Stockholders Reference-Dependent Preferences and the Market Reaction to Financial Disclosures

Transcription

1 Stockholders Reference-Dependent Preferences and the Market Reaction to Financial Disclosures Eric Weisbrod School of Business Administration University of Miami July 2015 Abstract: I examine the relation between stockholders reference-dependent risk preferences and the market response to earnings announcements using both security-level and investor-level data. I demonstrate that stockholders unrealized gain/loss position moderates their trading behavior in response to earnings announcements. I also present evidence that this behavior generates a shortwindow return underreaction to earnings news. My results vary along a number of dimensions predicted by recent models of stockholder behavior given reference-dependent preferences and address a number of concerns raised in prior studies. Keywords: Prospect Theory, Risk Preferences, Disposition Effect, Capital Gains, Momentum, Earnings Announcements, Information Content This paper is based on my dissertation at Arizona State University. I am grateful for the guidance provided by my dissertation co-chairs Steve Hillegeist and Dan Dhaliwal, and committee members Steve Kaplan and Mike Mikhail. I am also grateful for helpful comments from Khrystyna Bochkay, Larry Brown, Michael Donohoe (discussant), Katharine Drake, Diana Falsetta, Alok Kumar, Rick Laux, Andy Leone, Miguel Minutti-Meza, DJ Nanda, Sundaresh Ramnath, Laura Wellman, two anonymous JATA Conference mini-reviews, and seminar participants at Arizona State University, UT Dallas, London Business School, The University of Miami, Singapore Management University, Georgia State University, The NYU Stern School of Business, The University of Missouri, the 2013 JATA conference, and the 2013 South Florida Accounting Research Conference.

2 A large and growing body of research suggests that investors risk/utility preferences (hereafter, preferences) vary systematically with their reference point in an investment. 1 Most commonly, investors preferences are assumed to vary depending on whether the investment has increased or decreased in value since purchase. Recent experimental research presents strong evidence, from neural data, that investors reference-dependent preferences affect their trading decisions (i.e. Frydman et al. (2014)). A large body of archival research is also suggestive of a link between investors reference-dependent preferences and their trading decisions. For example, a well-documented result in prior literature is that investors appear eager to sell investments with unrealized gains and reluctant to sell investments with unrealized losses. This behavior is known as the disposition effect. 2 However, questions remain as to whether and how investors reference-dependent preferences are linked to average patterns in observed trading behavior such as the disposition effect (e.g. Ben-David and Hirshleifer (2012); Barberis (2013)). Questions also remain as to whether and how behavior such as the disposition effect affects asset prices in equity markets (Novy-Marx (2012)). One proposed explanation is that the disposition effect can arise from investors referencedependent preferences moderating their trading decisions in response to belief shocks. If so, such behavior also has the potential to affect the degree to which investors beliefs are reflected in asset prices following the disclosure of financial information. In this regard, the manner in which investors update and trade upon their beliefs surrounding public financial disclosures, such as 1 Perhaps the most common theory of reference-dependent preferences, as applied to investors, is Prospect Theory (Kahneman and Tversky (1979), Tversky and Kahneman (1992)), which posits, in part, that investors evaluate outcomes, not according to final wealth levels, but according to their perception of gains and losses relative to a reference point (Li and Yang (2013)). See Barberis (2013) for a recent review of research on prospect theory in finance and economics. Recently, an alternate theory, referred to as Realization Utility predicts that investors exhibit reference-dependent behavior because they derive direct utility (disutility) from the act of realizing gains (losses) (Barberis and Xiong (2012); Ingersoll and Jin (2013)). In the context of my study, prospect theory and realization utility generate many of the same predictions and I do not attempt to differentiate between the two theories. Thus, throughout the text, I utilize the general term reference-dependent preferences. Furthermore, my study focuses on investors reference-dependent preferences with respect to their cost basis in a purchased investment, but examples of alternate reference points and alternate models of reference-dependent preferences also exist in the literature (for example Koszegi and Rabin (2006), Huddart et al. (2009)). 2 The term disposition effect is attributed to Shefrin and Statman (1985). The disposition effect has been documented in the trading behavior of individual stock investors (Odean (1998); Shapira and Venezia (2001); Grinblatt and Keloharju (2001)), mutual fund managers (Frazzini (2006)), professional futures traders (Locke and Mann (2005); Coval and Shumway (2005)), individual home owners (Genesove and Mayer (2001)), as well as other settings. See Kaustia (2010) for a review of the literature. 1

3 earnings announcements, is of longstanding interest to researchers. 3 Nevertheless, prior research has not directly examined whether investors trading response to the belief shock contained in a financial disclosure generates an announcement-window disposition effect in the manner predicted by theories of investors reference-dependent preferences, nor has it examined whether such behavior can affect the degree to which the information contained in the disclosure is reflected in announcement-window returns. In this study, I bring both new data and recent theory to bear on these questions. I leverage the short three-day window around earnings announcements to examine the relation between stockholders average unrealized capital gain/loss position in a firm s equity (hereafter, stockholders capital gains overhang, or CGO) and the market response to earnings news. I motivate my study using the recent analytical model proposed by Li and Yang (2013) (hereafter, LY ). 4 LY develop a general equilibrium model to examine the capital market implications of investors prospect theory preferences. My empirical setting is similar to the stylized setting examined by LY. LY examine a market populated by overlapping generations of prospect theory investors, who update their beliefs about the value of a stock each period after observing a dividend news signal. LY find that, for a reasonable set of parameter values for the dividend process and investors preferences, their model can jointly predict the disposition effect, a large equity premium, and stock return momentum. Further, by modeling investors trading decisions around a dividend-news signal, LY are able to develop novel predictions about how the disposition effect varies with properties of the expected dividend stream. Specifically, LY predict that the strength of the disposition effect is positively associated with volatility and negatively associated with skewness in expected dividend growth. LY note that, empirically, this suggests that the disposition effect should be positively associated with return volatility and negatively associated with return 3 This literature dates back to at least Beaver (1968). Many literature reviews exist covering various aspects of research on investors reactions to financial disclosures. A few helpful examples include Kothari (2001), Verrecchia (2001), and Bamber et al. (2011). 4 While I motivate my analyses using the prospect-theory framework of Li and Yang (2013), I acknowledge that other recent models of investors reference-dependent preferences make similar predictions. Most notably, Ingersoll and Jin (2013) develop a model of realization utility with reference-dependent preferences that motivates similar predictions. I do not attempt to differentiate between prospect-theory and realization utility explanations for my results. While the LY framework is based on prospect-theory and the Ingersoll and Jin (2013) framework is based on realization utility, both frameworks share a key assumption that investors possess differential sensitivity to risk across gains and losses. I focus on the LY framework due to the similarity of their analytical setting with my empirical setting, leading to testable empirical predictions in the short window around earnings announcements. 2

4 skewness. Consistent with prior empirical research, LY also predict that the disposition effect and its pricing implications are decreasing in investor sophistication. I examine abnormal trading volume and abnormal returns around quarterly earnings announcements for evidence of investor behavior consistent with these predictions. Similar to the dividend news announcements in LY, earnings announcements provide investors with recurring periodic information about future cash flows. Using each firm s historical volume and reference prices as in Grinblatt and Han (2005), I estimate a measure of stockholders average CGO at the time earnings are announced. 5 I then examine the relation between abnormal trading volume and the CGO proxy. Employing multivariate regressions to control for known determinants of abnormal announcement-window trading volume, I find that, on average, the relation between stockholders CGO and abnormal trading volume is positive, consistent with a disposition effect in stockholders announcement-induced trading. I find that the average spread between the highest and lowest capital gains deciles is associated with a sizeable estimated disposition effect, equivalent to approximately a 38.8% difference in incremental three-day announcement-window trading volume, relative to median non-announcement volume. More importantly, a number of additional tests provide evidence that the observed disposition effect is likely driven by sellers reference-dependent preferences moderating their trading response to the announcement-induced belief shock. First, the relation between stockholders CGO and abnormal trading volume is stronger among seller-initiated trades than buyer-initiated trades. Second, the disposition effect in abnormal volume increases with the absolute magnitude of the belief shock contained in earnings news. Third, I find a stronger abnormal announcement-window disposition effect when investors are less sophisticated (Dhar and Zhu (2006); Li and Yang (2013)) and the firm s information environment is sparse (Kumar (2009); Li and Yang (2013)). 6 I also present evidence on the interaction between investors risk preferences and the characteristics of the expected return distribution. Consistent with LY, I find that the announcement-window 5 In sensitivity tests, I also examine a CGO proxy estimated from quarterly institutional holdings data, following Frazzini (2006). 6 In additional sensitivity tests provided in an internet appendix, I also find that the observed disposition effect is weaker during times when tax incentives are stronger or more salient, consistent with the capital gains tax lock-in effect mitigating the disposition effect in abnormal trading volume (Blouin et al (2003); Jin (2006); Ivković et al. (2005)). 3

5 disposition effect unambiguously increases with idiosyncratic return volatility. However, throughout my analyses, I find mixed evidence for the skewness prediction in LY. Moving beyond evidence of stockholders reference-dependent preferences generating a disposition effect in their abnormal trading response to earnings news, I document significant pricing implications associated with this behavior. First, I find an average negative relation between stockholders CGO and abnormal announcement-window returns. I regress three-day announcement-window Carhart (1997) four-factor abnormal returns on stockholders CGO, controlling for other determinants of the return response to earnings news. On average, the estimated three-day abnormal return spread between high and low CGO deciles is -1.5%. This is consistent with reference-dependent stockholders eagerness (reluctance) to trade when in an unrealized gain (loss) position placing downwards (upwards) pressure on price during the announcement-window, consistent with the volume-based evidence. Similar to the volume-based evidence, I also find that this association between CGO and announcement-window returns varies in a number of the ways predicted by LY, consistent with a preference-based explanation. Further, I find that these preference-related pricing effects generate an underreaction to earnings news. Specifically, estimated regression coefficients indicate that when preferencerelated effects move prices in the opposite direction to earnings news (opposed to the same direction), it reduces the announcement-window return sensitivity to earnings news by approximately 36.6%, relative to the average return response coefficient. I also find evidence of a corresponding correction in post-announcement returns. CGO-related pricing effects slow the reaction to earnings news when earnings news and CGO have the same sign (Frazzini (2006); Li and Yang (2013)). Sorting stocks independently on earnings surprise and stockholders CGO, I find that 60-day buy-and-hold post-announcement abnormal returns vary as predicted. The interquartile spread between high and low earnings surprise firms is 8.33% for observations in high and low CGO quintiles with the same sign as earnings news, but only 1.96% for observations in high and low CGO quintiles with the opposite sign as earnings news. This difference of approximately 6.38% is significant at the 1% level. Evidence from multivariate regressions is consistent with the portfolio sorts, and further indicates that the underreaction to earnings generally varies along the dimensions predicted by a preference-based explanation. 4

6 My results extend prior work by Frazzini (2006), who examines whether stockholders CGO moderates the degree to which post-earnings-announcement price drift is observed following the firm s quarterly earnings announcements. Using an intuitive combination of prospect theory and mental accounting, Frazzini (2006) develops predictions similar to those that arise in LY s formal setting. Frazzini (2006) examines the monthly returns on portfolios of stocks sorted on both recent earnings news and estimates of stockholders CGO and, as predicted, finds that post-earningsannouncement drift (as measured by average monthly calendar-time three-factor portfolio alphas) is most severe when capital gains and earnings news have the same sign. A similar study by Grinblatt and Han (2005) documents a more general association between stockholders CGO and momentum. Notably, both studies assume that their results are driven by the preference-related mechanism documented in my study. However, neither study demonstrates evidence of the assumed short-window disposition effect or associated price pressure, instead focusing on the association between stockholders CGO and subsequent price drift/momentum. While these studies represent important progress towards linking research on investors reference-dependent preferences to asset prices, as mentioned above, subsequent studies continue to question this link on a number of levels. First, at the individual level, recent analytical and empirical studies have questioned the underlying link between investors preferences and disposition effect behavior. For example, Barberis (2013, p. 183) notes that formalizing the link between prospect theory and the disposition effect analytically turns out to be harder than expected and that this issue continues to be debated. 7 Empirically, Ben-David and Hirshleifer (2012) also present evidence that, they argue, challenges preference-based explanations for the disposition effect. Using brokerage account data from the accounts of individual retail investors, Ben-David and Hirshleifer (2012) document a V-shape in the probability of selling as a function of an investors unrealized gain or loss, indicating that investors are eager to sell stocks with both large gains and large losses. Particularly for investors with unrealized losses, the evidence in Ben- David and Hirshleifer (2012) challenges the preference-based assumptions underlying Frazzini 7 Researchers have raised multiple issues in recent literature. One problem is that the differentially sensitive risk preferences generally used to explain the disposition effect are only one aspect of prospect theory, and other aspects of prospect theory could actually predict the reverse of the disposition effect (Li and Yang (2013)). Another area of debate is whether the risk-preferences exhibited by experimental subjects are strong enough to generate the behavior observed in actual markets (Barberis (2013)). 5

7 (2006) and Grinblatt and Han (2005). 8 A lack of evidence on the mechanism driving the results in Frazzini (2006) and Grinblatt and Han (2005) has also opened the door for researchers to revisit the monthly evidence linking stockholders CGO to returns. Focusing on general return momentum, as in Grinblatt and Han (2005), Novy-Marx (2012) employs an alternate research design and concludes that stockholders CGO cannot explain return momentum, contrary to the results in Grinblatt and Han (2005). Novy-Marx (2012) argues that any improvement to momentum-based calendar time trading strategies from sorting on stockholders CGO likely arises from mitigating the tax-related effects of poor trading strategy performance during January. The evidence presented by Novy-Marx (2012) also implies that Frazzini s (2006) calendar-time result may be driven by tax-related return seasonality, rather than stockholders preferences moderating their response to earnings news. My study addresses both types of concerns. My event-time design is less susceptible to the seasonal effects of tax-motivated trading proposed as an alternate explanation by Novy-Marx (2012). Further, in sensitivity tests I examine the sensitivity of my results to tax-motivated trading and find that inferences remain unchanged. To address concerns raised by Ben-David and Hirshleifer (2012), in addition to providing short-window security-level evidence of a preferencebased mechanism driving my results, I also validate my firm-level analyses using investor-level data. As mentioned above, Ben-David and Hirshleifer (2012) challenge preference-based explanations for the disposition effect using investor-level data. As part of their criticism of investor-level studies of the disposition effect, Ben-David and Hirshleifer (2012, p. 2515) note that preference-based explanations for the disposition effect imply that, other things equal, having a loss rather than a gain reduces the probability that the stock will be sold. However, tests of the disposition effect do not hold constant other factors influencing selling decisions that may be correlated with profit [emphasis in original]. An advantage of my study is that by leveraging the short window around earnings announcements, it is possible to at least partially control for other factors motivating investors selling decisions. Accordingly, I examine whether the shape of individual investors announcement-window selling schedule with respect to their returns since purchase is consistent with preference-based theories. 8 The recent realization utility model of Ingersoll and Jin (2013) offers a preference-based explanation for the V-shape documented by Ben-David and Hirshleifer (2012), but the whether this framework would also generate the pricing effects in Grinblatt and Han (2005) and Frazzini (2006) has yet to be formalized analytically. 6

8 I obtain investor-level data from Ancerno Ltd. s database of institutional trading activity, focusing on Ancerno clients classified as fund managers. 9 An advantage of examining trading by investors in the Ancerno database, who have collectively been estimated to account for approximately 8% of CRSP dollar volume (Puckett and Yan (2011)), is that Ancerno investors are more likely to determine the security-level prices and volumes I examine at the stock-level than the retail investors examined in prior studies. Any results obtained using Ancerno investor data are also likely to represent a conservative estimate of investors preference-related behavior given the investor sophistication results described above. I use Ancerno-provided identity codes to track daily unrealized gains and losses in individual positions taken by Ancerno fund managers. Using these data, I examine the shape of the relation between a fund s unrealized gain/loss in a stock and the fund managers decision to sell during the earnings announcement-window. Ben-David and Hirshliefer (2012) find that the relation between retail investors gain/loss position and their selling decision, on average, forms a V-shaped pattern. In contrast, a reduced partial-equilibrium specification of the model presented in LY generally predicts an inverted V-shape in the selling probability schedule. 10 I find that, at short holding periods, fund managers exhibit a V-shaped pattern in their sales decisions around earnings announcements, similar to the average pattern observed by Ben-David and Hirshleifer (2012) among retail investors. However, I find no evidence of a disposition effect in these short holding period trades. 11 Further, fund managers announcement-window sales decisions over short holding periods show no evidence of a positive association with the magnitude of the earnings surprise (i.e. the magnitude of the belief shock), suggesting that their sales decisions during the announcement-period may not be related to the announcement. In contrast, over intermediate and long investment horizons, fund managers exhibit an inverted V-Shape in their selling decisions with respect to returns since purchase, and become more likely to sell stocks with 9 The Ancerno database has been used in a number of prior studies examining institutional investor trading behavior. See, for example, Puckett and Yan (2011), Choi and Sias (2012), and Cready et al. (2014). 10 I thank an anonymous reviewer for suggesting the partial-equilibrium specification of the LY model. I discuss this specification in Section III and Appendix B of the paper. Kaustia (2010b) and Meng (2012) also derive preferencebased partial-equilibrium models which predict an inverted-v shape in investors selling schedule. Ingersoll and Jin (2013) present a specification of a preference-based (realization utility) model which can predict the empirical V- shape documented by Ben-David and Hirshleifer (2012). However, it is possible that alternate realization utility specifications could also predict the inverted V-shape. Examining this issue is beyond the scope of my study. 11 Despite the V-shaped pattern, Ben-David and Hirshleifer (2012) do find evidence of an average disposition effect at short holding periods. In fact, in their sample, the disposition effect is strongest for short holding periods. 7

9 large gains as the magnitude of earnings news increases. These results are consistent with fund managers reference-dependent preferences moderating their trading response to announcementinduced belief-shocks, as predicted by LY. Given that the majority of announcement-window positions held by fund managers in my sample are observed at intermediate to long holding periods, the aggregate behavior of Ancerno fund managers is consistent with the theoretical predictions modelled by LY. Furthermore, in aggregate, fund managers individual behavior is consistent with the stock-level evidence presented earlier in the paper. Taken together, the investor-level and security-level evidence presented in my study provide strong support for the notion that investors reference-dependent preferences moderate their trading response to financial disclosures. My findings contribute to existing research along a number of dimensions. Extant empirical studies examining investors reference-dependent preferences either focus on average individual trading behavior, or aggregate stock-level trading behavior over relatively long monthly or quarterly horizons. Studies that document the disposition effect at the individual level generally do not provide evidence about how such behavior aggregates to affect security-level volume or returns. Alternately, studies examining longer-horizon trading patterns at the security or market level often assume that the patterns they observe are driven by short-window underreaction to news announcements. I demonstrate that by isolating investors abnormal trading activity induced by a belief shock, it is possible to observe a consistent chain of evidence supporting a specific mechanism linking investors reference-dependent preferences to asset prices. Specifically, I observe consistent evidence in data taken from a) the investor-level, b) a short three-day security-level announcement-window, and c) a 60 trading-day security-level postannouncement window. In this regard, my results are consistent with the recent model formalized by LY, and support the longstanding notion that the disposition effect and price momentum in security-level volume and returns are, at least in part, driven by investors differential risk sensitivity across gains and losses. Further, my results are generally consistent with the recently introduced concept of realization utility (Barberis and Xiong (2012), Ingersoll and Jin (2013)) which has been documented at the neural level in experimental data (Frydman et al. (2014)) and can be combined with reference-dependent preferences (Ingersoll and Jin (2013)), which are a key component of LY s model. Overall, my results highlight the importance of controlling for 8

10 investors non-preference-related trading motivations, such as their beliefs (or changes in beliefs), when examining the effects of stockholders preferences on their trading behavior. My results also demonstrate the importance of investors reference-dependent preferences in understanding the market response to financial disclosures. In this regard, my results should be of interest to researchers or market participants interested in understanding the information content of financial disclosures. Bamber et al. (2011) argue that developing a better understanding of how factors such as investors risk preferences affect their reaction to financial disclosures is one of the fundamental unanswered questions for research interpreting trading volume around financial disclosures. My results extend prior studies documenting that investor attention moderates the market reaction to earnings news (DellaVigna and Pollet (2009); Hirshleifer et al. (2009)). Barber and Odean (2008, p.785) state that preferences determine [investors ] choices after attention has determined the choice set, which suggests that both preferences and attention should affect investors reaction to financial disclosures. Consistent with this notion, my results indicate that research examining the market reaction to financial disclosures should incorporate proxies for investors reference-dependent preferences in addition to proxies for investor attention. The remainder of the paper is organized as follows: Section I presents evidence of stockholders preferences inducing abnormal disposition effects and pricing pressure around earnings announcements, Section II demonstrates how these effects generate an underreaction to earnings news, and Section III validates the security-level results using investor-level data. Section IV provides conclusions and a discussion of the sensitivity of my results. I. STOCKHOLDERS REFERENCE-DEPENDENT PREFERENCES AND THE DISPOSITION EFFECT AROUND EARNINGS ANNOUNCEMENTS A. Methodology and Predictions In order to isolate the potential effects of stockholders reference-dependent preferences on their trading behavior, and, in turn, asset prices, I focus on stockholders short-window trading activity in response to the belief shock contained in periodic quarterly earnings announcements. While ample evidence exists of investors displaying disposition effect behavior in a number of settings, to link disposition effect behavior to the preference-related mechanism of interest, I must 9

11 show that a disposition effect arises in investors abnormal trading around earnings announcements, and that it varies in a manner consistent with a theory of stockholders reference dependent preferences. Accordingly, I examine abnormal volume and returns around earnings announcements for evidence that investors abnormal trading behavior varies according to predictions from LY. 12 As discussed in the introduction, LY s model predicts that, on average, when updating their beliefs about the future value of a stock, stockholders are more likely to sell their shares when the stock is in an unrealized gain position than an unrealized loss position due to their differential risk sensitivity. This suggests that, around the disclosure of an earnings announcement, there will be a positive association between stockholders CGO and abnormal announcement-window trading volume. 13 To the extent that the mechanism underlying this positive association is stockholders preferences moderating their trading decisions in response to the belief shock contained in earnings, this also suggests a stronger association between CGO and abnormal volume when the magnitude of the belief shock contained in earnings is larger. 14 LY s model also predicts that stockholders reference-dependent preferences will impact abnormal returns around financial disclosures. In LY s model, when investors review their investments and make selling decisions in response to their belief shocks, increased supply of shares from discretionary liquidity traders in the risk-averse unrealized gain portion of their value function suppresses current stock prices. Similarly, when discretionary liquidity traders are in the convex loss portion of their value function at the time of the belief shock, they are less likely to 12 LY leverage two key assumptions in order to develop a tractable general equilibrium setting around a belief shock and isolate the effect of investors preferences. First, they model a market populated by investors of overlapping generations who possess the standard prospect theory value function of Tversky and Kahneman (1992). Second, investors hold heterogeneous beliefs about the dividend growth rate of the single stock-like risky asset in the model, and investors beliefs about the dividend growth rate can change over time in response to periodic belief shocks. Investors also observe periodic realizations of the dividend growth rate. Investors in the model trade for three periods. LY calibrate the model such that investors beliefs in each period are random and i.i.d. in order to focus on the impact of investors preferences. See Li and Yang (2013) for further details of the model. 13 The LY model demonstrates the importance of examining abnormal trading volume as opposed to raw trading volume. In LY, there are both pure noise traders as well as discretionary liquidity traders. The pure noise traders are forced to sell to meet liquidity needs and thus do not exhibit the disposition effect. Accordingly, I adjust for normal non-announcement-related trading activity in my analysis. 14 Note that this interaction is symmetric: Prior literature demonstrates that investors are more likely to trade when the magnitude of the belief shock in earnings is larger (Bamber 1987), and LY s model suggests that for any given belief shock which would motivate a shareholder to sell, the shareholder will be more likely to sell when in the gain domain of their value function. 10

12 sell absent a price premium. This suggests that, on average, there will be a negative association between stockholders CGO and abnormal announcement-window returns. Employing a less formal framework, Frazzini (2006) makes similar predictions about the effects of investors differential risk sensitivity on stock returns around earnings announcements. Notably, while the differential sensitivity aspect of investors preferences generates a disposition effect in LY s setting, the loss aversion component of investors preferences sometimes motivates a reverse disposition effect. The often countervailing forces of the two preference components lead to interesting model dynamics, which LY analyze to develop additional predictions. I focus on three of LY s empirical predictions, which posit that the disposition effect in volume and its pricing implication for returns are stronger for stocks with 1) higher expected return volatility, 2) lower expected return skewness, and 3) lower investor sophistication. 15 To test these predictions, I analyze the following models: AAAAAAAA tttttttt = αα 0 + αα 1 CCCCCC + αα 2 AAAASS UUUU + αα 3 (CCCCCC AAAASS UUUU ) + αα 4 IIIIIIII + αα 5 (CCCCCC IIIIIIII) + αα 6 IIIIIIIIII + αα 7 (CCCCCC IIIIIIIIII) + αα 8 FFFFFFFFFFFFFFFFFF + αα 9 (CCCCCC FFFFFFFFFFFFFFFFFF) + αα 10 IIIIII nn + αα 11 (CCCCCC IIIIII) + cc ii AAAAAAAA_CCCCCCCCCCCCCCCC ii + εε ii=1 (1) BBBBBBRR ( 1,1) = ββ 0 + ββ 1 CCCCCC + ββ 2 UUUU + ββ 3 (CCCCCC UUUU) + ββ 4 IIIIIIII + ββ 5 (CCCCCC IIIIIIII) + ββ 6 IIIIIIIIII + ββ 7 (CCCCCC IIIIIIIIII) + ββ 8 FFFFFFFFFFFFFFFFFF + ββ 9 (CCCCCC FFFFFFFFFFFFFFFFFF) + ββ 10 IIIIII + ββ 11 (CCCCCC IIIIII) nn + cc ii BBBBBBBB_CCCCCCCCCCCCCCCC ii + εε ii=1 (2) Where AVOLtype is abnormal announcement-window trading volume for various trade-types, and BHAR(-1,1) refers to firm i s three-day buy-and-hold abnormal return around earnings announcement date t, relative to the Fama-French-momentum four-factor benchmark return (Carhart (1997)). Formal definitions for all variables are provided in Appendix A. 15 Barberis and Xiong (2012, p. 257) make similar predictions about volatility and investor sophistication within a realization utility framework. They write: [w]e emphasize that our model is not a model of sophisticated investors. It is a model of unsophisticated investors 11

13 I employ a transaction-based (i.e. number-of-trades-based) measure of abnormal trading volume to examine the relation between stockholders CGO and abnormal trading volume around earnings announcements for three different trade-types. Trade type indicates that the measure includes either: all trades, denoted AVOLTOTAL TRADES, buyer-initiated trades, denoted AVOLBUYER- INIT TRADES, or seller-initiated trades, denoted AVOLSELLER-INIT TRADES. 16 A transaction-based measure of trading volume is most closely aligned with prior research on the disposition effect. For example, studies documenting the disposition effect in individual data generally examine whether a sale took place, rather than the magnitude of the sale (e.g. Odean (1998); Ben-David Hirshleifer (2012)). 17 Further, if the disposition effect in abnormal trading volume arises from sellers reference-dependent preferences, the positive association between stockholders CGO and abnormal volume should be strongest for seller-initiated trades. 18 Accordingly, I focus on sellerinitiated abnormal volume in most tests, but estimate models of both seller-initiated and buyerinitiated abnormal volume to test this additional prediction. I measure CGO, my proxy for stockholders average capital gains overhang at the time they receive the belief shock, as (Pt-3 RPt-3)/ RPt Pt-3 is the stock price at trading day t-3 relative to earnings announcement date t, and RPt-3 is the most recent monthly estimate of stockholders average reference price in the stock available as of trading day t-3. Similar to Grinblatt and Han (2005), monthly reference prices are computed as follows: First, I calculate VV iiii,tt nn, the percentage of firm i's outstanding shares purchased at date t-n that are still held by their original purchasers on date t, as n 1 V t, t n= TOt n ( 1 TOt n+ τ ) τ = 1 16 Trades are classified as buyer or seller initiated using the Lee-Ready (1991) algorithm. See Appendix A for full variable definition. 17 Li and Yang (2013) also examine a binary choice model, but note that the inferences from their model are not sensitive to this assumption. 18 As noted in LY and prior literature, sellers reference-dependent preferences can also affect buyers decisions, but this effect occurs indirectly through possible supply shortages or liquidity premiums that they face when sellers are reluctant to transact. 19 Frazzini (2006) and Grinblatt and Han (2005) scale CGO by current price. Here I scale CGO by the reference price so that descriptive statistics are comparable to individual investor returns since purchase. In all tests throughout the paper, I use ranked measures, such that the choice of scalar is irrelevant. 12

14 where TOt is turnover for firm i in month t. The reference price is then estimated as t 1 t= φ t, t n t n n= 0 RP V P where φ φ =, is a normalizing constant such that V n= 0 tt n, and Pt is the stock price at the end of month t. Following Grinblatt and Han (2005), I truncate the estimation period to include the prior five years of data and normalize the monthly trading probabilities so that they sum to one. 20 I predict a positive coefficient on CGO in model (1) and negative coefficient in model (2). To test whether these associations vary as predicted by a preference-based explanation, I interact CGO with relevant proxies for each prediction. First, in model (1), to test whether the association between stockholders CGO and abnormal volume varies with the magnitude of the belief shock contained in earnings, I interact CGO with ABS_UE, the absolute value of unexpected earnings, and predict a positive coefficient. Unexpected earnings is measured as the forecast error relative to I/B/E/S analyst forecasts following Hirshleifer et al. (2009). To test LY s predictions about volatility and skewness, I interact CGO with idiosyncratic return volatility (IVOL) (e.g. Kumar 2009) and idiosyncratic return skewness (ISKEW) in both models. 21 I predict a positive (negative) coefficient on CGO*IVOL and negative (positive) coefficient on CGO*ISKEW in model (1) (model (2)). I interact CGO with two proxies to test LY s prediction about investor sophistication: analyst following (FOLLOWING) and institutional ownership ratio (IOR). Analyst following is consistent with the notion that investors decisions are more strongly influenced by cognitive biases and simple heuristics when the information environment is spare and the valuation task is more difficult (Hirshleifer (2001); Kumar (2009)). Institutional ownership is the proxy mentioned by LY and is consistent with prior investor-level evidence that individual investors exhibit stronger disposition effects than institutional investors (e.g. Dhar and Zhu (2006); Frazzini (2006)). I predict negative coefficients on CGO*FOLLOWING and CGO*IOR in model (1) and positive coefficients in model (2). t 20 Grinblatt and Han (2005) note that distant market prices likely have little influence on the reference price, and report that their results were robust to alternately using three or seven years of prior data to estimate the reference price. 21 In section IV, I discuss the sensitivity of my results using alternate proxies to test these predictions. 13

15 In each model, I include a number of controls for variables which have been demonstrated to be correlated with either CGO or the dependent measures. In model (1), I include controls for firm size (Bamber (1987)), absolute announcement-window return (Karpoff (1987)), market-wide announcement-window turnover (Bamber et al. (1997)), closing price at the end of the fiscalquarter (Utama and Cready (1997)), average monthly share turnover for firm i over the prior twelve months, and momentum (Jegadeesh and Titman (1993); Grinblatt and Han (2005); Frazzini (2006)). I also include an indicator variable for NASDAQ firms since trading volume is captured differently on NASDAQ. 22 In model (2), the dependent measure controls for the Carhart (1997) risk factors, including momentum. I also control for UE, the signed equivalent of ABS_UE defined above, as well as any possible interaction between the level of CGO and the level of earnings news. I also include controls for price (Bhushan (1994)), average turnover (Bhushan (1994)), return on assets (Balakrishnan et al. (2010); Fama and French (2015)), and losses (Hayn (1995)). In both models (1) and (2) I include year and Fama-French 10 industry classification indicators as controls, similar to Hirshleifer et al. (2009). In estimating models (1) and (2) and all subsequent regression analyses specified in the paper, I rank all independent measures into deciles each quarter prior to estimation. I also scale decile rankings to have a mean of zero and a range of one. This serves a number of purposes. It mitigates the impact of extreme outliers, controls for the nonlinear relation between returns and earnings (Hirshleifer et al. 2009), and facilitates interpretation of the many interaction terms included in the regressions. Mean-centering interaction terms also mitigates potential multicollinearity problems. B. Data and Sample Selection To analyze the models specified in section I.A, I collect data from a number of different sources. Accounting data is obtained from Compustat, daily stock price and share volume data are from CRSP, and analyst forecasts and reported actual EPS are from I/B/E/S. My study also incorporates stock quotes and detailed trade data from the NYSE s Trade and Quote (TAQ) database, as well as 13-F institutional holdings data from the Thompson Reuters CDA/Spectrum 22 In untabulated tests, I also interacted the NASDAQ indicator with all other variables and all inferences remain unchanged. 14

16 database. Following prior literature (Lee (1992), Bhattacharya (2001)), my study includes TAQ trades with a condition code of "regular sale" between 9:30 AM and 4:15 PM EST, excluding each day's opening trade. Using these data, I examine a sample of quarterly earnings announcements for the years 1994, the first full year for which required TAQ data is available, through 2010, the final year of data availability from Ancerno Ltd, which is required for later analyses described in section III. I require each firm-quarter observation in the sample to have sufficient data to calculate the variables defined in equations (1) & (2), resulting in a sample size of 192,918 firm-quarter observations for 8,947 unique firms. C. Results C.1 Descriptive Statistics and Univariate Results Table 1 presents descriptive statistics for the variables included in equations (1) and (2), both for the full sample (N=192,918), and separately for the unrealized gain (N=100,097) and loss (N=92,821) samples. The mean value of AVOLTOTAL TRADES (0.510) in the sample represents an increase in total trades of roughly 66.5% during the announcement window, relative to the median number of non-announcement trades, while mean three-day abnormal returns are close to zero. The means of all of the variables presented in Table 1, with the exception of BHAR(-1,1) are significantly different across unrealized gain and loss observations (p < 0.01). Consistent with a univariate gain/loss disposition effect, AVOL is significantly higher for unrealized gain observations than unrealized loss observations for all three measures presented. Further, the difference in mean abnormal volume is larger for AVOLSELLER-INIT TRADES than AVOLBUYER-INITIATED TRADES. [INSERT TABLE 1 HERE] Table 2 presents Spearman correlations among key variables. Consistent with a disposition effect, CGO is positively correlated with AVOLSELLER-INIT TRADES (0.169). The slight positive correlation (.005, p <.05) between CGO and BHAR(-1,1) is inconsistent with the predicted negative association. However, in subsequent tests I find that a negative relation between CGO and BHAR(- 15

17 1,1) emerges after controlling for UE (and remains significant in analyses with multiple controls). CGO is significantly correlated with a number of the control variables, but none so high as to make multivariate analysis unfeasible. Intuitively, CGO is most highly correlated with PRICE (.361) and MOMENTUM (.518), indicating the importance of controlling for these variables in the multivariate analysis. [INSERT TABLE 2 HERE] C.2 Multivariate Results [INSERT TABLE 3 HERE] Table 3 presents coefficient estimates from OLS regressions of model (1) using AVOLSELLER-INIT TRADES as the dependent measure. T-statistics reported in parenthesis are calculated using two-way clustered standard errors, clustered by firm and event date (Hirshleifer et al. (2009); Petersen (2009); Gow et al. (2010)). Prior to estimating the full version of model (1), I estimated a basic version of the model to test for the presence of a disposition effect in all three trade-types and found, as predicted, that seller-initiated trades had the strongest positive association with CGO. The results from the basic model are included in the internet appendix. Accordingly, I focus on preference-related variation in the association between stockholders CGO and abnormal sellerinitiated volume in Table 3. Column (1) presents results for the basic prediction that the relation between CGO and abnormal volume is stronger for larger magnitude belief shocks, column (2) examines the volatility and skewness predictions, column (3) examines the investor sophistication prediction, and column (4) estimates the full specification of model (1). Consistent with an average disposition effect in abnormal seller-initiated volume, the coefficients on CGO are positive and significant (p < 0.01) across all specifications. Given that all interaction terms represent decile ranks with mean zero and range of one, the coefficients can be interpreted as the average marginal effect of moving from the lowest to highest CGO decile, evaluated at the means of the interacted covariates. Relative to the sample mean, the coefficient of on CGO in column (1) implies that the marginal difference between the lowest and highest 16

18 CGO deciles is associated with an incremental difference in abnormal volume of approximately 38.8% of median non-announcement trading. 23 More importantly, with the exception of CGO*ISKEW, all interaction terms examined in Table 3 are significant in the predicted direction. Thus, Table 3 presents evidence that the disposition effect in abnormal seller-initiated volume increases with the magnitude of investors belief shocks as well as expected idiosyncratic return volatility, and decreases with investor sophistication and the richness of the firm s information environment. The coefficient on CGO*ISKEW is significantly positive, which is inconsistent with the skewness prediction from LY. As discussed further below, I find mixed results for the skewness prediction from LY throughout the various analyses in my study. With that said, of all variables examined in the paper, expected skewness is arguably the most difficult proxy to measure. Further, in LY s analytical setting, LY are able to examine the effects of skewness while holding volatility constant, while empirically I find a strong positive correlation (0.357) between IVOL and ISKEW in Table Thus, it is difficult to empirically isolate the skewness effect from the volatility effect. All control variables included in Table 3 are significant in the predicted direction across all specifications, with the exception of an insignificant coefficient on AVG_TURN in Column (4). [INSERT TABLE 4 HERE] Table 4 presents coefficient estimates from OLS regressions of model (2) where BHAR(- 1,1) is the dependent measure. T-statistics reported in parenthesis are calculated using two-way clustered standard errors, clustered by firm and event date (Hirshleifer et al. (2009); Petersen (2009); Gow et al. (2010)). Columns (1) (4) are organized as in Table 3. As predicted, the coefficient on CGO is significantly negative and approximately across all four columns of Table 3. This indicates that, ceteris paribus, three-day announcement-window abnormal returns are approximately -1.5% lower for observations in the highest quarterly CGO deciles than observations in the lowest quarterly CGO deciles. This is consistent with LY s prediction that 23 To determine the economic significance of the coefficient I examine a one unit change centered around the sample mean of AVOL SELLER-INIT TRADES, which is a logged quotient, and then compare the high and low exponentiated values. 24 In fact, while not a focus of this study, LY also note (p.735) that their general equilibrium model predicts this positive association between return volatility and return skewness. The positive association between idiosyncratic return volatility and skewness is well-documented in prior research (e.g. Boyer et al. (2010)). 17

19 increased supply of shares by stockholders with reference dependent preferences who are in the gain portion of their value function places downwards announcement-window pressure on price. Further, the interaction results presented in Table 4 are consistent with a number of the predictions from LY. As predicted, the coefficients on CGO*IVOL and CGO*ISKEW are negative and positive, respectively, in both columns (2) and (4). Note that this contrasts with the unexpected coefficient on ISKEW from Table 3 and provides some moderate support for LY s skewness prediction. In column (3) the positive coefficient on CGO*FOLLOWING is consistent with the investor sophistication prediction, while the coefficient on CGO*IOR is insignificant. In column (4), when the investor sophistication proxies are included in the model together with the return characteristics, the coefficient on CGO*FOLLOWING becomes insignificant and the coefficient on CGO*IOR becomes marginally negative (-0.005, p <.10), contrary to predictions. It appears that the explanatory power of return characteristics overwhelms that of investor sophistication in determining the relation between CGO and announcement-window abnormal returns. I view the marginally negative coefficient on CGO*IOR in column (4) as spurious. 25 Overall, Table 4 provides strong support for the return characteristic predictions and moderate support for the investor sophistication prediction.. Across all specifications of model (2), I find no evidence of an interaction between levels of CGO and levels of UE. 26 The PRICE control is also insignificant across all specifications, while ROA and LOSS are significant in the predicted direction across all specifications of Table 4. II. THE DISPOSITION EFFECT AND UNDERREACTION TO EARNINGS NEWS A. Model Development The results in Section I demonstrate average announcement-window volume and price effects associated with stockholders CGO, which vary as predicted by LY. Similar to earlier frameworks developed by Grinblatt and Han (2005) and Frazzini (2006), LY predict that these effects can generate an underreaction to earnings news, leading to subsequent price 25 In addition to the marginal statistical significance, this coefficient is likely spurious because there is strong support for the investor sophistication prediction in all other tests throughout the paper. 26 Note that this differs from later analysis in section II (and the analysis in Frazzini (2006)), where an interaction is expected when CGO and UE have the same sign. 18

20 drift/momentum. The key notion is that, when the short-window price effect documented above runs counter to earnings news, prices will be slow to fully reflect the information contained in earnings. This occurs when earnings news and CGO have the same sign. For example, positive earnings surprises are associated with positive announcement-window returns, however, if investors with reference-dependent preference are in a gain position at the time of the announcement, they will be eager to sell their shares, and this downward pressure on price counteracts the effect of positive earnings news. 27 If this mechanism exists around earnings announcements, it predicts that CGO and earnings news of the same sign will be associated with a reduced return sensitivity to earnings news during the announcement window and increased postearnings announcement drift (as in Frazzini (2006)). These predictions are similar to those in the literature on investor inattention around earnings announcements. For example, using similar research designs, DellaVigna and Pollet (2009) and Hirshleifer et al. (2009) show that earnings announcements on days where investors are distracted are associated with a lower announcement-window return sensitivity to earnings news, and subsequently higher levels of post-earnings-announcement drift. Accordingly, I adopt a similar research design to test for preference-related underreaction to earnings news. I examine both quarterly characteristic sorts and multivariate regression sorts in line with the following model: BBBBBBBB (ppppppppoodd) = δδ 0 + δδ 1 CCCCCCCCCCCCCCCCCC + δδ 2 UUUU + δδ 3 (CCCCCCCCCCCCCCCCCC UUUU) nn + cc ii CCCCCCCCCCCCCCCC ii + εε ii=1 (3) where BHAR(period) is BHAR(-1,1) for announcement-window tests and BHAR(2,61) for postannouncement tests. CGOSPREAD is equal to CGO when UE is positive and 0-CGO (i.e. negative CGO) when UE is negative. Thus, CGOSPREAD is increasing in the degree to which earnings news and CGO have the same sign. Preference-based underreaction to earnings news predicts a negative coefficient on CGOSPREAD*UE when BHAR(-1,1) is the dependent measure and a positive coefficient on CGOSPREAD*UE when BHAR(2,61) is the dependent measure. 27 An equivalent argument suggests temporarily inflated prices when investors with reference-dependent preferences receive bad news while in the loss portion of their value function. 19

21 CONTROLS is the same vector of control variables from Model 2, which include PRICE, AVG_TURN, ROA, LOSS, and industry and year indicator variables. 28 B. Results Figures 1&2 present results from independent quarterly quintile sorts on UE and CGO. In Panel A of each figure, bars depict mean abnormal returns by CGO quintile, within each quintile of unexpected earnings (UE). Lighter colored left-hand bars represent lower quintiles of CGO and darker colored right-hand bars represent higher quintiles of CGO. Similar to Frazzini (2006), Panel B of each figure tests differences in mean returns for low and high UE quintiles with the highest (positive) and lowest (negative) spreads in capital gains. Spread quintiles are extreme CGO quintiles with the same sign as UE (i.e. Low UE, Low CGO & High UE, High CGO). Negative spread quintiles are extreme CGO quintiles where CGO is news-contrarian (i.e. Low UE, High CGO & High UE, Low CGO). Thus, spread quintiles correspond to high values of CGOSPREAD in model (3) and negative spread quintiles correspond to low values of CGOSPREAD in model (3). Figure 1 examines BHAR(-1,1). First, consistent with the results presented in Section I, Panel A shows that there is a significant negative average relation between CGO and BHAR(-1,1) across four out of five UE quintiles. Consistent with this effect generating return underreaction to earnings news, Panels A & B show that High UE quintiles with high CGO (spread) have lower announcement-window returns than High UE quintiles with low CGO (negative spread) (difference of -0.64%, p <.01). For low UE quintiles, underreaction would predict a positive difference between the spread and negative spread quintiles, but I find that this difference is insignificant and descriptively slightly negative at -0.20%. However, the net spread negative spread underreaction of -0.43% for full interquartile spreads of earnings news remains significant in the predicted direction at the 10% level. In Figure 2, which examines BHAR(2,61), predictions are reversed in the post-announcement window. Both quintiles of extreme news display significantly positive average relations between CGO and BHAR(2,61). The interquartile spread between high 28 Hirshleifer et al. (2009) also interact all control variables, including indicator variables, with earnings news. In untabulated tests, I find that my inferences remain unchanged by adding this large number of interaction terms, while the variance inflation factor on UE becomes very large. Inferences also remain unchanged when I add additional controls for Friday earnings announcements (Dellavigna and Pollet (2009)) and days with many earnings announcements (Hirshleifer et. al (2009)), and interact these proxies with UE. 20

22 and low earnings surprise firms is 8.33% for observations in spread quintiles, but only 1.96% for negative spread quintiles. Consistent with post-announcement reversal of the negative announcement-window difference, this positive difference of approximately 6.38% is significant at the 1% level. [INSERT FIGURES 1&2 HERE] Table 5 presents coefficient estimates from OLS regressions of model (3) among various sample partitions. T-statistics reported in parenthesis are calculated using two-way clustered standard errors, clustered by firm and event date (Hirshleifer et al. (2009); Petersen (2009); Gow et al. (2010)). Panel A (B) presents results where BHAR(-1,1) (BHAR(2,61)) is the dependent measure. As predicted, the interaction between CGOSPREAD*UE is significantly negative (-0.026, p <.01) in panel A, and significantly positive (0.058, p <.10) in panel B. In panel A, the average return sensitivity to earnings news (δ2) is 0.071%. Recall that all regression variables represent meanzero, range-one quarterly decile sorts. Thus, the reduction in return sensitivity associated with increasing from the lowest to the highest decile of CGOSPREAD is equivalent to approximately 36.6% (0.026/0.071) of the average announcement-window return sensitivity to earnings news. Both panels A and B also show that the underreaction to earnings news is more severe in two of the three dimensions predicted by LY. For example, the post-announcement coefficient on CGOSPREAD*UE is only significant for low following, low institutional ownership, and high volatility partitions of the data. 29 Similar to the volume results in Section I, the results in Table 5 are inconsistent with the skewness prediction from LY. 30 [INSERT TABLE 5 HERE] 29 Similarly, the negative coefficients on CGOSPREAD*UE in Panel A are more negative for the low following, low institutional ownership, and high volatility subsamples. In untabulated tests, I run full-sample regressions with threeway interactions between CGOSPREAD*UE and indicator variables for the high-low subsamples of each characteristic and find that all differences between low and high subsample coefficients on CGOSPREAD*UE are significant at the 10% level or better with the exception of the low-high skewness partition. 30 The difference in coefficients on CGOSPREAD*UE between the low and high skewness subsamples in Panel A is insignificant, and the finding in Panel B that the coefficient on CGOSPREAD*UE is positive in the high skewness subsample but not the low skewness subsample is inconsistent with LY. 21

23 III. VALIDATION AT THE INVESTOR-LEVEL A. Model Development As discussed in the introduction, Ben-David and Hirshleifer (2012) find a V-shaped pattern in the relation between individual investors propensity to sell a stock and their returns since purchase, and argue that the V-shaped pattern is difficult to reconcile with preference-based explanations for the disposition effect. It is not possible to directly compare the V-shape documented by Ben-David and Hirshleifer (2012), which occurs across a continuum of unrealized gains, with the shape of the relation predicted by LY, because LY consider a binary dividend news signal. However, it is possible to derive a simple reduced-form partial equilibrium model with similar assumptions to those of LY in order to calibrate such predictions. 31 I describe this reducedform model in Appendix B. Figure 3, panel A, depicts the expected relation between an investor s propensity to sell in response to a belief shock and their returns since purchase, assuming the model described in Appendix B is calibrated with reasonable parameter values for investors preferences and the underlying investments return generating process. Similar to extant partial equilibrium models in related prior literature (e.g. Kaustia (2010b); Meng (2012)), the reduced-form model based on LY predicts an inverse V-shaped relation. In LY s original model, investors differential sensitivity preference parameter (α) drives the disposition effect, and generates stronger disposition effects and return momentum when calibrated to lower values, in line with updated experimental evidence (e.g. Wu and Gonzalez (1996)). I demonstrate this by lowering α from 0.88 to 0.5 between figure A.1 and A This continues to generate a general inverted V-shaped pattern, but the maximum propensity to sell moves slightly into the gain domain, and the average likelihood of sale becomes higher in the gain domain and lower in the loss domain, consistent with a stronger expected disposition effect. A key difference between my study and that of Ben-David and Hirshleifer (2012) is that I examine announcement-window trading in response to a belief shock, such that, on average, trades occurring during the announcement window share a common announcement-related trading 31 I am extremely grateful to an anonymous reviewer for suggesting this. 32 As in Li and Yang (2013), λ is calibrated to the Tversky and Kahneman (1992) estimate of

24 motivation, allowing me to isolate the marginal effect of investors preferences. Thus, I examine announcement-window data at the investor-stock-day level to determine whether, in this controlled setting, investors selling decisions appear more in line with a preference-based explanation such as that proposed by LY. I perform three sets of analyses: First, similar to the graphical evidence presented in Ben-David and Hirshleifer (2012), I use local polynomial smoothing to fit a line to the empirical data, and plot 95% confidence intervals around the fitted curve. Second, to examine the interaction between investors preferences and the belief shock motivating them to trade, I fit a three-dimensional surface to the data and present heat maps demonstrating how investors propensity to sell varies along both dimensions. Finally, similar to Ben-David and Hirshleifer (2012), I estimate the following probit regression model: II(SSSSSSSS) = γγ 0 + γγ 1 RRRRRR + γγ 2 AAAAAA_UUUU + γγ 3 (RRRRRR AAAAAA_UUUU) + cc ii CCCCCCCCCCCCCCCC ii + εε nn ii=1 (4) where I(SELL) is a sale indicator variable and RET is the investors return since purchase. I allow all coefficients in the model to vary across the gain and loss domains of investors returns since purchase. I also estimate the model over three sub-samples based on investment holding period, as Ben-David and Hirshleifer (2012) demonstrate that the shape of the relation between selling propensity and returns since purchase can vary significantly across holding periods. A V-shaped relation between I(SELL) and RET predicts a negative coefficient on RET in the loss domain and positive coefficient on RET in the gain domain, while the inverted V-shape derived from LY predicts the opposite. Similar to the interaction between CGO*ABS_UE in model (1), I predict a positive coefficient on RET*ABS_UE. As in Ben-David and Hirshleifer (2012), I control for the time since the investor opened the position, the investors purchase price in the investment, and stock volatility. I also add relevant controls from the stock-level sample including market capitalization, momentum, average turnover in the stock over the previous year, market turnover during the announcement window, and year and industry indicators. 23

25 B. Data and Sample Selection To estimate model (4), I obtain investor-level data from the Ancerno Ltd. institutional trading database. 33 This database tracks individual transactions made by large institutional investors who hire Ancerno to assist them in monitoring their trading costs. As described by Puckett and Yan (2011), the database should include the complete transaction history for each investor during the time period over which they contract with Ancerno. A key feature of the database is that from approximately Ancerno provides a unique (anonymized) identifier for each investor in the database. I use these identifiers to accumulate daily investor-stock share positions over time. I focus on Ancerno investors classified as fund managers. Similar to Ben-David and Hirshliefer (2012), I conduct several procedures to collect and clean the data. I provide a more detailed description of the data collection process in the internet appendix. Table 6, panel A summarizes the sample I obtain from the Ancerno database. In total, I am able to cleanly track 159,032 unique stock positions taken by Ancerno fund managers over my sample period, which generate a total of 70,101,493 investor-stock-days. Some positions are closed during the sample period and some positions remain open through the end of the sample collection period. I merge this sample with the stock-level sample of earnings announcements described in Section I. I match the stock-level data to investor-stock-days which fall during the (-1,1) three day announcement-window using CRSP PERMNOs. 34 A unique issue in the Ancerno database is that Ancerno clients may stop contracting with Ancerno at any point during the sample period, such that investors can disappear from the data without closing their positions. I require two filters to prevent this from affecting my analysis. First, in the overall sample, I stop tracking all positions for an investor on the last date on which the investor reports a trade to Ancerno. Second, in the sample I analyze in my study, I only consider investor-stock-days on which the investor made a sale in at least one stock in his portfolio, following Odean (1998) and Kaustia (2010b). This ensures that the investor was active in the database and considering a sale transaction on the date of any observation included in the data. Consistent with Ben-David and Hirshleifer (2012), I do not consider initial purchase dates for any position, such that I delete round-trip positions opened and 33 As mentioned in footnote 9, the Ancerno database has been used in a number of prior studies. The data provider is generally referred to as Ancerno Ltd. in prior literature, but also does business under the name AbleNoser Solutions. Puckett and Yan (2011) provide an excellent description of the database. 34 As in Ben-David and Hirshleifer (2012) I match the investor level data to CRSP and require that CRSP data is available for each investor-stock-day that a fund manager holds a position. 24

26 closed on the same day. Given these requirements, I am able to match 97,285 (50.4%) of the earnings announcements in the stock-level dataset to announcement-window holdings of Ancerno investors. Similar to some of the analyses in Ben-David and Hirshleifer (2012), within each of the three holding-period sub-samples I examine, I delete extreme observations for which logged gross returns are more than three standard deviations from the mean or logged absolute unexpected earnings is greater than three standard deviations from the mean. As shown in Table 6, Panel A, announcement-window dates on which an investor makes a sale in at least one investment in their portfolio make up a small proportion of the overall Ancerno sample, resulting in a final announcement-window sample of 1,177,583 unique investor-stock-days. C. Results Table 6, Panel B presents simple statistics on the unconditional probability of sale and average gain-loss disposition effect for the full sample and three holding-period partitions: days, 101 to 500 days, and > 500 days. 35 The unconditional probability of sale of 4.75% in my sample is higher than that in Ben-David and Hirshleifer (2012) since both the announcement-window and sale-days sample requirements increase the probability of sale relative to the overall sample. In contrast to Ben-David and Hirshleifer (2012), I find that the average disposition effect is increasing over investors holding periods. This is consistent with the mechanism examined in my study and additional results that I describe below. At longer holding periods, where fund managers have previously committed to a long-term position in a stock, investors announcement-window selling decisions are more likely to be motivated by the information contained in the announcement. Consistent with this, Figure 3 panel C, described below, shows a stronger positive association between the magnitude of the belief shock contained in earnings and investors selling decisions at longer holding horizons. In essence, I find the strongest disposition effect in the sample where I am able to best isolate the preference-based mechanism predicted to generate a disposition effect. While I do find an average disposition effect among Ancerno fund managers, the overall magnitude is much smaller than that reported in Ben-David and Hirshleifer (2012) (15.58% of the unconditional probability of sale compared with 44.68%), consistent with LY s investor 35 The mean holding period in my sample is higher than that reported in Ben-David and Hirshleifer (2012) for individual investors and I adjust my holding period partitions accordingly. Similar to Ben-David and Hirshleifer (2012), the majority of the sample is made up of holding days for intermediate to long-term positions. 25

27 sophistication prediction and prior research (Frazzini (2006); Dhar and Zhu (2006)). Panel C of Table 6 reports descriptive statistics for the variables included in model (4). Descriptive statistics are in line with expectations and show that firms with Ancerno holdings are generally larger and more frequently traded than the firms in the full stock-level sample. Figure 3, Panel B presents Ancerno fund managers announcement-window selling schedules with respect to their returns since purchase for each holding period sub-sample, as well as the full sample. While Ben-David and Hirshleifer (2012) demonstrate the importance of partitioning on holding-period, in my setting it is also of interest to observe the manner in which investors behavior aggregates over holding periods, because the stock-level results in section I and II represent aggregate behavior (aggregated across more dimensions than investors holding periods). Figure 3, Panel B, does not control for the belief shock contained in the earnings announcement. Fitted curves are based on 3rd-degree polynomials fitted with separate parameters for positive and negative regions, with 95% confidence intervals shaded in grey. 36 The selling schedule forms a V-shape, as in Ben-David and Hirshleifer (2009), for the day holding period, but becomes inverted, as predicted, over longer holding periods. 37 The aggregated data reflects the fact that longer holding-period investor-stock-days make up the majority of the sample. Figure 3, Panel C presents heat maps of the empirical relation between return since purchase and likelihood of announcement-window sale for Ancerno fund managers, conditional on absolute unexpected earnings. The y-axis (x-axis) of each figure denotes values of absolute unexpected earnings (returns since purchase). Lighter shaded regions correspond to higher estimated selling probabilities and darker shaded regions correspond to lower estimated selling probabilities. The colorbar to the right of each panel denotes the shading scale used to display estimated selling probabilities for each figure. 38 The overall V-shape in the holding day subsample is evident from the darker mid-regions of the figure and lighter left and right side regions. At intermediate and long-term holding periods, the predicted inverted-v pattern is evident at lower levels of earnings surprise with lighter mid-regions and darker outer regions. The predicted 36 Green markers present the local average sales frequencies at return intervals of 5% (2.5% for <=100 days). 37 In contrast to Ben-David and Hirshleifer (2012), the loss region of the V is slightly steeper than the gain region in this sample, generating the slight reversed average disposition effect observed for the day subsample in Table 6, Panel B. 38 The surfaces plotted in Panel C are fit from the empirical data using the MATLAB gridfit package (D Errico (2006)). 26

28 positive interaction between absolute unexpected earnings and return since purchase is evident in the upper regions of the figures where the highest selling probabilities are found for the region of the data with large gains as well as high absolute unexpected earnings. Table 7 presents estimated average marginal effects from probit regressions of model (4). Z- statistics reported in parenthesis are calculated using standard errors clustered at the investor level (Ben-David and Hirshleifer (2012)). The results are generally consistent with the graphical evidence. The short-term holding subsample demonstrates an average V-shape in the announcement-window selling schedule, with a negative coefficient on RET in the loss sample and positive coefficient in the gain sample. At longer holding periods, the slope in the loss region is clearly inverted, with strong positive coefficients on RET in both the intermediate and long-term subsamples. The coefficient on RET for the gain region is insignificant in the intermediate holding sample and significantly negative, consistent with an average inverted-v shape in the selling schedule, in the long-term holding sample. Evidence of a positive coefficient on RET*ABS_UE is concentrated in the gain regions of the intermediate and long-term holding samples, consistent with Figure 3, Panel C. The significant negative coefficients on ABS_UE in the loss regions of all holding periods is slightly puzzling, and indicates that investors in the loss region of their value function become more reluctant to sell as the magnitude of the belief shock in earnings news increases. 39 However, the marginal effects are small in magnitude. Overall, the results from the investor-level analysis are consistent with the preference-related mechanism predicted by LY and demonstrate the importance of controlling for investors trading motivations/belief shocks when examining the relation between investors preferences and their trading decisions. Table 7 also identifies additional control variables, SIZE, MOMENTUM, AVG_TURN, and MKT_TURN, which should be considered in future research examining individual investors trading decisions. 39 While I have not explored the data for possible explanations for this result, one possibility is that large earnings surprises for stocks with previous losses contain good news about the investment s future prospects, confirming these investors dispositions towards holding the investment. For example, R&D intensive firms can report long periods of sustained losses and negative returns before developing successful products that generate positive earnings surprises and increase investors conditional expected return on their holdings. 27

29 IV. DISCUSSION A. Robustness In addition to the analyses presented in the text, I performed several tests to examine whether my findings are sensitive to my research design choices. Some of these have been footnoted throughout the text, and some are presented in the internet appendix and briefly mentioned here. First, I examine whether my findings are sensitive to my use of CGO as a proxy for the representative investor s unrealized capital gain/loss position in a given stock. In untabulated tests, I repeat all of my analyses using the Frazzini (2006) CGO proxy, based on quarterly institutional holdings data, for the subsample of firms with available data to compute the measure. All qualitative inferences from the paper remain unchanged, although the investor sophistication and earnings underreaction results are generally weaker using the Frazzini (2006) given the institutional ownership requirements. In the internet appendix, I examine seasonal and time-series variation in my results due to tax-motivated trading. Consistent with prior research, I find that the observed announcementwindow disposition effect is weaker during times when tax incentives are stronger or more salient, consistent with the capital gains tax lock-in effect mitigating the disposition effect in abnormal trading volume (Blouin et al (2003); Jin (2006); Ivković et al. (2005)). I also examine the robustness of my results to the alternate January-performance explanation for CGO s ability to predict returns presented in Novy-Marx (2012). I repeat all stock-level analyses excluding observations near the turn-of-the-year and find that all inferences remain unchanged. I also replicate Frazzini s (2006) results using daily calendar time regressions for the (2,61) postannouncement window in my study and find results consistent with those in Frazzini (2006). All calendar-time inferences also remain unchanged if January returns are deleted from the calendartime sample. Finally, in untabulated tests I examine the sensitivity of my results to alternate proxies for investors beliefs about the volatility and skewness of future dividend growth. I examined proxies for earnings variance and skewness following Gu and Wu (2003) instead of return variance and skewness and found results that are generally consistent with those presented in the paper. I also 28

30 examined the more complex expected idiosyncratic return skewness proxy in Boyer et al. (2010). 40 I find consistent results across alternate proxies for return and earnings variance. While some of the skewness proxies provide different sets of mixed results than others, I continue to find mixed results for my skewness predictions across all skewness proxies, highlighting the difficulty of selecting an empirical proxy for the skewness beliefs examined in LY. B. Conclusion This paper presents empirical evidence from a) the investor-level, b) a short three-day securitylevel announcement-window, and c) a 60 trading-day security-level post-announcement window, consistent with investors reference-dependent preferences moderating their trading response to financial disclosures. My results also demonstrate that investors preference-motivated behavior can affect asset prices by generating a return underreaction to earnings news. These results address concerns in recent literature questioning both the link between investors preferences and behavior such as the disposition effect, as well as the link between disposition effect behavior and asset returns. A key takeaway from my analysis is the importance of isolating and controlling for investors trading motivations, such as their belief shocks, when examining theoretical predictions about the role of investors preferences in determining their trading decisions. My findings motivate future research isolating the role of investors preferences when making alternate types of trading decisions. For example, future research might examine whether similar results obtain when examining the role of investors preferences when investors trade in response to liquidity shocks instead of belief shocks. Factors such as investors narrow framing/mental accounting behavior, the degree to which investors weight their preferences, or the degree to which preferencerelated effects aggregate to affect asset returns, may differ across different types of trading decisions. 40 I obtained these data from Dr. Boyer s website: 29

31 Appendix A: Variable Definitions AVOL type = ln(1+number of firm i announcement-window trades of type j) ln(1+ Median number of firm i trades of type j during rolling 3-day non-announcement windows). The announcement-window is defined as the [-1,1] three trading-day window centered on earnings announcement date t. Earnings announcement dates are defined as the earlier of the Compustat and I/B/E/S reported announcement date (DellaVigna and Pollet (2009); Hirshleifer et al. (2009)). The non-announcement period includes all contiguous three-day periods from trading days [-250, -2] relative to the earnings announcement date, excluding any three-day periods containing previous earnings announcements. Trade type j is defined as: TOTAL TRADES = All trades within TAQ sample selection requirements. BUYER-INIT TRADES = Buyer-Initiated Trades, from the Lee-Ready (1991) algorithm. SELLER-INIT TRADES = Seller-Initiated Trades, from the Lee-Ready (1991) algorithm. ABS_RETURN = Absolute value of the announcement-window raw cumulative return on firm i's stock. ABS_UE = Absolute value of UE. AVG_TURN = Average monthly share turnover in the stock of firm i over the twelve months prior to earnings announcement t. tt+1 tt+1 BHAR (-1,+1) = kk=tt 1(1 + RR iiii ) kk=tt 1 (1 + RR eeee ), where R ik is the return of firm i and R ek is the expected return from the Carhart (1997) four-factor model estimated using a 40-trading-day holdout period starting 55 days prior to the earnings announcement date (see also, Balakrishnan et al (2010)). tt+61 tt+61 BHAR (2,61) = kk=tt+2(1 + RR iiii ) kk=tt+2 (1 + RR eeee ), where R ik is the return of firm i and R ek is the expected return from the Carhart (1997) four-factor model estimated using a 40-trading-day holdout period starting 55 days prior to the earnings announcement date (see also, Balakrishnan et al (2010)). BUYPRICE = The fund managers logged purchase price in the position, as in Ben-David and Hirshliefer (2012). CGO = Capital Gains Overhang, defined as (P t-3 RP t-3)/ RP t-3. P t-3 is the stock price at trading day t-3 relative to earnings announcement date t, and RP t-3 is the most recent monthly reference price available as of trading day t-3. Similar to Grinblatt and Han (2005), monthly reference prices are computed as follows: First, I calculate VV iiii,tt nn, the percentage of firm i's outstanding shares purchased at date t-n that are still held by their original purchasers on date t, as n 1 V t, t n= TOt n ( 1 TOt n+ τ ) τ = 1 where TO t is turnover for firm i in month t. The reference price is then estimated as t 1 t= φ t, t n t n n= 0 RP V P 30

32 where φ φ =, is a normalizing constant such that V n= 0 tt n, and P t is the stock price at the end of month t. Following Grinblatt and Han (2005), I truncate the estimation period to include the prior five years of data and normalize the monthly trading probabilities so that they sum to one. CGOSPREAD = CGO when UE 0, and (0 CGO), i.e. negative CGO, when UE < 0. FOLLOWING = The number of I/B/E/S analysts who issue forecasts for firm i over the twelve months prior to earnings announcement t. IOR = Institutional ownership ratio as of the most recent calendar quarter prior to the earnings announcement date. I(SELL) = 1 if an investor makes a net sale in the stock on the investor-stock-day, and zero otherwise. Net sales can be partial or liquidating sales. ISKEW = Idiosyncratic return skewness, defined as 1 NN(tt) t 3 dd SS (tt) εε ii,dd IIIIIIII ii,tt 3. Similar to Boyer et al. (2010), S(t) denotes all trading days during the 12 months prior to the month of earnings announcement t, and N(t) denotes the number of elements in this set. ε i,d is the regression residual from the Carhart (1997) four-factor model on day d for firm i, where the regression coefficients that define this residual are estimated using daily data firm i for days in S(t). IVOL = Idiosyncratic return volatility, defined as ( 1 NN(tt) dd SS (tt) εε ii,dd 2 ) 1/2. See above definition for ISKEW. LOSS = 1 if reported earnings before extraordinary items are negative, and 0 otherwise. MKT_TURN = The natural log of the percentage of all CRSP stocks outstanding shares that are traded over the three-day event window. MOMENTUM = The 11-month buy-and-hold return on firm i's stock beginning 12 months prior to the month of the earnings announcement. NASDAQ = 1 if firm i's stock is listed on NASDAQ during quarter t, and 0 otherwise. PRICE = The natural log of closing stock price for firm i at the end of fiscal quarter t, (the same price that is used as the scalar for UE following Hirshleifer et al. (2009)). RET = The fund managers return since purchase on the stock. The current price used to compute returns is either the fund managers transaction price on the current date, or the CRSP closing price when no transaction occurs on the current date. Returns are adjusted for splits and dividends using CRSP. ROA = Income before extraordinary items scaled by beginning of quarter total assets. SIZE = The natural log of market value of equity at the beginning of quarter t. TIME_OWNED = The square root of the number of days since the fund manager opened the position in the stock (i.e. initially purchased the stock), as in Ben-David and Hirshleifer (2012). 31

33 UE = Unexpected earnings, defined as (E it F it) / P it, following Hirshleifer et al. (2009). E it is firm i's I/B/E/S actual reported earnings for quarter t. F it is the consensus forecast for firm i's reported earnings for quarter t. P it is the closing stock price for firm i at the end of fiscal quarter t. The consensus forecast is calculated as the median of analysts most recent forecasts from the I/B/E/S detail file. Only forecasts for quarter t s earnings that are classified as one-quarter-ahead or twoquarter-ahead forecasts and issued or reviewed within 60 calendar days prior to the earnings announcement are included in the consensus. Earnings, forecasts, and prices are all split-adjusted. To minimize possible data errors, I delete observations when earnings or forecasts are greater than the stock price, or when the stock price is less than $1 before split-adjustment. VOLATILITY = Stock volatility for investor-stock-day t. For each investor-stock-day, the stock s volatility is calculated using the standard deviation of daily returns for the 250 trading days prior to day t. 32

34 Appendix B: A Reduced-Form Partial Equilibrium Model Based on the General Equilibrium Model Developed by Li and Yang (2013) I consider a prospect theory investors selling decision in response to a belief shock given the following assumptions 41 : There are three dates: t = 0, 1, and 2. There is one risky stock, whose returns R1 and R2 are i.i.d. over time, and log normally distributed: log R1 ~ N(μ,σ 2 ) and log R2 ~ N(μ,σ 2 ). Let Pt be the price at date t, so that R1= P1/ P0 and R2= P2/ P1. At date 0, the prospect theory investor buys one unit of the stock at price P0. Consider the investor s decision at date 1 given the realization of R1: Will the investor sell or hold the stock? If the investor sells the stock, the gain/loss is P1 P0 = (R1 1)P0, and if the investors keeps the stock, then the gain/loss is P2 P0 = (R2R1 1)P0. The investor evaluates utility from gains and losses using the following prospect theory value function: GG vv(gg) αα, iiii GG > 0 = λλ( GG αα, iiii GG 0, where GG indicates gains or losses, 0 < αα <1 and λλ > 1. Similar to the setting in Li and Yang (2013), at date 1, the investor experiences an unexpected belief shock. Specifically, assume that the investor believes log R2 ~ N(μ+Δ,σ 2 ), with Δ~N(0,σ 2 Δ), where Δ captures the belief shock. As a result, given the realization of R1 (and price P1) and belief shock Δ, the investor s utility from selling the stock is Vsell(P1) = v(p1 - P0), and the investors expected utility from holding the stock is Vhold(P1 Δ)= E[v(R2P1- P0) Δ]. The investor will hold the stock if and only if Vhold(P1 Δ) > Vsell(P1), which is equivalent to the belief shock Δ being greater than a threshold value Δ(P1). Thus, the investors expected selling probability can be calculated as Pr[Δ<Δ(P1)]. Figure 3, Panel A, plots this expected selling probability assuming the following calibrated parameter values: P0=1, μ=10%, σ = 25%, and σδ = 10%. Figures A.1 and A.2 are calibrated using preference parameters of α=.88, λ=2.25, and α=.50, λ=2.25, respectively. 41 I am extremely grateful to an anonymous reviewer for suggesting this reduced-form partial equilibrium model specification. 33

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41 Figure 1: Mean Announcement-Window Abnormal Returns for Portfolios Formed on Unexpected Earnings and Stockholders Capital Gains Overhang Panel A: Tests of a negative relation between announcement-window returns and stockholders CGO BHAR (-1,1) 5.00% 4.00% 3.00% 2.00% 1.00% 0.00% -1.00% -2.00% -3.00% -4.00% -5.00% Low UE 2 Low CGO High CGO 3 UE Quintile Panel B: Differences in announcement-window returns between low and high UE quintiles, by overhang spread CGO Quintiles Low UE High UE High Low UE Negative Spread Quintiles -2.50% 3.91% 6.41% Spread Quintiles -2.71% 3.27% 5.98% Difference (Spread Neg. Spread) -0.20% -0.64% -0.43% * This figure depicts mean three-day abnormal returns (BHAR (-1,1)) centered on earnings announcement dates, based on independent sorts of unexpected earnings (UE) and stockholders capital gains overhang (CGO). Each calendar quarter, announcements are independently sorted into quintiles of UE and CGO. Three-day buy-and-hold abnormal returns centered on the earnings announcement date (BHAR (-1,1)) are calculated relative to benchmark returns from the Fama-French-Momentum four-factor model (Carhart 1997). Panel A presents mean abnormal returns by CGO quintile, within each quintile of unexpected earnings (UE). Lighter colored left-hand bars represent lower quintiles of CGO and darker colored right-hand bars represent higher quintiles of CGO. Within each quintile of UE, I test the prediction that mean abnormal returns are decreasing in CGO by regressing BHAR (-1,1) on CGO quintile. *,**,, indicate (one-tailed) significance at the 10%, 5%, and 1% levels respectively based on two-way clustered standard errors, clustered by firm and event date. Panel B presents mean returns for low and high UE quintiles with the highest (positive) and lowest (negative) spreads in capital gains. Spread quintiles are extreme CGO quintiles with the same sign as UE (i.e. Low UE, Low CGO & High UE, High CGO). Negative spread quintiles are extreme CGO quintiles where CGO is news-contrarian (i.e. Low UE, High CGO & High UE, Low CGO). *,**,, indicate that differences in abnormal returns are statistically significant at the (two-tailed) 10%, 5%, and 1% levels respectively, based on twoway clustered standard errors, clustered by firm and event date. All variables are defined in Appendix A. 4 High UE 40

42 Figure 2: Mean 60-day Post-Announcement Abnormal Returns for Portfolios Formed on Unexpected Earnings and Stockholders Capital Gains Overhang Panel A: Tests of a positive relation between post-announcement returns and stockholders CGO BHAR (2,61) 4.00% 3.00% 2.00% 1.00% 0.00% -1.00% -2.00% -3.00% -4.00% -5.00% -6.00% -7.00% Low UE ** Low CGO High CGO UE Quintile ** High UE Panel B: Differences in post-announcement returns between low and high UE quintiles, by overhang spread CGO Quintiles Low UE High UE High Low UE Negative Spread Quintiles -0.83% 1.13% 1.96% Spread Quintiles -5.72% 2.61% 8.33% Difference (Spread Neg. Spread) -4.89% 1.48% ** 6.38% ** This figure depicts mean 60-day abnormal returns (BHAR (2,61)) following earnings announcements, based on independent sorts of unexpected earnings (UE) and stockholders capital gains overhang (CGO). Each calendar quarter, announcements are independently sorted into quintiles of UE and CGO. 60-day buy-and-hold abnormal returns beginning two days after the earnings announcement date (BHAR (2,60)) are calculated relative to benchmark returns from the Fama-French-Momentum four-factor model (Carhart 1997). Panel A presents mean abnormal returns by CGO quintile, within each quintile of unexpected earnings (UE). Lighter colored left-hand bars represent lower quintiles of CGO and darker colored right-hand bars represent higher quintiles of CGO. Within each quintile of UE, I test the prediction that mean abnormal returns are increasing in CGO by regressing BHAR (2,61) on CGO quintile. *,**,, indicate (one-tailed) significance at the 10%, 5%, and 1% levels respectively based on two-way clustered standard errors, clustered by firm and event date. Panel B presents mean returns for low and high UE quintiles with the highest (positive) and lowest (negative) spreads in capital gains. Spread quintiles are extreme CGO quintiles with the same sign as UE (i.e. Low UE, Low CGO & High UE, High CGO). Negative spread quintiles are extreme CGO quintiles where CGO is news-contrarian (i.e. Low UE, High CGO & High UE, Low CGO). *,**,, indicate that differences in abnormal returns are statistically significant at the (two-tailed) 10%, 5%, and 1% levels respectively, based on two-way clustered standard errors, clustered by firm and event date. All variables are defined in Appendix A. 41

43 Figure 3: Individual Investor Likelihood of Sale around Earnings Announcements Panel A: Expected relation between return since purchase and likelihood of sale derived from a reduced partial equilibrium model based on Li and Yang (2013) Panel B: Empirical relation between return since purchase and likelihood of sale around earnings announcements for Ancerno fund managers, unconditioned on the magnitude of earnings news 42

44 Figure 3 (Continued): Individual investor likelihood of sale around earnings announcements Panel C: Empirical relation between return since purchase and likelihood of sale around earnings announcements for Ancerno fund managers, conditioned on the magnitude of earnings news This figure depicts the expected and empirical relations between investors unrealized returns since purchase and their likelihood of selling a stock at the time when they experience a belief shock. Panel A presents illustrations of the expected relation between return since purchase and likelihood of sale derived from a reduced partial equilibrium model based on the general equilibrium model developed by Li and Yang (2013). The full model specification appears in Appendix B. Figures A.1 and A.2 are calibrated using preference parameters of α=.88, λ=2.25, and α=.50, λ=2.25, respectively. All other parameter calibrations are defined in Appendix B. Panel B presents the empirical relation between return since purchase and likelihood of sale around earnings announcements for Ancerno fund managers. The samples used in each chart include investor-stock-days for prior holding periods within the ranges specified above each chart. The chart samples correspond to the Ancerno samples described in Table 6. Green markers present the local average sales frequencies at return intervals of 5% (2.5% for <=100 days). Fitted curves are based on 3rd-degree polynomials fitted with separate parameters for positive and negative regions, with 95% confidence intervals shaded in grey. Panel C presents heat maps of the empirical relation between return since purchase and likelihood of announcement-window sale for Ancerno fund managers, conditional on absolute unexpected earnings. The y-axis (x-axis) of each figure denotes values of absolute unexpected earnings (returns since purchase). Lighter shaded regions correspond to higher estimated selling probabilities and darker shaded regions correspond to lower estimated selling probabilities. The colorbar to the right of each panel denotes the shading scale used to display estimated selling probabilities for each figure (i.e..08 corresponds to an 8.0% probability of selling). The surfaces plotted in Panel C are fit from the empirical data using the MATLAB gridfit package (D Errico (2006)). 43