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HE JOURNAL OF FINANCE· VOL. XL NO.3·JULY1985 Does the Stock Market Overreact? WERNER F M. De bondt and RICHARD THALER* ABSTRACT Research in experimental psychology suggests that, in violation of Bayes'rule, most people tend to"overreact "to unexpected and dramatic news events. This study of market efficiency investigates whether such behavior affects stock prices. The empirical evidence, based on CRSP monthly return data, is consistent with the overreaction hypothesis. Substantial weak form market inefficiencies are discovered. The results also shed new light on the January returns earned by prior"winners"and"losers "Portfolios portfolio formation As ECONOMISTS INTERESTED IN both market behavior and the psychology of individual decision making, we have been struck by the similarity of two sets of mpirical findings Both classes of behavior can be characterized as displaying overreaction. This study was undertaken to investigate the possibility that these phenomena are related by more than just appearance. We begin by describing briefly the individual and market behavior that piqued our interest. The term overreaction carries with it an implicit comparison to some degree of reaction that is considered to be appropriate. what is an appropriate reaction? One class. of tasks which have a well-established norm are probability revision problems for which Bayes'rule prescribes the correct reaction to new information It has now been well-established that Bayes'rule is not an apt characterization of how individuals actually respond to new data(Kahneman et al. [14). In revising their beliefs, individuals tend to overweight recent information and underweight prior(or base rate)data. People seem to make predictions according to a simple matching rule: "The predicted value is selected so that the standing of the case in the distribution of outcomes matches its standing in the distribution of impressions"(Kahneman and Tversky [14, p. 416]). This rule-of-thumb, a instance of what Kahneman and Tversky call the representativeness heuristic violates the basic statistical principal that the extremeness of predictions must be moderated by considerations of predictability Grether [12] has replicated this finding under incentive compatible conditions. There is also considerable evi- dence that the actual expectations of professional security analysts and economic forecasters display the same overreaction bias(for a review, see De Bondt [7]) One of the earliest observations about overreaction in markets was made byJ M. Keynes: .. day-to-day fluctuations in the profits of existing investments University of wisconsin at Madison and Cornell University, respectively. The financial support the C.I.m. Doctoral Fellowship Program(Brussels, Belgium)and the Cornell G Management is gratefully acknowledged. We received helpful comments from Seymour Smidt, Dale Morse, Peter Bernstein, Fischer Black, Robert Jarrow, Edwin Elton, and Ross Watts 793

The Journal of finance which are obviously of an ephemeral and nonsignificant character, tend to have an altogether excessive, and even an absurd, influence on the market"[17, pp 153-154]. About the same time, Williams noted in this Theory of Investment value that"prices have been based too much on current earning power and too little on long-term dividend paying power"[28, p. 19]. More recently, arrow has concluded that the work of Kahneman and T'versky"typifies very precisely the exessive reaction to current information which seems to characterize all the securities and futures markets "[1, p. 5]. Two specific examples of the research to which Arrow was referring are the excess volatility of security prices and the so-called price earnings ratio anomaly The excess volatility issue has been investigated most thoroughly by Shill [27]. Shiller interprets the Miller-Modigliani view of stock prices as a constraint on the likelihood function of a price-dividend sample. Shiller concludes that, at least over the last century, dividends simply do not vary enough to rationally justify observed aggregate price movements. Combining the results with Kleidon's [18 ] findings that stock price movements are strongly correlated with the follow- ing year's earnings changes suggests a clear pattern of overreaction. In spite of the observed trendiness of dividends, investors seem to attach disproportionate importance to short-run economic developments The price earnings ratio(P/E)anomaly refers to the observation that stocks with extremely low P/E ratios(i. e, lowest decile)earn larger risk-adjusted returns than high P/E stocks(Basu [31). Most financial economists seem to regard the anomaly as a statistical artifact. Explanations are usually based on alleged misspecification of the capital asset pricing model (CAPm). Ball [2] emphasizes the effects of omitted risk factors. The P/E ratio is presumed to be a proxy fo some omitted factor which, if included in the correct"equilibrium valuatic model, would eliminate the anomaly Of course, unless these omitted factors can be identified, the hypothesis is untestable. Reinganum [21] has claimed that the small firm effect subsumes the P/E effect and that both are related to the sam set of missing(and again unknown) factors. However, Basu[4] found a significant P/E effect after controlling for firm size, and earlier Graham [11] even found ar effect within the thirty dow Jones Industrials, hardly a group of small firms! An alternative behavioral explanation for the anomaly based on investor overreaction is what Basu called the "price-ratio"hypothesis (e.g, Dreman [8]) Companies with very low P/E's are thought to be temporarily "undervalued because investors become excessively pessimistic after a series of bad earnings reports or other bad news. Once future earnings turn out to be better than the unreasonably gloomy forecasts, the price adjusts. Similarly, the equity of com panies with very high P/E's is thought to be"overvalued, " before (predictably) While the overreaction hypothesis has considerable a priori appeal, the obt question to ask is: How does the anomaly survive the process of arbitrage? There Of course, the variability of stock prices may also reflect changes in real interest rates. If so, the ally observed. A third hypothesis, advocated by Marsh and Merton [19], is that gs are a result of his misspecification of the dividend process

is really a more general question here. What are the equilibria conditions for markets in which some agents are not rational in the sense that they fail to revise their expectations according to Bayes'rule? Russell and Thaler [24] address this issue. They conclude that the existence of some rational agents is not sufficient to guarantee a rational expectations equilibrium in an economy with some of what they call quasi-rational agents. ( The related question of market equilibria with agents having heterogeneous expectations is investigated by Jarrow [13].) While we are highly sensitive to these issues, we do not have the space to address them here Instead, we will concentrate on an empirical test of the overreaction hypothesis. If stock prices systematically overshoot, then their reversal should be predict able from past return data alone, with no use of any accounting data such as earnings. Specifically, two hypotheses are suggested: (1)Extreme movements in stock prices will be followed by subsequent price movements in the opposite direction.(2) The more extreme the initial price movement, the greater will be the subsequent adjustment. Both hypotheses imply a violation of weak-form market efficiency. To repeat, our goal is to test whether the overreaction hypothesis is predictive In other words, whether it does more for us than merely to explain, ex post, the P/E effect or Shiller's results on asset price dispersion. The overreaction effect deserves attention because it represents a behavioral principle that may apply in many other contexts. For example, investor overreaction possibly explains Shill er's earlier [26] findings that when long-term interest rates are high relative to short rates, they tend to move down later on. Ohlson and Penman [20 have further suggested that the increased volatility of security returns following stock splits may also be linked to overreaction. The present empirical tests are to our knowledge the first attempt to use a behavioral principle to predict a new market The remainder of the paper is organized as follows. The next section describes the actual empirical tests we have performed. Section II describes the results Consistent with the overreaction hypothesis, evidence of weak-form market inefficiency is found. We discuss the implications for other empirical work on asset pricing anomalies. The paper ends with a brief summary of conclusions I. The Overreaction Hypothesis: Empirical Tests The empirical testing procedures are a variant on a design originally proposed by beaver and Landsman [5]in a different context. Typically, tests of semistror form market efficiency start, at time t=0, with the formation of portfolios on the basis of some event that affects all stocks in the portfolio, say, an earnings announcement. One then goes on to investigate whether later on(t>0)the estimated residual portfolio return iptmeasured relative to the single-period CAPM--equals zero Statistically significant departures from zero are interpreted as evidence consistent with semistrong form market inefficiency, even though the results may also be due to misspecification of the CAPm, misestimation of the relevant alphas and or betas or simply market inefficiency of the weak form

In contrast, the tests in this study assess the extent onzero residual return behavior in the period after portfolio formation(t>0) is associated with systematic residual returns in the preformation months (t< 0). We will focus on stocks that have experienced either extreme capital gains or xtreme losses over periods up to five years. In other words, winner"(w)and loser"portfolios(L)are formed conditional upon past excess returns, rather than some firm-generated informational variable such as earnings. on Following Fama [9], the previous arguments can be formalized by writing the fficient market's condition E(Rit -Em(Rt FmiIFi-n=E(untI Ft-1)=0 where F-I represents the complete set of information at time t-1, Rit is the return on security j at t, and Em(Rit| Fr-1)is the expectation of Rit, assessed by the market on the basis of the information set Fm. The efficient market hypothesis implies that e(uwt Ft-1)= E(uu I Ft-1)=0. As explained in the introduction, the overreaction hypothesis, on the other hand, suggests that In order to estimate the relevant residuals, an equilibrium model must be specified. a common procedure is to estimate the parameters of the market model (see e. g, Beaver and Landsman [5). what will happen if the equilibrium model is misspecified? As long as the variation in Em(Rt I Fr-1)is small relative to the movements in uit, the exact specification of the equilibrium model makes little difference to tests of the efficient market hypothesis. For, even if we knew the correct"model of Em(Rit I F1), it would explain only small part of the variation in rit. Since this study investigates the return behavior of specific portfolios over extended periods of time (indeed, as long as a decade), it cannot be merely assumed that model misspecification leaves the conclusions about market effi iency unchanged. Therefore, the empirical analysis is based on three types of return residuals: market-adjusted excess returns; market model residuals; and excess returns that are measured relative to the Sharpe-Lintner version of the CAPM. However, since all three methods are single- index models that follor from the CAPM, misspecification problems may still confound the results De bondt [7 formally derives the econometric biases in the estimated market djusted and market model residuals if the true?"model is multifactor, e.g A,+B Rmt+CiX,+ejt. As a final precaution, he also characterizes the securities in the extreme portfolios in terms of a number of financial variables If there were a persistent tendency for the portfolios to differ on dimensions that may proxy for "risk, then, again, we cannot be sure whether the empirical results It turns out that, whichever of the three types of residuals are used, the results 2 Presumably this same reasoning underlies the c f measuring abnormal security E(R,)equals (where, by assump 1 for all]), rather than more complicated market mo iduals, let along residuals relative to some

Does the stock market Overreact? of the empirical analysis are similar and that the choice does not affect our main conclusions. Therefore, we will only report the results based on market-adjusted excess returns. The residuals are estimated as ujt=Rjt-Rmt. There is no risk adjustment except for movements of the market as a whole and the adjustment is identical for all stocks. Since, for any period t, the same(constant) market return Rmt is subtracted from all R; s, the results are interpretable in terms of raw(dollar)returns. As shown in De Bondt [7], the use of market-adjusted excess returns has the further advantage that it is likely to bias the research desig against the overreaction hypothesis. Finally, De Bondt shows that winner and loser portfolios, formed on the basis of market-adjusted excess returns, do not systematically differ with respect to either market value of equity, dividend yield We will now describe the basic research design used to form the winner and loser portfolios and the statistical test procedures that determine which of the two competing hypotheses receives more support from the data. A. T'est Procedures: Details Monthly return data for New York Stock Exchange(NYSE) common stocks, as compiled by the Center for Research in Security Prices(CRSP)of the University of Chicago, are used for the period between January 1926 and December 1982. An equally weighted arithmetic average rate of return on all CRSP listed securities serves as the market index 1. For every stock j on the tape with at least 85 months of return data( months 1 through 85), without any missing values in between, and starting in January 1930(month 49), the next 72 monthly residual returns ujt(months 49 through 120)are estimated. If some or all of the raw return data beyond month 85 are missing, the residual returns are calculated up to that point. The procedure is repeated 16 times starting in January 1930, January 1933,..., up to January 1975. As time goes on and new securities appear on the tape, more and more stocks qualify for this step. 2. For every stock j, starting in December 1932(month 84; the " portfolio formation date")(t=O), we compute the cumulative excess returns CUj Ei=-35 Ujt for the prior 36 months(the"portfolio formation period, months 49 through 84). The step is repeated 16 times for all nonoverlapping three year periods between January 1930 and December 1977. On each of the 1 relevant portfolio formation dates(December 1932, December 1935, December 1977), the CU,'s are ranked from low to high and portfolios are formed. Firms in the top 35 stocks(or the top 50 stocks, or the top decile) are assigned to the winner portfolio W; firms in the bottom 35 stocks(or the bottom 50 stocks, or the bottom decile)to the loser portfolio L. Thus, the portfolios are formed conditional upon excess return behavior prior to t 0, the portfolio formation date. 3. For both portfolios in each of 16 nonoverlapping three-year periods(n 3 We will come back to this bias in Section II

The Journal of finance l,..., N; N= 16), starting in January 1933(month 85, the " starting month")and up to December 1980, we now compute the cumulative average residual returns of all securities in the portfolio, for the next 36 months (the "test period, months 85 through 120), i.e from t= 1 through t= 36 We find CAR w n, t and CARLn,t. If a security s return is missing in a month ubsequent to portfolio formation, then, from that moment on, the stock is permanently dropped from the portfolio and the Car is an average of the available residual returns. Thus, whenever a stock drops out, the calculations involve an implicit rebalancing 4. Using the CAr's from all 16 test periods, average CAr's are calculated for both portfolios and each month between t=l and t= 36. They are denoted ACARw and ACARL t. The overreaction hypothesis predicts that, for t> 0, ACARw, t0, so that, by implication, [ACARL, ACARw >0. In order to assess whether, at any time t, there is indeed a statistically significant difference in investment performance, we need a pooled estimate of the population variance in CARt ACARL,)2/2(N-1) With two samples of equal size N, the variance of the difference of sample means equals 2S/N and the t-statistic is therefore T=[ACARL:-ACARw1/2S2/N Relevant t-statistics can be found for each of the 36 postformation months but they do not represent independent evidence 5. In order to judge whether, for any month t, the average residual return makes a contribution to either ACARwt or ACARLt, we can test whether it is significantly different from zero. The sample standard deviation of the winner portfolio is equal to √∑N1( ARw-ARw2)2/N-1. Since s //N represents the sample estimate of the standard error of ARw the t-statistic equals T=ARw:/(s:/√N Similar procedures apply for the residuals of the loser portfolio B. Discussion Several aspects of the research design deserve some further comment. The choice of the data base, the CRSP Monthly Return File, is in part justified by 4 Since this study concentrates on companies that experience extraordinary returns, either positive or negative there may be some concern that their attrition rate sufficiently deviates from the rmal"rate so as to cause a survivorship bias. however this concern is unjustified. when a security delisted, suspended or halted, crsP determines whether or not it is possible to trade at the las CRSP tries to find a subsequent quote and uses it to compute a ch quote is available because the stockholders receive nothing for as minus one. If trading continues the last return ends with the last listed price

Does the Stock Market Overreact our concern to avoid certain measurement problems that have received much attention in the literature. Most of the problems arise with the use of daily data both with respect to the risk and return variables. They include, among others the " bid -ask"effect and the consequences of infrequent trading The requirement that 85 subsequent returns are available before any firm is allowed in the sample biases the selection towards large, established firms. But if the effect under study can be shown to apply to them, the results are, if anything, more interesting. In particular, it counters the predictable critique that the overreaction effect may be mostly a small-firm phenomenon. For the exper iment described in Section A, between 347 and 1,089 NYSE stocks participate in the various replications The decision to study the CAr's for a period of 36 months after the portfolio formation date reflects a compromise between statistical and economic consid erations, namely, an adequate number of independent replications versus a time period long enough to study issues relevant to asset pricing theory. In addition the three-year period is also of interest in light of Benjamin grahams contention that the interval required for a substantial undervaluation to correct itself averages approximately 11 to 21 years"[10, p. 37). However, for selected experiments, the portfolio formation(and testing) periods are one, two, and five years long. Clearly, the number of independent replications varies inversely with the length of the formation period Finally, the choice of December as the " portfolio formation month"(and, therefore, of January as the starting month")is essentially arbitrary. In order to check whether the choice affects the results, some of the empirical tests use May as the portfolio formation month I. The Overreaction Hypothesis: Empirical Result A. Main Findings The results of the tests developed in Section I are found in Figure 1. They are consistent with the overreaction hypothesis. Over the last half-century, loser portfolios of 35 stocks outperform the market by, on average, 19.6%, thirty-six months after portfolio formation. winner portfolios, on the other hand, earn about 5.0% less than the market, so that the difference in cumulative average residual between the extreme portfolios, [ACARL, 36- ACARw, 3] equals 24.6% (t-statistic: 2.20). Figure 1 shows the movement of the ACAR's as we progress through the test period The findings have other notable aspects First, the overreaction effect is asymmetric; it is much larger for losers than for winners. Secondly, consistent with previous work on the turn-of-the-year effect and seasonality, most of the excess returns are realized in January. In months t=l, t= 13, and t= 25, the pectively, 8.1%(t-statistic: 3.21), 5.6% (3.07), and 4.0%(2.76). Finally, in surprising agreement with Benjamin Grahams claim, the overreaction phenomenon mostly occurs during the second and thire hs into performance between the extreme portfolios is a mere 5.4%(t-statistic: 0.77)

Does the stock market Overreact Table I Differences in Cumulative Average(Market-Adjusted) Residual Returns Between the winner and Loser Portfolios at the End of the Formation Period, and 1, 12, 13, 18, 24, 25, 36, and 60 Months CAR at the end the Formation Difference in CAR (t-Statistics) he Formation Period ndependent Replications sos Minters Months After Port folio Form Loser Portfolio 16 three-year periods 24 two-year periods' 351.130-08570062-0.00600740.1360.101 NANANA 25 twoyear periods 1119-0.8660.08900110.0920.1070115 NA NA NA )(147)(1.55) 24 two- year periods 820875-0.7110.05 NA NA NA 19)(171)(1.99) 25 two-year periods" 820868-07140.068000 NA NA NA 19)(1,46)(141) 0.774-0585 0.076-0.0060.007-0.005 NANA NA The formation month for these portfolios is the month of December in all even years between 1932 and 1980. ality in stock prices. Throughout the test period, the difference in ACAR for the experiment with a three-year formation period (the upper curve) exceeds the same statistic for the experiments based on two-and one-year formation periods (middle and lower curves ). But all three experiments are clearly affected by the same underlying seasonal pattern. In Section I, it was mentioned that the use of market-adjusted excess returns is likely to bias the research design against the overreaction hypothesis. The bias can be seen by comparing the CAPM-betas of the extreme portfolios For experiments listed in Table I, the average betas of the securities in the w portfolios are significantly larger than the betas of the loser portfolios 5 example, for the three-year experiment illustrated in Figure 1, the relevant numbers are respectively, 1.369 and 1.026 (t-statistic on the difference: 3.09 Thus, the loser portfolios not only outperform the winner portfolios; if the CaPm is correct, they are also significantly less risky. From a different viewpoint particularly severe with respect to the winner portfolio. Rather than 1.369, the residual return calculations assume the CAPM-beta of that portfolio to equal The CAPM-betas are found by estimating the market model over a period of 60 months prior