Short sale constraints, heterogeneous interpretations, and asymmetric price reactions to earnings announcements

J. Account. Public Policy 32 (2013) 435–455

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Short sale constraints, heterogeneous interpretations, and asymmetric price reactions to earnings announcements Eric C. Chang a, Jianguo Xu b, Liu Zheng c,⇑ a

University of Hong Kong, Faculty of Business and Economics, Pokfulam Road, Hong Kong Beijing University, National School of Development/CCER, Beijing, China c City University of Hong Kong, Department of Accountancy, Tat Chee Avenue, Hong Kong b

a b s t r a c t This study tests Miller’s (1977) overpricing hypothesis from a new angle. Specifically, we investigate the effects of heterogeneous interpretations on price reactions to earnings announcements. We find that the difference between good news and bad news earnings response coefficients increases with the degree of heterogeneous interpretations in the presence of short sale constraints. This pattern is more pronounced when short sale constraints are more binding. These findings support the notion that, under short sale constraints, stock prices selectively incorporate more optimistic opinions rather than the average opinion of all investors. Therefore, reducing short sale constraints should facilitate price discovery and improve price efficiency. This study complements recent studies examining the joint effect of short sale constraints and ex ante opinion divergence on price reactions to earnings announcements. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction Earnings announcements convey important information for security valuation (Ball and Brown, 1968). However, deriving the valuation implications from earnings announcements is far from straightforward, leaving ample room for heterogeneous interpretations of earnings signals. An extensive literature investigates how heterogeneous interpretations stimulate trading around earnings announcements (e.g., Kim and Verrecchia, 1994, 1997; Bamber and Cheon, 1995; Bamber et al., ⇑ Corresponding author. Tel.: +852 34427928; fax: +852 34420349. E-mail addresses: [email protected] (E.C. Chang), [email protected] (J. Xu), [email protected] (L. Zheng). 0278-4254/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jaccpubpol.2013.08.001

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1997). However, the implication of heterogeneous interpretations on price reactions to earnings announcements has received limited attention. This lack of attention reflects the view that heterogeneity in interpretations stimulates trading but does not affect equilibrium prices (Beaver, 1968; Hong and Stein, 2007). Extending Miller’s (1977) idea, Xu (2007) analytically demonstrates that heterogeneous interpretations of public news affect equilibrium prices when short sale constraints are present.1 In particular, Xu (2007) proposes that price changes around public announcements are a convex function of information surprise due to the selective incorporation of more optimistic interpretations of the news. This convexity, that is, the asymmetry in price reaction to good versus bad news, increases jointly with the degree of interpretation heterogeneity and short sale constraints. This study empirically examines the asymmetry in price reactions to good versus bad news conditional on the degree of interpretation heterogeneity and tightness of short sale constraints. Prior research suggests that short sale constraints are more binding in stocks with low institutional ownership (e.g., D’Avolio, 2002; Nagel, 2005). We employ institutional ownership as an inverse proxy for short sale constraints. Following Garfinkel and Sokobin (2006), we employ standardized unexpected volume around earnings announcements to proxy for the heterogeneity of interpretations. This measure explicitly controls for liquidity needs and the informedness effect on trading volume. We use the three-day market-adjusted return around quarterly earnings announcements as a measure of price reactions to earnings surprises. Earnings surprises are calculated as the difference between I/B/E/S actual earnings per share (EPS) and the I/B/E/S consensus analyst forecast, scaled by the stock price at the beginning of the fiscal quarter. Our results suggest that the difference between good and bad news earnings response coefficients increases with the degree of heterogeneous interpretation and this pattern is more pronounced when short sale constraints are more binding. These findings are consistent with the theoretical prediction that short sale constraints keep pessimistic opinions out of the market when the market is reacting to information (Miller, 1977; Xu, 2007). This paper extends the literature in three directions. First, it contributes to the accounting research on price and volume reactions to earnings announcements. Prior studies suggest that heterogeneous interpretations are an important stimulus for trading around earnings announcements but remain silent on their role in equilibrium price formation. Our evidence suggests that heterogeneous interpretations also have important implications for price reactions to earnings announcements. This study complements recent studies (Berkman et al., 2009; Mashruwala et al., 2010) on the impact of short selling constraints on price reactions to earnings announcements. These concurrent studies assume that earnings announcements narrow opinion divergence that exists prior to earnings announcements and hence reduce overpricing. We examine the opposite effect of earnings announcements, where opinion divergence can increase rather than decrease due to difficulties in interpreting information. In fact, we argue that noisy signals, which allow for heterogeneous interpretations, can further increase rather than reduce overpricing in the presence of short sale constraints. Second, this paper presents a new angle to test the idea of the selective registration of optimistic opinions pioneered by Miller (1977). Although many studies examine and support Miller’s overpricing hypothesis, no consensus has been reached. Some concerns are related to measurement and methodology issues. For example, Diether et al. (2002) find that stocks with higher dispersion in analyst earnings forecasts earn lower future returns than otherwise similar stocks. However, using a more accurate measure of divergence of opinion that is free from the confounding effects of uncertainty in analyst forecasts, Doukas et al. (2006) provide no support for Miller’s (1977) overvaluation hypothesis. In addition, most existing evidence relies on lower future returns in stocks with more dispersed beliefs and/or higher short selling costs to backwardly infer ex ante overpricing. Berkman et al. (2009) argue 1 Short sale constraints are almost as old as organized exchanges and short sellers are often blamed for stock market declines, leading to calls for regulations against short sales (Bris et al., 2007). The implications of short sale constraints on price discovery have recently received revived interest in the finance and accounting literature. Typically, short selling involves the costs of only receiving a small fraction of the return earned by the margin collateral (the received return is called the rebate rate), the forfeit of stock dividends, and the risk of being squeezed, in addition to the potentially unlimited loss of a short position. Besides the direct cost of shorting, institutional or cultural biases also constrain short selling (Jones and Lamont, 2002). Almazan et al. (2004) find that only about 30% of mutual funds are allowed to sell short and, among the 30% of mutual funds, only 11% actually did sell short. Short sales are also subject to many regulations, such as the up-tick rule and margin requirements.

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that such a research design relies on the assumption that differences of opinions are reduced over a long time horizon of several months. Without knowledge of when and how this happens, subsequent low returns can indicate either mispricing or errors in risk premium measurement. We examine immediate price reactions to earnings news, which is less subject to this criticism. More importantly, our design demonstrates more directly how overpricing, in the sense of Miller (1977), happens. Finally, our findings that pessimistic opinions are not fully reflected in prices provide useful insights for policy makers, especially in light of recent attempts in the United States and other countries to further regulate short selling.2 Our evidence indicates that relaxing short sale constraints leads to a more comprehensive incorporation of divergent opinions into prices and hence improved price efficiency. This paper complements recent research examining the role of short selling in facilitating price discovery (e.g., Dechow et al., 2001; Desai et al., 2002; Christophe et al., 2004; Drake et al., 2011). The paper proceeds as follows. Section 2 reviews the literature and develops our hypothesis. Section 3 discusses the research design. Section 4 describes the data and empirical results. Section 5 discusses related studies and further analysis. Section 6 concludes the paper.

2. Literature review and hypothesis development It is well recognized that investors observing the same information often disagree about its interpretation (Karpoff, 1986). Varian (1989), Harris and Raviv (1993), and Kandel and Pearson (1995) explore the possibility that market participants possess different prior beliefs or likelihood functions to process information and thus public announcements create idiosyncratic beliefs. Prior studies provide compelling evidence that public announcements can trigger differential interpretations. Both Kandel and Pearson (1995) and Bamber and Cheon (1995) provide evidence that trading volume is higher around earnings announcements, even without price changes, supporting the existence of differential interpretations as postulated by Beaver (1968).3 Bamber et al. (1999) provide evidence that differential interpretations are an important stimulus for speculative trading. Barron et al. (2002) find that the commonality of information in analyst forecasts decreases rather than increases around earnings announcements. Although heterogeneous interpretations are well recognized, their effect on price reactions to public announcements has received limited attention.4 The conventional wisdom is that there is no effect, because different opinions are ‘‘canceled out’’ in the price aggregation process (Lintner, 1969; Ross, 1977). Miller (1977) challenges this conventional wisdom by introducing short sale constraints into consideration. The author argues that when short selling is costly, some pessimistic opinions may be kept out of the market, leading to upward biases in prices. Diamond and Verrecchia (1987) propose a different view. In a rational expectations framework with private information, they show that short sale constraints cause stock prices to adjust more slowly to unfavorable private information than to favorable private information. However, the authors argue that, on average, no overpricing should exist, since rational investors take the existence of short sale constraints and pessimistic opinions into consideration. In testing Miller’s overpricing hypothesis, most studies assume that differences of opinions exist and are reduced gradually (e.g., Diether et al., 2002; Boehme et al., 2006). These studies rely on lower future returns in stocks with more dispersed beliefs and/or higher short selling costs to backwardly 2 For example, the U.S. Securities and Exchange Commission suspended short sales of financial firms to slow the decrease of banking stock prices on September 19, 2008. Similar or more aggressive actions against short selling have been taken by regulators in the United Kingdom, Australia, and Spain. 3 Evidence of differential price and volume reactions to information has also been documented in many other settings, such as during the enactment of new legislation (e.g., Courtenay et al., 1989). 4 One exception is Rees and Thomas (2010), who examine the effects of changes in the dispersion of investor beliefs on stock prices around earnings announcements. They find that the three-day price reactions to earnings announcements are negatively associated with changes in the dispersion of individual analysts’ forecasts, which they argue is consistent with the cost of capital hypothesis and inconsistent with Miller’s (1977) overpricing hypothesis. Our paper differs from that of Rees and Thomas (2010) in that we focus on the asymmetry in price reactions to good versus bad news. We hypothesize that more dispersed beliefs imply larger asymmetry in price reactions under short sale constraints. If increased dispersion in beliefs also implies increased costs of capital, this creates a counteracting effect that works against our finding since higher costs of capital imply smaller price reactions (e.g., Collins and Kothari, 1989).

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infer ex ante overpricing. Berkman et al. (2009) argue that one important shortcoming of the aforementioned approach is that no specific event is employed to study the reduction in differences of opinion and hence its effect on stock prices. They propose that, because pessimistic investors face short-sales constraints, optimistic investors betting on the outcome of the earnings release drive up stock prices. On average, earnings announcements reduce differences of opinion among investors and, consequently, these announcements should reduce overvaluation. Consistent with their conjecture, the authors find that stocks with higher differences of opinion prior to earnings announcements and more binding short sale constraints earn significantly lower returns around earnings announcements. Xu (2007) studies an opposite effect of public announcements. Motivated by extensive evidence on the heterogeneous interpretation of public signals, Xu (2007) argues that public news could increase rather than reduce opinion divergence when the interpretations are widely heterogeneous. Consequently, it is not clear that overpricing is necessarily corrected by public announcements. In the setting of stock price reactions to public announcements, Xu (2007) analytically demonstrates that, rather than being canceled out, heterogeneous interpretations of public signals affect equilibrium prices when short sale constraints are present. The selective incorporation of more optimistic opinions is revealed by asymmetric price reactions to good versus bad news. The author argues that this is a more direct demonstration of how overpricing, in the sense of Miller (1977), happens. In Xu’s (2007) model, investors are prohibited from short selling. They initially agree on the value of a stock and enter the market with one unit endowment of the risky asset at time 0. A signal that equals the asset’s payoff x plus noise e is publicly observed at time 1. The payoff is realized at time 2. The random variables x and e follow independent normal distributions. Investors agree over the distribution of x but disagree over the precision (inverse of the variance) of e. Since ‘‘high-precision’’ investors think that the signal’s quality is higher than ‘‘low-precision’’ investors do, they react more to the signal than low-precision investors. As a result, upon receiving a piece of good news, high-precision investors have higher asset valuation than low-precision investors; conversely, upon receiving a piece of bad news, low-precision investors have higher asset valuation than high-precision investors. Coupled with Miller’s intuition that short sale constraints prevent pessimistic opinions from being reflected in prices, the implication is that the equilibrium price is a convex function of the public signal. This is because in the good news case, the market reactions correspond to those who react the most to the signal (i.e., ‘‘high-precision’’ investors), whereas in the bad news case, the market reactions correspond to those who react the least to the signal (i.e., ‘‘low-precision’’ investors). Graphically, the price reaction function is steeper when the news is positive and flatter when the news is negative. Furthermore, because this asymmetry is driven by short sale constraints and heterogeneous interpretations, it should increase with heterogeneity in interpretation and the costs of short selling.5 The basic model set-up assumes that at time 2 the payoff is realized, with investors effectively observing a conclusive signal that leaves no room for disagreement. Consequently, all earlier mispricing will be corrected completely and instantly. In the real world, however, investors usually only observe noisy signals. Such noisy signals may partially and gradually (as opposed to completely and instantly) correct earlier mispricing. At the same time, noisy signals allow for disagreement, which creates more convexity when combined with short sale constraints, as demonstrated in the basic model set-up. Both partial corrections and disagreements over each signal suggest that the multiple period price function is still convex.

5 The prediction, as pointed out by Xu (2007), does not depend on maintained assumptions. For example, investors may disagree about whether an announcement represents changes in long-run growth trends or merely a temporary fluctuation. This dimension of disagreement can be captured by assuming disagreement on the signal’s precision. Assuming that investors differ in the precision of their pre-disclosure information but attach the same precision to public information, as Kim and Verrecchia (1991), leads to the same prediction. Modeling heterogeneous prior confidence and modeling heterogeneous precision in a new public signal produce similar results in both a simple two-period model and a dynamic model. Assuming that investors employ different private information, which can be used only in conjunction with a public announcement, as Kim and Verrecchia (1997), will not change the prediction either. This is because such an assumption offers only a particular reason about why investors revise their beliefs differentially. Finally, the prediction holds if we allow investors to have heterogeneous prior expectations about stock value. According to Bayesian updating, disagreement in prior expectations has no implications for value updating. In fact, as long as prior asset valuations and interpretations of the new signals are not perfectly negatively correlated, Xu’s (2007) prediction holds qualitatively.

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We test Xu’s (2007) prediction in the setting of earnings announcements, which is particularly suitable for the test. First, it serves as one of the important events in which both information surprises and the corresponding price reactions are measurable. Other information events such as dividend announcements and management forecasts usually occur less often, so they convey less information than earnings announcements (Basu et al., 2011). In addition, since these other information events are not mandated in most countries, forecasts or measures of market expectations are generally lacking. Second, the setting of earnings announcements is characterized by a significant amount of differential interpretations (Kandel and Pearson, 1995; Bamber et al., 1999).6 In the setting of earnings announcements, Xu’s (2007) prediction of a convex price function implies an earnings response coefficient that is larger for good news than for bad news. We formalize our hypotheses as follows. Hypothesis (1). In the presence of short sale constraints, the difference between good news and bad news earnings response coefficients increases with the degree of heterogeneity in interpretations and (2) this pattern is more pronounced when short sale constraints are more binding. Xu’s (2007) predictions hinge closely on the existence of both the heterogeneous interpretations of a public signal and short sale constraints. Examining price reaction asymmetry conditional on heterogeneous interpretations and short sale constraints serves as a sharp test, while examining the asymmetry per se is confounded by alternative explanations. For example, Basu (1997) suggests that accounting conservatism induces stronger price reactions to positive earnings news than to negative earnings news. Reed (2007) predicts prices react more strongly to bad news than to good news, especially when short sale constraints are more binding. This prediction is based on Diamond and Verrecchia’s (1987) intuition that short sale constraints decrease the speed of price adjustments to information, especially bad news; thus market prices react more strongly to bad news when public announcements reveal previously withheld negative private information.7 Several papers attribute the stronger price reaction to negative earnings news to managers’ incentive to disclose good news early but withhold bad news (McNichols, 1988; Kothari et al., 2009; Roychowdhury and Sletten, 2012). 3. Research design 3.1. Proxies for short sale constraints The existing literature provides several proxies for short sale constraints. We follow the more recent literature to employ institutional ownership to inversely proxy for short sale constraints (D’Avolio, 2002; Asquith et al., 2005; Nagel, 2005; Berkman et al., 2009).8 First, for stocks with low institutional ownership, the direct cost of short selling is high. D’Avolio (2002) shows that institutional investors are the main suppliers of equity loans, that the degree of institutional ownership can explain 6 In recent years, earnings announcement press releases have included more information than earnings, for example, detailed financial statements such as balance sheets, statements of cash flows, information about current operating data or non-recurring earnings components, and bundled management earnings forecasts for future periods (Francis et al., 2002; Rogers and Van Buskirk, 2013). Chen et al. (2002b), among others, suggest that this trend is consistent with firms providing voluntary disclosure in response to investor demand for value-relevant information to supplement earnings. If these concurrent disclosures cause high volume through triggering greater divergence among investors, it will not complicate our interpretation. However, these disclosures can trigger high volume through increasing the informedness of earnings announcements. We use the trading volume unexplained by the magnitude of price changes as our key proxy for heterogeneous interpretations to mitigate the informedness effect. 7 Reed (2007) does not consider the effect of the heterogeneous interpretation of earnings news. The implication of Xu (2007) is that as the degree of heterogeneity in news interpretations increases, the selective registration of more optimistic opinions implies a convex function of price in the public signal, which imposes an opposite force on the asymmetry induced by the adjustment to private information, and, depending on which force is stronger, even leads to an opposite pattern (i.e., prices react more strongly to good than to bad news). These two arguments, contradictory on the surface, can be easily reconciled by considering heterogeneous interpretations. 8 Another proxy for short sale constraints is the level of short interest. We do not use this proxy because Chen et al. (2002a) suggest it is not a good measure of how binding short sale constraints are. They argue that stocks with a low or zero value of short interest may be exactly those that are more costly to sell short. Jones and Lamont (2002) suggest that the short stock rebate rate is a better proxy for measuring the magnitude of short sale constraints. However, the data on rebate rates are proprietary.

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much of the variation in loan supplies across stocks, and that stocks with lower institutional ownership are more expensive to borrow. Second, most institutional investors never sell short due to regulatory or contractual constraints.9 In the presence of these indirect short sale constraints, sophisticated institutional investors can easily sell an overpriced stock that they own but will not trade against an overpriced stock that they do not own. As a result, short sale constraints are effectively more binding in stocks with low institutional ownership (Nagel, 2005). From the Spectrum database, we measure institutional ownership (IO) as the last reported percentage of shares outstanding held by institutional investors within 180 days prior to quarterly earnings announcements.10 3.2. Proxies for heterogeneous interpretations Beaver (1968), Harris and Raviv (1993), and Kandel and Pearson (1995), among others, suggest that when the differences in investors’ interpretations of public news are great, trading volume tends to be high. Many empirical studies employ volume to proxy for opinion divergence (e.g., Garfinkel and Sokobin, 2006; Berkman et al., 2009).11 However, one concern is that volume can also reflect other reasons for trading. For example, volume can reflect liquidity (Benston and Hagerman, 1974; Petersen and Fialkowski, 1994), the portfolio rebalancing effect (Admati and Pfleiderer 1988; Dey and Radhakrishna 2007), and the informedness effect (Holthausen and Verrecchia, 1990). To control for these effects, we follow recent studies and use standardized unexpected volume (SUV) to proxy for interpretation heterogeneity (Crabbe and Post, 1994; Garfinkel and Sokobin, 2006; Garfinkel, 2009). In examining the empirical validity of various proxies, Garfinkel (2009) finds that SUV is highly correlated with the construct for opinion divergence when using proprietary data on investors’ orders. The basic idea in estimating SUVi,j, the standardized unexpected volume for the jth earnings announcement made by firm i, is similar to using the market model to estimate abnormal returns. Specifically, SUVi,j is calculated as the average prediction error over the three–trading-day window [t  1, t + 1] around the earnings announcement date t from a univariate regression of the trading volume on the absolute value of returns, scaled by the standard deviation of residuals (Si,j) over the model’s estimation window:

SUV i;j ¼ UVi;j =Si;j ; UV i;j ¼ Volumei;j  E½Volumei;j ; ^1  jRi;j jþ þ b ^2  jRi;j j : ^i þ b E½Volumei;j  ¼ a The plus and minus superscripts on the absolute values of returns indicate positive and negative returns, respectively. Garfinkel and Sokobin (2006) propose this model specification to accommodate the observed empirical regularity that the relations between volume and the absolute values of returns are different for positive and negative price changes (Karpoff, 1987).12 The authors argue that 9 According to Almazan et al. (2004), investment activities of funds are restricted by regulations (e.g., the Investment Company Act of 1940) and the contracts between fund managers and investors. A total of 70% of investment managers are precluded from short selling by charter and strategy restrictions. Only 11% of those eligible to sell short actually do so. Market short interest is typically only about 1.5% of all shares outstanding. 10 Following Berkman et al. (2009), IO is set to zero if there is no institutional ownership data available within 180 days prior to earnings announcements, and set to missing if it is greater than or equal to 100%. We obtain similar results if we set IO to 100% if it is greater than or equal to 100%. 11 The Kandel and Pearson (1995) index, which compares analyst forecasts shortly before and after these announcements, is a potential alternative proxy for differential interpretations of earnings news. However, it requires that the same analyst issue forecasts both shortly before and shortly after the earnings announcements. Adoption of this measure would significantly reduce sample size and statistical power, since most of the small firms (arguably more subject to short sale constraints) would have to be dropped from the sample. As for the change in the dispersion of analyst forecasts, this measure shares the same weakness as the KP index; in addition, it can capture only situations where paired forecasts move in opposite directions and diverge, but not situations where paired forecasts move in opposite directions and flip (Karpoff, 1986). Garfinkel (2009) examines the empirical validity of extant proxies for opinion divergence and finds that measures based on analyst forecast divergence are negatively related to the new construct for opinion divergence when using proprietary data on investors’ orders. 12 It is possible that the volume–return relation is non-linear, even within the positive or negative announcement return groups. We also estimate the volume–return relation in quadratic form to capture the possibly convex relation between volume and returns, as depicted in Figure 1 of Kandel and Pearson (1995). We obtain similar results.

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^ 1 term is isomorphic to the liquidity trading adjustment and subtracting subtracting the a ^ð1&2Þ  jRi;j jðþ=Þ controls for the informedness effect on trading volume. The residual volume captures b opinion divergence. To estimate the relation between volume and returns around earnings announce^ð1&2Þ , we regress volume on absolute returns using daily volume ^ i term and b ments (i.e., to obtain the a and returns over [t  1, t + 1] of each earnings announcement event over the past 20 quarters.13 3.3. Data sources and sample selection Our data come from the Center for Research in Security Prices (CRSP), Compustat, I/B/E/S, and the Spectrum database. Our initial sample consists of all common stocks (i.e., with CRSP share code 10 or 11) listed on the New York Stock Exchange (NYSE)/American Stock Exchange (AMEX)/NASDAQ during 1985-2011. We exclude firms in finance (Standard Industrial Classification, or SIC, codes 6000-6999) and regulated utilities (SIC codes 4900–4999) because operations of firms in these two industries are significantly different from those in other industries and the financial reporting format is also different (McAnally et al., 2008; Kama and Weiss, 2013). Furthermore, the regulatory nature of these two industries also affects the interpretation of some financial measures we use in the regression. For example, the debt-like liabilities of financial firms are not strictly comparable to the debt issued by non-financial firms (Pittman and Fortin, 2004). In addition, we eliminate observations with stock prices below $1 to avoid a stark asymmetry in price reactions because of a small deflator.14 We also exclude observations with a forecast date on or after the corresponding earnings announcement date or an earnings announcement before or more than 90 days after the corresponding fiscal quarter-end because such observations are potentially subject to data error and other irregularities. Further sample selection criteria require non-missing data for all variables used in the regression analysis. The final sample consists of 124,247 quarterly earnings announcements of NYSE/AMEX/NASDAQ firms. 3.4. Empirical model Our first hypothesis predicts that, in the presence of short sale constraints, the difference between good and bad news earnings response coefficients increases with the degree of heterogeneity in interpretations.15 To test this prediction, we estimate the regression

RET ¼ b0 þ b1 GOOD þ b2 ESURP þ b3 ESURP  GOOD þ b4 ESURP  RankSUV þ b5 ESURP  GOOD  RankSUV þ Control Variables þ e;

ð1Þ

where RET is the three-day [1, +1] market-adjusted return around earnings announcements. The adjustment is based on the CRSP value-weighted market return over the same three-day time window.16 The variable ESURP is calculated as the difference between the I/B/E/S actual EPS and the I/B/E/ S consensus analyst forecast, scaled by the stock price at the beginning of the fiscal quarter. The stock price deflator renders earnings surprises comparable across stocks and helps to mitigate heteroskedasticity (Christie, 1987; Kothari, 2001). We use unadjusted (for splits and stock dividends) I/B/E/S forecasts to avoid the potential rounding problem pointed out by Baber and Kang (2002) and Payne and Thomas (2003). We calculate the consensus forecast as the median value of individual analyst forecasts. To re13 To obtain reliable estimation, we require at least 30 observations available in this estimation window. In the sensitivity check, we also relax the requirement by requiring that at least 15 observations be available and the results are qualitatively similar. In addition, we use the same estimation window [t - 54, t - 5] as Garfinkel and Sokobin (2006), where t is the Compustat current earnings announcement date. The results remain qualitatively similar. 14 Our results are qualitatively similar when we exclude observations with stock prices under $5. Our results are also qualitatively similar if we include firms in finance and utilities. 15 Note that, in the complete absence of short sale constraints, the difference between good and bad news earnings response coefficients does not change with the degree of heterogeneous interpretations. However, we believe that short sale constraints generally exist and vary only in degree. 16 We also tried various alternative benchmarks, including the market model, the Fama–French model, the Carhart (1997) fourfactor model, and the five-factor model—that is, the four-factor model plus the Pastor and Stambaugh(2003) traded liquidity factor—in the traditional two-step event study approach (see the Eventus 8.0 User’s Guide). We use both equal-weighted and valueweighted returns in each of the benchmark settings. Our results are similar, regardless of the choice of benchmarks.

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duce contamination from stale forecasts, we use only forecasts made within the 60 days prior to the earnings announcement. If one analyst issues more than one forecast within this 60-day window, only the most recent forecast is included. The variable GOOD is a dummy that equals one if ESURP is equal to or greater than zero, and zero otherwise. The term RankSUV is constructed based on the standardized unexpected volume (SUV) described in Section 3.2. We first rank SUV into deciles each quarter, with zero representing the lowest and nine representing the highest decile. The resulting ranks are then divided by nine to create a ranked variable that ranges between zero and one. We allow both the coefficients of ESURP and ESURP  GOOD to vary across degrees of heterogeneous interpretation. The slope coefficient b5 captures the change in asymmetric stock price reactions to good versus bad news as we move from the lowest to the highest heterogeneous interpretation group. Our second hypothesis predicts that changes in asymmetry across groups with different degrees of heterogeneous interpretation are more salient when short sale constraints are more binding. To test this hypothesis, we run the above regression separately for subsamples that are partitioned on institutional ownership (IO). In particular, we first sort observations into three groups based on IO in each quarter. The low, medium, and high groups represent stocks in the bottom 30%, middle 40%, and top 30% of the distribution, respectively. Within each IO group, we then construct RankSUV within each quarter based on the SUV around earnings announcements. Since IO inversely proxies for short sale constraints, we expect b5 to increase when we move from a high-IO to a low-IO group. 3.5. Control variables In addition to our test variables, we also control for variables that may affect the coefficients of ESURP and ESURP  GOOD. To do this, we rely on prior literature on economic determinants of earnings response coefficients and alternative theories of asymmetric price reactions to earnings news, respectively. Kormendi and Lipe (1987) and Easton and Zmijewski (1989) suggest that more persistent earnings surprises lead to larger price changes. Some studies focus on the time-series property of earnings persistence. Freeman and Tse (1992) find that the magnitude of |ESURPB| provides more explanatory power than the time-series persistence of earnings. They argue that the results are consistent with small earnings surprises being viewed as more persistent and large earnings surprises being viewed as more transitory. Subramanyam (1996) suggests an alternative explanation, that is, the market associates more noise with extreme news and therefore discounts extreme news. Following the literature (e.g., Subramanyam and Wild, 1996; Lipe et al., 1998), we include an interaction term between |ESURP| andESURP to control for the S-shaped relation between price reactions and earnings surprises. In addition, several studies suggest that price reactions to earnings announcements increase with growth expectation (e.g., Collins and Kothari, 1989), but decrease with risk and interest rates (Collins and Kothari, 1989; Easton and Zmijewski, 1989). A higher degree of risk or interest rate means a lower discounted present value for future earnings innovations. Following the literature, we use the book-tomarket ratio (BTM) at the beginning of the fiscal quarter as an inverse proxy for growth opportunities. Because the negative book-to-market ratios do not have an intuitive interpretation as a growth proxy, we follow prior studies to set BTM to missing when the book value is negative in the main analysis and include those negative observations in a sensitivity test (Fama and French, 1992; Desai et al., 2004). We measure systematic risk (BETA) using a market model estimated over the year ending the day before the start of the relevant fiscal quarter. We measure interest rates by the yield on the CRSP 30-year bond index (BOND30) at the month-end prior to earnings announcement. Since information environments also affect price reactions to earnings announcements, we include firm size (SIZE) and analyst following (AFOL) to control for these (Bhushan, 1989). The inclusion of AFOL also controls for the effect of the precision of the earnings expectation measure on price reactions (Teoh and Wong, 1993). We measure SIZE as market capitalization at the beginning of the fiscal quarter and AFOL as the number of analyst forecasts used in computing the consensus forecasts. Several alternative explanations have been proposed to explain asymmetric price reactions to good versus bad news. Hayn (1995) argues that because shareholders have an abandonment put option to liquidate firms rather than bear indefinite losses, losses are likely to be temporary and hence have a weaker association with returns. Along a similar line of thought, Burgstahler and Dichev (1997) argue

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that poor performance is less likely to persist because firms are more likely to exercise the option to adapt their resources to a superior alternative use when earnings are low. Both these authors and Hayn attribute asymmetric price reactions to the put-option–like nature of equity that allows equity holders to liquidate, change strategy, or change management. Fisher and Verrecchia (1997) argue that differential price responses to good versus bad news can also arise when equity is viewed as a call option (i.e., equity holders have limited liability). The intuition is that equity holders capture all the upward potential while bearing limited downside risk. The authors propose that the earnings response coefficient decreases with firm leverage because the market’s assessment of the prior default probability is an increasing function of leverage. Finally, the implication of accounting conservatism on asymmetry in price reactions to good versus bad earnings news has been well recognized since Basu (1997). The asymmetrical verification requirements for gains and losses under conservative accounting principles imply a timely recognition of economic losses and a gradual recognition of economic gains. Basu (1997) hypothesizes and finds that positive earnings surprises are more persistent and have a larger valuation impact than negative earnings surprises. To alleviate the concern that the correlated variables rather than standardized unexpected volume (SUV) are driving our result, we include variables that capture the above-mentioned explanations and allow the coefficients of ESURP and ESURP  GOOD to vary with these variables. In particular, to capture the liquidation- or adaptation-based explanation, we include an indicator variable (LOSS) that equals one when the firm reports a loss, and zero otherwise. To capture the limited liability-based explanation, following prior studies, we include a firm leverage measure (LEV) where the variable LEV is calculated as the ratio of liability to assets at the beginning of the fiscal quarter (Dhaliwal et al., 1991; Subramanyam and Wild, 1996). Controlling for LEV is also motivated by the accounting conservatism-based explanation for asymmetry. Watts (2003) suggests that conservatism varies with four factors: contracting, litigation, taxation, and regulation. Khan and Watts (2009) propose a parsimonious set of firm characteristics—the book-to-market ratio (BTM), size (SIZE), and leverage (LEV)—as summary measures of the four Watts (2003) factors that explain cross-sectional variations in conservatism. To summarize, we specify our full model as follows17:

RET ¼ b0 þ b1 GOOD þ b2 ESURP þ b3 ESURP  GOOD þ b4 ESURP  RankSUV þ b5 ESURP  GOOD  RankSUV þ c1 ESURP  jESURPj þ c2 ESURP  BTM þ c3 ESURP  GOOD  BTM þ c4 ESURP  BETA þ c5 ESURP  GOOD  BETA þ c6 ESURP  BOND30 þ c7 ESURP  GOOD  BOND30 þ c8 ESURP  LOSS þ c9 ESURP  GOOD  LOSS þ c10 ESURP  LEV þ c11 ESURP  GOOD  LEV þ c12 ESURP  LogSIZE þ c13 ESURP  GOOD  LogSIZE þ c14 ESURP  LogAFOL þ c15 ESURP  GOOD  LogAFOL þ e:

ð2Þ

4. Empirical results 4.1. Descriptive statistics Table 1 reports the summary statistics for the variables used in the regression analysis. To mitigate the influence of extreme values, we winsorize all continuous variables at the first and 99th percentiles. Panel A of Table 1 reports the mean and standard deviation of each variable after winsorization. The mean of RET is positive, 0.3%. This finding is consistent with the observation of Ball and Brown (1968), Bamber and Cheon (1995), and Frazzini and Lamont (2007), that on average, stock prices rise around earnings announcement dates. The mean value of GOOD is 67%, suggesting that meeting or beating analyst forecasts in our sample period is much more likely than missing them. In analyzing temporal 17 Though not directly derived from theories that explain asymmetric price reactions to good versus bad news, we also allow the coefficient of ESURP  GOOD to vary with the risk-free interest rate (BOND30) and the firms’ beta risk (BETA) because these discount factors affect earnings response coefficients and hence should also affect the asymmetry of the earnings response coefficient between good and bad news; we allow the coefficient of ESURP  GOOD to vary with the number of analysts following (AFOL) because it is possible that the impact of the number of analysts following on forecast accuracy differs between good and bad news.

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Table 1 Descriptive statistics for variables in the main regression analysis. RET

ESURP

Panel A: Means and standard deviations Mean 0.003 0.000 Std 0.076 0.015 0.28 0.48 0.08 0.02 0.08 0.20 0.01 0.07 0.04 0.04 0.07

0.670 0.470 0.24 0.82 0.11 0.03 0.15 0.20 0.01 0.15 0.06 0.03 0.14

BTM 0.518 0.351 0.00 0.02 0.12 0.13 0.06 0.18 0.05 0.36 0.12 0.18 0.10

BETA 1.029 0.553 0.01 0.03 0.03 0.14 0.14 0.11 0.13 0.18 0.16 0.10 0.21

BOND30 5.925 1.514 0.01 0.10 0.13 0.07 0.17 0.12 0.04 0.21 0.07 0.01 0.42

LOSS 0.207 0.405 0.10 0.18 0.20 0.12 0.10 0.12 0.03 0.22 0.07 0.07 0.12

LEV 0.479 0.204 0.02 0.02 0.01 0.04 0.12 0.05 0.03 0.18 0.13 0.00 0.06

LogSIZE 6.626 1.774 0.02 0.06 0.15 0.35 0.22 0.21 0.23 0.19 0.54 0.14 0.46

LogAFOL 0.892 0.828 0.01 0.02 0.06 0.11 0.18 0.06 0.07 0.13 0.53 0.07 0.29

SUV 0.628 1.443 0.04 0.06 0.07 0.24 0.13 0.03 0.11 0.01 0.23 0.13

IO 57.030 23.275 0.03 0.09 0.14 0.09 0.23 0.46 0.12 0.06 0.49 0.28 0.11

0.07

In this table RET is the three-day [1, 1] return around quarterly earnings announcements, adjusted by the CRSP value-weighted market return. The variable ESURP is the difference between the I/B/E/S actual EPS and the consensus analyst forecast scaled by the stock price at the beginning of the fiscal quarter. The consensus analyst forecast is the median value of individual analyst forecasts made within 60 days prior to the earnings release date. If an analyst issued more than one forecast within this 60-day window, only the most recent forecast is used. The variable GOOD is a dummy variable coded as one if ESURP is equal or greater than zero, and zero otherwise; BTM is the book-to-market ratio at the beginning of the fiscal quarter, where a negative BTM is set to missing; BETA is the systematic risk measured through a market model estimated over the year ending the day before the start of the relevant fiscal quarter; BOND30 (in percent) is the yield on the CRSP 30-year bond index measured at the month-end prior to earnings announcements; the variable LOSS is a dummy variable that equals one when the firm reports a loss, and zero otherwise; LEV is the ratio of liabilities to assets at the beginning of the fiscal quarter; SIZE is the market capitalization of the stock at the beginning of the fiscal quarter; and AFOL equals the number of analyst forecasts used in computing the consensus forecasts. We take the logarithms of SIZE and AFOL to adjust for their asymmetric distributions. The standardized unexpected volume (SUV) is the scaled three-day average prediction error over the three-day window [1, +1] around earnings announcements from a market model-style regression of volume on the absolute values of returns. The term IO (in percent) is the last reported percentage of shares outstanding held by institutional investors within 180 days prior to earnings announcements. We winsorize all continuous variables at the first and 99th percentiles to mitigate the influence of extreme values. We exclude firms in the financial sector (SIC codes 6000-6999) and regulated utilities (SIC codes 4900-4999). We also exclude observations with stock prices below $1. The final sample consists of 124,247 quarterly earnings announcements of NYSE/AMEX/NASDAQ firms during 1985–2011 with non-missing data for all variables used in the regression analysis. Panel A reports the means and standard deviations. Panel B reports the Spearman rank correlations above the diagonal and the Pearson correlations below the diagonal. All correlations are significant at the 1% level except for the numbers in italics.

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Panel B: Correlations RET ESURP 0.16 GOOD 0.23 BTM 0.01 BETA 0.01 BOND30 0.01 LOSS 0.09 LEV 0.01 LogSIZE 0.01 LogAFOL 0.00 SUV 0.01 IO 0.03

GOOD

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patterns of earnings surprises, Brown (1997) shows that this phenomenon only occurs in more recent years. It is noteworthy that there is a significant amount of variation in SUV (mean 0.628, standard deviation 1.443), which is consistent with prior findings that earnings announcements are characterized by a significant number of differential interpretations (e.g., Bamber and Cheon, 1995; Bamber et al., 1999). Panel B of Table 1 reports the correlations of the variables. Due to the large sample size, all correlation coefficients are significant at the 1% level, except for the numbers in italics, even when the magnitude is small. As expected, the three-day market-adjusted returns (RET) are positively correlated with earnings surprises (ESURP) and the good news dummy (GOOD). The variable GOOD is positively associated with logSIZE, IO, andAFOL, suggesting that large firms, firms with high institutional ownership, and firms with more analysts following, respectively, are more likely to report good earnings news. The variable GOOD is negatively associated with the book-to-market ratio (BTM) and LOSS, suggesting that high-growth firms and profit firms are more likely to report good news. Consistent with Garfinkel and Sokobin (2006), the degree of heterogeneous interpretation (SUV) is positively correlated with firm market cap (LogSIZE). The variable SUV is also positively correlated with firm risk (BETA) and institutional ownership (IO) and negatively correlated with BTM. Finally, as expected, institutional ownership (IO) is positively correlated with firm size.

4.2. Main regression results Table 2 reports the effect of heterogeneous interpretations on the asymmetry of price reactions to good and bad earnings news for the full sample.18 Column (1) replicates prior studies and shows regression results for the full sample without considering the implication of the degree of heterogeneous interpretation. The slope coefficient (b3) of the interaction term between GOOD and ESURP is positive and statistically significant (b3 = 1.03, t = 10.47), consistent with Xu’s (2007) prediction. That is, the selective incorporation of optimistic opinions implies stronger price reactions to good news than to bad news. However, the results can also be explained by alternative theories, as discussed in Section 3.5. To differentiate our story from alternative explanations, we next turn to the regression that explicitly examines how heterogeneous interpretations (SUV) affect asymmetry in the price reactions to good versus bad news. Specifically, we add ESURP  RankSUV and ESURP  GOOD  RankSUV to the regression. Our hypothesis posits that the difference between good and bad news earnings response coefficients increases with the degree of heterogeneous interpretation; hence we expect the coefficient of ESURP  GOOD  RankSUV (b5) to be significantly positive. Since RankSUV is scaled to range from zero to one, the coefficient of ESURP*  GOOD (b3) captures the price reaction asymmetry in the lowest SUV decile when RankSUV equals to zero, while the sum of the coefficients b3 and b5 captures the price reaction asymmetry in the highest-SUV decile when RankSUV equals one. The coefficient of b5 can therefore be conveniently interpreted as a direct measure of the difference in price reaction asymmetry between the lowest- and highest-SUV decile groups after controlling for the other variables in the regression. The results in Column (2) of Table 2 suggest that price reactions are stronger to good news than to bad news in the lowest SUV group (b3 = 0.47, t = 4.32). But the asymmetry is significantly larger in the highest-SUV group (b5 = 1.05,t = 6.97). To gauge the economic significance of the change of asymmetry from the lowest- to the highest-SUV groups, we note that in the highest-SUV group, the price sensitivity to positive earnings surprises is 1.66 (b2 + b3 + b4 + b5), compared to only 0.14 (b2 + b4) to negative earnings surprises. In view of the level of price sensitivity to earnings surprises, the magnitude of change in asymmetry (b5 = 1.05) across SUV groups is large and economically significant. To summarize, the result suggests that when interpretations of earnings news become more heterogeneous, prices react more strongly to good news than to bad news, which is consistent with the prediction derived from the selective incorporation of optimistic opinions in the market with short sale constraints. 18 Throughout this paper, all reported t-values (in parentheses) in the regression analyses are based on standard errors clustered by firm and by fiscal quarter to account for time-series and cross-sectional dependence in the error terms (Petersen, 2009; Gow et al., 2010; Thompson, 2011).

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Table 2 Asymmetric price reactions to earnings surprises: effects of heterogeneous interpretations. Variables

Predicted sign Dependent variable = RET (1)

Intercept GOOD ESURP ESURP  GOOD ESURP  RankSUV ESURP  GOOD  RankSUV ESURP  |ESURP| ESURP  BTM ESURP  GOOD  BTM ESURP  BETA ESURP  GOOD  BETA ESURP  BOND30 ESURP  GOOD  BOND30 ESURP  LOSS ESURP  GOOD  LOSS ESURP  LEV ESURP  GOOD  LEV ESURP  LogSIZE ESURP  GOOD  LogSIZE ESURP  LogAFOL ESURP  GOOD  LogAFOL Adjusted R2

+ + + + + 

(2)

Coeff.

t-Value

Coeff.

0.02*** 0.03*** 0.05 1.03***

(19.70) 0.02*** (26.21) 0.03*** (1.24) 0.01 (10.47) 0.47*** 0.15 1.05***

+

+ 

5.75%

5.92%

(3) t-Value

Coeff.

(19.69) 0.02*** (26.28) 0.03*** (0.32) 0.78*** (4.32) 3.98*** (1.50) (6.97) 0.43*** 0.06 0.14 0.09 0.23** 0.11*** 0.32*** 0.28*** 1.70*** 0.02 0.25 0.01 0.12*** 0.01 0.05 6.67%

(4) t-Value

Coeff.

(19.93) 0.02*** (25.96) 0.03*** (3.73) 0.69*** (9.52) 3.47*** 0.28** 0.79*** (3.29) 0.42*** (0.73) 0.04 (1.03) 0.21 (1.57) 0.08 (2.22) 0.19* (5.01) 0.11*** (5.90) 0.31*** (4.32) 0.30*** (12.05) 1.58*** (0.14) 0.01 (0.97) 0.3 (0.34) 0.00 (2.76) 0.11** (0.20) 0.01 (0.58) 0.01 6.80%

t-Value (19.97) (26.12) (3.48) (8.39) (2.46) (4.90) (3.30) (0.54) (1.49) (1.33) (1.88) (5.05) (5.80) (4.61) (11.14) (0.10) (1.17) (0.07) (2.45) (0.26) (0.12)

Each quarter we rank the standardized unexpected volume (SUV) into deciles, with zero representing the lowest decile and nine representing the highest. The resulting ranks are then divided by nine to create a ranked variable that ranges between zero and one. We label this rank variable RankSUV. The other variables are defined in Table 1. We winsorize all continuous explanatory variables at the first and 99th percentiles. We set negative BTM values to missing and take the logarithms of SIZE and AFOL to adjust for their asymmetric distributions. We exclude firms in the financial sector (SIC codes 6000-6999) and regulated utilities (SIC codes 4900-4999). We also exclude observations with stock prices below $1. The final sample consists of 124,247 quarterly earnings announcements of NYSE/AMEX/NASDAQ firms during 1985–2011 with all the data necessary for the regression analysis available. We calculate the t-statistics (in parentheses) using standard errors clustered by firm and fiscal quarter to account for the time-series and cross-sectional dependence in the error terms (Petersen, 2009; Gow et al., 2010; Thompson, 2011). * Significance at 10% level using a two-tailed test. ** Significance at 5% level using a two-tailed test. *** Significance at 1% level using a two-tailed test.

Columns (3) and (4) of Table 2 repeat the analysis in Columns (1) and (2), respectively, except that we include more control variables derived from alternative explanations for asymmetric price reactions. The purpose is to alleviate the concern that correlated variables, rather than standardized unexpected volume (SUV), are driving our result. Column (4) uses the full model as specified in Eq. (2). It shows that the coefficient of ESURP  GOOD  RankSUV (b5) continues to be highly significant, which corroborates the earlier finding without control variables: The asymmetry in price reactions to good versus bad news varies across degrees of heterogeneous interpretation. Table 2 also suggests that inclusion of the SUV interaction contributes significantly to the explanatory power of the regression. Specifically, adjusted R2 increases from 5.75% in Column (1) to 5.92% in Column (2) and from 6.67% in Column (3) to 6.80% in Column (4), with the F-statistics of the incremental contributions in R2 being 48.48 and 35.81, respectively. The estimation results on the control variables are generally in line with prior literature. Consistent with Freeman and Tse (1992) and Subramanyam (1996), the coefficient of the interaction term between earnings surprises and the absolute value of earnings surprises is negative. The coefficient of the interaction term between earnings surprises and BOND30 is significantly negative, consistent with a high degree of interest rate implying a low discounted present value for future earnings innovations. The interaction term between earnings surprises and BETA has a significantly positive coeffi-

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cient, inconsistent with Collins and Kothari (1989) but consistent with Cready et al. (2000). Chambers et al. (2005) offers the possible explanation that the risk measure also captures the market’s underlying uncertainty about expected dividends, which increases the sensitivity of dividend expectations to firm-specific news, thus increasing the earnings response coefficients (ERCs). Basu (2005) suggests that a full understanding of the phenomenon requires a systematic empirical evaluation of the effects of research design choices on observed ERCs, as well as better option-based theoretical models of ERCs. The coefficients are significantly negative for ESURP  GOOD  LOSS but positive for ESURP  LOSS, suggesting that the lower association between returns and earnings for loss firms relative to profit firms is driven by good news announcements. Finally, the coefficient of ESURP  GOOD  LogSIZE is negative, consistent with a lower contracting demand for conservatism in larger firms where information asymmetry and agency problems are less severe (LaFond and Watts, 2008). Table 3 reports regression results using the full model as specified in Eq. (2) for subsamples partitioned on institutional ownership (IO). The purpose is to test the hypothesis that changes in asymmetry across SUV are more pronounced for low-IO stocks, for which short sale constraints are more binding. Low, medium, and high in Table 3 represent stocks in the bottom 30%, middle 40%, and top 30% of the IO distribution in each year quarter, respectively. Consistent with our prediction, the coefficients of ESURP  GOOD  RankSUV (b55) are significantly positive for the low- and medium-IO groups, but not for the high-IO group. Specifically, the magnitude of b5 in the low-IO group is 1.02 (t = 3.55), while b5 in the high-IO group is 0.21 (t = 0.65). The difference in b5 between the highand low-IO groups is statistically significant (t = 1.82, p < 0.05 for one-sided test).19 The results in Table 3 suggest that heterogeneity in the interpretation of earnings news plays an important role in explaining the asymmetric price reactions to good versus bad news, but only when short sale constraints are binding. Put differently, the impact of heterogeneous interpretations on price reaction asymmetry only appears when bundled with binding short sale constraints. In sum, Tables 2 and 3 support the theoretical prediction that pessimistic opinions are kept out of the market during the price discovery process in the presence of short sale constraints (Miller, 1977; Xu, 2007). 4.3. Robustness checks 4.3.1. Firm-characteristic–based proxy for heterogeneous interpretations Lamont (2004) suggests that firms with a short track record, within tangible prospects, or that are highly visible are likely to be subject to a greater divergence of opinion and attract more optimists.20 If this is true, we expect larger price reaction asymmetry in these firms, ceteris paribus. The evidence based on cross-sectional variation in firm characteristics could further corroborate our main findings, which are based on the event-specific measure (i.e., the abnormal volume measure or SUV) to capture heterogeneous interpretations. We use principal component analysis to construct a parsimonious factor score that summarizes various firm characteristics associated with heterogeneous interpretations, as suggested by Lamont (2004). In particular, we use the following four measures: 1/MV, the reciprocal of the market capitalization (in millions of dollars) at the beginning of the quarter; 1/AGE, the reciprocal of the number of years since the firm was first covered by the CRSP; HITECH, coded as one if firms belong to a high-tech industry, and zero otherwise, where a high-tech industry is defined according to Francis and Schipper 19 To compare the differences in coefficients (b5) in the three separate regressions across IO groups, we first set two dummy variables, MedIO and HighIO, where MedIO (HighIO) is coded as one if observations belong to the medium-IO (high-IO) group and zero otherwise. We then interact these two dummies with all the variables in the main regression and run the expanded regression for the full sample. The adjustedR2 increases from 6.80% (see Column (4) of Table 2) to 6.92% after including these interaction terms. The F-statistic of the incremental contribution in R2 is 5.26, suggesting that IO also contributes to the explanatory power in a statistically significant way. The coefficient of ESURP  GOOD  RankSUV in the expanded regression captures b5 in the low-IO group and the coefficient of MedIO  ESURP  GOOD  RankSUV (HighIO  ESURP  GOOD  RankSUV) captures the difference in b5 between the low- and medium-IO (high-IO) groups and the associated t-value provides a significance test. 20 Harrison and Kreps (1978) show that differences of opinion give rise to a speculative premium, which makes asset prices even higher than the most optimistic investor’s opinion. The speculative premium may further enlarge the effect of different opinions on price reaction asymmetry.

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Table 3 Asymmetric price reactions to earnings surprises: Effects of heterogeneous interpretations across different degrees of short sale constraints. Variables

Predicted sign

Dependent variable = RET Low IO Coeff.

Intercept GOOD ESURP ESURP  GOOD ESURP  RankSUV ESURP  GOOD  RankSUV ESURP  |ESURP| ESURP  BTM ESURP  GOOD  BTM ESURP  BETA ESURP  GOOD  BETA ESURP  BOND30 ESURP  GOOD  BOND30 ESURP  LOSS ESURP  GOOD  LOSS ESURP  LEV ESURP  GOOD  LEV ESURP  LogSIZE ESURP  GOOD  LogSIZE ESURP  LogAFOL ESURP  GOOD  LogAFOL Observations Adjusted R2 t-Statistics to test the difference in coefficients ESURP  GOOD  RankSUV High IO vs. low IO Med IO vs. low IO

+ + + + +  +

+ 

0.02*** 0.03*** 0.18 3.57*** 0.20 1.02*** 0.18 0.04 0.17 0.13 0.08 0.10*** 0.25*** 0.47*** 1.85*** 0.04 0.09 0.03 0.21*** 0.06 0.26* 37,253 7.01%

Med IO t-Value (18.08) (22.42) (0.57) (6.11) (1.21) (3.55) (0.96) (0.47) (1.17) (1.47) (0.52) (3.36) (4.36) (4.54) (9.41) (0.22) (0.26) (0.88) (3.36) (0.64) (1.77)

Coeff. 0.02*** 0.03*** 1.03*** 3.49*** 0.32** 0.66*** 0.69*** 0.05 0.08 0.03 0.39** 0.12*** 0.33*** 0.27*** 1.20*** 0.05 0.32 0.02 0.10* 0.00 0.06

High IO t-Value (17.04) (21.87) (2.84) (4.82) (2.27) (2.69) (2.87) (0.35) (0.34) (0.36) (2.24) (3.24) (4.46) (2.75) (5.21) (0.20) (0.65) (0.58) (1.67) (0.01) (0.58)

49,732 6.73%

Coeff. 0.02*** 0.03*** 1.43*** 5.43*** 0.40** 0.21 0.57** 0.03 0.46 0.08 0.32 0.16*** 0.45*** 0.08 1.15*** 0.02 1.45*** 0.06 0.12 0.07 0.28*

t-Value (15.38) (20.32) (2.95) (7.12) (2.10) (0.65) (2.40) (0.12) (1.29) (0.74) (1.53) (3.45) (5.96) (0.81) (3.69) (0.06) (2.72) (1.39) (1.25) (1.05) (1.94)

37,262 6.92%

0.81* 0.36

(1.82) (0.95)

We first sort the sample based on institutional ownership (IO) in each quarter. Here low, medium, and high denote stocks in the bottom 30%, middle 40%, and top 30% of the IO distribution, respectively. We estimate the regression separately for each IO group. Within each IO group, we rank the standardized unexpected volume (SUV) into decile each quarter, with zero representing the lowest SUV decile and nine representing the highest. The resulting ranks are then divided by nine to create a ranked variable that ranges between zero and one. We label this rank variable RankSUV. The other variables are defined in Table 1. We winsorize all continuous explanatory variables at the first and 99th percentiles. We set negative BTM values to missing and take the logarithms of SIZE and AFOL to adjust for their asymmetric distributions. We exclude firms in the financial sector (SIC codes 6000-6999) and regulated utilities (SIC codes 4900-4999). We also exclude observations with stock prices below $1. The final sample consists of 124,247 quarterly earnings announcements of NYSE/AMEX/NASDAQ firms during 1985–2011 with all the data necessary for the regression analysis available. We calculate thet-statistics (in parentheses) using standard errors clustered by firm and fiscal quarter to account for the time-series and cross-sectional dependence in the error terms (Petersen, 2009; Gow et al., 2010; Thompson, 2011). * Significance at 10% level using a two-tailed test. ** Significance at 5% level using a two-tailed test. *** Significance at 1% level using a two-tailed test.

(1999); and VISIBILITY, proxied by the past 12-month firm stock performance prior to the earnings announcements. Firms with higher factor scores are expected to be subject to more heterogeneous interpretations and attract more optimists; they are also expected to be subject to greater short sale constrains. D’Avolio (2002) suggests that the cost of borrowing stock, though small on average, is particularly high when the dispersion of investor valuations is high and when there are more optimistic investors. The principal component analysis yields one factor that has an eigenvalue greater than one and accounts for 32% of the variance. Similar to our treatment of SUV, we rank the factor score into deciles each quarter, with zero representing the lowest decile and nine representing the highest. The resulting ranks are then divided by nine to create a ranked variable that ranges between zero and one. We estimate the full model as specified in Eq. (2), using the rank of factor score (RankScore)

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to replace RankSUV. We find a significant positive coefficient of ESURP  GOOD  RankScore, suggesting that asymmetry (stronger for good news) is more salient in firms that are more likely to be subject to opinion divergence and short sale constraints. The result further corroborates our main results and supports our conclusion. 4.3.2. Interim quarters versus the fourth fiscal quarter Prior studies suggest that earnings response coefficients are different for the interim and fourth fiscal quarters (e.g., Jones and Bublitz, 1990; Salamon and Stober, 1994) and, more importantly, the asymmetry in earnings response coefficients between good and bad news also differs between the interim and fourth fiscal quarters (e.g., Mendenhall and Nichols, 1988; Dempsey, 1994). Basu et al. (2001) attribute the difference in asymmetry to the role of auditors, whose preference for conservatism causes fourth quarter earnings to be more conservative. Our prediction of the change of asymmetry in price reactions to good versus bad news across different degrees of interpretation heterogeneity and short sale constraints does not have any differential effect on the interim and fourth quarters. Consistent with our expectations, our results are qualitatively similar after excluding observations in the fourth fiscal quarters. 5. Related studies and further analysis Several recent studies also examine the effects of short sale constraints on price reactions to earnings announcements. These studies examine stock reactions from the angle that earnings announcements enhance agreement among investors. Reed (2007) argues that earnings announcements reduce information asymmetry between informed and uninformed investors and finds that stocks with higher short selling costs have larger price reactions to earnings announcements, especially to bad news. This result supports Diamond and Verrecchia’s (1987) prediction that short sale constraints reduce the speed with which prices adjust to private (especially negative) information. Reed (2007) does not consider opinion divergence. More closely related to our paper, Berkman et al. (2009) and Mashruwala et al. (2010) explicitly consider opinion divergence. Both papers focus on opinion divergence that exists prior to earnings announcements and assume earnings announcements narrow prior opinion divergence. Consistent with Miller’s (1977) overpricing hypothesis, Berkman et al. (2009) find that stocks with higher prior differences of opinions earn lower returns around earnings announcements, especially for stocks with high short selling costs. Mashruwala et al. (2010) find that when short sale constraints and disagreement prior to earnings announcements are high, the magnitude of bad news returns is significantly greater than that of good news returns.21 Unlike these existing studies, we focus on heterogeneous valuation interpretations triggered by earnings announcements. Holthausen and Verrecchia (1990) and Kim and Verrecchia (1997) suggest that public announcements such as earnings announcements can lead investors to disagree about firm value. Kim and Verrecchia (1997) assume that the announcements stimulate the development of private event period information, which leads to disagreement about firm value. Barron et al. (2005) provide empirical evidence supporting the descriptive validity of Kim and Verrecchia’s (1997) model. It is our belief that investors can disagree even without different private information. Noisy signals leave plenty of room for different interpretations among investors. Thus, a richer description of real markets needs to consider both the ex ante opinion divergence and differential interpretations triggered by earnings announcements. In the analysis below, we first replicate Berkman et al. (2009) by considering ex ante opinion divergence alone. We then replace the ex ante opinion divergence measure with our key variable: differential interpretations triggered by earnings announcements. After the separate analysis of both measures, we run a joint test to further differentiate our findings from those of Berkman et al. (2009) and provide evidence that these two measures capture distinct concepts. Following Berkman 21 Berkman et al. (2009) suggest that correction of prior overpricing occurs regardless of the nature of earnings, as long as earnings announcements narrow opinion divergence, whereas Mashruwala et al. (2010) suggest that correction occurs only when bad news is disclosed. While these two papers focus on total returns around earnings announcements, our theory and empirical tests focus on the differences in price response slopes between good news and bad news.

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et al. (2009), we use a volume measure, TURN, to proxy for differences of opinion prior to earnings announcements, where TURN is the average turnover over the time window [t  55, t  11], that is, from trading day 55 to trading day 11 relative to the earnings announcements.22 We continue to use SUV to proxy for the heterogeneous interpretations of earnings news, that is, differences of opinion triggered by earnings news. Note that, since SUV captures a distinct concept from that of TURN, the predictions of SUV and TURN on stock returns around earnings announcements are opposite. Specifically, Berkman et al. (2009) predict lower returns for stocks with high TURN values than with low TURN values. They examine from the angle that earnings announcements narrow prior opinion divergence and hence correct overpricing and higher prior opinion divergence implies more overpricing prior to announcements. In contrast, we expect higher returns for stocks with a high SUV than for those with a low SUV because we examine from the angle that earnings announcements trigger disagreements and selective incorporation of optimistic opinions gives rise to overpricing.23 To make our results comparable to those of Berkman et al. (2009), we follow the authors in both sample selection and research design. Our initial sample consists of all quarterly earnings announcement data during 1985–2011 with the earnings announcement dates and stock return information available. We exclude firms in the financial and regulated industries. We further exclude the earnings announcements of firms with $10 million or less in total assets or $10 million or less in the market value of equity or whose stocks are priced at less than $1 per share, as reported by Compustat the start of the current fiscal quarter. Our final sample consists of 265,087 firm–quarters with sufficient information to measure both TURN and SUV. Following Berkman et al. (2009), low, medium, and high represent stocks in the bottom 30%, middle 40%, and top 30% of the distribution, respectively. The average three-day abnormal return is first computed for every portfolio in each of the 108 calendar quarters. The reported portfolio returns are weighted averages of this sequence of quarterly averages, where the weights correspond to the inverse of the standard deviation of the estimate in each quarter. Panel A of Table 4 replicates the main findings in Berkman et al. (2009). We report the average three-day market-adjusted abnormal returns for portfolios formed (1) on the basis of TURN alone to examine the average effect and (2) by sequential sorting, first on IO and then on TURN, to examine the cross-sectional variation across the degree of short sale constraints. Consistent with Berkman et al. (2009), the average abnormal earnings announcement period returns are significantly lower in the high-TURN portfolio than in the low-TURN portfolio. Furthermore, this effect exists only when stocks are difficult to sell short, that is, in the low- and medium-IO groups. In the high-IO group, there is no systematic pattern of stock returns as we move from the low- to the high-TURN portfolio. This suggests that the effect of opinion divergence on price reactions only occurs when short sale constraints are sufficiently binding. Panel B of Table 4 repeats the analysis in Panel A, except that we replace TURN with SUV, our proxy for heterogeneous interpretations of earnings announcements. Consistent with our expectations, the first row of Panel B shows that firms with a high SUV earn significantly higher average returns than firms with a low SUV. Further evidence from the two-dimensional sequential sorts on SUV and IO suggests that this pattern is more pronounced for the low- and medium-IO groups, that is, when stocks are more difficult to sell short. This result suggests that when earnings announcements trigger heterogeneous interpretations, optimistic opinions are more likely to be incorporated into stock prices, especially when short sale constraints are sufficiently binding. Since Panels A and B examine TURN and SUV separately, there is a possibility that the results in SUV are driven by its association with TURN. To rule out the possibility that one effect is subsumed by the other, in Panel C, we follow prior studies (e.g., Desai et al., 2004) to implement a two22 Berkman et al. (2009) employ five different proxies for differences of opinion prior to earnings announcements. We choose TURN in our replication because Garfinkel (2009) suggests that the unexplained volume is a better proxy for opinion divergence than variability in stock returns and analyst forecast dispersion. 23 Hong and Stein (2007) suggest that news announcements can simultaneously spark increased disagreement among those investors who were already following the stock and grab the attention of those who were not. The authors further argue that in either case the same result is expected: both more trading volume and—in the presence of short sale constraints—concurrent upward pressure on price. The attention-grabbing story has drawn attention in the recent literature (e.g., Frazzini and Lamont, 2007). We believe both attention grabbing and increased disagreement contribute to the observed phenomenon. Disentangling these two effects is beyond the scope of our study.

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E.C. Chang et al. / J. Account. Public Policy 32 (2013) 435–455 Table 4 Abnormal returns around quarterly earnings announcements. Low TURN Ave. obs. per quarter

Med. TURN RET (%)

Ave. obs. per quarter

High TURN

High–low

RET (%)

Ave. obs. per quarter

RET (%)

RET (%)

t-Stat.

Panel A: Dependent sorts on IO and TURN [55, 11] Full sample 736 0.49*** 982 High IO 221 0.30*** 295 Med IO 294 0.42*** 393 Low IO 221 0.81*** 295

0.11** 0.31*** 0.08 0.16**

736 221 295 221

0.09 0.20** 0.08 0.81***

0.58*** 0.09 0.52*** 1.65***

8.98 1.00 5.80 14.53

Panel B: Dependent Sorts on IO and SUV [1, +1] Full sample 736 0.29*** High IO 221 0.03 Med IO 294 0.33*** Low IO 221 0.34***

982 295 393 295

0.13*** 0.61*** 0.22*** 0.47***

736 221 295 221

0.65*** 0.12 0.47*** 1.13***

0.95*** 0.15* 0.80*** 1.50***

13.27 1.79 8.70 11.84

Panel C: Independent sorts on TURN [55, 11] and Full sample 736 0.29*** High TURN 117 0.87*** Med TURN 294 0.40*** Low TURN 325 0.01

SUV [1, +1] 982 271 413 299

0.13*** 0.00 0.14*** 0.23***

736 348 276 112

0.65*** 0.11 0.57*** 2.28***

0.95*** 1.00*** 0.97*** 2.36***

13.27 7.91 10.17 14.59

This table reports average abnormal returns (RET) around earnings announcements for portfolios formed using proxies for differences of opinion and institutional ownership (IO). We first calculate the average abnormal returns for each portfolio in each quarter. We then calculate and report the weighted average values across these 108 quarterly average abnormal returns, where the weights correspond to the inverse of the standard deviation of the estimate in each quarter. The variable RET is the three-day [1, +1] return around quarterly earnings announcements adjusted by the CRSP value-weighted market return. Panel A shows the mean abnormal returns around the quarterly earnings announcements for the portfolios formed using TURN alone, as well as the portfolios formed using IO and TURN (more specifically, the stocks are first sorted by IO for each year quarter and then, within each IO portfolio, further sorted into TURN portfolios). The variable TURN is the average turnover from trading day 55 to trading day 11 relative to the earnings announcement, the proxy used for differences of opinion prior to earnings announcements in Berkman et al. (2009). Panel B performs the same analysis as Panel A, except that we use SUV, a proxy for differential interpretations of earnings announcements, to replace TURN. The standardized unexpected volume (SUV) is the scaled three-day average prediction error over [1, +1] around earnings announcements from a market model-style regression of volume on the absolute values of returns. Panel C reports the mean abnormal returns around the quarterly earnings announcements for portfolios independently sorted into low, medium, and high groups based on TURN and SUV. Throughout the table, low, medium, and high denote stocks in the bottom 30%, middle 40%, and top 30% of the distribution, respectively. Our initial sample consists of all firm quarters in the period 1985–2011 with available earnings announcement dates and stock return information. To be consistent with Berkman et al. (2009), we exclude firms in the financial industries (SIC codes 60006999) and regulated industries (SIC codes 4900-4999). We further exclude the earnings announcements of firms with $10 million or less in total assets or $10 million or less in the market value of equity or a price of less than $1 per share, as reported in Compustat, at the start of the current fiscal quarter. The final sample consists of 265,087 firm-quarters with sufficient information to measure both TURN and SUV. * Significance at 10% level using a two-tailed test. ** Significance at 5% level using a two-tailed test. *** Significance at 1% level using a two-tailed test.

dimensional independent sorting strategy where low, medium, and high represent stocks in the bottom 30%, middle 40%, and top 30% of the distribution of each variable, respectively. The independent sorting design is to assess whether the return pattern across SUV portfolios is sustained after holding TURN constant and vice versa. For each of the three-by-three portfolios, we report the average observations per quarter and the average three-day market-adjusted market returns. This presentation format helps reveal several insights into the individual and joint effects of TURN and SUV. First, we observe a positive association between TURN and SUV. In particular, the observations in the high-TURN (low-TURN) group have some concentration in the high-SUV (low-SUV) group. This is consistent with the view that earnings announcements may not necessarily narrow opinion divergence. Stocks with high pre-announcement opinion divergence can be subject to more heterogeneous interpretations of earnings news.24 Second, we observe a monotonic increase of abnormal re-

24 As a sensitivity test, we also run the main regression (Eq. (2)) for subsamples partitioned on TURN and we observe significant positive coefficients for ESURP  GOOD  RankSUV within each TURN subsample.

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turns from low to high SUV in all three TURN groups. These observations suggest that the results in Panel B of Table 4 are unlikely to be driven by some mechanical relation between TURN and SUV. Finally, regarding the joint effect of TURN and SUV, we observe that the average abnormal return conditional on both the TURN and SUV groups (3.15% = 2.28% + 0.87%) is much higher than that conditioning on TURN alone (Panel A, 0.58%) or on SUV alone (Panel B, 0.95%). In sum, the results in Table 4 suggest that price reactions to earnings announcements are affected by both ex ante opinion divergence and ex post heterogeneous interpretations of earnings news. On the one hand, earnings announcements can narrow ex ante opinion divergence and constitute a corrective force for the possible overvaluation that exists prior to these announcements. On the other hand, disagreements over value implications of earnings news and the selective incorporation of optimistic opinions under short sale constraints give rise to new overpricing. The evidence presented here confirms the dual-role notion of earnings announcements. Namely, earnings announcements can narrow the heterogeneity of prior beliefs by resolving uncertainty about the earnings news and, at the same time, it is well recognized that earnings announcements can increase the heterogeneity of beliefs because market participants often possess different private information and differ in the way in which they interpret earnings announcements (Beaver, 1968; Kothari, 2001). 6. Conclusion Heterogeneous interpretations have received growing attention in the accounting and finance literature. Different investors can interpret the same information differently. In testing Miller’s (1977) overpricing hypothesis, many papers simply assume that opinion divergence is reduced and hence overpricing is corrected over time. We argue that the difficulty in interpreting asset pricing information makes the correction of prior mispricing difficult and time-consuming; furthermore, noisy signals, which allow for agreement to disagree, can further increase rather than reduce mispricing. We provide evidence that heterogeneous interpretations have important implications for price reactions to earnings announcements in the presence of short sale constraints. The evidence suggests that heterogeneous interpretations and short sale constraints jointly lead to overpricing in the price discovery process. Overall, our evidence supports Miller’s (1977) insight that prices are upwardly biased and price bubbles may persist. Our evidence also has policy implications. Reducing short sale constraints should help improve price discovery and price efficiency. Acknowledgements We thank two anonymous referees, Kalok Chan, Jie Gan, Prem Jain, Oliver Kim, Amy H. L. Lau, TseChun Lin, Laura Liu, Martin P. Loeb (the editor), Chul W. Park, Mort Pincus, Charles Shi, Siew Hong Teoh, and John Wei for helpful comments and discussions. We also thank seminar participants at the Chinese Accounting Professors’ Association of North America’s Annual Conference, the City University of Hong Kong, Hong Kong Baptist University, the Hong Kong University of Science and Technology, the University of California at Irvine, and the University of Hong Kong for helpful comments and suggestions. We thank He Li for his excellent research assistance. Eric C. Chang gratefully acknowledges funding support from the Research Grant Council of the Hong Kong Special Administrative Region, China (HKU 7403/06H). Liu Zheng gratefully acknowledges funding support from the Research Grant Council of the Hong Kong Special Administrative Region, China (HKU 7551/08H). All errors are our own. References Admati, A.R., Pfleiderer, P., 1988. A theory of intraday patterns: volume and price variability. Review of Financial Studies 1 (1), 3–40. Almazan, A., Brown, K.C., Carlson, M., Chapman, D.A., 2004. Why constrain your mutual fund manager? Journal of Financial Economics 73 (2), 289–321. Asquith, P., Pathak, P.A., Ritter, J.R., 2005. Short interest, institutional ownership, and stock returns. Journal of Financial Economics 78 (2), 243–276.

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