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the portfolio with the largest (smallest) historical value for C#J (1.54 percent versus 1.21 percent), and the abnormal return at quarter t + 4 was most (least) negative for the portfolio with the largest (smallest) historical value for 8 (- 1.09 percent versus -0.74 percent). However, the differences were not statistically significant. One possible explanation is that cross-sectional differences in time-series parameters are too small to provide much predictive power. (Recall the similarity in time-series behavior across industries in table 1.) Another possibility is that while cross-sectional differences exist, they are unstable or estimated with considerable error. Much of the time-series literature [e.g., Albrecht, Lookabill, and McKeown (1977), Foster (1977), Watts and Leftwich (1977)] is consistent with such cross-sectional differences not being predictable out of sample. 4. Alternative
explanations and additional evidence
It is difficult to understand how stock prices could fail to reflect the implications of current earnings for future earnings in such a systematic way. The evidence naturally raises several questions, which we discuss below. (1) Can this ecidence be explained in terms of rational incestors desire to await confirmation that a precious earnings change is not transitory? An immediate problem with this explanation is that, at best, it fits only the patterns observed around the announcements of earnings for quarters t + 1, t + 2, and t + 3; the reactions for quarter t + 4 are consistent with investors treating previous earnings as if they were more permanent than they turned out to be. There is a more fundamental problem with this explanation, however. No matter how much uncertainty surrounds the implications of earnings already announced for quarter t, prices in an efficient market would immediately reflect an unbiased expectation of future earnings, and future abnormal returns would be uncorrelated with past earnings changes. Even if increased uncertainty caused by extreme earnings changes is relevant for pricing, it could not explain the evidence. While it is true in that case that a postannouncement drift (actually, a risk premium) would be observed, it would be positive for both extreme-bad-news and extreme-good-news firms. [See Brown, Harlow, and Tinic (1988X] Both the existing literature on post-announcement drift and this study (see table 2) document a negative drift for bad-news
filllls.
(2) Does the evidence reflect autocorrelations in earnings that were observable ex post, but not predictable ex ante? Two pieces of evidence contradict this explanation. First, the autocorrelation patterns we observed in our sample period were also observed by Foster for
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Table 7 Consistency (over time) of relation between market reactions to future earnings announcements and current-quarter earnings information. Mean abnormal return during three-day I-2,0] window around earnings announcement for quarter t + k, for portfolio including long (short) position in firms in highest (lowest) decile of SUE in quarter ta (predicted sign of abnormal return in parentheses)
t+l
t+t
(+I 3.05c 0.80C 0.41 o.87c 0.78C 0.76c 0.87c 0.78 0.26 0.73c o.50c 0.19 0.81
t-+3
(+I 0.89 - 0.43 -0.15 -0.01 0.69 -0.10 0.21 0.20 -0.19 0.12 0.27 - 0.70 0.54
t+4
f-J NAb - 1.32c - 0.9gc -0.41 -0.15 - 0.39 - 0.9ac - 0.57c - 1.05c - o.75c - 0.06 - 0.91= -0.19
Year 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
(+I 3.74= 2.28 1.30c 1.69 1.06= 1.08 1.48c l.lOC 1.08c l.llC o.70c 1.12c 0.84
SUE represents forecast error from the seasonal random-walk (with trend) earnings-expectation model, scaled by its estimation-period standard deviation. Abnormal returns are the differences between daily returns for individual firms in the SUE decile portfolio and returns for NYSE-AMEX firms of the same size decile, based on January 1 market values of equity. bSince SUES are calculated beginning in the first quarter of 1974, four-quarter-ahead predictions are not possible for any quarter in that year. ?Statistically significant at 0.05 level, one-tailed test.
1946-1974. In fact, the positive autocorrelations in earnings changes at lags 1, 2, and 3 are weaker during our sample period than in Fosters earlier period, making it difficult to argue that the market was justified in being surprised at the degree of autocorrelation in earnings observed in our sample. [Our own expectations were based largely on the evidence in Foster (19771, and the evidence in tables 2 through 5 was generated before we produced the autocorrelations reported in table 1.1 The second piece of evidence is presented in table 7. Although the market might err in its expectations about the degree of autocorrelation in earnings, it is difficult to explain how it could justifiably err in the same direction year after year. Table 7 shows that the mean three-day abnormal returns around the announcement for quarter t + 1 and t + 2 (for portfolios formed based on earnings of quarter t, as they were for table 2) is positive for 13 consecutiue years. The mean abnormal return around the announcement of quarter t + 4 earnings is negative for each of the 12 years for which we have data. (Results for quarter t + 3 are weak, but that is not unexpected, given the weak third-order autocorrelation in seasonally differenced earnings.) Of
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course, the consistency in the results also makes it that much harder to understand how competitive market forces could fail to eliminate the anomaly. Incidentally, there is a suggestion in table 7 that the predictable component of the reaction to earnings announcements is larger in the first two to four years of our sample period (that is, 1974, 1975, and perhaps 1976 and 1977) than in subsequent years. This may raise questions about whether the effect has for some reason dissipated over time. However, when we conduct similar tests for the years 1971-1973, the results are quite similar to those for years after 1977.14 (3) Is the evidence explainable in terms of transactions costs? One immediate response to this question is that, when the entire period from one earnings announcement to the next is considered, the abnormal returns appear to be in excess of transactions costs, perhaps even for small investors. (Recall the implied abnormal returns between the announcements for quarters t and t + 1 of about 9 percent for the combined long and short positions underlying the last two regressions in table 5, panel A, the more simple strategy of going long (short) in extreme-good-news (extreme-bad-news) firms yields an abnormal return over 180 days of 4.5 percent, 8.9 percent, and 9.9 percent for large, medium, and small firms [Bernard and Thomas (1989, table 111.Moreover, Freeman and Tse (1989, table 7) document that when SUES are measured using analysts forecasts, the indicated drift is even larger - by 50 percent - than when SUES are based on the statistical forecasts used by Bernard and Thomas. Even if the abnormal returns are within transactions costs for small investors, a transactions-cost argument can at best provide only a partial explanation. First, and most important, elen if transactions costs cause
sluggishness in prices, it is hard to understand why the resulting misprking would last for months, or why it would be related to the histoncal time-series behavior of earnings. It is particularly difficult to reconcile price sluggishness with the return reversal we detect upon the announcement of earnings for quarter t + 4. Second, any transactions-cost-based explanation raises ques-
tions about why information cant be impounded in prices by traders for whom transactions costs are low, or other traders for whom the transactions costs are irrelevant (because they have already committed to buy or sell for reasons unrelated to earnings information). Third, while transactions costs may prevent trades and therefore prevent the impounding of new inforrnation, they cannot explain why information is not completely impounded, gicen that trades hate occurred.
14Since our earnings data begin only in 1970, we have insufficient data to calculate the denominator of the SUE for years prior to 1974. Thus, for this supplemental analysis, we scaled unexpected earnings by the beginning-of-quarter stock-market value of equity. For the years for which both scale factors were available (1974-1986). the choice of scale factor does not alter the general nature of the results.
J.A.E.-
B
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(4) Could a research design flaw, such as a failure to control for risk. explain the evidence?
While these possibilities can never be completely dismissed, we believe the evidence is more difficult to explain as a research design flaw than any previous evidence on post-announcement drift. Consider, for example, what would be necessary to explain the results in terms of a failure to control for risk shifts. Firms announcing good (bad) news at quarter t would need to experience a temporary upward (downward) shift in risk that occurs three months later, six months later, and nine months later, and then a downward (upward) shift in risk twelve months later. In addition to requiring risk changes in opposite directions for the same portfolios, this explanation also requires that the changes occur over short periods that coincide with an earnings-announcement date. Moreover, one would have to explain why the risk shifts are large, relative to those that generate normal risk premia. Note that the three-day abnormal return around the announcement for quarter t + 1 in table 2, panel A represents an annualized amount on the order of 200 percent (with no compounding). Even if an explanation based on risk shifts could accommodate each of the above-mentioned features of the data, one important feature would remain to be explained. If the positive mean abnormal returns to zero-investment portfolios represent only a compensation for risk-bearing, then that risk should surface from time to time in the form of a loss. However, the consistent behavior of the abnormal returns through time (see table 7) indicates that the zero-investment strategy suggested by the anomaly would have earned positive abnormal returns for 13 consecutive years. Even though risk shifts seem unlikely to explain the evidence, other research design flaws remain to be considered. Marais (1989), in discussing the post-announcement drift documented by Bernard and Thomas, notes that one cannot rule out consideration of measurement errors in CRSP returns caused by an imbalance of bids and asks at the end of earnings-announcement days. Note that since CRSP prices are not true prices, but may equal either the closing bid or closing ask, CRSP returns may be biased for any portfolio where there are more end-of-day transactions recorded at the bid than the ask, or vice versa [Keim (1989)]. Although such a bias could possibly play a role in our results, there is no compelling reason to expect it ex ante. It is not obvious why earnings for quarter t would have any bearing on whether closing prices are recorded at the bid or the ask after announcements that occur three to twelve months later. Further, it is not obvious why the bias from the imbalance would be a function of quarter t SUES, or why it would switch signs from quarter t + 3 to quarter t + 4. One possibility is that institutional arrangements might lead some investors to prefer to buy (sell) after a year-to-year earnings increase (decrease) in earnings, even though the inPotential bias related to imbalances in bids and asks.
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crease (decrease) was predictable and already reflected in prices. If so, their actions could cause stocks with good (bad) earnings news for quarter t to tend to close at the ask (bid) after the earnings announcement for quarter t + 1, t + 2, and f + 3, and at the bid (ask) for quarter t + 4. The resulting measurement error in CRSP returns would then give the appearance of abnormal returns in the directions we hypothesize. To investigate this explanation, we conducted a test for bias due to imbalances in bid-ask spreads. If there is an imbalance between bids and asks on a given earnings announcement day, the bias should be reversed in subsequent days as the proportion of bids and asks returns to normal. Therefore, the positive (negative) estimated abnormal returns in the announcement period would be offset by negative (positive1 estimated abnormal returns over the subsequent days. However, we find no compelling evidence of such a reversal in the two-day returns subsequent to the earningsannouncement day. Recall from table 2 that the abnormal returns for the three days prior to and including announcements for quarters t + 1, r + 2, t + 3, and t + 4 are 1.32 percent, 0.70 percent, 0.04 percent, and -0.66 percent for portfolios based on extreme SUE deciles. The corresponding abnormal returns for the two days after the announcement are -0.04 percent, - 0.07 percent, -0.03 percent, and 0.05 percent. The signs of these abnormal returns are all consistent with a reversal of a bid-ask bias, but the magnitudes are statistically insignificant and fall far short of the amounts necessary to offset the announcement period returns. (Upon detecting evidence at least weakly consistent with a partial reversal over the first two post-announcement days, we then examined the ten-day post-announcement period, but again there was little or no evidence of a reversal.)
Potential hindsight bias arising from restatements of Compwtat data. An-
other possibility is that our results are biased by the use of earnings data that represent Compustat restatements, rather than the earnings information actually made available on the announcement day. Compustat restates prior quarter earnings when firms undergo major acquisitions, make accounting changes, or separately report income from discontinued operations. Evidence in at least two prior studies [Watts (1978) and Foster, Olsen, and Shevlin (1984)] suggests that these restatements are not responsible for inducing post-announcement drift. I5 Furthermore, we can conceive of no reason why such restatements would induce a bias related to the autocorrelation structure of earnings.
151n his study of post-announcement drift, Watts (1978) used earnings data as originally reported. Foster, Olsen, and Shevlin (1984) collected earnings data as it was originally reported for a subsample of firms and detected post-announcement drift for that sample. [Foster, Olsen, and Shevlin (1984, p. 580) report that they hand-collected earnings-announcement dates. However, conversation with Olsen revealed that the earnings information itself was also hand-collected for this subsample.]
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Despite the indications that Compustat restatements are unlikely to explain our results, we conducted an additional test for this form of hindsight Our bias. approach was to identify the 275 sample firms for which Compustats annual earnings amount (which is not restated) matched (within one thousand dollars) the sum of quarterly earnings per Compustat for each of the 13 years in the dataset. When Compustat restatements occur in the first three quarters of the year, prior-year quarterly numbers are affected, thus destroying the articulation between Compustats quarterly and annual amounts. Thus, our subsample includes firms for which over a 13-year period there was either never a restatement or only restatements that occurred in the fourth quarter (affecting only the first three interim reports of the current year). Thus, this subsample includes firms for which restatements (1) were probably less frequent than for the sample as a whole and (2) should not have affected the reported fourth-quarter earnings. Therefore, if restatements of Compustat data explain our results, then within this subsample we would expect (1) a weakening of the results across all quarters and (2) no ability to predict reactions to future earnings announcements based on fourth-quarter earnings information. In contrast, however, whether we use earnings information from all quarters or the fourth quarter only, we obtain results that are similar to (and actually somewhat stronger than) those for the full sample.
(5) Do the three-day abnormal returns documented here represent the return on an implementable trading strategy, particularly since earnings-announcement dates cannot be predicted perfectly in adcance?
The evidence based on three-day abnormal returns is not intended as a study of an implementable strategy; rather, it is intended to help us better understand a previously documented, more readily implementable trading strategy that involves holding stocks over much longer intervals beginning the day after an earnings announcement [see table 2, panel B, the bottom half of table 5, panel A, and Bernard and Thomas (1989, especially section 3.2511. Nevertheless, since post-announcement drift is concentrated around subsequent earnings announcements and since the timing of those announcements is rather predictable [Chambers and Penman (198411, an interesting question arises. How large an abnormal return per unit time could be generated by taking positions just prior to the expected dates of earnings announcements? To examine the issue, we assume investors construct portfolios in the same way implicit in regression eq. (81, and that the positions are taken 15 trading days prior to the expected announcement date, where the expected date is the actual announcement date for the comparable quarter of the prior year. We hold the position until the day earnings are announced, or for 30 days, whichever occurs first. The actual holding period is, on average, 15 days. The implied abnormal return to this strategy is 4.2 percent. On an annualized basis (before compounding), this is equivalent to 67 percent.
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5. Relation to other research Aside from Bernard and Thomas (1989) and Freeman and Tse (19891, the evidence presented here is most closely related to that of Wiggins (1990) and Mendenhall (forthcoming). Wiggins documents abnormal returns around subsequent earnings announcements that are consistent with those reported in our table 2; the most important distinction between this paper and Wiggins is that we develop the detailed relations between the signs and magnitudes of the abnormal returns and the autocorrelation structure of earnings.16 Mendenhall tests the validity of the Bernard and Thomas (1989) conjecture that market prices fail to reflect the full implications of current earnings for future earnings. Mendenhall first documents that Value Line earnings forecasts are not efficient with respect to information in the latest earnings announcement - which is consistent with at least one set of market participants failing to respond completely to recent earnings information. Mendenhall then documents that reactions to earnings announcements can be partially predicted in advance, based on the most recent Value Line earnings-forecast revision. Thus, in forming earnings expectations, stock prices appear to ignore not only the full implications of prior earnings information, as documented here, but also previously announced analyst forecasts. The evidence summarized here is also related to several other streams of research that are not focused directly on the issue of post-announcement drift.
earnings forecasts as proxies for market expectations. Several studies have compared earnings-forecast errors from alternative sources (analysts, statistical models, etc.) in terms of their ability to explain contemporaneous stock returns. Surprisingly, Foster (1977) finds that forecast errors from a seasonal random-walk model yield marginally greater explanatory power than errors from more accurate statistical models. Bathke and Lorek (1984) and OBrien (1988) provide evidence that is inconsistent with Fosters anomalous result, but OBrien offers another anomaly that is at least as surprising. Specifically, she finds that forecast errors from the Foster model provide better explanations of contemporaneous stock returns than forecast errors of analysts who report to IBES, even though the analysts forecasts are more accurate. [However, Brown, Griffin, Hagerman, and Zmijewski (1987) find that forecast errors based on Value Line are more highly associated with contemporaneous returns.] The evidence presented here suggests that the anomalies uncovered in prior research may in fact reflect predictable errors in the earnings expecta16Ahhough the first draft of this paper predates the first draft of the Wiggins (1990) paper, the two papers were developed independently.
Alfematice
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tions underlying stock prices, as opposed to a research design flaw or some other explanation. If prices fail to reflect the implications of all publicly available information for future earnings, then it is possible that contemporaneous movements in stock prices are better explained by forecast errors based on an inferior forecasting source.
Rationality of the contemporaneous stock-price response to earnings.
Kormendi and Lipe (1987) and Easton and Zmijewski (1989) find evidence consistent with stock prices reflecting cross-sectional differences in the timeseries behavior of earnings, in terms of differences in the response to current earnings. Freeman and Tse (1989) find evidence consistent with stock prices reflecting at least some of the implications of current earnings for future earnings. The evidence presented here suggests that, while stock prices may partially reflect such information, they evidently do not reflect all available information. In fact, given that post-announcement drift per unit time is not much smaller than pre-announcement drift [see Bernard and Thomas (1989, figs. 1 and 211, the evidence suggests that the markets impounding of available information may be far from complete. Several recent studies offer evidence interpreted as inconsistent with semi-strong market efficiency. At least two of these [Hand (1990) and Ou and Penman (1989)] could be viewed as indications that stock prices reflect a naive earnings expectation. In that sense, the studies are consistent with the evidence presented here. However, Hand focuses on an unusual sample (firms that reported gains from debt-equity swaps), and thus it is not clear that the phenomenon underlying his results is linked with that studied here. Ou and Penman (1989, p. 327) conclude that their ability to predict future abnormal returns based on fundamental analysis is distinct from the phenomenon of post-announcement drift. Perhaps no single theme could explain each of these anomalies. 6. Concluding
remarks Other evidence on market efficiency.
The evidence summarized here is consistent with the hypothesis that stock prices partially reflect a naive earnings expectation: that future earnings will be equal to earnings for the comparable quarter of the prior year. We considered a variety of alternative explanations for the evidence, including problems with risk adjustment and the impact of transactions costs, but were unable to support the viability of any of them. In some ways, evidence like that presented here raises more questions than it answers. Why markets as competitive as the NYSE or AMEX would behave as if they are influenced by naive earnings expectations is difficult to understand.
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Another question concerns the economic importance of the effects documented here. In one sense, the degree of mispricing that might be indicated by post-announcement drift is small - less than 5 percent of price per position, even for cases of extreme earnings realizations [see Bernard and Thomas (1989) and the long-interval results in tables 2 and 4 of this paper]. However, in some other ways, the potential effect is large. First, previous studies [e.g., Bernard an...