Disagree with review paper behavioral finance năm 2024
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In this paper, we infer how the estimates of firm value by “optimists” and “pessimists” evolve in response to information shocks. Specifically, we examine returns and disagreement measures for portfolios of short-sale-constrained stocks that have experienced large gains or large losses. Our analysis suggests the presence of two groups, one of which overreacts to new information and remains biased over about 5 years, and a second group, which underreacts and whose expectations are unbiased after about 1 year. Our results have implications for the belief dynamics that underlie the momentum and long-term reversal effect. Show
Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online. Over the last several decades, financial economists have begun to carefully examine the consequences of disagreement or differences of opinion. In part, this attention has been motivated by large trading volumes in securities markets, which are difficult to explain without large levels of and changes in disagreement (see, e.g., Hong and Stein 2007). In this paper, we measure how the distribution of beliefs about security values evolves over time in response to information shocks. That is, we examine the dynamics of disagreement. When opinions differ regarding the value of a security, and investors can costlessly short-sell that security, the security price will reveal only the weighted mean of the distribution of beliefs, and nothing about the dispersion of agents’ beliefs. However, if a security becomes hard to borrow, then the price will reflect only the beliefs of the most optimistic agents (Miller 1977). Moreover, as we will show here, using the cost of borrowing we can learn about the dispersion of beliefs. For example, consider a constant absolute risk aversion (CARA)-normal framework with a single security that will pay an uncertain liquidating dividend |$\tilde D$| in one period. For simplicity, assume the risk-free rate is zero and that risk aversion is small (so that we can ignore risk premiums). Most importantly, assume only a fixed number of shares are available for lending, and any shares lent and sold cannot be rehypothecated. If a frictionless market exists for lending these shares, the cost of borrowing will be the cost that matches this (inelastic) supply with demand from pessimists who wish to borrow the shares for the purpose of short selling. In this setting, without disagreement, the price will equal the expected liquidating dividend (|$P = \mathbb{E}[\tilde D]$|), and both the short interest and the marginal lending fee will be zero. However, what if there is disagreement? First, assume there are two masses of investors A and B of equal measure and with equal risk aversion who disagree about the expected payoff. Specifically, assume |$\mathbb{E}_A[\tilde D] = \$30$| and |$\mathbb{E}_B[\tilde D] = \$20$|, where |$\mathbb{E}_i[\cdot]$| denotes the expectation of an investor of type |$i$|. If the number of shares available for borrowing is large, the security price will be the average of |$\mathbb{E}_A[\tilde D]$| and |$\mathbb{E}_B[\tilde D]$|: $25. Note also that if a “wisdom of crowds” effect is at work, meaning that the average across agents’ expectations is “rational” (i.e., that |$\mathbb{E}_{R}[\tilde D] = 0.5 \cdot \mathbb{E}_A[\tilde D]+ 0.5 \cdot \mathbb{E}_B[\tilde D]= \$25$|), then the expectation of the security price change over the period will be zero (since |$P=\mathbb{E}_{R}[\tilde D]$|). However, according to the Miller (1977) intuition, when the number of shares available for borrowing is small the price will reflect primarily the views of the most optimistic agents. In this example, as the number of shares available for borrowing approaches zero, the security price will approach |$\mathbb{E}_A[\tilde D]= \$30$|. Also, the borrowing cost will approach the difference in the agents’ valuations (|$\mathbb{E}_A[\tilde D] - \mathbb{E}_B[\tilde D]= \$10$|): the pessimistic agents in B will be willing to pay up to $10 to short a share they view as being overvalued by $10. Here, the rational expectation of the security price change will be |$-$|$5, so the optimistic agents in A earn a per-share expected payoff of |$-$|$5. However, the pessimistic agents (in B) who short the security also earn an expected payoff per share of |$-$|$5; they benefit from the $5/share expected price decline but are required to pay the $10/share borrow cost. Thus, an observer can unambiguously infer the beliefs of both optimists and pessimists from the price and the borrowing cost of the constrained stock.1 The objective of this paper is to extend this intuition to a multiperiod setting and bring it to the data. Specifically, we examine returns to portfolios of securities that have experienced either a large positive or a large negative price shock, presumably as a result of the arrival of new information about the security’s future payoffs. Moreover, motivated by the above toy model, we examine the returns of these portfolios, both when the securities in the portfolios are unconstrained, namely, when they can be borrowed at low cost, and when borrowing is costly. Consistent with the above example, this allows us to make inferences about how the distribution of beliefs of market participants evolves over time in response to these shocks. As a prelude to our main empirical tests, we first examine the returns to high- and low-past-return portfolios of unconstrained firms.2 Specifically, we classify firms as “winners” or “losers” based on their returns over the preceding 1 year, excluding the last month. We then examine the cumulative abnormal returns (CARs) for a period of 5 years following the point in time at which the firms are classified as winners or losers. The abnormal returns are relative to the value-weighted (VW) U.S. equity market benchmark generated by Kenneth French and taken from his data library. Panel A of Figure 1 plots the CARs for the past-winner and past-loser portfolios. It is not surprising that their CARs are roughly consistent with the momentum and reversal effects documented in the literature (see, e.g., Jegadeesh and Titman, 1993, 2001; DeBondt and Thaler, 1985): for the first 6–12 months there is some continuation of the past return, and in years 2–5 we observe some reversal of the initial return, at least for the past-loser portfolio. Figure 1 Returns following positive and negative price shocks We calculate abnormal returns for each portfolio for each holding month |$k$| by regressing the time series of month-|$k$| excess returns on the capital asset pricing model (CAPM)-MktRF factor. Returns are then cumulated and plotted for the past winner and past loser portfolios (dashed lines) in panel A. The universe is all U.S. common stocks listed on the NYSE, AMEX, or NASDAQ in the sample from January 1927 to June 2020. Winners are defined as the firms whose returns from 12 months to 1 month before the portfolio-formation date were in the top 30|$\%$| of all firms, and the past losers are the firms in the bottom 30|$\%$|. The universe for the solid lines consists of short-sale constrained stocks, meaning they are in the bottom 30|$\%$| of institutional ownership and the top 30|$\%$| of short interest. For the constrained losers, we additionally impose the condition that they have not been in the constrained-winner portfolio within the past 5 years, to isolate the long-run effects of winners and losers (see Section ). The time period for constrained stocks is May 1980 to June 2020. We add preformation abnormal returns in panel C. To focus on the differences after 12 months, we center CARs on |${t}=12$| in panel D. We obtain 95|$\%$| confidence intervals using bootstrapping (details in Internet Appendix B.III). In panel B of Figure 1, we first rescale the axes. Note that the dotted lines that represent the CARs of the unconstrained past-winner and loser portfolios are the same as in panel A, but rescaled. We add to panel B the CARs for high- and low-past-return portfolios, but which are formed using only stocks that are hard-to-borrow based on proxies we will describe below. The two sets of CAR plots suggest that limited predictability exhibited by the unconstrained past winners and losers becomes both far stronger and strikingly asymmetric. Specifically, as of the formation date the constrained past winners start to earn negative abnormal returns and continue doing so for 5 years postformation. The portfolio earns a compounded market-adjusted return of |$-13\%$| (|$t=-4.96$|) in the first 12 months postformation, and also earns a statistically significant negative alpha in each of the next 4 years, earning a compounded market-adjusted return over these 4 years of |$-42\%$| (|$t=-7.39$|).3 Like the portfolio of constrained past winners, the portfolio of constrained past losers also earns a strongly negative compounded market-adjusted return over the first 12 months postformation, specifically a return of |$-19\%$|. However, in contrast with the portfolio of constrained past winners, the negative abnormal returns do not persist: the abnormal return of this portfolio in each of the next 4 years postformation is never statistically different from zero, and over the full 4-year period (from 2–5 years postformation) the portfolios’ compounded market-adjusted return is |$5\%$| (|$t=0.44$|). Panel C extends the plot in panel B to include the abnormal returns in the formation period. Note the relative magnitudes of the preformation and the postformation returns, particularly for the constrained-winner portfolio. The difference in mispricing persistence between constrained past winners and losers is our key empirical finding, and we confirm this finding using a variety of different statistical tests (e.g., panel D centers postformation CARs on |$t=12$| and shows bootstrapped confidence intervals). Section reports the details of the empirical tests. We find similar differences in mispricing persistence out-of-sample in time (NYSE/AMEX stocks in the 1980s) and out-of-sample in regions (i.e., international firms). Internet Appendix E reports the results of these tests. Based on this difference in mispricing persistence and on the intuition coming from the toy model, one might be tempted to conclude that the disagreement persistence simply remains high for the constrained past winners out to 5 years postformation, while the disagreement is resolved more quickly for the constrained past losers. Interestingly, this asymmetry between constrained past losers and winners in return persistence is not mirrored in disagreement persistence. Panel A in Figure 2 plots the lending fee (from Markit) for our constrained past-winner and past-loser portfolios over the period from August 2004 through June 2020 for which we have borrow-cost data. Note that borrowing costs for the firms in our portfolios are high at portfolio formation and subsequently decline but remain elevated for about 5 years following both positive and negative shocks.4 Figure 2 Fees and disagreement following positive and negative price shocks Panel A plots the indicative lending fee from Markit in event time for the constrained winners and losers, as well as portfolios containing matched unconstrained stocks (see Section ). The Markit sample goes from August 2004 to June 2020. Panel B plots earnings forecast dispersion for portfolios independently sorted on past return (30|$\%$| breakpoints as above) and the 1-year change in dispersion of analyst earnings forecasts (|$\Delta FD$|) from IBES (quintiles, see Section ) among unconstrained stocks. 95|$\%$| confidence intervals are based on Newey-West standard errors. This pattern of long persistence in disagreement implied by the lending fees similarly crops up for unconstrained winners and losers if we look at disagreement proxies other than lending fees. Panel B shows the average dispersion of analysts’ earnings forecasts for unconstrained winners and losers that are additionally in the top quintile of changes in forecast dispersion over the formation period.5 We observe an increase in analyst disagreement preformation and a gradual decrease postformation, lasting about 5 years. In summary, we establish three empirical facts about short-sale constrained firms: (1) strong negative abnormal returns following positive price shocks that persist for about 5 years, (2) strong negative abnormal returns following negative price shocks that persist for about 1 year, and (3) strong disagreement following both positive and negative price shocks that persists for about 5 years. What do these empirical findings imply for the impulse responses of optimists’ and pessimists’ beliefs about firm values? Figure 3 illustrates the implications using stylized plots of impulse responses. The plots are generated from the model we will develop in Section . First, the strong, persistent negative abnormal returns following a positive price shock suggest the beliefs of the most optimistic agents are too optimistic at time 0 and decay towards rational beliefs over a roughly 5-year period (the upper green line in panel A of Figure 3). These optimistic agents appear to overreact to positive information that is part of the shock. Figure 3 Dynamics of beliefs and prices Panel A plots belief (i.e., the expectation of the single liquidating dividend of the risky asset) paths for overreacting (green) and underreacting (pink) agents, for positive and negative information shocks (at time |$t=0$|). The dotted lines represent rational expectations beliefs for those same shocks. The dashed blue line (labeled disagreement) plots the difference between the overreacting and underreacting agents’ beliefs. Panel B plots the resultant prices in unconstrained (dashed blue) and fully short-sale constrained (solid green and pink) markets. The dashed gray line represents the opinions of the sidelined agents. See Internet Appendix A for the details of the model and the parametrization that generates these belief and price paths. Second, the shorter-lived negative abnormal returns following the negative price shocks imply that, following these shocks, the beliefs of the most optimistic agents (the lower pink line in panel A of Figure 3) are also too optimistic, suggesting these agents initially underreact to the new negative information, but that this underreaction is resolved after only 1 year. Finally, the empirical finding that disagreement persists for about 5 years suggests the distance between the beliefs of optimists and pessimists decays toward zero over a period of about 5 years. In panel A of Figure 3, the blue line plots the level of disagreement coming out of our model, which is roughly consistent with what we see in panels A and B of Figure 2. Combined with the optimists’ beliefs inferred from prices that we plotted in Figure 3, panel B, the level of disagreement allows us to identify the pessimists’ beliefs, which are just the optimists’ beliefs minus the level of disagreement at that time. Figure 3, panel A, shows graphically that the implied impulse responses of the agents’ beliefs to the positive and negative shocks are symmetric, in the sense that the optimist’s/pessimist’s beliefs following a positive shock are the mirror image of the pessimist’s/optimist’s beliefs following a negative shock. What are the implications for the impulse response in prices that would be observed for unconstrained stocks in response to positive and negative price shocks? Again, relying loosely on the intuition from the simple two-type model above, the price would be the average of the beliefs, which would be the dashed blue line in panel B of Figure 3. These price paths are consistent with the large literature on momentum and subsequent long-term reversals, as discussed extensively in the behavioral literature and shown in panel A of Figure 1. One type of shock that we have not yet discussed is one that is not accompanied by an increase in disagreement. In practice, such unambiguous news shocks certainly exist, and firms that have experienced these shocks will enter both winner and loser portfolios. However, for our baseline analysis of short-sale constrained stocks, the fact that we are considering only high short interest securities should filter out most low-disagreement shocks. To the extent that our mechanism partly drives the momentum and long-term reversal effects for unconstrained stocks, these effects should be more muted for low-disagreement shocks. Consistent with this hypothesis, compelling evidence indicates that momentum is stronger in high-disagreement (Lee and Swaminathan 2000; Zhang 2006; Verardo 2009), and in low-quality or difficult-to-value information environments (Daniel and Titman 1999; Hong, Lim, and Stein 2000; Cohen and Lou 2012). In summary, this paper looks at constrained stocks to learn more about the dynamics of disagreement after large information shocks. High-energy physics provides a useful analogy to our exercise here: physics researchers examine the behavior of fundamental particles at high energies to test alternative models of particle interactions. By examining matter in extreme settings, they can pull apart the underlying components of these particles, leading to a deeper understanding of the structure that results in the behavior the we observe in more standard (low-energy) settings. Here, we examine “extreme” (constrained) securities in order to infer the distribution of beliefs that would otherwise be aggregated into the price. Results for the set of constrained stocks allow us to look at our existing models for unconstrained stocks from a new and different perspective that challenges existing models of momentum and long-term reversal, as these models are unable to explain the patterns for constrained and unconstrained stocks simultaneously. In Section , we briefly relate the empirical results to existing models and propose a new dynamic heterogeneous-agent model featuring overconfidence (Daniel, Hirshleifer, and Subrahmanyam 1998) and slow information diffusion (Hong and Stein 1999) that is able to both explain this asymmetry in mispricing persistence among short-sale constrained stocks, and to match momentum and long-term reversal effects for unconstrained stocks. 1. Related LiteratureMiller (1977) argues that when investors disagree about the expected return on a security, and when short selling of that security is restricted, the security will be overpriced. Subsequent empirical research has explored this argument in detail. Consistent with the divergence-of-opinion part of Miller’s argument, firms for which the dispersion of analysts’ forecasts is high earn low future stock returns (Danielsen and Sorescu 2001, Diether, Malloy, and Scherbina 2002). Moreover, the returns are still lower when disagreement is large and when short-sale constraits are binding (Boehme, Danielsen, and Sorescu 2006). These negative abnormal returns are concentrated around earnings announcements, consistent with the idea that earnings announcements at least partly resolve disagreement (Berkman et al. 2009). Shocks in the lending market have predictive power for future returns (Asquith, Pathak, and Ritter 2005, Cohen, Diether, and Malloy 2007). Finally, some evidence suggests long-short anomaly strategy profitability tends to be concentrated in the short leg, and in stocks that are expensive to short (Hirshleifer, Teoh, and Yu 2011; Stambaugh, Yu, and Yuan 2012; Drechsler and Drechsler 2016).6 D’Avolio (2002) and Geczy, Musto, and Reed (2002) are early papers that examine the stock-lending market using proprietary borrow-cost data. A major takeaway of these studies is that, at least historically, all but a small percentage of common stocks can be borrowed at low cost for short selling purposes. Kolasinski, Reed, and Ringgenberg (2013) argue the lending supply curve is almost perfectly elastic at low levels of demand, but above a certain level, it becomes highly inelastic. They argue that this structure is a result of some shareholders being willing to make their shares available for borrowing at any cost, but where, once this supply is exhausted, the search costs associated with finding additional shares increases rapidly. Data on borrowing costs are not always available and may not reflect the full set of costs associated with borrowing shares. However, a large literature has explored proxies for borrowing costs. We follow Asquith, Pathak, and Ritter (2005) who show that a combination of low institutional ownership and high short interest generally results in high borrowing costs. Our analysis of Markit reported lending fees confirms this finding. For a shorter subsample, we can calculate the Markit indicative and average lending fees and find that, among low institutional ownership firms, such fees are about three to five times higher for firms that also have high short interest at the same time, relative to firms with low short interest (see panel N of Table C.7 in the Internet Appendix). By contrast, using residual institutional ownership (Nagel 2005) leads to portfolios of firms for which the fee is substantially smaller, on average, even when focusing on high-short-interest firms (see Table C.8, panel N, in the Internet Appendix). The combined use of low institutional ownership and high short interest is also consistent with the model we present in Section , with the model in Blocher, Reed, and Van Wesep (2013), and with the empirical results reported in Asquith, Pathak, and Ritter (2005) and Cohen, Diether, and Malloy (2007). To our knowledge, no one in the literature has simultaneously analyzed past returns and disagreement proxies, as we do here, with the goal of analyzing the evolution of the dynamic response of disagreement to large information shocks. However, a few studies have reported longer-term returns of short-sale constrained stocks (Chen, Hong, and Stein 2002; Nagel 2005; Lamont 2012; Weitzner 2020). The results of these studies are broadly consistent with our hypotheses. Specifically, Nagel (2005) documents short-term overreaction to good cash flow news and short-term underreaction to bad cash flow news among stocks with low residual institutional ownership and that prices do not reverse over a 3-year period postformation. Our empirical approach is based on the premise that large disagreement shocks coincide with large price shocks. The approach has a natural link to theories of momentum (see, e.g., the model in Hong and Stein 2007). In Section , we point out that our empirical results are inconsistent with existing explanations (for a survey, see Subrahmanyam 2018) and with straightforward extensions of these explanations. We further present the intuition of a new model based on established behavioral concepts that provides a first explanation of the new evidence, and we relate this model to existing theoretical approaches. Our paper further speaks to the ongoing debate on whether bubbles are empirically identifiable. The empirical challenge in identifying asset pricing bubbles has been the lack of observability of the fundamental value, which leads to the joint hypothesis problem (Fama 1970). Recent work by Greenwood, Shleifer, and You (2019) shows sharp price increases of industries, along with certain characteristics of this run-up, help forecast the probability of crashes and thereby help identify and time a bubble. Our analysis of constrained winners adds to this strand of literature. Specifically for individual stocks, price run-ups paired with indications of limits to arbitrage strongly forecast low future returns. Our theoretical and empirical approach can be interpreted as a methodology for identifying individual stock bubbles, and determining the decay rates of these bubbles. 2. DataWe collect daily and monthly returns, market capitalizations, and trading volumes from the Center for Research in Security Prices (CRSP). Our sample consists of all common ordinary NYSE, AMEX, and NASDAQ stocks from May 1980 through June 2020.7 We form portfolios of these individual stocks at the start of each month |$t$| based on three firm-specific variables. The first sorting variable is each firm’s cumulative past return from month |$t-12$| through month |$t-2$|. Note that this cumulative return is the same as the measure of momentum used in Carhart (1997), Fama and French (2008), and numerous other studies. The second sorting variable is the institutional ownership ratio (IOR). Our measure of IOR is constructed using Thomson-Reuters Institutional 13-F filings through June 2013, and on WRDS-collected SEC data after June 2013.8 We calculate IOR as the ratio of the number of shares held by institutions, scaled by the number of shares outstanding from CRSP, lagged by one month.9 Our third sorting variable is the short-interest ratio (SIR), which we calculate as short interest scaled by the number of shares outstanding (from CRSP). Short interest comes from two sources: from April 1980 to May 1988, and after June 2003, we get short-interest data at the security level from Compustat.10 From June 1988 through June 2003, our short-interest data come directly from NYSE, AMEX and NASDAQ.11 However, prior to June 2003, if short-interest data from an exchange are missing for a given firm-month, we use short interest as reported by Compustat if available. After June 2003, if Compustat short-interest data are missing for a given firm-month, we use data from the exchanges if available.12 We merge quarterly book-equity data from Compustat with CRSP data using the linking table provided by CRSP. To calculate the monthly updated book-to-market ratio, we divide the most recently observed book value by the sum of the most recent market equity of all equity securities (PERMNOs) associated with the company (PERMCO). We assume that the book value of quarter |$q$| can be observed by investors at the time of the earnings announcement for quarter |$q$|. Our data on stock lending fees come from IHS Markit. These data start in August 2004.13 We use the indicative fee (a proxy for marginal costs) and simple average fee (equal-weighted average of all contracts for a particular security) averaged within a month to assess the cost of short selling. Analyst forecasts of fiscal-year-end earnings are from IBES. We use the summary file unadjusted for stock splits, to avoid the bias induced by ex post split adjustment, as pointed out by Diether, Malloy, and Scherbina (2002). Forecast dispersion (|$FD$|) is the standard deviation of fiscal year-end forecasts normalized by the absolute value of the mean forecast. We eliminate values for which the mean forecast is between |$-$|$0.1 and |$+$|$0.1 per share to avoid scaling by small numbers.14 3. Empirical ResultsIn this section, we analyze the short- and long-term price dynamics of short-sale-constrained stocks following large information shocks, with the goal of characterizing the evolution of beliefs following such shocks. Once again, the idea is that the price of a constrained security will reveal the beliefs of the optimistic agents. For the constrained winners, the beliefs will be those of the agents who became most optimistic following a positive information shock in the formation period, that is, those who overreacted to the information. In contrast, from the prices of the constrained losers, we can infer the beliefs of the agents who underreacted to the (negative) information shock in the formation period. To select stocks for which short-sale constraints are binding, we follow Asquith, Pathak, and Ritter (2005) and independently sort on IOR and SIR. This explicitly accounts for the supply and demand sides of the shorting market (see also Cohen, Diether, and Malloy 2007). IOR has been shown to be closely related to lending supply (see, e.g., D’Avolio 2002). Assuming, for example, that IOR is a direct proxy for easily available lending supply, and it is at 10|$\%$|, an SIR of 10|$\%$| would indicate that easily available supply is exhausted and short selling is likely constrained.15 IOR and SIR are available from 1980, giving us an approximately 40-year sample with which to measure long-term returns. Finally, to identify the shocks that drive disagreement, at the start of each month |$t$| we sort on each stock’s cumulative return from month |$t\!-\!12$| through month |$t\!-\!2$|.16 These returns incorporate all information that cause valuation changes, including the effect of the disagreement shocks. For all three sorts, namely, past return, SIR, and IOR, the breakpoints are the 30th and the 70th percentile. We use independent sorts to maximize independent variation in all three variables. This 3|$\times$|3|$\times$|3 sort provides us with 27 portfolios. Each portfolio is value weighted, both to avoid liquidity-related biases associated with equal-weighted portfolios (Asparouhova, Bessembinder, and Kalcheva 2013) and to ensure the effects that we document are not driven by extremely low market-capitalization stocks. We label as constrained the set of stocks that are simultaneously in the low IOR and the high SIR portfolio. We designate the firms with the highest past returns as the past winners (|$W$|), and those with the lowest past returns as the past losers (|$L$|). The firms that are simultaneously constrained and either past losers or past winners are labeled as constrained winners (|$W^*$|) and constrained losers (|$L^*$|), respectively. Furthermore, we want to make sure we do not confound results for our constrained-loser portfolio by unintentionally blending in former constrained winners that are in the process of falling.17 In the constrained-loser portfolio, we therefore only include those constrained losers that were not constrained winners at any point during the preceding 5 years.18 This subset of losers better reflects the return patterns of short-sale constrained stocks with initially negative news.19 3.1 CharacteristicsThe left two columns of Table 1, labeled |$W^*$| and |$L^*$|, report summary statistics for the constrained winner and loser portfolios, respectively.20 On average each month, 49 stocks are classified as constrained winners and 36 as constrained losers.21 The representative constrained winner stock has a market capitalization of $3 billion. Constrained losers are about half as big, on average. The formation-period returns are large in magnitude for the stocks in both portfolios: the average firm in the |$W^*$| portfolio almost doubles in size over the formation period, and the |$L^*$| portfolio almost halves. Table 1 Characteristics of constrained and matched portfolios |$W^{*}$||$L^{*}$||$W^{*,m}$||$L^{*,m}$|Number of stocks49364936Average market equity (B$)3.001.473.111.22Formation-period return (|$\%$|)82.36–47.3771.37–36.07Institutional ownership (IOR, |$\%$|)16.9117.5576.3374.40Change in IOR over preceding year (PP)1.18–5.069.120.95Short interest (SIR, |$\%$|)6.526.415.366.33Change in SIR over preceding year (PP)2.281.050.691.07Book-to-market ratio0.300.910.350.90Idiosyncratic volatility (|$\%$|, daily)3.043.952.112.69Turnover (|$\%$|)32.6428.2224.3623.51Change in turnover over preceding year (PP)15.951.865.161.65Ind. fee (|$\%$|)6.987.610.651.11Change in ind. fee over preceding year (PP)1.693.07–0.240.38Simple avg. fee (SAF, |$\%$|)5.266.590.431.08Change in SAF over preceding year (PP)0.673.16–0.220.39SIRIO (|$\%$|)100.3173.306.477.79Option volatility spread (|$\%$|)–5.47–6.34–0.96–1.04 |$W^{*}$||$L^{*}$||$W^{*,m}$||$L^{*,m}$|Number of stocks49364936Average market equity (B$)3.001.473.111.22Formation-period return (|$\%$|)82.36–47.3771.37–36.07Institutional ownership (IOR, |$\%$|)16.9117.5576.3374.40Change in IOR over preceding year (PP)1.18–5.069.120.95Short interest (SIR, |$\%$|)6.526.415.366.33Change in SIR over preceding year (PP)2.281.050.691.07Book-to-market ratio0.300.910.350.90Idiosyncratic volatility (|$\%$|, daily)3.043.952.112.69Turnover (|$\%$|)32.6428.2224.3623.51Change in turnover over preceding year (PP)15.951.865.161.65Ind. fee (|$\%$|)6.987.610.651.11Change in ind. fee over preceding year (PP)1.693.07–0.240.38Simple avg. fee (SAF, |$\%$|)5.266.590.431.08Change in SAF over preceding year (PP)0.673.16–0.220.39SIRIO (|$\%$|)100.3173.306.477.79Option volatility spread (|$\%$|)–5.47–6.34–0.96–1.04 This table shows time-series averages of value-weighted mean characteristics of the portfolios in the month of portfolio formation. Shown are the average number of stocks, the average market equity (in billion U.S. dollars), return from month t-12 to the end of month t-2 (in |$\%$|), level of short interest 2 weeks prior to formation (in |$\%$|), and change from 11.5 months ago to 2 weeks ago (in PP), institutional ownership (in |$\%$| of number of shares outstanding) and its change over the preceding year (in PP), the ratio of book equity of the most recently observed fiscal year to last month’s market equity, the average standard deviation of daily idiosyncratic returns in each portfolio (daily, in |$\%$|) over the month prior to formation (Ang et al. 2006), levels (in |$\%$|) and changes (in PP) over the preceding 12 months in monthly turnover, the level (in |$\%$|, annualized) and change (in PP, over the preceding 12 months) in the Markit indicative as well as simple average loan fee, the ratio of short interest to institutional ownership (SIRIO) as in Drechsler and Drechsler (2016) (in |$\%$|), and last, the open-interest weighted average of differences in implied volatilities between matched put and call option pairs at month-end (in |$\%$|), as in Cremers and Weinbaum (2010). The sample period is April 1985 (to account for the 5-year lookback period for losers that were not constrained winners before) to June 2020, except for Markit data, which are available from August 2004. For a comparison with the broader universe of stocks, see the averages for the remaining portfolios displayed in Table C.7 in Internet Appendix C.V. Table 1 Characteristics of constrained and matched portfolios |$W^{*}$||$L^{*}$||$W^{*,m}$||$L^{*,m}$|Number of stocks49364936Average market equity (B$)3.001.473.111.22Formation-period return (|$\%$|)82.36–47.3771.37–36.07Institutional ownership (IOR, |$\%$|)16.9117.5576.3374.40Change in IOR over preceding year (PP)1.18–5.069.120.95Short interest (SIR, |$\%$|)6.526.415.366.33Change in SIR over preceding year (PP)2.281.050.691.07Book-to-market ratio0.300.910.350.90Idiosyncratic volatility (|$\%$|, daily)3.043.952.112.69Turnover (|$\%$|)32.6428.2224.3623.51Change in turnover over preceding year (PP)15.951.865.161.65Ind. fee (|$\%$|)6.987.610.651.11Change in ind. fee over preceding year (PP)1.693.07–0.240.38Simple avg. fee (SAF, |$\%$|)5.266.590.431.08Change in SAF over preceding year (PP)0.673.16–0.220.39SIRIO (|$\%$|)100.3173.306.477.79Option volatility spread (|$\%$|)–5.47–6.34–0.96–1.04 |$W^{*}$||$L^{*}$||$W^{*,m}$||$L^{*,m}$|Number of stocks49364936Average market equity (B$)3.001.473.111.22Formation-period return (|$\%$|)82.36–47.3771.37–36.07Institutional ownership (IOR, |$\%$|)16.9117.5576.3374.40Change in IOR over preceding year (PP)1.18–5.069.120.95Short interest (SIR, |$\%$|)6.526.415.366.33Change in SIR over preceding year (PP)2.281.050.691.07Book-to-market ratio0.300.910.350.90Idiosyncratic volatility (|$\%$|, daily)3.043.952.112.69Turnover (|$\%$|)32.6428.2224.3623.51Change in turnover over preceding year (PP)15.951.865.161.65Ind. fee (|$\%$|)6.987.610.651.11Change in ind. fee over preceding year (PP)1.693.07–0.240.38Simple avg. fee (SAF, |$\%$|)5.266.590.431.08Change in SAF over preceding year (PP)0.673.16–0.220.39SIRIO (|$\%$|)100.3173.306.477.79Option volatility spread (|$\%$|)–5.47–6.34–0.96–1.04 This table shows time-series averages of value-weighted mean characteristics of the portfolios in the month of portfolio formation. Shown are the average number of stocks, the average market equity (in billion U.S. dollars), return from month t-12 to the end of month t-2 (in |$\%$|), level of short interest 2 weeks prior to formation (in |$\%$|), and change from 11.5 months ago to 2 weeks ago (in PP), institutional ownership (in |$\%$| of number of shares outstanding) and its change over the preceding year (in PP), the ratio of book equity of the most recently observed fiscal year to last month’s market equity, the average standard deviation of daily idiosyncratic returns in each portfolio (daily, in |$\%$|) over the month prior to formation (Ang et al. 2006), levels (in |$\%$|) and changes (in PP) over the preceding 12 months in monthly turnover, the level (in |$\%$|, annualized) and change (in PP, over the preceding 12 months) in the Markit indicative as well as simple average loan fee, the ratio of short interest to institutional ownership (SIRIO) as in Drechsler and Drechsler (2016) (in |$\%$|), and last, the open-interest weighted average of differences in implied volatilities between matched put and call option pairs at month-end (in |$\%$|), as in Cremers and Weinbaum (2010). The sample period is April 1985 (to account for the 5-year lookback period for losers that were not constrained winners before) to June 2020, except for Markit data, which are available from August 2004. For a comparison with the broader universe of stocks, see the averages for the remaining portfolios displayed in Table C.7 in Internet Appendix C.V. SIR is close to IOR for the stocks in the constrained portfolios, indicating a good chance of these stocks being hard to borrow. On average, the constrained stocks in both |$W^*$| and |$L^*$| have high idiosyncratic volatilities and high turnovers, consistent with disagreement among traders. To check whether we have accurately identified stocks with binding short-sale constraints, we calculate the level and 12-month changes of the Markit indicative and simple average loan fee over the time period for which we have these data. The fees in the constrained portfolios are large, and they have generally increased leading up to the formation date, suggesting a high and increased level of disagreement.22 Because the Markit data are only available from 2004, we calculate two additional measures for the full sample period going back to 1980. The first one is SIRIO, that is, the number of shares sold short (short interest), divided by the number of shares held by institutions (institutional ownership), following Drechsler and Drechsler (2016). These summary statistics also suggest this combination of low IOR and high SIR successfully identifies constrained firms. On average, constrained winners exhibit a SIRIO of 100.31|$\%$|, which likely pushes them above the point of cheap lending and makes short selling these stocks highly expensive. For the firms and dates for which options data are available, we calculate the option volatility spread (Cremers and Weinbaum 2010), defined as the difference in annualized implied volatilities between at-the-money, 1- to 12-month-to-maturity put and call options. Note that if the volatility spread is negative, put-call parity will be violated in the sense that the price of an actual share will be higher than the price of a synthetic share (constructed using a bond, put, and call). Such a violation would indicate that arbitraging this put-call parity violation is costly, likely because borrowing and shorting the underlying stock is costly (Ofek, Richardson, and Whitelaw 2004). Note both constrained portfolios have large negative volatility spreads, consistent with the other data, suggesting that shorting the stocks in the |$W^*$| and |$L^*$| portfolios is costly. 3.2 Strategy performance over different horizonsNext, we will examine trading strategy returns at horizons from 1 to 5 years after portfolio formation. Our 1-year trading strategy, like that of Jegadeesh and Titman (1993), purchases at the start of each month $1 worth of the new (value-weighted) |$W_t^*$| or |$L_t^*$| portfolio, holds that portfolio for the following |$T=12$| months, and then sells it. Thus the short-horizon (S, 1 year) strategy |$W^{*}_{\rm S}$|, at the start of month |$t$| just after trading, consists of $1 of the newest |$W_t^*$| portfolio, plus some amount of each of the last eleven |$W^*$| portfolios formed in months |$t\!-\!11$| through |$t\!-\!1$|. In contrast to Jegadeesh and Titman (1993), we weight each of these additional 11 portfolios by their cumulated dollar value, meaning we do not rebalance the invested amount until they are sold at |$T$| (here, |$T\!=\!12$|) months.23 Thus, the construction of our one-year strategy is consistent with the calendar-time portfolio approach advocated by Fama (1998). Note that we can assess the performance of these strategies with standard asset pricing tests applied to the monthly strategy returns, and these tests will summarize the portfolios’ forecastable performance for the first year postformation, much like the event-study plots in Figure 1, but without the econometric issues typically associated with studies of CARs (Barber and Lyon 1996; Fama 1998). The first three columns of Table 2 display summary statistics for the returns of the 1-year strategies (the remaining columns present results for matched-firm strategies, which we discuss in Section ). Panel A shows the raw average monthly excess returns, the number of months in the sample (T), the average number of unique stocks in the strategy in any given month (AvgN), and the realized annualized strategy Sharpe ratio (SR). Table 2 Short-horizon (S, 1-year) performance of constrained and matched portfolios |$W^{*}_{\rm S}$||$L^{*}_{\rm S}$||$W^{*}_{\rm S}$|-|$L^{*}_{\rm S}$||$W^{*,m}_{\rm S}$||$L^{*,m}_{\rm S}$||$W^{*,m}_{\rm S}$|-|$L^{*,m}_{\rm S}$||$W^{*}_{\rm S}$|-|$W^{*,m}_{\rm S}$||$L^{*}_{\rm S}$|-|$L^{*,m}_{\rm S}$||${\it DiD}$|A. Raw excess returnsAverage–0.18–0.900.730.940.830.11–1.12–1.740.62 (–0.54)(–1.81)(2.00)(3.47)(2.04)(0.43)(–4.38)(–4.60)(1.80)No. of months411411411411411411411411411AvgN188106 262203 SR–0.0760–0.30760.35280.50960.36760.0772–0.7663–0.87280.3160B. CAPM regressionsIntercept–1.07–1.890.820.14–0.100.24–1.21–1.790.58 (–4.28)(–5.55)(2.27)(0.85)(–0.36)(0.98)(–4.52)(–4.67)(1.70)MktRF1.371.51–0.141.231.43–0.200.140.080.06 (14.94)(11.97)(–1.02)(30.36)(12.76)(–1.56)(1.57)(0.61)(0.63)|$R^2$|.5783.4432.0081.7393.6643.0343.0145.0026.0014IR–0.7096–0.86370.40000.1458–0.07740.1739–0.8334–0.90000.2970C. Four-factor regressionsIntercept–0.95–1.370.420.090.21–0.12–1.04–1.580.54 (–4.07)(–3.96)(1.20)(0.73)(1.29)(–0.65)(–3.79)(–3.94)(1.50)MktRF1.171.160.011.151.22–0.070.02–0.050.08 (17.18)(16.01)(0.11)(30.60)(39.35)(–1.44)(0.28)(–0.71)(0.94)HML–0.31–0.10–0.21–0.040.46–0.50–0.28–0.560.29 (–2.73)(–0.64)(–1.27)(–0.55)(4.22)(–4.60)(–1.76)(–2.62)(2.00)SMB1.001.22–0.220.680.96–0.280.320.250.07 (11.63)(8.09)(–1.41)(8.27)(17.40)(–3.15)(2.68)(1.57)(0.45)MOM0.01–0.630.640.17–0.470.64–0.16–0.160.00 (0.09)(–5.18)(5.04)(4.09)(–4.38)(5.85)(–1.51)(–0.85)(0.02)|$R^2$|.7505.6365.1942.8645.8844.5551.0932.0801.0163IR–0.8177–0.77490.22810.13210.2711–0.1276–0.7470–0.82760.2788 |$W^{*}_{\rm S}$||$L^{*}_{\rm S}$||$W^{*}_{\rm S}$|-|$L^{*}_{\rm S}$||$W^{*,m}_{\rm S}$||$L^{*,m}_{\rm S}$||$W^{*,m}_{\rm S}$|-|$L^{*,m}_{\rm S}$||$W^{*}_{\rm S}$|-|$W^{*,m}_{\rm S}$||$L^{*}_{\rm S}$|-|$L^{*,m}_{\rm S}$||${\it DiD}$|A. Raw excess returnsAverage–0.18–0.900.730.940.830.11–1.12–1.740.62 (–0.54)(–1.81)(2.00)(3.47)(2.04)(0.43)(–4.38)(–4.60)(1.80)No. of months411411411411411411411411411AvgN188106 262203 SR–0.0760–0.30760.35280.50960.36760.0772–0.7663–0.87280.3160B. CAPM regressionsIntercept–1.07–1.890.820.14–0.100.24–1.21–1.790.58 (–4.28)(–5.55)(2.27)(0.85)(–0.36)(0.98)(–4.52)(–4.67)(1.70)MktRF1.371.51–0.141.231.43–0.200.140.080.06 (14.94)(11.97)(–1.02)(30.36)(12.76)(–1.56)(1.57)(0.61)(0.63)|$R^2$|.5783.4432.0081.7393.6643.0343.0145.0026.0014IR–0.7096–0.86370.40000.1458–0.07740.1739–0.8334–0.90000.2970C. Four-factor regressionsIntercept–0.95–1.370.420.090.21–0.12–1.04–1.580.54 (–4.07)(–3.96)(1.20)(0.73)(1.29)(–0.65)(–3.79)(–3.94)(1.50)MktRF1.171.160.011.151.22–0.070.02–0.050.08 (17.18)(16.01)(0.11)(30.60)(39.35)(–1.44)(0.28)(–0.71)(0.94)HML–0.31–0.10–0.21–0.040.46–0.50–0.28–0.560.29 (–2.73)(–0.64)(–1.27)(–0.55)(4.22)(–4.60)(–1.76)(–2.62)(2.00)SMB1.001.22–0.220.680.96–0.280.320.250.07 (11.63)(8.09)(–1.41)(8.27)(17.40)(–3.15)(2.68)(1.57)(0.45)MOM0.01–0.630.640.17–0.470.64–0.16–0.160.00 (0.09)(–5.18)(5.04)(4.09)(–4.38)(5.85)(–1.51)(–0.85)(0.02)|$R^2$|.7505.6365.1942.8645.8844.5551.0932.0801.0163IR–0.8177–0.77490.22810.13210.2711–0.1276–0.7470–0.82760.2788 This table shows average monthly excess returns (in |$\%$|, panel A) as well as results from CAPM (panel B) and Fama-French-Carhart four-factor regressions (panel C) for short-horizon (1 year) buy-and-hold strategies of constrained winners, constrained losers, and their matched counterparts, as described in the text, as well as their differences. |${\it DiD}$| is the difference-in-differences, namely, |$(W^{*}_{\rm S}-W^{*,m}_{\rm S})-(L^{*}_{\rm S}-L^{*,m}_{\rm S})$|. Newey and West (1987)|$t$|-statistics are shown in parentheses. AvgN is the average number of unique stocks in the portfolio. The row labeled SR displays the Sharpe ratios and IR the information ratios. The sample period is May 1980 to June 2020. The first return is calculated in April 1986; that is, the first time we invested 12 times in a row and had the chance to see whether a constrained loser had been a constrained winner over the previous 5 years. Table 2 Short-horizon (S, 1-year) performance of constrained and matched portfolios |$W^{*}_{\rm S}$||$L^{*}_{\rm S}$||$W^{*}_{\rm S}$|-|$L^{*}_{\rm S}$||$W^{*,m}_{\rm S}$||$L^{*,m}_{\rm S}$||$W^{*,m}_{\rm S}$|-|$L^{*,m}_{\rm S}$||$W^{*}_{\rm S}$|-|$W^{*,m}_{\rm S}$||$L^{*}_{\rm S}$|-|$L^{*,m}_{\rm S}$||${\it DiD}$|A. Raw excess returnsAverage–0.18–0.900.730.940.830.11–1.12–1.740.62 (–0.54)(–1.81)(2.00)(3.47)(2.04)(0.43)(–4.38)(–4.60)(1.80)No. of months411411411411411411411411411AvgN188106 262203 SR–0.0760–0.30760.35280.50960.36760.0772–0.7663–0.87280.3160B. CAPM regressionsIntercept–1.07–1.890.820.14–0.100.24–1.21–1.790.58 (–4.28)(–5.55)(2.27)(0.85)(–0.36)(0.98)(–4.52)(–4.67)(1.70)MktRF1.371.51–0.141.231.43–0.200.140.080.06 (14.94)(11.97)(–1.02)(30.36)(12.76)(–1.56)(1.57)(0.61)(0.63)|$R^2$|.5783.4432.0081.7393.6643.0343.0145.0026.0014IR–0.7096–0.86370.40000.1458–0.07740.1739–0.8334–0.90000.2970C. Four-factor regressionsIntercept–0.95–1.370.420.090.21–0.12–1.04–1.580.54 (–4.07)(–3.96)(1.20)(0.73)(1.29)(–0.65)(–3.79)(–3.94)(1.50)MktRF1.171.160.011.151.22–0.070.02–0.050.08 (17.18)(16.01)(0.11)(30.60)(39.35)(–1.44)(0.28)(–0.71)(0.94)HML–0.31–0.10–0.21–0.040.46–0.50–0.28–0.560.29 (–2.73)(–0.64)(–1.27)(–0.55)(4.22)(–4.60)(–1.76)(–2.62)(2.00)SMB1.001.22–0.220.680.96–0.280.320.250.07 (11.63)(8.09)(–1.41)(8.27)(17.40)(–3.15)(2.68)(1.57)(0.45)MOM0.01–0.630.640.17–0.470.64–0.16–0.160.00 (0.09)(–5.18)(5.04)(4.09)(–4.38)(5.85)(–1.51)(–0.85)(0.02)|$R^2$|.7505.6365.1942.8645.8844.5551.0932.0801.0163IR–0.8177–0.77490.22810.13210.2711–0.1276–0.7470–0.82760.2788 |$W^{*}_{\rm S}$||$L^{*}_{\rm S}$||$W^{*}_{\rm S}$|-|$L^{*}_{\rm S}$||$W^{*,m}_{\rm S}$||$L^{*,m}_{\rm S}$||$W^{*,m}_{\rm S}$|-|$L^{*,m}_{\rm S}$||$W^{*}_{\rm S}$|-|$W^{*,m}_{\rm S}$||$L^{*}_{\rm S}$|-|$L^{*,m}_{\rm S}$||${\it DiD}$|A. Raw excess returnsAverage–0.18–0.900.730.940.830.11–1.12–1.740.62 (–0.54)(–1.81)(2.00)(3.47)(2.04)(0.43)(–4.38)(–4.60)(1.80)No. of months411411411411411411411411411AvgN188106 262203 SR–0.0760–0.30760.35280.50960.36760.0772–0.7663–0.87280.3160B. CAPM regressionsIntercept–1.07–1.890.820.14–0.100.24–1.21–1.790.58 (–4.28)(–5.55)(2.27)(0.85)(–0.36)(0.98)(–4.52)(–4.67)(1.70)MktRF1.371.51–0.141.231.43–0.200.140.080.06 (14.94)(11.97)(–1.02)(30.36)(12.76)(–1.56)(1.57)(0.61)(0.63)|$R^2$|.5783.4432.0081.7393.6643.0343.0145.0026.0014IR–0.7096–0.86370.40000.1458–0.07740.1739–0.8334–0.90000.2970C. Four-factor regressionsIntercept–0.95–1.370.420.090.21–0.12–1.04–1.580.54 (–4.07)(–3.96)(1.20)(0.73)(1.29)(–0.65)(–3.79)(–3.94)(1.50)MktRF1.171.160.011.151.22–0.070.02–0.050.08 (17.18)(16.01)(0.11)(30.60)(39.35)(–1.44)(0.28)(–0.71)(0.94)HML–0.31–0.10–0.21–0.040.46–0.50–0.28–0.560.29 (–2.73)(–0.64)(–1.27)(–0.55)(4.22)(–4.60)(–1.76)(–2.62)(2.00)SMB1.001.22–0.220.680.96–0.280.320.250.07 (11.63)(8.09)(–1.41)(8.27)(17.40)(–3.15)(2.68)(1.57)(0.45)MOM0.01–0.630.640.17–0.470.64–0.16–0.160.00 (0.09)(–5.18)(5.04)(4.09)(–4.38)(5.85)(–1.51)(–0.85)(0.02)|$R^2$|.7505.6365.1942.8645.8844.5551.0932.0801.0163IR–0.8177–0.77490.22810.13210.2711–0.1276–0.7470–0.82760.2788 This table shows average monthly excess returns (in |$\%$|, panel A) as well as results from CAPM (panel B) and Fama-French-Carhart four-factor regressions (panel C) for short-horizon (1 year) buy-and-hold strategies of constrained winners, constrained losers, and their matched counterparts, as described in the text, as well as their differences. |${\it DiD}$| is the difference-in-differences, namely, |$(W^{*}_{\rm S}-W^{*,m}_{\rm S})-(L^{*}_{\rm S}-L^{*,m}_{\rm S})$|. Newey and West (1987)|$t$|-statistics are shown in parentheses. AvgN is the average number of unique stocks in the portfolio. The row labeled SR displays the Sharpe ratios and IR the information ratios. The sample period is May 1980 to June 2020. The first return is calculated in April 1986; that is, the first time we invested 12 times in a row and had the chance to see whether a constrained loser had been a constrained winner over the previous 5 years. The short-horizon constrained-loser (|$L^{*}_{\rm S}$|) and -winner (|$W^{*}_{\rm S}$|) strategies both exhibit negative excess returns (panel A) and negative alphas relative to CAPM and Fama-French-Carhart four-factor model benchmarks (panels B and C).24 These negative alphas suggest that, following both positive and negative information shocks, the marginal investors (i.e., the most optimistic agents) are too optimistic initially, but revise their beliefs downward over the first year following the information shock. Panel B of Figure 1 suggests that the predictable negative abnormal returns of the constrained-winner (|$W^*$|) portfolios persist longer than the negative abnormal returns of the constrained-loser stocks (|$L^*$|). To assess the statistical significance of the differences in persistence of the negative abnormal returns, we next focus on years 2 through 5 postformation. We now form long-horizon (L, years 2–5) strategies |$W^{*}_{\rm L}$| and |$L^{*}_{\rm L}$|, like the short-horizon (1 year) strategies described above, but which now hold the |$W^{*}$| and |$L^{*}$| portfolios formed in months |$t-59$| to |$t-12$|; that is, we skip the most recent year and hold the 48 portfolios from the preceding 4 years.25 Table 3 presents the results of this analysis. The average number of unique stocks held in the strategy is quite large now: on average, |$417$| unique stocks are classified as constrained winners in at least one month between 2 and 5 years prior to strategy formation.26 Panel A presents raw excess returns and Sharpe ratios, and panels B and C present CAPM and four-factor alphas, respectively, for the strategies. Strikingly, whereas the constrained-loser strategy has positive alphas over this period, the constrained-winner strategy significantly underperforms relative to both benchmarks; the monthly four-factor alpha is |$-0.62$||$\%$| (|$t = -4.93)$|.27 The difference in the monthly four-factor alphas of |$W^{*}_{\rm L}$| and |$L^{*}_{\rm L}$| is |$-0.88$||$\%$||$(t=-4.33)$|.28 Table 3 Long-horizon (L, 2- to 5-year) strategy performance for constrained and matched portfolios |$W^{*}_{\rm L}$||$L^{*}_{\rm L}$||$W^{*}_{\rm L}$|-|$L^{*}_{\rm L}$||$W^{*,m}_{\rm L}$||$L^{*,m}_{\rm L}$||$W^{*,m}_{\rm L}$|-|$L^{*,m}_{\rm L}$||$W^{*}_{\rm L}$|-|$W^{*,m}_{\rm L}$||$L^{*}_{\rm L}$|-|$L^{*,m}_{\rm L}$||${\it DiD}$|A. Raw excess returnsAverage0.231.03–0.801.010.830.18–0.780.20–0.98 (0.66)(2.81)(–3.87)(3.69)(3.01)(1.58)(–4.88)(1.01)(–6.38)No. of months363363363363363363363363363AvgN417203 621461 SR0.10940.4849–0.60610.58480.46280.2941–0.72630.1694–0.7450B. CAPM regressionsIntercept–0.740.14–0.870.17–0.030.20–0.900.17–1.07 (–3.61)(0.59)(–4.34)(1.30)(–0.20)(1.72)(–5.39)(0.89)(–5.76)MktRF1.431.320.111.251.27–0.020.180.050.14 (19.51)(17.57)(1.26)(29.01)(30.90)(–0.48)(3.03)(0.70)(1.72)|$R^2$|.7016.6029.0115.8197.7893.0021.0458.0025.0166IR–0.62800.1039–0.66780.2255–0.03730.3192–0.86190.1427–0.8215C. Four-factor regressionsIntercept–0.620.26–0.880.14–0.050.19–0.760.31–1.07 (–4.93)(1.20)(–4.33)(1.53)(–0.52)(2.20)(–5.29)(1.38)(–5.24)MktRF1.251.130.131.171.150.010.08–0.030.11 (18.03)(22.15)(1.64)(42.36)(35.76)(0.41)(1.21)(–0.45)(1.39)HML–0.280.11–0.39–0.170.17–0.34–0.11–0.06–0.04 (–5.08)(1.56)(–4.99)(–3.78)(3.66)(–7.28)(–1.16)(–0.60)(–0.59)SMB0.740.88–0.140.510.79–0.280.220.090.14 (8.87)(12.29)(–1.73)(13.06)(18.48)(–6.17)(2.59)(1.14)(1.43)MOM–0.08–0.140.060.080.040.05–0.16–0.180.02 (–1.29)(–2.44)(0.64)(3.55)(1.84)(2.11)(–3.04)(–2.18)(0.16)|$R^2$|.8190.7352.0893.9159.9360.3511.1183.0410.0277IR–0.68480.2342–0.70080.2790–0.11460.3871–0.76060.2641–0.8277 |$W^{*}_{\rm L}$||$L^{*}_{\rm L}$||$W^{*}_{\rm L}$|-|$L^{*}_{\rm L}$||$W^{*,m}_{\rm L}$||$L^{*,m}_{\rm L}$||$W^{*,m}_{\rm L}$|-|$L^{*,m}_{\rm L}$||$W^{*}_{\rm L}$|-|$W^{*,m}_{\rm L}$||$L^{*}_{\rm L}$|-|$L^{*,m}_{\rm L}$||${\it DiD}$|A. Raw excess returnsAverage0.231.03–0.801.010.830.18–0.780.20–0.98 (0.66)(2.81)(–3.87)(3.69)(3.01)(1.58)(–4.88)(1.01)(–6.38)No. of months363363363363363363363363363AvgN417203 621461 SR0.10940.4849–0.60610.58480.46280.2941–0.72630.1694–0.7450B. CAPM regressionsIntercept–0.740.14–0.870.17–0.030.20–0.900.17–1.07 (–3.61)(0.59)(–4.34)(1.30)(–0.20)(1.72)(–5.39)(0.89)(–5.76)MktRF1.431.320.111.251.27–0.020.180.050.14 (19.51)(17.57)(1.26)(29.01)(30.90)(–0.48)(3.03)(0.70)(1.72)|$R^2$|.7016.6029.0115.8197.7893.0021.0458.0025.0166IR–0.62800.1039–0.66780.2255–0.03730.3192–0.86190.1427–0.8215C. Four-factor regressionsIntercept–0.620.26–0.880.14–0.050.19–0.760.31–1.07 (–4.93)(1.20)(–4.33)(1.53)(–0.52)(2.20)(–5.29)(1.38)(–5.24)MktRF1.251.130.131.171.150.010.08–0.030.11 (18.03)(22.15)(1.64)(42.36)(35.76)(0.41)(1.21)(–0.45)(1.39)HML–0.280.11–0.39–0.170.17–0.34–0.11–0.06–0.04 (–5.08)(1.56)(–4.99)(–3.78)(3.66)(–7.28)(–1.16)(–0.60)(–0.59)SMB0.740.88–0.140.510.79–0.280.220.090.14 (8.87)(12.29)(–1.73)(13.06)(18.48)(–6.17)(2.59)(1.14)(1.43)MOM–0.08–0.140.060.080.040.05–0.16–0.180.02 (–1.29)(–2.44)(0.64)(3.55)(1.84)(2.11)(–3.04)(–2.18)(0.16)|$R^2$|.8190.7352.0893.9159.9360.3511.1183.0410.0277IR–0.68480.2342–0.70080.2790–0.11460.3871–0.76060.2641–0.8277 See caption to Table 2. The only difference here is that we hold stocks that were allocated to one of the portfolios at some point during months |$\{t-60,...,t-13\}$| before formation. The first monthly return is calculated in April 1990, that is, the first time we invested 48 times in a row. Table 3 Long-horizon (L, 2- to 5-year) strategy performance for constrained and matched portfolios |$W^{*}_{\rm L}$||$L^{*}_{\rm L}$||$W^{*}_{\rm L}$|-|$L^{*}_{\rm L}$||$W^{*,m}_{\rm L}$||$L^{*,m}_{\rm L}$||$W^{*,m}_{\rm L}$|-|$L^{*,m}_{\rm L}$||$W^{*}_{\rm L}$|-|$W^{*,m}_{\rm L}$||$L^{*}_{\rm L}$|-|$L^{*,m}_{\rm L}$||${\it DiD}$|A. Raw excess returnsAverage0.231.03–0.801.010.830.18–0.780.20–0.98 (0.66)(2.81)(–3.87)(3.69)(3.01)(1.58)(–4.88)(1.01)(–6.38)No. of months363363363363363363363363363AvgN417203 621461 SR0.10940.4849–0.60610.58480.46280.2941–0.72630.1694–0.7450B. CAPM regressionsIntercept–0.740.14–0.870.17–0.030.20–0.900.17–1.07 (–3.61)(0.59)(–4.34)(1.30)(–0.20)(1.72)(–5.39)(0.89)(–5.76)MktRF1.431.320.111.251.27–0.020.180.050.14 (19.51)(17.57)(1.26)(29.01)(30.90)(–0.48)(3.03)(0.70)(1.72)|$R^2$|.7016.6029.0115.8197.7893.0021.0458.0025.0166IR–0.62800.1039–0.66780.2255–0.03730.3192–0.86190.1427–0.8215C. Four-factor regressionsIntercept–0.620.26–0.880.14–0.050.19–0.760.31–1.07 (–4.93)(1.20)(–4.33)(1.53)(–0.52)(2.20)(–5.29)(1.38)(–5.24)MktRF1.251.130.131.171.150.010.08–0.030.11 (18.03)(22.15)(1.64)(42.36)(35.76)(0.41)(1.21)(–0.45)(1.39)HML–0.280.11–0.39–0.170.17–0.34–0.11–0.06–0.04 (–5.08)(1.56)(–4.99)(–3.78)(3.66)(–7.28)(–1.16)(–0.60)(–0.59)SMB0.740.88–0.140.510.79–0.280.220.090.14 (8.87)(12.29)(–1.73)(13.06)(18.48)(–6.17)(2.59)(1.14)(1.43)MOM–0.08–0.140.060.080.040.05–0.16–0.180.02 (–1.29)(–2.44)(0.64)(3.55)(1.84)(2.11)(–3.04)(–2.18)(0.16)|$R^2$|.8190.7352.0893.9159.9360.3511.1183.0410.0277IR–0.68480.2342–0.70080.2790–0.11460.3871–0.76060.2641–0.8277 |$W^{*}_{\rm L}$||$L^{*}_{\rm L}$||$W^{*}_{\rm L}$|-|$L^{*}_{\rm L}$||$W^{*,m}_{\rm L}$||$L^{*,m}_{\rm L}$||$W^{*,m}_{\rm L}$|-|$L^{*,m}_{\rm L}$||$W^{*}_{\rm L}$|-|$W^{*,m}_{\rm L}$||$L^{*}_{\rm L}$|-|$L^{*,m}_{\rm L}$||${\it DiD}$|A. Raw excess returnsAverage0.231.03–0.801.010.830.18–0.780.20–0.98 (0.66)(2.81)(–3.87)(3.69)(3.01)(1.58)(–4.88)(1.01)(–6.38)No. of months363363363363363363363363363AvgN417203 621461 SR0.10940.4849–0.60610.58480.46280.2941–0.72630.1694–0.7450B. CAPM regressionsIntercept–0.740.14–0.870.17–0.030.20–0.900.17–1.07 (–3.61)(0.59)(–4.34)(1.30)(–0.20)(1.72)(–5.39)(0.89)(–5.76)MktRF1.431.320.111.251.27–0.020.180.050.14 (19.51)(17.57)(1.26)(29.01)(30.90)(–0.48)(3.03)(0.70)(1.72)|$R^2$|.7016.6029.0115.8197.7893.0021.0458.0025.0166IR–0.62800.1039–0.66780.2255–0.03730.3192–0.86190.1427–0.8215C. Four-factor regressionsIntercept–0.620.26–0.880.14–0.050.19–0.760.31–1.07 (–4.93)(1.20)(–4.33)(1.53)(–0.52)(2.20)(–5.29)(1.38)(–5.24)MktRF1.251.130.131.171.150.010.08–0.030.11 (18.03)(22.15)(1.64)(42.36)(35.76)(0.41)(1.21)(–0.45)(1.39)HML–0.280.11–0.39–0.170.17–0.34–0.11–0.06–0.04 (–5.08)(1.56)(–4.99)(–3.78)(3.66)(–7.28)(–1.16)(–0.60)(–0.59)SMB0.740.88–0.140.510.79–0.280.220.090.14 (8.87)(12.29)(–1.73)(13.06)(18.48)(–6.17)(2.59)(1.14)(1.43)MOM–0.08–0.140.060.080.040.05–0.16–0.180.02 (–1.29)(–2.44)(0.64)(3.55)(1.84)(2.11)(–3.04)(–2.18)(0.16)|$R^2$|.8190.7352.0893.9159.9360.3511.1183.0410.0277IR–0.68480.2342–0.70080.2790–0.11460.3871–0.76060.2641–0.8277 See caption to Table 2. The only difference here is that we hold stocks that were allocated to one of the portfolios at some point during months |$\{t-60,...,t-13\}$| before formation. The first monthly return is calculated in April 1990, that is, the first time we invested 48 times in a row. These results suggest that, following a positive information shock, the most optimistic agents continue to revise their beliefs downward in years 2 through 5 postformation. By contrast, following a negative information shock, the beliefs of the optimistic agents are relatively stable after about 1 year; we see no evidence of belief revisions either upward or downward. As a robustness check, in Internet Appendix F.I we repeat these tests using Fama and MacBeth (1973) regressions. This allows us to control for various other measures and generates consistent results. Panel A of Figure 4 plots the cumulative returns to the |$W^{*}_{\rm S}$| and |$L^{*}_{\rm S}$| strategies, hedged with respect to the CAPM-market factor over the sample period.29 Both strategies fall consistently over the full sample period, suggesting the strategy underperformance is not concentrated in a particular subperiod. The magnitude of the underperformance results in a dramatic negative cumulative return: an initial investment of $1,000 into the 1-year hedged constrained-winner (constrained-loser) strategy is worth |$\$18.90$| (|$\$0.34$|) at the end of June 2020. Figure 4 Performance of hedged constrained strategies over calendar time This figure presents the investment value for a set of hedged portfolios. To calculate the portfolio value, we assume an investment at the beginning of the sample of $1,000. We also assume the exposure to the market is hedged. We calculate the hedging coefficient by running a full-sample regression of the strategy excess returns on the market excess returns. Then, using the full-sample regression coefficients, we subtract the returns of the (zero-investment) hedge-portfolio |$[\text{b}_{\text{Mkt}}(\text{R}_{\text{Mkt}}\text{-}\text{R}_{\text{f,t}})]$| from the strategy excess returns and add the risk-free rate to generate the hedged strategy returns. Panel A plots the evolution of $1,000 invested in hedged calendar-time short-horizon (1 year) buy-and-hold constrained-winner and -loser (that were not constrained winners in the past 5 years) strategies. Panel B shows results for the corresponding long-horizon (2–5 years) strategies. For comparison, panel B plots the cumulative returns for the market-hedged long-horizon strategies (|$W^{*}_{\rm L}$| and |$L^{*}_{\rm L}$|). The cumulative returns over the sample period are strongly negative for the constrained-winner strategy, but are positive for the constrained-losers strategy. Moreover, the difference between the two strategies does not appear to be driven by a particular subsample. As a further robustness check, we replicate our main findings on a sample of international equities, and for an out-of-sample time-period prior to the availability of short interest data for NASDAQ stocks (see Internet Appendices E.I and E.II). In all cases, we see strong negative abnormal returns over the 1 year following portfolio formation for constrained losers. Over years 2–5 postformation, only the constrained winners underperform. Thus, the finding of differential performance-persistence appears robust. 3.3 MatchingIn the preceding subsection, we documented that portfolios of constrained winners and constrained losers exhibit strong negative abnormal returns, and that these negative abnormal returns persist for approximately 5 years and 1 year, respectively. We hypothesize that this asymmetric persistence in predictability results from a combination of short-sale constraints and differential interpretation of information shocks among investors. Each of the firms in these two portfolios, on the portfolio formation date, has low IOR and high SIR. We argue that the low IOR is a proxy for a low lending supply (because noninstitutional holders are less likely to make their shares available for lending). Then, when increased disagreement leads to an increased demand by pessimistic investors to borrow and (short) sell shares that likely exceeds the supply of easily borrowed shares, borrowing becoming costly. That is, the stocks become constrained. However, another possibility is that, in sorting on IOR, SIR, and past return to form our portfolios, we are inadvertently selecting some other firm characteristic directly linked to return predictability. For example, the previous literature has argued that short interest is a proxy for informed demand and thus predicts future returns (Boehmer, Jones, and Zhang 2008; Boehmer, Huszar, and Jordan 2010; Engelberg, Reed, and Ringgenberg 2012; Rapach, Ringgenberg, and Zhou 2016). Sorting on high short interest alone, in combination with high or low past return, could give the same results. To examine this possibility, for each constrained portfolio, we create a matched portfolio that contains firms that are as close to identical as possible to the firms in our constrained portfolio on the dimensions of size, short interest, past return, and the logarithm of book-to-market, except these matched firms are not short-sale constrained (i.e., they have high institutional ownership). Specifically, for each stock in the constrained-winner portfolio (|$W^*$|) and the constrained-loser portfolio (|$L^*$|), we run a matching procedure based on the Mahalanobis (1936) distance for these four metrics to find a statistical twin stock in a universe of unconstrained potential matches. We limit the unconstrained matching universe to stocks above the 70th percentile cutoff for institutional ownership to ensure that the matched firm is unconstrained. In addition, we impose the constraint that the matched firm must fall in the same past-return bucket and that, for the firms in the constrained-loser portfolio, the matched firm not be a constrained-winner stock at any time within the past 5 years (equivalent to the constraint we place on the actual constrained losers).30 The last two columns in Table 1 reveal that, not surprisingly, the value-weighted portfolios of matched stocks for |$W^*$| and |$L^*$|, that is, |$W^{*,m}$| and |$L^{*,m}$|, are similar along the matching dimensions of size, short interest, past return, and book-to-market. They are also similar along related dimensions (e.g., turnover and volatility). However, they differ substantially on dimensions that proxy for short-sale constraints, such as SIRIO, volatility spread, and Markit loan fees. This finding suggests the matched firm-portfolios should be well suited to uncovering differences solely based on the fact that one set of firms is short-sale constrained, while the other is not. Table 2 shows that short-horizon strategies based on matched-firm portfolios, |$W^{*,m}_{\rm S}$| and |$L^{*,m}_{\rm S}$|, exhibit no abnormal performance relative to a CAPM or four-factor model. Consistent with this and our earlier findings, the final three columns show the strategies based on constrained winners and losers dramatically underperform their matched-firm strategies. The final column of this table shows the difference-in-differences ( DiD) is statistically indistinguishable from zero. The results are also consistent with the hypothesis that the short-sale constraints are responsible for the underperformance of the constrained winner portfolio in years 2–5 postformation. Table 3 shows that the long-horizon strategies based on matched firms, |$W^{*,m}_{\rm L}$| and |$L^{*,m}_{\rm L}$|, exhibit no abnormal performance relative to a CAPM. The DiD—testing whether the constrained portfolios underperform the matched firms by different amounts for the winners and losers—is now highly statistically significant,31 in all three panels. Figure 5 adds more background to the matching approach. It shows the buy-and-hold performance of the constrained and matched portfolios on a year-by-year basis.32 Whereas the portfolios of constrained stocks exhibit distinct return predictability, the matched portfolios’ returns can be explained by the CAPM in each of the 6 years postformation.33 Strikingly but consistent with the asymmetry in persistence we document elsewhere, the constrained winners underperform significantly relative to the CAPM for each of the 5 years following formation (panel A), while the constrained losers only exhibit a significantly negative alpha in the first year (panel B). This visual assessment is consistent with the time-series regressions presented throughout the paper. Figure 5 CAPM alphas of constrained and matched 1-year strategies The first set of points show the annualized CAPM alphas of strategies of value-weighted portfolios of constrained past winners (panel A) and losers (panel B), respectively, in years 1 through 6 postformation. The second set of points in panels A and B is the result of strategies of matched stock-portfolios, based on the Mahalanobis distance calculated on size, log(book-to-market), past return, and short interest. The whiskers represent 95|$\%$| confidence intervals based on Newey-West standard errors. For details, see Section . 3.4 Earnings announcementsThis paper builds on the Miller (1977) insight that constrained securities with restricted short selling will be generally overpriced, since their prices will reflect the beliefs of the more optimistic investors. This implies that the arrival of new information will generally cause these optimists to revise their beliefs about firm value downward, resulting in a negative event return. One point in time when disagreement is likely to be resolved is when firms announce their earnings, which usually happens once per quarter.34 This means that, for overpriced securities, we should see more extreme negative returns immediately following earnings announcements than at other times. Figure 6 plots the average cumulative abnormal returns (ACAR) around earnings announcements for the constrained winner and loser strategies and the corresponding matched-firm strategies explored in Sections and . Panel A plots the ACARs for the 1-year strategies |$W^{*}_{S}$| and |$L^{*}_{S}$| and their matched-firm counterparts, and panel B does the same for the 2- to 5-year strategies |$W^{*}_{L}$| and |$L^{*}_{L}$| and their corresponding matched-firm strategies.35 Consistent with the mispricing hypothesis and the return predictability discussed earlier, both the 1-year portfolios of constrained winners and losers significantly decline immediately following earnings announcements. For the 2- to 5-year strategies, the strong negative returns immediately following earnings announcements are present only for the constrained-winner-based strategies. This finding is again consistent with the hypothesis that overpricing is eliminated in the first year following portfolio formation for the |$L^{*}$| portfolios, but that the overpricing persists out to 5 years for the constrained winners, and that much of this mispricing is eliminated on earnings announcement dates. Figure 6 CAR around earnings announcements This figure shows cumulated abnormal returns of the constrained winners (|$W^{*}$|) and losers (|$L^{*}$|) as well as their unconstrained matched counterparts (|$W^{*,m}$| and |$L^{*,m}$|) around the day (D=0) of an earnings announcement that occurs in the quarter after portfolio formation (months t to t+2). We include all stocks that were in the respective portfolio in months t-12 through t-1 (panel A, short horizon) and t-60 to t-13 (panel B, long horizon) and calculate their buy-and-hold weight from formation to each day plotted, by using the price change adjusted by the cumulative price adjustment factor (CFACPR in CRSP). Abnormal returns are calculated by adjusting for beta times the CAPM-market-factor. For each stock, beta is estimated in a 1-year window of daily returns prior to the month in which the earnings announcement occurs. To construct the figure, we first center daily abnormal returns on the day of announcement (D=0). They are then cumulated by stock (cumulative abnormal return, CAR) and averaged (ACAR, weighted by the buy-and-hold weight) by portfolio and day relative to announcement. See Internet Appendix B.V for details. 3.5 Lending feesThe market price of a constrained security will reflect the valuation of the agents who are most optimistic about the firm value. In a similar vein, the per-period marginal cost of short selling a security, at a given point in time, likely reflects the beliefs of the most pessimistic investors about how much the security price is likely to fall per period. That is, it is a direct measure of disagreement. Here, we use the Markit indicative lending fee as a proxy for the marginal costs of short selling. This lending fee clearly will not capture all of the costs or risks associated with short selling, and therefore may not be a good proxy for the all-in cost of short selling. However, changes in the fee over time should be correlated with changes in the pessimistic agents’ willingness to pay to borrow shares for the purpose of shorting, and therefore with changes in disagreement between pessimists and optimists for constrained stocks. Panel A of Figure 2 reveals that the fees increase leading up to portfolio formation and then fall slowly over about 5 years postformation, that is, at a symmetric rate for constrained winners and losers. On the surface, this finding might seem puzzling, given the evidence earlier in this Section that the abnormal return persistence for past-winners and losers is so different. However, it is consistent with a model in which, for the constrained losers between 2 and 5 years postformation, the optimists’ beliefs about the security value are unbiased, while the beliefs of the most pessimistic investors—those agents whose beliefs determine the borrowing costs—are too pessimistic initially but then fall over time. This model is discussed in the Introduction and is presented in Section . We confirm the finding that the postformation decline in lending fees is symmetric across constrained winners and losers by regressing changes in portfolio lending fees on dummy variables that equal one when an observation corresponds to the first year postformation (|$I_{0 Table 4 Regressions of changes in lending fees on event-time dummies |$W^*$||$L^*$||$W^* - L^*$||$I_{0 |$W^*$||$L^*$||$W^* - L^*$||$I_{0 For each value-weighted portfolio, we calculate the change in the value-weighted Markit indicative lending fee (in |$\%$|, annualized) between months |$t$| and |$t-1$|. We then regress these changes on indicator variables that control for whether an observation falls into the first year postformation (|$I_{0 Table 4 Regressions of changes in lending fees on event-time dummies |$W^*$||$L^*$||$W^* - L^*$||$I_{0 |$W^*$||$L^*$||$W^* - L^*$||$I_{0 For each value-weighted portfolio, we calculate the change in the value-weighted Markit indicative lending fee (in |$\%$|, annualized) between months |$t$| and |$t-1$|. We then regress these changes on indicator variables that control for whether an observation falls into the first year postformation (|$I_{0 3.6 Analyst disagreementThus far, we have inferred beliefs about firm value and levels and changes in disagreement from market prices. An alternative approach is to directly infer beliefs from analyst forecasts. An advantage to this alternative approach is that forecasts are direct measures of beliefs, albeit beliefs about earnings. Disadvantages are that analyst forecasts may be biased, perhaps as a result of analysts’ incentive structure, and their forecasts may be different from those of the marginal investor (Hong, Kubik, and Solomon 2000; Lim 2001; Hong and Kubik 2003). With these caveats in mind, these data nonetheless allow us to test belief dynamics out of sample.36 Hence, we generate some stylized empirical facts about the dynamics of the disagreement process of analysts in this section. To analyze the dynamics of analyst beliefs, we first sort stocks into five portfolios based on the preceding year’s change in dispersion, |$\Delta FD$|. We exclude constrained stocks, that is, stocks in the low IOR and high SIR bucket, to focus on belief dynamics among unconstrained stocks.37Figure 7 plots forecast dispersion from 1 year before until 5 years after portfolio formation. Interestingly, after the strong positive shock to forecast dispersion experienced by firms in the high-|$\Delta FD$| portfolio, disagreement falls persistently for about 5 years. Note that this is consistent with the resolution of disagreement taking about 5 years and is consistent with the long persistence of the negative abnormal returns we observe for constrained winners. Figure 7 Dynamics of earnings forecast dispersion Stocks are sorted based on their past 1-year change in forecast dispersion into five portfolios. We exclude constrained stocks, that is, stocks in the low IOR and high SIR buckets. Forecast dispersion is the standard deviation of quarterly earnings forecasts divided by the absolute value of the mean. Data are from IBES from May 1980 to June 2020. The time-series average of the value-weighted portfolio average level of forecast dispersion is tracked over event time, from 12 months before until 60 months after portfolio formation (t=0). In addition to these |$\Delta FD$|-sorted portfolios, we examine the same |$FD$| measure for the intersection of the high-|$\Delta FD$| and momentum portfolios in Figure 2, panel B. We observe a symmetric pattern for winners and losers, consistent with the evidence from lending fees. In Table 5, we predict future changes in |$FD$| over the next year (columns 1 and 2), the following 4 years (columns 3 and 4), and over 5 years (columns 5 and 6) with positive and (the absolute value of) negative changes in analyst disagreement over the past year (ΔFD(t−12)—t+ and |ΔFD(t−12)—t−|), using the market-capitalization-weighted Fama and MacBeth (1973) procedure. The results confirm that positive past changes strongly predict negative future changes both for 1 year and the following 4 years (months |$t+12$| through |$t+60$|. By contrast, including negative past changes in the regression barely increases the time-series average of the cross-sectional |$R^2$|, and, despite being statistically significant for the first year, the coefficient estimate for negative past changes is smaller by an order of magnitude in the first year than that of the positive past changes. Table 5 Fama-MacBeth regressions of future changes on past changes in forecast dispersion ΔFDt—(t+12)ΔFDt—(t+12)ΔFD(t+12)—(t+60)ΔFD(t+12)—(t+60)ΔFDt—(t+60)ΔFDt—(t+60)Intercept0.050.040.030.030.070.07 (8.14)(8.11)(2.90)(3.08)(6.85)(6.91)ΔFD(t−12)—t+–0.87–0.87–0.13–0.13–0.98–0.98 (–39.66)(–39.00)(–5.74)(–5.71)(–73.94)(–73.94)|ΔFD(t−12)—t−| 0.06 –0.05 0.02 (3.07) (–1.44) (1.32)Avg. |$R^2$|.3839.3889.0083.0149.3214.3237No. of months470470427427427427Avg. no. of stocks2,0152,0151,4161,4161,4591,459 ΔFDt—(t+12)ΔFDt—(t+12)ΔFD(t+12)—(t+60)ΔFD(t+12)—(t+60)ΔFDt—(t+60)ΔFDt—(t+60)Intercept0.050.040.030.030.070.07 (8.14)(8.11)(2.90)(3.08)(6.85)(6.91)ΔFD(t−12)—t+–0.87–0.87–0.13–0.13–0.98–0.98 (–39.66)(–39.00)(–5.74)(–5.71)(–73.94)(–73.94)|ΔFD(t−12)—t−| 0.06 –0.05 0.02 (3.07) (–1.44) (1.32)Avg. |$R^2$|.3839.3889.0083.0149.3214.3237No. of months470470427427427427Avg. no. of stocks2,0152,0151,4161,4161,4591,459 The change in forecast dispersion (|$\Delta FD$|) over the following year (columns 1 and 2), the next 4 years (columns 3 and 4), and the full 5-year period (columns 5 and 6) is regressed on positive and negative changes in forecast dispersion over the previous year. We value-weight observations in the cross-sectional regressions by their market capitalization. Following the Fama and MacBeth (1973) procedure, the time-series average of the regression coefficients is presented. Standard errors are calculated following Newey and West (1987). Avg. |$R^{2}$| denotes the time-series average of the cross-sectional |$R^2$|s. The sample period is May 1980 to June 2020. Table 5 Fama-MacBeth regressions of future changes on past changes in forecast dispersion ΔFDt—(t+12)ΔFDt—(t+12)ΔFD(t+12)—(t+60)ΔFD(t+12)—(t+60)ΔFDt—(t+60)ΔFDt—(t+60)Intercept0.050.040.030.030.070.07 (8.14)(8.11)(2.90)(3.08)(6.85)(6.91)ΔFD(t−12)—t+–0.87–0.87–0.13–0.13–0.98–0.98 (–39.66)(–39.00)(–5.74)(–5.71)(–73.94)(–73.94)|ΔFD(t−12)—t−| 0.06 –0.05 0.02 (3.07) (–1.44) (1.32)Avg. |$R^2$|.3839.3889.0083.0149.3214.3237No. of months470470427427427427Avg. no. of stocks2,0152,0151,4161,4161,4591,459 ΔFDt—(t+12)ΔFDt—(t+12)ΔFD(t+12)—(t+60)ΔFD(t+12)—(t+60)ΔFDt—(t+60)ΔFDt—(t+60)Intercept0.050.040.030.030.070.07 (8.14)(8.11)(2.90)(3.08)(6.85)(6.91)ΔFD(t−12)—t+–0.87–0.87–0.13–0.13–0.98–0.98 (–39.66)(–39.00)(–5.74)(–5.71)(–73.94)(–73.94)|ΔFD(t−12)—t−| 0.06 –0.05 0.02 (3.07) (–1.44) (1.32)Avg. |$R^2$|.3839.3889.0083.0149.3214.3237No. of months470470427427427427Avg. no. of stocks2,0152,0151,4161,4161,4591,459 The change in forecast dispersion (|$\Delta FD$|) over the following year (columns 1 and 2), the next 4 years (columns 3 and 4), and the full 5-year period (columns 5 and 6) is regressed on positive and negative changes in forecast dispersion over the previous year. We value-weight observations in the cross-sectional regressions by their market capitalization. Following the Fama and MacBeth (1973) procedure, the time-series average of the regression coefficients is presented. Standard errors are calculated following Newey and West (1987). Avg. |$R^{2}$| denotes the time-series average of the cross-sectional |$R^2$|s. The sample period is May 1980 to June 2020. We conclude that the dynamics of analyst disagreement are consistent with the results from our analysis of lending fees in that, following large shocks to disagreement, disagreement falls over the course of about 5 years. Moreover, this decay is symmetric for securities that experienced either positive or negative information shocks. 4. Theoretical ImplicationsIn this section, we discuss the implications of the empirical findings presented in Section for belief and disagreement evolution following information shocks. In Section , we link these implied patterns to existing theories of momentum and long-term reversals, and in Section we lay out a new model that is consistent with our empirical findings on the behavior of both constrained and unconstrained stocks. 4.1 Existing explanations of momentum and reversalsRational models of momentum posit that the premium earned by high momentum is compensation for risk, either because of high unconditional exposure to priced factors (see, e.g., Berk, Green, and Naik 1999; Johnson 2002; Sagi and Seasholes 2007) or because momentum serves as a proxy for time-varying exposure to factors with a time-varying premium (Kelly, Moskowitz, and Pruitt 2021). Rational models are unlikely to explain the returns of the constrained-stock strategies we have examined here, given their large squared Sharpe ratios. Alternative starting points are the existing behavioral explanations offered for momentum and long-term reversal among unconstrained stocks, such as Daniel, Hirshleifer, and Subrahmanyam (1998), Barberis, Shleifer, and Vishny (1998), and Hong and Stein (1999), combined with the explanation for the underperformance of short-sale constrained stocks in the presence of disagreement offered in Miller (1977). Miller argues that when disagreement exists about the value of a security and when pessimists are constrained from short selling, the security price will reflect only the views of the optimists. When disagreement is resolved over time, this overvaluation is eliminated, leading to predictably low returns. However, naive combinations of the Miller (1977) model with any of these three models yield predictions that are inconsistent with empirical findings: both Daniel, Hirshleifer, and Subrahmanyam (1998) and Barberis, Shleifer, and Vishny (1998) offer representative-agent models with no disagreement. Without disagreement, introducing short-sale constraints would have no effect on prices and thus could not generate the return patterns we document here. Hong and Stein (1999) is a heterogeneous-agents model, but the nature of the newswatcher and momentum-trader belief-formation process in their model implies that even in the presence of short-sale constraints, expected returns would still be positive for past winners, which is inconsistent with the evidence we present here.38 In sum, none of the approaches above is able to offer a satisfying explanation of the strong asymmetry in mispricing persistence that we observe between constrained winners and losers. 4.2 A model of the dynamics of disagreementWe now propose a model that combines key features of models from the literature reviewed in Section in a parsimonious way. Here, we present an overview of the model and provide the intuition for the key implications. Internet Appendix A provides a formal development of the model. Specifically, we combine overconfidence and slow information diffusion in a model that generates beliefs and price dynamics consistent with the empirical findings we have documented in Section . Our model is in the tradition of other models that formalize the idea that differences of opinion combined with short-sale constraints will influence asset prices (see, e.g., Harrison and Kreps 1978; Diamond and Verrecchia 1987; Duffie 1996; Chen, Hong, and Stein 2002; Duffie, Gârleanu, and Pedersen 2002; Hong and Stein 2003; Scheinkman and Xiong 2003; Gallmeyer and Hollifield 2007; Ang, Shtauber, and Tetlock 2013; Blocher, Reed, and Van Wesep 2013; Hong and Sraer 2016). In our model, heterogeneous agents with CARA preferences trade a single risky asset that pays a single uncertain liquidating dividend at a final date. The liquidating dividend is the sum of dividend innovations, which are observed each period by the agents. As a result of differential interpretation of the initial information shock, agents disagree about the distribution from which these innovations are drawn. However, as these agents observe each innovation each period, they update their estimates of the mean of this distribution. Priors and innovations are normally distributed, so Bayesian updating is straightforward. In a single-period CARA-normal setting without frictions and where investors ignore the information contained in prices, all investors participate in the market and the equilibrium price is a linear function of their beliefs (see, e.g., the discussion of the competitive equilibrium in chap. 12 of Campbell 2018). However, if the supply of shares freely available for borrowing is less than the demand, then the cost of borrowing shares will increase to a level that equilibrates supply and demand. In markets with limited supply, this cost will generally increase when disagreement increases (Blocher, Reed, and Van Wesep 2013). These short-sale costs can partly or fully sideline some of the more pessimistic agents, leading to a higher equilibrium price, one that no longer reflects the beliefs of these agents.39 For modeling convenience, we follow recent behavioral models (see, e.g., Barberis et al. 2018; Da, Huang, and Jin 2021) in assuming that in each period |$t$|, each agent maximizes her expected utility over period |$t+1$| wealth. To solve this portfolio optimization, each agent needs to forecast the distribution of the equilibrium price in period |$t+1$|, which will be based on the agents’ beliefs at that time. We assume that, in calculating this distribution, each agent makes the strong assumption that disagreement will be resolved in the following period in such a way that each other agent will come to agree with her. This assumption makes the solution far more tractable, and is consistent with the “illusion of validity” of Kahneman and Tversky (1973).40 In other words, agents believe their views are correct and that others will agree with them sooner rather than later. A model feature that drives our results is that access to private information is paired with overconfidence. Motivated by this feature, our model has two types of agents. The first set of agents are informed and overconfident. They receive all new information immediately. Consistent with Daniel, Hirshleifer, and Subrahmanyam (1998) and Gervais and Odean (2001), this access to information makes them overconfident about the information they receive, in that they assess the precision of their information to be higher than it actually is.41 We label the second set of agents as newswatchers, following Hong and Stein (1999). In our setting, the new information about cash flows (i.e., the dividend innovations that the informed overconfident agents observe immediately) slowly diffuses through the population of newswatchers. Crucially, we follow Hong and Stein (1999) in assuming newswatchers ignore the information content of prices; that is, they fail to infer overconfident informed agents’ signals from prices (see also Luo, Subrahmanyam, and Titman (2020) where traders are skeptical about the ability of others). Hong and Stein (1999) put forth slow information diffusion as an explanation of shorter-term momentum effects, and Daniel, Hirshleifer, and Subrahmanyam (1998) argue the resolution of overconfidence can explain longer-term reversal effects. Consistent with these papers, we assume that the resolution of overconfidence requires more time than the information-diffusion process.42 In the model we propose here, the interaction of newswatchers and overconfident agents generates standard short-horizon momentum and long-term reversal effects for unconstrained stocks. The intuition for this implication is as follows: first assume that at |$t=-1$|, the risky asset is believed to be fairly priced by both types—overconfident and newswatchers—implying that none of these agents holds any of the risky asset. However, assume that at time 0, the informed overconfident agents receive positive news about the asset’s cash flows. This information is initially observed only by the overconfident agents who, by virtue of their overconfidence, put too much weight on the signal and thus become overoptimistic about the security value. In contrast, the newswatchers do not receive the information in full and, by assumption, fail to infer the information from prices. Thus, in response to the new information, the price moves up as overconfident agents buy in response to the new information and newswatchers short sell in response to the resultant price rise. However, over the next few periods this positive information diffusing through the population of newswatchers will result in an increase in their optimism, a reduction in their short positions, and an increase in the equilibrium stock price. This continuing upward price move results in a positive momentum effect. The fact that momentum persists for about a year suggests that slightly more than a year is required for this information to fully diffuse through the newswatcher population. After a year, the price will start to decline as more information is released and, on average, the overreaction of the informed overconfident agents is corrected, producing a long-term reversal effect. For unconstrained stocks, this momentum/reversal effect is symmetric for positive and negative information releases: in either case there will be a price-continuation for about a year, followed by reversal. The predictable price patterns are different for constrained stocks, and no longer exhibit symmetry with respect to positive and negative shocks. In response to a positive information shock, a heavily constrained stock will increase in price as the informed overconfident agents overweight this new information. Moreover, for the heavily constrained stock the pessimistic newswatchers are now “sidelined” from the market. Since these pessimistic agents are not shorting the risky asset and moderating its price rise, the price increase that results from the information release is stronger and immediate. There will be no momentum. Also, the “reversal” of the resultant price rise, that results as the overconfident agents’ optimism declines with subsequent information releases, starts immediately (i.e., at |$t=1$|) and continues until the overoptimism is eliminated. In response to a negative information shock, the informed overconfident agents again overreact and the newswatchers underreact, but now the overconfident agents are the “pessimists” relative to the newswatchers and are therefore sidelined. Thus, the security price now reflects the beliefs of the newswatchers. This means that, starting in period 1, the constrained risky asset will earn negative returns as the bad news diffuses through the newswatchers population, causing them to revise their beliefs downward. In this case, however, the negative returns will only persist over the short horizon over which information diffuses, that is, for about 1 year. Thus, this model implies that, for constrained winners, there will be no price momentum. Rather, the constrained winners start to reverse (earn negative returns) immediately after the initial positive information shock, and continue doing so for about 5 years. In contrast, constrained losers experience an exaggerated momentum effect (i.e., continuing negative returns) for about a 1-year horizon following the formation date. These predictions are consistent with the empirical findings documented in Section . To make this more concrete, for one parameterization of the model in Internet Appendix A we plot the model-implied beliefs and equilibrium prices in Figure 3. Panel A plots the evolution of posterior beliefs over time |$t$| of overconfident agents (labeled “Overreacting agent”) |$\mathbb{E}_{O,t} \left\lbrack D_T \right\rbrack$| and newswatchers (labelled “Underreacting agent”) |$\mathbb{E}_{N,t} \left\lbrack D_T \right\rbrack$| about the liquidating dividend |$D_T$|, as well as the beliefs of an agent with rational expectations who observes the information release at |$t=0$|. Beliefs and prices are plotted both for a positive and for a negative information release at time |$0$|. Finally, the line labeled “Disagreement” plots the difference between the beliefs of the two types of agents. We begin by focusing on the case with a positive information release at |$t=0$|. Overconfident agents immediately observe the new information, overestimate its precision and therefore overreact to it, and as a consequence become far too optimistic about the value of the final liquidating dividend |$D_T$|. Over time, the overconfident agents learn (slowly) from further dividend innovations and converge toward the Bayesian price expectation. In contrast, it takes three periods for the information in the signal to fully diffuse out to the newswatchers. Thus, the newswatcher beliefs converge to the rational expectations belief at |$t=2$|. In our model, these beliefs determine the asset’s expected price path following the positive and negative shocks. Panel B of Figure 3 shows the resultant price paths for two extreme cases: a stock that can be freely shorted (labeled “Unconstrained”), and a stock that cannot be shorted at all (labeled “Constrained”). As discussed above, if the stock can be freely shorted, the equilibrium price will be a weighted average of agents’ beliefs. The resultant “Unconstrained price” is represented by the dashed blue line in panel B of Figure 3 and exhibits short-horizon momentum caused by slow information diffusion among the newswatchers (as in Hong and Stein 1999), and the long-horizon reversal that results from the gradual learning of the overconfident agents. However, the price dynamics are fundamentally different when the risky asset is constrained. Following a positive shock, the price will reflect only the beliefs of the overreacting agents. The newswatchers, who become relatively pessimistic following a positive shock, are now completely sidelined. As a consequence, the price overshoots in response to the large dividend innovation in period |$t=0$|, and then gradually reverses, mirroring the beliefs of the overconfident-informed agents. The prices following a negative shock instead mirror the beliefs of the newswatchers (labeled “underreacting agent” in panel A), because now the overreacting agents are pessimistic and as a result are sidelined. This results in an exaggerated momentum effect. However, now there is no longer-term reversal effect; the opinions of pessimistic overreacting agents, who are causing the long-term reversal effect in the unconstrained case, are still sidelined from the market valuation.43 We conclude this discussion with three remarks: First, the beliefs of the informed overconfident agents and the newswatchers in our model match the belief patterns of optimists for constrained stocks that the empirical analysis has suggested. In principle, behavioral assumptions of each group can be substituted with alternative assumptions that imply similar dynamics of beliefs. Agents in these groups may suffer from different biases or face information structures currently unexplored in our model. For example, in an alternative model with the right assumptions, return-extrapolation beliefs could be consistent with those of the informed overconfident agents in this model. We do not attempt to distinguish between competing or complementary assumptions. Matching these belief dynamics likely requires that at least two groups of agents exist: one group that overreacts and whose miscalibration is highly persistent, and a second group that underreacts over a shorter horizon. Second, agents within a group have homogeneous preferences in our model. A useful extension could introduce wavering (Barberis et al. 2018); that is, the idea that agents’ beliefs are weighted averages of Bayesian and non-Bayesian beliefs. Agents within a group have similar, but not the same weights. These weights fluctuate over time, causing disagreement within a group. With wavering, the large price shocks that drive large wedges between Bayesian and non-Bayesian beliefs would lead to within-group disagreement. Such an extension could help to explain high turnover during the formation period of momentum stocks.44 To the extent that overconfident investors hold more extreme non-Bayesian beliefs and are generally more prone to wavering, turnover for constrained winners should increase more than turnover for constrained losers (see Table 1 for evidence broadly consistent with this prediction). Third, in our empirical analysis, we use constrained stocks to draw inferences about how disagreement evolves following information shocks in general. A basic assumption supporting this approach is that information processing is fairly general, when in fact there may be differences in information frictions, etc., between constrained and unconstrained stocks. We have presented empirical results consistent with our assumption (see, e.g., Figure 2 panel B), but we cannot rule out a more complicated theory. 5. ConclusionWe document a strong asymmetry in mispricing persistence between constrained winners and constrained losers. Constrained past losers exhibit no abnormal returns 1 year after portfolio formation, but constrained past winners continue to underperform for another 4 years. The overpricing of the portfolio of constrained winners is economically large: this portfolio loses more than |$50\%$| relative to the market in the 5 years following portfolio formation. Proxies for disagreement, such as lending fees or analyst forecast dispersion, indicate that belief dispersion between pessimists and optimists decays slowly over about 5 years. Strikingly, we find no difference in disagreement persistence between constrained winners and losers, or between unconstrained winners and losers. Our explanation for the asymmetry in mispricing persistence and the symmetry in disagreement persistence relies on the intuition developed in Miller (1977): for constrained stocks prices mirror the beliefs of optimists. The prices of constrained winners reflect the optimism of overreacting agents, who slowly revise their beliefs, leading to persistent negative returns. The strong but less persistent negative returns for constrained losers suggest optimism for these stocks disappears quickly. These facts, combined with the high persistence in disagreement for both positive and negative shocks, is consistent with the existence of two groups of agents whose beliefs evolve in different ways in response to these shocks: one group overreacts to this new information, and the bias associated with this overreaction remains strong for out to 5 years. A second group underreacts, but this underreaction is corrected over about a year. We propose a model grounded in documented psychological regularities that explains these dynamics based on overconfidence and slow information diffusion. The agents with immediate access to the new information place too much weight on this new information as a result of overestimating its precision. Over time, as new information is received, these agents necessarily start to put less weight on the initial signal, but this is a slow process, so the overreaction is persistent. The agents who do not immediately observe the full signal do not overestimate its precision. However, they only observe the full signal with a lag as a result of slow information diffusion. This model generates beliefs consistent with the price and disagreement dynamics observed for the constrained and the unconstrained stocks. However, we remain circumspect on the question of whether it is necessarily this set of mechanisms that is responsible for the dynamics of disagreement we observe. For future research, our analysis suggests short-sale constrained stocks can be used as a unique testing ground for heterogeneous-agents models. The prices of constrained securities, particularly when combined with proxies for disagreement, provide a new window into belief dynamics, and thus can help us understand how prices are set for unconstrained assets. Our empirical analysis provides an example of this idea. AcknowledgementWe thank Nick Barberis, John Campbell, Jie Cao, Tolga Caskurlu, Alex Chinco, Lauren Cohen, Robin Greenwood, Alexander Hillert, David Hirshleifer, Heiko Jacobs, Ravi Jagannathan, Lawrence Jin, Urooj Khan, Sven Klingler, Dong Lou, Stefan Nagel, Andreas Neuhierl, Florian Peters, Mitchell Petersen, Jeff Pontiff, Adam Reed, Tano Santos, Andrei Shleifer, Valeri Sokolovski, Avanidhar Subrahmanyam, Sheridan Titman, Luis Viceira, Tuomo Vuolteenaho, Ed van Wesep, Greg Weitzner, Wei Xiong, and two anonymous referees for helpful comments, as well as Zahi Ben-David, Sam Hanson, and Byoung Hwang for helpful insights about the short-interest data. We appreciate the feedback from seminar and conference participants at the Miami Behavioral Finance Conference, NBER Spring Meeting, American Finance Association, European Finance Association, Cavalcade Asia-Pacific, Oxford Man Quantitative Finance Seminar, Paris December Finance Meeting, German Finance Association, Amsterdam, Brandeis, Columbia, Copenhagen, Hannover, HEC Montréal, HU Berlin, Kiel, Lausanne, LBS, LSE, Maryland, Münster, Notre Dame, Oxford, Rochester, Stockholm, UCLA, Washington, WashU, AQR, Arrowstreet, Barclays, Institutional Assets, Martingale Asset Management, and the Society of Quantitative Analysts. Financial support from the German Research Foundation [grant KL2365/3-1] is gratefully acknowledged. All remaining errors are our own. The paper subsumes our older work circulated under the titles “Overconfidence, Information Diffusion, and Mispricing Persistence,” “Overpriced Winners,” and “Betting against Winners.” Supplementary data can be found on The Review of Financial Studies web site. Footnotes1In more complicated settings, the links between optimists’ beliefs and prices as well as pessimists’ beliefs and lending fees are not as direct as in our simple two-type example. Risk aversion, indirect short selling costs (other than lending fees), and dynamics complicate matters. However, the claim that prices of heavily constrained stocks are set by optimists is fairly general. Similarly, higher borrowing fees will proxy for higher belief dispersion even in more general settings with a continuous distribution of beliefs. In such a setting, the borrowing cost will reflect the difference in beliefs between the marginal buyer and the marginal seller. 2Note we do not have data to identify whether firms are constrained pre-1980. However, in these value-weighted portfolios, constrained firms have a negligible weight. We confirm this in the post-1980 period. 3The compounded market-adjusted return from years 2 through 5 postformation for each portfolio is the difference between the 4-year (years 2 through 5 postformation) buy-and-hold return of the portfolio and the 4-year buy-and-hold return of the market. The numbers in the text are the overall averages of all |$363$| (|$411$| for the first year postformation) compounded market-adjusted returns for constrained winner and loser portfolios formed during our sample period, respectively. Although the methodology used to calculate the compounded market-adjusted return is different from that used to calculate the cumulative abnormal returns (in Figure 1), both methods deliver consistent results. 4Constrained losers do not earn negative risk-adjusted returns 1 year after portfolio formation, although disagreement is still high. This result is at odds with the wisdom-of-crowds hypothesis that the consensus forecast is rational. Specifically, based on the reasoning above, it suggests short sellers of these securities are losing money by paying high shorting fees and are overly pessimistic, whereas the optimistic agents holding these hard-to-borrow securities have approximately correct beliefs. Most empirical results in the short selling literature, including our results for constrained winners, emphasize that short sellers tend to be right, and buyers are too optimistic. However, for this portfolio of constrained losers, the consensus view is too pessimistic, not too optimistic. 5Specifically, these stocks are in the top/bottom 30|$\%$| of past returns over the past 12 months (skipping the last month) and the top 20|$\%$| of changes in analyst forecast dispersion over the past 12 months. Additionally, we exclude short-sale constrained stocks, that is, those in the bottom 30|$\%$| of IOR or the top 30|$\%$| of SIR. The characteristics associated with these portfolios can be found in Table C.10 in Internet Appendix C.VII. 6By contrast, Israel and Moskowitz (2013) provide evidence that momentum, value, and size are robust on the long side and thus do not overly rely on short selling. 7Specifically, we only consider stocks with an exchange code of 1, 2, or 3, and a share code of 10 or 11. Returns are adjusted for delisting (Shumway 1997) using the CRSP delisting return, where available. Where the delisting return is missing, we follow Scherbina and Schlusche (2015) and assume a delisting return of |$-$|100|$\%$|, or, if the delisting code is 500, 520, 551–573, 574, 580, or 584, we assume a delisting return of |$-$|30|$\%$|. 8See the note issued by WRDS in May 2017. We perform some additional data cleaning. For example, we identify some firms with implausibly large jumps in IOR in a given quarter that are generally followed by roughly equal jumps in the opposite direction in the following quarter. See Internet Appendix B.II for the procedure we employ to correct such errors. 9For example, the first trade based on December ownership data occurs in February of the following year. Note also that the 30|$\%$| and 70|$\%$| breakpoints are based on a sample that excludes stocks with missing ownership data. Following Nagel (2005), we assign stocks with missing ownership zero institutional ownership and consequently allocate them to the low IOR portfolio. We do this so that the secular increase in IOR data coverage over our sample period does not influence our sorts. 10In previous versions of the paper we exclusively used data starting from June 1988, when NASDAQ data started being available. Therefore, the additional 8 years of data can be considered an out-of-sample test. We run our key tests in this subperiod and report the findings in Internet Appendix E.II. In short, the findings are consistent. We thank a referee for making this suggestion. 11We apply additional procedures to better match these short interest data with CRSP data. This approach increases the number of firm-month observations, reduces noise, and strengthens all results. See Internet Appendix B.II for details. 12Exchange data from NYSE are available after September 1991 and from AMEX starting in December 1994. Compustat data are used prior to these dates. Because Compustat coverage of NASDAQ firm was low prior to June 2003, exchange data are the primary source for NASDAQ before that date. Furthermore, data from NASDAQ in February and July 1990 are missing (Hanson and Sunderam 2014). Other papers using these data sources include Curtis and Fargher (2014), Ben-David, Drake, and Roulstone (2015), and Hwang and Liu (2014). 13From August 2004, Markit data frequency is weekly; daily coverage began in July 2006. 14As an alternative specification, we follow Johnson (2004) and use total assets to normalize. Furthermore, we replicate the result with one-quarter-ahead quarterly earnings forecasts. Another alternative is to use the standard deviation in long-term growth forecasts of earnings (see, e.g., Yu 2011; Hong and Sraer 2016), which does not need to be scaled. Results are consistent with the findings presented in Section and can be found in Tables F.17 to F.19 in Internet Appendix F.IX. 15This intuition is reflected in the design of the securities lending market in our model, outlined in more detail in Internet Appendix A.I.3. It is also consistent with the empirical results in Kolasinski, Reed, and Ringgenberg (2013) showing search frictions strongly affect the costs of short selling. 16We present the main results for alternative shorter momentum signals (3 and 6 months) in Internet Appendix F.VII. Furthermore, we use abnormal returns around earnings announcements and outside of earnings announcements over the |$t-12$| through |$t-2$| window in Internet Appendix F.VIII. Results remain consistent in each of these alternative specifications. 17Results for all constrained losers and the subset of constrained losers that were constrained winners within the past 5 years can be found in Internet Appendix C.III. 18 In our model, where, ceteris paribus, constrained winners will lose value over a number of years, they will continue to be constrained and potentially become constrained losers at some point. Such constrained losers are not losers based on a negative information shock (as in the pink profile in panel B in Figure 3). Rather, they are former constrained winners that are already somewhere in the process of disagreement (and prices) adjusting downward (e.g., a stock whose price behaves like the green line in panel B of Figure 3, at period 1 or 2). 19Note the same argument does not apply the other way around, that is, splitting the constrained winners into those that were/were not constrained losers in the past 5 years is not necessary. The postformation trajectory of a constrained loser is negative initially and then flat, but never positive, so it can never be classified as a constrained winner. 20The two rightmost columns present characteristics of matched-firm portfolios, which we introduce and discuss in Section . To allow for a comparison with the broader universe of stocks, we display averages for the remaining portfolios in Table C.7 in Internet Appendix C.V. 21Note, on average, 52 individual stocks are classified as constrained losers that were constrained winners at some point in the past 5 years. Recall that these stocks are not included in the |$L^*$| portfolio. 22The loan fees displayed here are high, especially relative to the results in D’Avolio (2002), indicating short selling our constrained stocks might be prohibitively expensive. However, investors can simply benefit from the insights of this paper by avoiding past constrained winners when running medium-/small-cap momentum strategies, as indicated by Table D.7 in the Internet Appendix. 23Interpreted differently, the numerator of the buy-and-hold weight |$W$| for stock |$i$| in portfolio |$p$| at portfolio formation time |$t-1$|, is the sum of market equity values (|$ME=PRC*SHROUT$|) of all |$\mathrm{T}$| occurrences at (|$t-\tau$|) this stock was allocated to portfolio |$p$| during the formation period, adjusted for the price change without dividends and adjusted for capital actions (e.g., splits, issuances, or repurchases): $$ W_{i,p,t-1} = \sum_{\tau \in \mathrm{T}} ME_{i,t-\tau} RET^{x}_{i,t-\tau, t-1}, $$ where |$PRC$| (price), |$SHROUT$| (shares outstanding), and |$RET^{x}$| (ex-dividend return) are the respective CRSP variables. The weight of stock |$i$| in portfolio |$p$| consisting of stocks |$I_{p,t-1}$| is then |$w_{i,p,t-1} = \frac{W_{i,p,t-1}}{\sum_{j \in I_{p,t-1}} W_{j,p,t-1}}$|. Traditional equal-weight calendar-time portfolios with overlapping holding-periods, as in Jegadeesh and Titman (1993), can be found in Internet Appendix F.V. In addition, we also construct a version of the portfolios, where we just include any stock that falls into portfolio |$p$| at any point in time during the formation period (i.e., the past 12 months) weighted by the stock’s market equity at the end of the formation period |$t-1$|. The main difference from our default buy-and-hold approach is that a stock that fell into a portfolio more than once during the past |$\mathrm{T}$| months is only considered once here. See Internet Appendix F.VI for the results of this simple value-weight specification. Note that we obtain similar results with both the Jegadeesh and Titman (1993) and the simple value-weight specifications. See Internet Appendix B.IV for a detailed discussion of measuring long-term returns. 24In Table F.3 in Internet Appendix F.II, panels A and B, we regress 12-month buy-and-hold excess returns of |$W^{*}_{\rm S}$| and |$L^{*}_{\rm S}$| on a number of other well-known factors. Their returns cannot be explained by any of the factors, not even a factor based on the ratio of short interest to institutional ownership, as in Drechsler and Drechsler (2016). In unreported results (available on request), we also examine the effect of using a monthly-updated version of HML as in Asness and Frazzini (2013) and characteristic-efficient versions of the right-hand-side portfolios as in Daniel et al. (2020). Alphas are virtually unaffected by either of these changes. 25Each month, $1 worth of the most recent (12-month-old) constrained portfolio is added, and then this portfolio is not rebalanced until it is sold 48 months later. The first holding month is April 1990, that is, the first time we are able to determine portfolio membership for 48 months in a row. 26Figures C.2 to C.4 show time variation in the number of stocks in the portfolios. The |$W^{*}_{\rm L}$| strategy portfolio (Figure C.4) contains between 200 and more than 700 stocks, while the |$L^{*}_{\rm L}$| strategy contains between 100 and 400 stocks. 27A 60-month buy-and-hold portfolio of constrained winners that does not skip the first 12 months after formation yields a four-factor information ratio of |$-0.73$| (see Internet Appendix C.III Table C.4). Such a portfolio has |$511$| unique stocks in it. Moreover, using the simple value-weight approach, described in Footnote 23, and a strategy using an allocation between months |$t-60$| and |$t-1$|, we are able to generate a four-factor information ratio of |$-1.02$|. 28In Table C.3 in Internet Appendix C.III, we contrast |$L^{*}_{\rm L}$| with a strategy of portfolios of constrained losers that were constrained winners in the 5 years before they became constrained losers (|$L^{*W}_{\rm L}$|). |$L^{*W}_{\rm L}$| has a negative (albeit insignificant) alpha. The difference between the two is significant at the 5|$\%$| level. Moreover, spanning tests, the results of which are reported in Table F.4, show constrained winners help explain the long-horizon returns of all constrained losers, whereas the opposite is not true. The result holds for raw returns as well as when the three Fama and French (1993) factors and momentum are included. Both results are consistent with the |$L^{*W}$| stocks (i.e., those constrained losers that were constrained winners within the past 5 years) driving the low long-horizon returns of the combined constrained-loser portfolios (|$L^{*all}$|). 29Specifically, we calculate the returns to the portfolios for each sample month. We then run a full-sample regression of the portfolio excess returns on Mkt-RF. Then, using the full-sample regression coefficient, we subtract the returns of the zero-investment hedge portfolio |$[\text{b}_{\text{Mkt}}(\text{R}_{\text{Mkt}}\text{-}\text{R}_{\text{f,t}})]$| from the respective portfolio excess returns to generate the hedged excess returns. The factor return data come from Kenneth French’s data library. 30We thank our discussant Adam Reed for suggesting the use of short interest as a matching variable. In Internet Appendix F.III, we redo this exercise with an alternative set of matching variables, namely, size, book-to-market, past return, and institutional ownership, making short interest the variable that distinguishes constrained from matched stocks. The results remain strong and statistically significant for this specification. Using past long-term return (months t-36 through t-13) instead of the log book-to-market ratio as a matching variable also has little impact on the results (available on request). Matching based on propensity scores instead of Mahalanobis distances produces very similar results as well (available on request). 31Standard errors are adjusted for heteroscedasticity and serial correlation using the Newey and West (1987) procedure, where the number of lags is determined automatically (Newey and West 1994). The detected lags vary between 8 and 11 (except for |$L^{*}_{L}$|, where it is 2). Furthermore, standard errors are slightly smaller than White standard errors, indicating negative residual autocorrelation. See Internet Appendix B.III for statistical inferences based on various bootstrapping techniques. 32Specifically, we calculate the buy-and-hold return, as explained in Section for the first holding-year, for each following year, in the same fashion. We then run a time-series regression of the monthly excess returns of these 12-month buy-and-hold portfolios on the CAPM-Mkt factor. The annualized alpha, as well as the 95|$\%$| confidence interval, constructed based on Newey-West standard errors, are plotted for each year after formation. 33Note we cannot reject the hypotheses that the average first-year returns of the matched winners and losers in Figure 5 are equal to those of the winners and losers in the full sample plotted in Figure 1 Panel A and tabulated in Table D.4. The |$p$|-values from Welch’s (unequal variances) |$t$|-tests are |$p=0.67$| for winners and |$p=0.55$| for losers. 34We directly test the assumption that earnings announcements decrease disagreement in Internet Appendix D.I by looking at dispersion in beliefs before and after announcements. Disagreement goes down significantly for firms with high initial disagreement, consistent with our assumption and with the evidence presented in Berkman et al. (2009). 35The daily abnormal return is defined as the return adjusted for the CAPM-MktRF factor. See Internet Appendix B.V for a detailed explanation of the abnormal returns calculation. 36Another caveat with these data is that they are only available for the largest stocks for which we typically do not observe binding short-sale constraints. For example, only 20|$\%$| of the stock-month observations that we identify as having low IOR (i.e., in the bottom 30|$\%$|) have a nonmissing forecast dispersion. Hence, to study returns, in the previous sections, we resort to the proxy based on past return and SIR. 38An ad hoc, empirically motivated explanation for the short-term patterns is what we call the additive effect hypothesis: suppose momentum and long-term reversal effects exist for all stocks. Further suppose constrained stocks generally underperform and that the constrained-stock effect is roughly as large as the long-term reversal effect at longer horizons. To reflect the effect of short-sale constraints, we could simply add a constant negative slope to the impulse-response function of both unconstrained winners and losers and assume this slope just cancels out with the positive long-term reversal of past losers (i.e., the magnitudes of both effects are about the same). This hypothesis would predict long-term mispricing persistence for winners, but not for losers, in addition to no winner momentum and amplified loser momentum in the short run. A testable implication of the additive effect hypothesis is that the DiD between constrained winners and unconstrained winners and constrained losers and unconstrained losers is the same at all horizons. The effect of short-sale constraints is always added to the empirical patterns of momentum and long-term reversals for winners and losers. In Section , we employ a matching approach to specifically test this. The data clearly reject the hypothesis: constrained winners underperform, whereas constrained losers exhibit no significant difference, relative to their matched counterparts, in years 2 through 5 postformation. The DiD is highly statistically significant (see Table 3). 39We define a “sidelined” agent as one who chooses not to short the security, but who would short if borrow costs were zero. Agents may be partly sidelined, in the sense that they short less of the security than they would if costs were zero, or may be fully sidelined, in the sense that they choose not to participate at all (i.e., to short zero shares). 40Kahneman and Tversky (1973) suggest the term “illusion of validity” for the observation that “people are prone to experience much confidence in highly fallible judgments.” Kahneman (2011) links this illusion to the financial industry (see pp. 212–6 for a discussion of what Kahneman calls “the illusion of stock-picking skills”). 41The behavioral sciences also provide evidence that overconfidence can increase with more information. Oskamp (1965) asked psychologists to assess the personality of a patient. Information was provided in chunks, and judges responded to a questionnaire after having received a new piece of information. With more information, judges believed they became more accurate in assessing the personality of the patient, although their predictive ability actually stayed constant. Applied to financial decision-making, this result implies overconfidence should be more pronounced among professionals than among novices. In a study by Glaser, Langer, and Weber (2013), traders indeed showed a higher degree of overconfidence than students in two forecasting tasks. 42This assumption is also consistent with the evidence reported in Boutros et al. (2020), who show strong-conviction/overconfident miscalibration is extremely persistent. Conformity bias (Wason 1960; Klayman and Ha 1987; Rabin and Schrag 1999) provides a plausible mechanism to explain why overconfident people are slow to revise their priors. 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2006 . Information uncertainty and stock returns . Journal of Finance 61 : 105 – 37 . © The Author(s) 2022. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. What are the criticisms of behavioral finance?The key criticisms of behavioral finance theory are that its assumptions about individual behavior are descriptively false and incomplete, and it often lacks predictive power. What are the flaws of Behavioural finance?Reduces Confidence: Another big problem with behavioral finance theory is that it drastically reduces investor confidence. After reading these theories, many investors have reported that they face difficulties while making decisions. This is because investors start second-guessing themselves. What are the limitations of Behavioural finance?Behavioural finance theory ignores the impact of social status on investment decisions. Some investments are made only to increase social status and investors do not care about the economic impact of such investments e.g. people purchase expensive houses and other goods to to 'keep up with the Jones's'. What are the biases revealed by behavioral finance?Some of the biases affecting financial decisions are confirmation bias, disposition bias, experiential bias, familiarity bias, loss aversion, mental accounting, and overconfidence. Understanding the psychological bias influence can help investors understand the market behavior and make better investment decisions. |
