994] also emphasize the role of earnings announcements in reducing information uncertainty and asymmetry, which should mitigate opinion divergence. Empirical research on investor disagreement associated with earnings announcements is inconclusive as well. On the one hand, many studies show that trading volume, stock 7 Harris and Raviv [1993] also assume that traders have different prior beliefs and different models for evaluating news. 6

9 return volatility, and dispersion in analyst earnings forecasts increase around earnings announcements (e.g., Beaver [1968], Ziebart [1990], Bamber and Cheon [1995], Barron [1995], Bamber, Barron, and Stober [1997], Hong and Stein [2007]), suggesting that earnings announcements increase disagreement in the short term. On the other hand, a few studies conclude in the opposite direction. For example, Brown and Han [1992] show that analyst forecast dispersion declines after the announcements. Berkman et al. [2009] find that stocks with high opinion divergence earn significantly lower returns around earnings announcements. They conclude that earnings announcements reduce opinion divergence because managers make conscious efforts to communicate information to the market. Rogers, Skinner, and Van Buskirk [2009] show that management earnings forecasts increase short-term volatility. The effect arises mainly from forecasts that convey bad news, especially when firms release forecasts sporadically. They show that in the longer run, the uncertainty declines after the earnings announcements. 8 Ingeneral,theargumentthat corporate public disclosures reduce information uncertainty/asymmetry in the long run is consistent with the intended purpose of accounting disclosures. Corporate news disclosures play a critical role in explaining the evolution of stock returns (e.g., Shin [2006]). Over past decades, numerous studies in accounting examine properties of corporate disclosures and effects of these disclosures such as implications for the cost of capital and liquidity (see Verrecchia [2001] and Healy and Palepu [2001] for reviews). To our knowledge, however, none of the studies tries to separate disclosure effects from price shock effects. For example, Kandel and Pearson [1995] focus on earnings announcements and naturally they do not touch the issue of different interpretations about no-news price shocks. Garfinkel and Sokobin [2006] find that unexpected trading volume at the earnings announcement positively correlates with future returns. Like other studies on earnings announcements, the benchmark for comparison in the testing is not set out to control for effects of price shocks on stock returns. Bali, Scherbina, and Tang [2010] 8 Patell and Wolfson [1981] and Jennings and Starks [1985] also discuss and test potential resolution of uncertainty from earnings announcements and the speed of adjustment of stock prices. 7

10 argue that news events generate large changes in idiosyncratic volatility, and hence they do not separate effects of news events and those of the volatility changes. Cutler, Poterba, and Summers [1989] show that nearly half of the return variance of the aggregate stock market cannot be explained by public news on fundamentals. The study, together with Roll [1988] which raised the same point, indicates that more studies are needed to understand price shocks. These papers are helpful for motivating our study, since they demonstrate that no-news price shocks are quite common. Our study differs from these papers in two important ways. First, we provide an investigation of crosssectional effects instead of the aggregated time-series variation considered in the above papers. Second, we demonstrate that no-news price shocks are important and offer a novel angle to examine disclosure effects. A tantalizing question generated from these studies is whether large price shocks without accompanying disclosures about fundamentals are important for investors. In other words, do such shocks have implications for future returns? Cutler, Poterba, and Summers and Roll do not address the issue, while in contrast we examine it carefully and our tests lead to interesting results. Intuitively, stock returns after large price shocks may be related to activities of retail investors. The role of retail trading has received considerable attention in recent years (e.g., Barber and Odean [2008], Kumar [2009]). In a related study, Bali, Cakici, and Whitelaw [2010] argue that retail investors prefer lottery-like stocks, which are stocks that are experiencing large positive shocks. They find that stocks with extreme positive pricechangesintherankingmonth havesignificantly negative returns in the subsequent month. Thelotteryexplanationisthatretailinvestorsprefersuchlottery-likestocksand their post-shock purchases inflate the prices of the stocks, generating the negative returns over the subsequent month. Their motivation and focus clearly differ from ours, as we pursue a disagreement explanation of price shocks and study effects of news disclosures. In our tests, we investigate whether there exist strong buying activities of retail investors after large positive price shocks. 8

11 2.2 EMPIRICAL PREDICTIONS We focus on large short-term stock price changes, which are referred to as price shocks throughout the paper. Based on investor disagreement theories while assuming both the existence of heterogeneous priors and the presence of short-sales constraints, our first prediction is that a jump in opinion divergence following large price shocks (especially no-news price shocks) gives rise to negative abnormal returns over a subsequent period. When price shocks lead to an increase of opinion divergence among investors and the disagreement decreases slowly, we should expect asymmetric abnormal return drifts, i.e., a negative shock is followed by a negative drift but a positive shock is also followed by a negative drift. The asymmetric drifts are illustrated in Diagrams A and B of Figure 1. Our second prediction is based on the informational role of disclosure events. We predict that the negative drifts following price shocksthatarenotassociatedwithnews events are stronger than those associated with news disclosures. This prediction, depicted in Diagrams C and D of Figure 1, follows from the hypothesis that corporate disclosures help reduce information uncertainty/asymmetry, and thus reduce investor opinion divergence. For both predictions, the key driver behind the novelty of our targets is no-news price shocks, which is based on an empirical division of stocks with price shocks into two groups. Stocks in the news group have firm-specific news in the window from three days before to three days after the price shocks while stocks in the no-news group do not. Corporate news events used in our study are analyst earnings forecasts, conference calls, earnings announcements, seasoned equity offerings, mergers and acquisitions, management earnings forecasts, analyst recommendations, and dividend declarations EMPIRICAL APPROACH Price shocks are defined by maximum and minimum three-day abnormal returns in the 9 The informativeness of these news events is examined by Ecker, Francis, Olsson, and Schipper [2006]. 9

12 ranking month (month t). 10 The three-day market adjusted abnormal return for a stock is the difference between the stock return and the market return over three consecutive trading days, where the market return is the return of the value-weighted portfolio of all NYSE, AMEX and NASDAQ stocks. The three-day window of either maximum or minimum abnormal return could be at any time in the ranking month. We sort all stocks into deciles based on the maximum three-day abnormal return (positive shock) or the minimum three-day abnormal return (negative shock). When sorting stocks using the maximum or minimum three-day abnormal return, we focus on the extreme deciles that contain the largest positive and negative shocks respectively (i.e., decile 10 ranked on positive shocks and decile 1 on negative shocks). Our first step is to examine links between price shocks and disagreement proxies. Using return volatility, turnover, unexpected volume and analyst earnings forecast dispersion as proxies for disagreement, we verify whether price shocks generate opinion divergence that will decrease gradually. We also examine variation in the sidedness measure of Sarkar and Schwartz [2009], which is available only for a short time period, to seek further evidence on the link between price shocks and disagreement. After confirming that price shocks increase investor opinion divergence, we test whether we can observe asymmetric drifts following negative and positive price shocks. Specifically, we examine the pattern of stock returns over the twelve months following these shocks. The overlapping portfolio approach of Jegadeesh and Titman [1993] is applied. Stocks are sorted into decile portfolios, using either maximum or minimum three-day abnormal returns in the ranking month. The 12-month holding period returns, the alphas with respect to the Fama-French three factor model (Fama and French [1993]) and the alphas with respect to the Carhart four factor model (Carhart [1997]), are obtained. We also construct a difference portfolio by holding a long position on decile 10 and a short position on decile Alternative definitions of one-day or five-day abnormal returns are considered. The results are similar. 10

13 The decile 1 ranked by negative shocks (containing largest negative shocks) and decile 10 ranked by positive shocks (containing largest positive shocks) are further divided into news and no-news subgroups, depending on whether at least one news event occurs for the stock within three days before and three days after the price shock. These sorts and the regressions tests discussed later on provide a novel way to test disclosures-related effects. Differing from studies in the extant literature, our tests use the no-news price shocks as the benchmark to investigate effects of news disclosures that generate large price changes. A basic presumption for our predictions is that short-sales constraints exist. We check whether short-sales constraints affect the degree of overpricing such that the postshock drifts are stronger for stocks with strong short-sales constraints. Furthermore, we examine whether our empirical findings are robust to various alternative explanations including post-earnings announcement drifts (Ball and Brown [1968]), changes in risk (Brown, Harlow, and Tinic [1988, 1993]), idiosyncratic volatility and its change (Ang et al. [2006, 2009], Bali, Scherbina, and Tang [2010]), and speculative preferences of retail traders (Han and Kumar [2009], Kumar [2009], and Bali, Cakici, and Whitelaw [2010]). Finally, we design a test to show the economic significance of our findings. Putting the price-shock effects in a momentum framework, we demonstrate that the profitability of the momentum strategy could be significantly improved by applying our results. 3. Data and Portfolio Characteristics 3.1 DATA We use stock returns, trade sizes, institutional holdings, and various firm-specificnews events in our analyses. The stock data are from CRSP. Our analyses include all stocks traded on NYSE, AMEX, and NASDAQ. To guard against microstructure effects associated with the small-cap and low-priced stocks, we exclude stocks in the smallest market capitalization decile and those with prices lower than $5 at the end of the ranking month. 11

14 We collect event dates of a number of firm-specific news events: analyst earnings forecasts, conference calls, earnings announcements, seasoned equity offerings, mergers and acquisitions, management earnings forecasts, analyst recommendations, and dividend declarations. The sample periods for these events vary with the availability of the databases. These events are collected from the following data sources: Standard and Poor s Compustat (earnings announcements, 1972 to 2006), CRSP (dividends, 1963 to 2006), IBES (analyst recommendations, 1993 to 2006), First Call (analyst revisions on annual earnings and management forecasts, 1989 to 2006), BestCalls.com (conference calls, 1999 to 2006), and SDC (M&A and SEO, 1978 to 2006). In addition, we use trade sizes to separate retail trades from non-retail trades. The trade sizes come from NYSE TAQ and ISSM intraday trading file from 1983 to We use Thomson-Reuters Mutual Fund Holdings and Institutional Holdings (13F) databases to compute the breadth of mutual fund and institutional ownership. 3.2 PORTFOLIO CHARACTERISTICS Table 1 presents characteristics of the decile portfolios constructed from sorting on either negative or positive shocks. The listed variables include firm size, book-to-market ratio, the ranking month return, and the 12-month return before the ranking month. These variables, used as control variables in the cross-sectional regressions in Section 5, correspond to the four known effects of the cross-section of stock returns: the size effect, the value effect, the short-run return reversal, and the Jegadeesh-Titman momentum effect. Idiosyncratic volatility (ivol) and retail trading proportion (RTP) are variables that we will use in Section 5 for checking alternative explanations. The magnitude of the minimum/maximum three-day shocks (r shock /r shock +) is presented in each panel. For each of these variables, we first obtain the cross-sectional mean in a given month, and then report the time-series average of the mean. The average number of stocks in each decile portfolio is shown at the bottom of each panel. 12

15 Panels A1 and A2 in Table 1 are for the decile portfolios from sorting on the minimum three-day abnormal return (negative shocks). Panel A1 is for negative shocks without accompanying news events, while Panel A2 is for stocks with news events. Most of the characteristics display significant variation across the deciles, and the patterns are similar for both stocks with and without news events. Firm size, for instance, increases monotonically from decile 1 to decile 10. For stocks with negative shocks and without news events, decile 1 has an average size of $169 million in contrast to $1,511 million for the stocks in decile 10. For stocks with negative shocks and news events, decile 1 (10) has the average size of $486 (3,849) million. The ranking month returns are lower for the bottom deciles than those for the top deciles. However, the pre-ranking 12-month returns are higher for the bottom deciles than those for the top deciles. There is no significant difference in the book-to-market ratio. Furthermore, both ivol and RTP decrease monotonically from decile 1 to decile 10. The mean of the minimum three-day abnormal return for decile 1 of the no-news group ( 15.21%) is close to the mean for decile 1 of the news group ( 16.12%). Panels B1 and B2 present cases in which the ranking is based on the maximum threeday abnormal returns (positive shocks). Panel B1 (B2) is for the case of positive shocks without (with) corporate news events. Both panels show that there are significant variations in most portfolio characteristics across the deciles. Stocks in the top deciles (i.e., deciles with large positive shocks) are smaller in size and stocks with news events are larger in size than stocks without news events. There is no significant difference in the book-to-market ratio. Both the ranking month returns and the pre-ranking 12-month returns are higher for the top deciles than those for the bottom deciles. Decile 10, the portfolio with the largest positive price shocks, has the largest values of ivol and RTP. The means of the maximum three-day abnormal returns for decile 10 for the no-news group and the news group are very close, 21.19% and 20.84% respectively. 13

16 4. Empirical Tests 4.1 PRICE SHOCKS AND INVESTOR DISAGREEMENT The hypothesis that price shocks increase opinion divergence is intuitive. It would be difficult for many investors to immediately assess the precise impact on the future cash flows when they observe a large sudden change in stock price, especially when there is no corporate disclosure associated with the price change. To examine whether opinion divergence responds to price shocks, we investigate variations of several proxies for opinion divergence around price shocks. We check whether they increase around the time of price shocks and then decline gradually after the price shocks. We investigate four measures of opinion divergence: idiosyncratic volatility, stock turnover, unexpected trading volume, and analyst earnings forecast dispersion. Though each of the measures is subject to certain limitations (e.g., Garfinkel [2009]), examining all of them may give us a useful view of the dynamics of opinion divergence around price shocks. Panels A and B of Table 2 report the change of disagreement proxies in raw value and percentage, respectively. We focus on stocks with extreme price shocks; that is, stocks in decile 1 of negative shocks and decile 10 of positive shocks. We do not separately report negative and positive shocks as they yield similar results. The first number in the third column of Panel A, under the term x t x t 1, shows that the median idiosyncratic volatility (ivol) increases from month t 1 to t by 0.773, which is significantly different from 0. The number in Panel B suggests that ivol increases by 30.2% from month t 1 to month t. Compared to the three-month average before the price shock (x t 3,t 1 ), ivol for month t (x t )isalsosignificantly higher. The difference is with a value of (column 4 of Panel A), equivalent to an increase of 26.2% (column 4 of Panel B). For the postshock quarters, however, Panel A shows that the signs of all the three-month changes for idiosyncratic volatility are negative, consistent with the hypothesis that disagreement drops after the initial jump in ranking month t. Panel B indicates that after a 21.4% drop 14

17 in the first quarter following the ranking month, ivol continues to drop by about 3.5% in the second quarter. The incremental drops in ivol in the next two quarters are 2.1% and 1.5% approximately, which are all statistically significant. For turnover and unexpected volume, the results are qualitatively similar to those for idiosyncratic volatility. For example, the median turnover for month t increases by in comparison to the value for month t 1, while for unexpected volume, the value increases by from month t 1 to t. The post-shock changes for turnover and unexpected volume are all negative. For unexpected volume, for instance, the largest change is over the first three-month post-shock period, over which the unexpected volume drops by The three-month changes of unexpected volume over quarters between t +3and t +12are all negative and statistically significant. Overall, the results from idiosyncratic volatility, turnover, and unexpected volume are consistent with the hypothesis that disagreement increases around price shocks and it decreases over a long post-shock period. For analyst dispersion, however, all the numbers are insignificant except for the changes from month t to the first quarter after the shocks. 11 The results are likely due to the fact that it is problematic to use analyst dispersion in a dynamic setting even though the measureisviewedby manyasanempiricalproxy for opinion divergence cross-sectionally. Because earnings are announced every quarter, the dispersion on annual earnings at month t +3 and at month t +9forinstancemaynotsharethesametarget.Whiletheformeris thedispersiononearningsforyearτ, the latter may be the dispersion on earnings for year τ +1. Therefore, the two dispersion estimates may not be directly comparable, and one may not observe any decline of the dispersion measure even if disagreement actually drops. This issue is much less serious for studies that focus on cross-sectional variation (rather than time-variation) of dispersion (e.g., Diether, Malloy, and Scherbina [2002]). Another issue is that analysts may not adjust their forecasts immediately after price shocks. Given 11 The percentage change in dispersion over the first post-shock quarter is 2.7%, which is quite modest. 15

18 the large uncertainty about implications from price shocks, analysts may play safe such that they may be reluctant to adjust the forecasts that are disclosed to the public. Thus analyst dispersion may not rise even if their opinions diverge. The sidedness measure of Sarkar and Schwartz [2009] is a new proxy for disagreement. The measure is constructed using the NYSE TAQ intraday data from 1993 to We treat the checks using the sidedness measure as supplementary because the measure is based on a short estimation period and limited to NYSE firms. The sidedness is estimated as the correlation between the numbers of buyer- and seller-initiated trades. The correlation is computed daily, using trades sampled at 5-minute intervals. 12 Sarkar and Schwartz argue that belief heterogeneity is reflected in sidedness. A relatively high value of the sidedness measure implies that trades are more likely to be driven by disagreement. We average daily sidedness into monthly sidedness and inspect its variation around large price shocks. The results are presented in Figure 2. Panels A and B of Figure 2 correspond to negative and positive shocks respectively, including both news and no-news cases. Variation in the sidedness measure is shown from two months before the shock to twelve months after the shock (from t 2 to t +12). The measure is typically negative, reflecting that large buyer- and seller-initiated trades tend to occur in differenttimeintervalsovertheday. Thepost-shockpatternforno-news shocks are supportive to the hypothesis that shocks generate or increase disagreement, andthenthedifferent opinions converge gradually after shocks. The post-shock pattern for shocks with news is somewhat surprising. The sidedness measure goes down over the first two months after the shocks and then stays fairly flat for a while. It is puzzling that the measure is relatively high at the end of the holding period. A potential explanation is that news events tend to be of periodic nature (e.g., quarterly earnings announcements) and one year is a common cycle that they share. It should be noted that trading-based 12 Choy and Wei [2009] construct the measure using all transactions from 9:30am to 4:00pm for each day and each stock. We thank Siu Kai Choy and Jason Wei for providing us with access to their sidedness dataset. 16

19 proxies such as turnover and sidedness may not capture investors who have negative opinions about a stock but do not trade it. For example, for mutual funds that have negative views about a stock but do not own any shares, the funds do not participate in the trading at all. The existence of such pessimistic investors can create the case in which negative information is gradually impounded into prices. In summary, the results of Table 2 and Figure 2 suggest that although there are various limitations of the disagreement proxies, the variations in the proxies are generally consistent with our hypothesis that opinion divergence increases around price shocks and decreases gradually afterward. 4.2 ASYMMETRIC POST-SHOCK DRIFTS In this section, we present findings about how price shocks and news events affect future stock returns. In Table 3, Panel A presents the results from portfolio sorts using the cross-section of stocks. Reported in the table are the average monthly returns, the Fama-French three factor alphas, and the Carhart four factor alphas for decile 1, decile 10, and the difference portfolio (decile 10 minus decile 1). The difference portfolio is constructed by taking both a long position on decile 10 and a short position on decile 1. The holding period consists of 12 months after the ranking month t. Columns 3 and 2 show that the three factor alpha is positive (0.16%) for decile 10 and negative ( 0.69%) for decile 1 of negative price shocks. The alphas imply annualized abnormal returns of 1.92% and 8.28% respectively. The evidence suggests that when there is a large price drop, a long term downward drift indeed occurs following the drop (decile 1). The annualized alpha for the difference portfolio (column 4) is 10.20%, which is significant with a robust t-value of In contrast, column 6 shows that stocks in decile 10 of positive shocks (large price hikes), have a monthly three-factor alpha of 0.40% (i.e., 4.80% annually) with a robust t-value of Thus, both extreme negative and positive price shocks are followed by negative abnormal returns over the next twelve-month period. 17

20 In addition, untabulated results suggest that negative abnormal returns are not limited to the extreme deciles. For negative shock deciles, the three factor alphas for deciles 2 and3areinannualtermequalto 3.96% and 2.04%, with robust t-values of 4.95 and 2.83 respectively. For positive shocks, both deciles 8 and 9 have significantly negative alphas. These results further support the robustness of our findings. Finally, the last row of Panel A shows that the above results are robust to the Carhart [1997] four factor model. Panel B of Table 3 reports the impact of news events on the price-shock effects. We focus on large positive shocks (decile 10) and large negative shocks (decile 1) as stocks in these deciles have the most extreme price shocks. For positive shocks, the news subset of stocks in decile 10 has significantly higher abnormal return than the no-news subset. The difference between the monthly three factor alphas (news minus no-news) is 0.48%. The difference is 0.52% when the alphas are calculated with the four factor model. News stocks in decile 1 of negative shocks also have significantly higher abnormal returns than no-news stocks. The difference in the monthly three factor alphas between the two subgroups is 0.12% with robust t-value These results are consistent with the argument that news events mitigate the negative drift associated with the increase of disagreement caused by price shocks. In contrast, untabulated analysis shows that decile 10 of negative shocks and decile 1 of positive shocks, which contain stocks having small price shocks (in terms of the magnitude of the shock), display no significant difference in alphas between the news and no-news groups. Again,thelastrowofPanelBshowsthatallresultsonthenewseffect are robust to the Carhart [1997] four factor model. The post-shock abnormal returns are persistent. Table 4 reports the average monthly returns, the Fama-French three factor alphas, and the Carhart four factor alphas for the difference portfolio (decile 10 minus decile 1) for four three-month intervals (quarters) after the ranking month t. Panel A illustrates the case where the ranking variable is the 18

21 minimum three-day abnormal return in month t. 13 Several conclusions can be drawn from Panel A. First, regardless of whether there is a news event accompanying the shocks, the difference portfolio always has significant long-lasting abnormal returns. Over the holding period from month t +1to month t +12, the three-factor and four-factor alphas for the difference portfolio (either with or without a news event) are positive and statistically significant for every three-month interval. Second, the alpha for the news group is always lower than the alpha for the no-news group. The difference in the alphas between the two groups (news minus no-news) is always negative. Panel B presents the case where stocks are ranked by the maximum three-day abnormal return. This panel shows that for the no-news group the three-factor and four-factor alphas of the difference portfolio are negative and statistically significant for the first three quarters after positive shocks. But most of the alphas for the news group are insignificant. In the last quarter (months 9 to 12), the four factor alpha for the news group even becomes significantly positive. The difference between the alphas from the no-news andnewsgroupsissignificant for all three-month intervals. These findings indicate that stocks with large positive shocks tend to suffer a relatively large, persistent reversal for the 12-month holding period after the ranking month. This reversal, however, is mitigated by the existence of news events. In sum, the results from Tables 3 and 4 support our predictions that are laid out in Figure 1. Diagrams A and B show that there are long-lasting negative abnormal returns following both negative and positive price shocks. Diagrams C and D show that for both negative and positive shocks, the effects are stronger for no-news shocks. 4.3 IMPACT OF SHORT-SALES CONSTRAINTS Existence of short-sales constraints is an important assumption of disagreement models. In this subsection, we test whether the post-shock drift pattern varies with the degree 13 Note that for the difference portfolio in Panel A, decile 1 contains largest negative price shocks. 19

22 of short-sales constraints. If the drifts are indeed related to opinion divergence, we expect that they are more significant among stocks with stronger short-sales constraints. Following Chen, Hong and Stein [2002], we use mutual fund holding breadth as a proxy for short-sales constraints. The measure is motivated by the fact that many mutual funds are not allowed to short-sell even if they hold pessimistic views about any of the stocks. The breadth is defined as the ratio of the number of mutual funds that hold a long position in the stock to the total number of mutual funds for that quarter reported in Thomson Financial Mutual Fund Holdings database. We define the smallest (largest) third as "Low (High) Breadth" sample. In other words, the "Low Breadth" sample consists of stocks in the lowest third when sorting by the value of their breadth. Based on disagreement models, we expect that the post-shock abnormal return drifts are more salient among stocks with low breadth which are associated with stronger short-sales constraints. In Table 5, Panel A presents the results. In the case where the sorting variable is the negative shock, the Fama-French three factor alpha for the difference portfolio (decile 10 minus decile 1) for low breadth stocks is 1.13% with t-statistic of The alpha for high breadth stocks is 0.61% with t-statistic of When using the Carhart four factor alphas, the contrast is more impressive. The four factor alpha for the difference portfolio for low breadth stock is 0.86% with t-statistic of 3.99, while that for high breadth stocks is only 0.05% with t-statistic of In the case where the sorting variable is the positive shock, the three factor and four factor alphas for the difference portfolio for low breadth stocks are 0.49% and 0.47% respectively, with t-statistics of 2.73 and In contrast, the alphas for high breadth stocks are 0.30% and 0.08% respectively, with t-statistics of 1.67 and These findings confirm that post-shock drifts are stronger for stocks with stronger short-sales constraints, providing further evidence that the persistent postshock abnormal returns are a disagreement-based effect. Panel B of Table 5 presents the news effect. For negative shocks, the news effect is insignificant in both low and high breadth groups. For positive shocks, although the news effect is significant in both low 20

23 and high breadth groups, the effect is much stronger in the low breadth group. Motivated by findings of Asquith, Pathak, and Ritter [2005] and Nagel [2005], we also use institutional ownership as an alternative proxy for short-sales constraints. Stocks with low institutional ownership are more expensive to borrow. Institutional ownership is the percentage of shares outstanding owned by institutions as reported in Thomson Financial Institutional Holdings (13F) database. Stocks are first divided into thirds based on institutional ownership. The lowest (highest) third is classified as Low (high) institutional ownership group. Similar to those in Table 5, untabulated results show that the price-shock effects are much stronger among stocks with low institutional ownership. For example, in the case of sorting on negative shocks, the Fama-French three factor alpha for the difference portfolio (decile 10 minus decile 1) for low institutional ownership stocks is 1.24% with t-statistic of The alpha for high institutional ownership stocks is 0.61% with t-statistic of The results in the case of sorting on positive shocks show that the alpha for the difference portfolio is significantly negative only for the stocks with low institutional ownership. 5. Other Potential Explanations In this section, we consider other potential explanations. We first distinguish the asymmetric drifts documented in our study from the well-known post-earnings announcement drifts. We then explore whether the asymmetric drifts can be captured by other potential explanations such as changes in risk, level and change of idiosyncratic volatility, and retail trading. Finally we test the robustness controlling for multiple effects including microstructure effects, liquidity, delay, and skewness. 5.1 POST-EARNINGS ANNOUNCEMENT DRIFTS Post-earnings-announcement drift (PEAD) is a well known phenomenon documented 21

24 in the accounting and finance literature (e.g., Ball and Brown [1968], Bernard and Thomas [1990]). It refers to the tendency of a stock s post-announcement cumulative abnormal return to move in the direction of an earnings surprise. As positive (negative) earnings surprises are more likely to be associated with positive (negative) price shocks, we expect a symmetric post-shock drift pattern due to PEAD. Does this symmetric drift pattern exist in our sample? Is the asymmetric drift pattern following price shocks mainly due to stocks without earnings announcements around the portfolio formation time? We report the results in Table 6. In Panel A, we focus on stocks with earnings announcement in the window from three days before to three days after the price shock. These stocks are ranked into deciles by the negative and positive shocks. Equal-weighted decile portfolios are formed and held for 12 months, following the overlapping portfolio approach of Jagadeesh and Titman [1993]. Reported in the panel are the Fama-French three factor alphas and the Carhart four factor alphas for decile 1, decile 10, and the difference portfolio (10-1). The difference portfolio is constructed by taking both a long position on decile 10 and a short position on decile 1. For this sample, we predict that the PEAD effect dominates the asymmetric drift pattern, and expect to observe positive (negative) drifts following positive (negative) shocks. Consistent with our expectation, Panel A shows that price shocks associated with earnings announcement are followed by symmetric instead of asymmetric drifts in the following year. For example, the monthly Carhart four factor alpha is 0.31% (with a robust t-statistic of 2.21) for earnings announcement associated with largest negative price shock (decile 1 of negative shocks). Earnings announcements associated with large positive price shocks, on the other hand, have a monthly Carhart four factor alpha of 0.26% (with a robust t-statistic of 2.26). Significantly positive drifts following positive price shocks with earnings announcement are in contrast to the negative drifts following no-news positive shocks. These findings present evidence that PEAD exists in our sample, and that the asymmetric drift pattern identified in Section 4.2 is mainly due to shocks 22