answer one question

Throughout the semester, we have created variables about “abnormal” return, “discretionary” accruals and so forth. Pick one of them, from a statistics/modelling perspective, explain what it is and how it is constructed. Make your answer as concise as possible

Accounting Research Center, Booth School of Business, University of Chicago
Post-Earnings-Announcement Drift: Delayed Price Response or Risk Premium?
Author(s): Victor L. Bernard and Jacob K. Thomas
Source: Journal of Accounting Research, Vol. 27, Current Studies on The Information
Content of Accounting Earnings (1989), pp. 1-36
Published by: Blackwell Publishing on behalf of Accounting Research Center, Booth School of Business,
University of Chicago
Stable URL: http://www.jstor.org/stable/2491062
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Journal of Accounting Research
Vol. 27 Supplement 1989
Printed in U.S.A.
Post-Earnings-Announcement
Drift: Delayed Price Response or
Risk Premium?
VICTOR
L. BERNARD*
AND
JACOB
K. THOMASt
1. Introduction
This study seeks to discriminate between competing explanations of
“post-earnings-announcementdrift.” Ball and Brown [1968] were the
first to note that even after earningsare announced,estimatedcumulative
“abnormal”returns continue to drift up for “goodnews” firms and down
for “badnews”firms.Foster, Olsen, and Shevlin [1984] (henceforthFOS)
are amongthe many who have replicatedthe phenomenon.’FOS estimate
that over the 60 trading days subsequentto an earnings announcement,
a long position in stocks with unexpected earnings in the highest decile,
combinedwith a short position in stocks in the lowest decile, yields an
annualized”abnormal”return of about 25%,before transactions costs.
Competing explanations for post-earnings-announcement drift fall
into two categories. One class of explanations suggests that at least a
portion of the price response to new information is delayed. The delay
* University of Michigan; tColumbia University. We appreciate the suggestions and
comments of Ray Ball, Bruce Bublitz, Werner DeBondt, George Foster, Robert Holthausen,
Jack Hughes, Gene Imhoff, Roger Kormendi, S. P. Kothari, Richard Leftwich, Laurentius
Marais, Rick Mendenhall, Jim Noel, Bob Officer, Steve Penman, Chris Olsen, Jay Ritter,
Abbie Smith, Tom Stober, Wanda Wallace, Ross Watts, Paul Zarowin, and participants at
the 1989 Journal of Accounting Research Conference and workshops at the University of
California at Berkeley, the University of Chicago, Columbia University, the University of
Connecticut, New York University, and Ohio State University. We also thank Carol Frost,
Kathy Petroni, and Jim Wahlen for their research assistance, and Gautam Kaul for
supplying data on certain macroeconomic variables. Professor Bernard is grateful for the
financial support of the University of Michigan and Dow Corning Corporation.
1 Among the others are Watts [1978] and Rendleman, Jones, and Latane [1982].
1
Copyright ?, Institute of Professional Accounting 1990
2
INFORMATION
CONTENT OF ACCOUNTING EARNINGS:
1989
might occur either because traders fail to assimilate available information, or because certain costs (such as the costs of transacting or the
opportunity costs of implementing and monitoring a trading strategy)
exceed gains from immediate exploitation of information for a sufficiently
large number of traders. A second class of explanations suggests that,
because the capital-asset-pricing model (CAPM) used to calculate abnormal returns is either incomplete or misestimated, researchers fail to
adjust raw returns fully for risk. As a result, the so-called abnormal
returns are nothing more than fair compensation for bearing risk that is
priced but not captured by the CAPM estimated by researchers. In the
case of post-earnings-announcement drift, this explanation requires that
firms with unexpectedly high (low) earnings become more (less) risky on
some unrecognized dimension.2
Several of the results in this paper are difficult to reconcile with
plausible explanations based on incomplete risk adjustment. However,
they are consistent with a delayed response to information.
What is less clear is why a delayed price response would occur. While
abnormal returns to trading on postannouncement drift may be within
the transactions costs for small individual investors, a transactions-costbased explanation raises several difficult unanswered questions. Moreover, one of our tests suggests an alternative explanation for a delay:
that prices are affected by investors who fail to recognize fully the
implications of current earnings for future earnings.
Section 2 summarizes the current state of understanding of postearnings-announcement drift and presents arguments for delayed price
response and CAPM misspecification as explanations for the drift. Section 3 describes the sample and some of the methods used in our empirical
tests. The tests themselves are summarized in section 4. A discussion of
the evidence and some conclusions are presented in section 5.
2. Post-Earnings-Announcement Drift: The Nature of the
Phenomenon
The postannouncement drift documented by FOS is duplicated in our
figure 1. The figure shows the cumulative abnormal returns (CARs) for
ten portfolios with different earnings news. To generate the CAR plots,
FOS used a statistical earnings forecast to estimate unexpected earnings
for a sample of NYSE and AMEX firms. The unexpected earnings, scaled
by the standard deviation of prior forecast errors, were then compared
to the cross-sectional distribution of scaled unexpected earnings for the
prior quarter. Based on their standing relative to that distribution, firms
were assigned to one of ten portfolios. Finally, the abnormal (size2
Finally, a third explanation-bias resulting from research design problems other than
CAPM misspecification-is
always possible. However, FOS do much to dismiss this
possibility. Our study also dismisses some research design problems as potential explanations for the drift.
3
DRIFT
POST-EARNINGS-ANNOUNCEMENT
CAR
10.00
-41Q0
800
-3
-+
6.00
9
4.00
7
2.00
– 2.00
_,
.
. EQ
.
.
.
..
.
,
-4.00
W
3
– 6.00
-8,00
– 10.00
-50
-40
-30
-20
-20
0
+210
+ 20
+ 30
+40
+50
EVENTTIME IN TRADING DAYS RELATIVETO EARNINGSANNOUNCEMENTDAY
FIG. 1.-Cumulative abnormal returns for FOS earnings-based model (EBM) tests.
Earnings announcements are assigned to deciles based on standing of standardized unexpected earnings (SUE) relative to prior-quarter SUE distribution. Portfolio 10 includes
firms with the highest SUE ranking. Based on data from 1974-81. Cumulative abnormal
returns are the sums over 120 trading days surrounding the earnings announcement, of the
difference between daily returns and returns for NYSE firms in the same size decile. SUE
represents forecast error from a first-order autoregressive earnings expectations model (in
seasonal differences) scaled by its estimation-period standard deviation. (Reprinted, by
permission of the publisher, from G. Foster, C. Olsen, and T. Shevlin, “Earnings Releases,
Anomolies, and the Behavior of Security Returns,” The Accounting Review [October 1984]:
589.)
adjusted) returns on those ten portfolios were plotted over the 120 trading
days surrounding the earnings announcement date.
In figure 1, the estimated post-earnings-announcement abnormal returns vary monotonically with the SUE deciles. A long position in
portfolio 10 (that with the highest unexpected earnings), combined with
a short position in portfolio 1 (that with the lowest), yields an estimated
abnormal return of 6.31% over the 60 trading days after the earnings
announcement, or about 25% on an annualized basis. The issue we now
address is whether this estimated abnormal return reflects an incomplete
adjustment for risk or a delayed price response.
2.1 THE CASE FOR CAPM MISSPECIFICATION
Ball [1988] argues that there is good reason to believe stock markets
to be efficient on a priori grounds, because such markets are “paradigm
examples of competition.” Some years earlier Ball [1978] argued that
even in an efficient market, trading strategies based on earnings numbers
might appear to generate abnormal returns, because of misspecifications
4
VICTOR L. BERNARD AND JACOB K. THOMAS
in the CAPM used to measure the abnormal returns. There is some
evidence consistent with this explanation in Ball, Kothari, and Watts
[1988] (henceforth BKW) and FOS [1984].
BKW suggest that betas shift upward (downward) for firms with high
(low) unexpected earnings. Since some prior studies assumed for purposes
of estimation that betas were stationary, this caused an upward (downward) bias in estimated abnormal returns. To overcome this bias, BKW
use an estimation approach that permits betas to shift annually. In so
doing BKW find that the postannouncement drift is no longer significant.
The question is whether BKW’s failure to detect a significant drift in
the year after annual earnings announcement extends to other sample
firms and shorter postannouncement periods. Since (as will be shown
later) most of the drift occurs within three months of the earnings
announcement, quarterly return periods should provide a more powerful
test. In addition, BKW’s sample includes primarily large firms, and FOS
[1984] have shown that the absolute magnitude of the drift is inversely
related to firm size. We examine whether beta shifts can explain much
of postannouncement drift in a design that uses quarterly data and a
sample that is not dominated by large firms.3
A second source of evidence consistent with CAPM misspecification is
the major result in FOS [1984]. FOS contrast two alternative approaches
to analyzing the postannouncement behavior of stock returns. The first
is that used to generate figure 1: the earnings-based model (EBM)
approach. The second approach assigns firms to portfolios on the basis
of firms’ estimated abnormal stock returns over the 60 days prior to and
including the earnings announcement day.4 This is labeled the SRM
(security-return model) approach. The essential result of the SRM tests
is that there is no indication of post-earnings-announcement drift. Thus,
postannouncement drift was observed only under the first (EBM) approach.
The results of the SRM tests in FOS have been interpreted by some
as indicating that postannouncement drift reflects some problem in risk
measurement. For example: “Using the (SRM) method of forming portfolios yields no unusual return behavior following the earnings announce’We have learned in private conversations with BKW that our results motivated them
to extend their tests to quarterly data. In contrast to their earlier results, their tests based
on quarterly data indicate significant postannouncement drift, even after adjusting for beta
shifts.
‘FOS also examined tests based on abnormal returns over the two-day window ending
on the earnings announcement day and obtained similar results. We do not focus on these
short-window tests, however, because in addition to the issues discussed below, they are
affected by a bias that would tend to obscure part of the drift. Specifically, when stock
returns are ranked over an interval as short as two days, good (bad) news stocks tend to be
those that closed on the second day at the ask (bid). Subsequent movement to an average
price between the ask and the bid causes an artificial “return reversal” that offsets a portion
of any drift.
POST-EARNINGS-ANNOUNCEMENT
DRIFT
5
ment and suggests again that the results of previous studies are caused
by a misspecified pricing model” (Dyckman and Morse [1986, p. 58]).
Although the same conclusion was not drawn by FOS, it is understandable that readers of FOS could draw such an inference. FOS explain that
the EBM tests are vulnerable to certain problems in risk adjustment
discussed by Ball [1978]; the SRM tests were motivated as one approach
to mitigate these problems. Given that the drift vanishes in the SRM
tests, the results could suggest that the drift in the EBM tests reflects a
premium for some unidentified risk.
However, Bernard and Thomas [1989] suggest that any such inference
is unwarranted. The reason is that the FOS results are consistent not
only with certain explanations under which the drift represents a risk
premium but also with certain other explanations where the drift is a
delayed price response. Specifically, they show that if (1) there exists
some delay in the response to earnings news, and (2) the fraction of the
total response that is delayedvaries sufficiently across firms, then it is
possible simultaneously to detect a drift in the EBM tests but not detect
a drift in the SRM tests.5 As a result, Bernard and Thomas suggest that
a more appropriate interpretation of FOS’s SRM test is that, rather than
discriminating between CAPM misspecification and delayed price response, it imposes restrictions on the nature of CAPMmisspecifications,
and on the delayed price response, that could explain the drift. Hence
the overall results from FOS still leave open the question of what causes
postannouncement drift.
2.2 THE CASE FOR A DELAYED PRICE RESPONSE
That post-earnings-announcement drift could represent a delayed response to information has been viewed as plausible by some academics.
For example, Lev and Ohlson [1982, p. 284] describe the evidence of
post-earnings-announcement drift as the “most damaging to the naive
and unwavering belief in market efficiency.” However, it is difficult to
explain why the market would fail to respond immediately to earnings
information.
One possibility is that transactions costs inhibit a complete and immediate response to earnings news. Examples of such costs include the
bid-ask spread, commissions (for some investors), the costs of selling
short, and the costs of implementing and monitoring a strategy (including
opportunity costs). We turn to a detailed discussion of this possibility
later in the paper.
A second possibility is that market prices are influenced by investors
who fail to appreciate the full implications of earnings information. That
is, some investors may fail to form an unbiased expectation of future
‘The analysis also requires a third (mild) assumption, that there is no positive serial
correlation in the component of stock returns not associated with earnings news.
6
VICTOR L. BERNARD AND JACOB K. THOMAS
earnings immediately upon revelation of current earnings, with some
portion of the response not occurring until analysts’ forecasts are revised
or future earnings are realized.6 Although this possibility departs dramatically from most academics’ view of market efficiency, there presently
is little evidence on this specific issue. Kormendi and Lipe [1987] and
Freeman and Tse [1989] indicate that responses to current earnings
reflect at least some of the implications for future earnings, but that does
not necessarily imply that the immediate response is complete. This and
other competing explanations are the focus of our empirical tests in
section 4.
3. Sample and Estimation Procedures
3.1 SAMPLE
SELECTION
Our sample includes 84,792 firm-quarters of data for NYSE/AMEX
firms for 1974-86. We also conduct some supplementary tests based on
15,457 firm-quarters of data for over-the-counter stocks on the NASDAQ
system for 1974-85. Criteria for inclusion in the sample are the same as
those used by FOS, who studied NYSE/AMEX firms for the period 197481. We require that the firm be listed on the CRSP daily files, and that
the firm’s earnings before extraordinary items and discontinued operations be available for at least ten consecutive quarters on Compustat.
Our NYSE/AMEX sample includes only firms that appeared on any of
the Compustat files released from 1982 through 1987.7 Since firms included in earlier files but dropped from Compustat before 1982 are
excluded from the sample, there is a potential for a survivorship bias in
the first half of our data set. However, FOS conducted tests which
indicated that postannouncement drift is not sensitive to this form of
bias. Moreover, our conclusions are insensitive to whether we include or
exclude “nonsurvivors” dropped from the Compustat files between 1982
and 1987.
3.2 ESTIMATION
PROCEDURES
3.2.1. Estimation of abnormal returns. For the NYSE/AMEX sample,
cumulative abnormal returns are calculated using an approach like that
of FOS. FOS use a companion portfolio approach designed to control for
6Clearly, an efficient market may resolve uncertainty about the implications of a
previously released earnings number when future earnings are released (Freeman and Tse
[1989]). Nevertheless, regardless of how much uncertainty surrounds current earnings,
stock prices in an efficient market should immediately reflect an unbiased expectation of
future earnings. If information uncertainty is not “priced out,” this implies no predictable
postannouncement drift. If information uncertainty is priced out, this implies positive
postannouncement drift for both good and bad earnings news, which is inconsistent with
the data.
‘The NASDAQ sample was selected from the 1987 Compustat file only.
POST-EARNINGS-ANNOUNCEMENT
DRIFT
7
the Banz-Reinganum size effect.8 Under this approach, abnormal returns
are calculated as follows:
ARjt = Rjt-
(1)
where AR1t= abnormal return for firm j, day t;
Rjt = raw return for firm j, day t;
Rpt= equally weighted mean return for day t on the NYSE/
AMEX firm size decile that firm j is a member of at the
beginning of the calendar year. Firm size is measured by
the market value of common equity.
In our tests based on abnormal returns, we preserve comparability
with FOS and sum abnormal returns over time to obtain cumulative
abnormal returns (CARs). One problem with summing abnormal returns
over time is that it implicitly assumes daily rebalancing and leads to an
upward bias in the returns cumulated over long periods (Blume and
Stambaugh [1983] and Roll [1983]). However, since this bias affects both
the primary and the companion portfolios, there may be no bias in our
estimated abnormal returns. In fact, we have conducted analyses that
indicate that the difference between abnormal returns on extreme good
news and bad news firms is similar, whether the returns are summed or
compounded.9 In addition, we describe in section 3.2.4 an alternative
abnormal return calculation that is free from the bias described by Blume
and Stambaugh [1983].
Observations were excluded from the analysis if the return for the
earnings announcement day was missing on CRSP, or if the CRSP
returns series did not encompass the 160 trading days surrounding the
earnings announcement.
3.2.2. Estimation of standardized unexpected earnings (SUE). Procedures for estimating unexpected earnings were patterned after those used
by FOS for the EBM Model 2. That is, earnings were forecasted by
estimating the Foster [1977] model with historical data.’0 The difference
8 This approach to measuring abnormal returns makes no attempt to control for systematic risk. Since our conclusions are based on comparisons of abnormal returns on high and
low unexpected earnings portfolios, this introduces a bias if systematic risk differs between
those two. We test for such a possibility in section 4.2.1.
9 If anything, our use of summed returns may understate the extent of postannouncement
drift. The indicated abnormal. returns are about 10% larger when we employ the FOS
approach but compound returns over time (using portfolios that are initially equalweighted). Details are available upon request.
10 The Foster model assumes that earnings follow a first-order autoregressive process in
seasonal differences. FOS indicate [1984, p. 582] that they used a maximum of 20 observations to estimate the Foster model. We used a maximum of 24 observations. FOS indicate
[1984, p. 581] that firms were included in the sample even if only ten consecutive quarters
of data were available. We retained such firms also, but where fewer than 16 observations
were available, we assumed that earnings followed a seasonal random walk. FOS indicate
[1984, p. 582] that they obtained essentially the same results when this model was
substituted for the Foster model.
8
VICTOR L. BERNARD AND JACOB K. THOMAS
between actual and forecasted earnings was then scaled by the standard
deviation of forecast errors over the estimation period to obtain standardized unexpected earnings or SUE.
3.2.3. Portfolio assignment. Holthausen [1983] and FOS describe a bias
that is introduced when firms are assigned to portfolios. When those
assignments are based on rankings of unexpected earnings within the
distribution for all firms, including some that have not yet announced
earnings for the quarter, there is a hindsight bias that tends to magnify
the drift. Like FOS, we overcome that bias by assigning firms to portfolios
on the basis of their standings relative to the distribution of unexpected
earnings in the prior quarter.
3.2.4. Alternative abnormal return calculation: continuously balanced
SUE strategy. Abnormal returns are typically viewed as returns in excess
of some benchmark, such as the market model. The FOS size-control
portfolio approach yields abnormal returns that can be interpreted in
this way. However, in the case of the FOS approach, an alternative
interpretation is also possible. Because FOS always offset a position in a
given firm with the position in a size-control portfolio, the resulting
abnormal returns represent the return on a zero-investment trading
strategy. The advantage of this interpretation is that, if the offsetting
positions are of equivalent risk, any nonzero expected return on the zeroinvestment portfolio contradicts the implications of market efficiency (at
least before considering transactions or other costs).
The difficulty with this interpretation is that the FOS strategy may be
difficult to implement as it stands. The strategy requires an investor to
take new positions in size-control portfolios every day, with each control
portfolio containing hundreds of stocks. Thus, results based on this
approach leave open the question of whether similar returns could be
generated by an easily implemented, zero-investment strategy.
To assess the sensitivity of our results to this issue, we replicated some
of our tests based on a zero-investment strategy that would be easier to
implement. Since it involves having the same amount invested in good
news and bad news firms at all points in time, we label this strategy the
“continuously balanced” SUE strategy. (To differentiate it, we sometimes
label the FOS approach the “FOS control portfolio” SUE strategy.)
The continuously balanced SUE strategy works as follows. On a given
trading day, we identify any firms that announced earnings, and where
standardized unexpected earnings fall in the upper quintile (good news)
or lower quintile (bad news) of the prior-quarter distribution. If both
good news and bad news firms exist for that day, we assume a long
position in the former and a short position in the latter. The long (short)
positions are initially equally weighted across the available good (bad)
news firms, with the total amount of the long position exactly offsetting
the total amount of the short position. We then compute buy-and-hold
(i.e., continuously compounded) returns on each of the stocks in the long
POST-EARNINGS-ANNOUNCEMENT
DRIFT
9
and short position, over the 60 trading days subsequent to the earnings
announcement.
On 14% of trading days, there were either no new good news or no bad
news firms available, and so no match could be created. In such cases,
we “wait” until a match becomes available. For example, if two good
news firms announced earnings on day 1, but no bad news firms announced, we would wait until at least one bad news firm announced
earnings. If the first available bad news firm announced on day 4, it
would be matched with all good news firms announcing from days 1
through 4, and we would then compound returns from day 5 through day
64.In 97% of all cases, a match became available within two days.
To provide some control for the Banz-Reinganum size effect, this
matching process was always conducted within groups of small, medium,
and large firms. Small firms are those whose January 1 market value of
equity was among the lowest four deciles of the NYSE/AMEX, whereas
large firms are those among the highest three deciles. Using only three
size groups increased the probability of finding matches of good news
and bad news firms within a short period of time. Since we used only
three size groups (versus ten in the FOS control portfolio approach), our
control for size is not as precise. However, if we assume that smaller
firms are as likely to announce bad news as good news, this introduces
no bias in the results.”
The continuously balanced SUE strategy is much easier to implement
than that used by FOS but would still be costly to the extent that short
selling must be used. There would be no significant difficulty, however,
for investors who already own the stocks that announce bad news.
4. Empirical Results
4.1
DESCRIPTIVE
RESULTS
4.1.1. Magnitude of the drift. FOS [1984] provide estimates of the
magnitude of post-earnings-announcement drift and show that the drift
varies inversely with firm size. In this and the following section, we
replicate those results and demonstrate that they persist over a longer
time period. Unless otherwise specified, the results in this section are
based on the procedures used by FOS, to maintain comparability; results
based on the continuously balanced SUE strategy are reported only as
supplement information.
Figure 2 presents CAR plots for the sample, after assigning firms to
portfolios on the basis of standardized unexpected earnings. In contrast
to the format used by FOS in figure 1, figure 2 separates CAR plots for
” If bad news firms are more likely to be small, due to price declines in anticipation of
the earnings announcement (and vice versa for good news firms), then the Banz-Reinganum
size effect would impart a downward bias in our estimated abnormal returns. That is, the
bias would tend to offset any postannouncement drift.
VICTOR L. BERNARD AND JACOB K. THOMAS
10
6 . .
……………………………………..
post-announcementperiod
pre-announcementperiod
SUE
deciles
…………………………………………….
4 . ………………………………….}
9
8SU
CR-2 . _………………..\>.
…………..
….. …………………….
6
. .. . …. 2 1
.. ………….
C~~~~~~~~~~~~~~~~~~~~~~~~
–
-8
-60
4
3
3
1
..
…………………-4…………..
-40
-20
0
0
…………..I….
20
40
60
event time in tradingdays relativeto earningsannouncementday
FIG. 2.-Cumulative abnormal returns (CARs)for SUE portfolios: all announcements.
Earnings announcements are assigned to deciles based on standing of standardized unexpected earnings (SUE) relative to prior-quarter SUE distribution. Based on 84,792 announcements from 1974 to 1986. CARs are the sums over pre- and postannouncement
holding periods (beginning day -59 and day 1, respectively) of the difference between daily
returns and returns for NYSE/AMEX firms of the same size decile. SUE represents
forecast errors from a first-order autoregressive earnings expectation model (in seasonal
differences) scaled by its estimation-period standard deviation (see section 3.2 for details).
the pre- and postannouncement periods, to make the postannouncement
abnormal returns easier to gauge. Our results for 1974-86 are similar to
those obtained by FOS for 1974-81. That is, there is a pronounced postearnings-announcement drift, increasing monotonically in unexpected
earnings. A long position in the highest unexpected earnings decile and
a short position in the lowest decile would have yielded an estimated
abnormal return of approximately 4.2% over the 60 days subsequent to
POST-EARNINGS-ANNOUNCEMENT
DRIFT
11
the earnings announcement, or about 18% on an annualized basis. (The
annualized abnormal return on the continuously balanced SUE strategy
is 17%.) For the 1974-81 period studied by FOS, we obtain an annualized
return of 19%, which is less than the 25% implied by their results.’2
4.1.2. Relation of drift to firm size. Figures 3 and 4 indicate how the
drift varies by firm size, by presenting results for large and small firms.’3
As noted by FOS, the postannouncement drift is larger for smaller firms.
Among small firms, a long position in the highest unexpected earnings
decile and a short position in the lowest decile yielded an abnormal
return of approximately 5.3% over the 60 days subsequent to the earnings
announcement. Comparable abnormal returns for medium-sized firms
(not shown) and large firms are 4.5% and 2.8%, respectively.
Results based on the continuously balanced SUE strategy are similar.
For 60-day holding periods, mean abnormal returns for small, medium,
and large firms are 5.1%, 4.3%, and 2.8%.
In regressions not reported here, we use the approach of FOS [1984, p.
595] to test the statistical significance of the postannouncement drift
and the effect of firm size. Our results confirm that the magnitude of the
drift is related to the magnitude of unexpected earnings, and that the
absolute magnitude of the drift is inversely related to firm size, both at
significance levels less than .01.
We do not present comparable plots of NASDAQ firms. However, the
same phenomenon observed for NYSE/AMEX firms was observed for
that sample. The magnitude of the drift for NASDAQ firms lies between
that observed for small and medium-sized firms on the NYSE/AMEX.
This is as expected, given that approximately 70% of our NASDAQ firms
would be classified as small (relative to the NYSE/AMEX firms), 20%
would be classified as medium, and 5% would be classified as large.
4.1.3. Longevity of the drift. Table 1 provides information about the
longevity of the postannouncement drift for stocks ranked in the lowest
and highest SUE decile, broken down by size and by subperiods extending
two years beyond the earnings announcement date.
Most of the drift occurs during the first 60 trading days (about three
months) subsequent to the earnings announcement, and there is little
evidence of statistically significant drift beyond 180 trading days. If we
assume all of the drift occurs within 480 days, then the fraction of the
12
Differences between our results and those of FOS are most pronounced for small, good
news firms. A possible explanation for the difference involves how control portfolios were
constructed. It appears that FOS included only NYSE firms in their control portfolios
[1984, p. 585], whereas we included both NYSE and AMEX firms.
13 Firms were assigned to SUE deciles before segregation by size. The large firms are
more heavily represented in the extreme deciles; in figure 3, SUE deciles 5 and 6 contain
approximately 2,400 observations each, while SUE deciles 1 and 10 contain approximately
3,100 observations each. For small firms, the reverse relation holds; in figure 4, SUE deciles
5 and 6 contain approximately 3,400 observations each, while SUE deciles 1 and 10 contain
approximately 2,700 observations each.
VICTOR L. BERNARD AND JACOB K. THOMAS
12
6 . . ……………………………………………….
pre-announcementperiod
4 . . ………………………..
…………..
post-announcementperiod
…….
. .
……………………………………….
SUE
deciles
SUE
AR 2
AL..
‘
I’
d
*
~~~~~~~~~~~~
”””””
‘~~~~~~~~~~
8
A
7/8
R6
R
-2 . …….
~~~~~~~~~~~
i s
@@@…………………………
s@
@ @ |@ @@
9 ………………………………………….de
4
2/3
3
2
–
-8
-60
…………….
;…………
-40
.
-20
5………………:
0
0
20
40
60
event time in tradingdays relativeto earningsannouncementday
FIG. 3.-Cumulative abnormal returns (CARs) for SUE portfolios: large firms only.
Earnings announcements are assigned to deciles based on standing of standardized unexpected earnings (SUE) relative to prior-quarter SUE distribution. Based on 27,584 announcements from 1974 to 1986. Large firms are in size deciles 8 to 10, based on January
1 market values of equity for all NYSE and AMEX firms. CARs are the sums over preand postannouncement holding periods (beginning day -59 and day 1, respectively) of the
difference between daily returns and returns for NYSE-AMEX firms of the same size
decile. SUE represents forecast errors from a first-order autoregressive earnings expectation
model (in seasonal differences) scaled by its estimation-period standard deviation (see
section 3.2 for details).
drift experienced within 60 days is 53%, 58%, and 76% for small, medium,
and large firms, respectively. Approximately 100% of the drift occurs
within nine months for small firms and within six months for large firms.
This result is consistent with the findings of Watts [1978], who found a
6
_
13
DRIFT
POST-EARNINGS-ANNOUNCEMENT
t.10
.
post-announcementperiod
SUE
deciles
pre-announcementperiod
9
4 . ._. . . . . . . . . . . .
.
. …………………………
…………….
9
0
7.
A6
R
6
~~~~~~~~~~5
(%)
– 4-_ ;0
…….
…….
5
4~~~~~~~~~~~~
..
…….
3
3~~~~~~~~~~~~~~~~~~~~~~~~~
3
~~~~~~~~~~~
-2
–
.
….
…………………………….
…….
2
-60
-40
-20
0
0
20
40
60
event time in tradingdays relativeto earningsannouncementday
FIG. 4.-Cumulative abnormal returns (CARs) for SUE portfolios: small firms only.
Earnings announcements are assigned to deciles based on standing of standardized unexpected earnings (SUE) relative to prior-quarter SUE distribution. Based on 29,796 announcements from 1974 to 1986. Small firms are in size deciles 1 to 4, based on January 1
market values of equity for all NYSE and AMEX firms. CARs are the sums over pre- and
postannouncement holding periods (beginning day -59 and day 1, respectively) of the
difference between daily returns and returns for NYSE-AMEX firms of the same size
decile. SUE represents forecast errors from a first-order autoregressive earnings expectation
model (in seasonal differences) scaled by its estimation-period standard deviation (see
section 3.2 for details).
significant drift lasting six months in his sample consisting primarily of
large firms.
A disproportionately large amount of the 60-day drift occurs within 5
days of the earnings announcement. If the drift were constant over the
14
VICTOR L. BERNARD AND JACOB K. THOMAS
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POST-EARNINGS-ANNOUNCEMENT
DRIFT
15
60-day interval, we would expect 8% of the drift to arise within 5 days.
However, the actual percentage of the 60-day drift that occurs within 5
days (not shown in table 1) is 13%, 18%, and 20% of the 60-day drift for
small, medium, and large firms, respectively.
Table 1 suggests that, if the drift is explained by an incomplete
adjustment for risk, the risk must exist only temporarily and must persist
longer for small firms than for large firms.
4.2 TESTS
DRIFT
OF RISK PREMIUMS
AS EXPLANATION
FOR THE
4.2.1. Shifts in betas as a potential explanation. We now present results
from a battery of tests designed to assess the plausibility of incomplete
risk adjustment as an explanation for postannouncement drift. We first
consider BKW’s [1988] suggestion that betas increase for firms with high
unexpected earnings and decrease for firms with low unexpected earnings.
Beta shifts are obviously a concern in a design that estimates betas in
one period and then uses those estimates in a different period. Such was
the case in much of the early research on postannouncement drift.
However, that is not a concern in the FOS design that we adopt, since
this design does not rely on estimates of betas. Instead, we assume that
betas for our long and short positions are equal during the postannouncement period. Under this assumption, the combined long and short positions have zero systematic risk. Thus, while we examine the BKW
hypothesis that betas shift around the time of earnings announcements,
our ultimate concern is with any differences in the levels of betas for
high- and low-SUE firms in the postannouncement period.
Before turning to the tests, we should note that there are indications
that failure to account for beta is unlikely to explain postannouncement
drift. If mismeasured betas are the explanation, then the sign of the drift
should vary according to whether the excess return on the market is
positive or negative. Specifically, good news stocks, which would have to
be riskier than assumed, should have positive estimated abnormal returns
in up markets but negative estimated abnormal returns in down markets.
The opposite should hold for bad news stocks. In contrast to this
prediction, however, the postannouncement estimated abnormal returns
for good news (highest SUE decile) stocks are actually positive in both
up and down markets. Similarly, estimated abnormal returns for bad
news stocks (lowest SUE decile) are actually -negative in both up and
down markets.14
Our tests are presented in table 2. Beta estimates were derived using
14 For good news stocks, the estimated abnormal returns over days (1, 60) are 2.5%
(1.1%) when the value-weighted market return is greater (less) than the risk-free rate. For
bad news stocks, the estimated abnormal returns are -2.3% (-2.4%) when the valueweighted market return is greater (less) than the risk-free rate. We thank George Foster
for suggesting this test.
16
VICTOR L. BERNARD AND JACOB K. THOMAS
TABLE
2
Beta Estimates by SUE Category, in Periods Surrounding Earnings Announcement’
SUEDecile
(1 = low;10 = high)
Preannouncement
PostannouncementPeriod
(-119, 60)
(-59,0)
(1, 60)
(61, 120)
(121, 180)
(181, 240)
Beta estimates
1
2
3
4
5
6
7
8
9
10
1.16
1.11
1.16
1.24
1.23
1.31
1.30
1.28
1.26
1.32
1.22
1.17
1.21
1.18
1.26
1.27
1.24
1.34
1.31
1.31
1.17
1.15
1.13
1.21
1.24
1.28
1.23
1.30
1.29
1.38
1.17
1.08
1.11
1.15
1.30
1.24
1.26
1.30
1.26
1.30
1.23
1.19
1.14
1.19
1.19
1.26
1.25
1.30
1.20
1.31
1.31
1.25
1.22
1.18
1.24
1.23
1.24
1.20
1.23
1.23
Rank correlation,
SUE and beta
.83*
.84*
.90*
.77*
.66*
-.38
Jensen’s alpha
0.6%*
SUE= 1
-1.6%*
-0.8%*
-0.8%*
-3.7%*
-5.3%*
6.1*
3.0*
1.4*
0.7*
0.7*
SUE = 10
3.4*
0.1
11.4*
4.6*
2.2*
1.5*
Combined
7.1*
1For each 60-daywindow,we calculatecompoundeddaily returnsfor individualstocks, the valueweighted CRSP index, and the treasury-billrate. These data constitute a single observationin a
regressionof individualstock returnsagainst market returns,both expressedin terms of differences
from the treasury-billrate. Such regressionsare estimated within each SUE category.There are
approximately8,500 (overlappingand thus nonindependent)observationsunderlyingestimatesfor the
(-59, 0) and (1, 60) windows,and slightlyfewerfor otherwindows.The standarderrorfor eachestimate
in the table is approximately0.02. Cross-sectionaldependencein the data may cause downwardbias in
the estimatedstandarderror(Bernard[1987]).
* Significantlydifferentfromzero, .05 level (two-tailedtest).
the BKW methodology for permitting betas to shift through time. For
each of several 60-day windows surrounding the earnings announcement,
we compounded total returns on individual stock (Rj,), treasury bills
(Rft),15 and the valued-weighted CRSP index (Rmt). These three data
points constitute a single observation for a regression based on the
Sharpe-Lintner-Mossin CAPM:
(2)
Rjt- Rft = a + b (Rmt -Rft) + eat.
The regression was estimated by pooling all observations for a given
SUE decile, within six 60-trading-day windows surrounding the earnings
announcement date. This approach permits the betas to shift from one
window to the next and to vary across SUE categories.
The estimates in table 2 show distinct evidence of the positive relation
between SUEs and betas predicted by BKW [1988]. The rank correlation
between beta and SUE is .83 in the (-119, -60) window, .84 in the (-59,
15 The treasury-bill returns are derived on a daily basis from weekly returns calculated
by Gautam Kaul for bills in their final week before maturity. Kaul’s weekly returns were
allocated to days assuming the same return for each day within the week.
POST-EARNINGS-ANNOUNCEMENT
DRIFT
17
0) window, .90 in the (1, 60) window, and .77 in the (61, 120) window.
Also consistent with BKW, the relation first appears during the fiscal
period in which the earnings are generated. That fiscal quarter would
typically bridge the (-119, -60) window and the (-59, 0) window; there
is no significant relation between SUE and beta in windows prior to day
-119. Finally, and again consistent with BKW, the relation is temporary
(it becomes insignificant beyond day 180).
Even though we find evidence of a positive relation between SUE and
betas, it is much smaller than would be necessary to explain fully the
magnitude of the drift. The difference between the excess returns (Rj, Rft) on SUE 10 firms and SUE 1 firms over days (1, 60) is 4.3%. (This is
slightly larger than the 4.2% abnormal return reported in section 4.1.1,
which was size-adjusted.) The corresponding mean excess market return
(Rmt – Rft) is 1.65%. Thus, if betas are to explain postannouncement
drift, the difference between betas for the SUE 10 firms and SUE 1 firms
would have to be 2.6 (= 4.3/1.65). In fact, the difference is only 0.21, or
less than 10% as large as required.
The failure of betas to explain the magnitude of the drift can be
confirmed by examining the “Jensen’s alpha” in equation (2). If beta risk
could fully explain the drift, then Jensen’s alpha should be zero. However,
in the 60-day postannouncement period, alpha is -1.6% for SUE portfolio
1, 3.0% for SUE portfolio 10, and 4.6% for a combined position (significant at the .0001 level). On an annualized basis, this represents an
abnormal return of approximately 18%.16
We conclude that while there is some merit to the BKW claim that
betas shift around earnings announcements, the magnitude of the shifts
falls far short of the amounts necessary to explain the magnitude of the
drift.17
4.2.2. Other commonly discussed asset-pricing factors as potential explanations: APT risk factors as potential explanations. In this section, we
test for the possibility that trading strategies based on SUEs are risky
on dimensions not captured by beta. The risk factors we consider are
those found in the literature on arbitrage-pricing theory. Chen, Roll, and
Ross [1986] provide evidence that risks associated with industrial production, changes in default risk premiums, and changes in term structure
appeared to be priced. They found weaker evidence that risks associated
with unanticipated inflation and changes in expected inflation also
affected asset prices.
16 Results based on the equally weighted market index yield similar conclusions. The
rank correlation between beta and SUE decile is weaker but still significant at the .05 level
in the (-119, -60) window, the (-59, 0) window, and the (1, 60) window. The difference
between betas for SUE 10 firms and SUE 1 firms in the (1, 60) window is 13% as large as
required to explain the drift; Jensen’s alpha indicates an annualized abnormal return of
16%.
17 Subsequent to conducting these tests, we became aware of similar evidence in Mendenhall [1986].
18
VICTOR L. BERNARD AND JACOB K. THOMAS
In table 3, we regress calendar-quarter returns1 on the FOS control
portfolio SUE strategy (CAR for SUE decile 10 minus CAR for SUE
decile 1) against quarterly measures of the five risk factors studied by
Chen, Roll, and Ross.19 In addition, we consider a regression that also
includes the return on the NYSE index (net of the treasury-bill rate).
Table 3 indicates whether a positive or negative correlation with a
particular factor would indicate that the portfolio is “risky,” as opposed
to offering a “hedge” against risk. The evidence from Chen, Roll, and
Ross suggests that assets with returns that are positivelycorrelated with
unanticipated growth in industrial production (QP) and unanticipated
changes in the default risk premium (UPR) are risky and have correspondingly higher required returns, as do assets with returns that are
negativelycorrelated with changes in expected inflation (DEI), unanticipated inflation (UI), and unanticipated changes in the term structure
(UTS).
Table 3 provides no evidence that the returns on the SUE strategy are
significantly correlated with any of the five risk factors proposed by
Chen, Roll, and Ross. (Three of the five coefficients are both insignificant
and have the “wrong” sign.) Moreover, the five factors as a group do not
explain a significant fraction of the variance in the strategy’s return.
If the right-hand-side variables in table 3 accurately measure ex post
premiums on all risk factors that are priced, then the intercept in the
regression provides a test of market efficiency. Given that the dependent
variable is the return on a zero-investment portfolio, the intercept should
be zero under the efficient markets hypothesis. However, the estimated
intercepts indicate an abnormal return of 4% per quarter, with t-values
of 8.63 and 8.70.
Results from the same tests based on the continuously balanced SUE
strategy are similar to those in table 3.
Dividend yield as a potential explanation.We also examined changes
in dividend yields on good news and bad news portfolios. If dividend
yields affect asset pricing, as predicted by the Brennan [1970] “after-tax”
CAPM, then they could conceivably explain post-earnings-announcement drift. But this would require a sufficiently large increase in the
difference between dividend yields on good news and bad news stocks.
Although we detect such a change, the magnitude (4/10 of 1% of price)
18 Generally, a position held for 60 trading days spans two calendar quarters. Thus,
calculation of calendar-quarter returns requires determination of how much of the 60-day
return was generated in each of the two quarters.
‘” The variables were measured using the procedures of Chen, Roll, and Ross [1986] as
they would be applied to quarterly data, with the following exceptions. First, for convenience, we used the GNP deflator as our measure of inflation rather than the Consumer
Price Index and used ASA-NBER forecasts as our measure of expected inflation. (Chen,
Roll, and Ross used the Fama-Gibbons inflation forecasting model.) Second, our measure
of the unanticipated default risk premium was the difference between the return on lowgrade and high-grade corporate bonds rather than the difference between low-grade corporate and government bonds. See table 3 for further information.
POST-EARNINGS-ANNOUNCEMENT
4~~
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20
VICTOR L. BERNARD AND JACOB K. THOMAS
would imply a trivial impact on expected returns, given economically
plausible dividend yield effects.
Our conclusion, then, is that the observed postannouncement drift
cannot be explained as a risk premium needed to compensate investors
for risk factors commonly discussed in the asset-pricing literature. In the
following sections, we examine whether some other unidentified risk
factor could plausibly explain the drift.
4.2.3. Consistent profitability of the strategy. In this section, we examine
how frequently a zero-investment SUE trading strategy generates a
negative return. If a zero-investment strategy yields a positive mean
return because it is risky, that risk must periodically reveal itself in the
form of losses.
Panels A and B of figure 5 present the abnormal returns on the two
SUE strategies for each calendar quarter from 1974:111through 1986:IV.
In panel A the returns are to the FOS control portfolio strategy, where
we assume a long (short) position in the firms whose unexpected earnings
are ranked in the highest (lowest) quintile.20 The returns to the continuously balanced SUE strategy appear in panel B. In both panels, we
began by calculating abnormal returns over 60-trading-day postannouncement windows and then determined how much of the 60-day
return was generated within the two calendar quarters spanned by those
60 days.
The interesting feature of figure 5 is the consistency with which the
zero-investment portfolios generate positive returns. The returns in panel
A are positive in 46 of 50 quarters and in 13 of 13 years. In panel B, the
returns are positive in 44 of 50 quarters and in 13 of 13 years. FOS
present similar evidence in their figure 2 [1984, p. 594], which shows a
positive abnormal return in 31 of 32 quarters.21
If the returns on a zero-investment portfolio represent compensation
for risk, then losses should occur with an expected cost (in terms of
utility) that is equal to the expected value of the risk premium. However,
for the overall sample, returns of nearly 200% (before compounding)
have been generated over the 50 quarters, with negative returns in only
4 or 6 quarters. These negative returns sum to less than 7%.
To better appreciate how surprising the consistency is, consider the
behavior of the ex post risk premium for beta. Fama and MacBeth [1973]
present returns on zero-investment, unit-beta portfolios for the period
1935-68. That portfolio generated a mean annualized return of about
10%. But among the 134 quarters represented there, returns on this
portfolio were negative 39% of the time. In contrast, the mean annualized
20 Although deciles are used elsewhere when results are presented for the FOS strategy,
we use quintiles here to make panel A (based on the FOS strategy) and panel B (based on
the continuously balanced SUE strategy) more comparable. Results for panel A are similar
when deciles are used.
21 However, FOS do not discuss the implications of this result for distinguishing among
alternative explanations for the drift.
POST-EARNINGS-ANNOUNCEMENT
DRIFT
21
Panel A: FOS control portfolio SUE strategy
C
A
RI5 ….. .. . .. … … . …. . .. …. . ……..l.
l…
0
74
75
76
77
78
79
80
81
82
83
84
85
86
82
83
84
85
86
year,by quarter
Panel B: Continuously balanced SUE strategy
(Af)15
10
L
1
C
A
o
-5
74
75
76
77
78
79
80
81
year,by quarter
S ……………………………………………………………………………………….
FIG. 5.-Cumulative abnormal returns (CARs) from SUE strategies, by calendar quarter.
In both panels, long (short) positions are assumed in the highest (lowest) quintiles of
standardized unexpected earnings (SUE) and held for 60 trading days. CARs are assigned
to calendar quarters based on the portion of the 60-day CAR generated within that calendar
quarter. SUE represents forecast errors from a first-order autoregressive earnings expectation model (in seasonal differences) scaled by its estimation-period standard deviation
(see section 3.2 for details). In panel A, CARs are the combined abnormal returns from a
long position in the highest SUE quintile and a short position -in the lowest SUE quintile.
Abnormal returns are the sums over the 60 trading days after the announcement of the
difference between daily returns and returns for NYSE-AMEX firms of the same size
decile. In panel B, continuous balancing requires that each $1 long position in the highest
SUE quintile is always offset by a short position in similar-sized stocks (small, medium, or
large) in the lowest SUE quintile. Balancing in this way sometimes requires waiting after
earnings announcements until an offsetting “match” is available. CARs, computed over the
60 trading days after matching, are a combination of the compounded (buy and hold)
returns for the long and short positions.
return on the zero-investment portfolio described in figure 5 is higher
(18%) and yet is negative only 8% or 12% of the time.
Some readers of prior drafts have questioned whether the consistent
profitability depicted in figure 5 could reflect some problem in the
benchmark we use to measure abnormal returns. But if our benchmark
fails to control for some risk that is priced in the market, then the results
22
VICTOR L. BERNARD AND JACOB K. THOMAS
are even more surprising.22 For example, if we have failed to control for
systematic risk and our combined long and short position has a positive
beta, the abnormal return on the strategy should be negative when the
overall market return is negative. Over the 50-quarter horizon, the equally
weighted NYSE index declined 16 times, and yet the abnormal return on
the strategy in panel A was positive in 13 of those 16 quarters (11 of 16
quarters for panel B).
In summary, we are able to reconcile our evidence with CAPM misspecification (i.e., failure to control fully for risk) only if at least one of the
following conditions hold: (1) the infrequency of losses in the 1974-86
period is extremely unusual, relative to what would be observed in a
longer time period; (2) the risk premium earned on the SUE strategies
represents compensation for the risk of infrequent but catastrophic
losses, none of which was observed within this 13-year time span; (3) the
disutility of the losses we observe is commensurate with the utility of the
gains, because the losses occur during periods when a $1 decline in wealth
is 28 times more important than the average $1 increase in wealth.
(Cumulative gains are 28 times larger than cumulative losses.)
We find conditions (1) and (3) implausible and note that there is no
evidence to support condition (2).
4.2.4. Raw returns on bad news firms. The large estimated negative
abnormal postannouncement returns for firms with extreme negative
unexpected earnings suggests that the total (raw) postannouncement
returns for those firms could be less than the risk-free rate or even
negative. Although such predictably low raw returns on risky assets are
not ruled out by most modern capital-asset-pricing models, they are
expected only under special conditions that many would find implausible
as applied to a broad cross-section of stocks. Essentially, the stocks would
have to offer some hedge, the value of which exceeds the cost of any
other risk to which the asset is exposed.
Table 4 summarizes the total returns, compounded over various periods, for bad news stocks which ranked in the lowest decile of the
unexpected earnings distribution. The bottom panel shows that the total
annualized returns on the bad news stocks (averaged over firms of all
sizes) were 1.5%, 12.6%, and 10.4% for periods ending 5, 20, and 40
22 The results could conceivably be explained by a failure to control for some factor that
causes returns to increase (decrease) for good (bad) news firms in all periods, regardless of
macroeconomic conditions. However, the only asset-pricing models we know of that could
possibly include such a factor are the Brennan [1970] “after-tax” CAPM (which includes a
dividend yield effect) and the Amihud and Mendelson [1986] CAPM, which includes a term
linked to the bid-ask spread. Earlier (section 4.2.2) we dismissed Brennan’s dividend yield
effect as an explanation. The Amihud-Mendelson CAPM could explain the result only if
an announcement of good news (bad news) caused a long-run increase (decrease) in the
proportional bid-ask spread. But one would expect the opposite given that the proportional
bid-ask spread varies inversely with price, and that good news (bad news) firms tend to
experience price increases (decreases).
POST-EARNINGS-ANNOUNCEMENT
23
DRIFT
4
TABLE
Total (Raw) Returns on “Bad News” (Lowest SUE decile) Portfolios’
HoldingPeriod
(TradingDays, Relativeto
Announcement)
Small Firms
MediumFirms
LargeFirms
Raw Cum.Raw Raw Cum.Raw Raw Cum.Raw
Return Return Return Return Return Return
Preannouncement period
(-79,0)
-1.8%*
-1.8%*
-.4%
-.4%
2.6%*
2.6%*
Postannouncement period
(1, 5)
(6,20)
(21, 40)
(41, 60)
(61, 80)
-.14
.89*
1.31*
2.36*
1.32*
-.14
.75*
2.05*
4.42*
5.74*
.00
.85*
.46
1.87*
.78*
.00
.85*
1.31*
3.18*
3.95*
.23
1.19*
.24
1.85*
1.07*
.23
1.42*
1.66*
3.51*
4.59*
Annualized postannouncement
raw return
(1, 5)
(1, 20)
(1, 40)
(1, 60)
(1, 80)
-7.0
9.4*
12.8*
18.4*
17.9*
0.0
10.6*
8.2*
13.2*
12.3*
11.5
17.8*
10.2*
14.6*
14.3*
Comparable annualized raw returns for “good news”
(highest decile SUE) portfolio
(1, 5)
(1, 20)
(1, 40)
(1, 60)
(1, 80)
32.5%*
26.6*
29.7*
32.9*
30.5*
41.6%*
33.7*
28.0*
27.8*
26.9*
35.5%*
27.5*
22.3*
21.4*
20.8*
Mean annualized returns across
all firm size categories
Low SUE
High SUE
36.5%*
1.5%
(1, 5)
12.6*
29.3*
(1, 20)
10.4*
26.7*
(1, 40)
15.4*
27.4*
(1, 60)
14.8*
26.1*
(1, 80)
1 SUE representsforecast error from a first-orderautoregressiveearningsexpectationsmodel (in
seasonal differences)scaled by its estimation-periodstandarddeviation.Firms are assigned to SUE
decilesbasedon the standingof their SUE relativeto the prior-quarterSUE distribution.
* Significantlydifferentfromzero, .05 level (two-tailedtest).
trading days subsequent to the earnings announcement.23 Total annualized returns for good news firms were 36.5%, 29.3%, and 26.7% for the
same periods. These returns were generated during 1974-86, when the
average annualized return on treasury bills one week from maturity was
23 The standard errors of the mean annualized raw returns over the intervals (1, 5), (1,
20), and (1, 40) are all less than 1%, across all categories in table 4. These standard errors
24
VICTOR L. BERNARD AND JACOB K. THOMAS
8.5% and the return on the equally weighted NYSE index was approximately 22% (13% for the value-weighted index).
The total annualized returns for small bad news stocks over the 5 days
after the earnings announcement were not only less than the average
treasury-bill rate, they were actually negative (although not significantly
different from zero). The total returns for medium firms over the same
5-day window were zero and remained less than the average T-bill rate
over the 40 days subsequent to the announcement. All other total returns
are in excess of the average T-bill rate. However, for two months following
the announcement, the difference was small. For the overall sample, the
40-trading-day return was only 10.4%, or 1.9% higher than the average
T-bill rate.24 In contrast, the 26.7% postannouncement return for the
good news firms exceeded the average T-bill rate by 18.2%.
In order to reconcile this evidence with CAPM misspecification, one
must believe either (1) that betas on the bad news stocks are near zero
(and negative for small and medium stocks shortly after the announcement), or (2) that the value of these stocks as hedges against some
unidentified risk causes their cash flows to be discounted at rates less
than treasury-bill rates during the 5-day postannouncement period, and
at rates nearly that low for two months thereafter. Condition (1) is
inconsistent with evidence in table 2, and we find it implausible that
condition (2) could apply to as broad a spectrum of stocks as those in
the bad news portfolios.
4.3 TESTS OF TRANSACTIONS
DRIFT
COSTS AS EXPLANATION
FOR
Since much of the above evidence is inconsistent with explanations
based on incomplete adjustment for risk, we now turn to the possibility
that the drift could represent a delayed price response. One possibility is
that the drift occurs because transactions costs create sufficient impediments to trading to prevent a complete and immediate response to
earnings announcements.
The abnormal returns reported in this paper appear to be within
round-trip transactions costs for the small individual investor. When
transactions costs are defined to include both bid-ask spreads and
commissions, they are about 4% and 2% for small and large stocks,
were calculated by scaling the standard deviation of raw returns underlying the mean
(before annualizing) by the square root of the sample size, and then multiplying by the
square root of the factor used to annualize the returns. To the extent the data overlap in
calendar time and are cross-sectionally dependent, the standard errors are understated.
24 A comparison of raw returns to the average treasury-bill rate is imprecise, in that it
assumes the event periods are evenly distributed in calendar time. We also calculated the
difference between raw returns and contemporaneous returns on treasury bills. For the
overall sample, the difference was negative for the first 5 days of the postannouncement
period (-7.0%) and positive for the first 40 days (2.1%).
POST-EARNINGS-ANNOUNCEMENT
DRIFT
25
respectively (Stoll and Whaley [1983]).25 To calculate the cost of the
SUE strategy, one must double these amounts to reflect the costs of a
combined long and short position. Then, taking into account that the
SUE strategy involves (on average) a 78% turnover in portfolio content
each quarter, the implied cost would be about 6% (3%) per quarter for
small and large stocks, respectively. These amounts are approximately
equal to that 60-day abnormal returns in table 1.
In this section, we consider how the data might behave if transactions
costs explain postannouncement drift, and then test for the existence of
that behavior.
4.3.1. Is the drift “constrained” by an upper bound? Our first test was
inspired by Ball [1978, p. 110], who argued that, “. . .if the ‘slow’ market
reaction is explained in terms of transactions costs (or costs of ‘professionals’ operating in the market), then small deviations from expectations
are those which imply market disequilibrium. Large deviations presumably attract more investors and are promptly incorporated in prices
because (under this hypothesis) the net gain, after costs, is higher. The
consistent interpretation of this hypothesis is that the excess returns
persist up to, but not beyond, the level of marginal transactions and
information processing costs.”
Under Ball’s depiction, a postannouncement drift would be observed
only when the implied excess returns are small. Alternatively, the drift
may be observed for all levels of implied excess returns but would never
exceed a threshold (equal to the cost of exploiting the information),
regardless of the magnitude of unexpected earnings.26 That is, regardless
of whether the total stock price response implied by an earnings announcement is 2%, 5%, or 20%, the price might move immediately to
within (say) 2% of the implied level. At that point, incentives to exploit
the earnings information would be eliminated for many traders, and the
remainder of the response would occur only with some delay. In such a
market, the postannouncement drift would increase as unexpected earnings increase, but only to some upper bound; beyond that bound, the
drift would remain constant, regardless of the magnitude of unexpected
earnings.
Ball [1978, p. 110] notes that existing evidence does not appear
consistent with this characterization: “. . the evidence… .is that extremerank earnings and dividend changes are associated with larger estimated
abnormal returns, contrary to the ‘transactions cost’ and ‘private cost’
explanations.” However, we consider here whether we (and prior re25 These amounts are based on data from the post-1975 era of negotiated commissions
and are calculated by grouping Stoll and Whaley’s deciles into three categories to conform
to our definitions of small, medium, and large.
26 Although we initially inferred that Ball’s depiction was consistent with the second
alternative, he has indicated to us that he intended to imply the first.
VICTOR L. BERNARD AND JACOB K. THOMAS
26
searchers) have failed to observe an upper bound because we have not
yet examined sufficiently extreme values of unexpected earnings.27 Our
approach is to divide our sample into progressively smaller portfolios,
based on rankings of unexpected earnings. That is, we first divide the
sample into halves, then thirds, quintiles, deciles, and so on, until finally
we divide the sample into 100 portfolios, based on rankings of unexpected
earnings. At each of these steps, we calculate the abnormal return from
a long position in the portfolio with the highest unexpected earnings,
and a short position in the portfolio with the lowest unexpected earnings.
Thus, at each step, the values of unexpected earnings in our portfolios
become more extreme. If postannouncement drift is caused by a cost that
impedes trading, we should observe that, at a point bounded by that cost,
the drift should cease to increase, even though unexpected earnings
continue to increase.
The results are presented in panel A of figure 6. We find that the drift
(over 60 days) grows larger, up to the point where the difference between
SUEs for extreme portfolios is equal to six. (This is the point at which
the sample is split into deciles, which is as fine a decomposition as any
prior study has used.) Beyond that point, the drift does not increase.
Note that the upper bound for the drift is about 4%, or 2% per position.
That amount is within the bounds of transactions costs for the average
firm (based on Stoll and Whaley [1983]), where such costs include both
commissions and the bid-ask spread. Figure 6, panel B shows that the
drift is bounded at approximately 5%, 4.3%, and 3% for small, medium,
and large firms, respectively. This is consistent with Stoll and Whaley’s
[1983] evidence that transactions costs vary inversely with firm size;
when their sample is segregated into thirds, transactions costs are 3.9%,
2.6%, and 2.0% for small, medium, and large firms. When these amounts
are doubled to account for a combined long and short position, they
exceed the bounds implied by figure 6, panel B.
One potential alternative explanation for the result is that the more
extreme values of unexpected earnings simply reflect estimation error.
That is, beyond some upper bound, any additional increases in our
measures of unexpected earnings represent nothing more than noise.
However, the data indicate that this is not the case. Figure 6, panel A
also presents the preannouncement abnormal returns for portfolios with
varying levels of unexpected earnings. Note that even though the postannouncement drift reaches a maximum when SUE difference equals 6, the
preannouncement drift continues to increase to the point where SUE
difference equals 14. Thus, increases in unexpected earnings (at least to
that point) have stock price impacts and are not purely the result of
noise.
Note also that the results of this test cast additional doubt on arguments based on CAPM misspecification. In order to accommodate these
27
We are grateful to Jim Noel, who suggested the tests in this section.
Panel A:
Overall sample:
POST-EARNINGS-ANNOUNCEMENT
DRIFT
27
and post-announcement
abnormal
returns.
Pre-announcement
+la
pro-announcement
period
A
R
Panel B: Comparisonbypfrmizeostanucmndbomlrtrs
6
–
0
2,,.-
i
–
8
0
.
. . . .
18
20
1
14
2
1
4
2
medium
c
…
. ..
..
-..
. ..
. . . . ..
. . . . ..
. . . .
..
.
..
A
differencebetweenmedianSUE values of extremeportfolios
04
0
4
2
8
6
10
12
14
16
22
FIG. 6.-Test of an explanation for the drift, based on costs that impede trading. The
over 60 days
(aARs)
presents the difference in drifts or cumulative abnormal returns
plot
after earnings announcements, between the most positive and most negative SUE (standardized unexpected earnings) portfolios, constructed by splitting the sample into 2, 3, 5, 10,
20,. .,100 portfolios based on SUE. The hypothesis predicts that, if the drift is caused by
costs that impede trading, the postannouncement drift should remain less than those costs,
regardless of the SUE difference between extreme portfolios. Thus, as differences between
SUEs of extreme portfolios increase (represented by movement toward the right of the
graph), the postannouncement CARsshould level out, despite increases in the preannouncement CARs.CARsare the sums over 60-trading-day pre- and postannouncement holding
periods of the difference between daily returns and returns for NYSE-AMEX firms of the
same size decile. SUE represents forecast errors from a first-order autoregressive earnings
expectation model (in seasonal differences) scaled by its estimation-period standard deviation
(see
section
3.2 for details).
5 to 7, and 8 to 10, respectively,
Small,
medium,
based on January
and
large
firms
are in size
deciles
1 to 4,
1 market values of equity for all NYSE
and AMEX firms.
results, the misspecification argument would have to introduce a “kink”
in the relation between unexpected earnings and risk. That is, unexpected
earnings would have to proxy for an omitted risk factor up to some point,
but then additional increases in unexpected earnings could no longer be
correlated with increases in risk.
28
VICTOR L. BERNARD AND JACOB K. THOMAS
4.3.2. Are abnormal returns for short positions greater than those for
long positions? If the costs of trading do play some role in explaining
postannouncement drift, then we might expect the abnormal returns to
short positions in bad news firms to exceed those for long positions in
good news firms, to compensate for restrictions on short sales.
When we calculate abnormal returns using the FOS approach, our data
appear consistent with this hypothesis. The estimated abnormal returns
to short positions in bad news firms are larger, and last longer, than the
estimated abnormal returns on good news firms. Across all size groups,
the abnormal return to the short position over 60 and 180 postannouncement days is 2.3% and 5.5%, respectively, compared to 2.0% and 2.6%
for the long position. However, recall that the FOS calculation of abnormal returns involves summing daily returns. As indicated in section 3.2.2,
summing returns can introduce noise in the calculations which can be
eliminated by compounding the returns. While summing and compounding yielded similar results for the combination of long positions in good
news and short positions in bad news stocks in all of the previous tests,
comparisons between the returns to the long and short positions are
sensitive to the choice between summing and compounding.
Using compounded returns in the FOS size-control portfolio strategy,
the differences between postannouncement abnormal returns to long
positions in good news stocks and to short positions in bad news stocks
are small. The abnormal return to the short position over 60 and 180
postannouncement days is 1.9% and 4.4%, respectively, compared to
2.8% and 5.4% for the long position.
In summary, we have some results which indicate that there is an
upper bound on the postannouncement drift, which is consistent with a
transactions-cost-based explanation. On the other hand, we find weaker
results that restrictions on short sales cause the returns to the short
position to exceed the returns to the long position.
Even if certain features of the data are consistent with a transactionscost-based explanation for the drift, the explanation raises several difficult questions, which we discuss in section 5.
4.4 TESTS
OF WHETHER PRICES FAIL TO REFLECT FULL
IMPLICATIONS OF CURRENT EARNINGS FOR FUTURE
EARNINGS
We now briefly consider one last possibility that could lead to a delayed
response to earnings information. Specifically, we consider whether market prices fail to reflect the full implications of current quarterly earnings
for future quarterly earnings. Although we initially doubted the viability
of this hypothesis, we were motivated to test it based on discussions with
a large insurance company that sells information necessary to trade on
postannouncement drift.
It is well known that seasonally differenced quarterly earnings tend to
be positively correlated from one quarter to the next (Foster [1977] and
POST-EARNINGS-ANNOUNCEMENT
DRIFT
29
Freeman and Tse [1989]). As a result, when earnings in quarter t are up,
relative to the comparable quarter of the prior year, an efficient market
would generate a higher expectation for earnings of quarter t + 1 than
otherwise. After factoring in the implications of quarter t earnings, the
expectation for quarter t + 1 would be unbiased and the mean reaction
to the announcement of quarter t + 1 earnings would be zero.
Suppose though that the market fails to recognize the full extent of
the serial correlation in seasonally differenced quarterly earnings. That
is, the market fails adequately to revise its expectations for quarter t +
1 earnings upon receipt of the news for quarter t. The full implications
of quarter t earnings might not be assimilated until analysts subsequently
revise and publish -forecasts or (in the extreme) until earnings for quarter
t + 1 are announced. In that extreme case, the market would tend to be
“pleasantly surprised” when earnings for quarter t + 1 are up relative to
the prior year (and vice versa), even though the increase could have been
predicted based on quarter t earnings.28
Table 5 provides results from our test of this possibility. We identify
firms in extreme deciles, based on the SUE from quarter t. We then
examine the average reaction to the announcement of quarter t + 1
earnings (measured over days (-4, 0) relative to that announcement).
Note that the portfolios held over those five trading days are completely
identified on the basis of information available approximately three
months earlier; the returns to those portfolios should, on average, reflect
no “surprise” under the hypothesis that stock prices fully reflect publicly
available information.
Table 5 indicates that one can predict the average reaction to quarter
t + 1 earnings, based on the SUE for quarter t. When extreme good news
arrives in quarter t, the market tends to be “pleasantly surprised” again
in quarter t + 1, producing average abnormal returns at the second
announcement of 1.3%, 0.7%, and 0.3% for small, medium, and large
firms, respectively. When extreme bad news arrives in quarter t, the
market tends to be “disappointed” again in quarter t + 1, with average
abnormal returns at the second announcement being -0.8%, -0.7%, and
-0.4% for small, medium, and large firms, respectively.
On the basis of our prior tests, one would expect to observe some
predictable abnormal returns surrounding the next earnings announcement. However, if the drift documented previously were “smooth” over
time, abnormal returns as large as those in table 5 would not be expected.
Since the five trading days examined in table 5 constitute an event period
28Some readers have suggested that such behavior is to be expected, because even
statistical models that attempt to take the serial correlation in earnings into account
generate estimates of unexpected earnings that are themselves serially correlated (see FOS
[1984, table 1]). However, note that this is a characteristic of the estimates of unexpected
earnings from an imperfect (inefficient) statistical model, not a characteristic of “actual”
unexpected earnings in an efficient market. In an efficient market, unexpected earnings
would not be serially correlated (by definition).
VICTOR L. BERNARD AND JACOB K. THOMAS
30
TABLE
5
Mean Stock Price Reactions to Quarter t+1 Earnings, for Firms Grouped on Quarter t
SUE’
SUE Decile for Quartert
PercentageAbnormalReturnin [-4,01
WindowSurroundingEarnings
Announcementfor Quartert + 1 (t-valuesin
parentheses)
Small
Firms
Medium
Firms
Large
Firms
10 (good)
1.32
(7.81)
.68
(5.84)
.31
(3.93)
1 (bad)
-.82
(-5.28)
-.65
(-5.26)
-.37
(-4.01)
Difference (CAR for long [short]
position in SUE 10 [SUE 1]
firm)
2.14
1.33
.68
As fraction of 60-day drift
40%
29%
25%
‘Firms are groupedaccordingto quartert SUE, and abnormalreturnsare cumulatedover the fivetrading-daywindow[-4,0] surroundingthe announcementof quartert + 1 earnings.If marketprices
fail to reflectthe full implicationsof quartert earningsfor quartert + 1 earnings,then the reactionto
quartert + 1 earningsshouldbe predictable,basedon quartert SUE.
Abnormalreturnsare differencesbetweendaily returnsand returnsfor NYSE firmsin the same size
decile.SUE representsforecasterrorfrom a first-orderautoregressiveearningsexpectationsmodel (in
seasonaldifferences)scaledby its estimation-periodstandarddeviation.
only 8% as large as the 60-trading-day period used in most of our tests,
a smooth drift would cause abnormal returns in table 5 equal to 8% of
the total drift observed over the 60-day period. However, the abnormal
returns in table 5 are 40%, 29%, and 25% as large as the 60-day drift
reported earlier for small, medium, and large firms, respectively. In other
words, a disproportionately large fraction of postannouncement drift is
concentrated in the few days preceding and including the next quarter’s
earnings announcement.
The results are consistent with a market that fails to recognize the full
implications of current earnings for future earnings. At the same time,
the results shed additional doubt on explanations for the drift based on
research design flaws, including a failure to adjust fully for risk. It is
difficult to imagine why extreme earnings would lead to risk shifts that
tend to occur three months later and are coincident with the announcement of the next quarter’s earnings.
The results in table 5 are related to, but distinct from, those reported
by Freeman and Tse (henceforth FT) [1989], who advance a hypothesis
for a “rational delayed reaction to earnings news.” As FT explain, the
reaction of an efficient market to quarter t + 1 earnings can be conditional
on earnings for quarter t. Given that earnings “innovations” (defined by
FT as seasonal differences) are serially correlated, quarter t + 1 innovations should be less surprising if they have the same sign as quarter t
POST-EARNINGS-ANNOUNCEMENT
DRIFT
31
innovations. For example, the reaction (abnormal return) to a quarter t
+ 1 positive innovation that follows a quarter t positive innovation (say,
Rpp)should be smaller in absolute value than the reaction to a negative
quarter t + 1 innovation that follows a positive quarter t innovation (say,
Rpn);that is, Rpp< -Rpn FT supply evidence consistent with Rpp< -Rpn, indicating at least some degree of "rationality" in the market. However, there is a stronger condition implied by market efficiency. Specifically, if the probability of a like-sign innovation is r, then lr(Rpp)+ (1 - r)(Rpn) = 0; that is, the weighted average abnormal return for all firms with positive innovations in quarter t should be zero. If this condition does not hold, one could simply hold all firms with a positive innovation in quarter t and expect to earn positive abnormal returns in quarter t + 1. Evidence presented throughout this paper (including table 5), in certain of FT's tests, and in prior research (e.g., FOS [1984]) indicates this stronger condition is violated. FT also present evidence that at least part of the drift following the announcement of quarter t earnings can be recharacterized as a response to the predictable portion of quarter t + 1 earnings. (Of course, this raises the question of why the market is responding to something that could have been predicted in a prior quarter.) That evidence is consistent with the results in our table 5 and with earlier evidence documented by Rendleman, Jones, and Latane [1987]. What table 5 demonstrates beyond FT and the prior research is that much of the response to the predictable portion of quarter t + 1 earnings does not occur until the five days surrounding the announcement of those earnings. 5. Discussion and Conclusions Much of the evidence presented here casts doubt on CAPM misspecification as an explanation for post-earnings-announcement drift. In section 5.1, we summarize implications of the evidence for various forms of misspecification. Section 5.2 then reviews the plausibility of alternative explanations. 5.1 IMPLICATIONS OF THE EVIDENCE FOR CAPM MISSPECIFICATION CAPMmisspecification can assume several different forms. They can be divided into (1) risk mismeasurement and (2) other misspecifications. In turn, risk mismeasurement can include (a) misestimation of systematic risk and (b) exclusion of risk factors other than systematic risk. 5.1.1.a. Risk mismeasurement: misestimation of beta. Our evidence fails to support the BKW [1988] suggestion that beta shifts might explain a large fraction of post-earnings-announcement drift. The key results are as follows. (1) Estimated beta shifts were only about 8% as large as would be necessary to explain fully the magnitude of the drift (section 4.2.1). 32 VICTOR L. BERNARD AND JACOB K. THOMAS (2) The BKW hypothesis suggests that a strategy based on postannouncement drift (long in good and short in bad news firms) would have a positive beta, thus performing poorly in bear markets. However, the SUE strategy yielded consistently positive returns in both bull and bear markets (sections 4.2.1 and 4.2.3). 5.1.1.b. Risk mismeasurement: exclusion of risk factors other than systematic risk. Our results are also inconsistent with this potential explanation for post-earnings-announcement drift. (1) We find no evidence that an SUE trading strategy is risky along any of the five dimensions identified by Chen, Roll, and Ross [1986] as important factors in asset pricing (section 4.2.2). (2) If the SUE strategies are risky on some unidentified dimension, then there is little evidence of that risk surfacing in the form of losses whose cost (in terms of utility) could plausibly be commensurate with the value of the supposed risk premium (section 4.2.3). The consistent profitability of the SUE strategies raises the question, "Where's the risk?" (3) According to capital-asset-pricing theory, expected total returns on risky assets can be less than risk-free returns only under special conditions that appear implausible in this context. However, subsequent to earnings announcements, bad news firms had mean total returns that were less than T-bill yields during the first week, and only slightly greater than T-bill yields during the first two months (section 4.2.4). (4) The drift is initially increasing in unexpected earnings but appears to reach an upper bound beyond which the drift remains constant as unexpected earnings rise (section 4.3.1). In order to reconcile this result with CAPM misspecification, one would have to believe that unexpected earnings proxy for an unidentified risk factor only to some point, with further increases in unexpected earnings being uncorrelated with the unidentified risk. (5) A disproportionate amount of the drift is concentrated around the following quarter's earnings announcement (section 4.4). It is difficult to imagine the reasons risk would tend to shift with a three-month delay, and why the risk shift would be most extreme at a point that coincides with the subsequent earnings announcement. 5.1.2. Other forms of CAPM misspecification. CAPM misspecification could also involve a failure to allow for market imperfections such as taxes. If the difference between ordinary and capital gains tax rates affects pricing, then a "dividend yield effect" would exist in stock returns. However, as indicated in section 4.2.2, differences in dividend yields between the high and low unexpected earnings firms are so small that they are unlikely to explain any significant fraction of the drift. 5.2 DELAYED PRICE RESPONSE AS AN EXPLANATION Since arguments based on CAPMmisspecification cannot plausibly be reconciled with our data, we turned to alternative explanations which view the drift as a delayed price response. POST-EARNINGS-ANNOUNCEMENT DRIFT 33 5.2.1. Transactions costs as an explanation. If transactions costs explain postannouncement drift, then the drift should not exceed transactions cost bounds, even for the most extreme values of unexpected earnings. Section 4.3.1 did indeed indicate that the drift appears to be "constrained" by an upper bound that is approximately equal to roundtrip transactions costs for the individual investor. Moreover, the bound varies across firm size in the same way transactions costs do.29 On the other hand, we did not find strong evidence that abnormal returns to short positions in bad news stocks exceed the abnormal returns to long positions in good news stocks, as would be predicted if restrictions on short sales play a role in causing the drift (section 4.3.2). Although some of our results in section 4.3.1 may support a transactions-cost-based explanation, this explanation still raises several difficult questions. First, why does trading continue throughout the postannouncement period? If a price response is delayed because transactions costs discourage traders from entering the market, then no trading should occur. Alternatively, if a trade ultimately does occur, it should occur at a price that fully reflects available information. Personally, we are unable to explain why investors are willing to trade even while the price appears not to reflect fully the available earnings information. A related question is, why don't specialists or other market makers move the price to the "appropriate"level upon the first trade after the earnings announcement? There are also other questions which undermine the viability of a transactions-cost argument. For example, why is the drift not eliminated by traders who face no commissions and can bypass the specialist's bidask spread (thus facing trivial transactions costs); or why would transaction costs necessarily cause underreaction to new information, as opposed to simply introducing noise in prices? Finally, if transactions costs cause the drift, why is so much of it concentrated around the next quarter's earnings announcement? 5.2.2. Failure of market to recognize fully the implications of current earnings for future earnings. The finding of section 4.4-that much of the drift is concentrated around the next quarter's earnings announcement-is difficult to explain except as a reflection of market prices that fail to recognize fully the extent of serial correlation in seasonally differenced quarterly earnings. Although the result is surprising, it is consistent with Foster's [1977] evidence that estimates of unexpected earnings which ignore such serial correlation (i.e., those based on a 29 If indeed trading costs (including direct transactions costs and other costs of implementation) do explain post-earnings-announcement drift, then we should observe drifts for other information events as well. It is interesting to note that drifts are observed after a variety of events, including, for example, 13-D filings to announce the acquisition of at least 5% of a firm's stock (Larcker and Lys [1987]), repurchase tender offers (Lakonishok and Vermalean [1988]), dividend announcements (Charest [1978]), bond rating downgrades (Holthausen and Leftwich [1986]), and earnings forecast revisions by managers (McNichols [1989]) and analysts (Brown, Foster, and Noreen [1985]). 34 VICTOR L. BERNARD AND JACOB K. THOMAS seasonal random walk model) are more highly correlated with stock returns than proxies that do reflect the serial correlation. Our only result that is not consistent with incomplete updating of earnings expectations is the one from section 4.3.1, which indicated the drift appears to have an upper bound (section 4.3.1). That is, if market prices fail to reflect fully the implications of current earnings for future earnings, then we would expect the drift to be always increasing in the magnitude of the current unexpected earnings rather than having some upper bound. One possibility that could reconcile the two results is that market prices fail to reflect the full implications of current earnings for future earnings, but once such a discrepancy exceeds a certain threshold, there are sufficient incentives for speculators to trade until it is reduced. But again, this leaves unanswered the question of why some investors are willing to trade at the "wrong" price in the meantime. However, the coexistence of some traders who are either uninformed or unsure about whether the price fully reflects past earnings information, and informed speculators who can exploit the others only at some cost, may be the only explanation that is simultaneously consistent with (1) the rational use of "recent earnings surprise" as a buy/sell signal among several institutions and investment houses, and (2) the persistence of the drift, despite this activity. Whether this or another explanation can resolve the enigma is left for future research. 5.3 CONCLUSIONS In this study we have attempted to discriminate between two alternative explanations for post-earnings-announcement drift: a failure to adjust abnormal returns fully for risk and a delay in the response to earnings reports. We conclude that much of our evidence cannot plausibly be reconciled with arguments built on risk mismeasurement but is consistent with a delayed price response. Although these results support a dismissal of an important category of explanations for postannouncement drift, they also raise some difficult unanswered questions. The nagging general question is what kind of equilibrium would support market prices that only partially reflect information as widely disseminated and freely available as earnings. A more specific question (also raised by Freeman and Tse [1989]) is why the market would appear to react with surprise to earnings information that is predictable, based on earnings for the prior quarter. 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