Psychological Barriers, Expectational Errors,
and Underreaction to News∗
Justin Birru†
The Ohio State University
July 2015
Abstract
This paper provides evidence that the 52-week high serves as a psychological barrier, inducing
expectational errors and underreaction to news. Two clear predictions emerge and are confirmed
in the data. First, nearness to a 52-week high induces expectational errors; evidence from
earnings surprises and analyst price targets indicates that investor and analyst expectations
are biased in a downward direction for stocks near a 52-week high and biased in an upward
direction for stocks trading far from a 52-week high. Second, nearness to a 52-week high
induces underreaction to news. Among positive earnings surprise stocks, post-announcement
drift exists only for those stocks near a 52-week high. The evidence suggests that in contrast to
currently offered preference-based explanations, a belief-based explanation may better explain
the previously documented 52-week high anomalies.
∗
I thank Jack Bao, Sergey Chernenko, David Hirshleifer, Kewei Hou, Joshua Pollet, Kenneth Singleton,
and seminar participants at the 2015 SFS Finance Cavalcade, Ohio University, Pomona College, The Ohio State
University, University of Illinois at Chicago, and the University of Rochester for helpful comments and discussion.
†
Fisher College of Business, The Ohio State University. Email: birru.2@fisher.osu.edu
1. Introduction
This paper explores the role of psychological price barriers in financial markets. Focusing on
one specific price barrier, the 52-week high, I offer new insight and evidence regarding the role
that price barriers play in influencing investor expectations and affecting the speed with which
prices react to news. Specifically, I provide evidence that expectations are overly pessimistic for
stocks near a 52-week high, and that stocks near a 52-week high underreact to good news.
Psychology abounds with evidence that individuals irrationally anchor on salient, but often
irrelevant numbers.1 Perhaps the most salient common reference price pertaining to a stock is
its 52-week high. The 52-week high of a stock is widely reported and easily found. For example,
along with prices and returns, prominent outlets such as the Wall Street Journal, Financial
Times, Bloomberg, and Yahoo Finance also report the 52-week high.
There is notable recent evidence that the 52-week high serves as a reference price that induces investors to behave irrationally. For example, Grinblatt and Keloharju (2001) find that
both retail and institutional investors are more likely to sell stocks trading at a historical high
and buy stocks trading at a historical low.2 Heath, Huddart, and Lang (1999) find that the
likelihood of employee option exercise doubles when the stock price exceeds its 52-week high.3
Examining acquisitions, Baker, Pan, and Wurgler (2012) find that target shareholders are substantially more likely to accept takeover offers that are made above the target firm’s 52-week
high. In the cross-section of stocks, George and Hwang (2004) find that a strategy taking a long
position in stocks near a 52-week high and a short position in stocks far from a 52-week high
generates abnormal future returns. Each of these studies exhibits the same common theme;
stocks near a 52-week high seem to be viewed as “expensive” leading to investor skepticism that
further price increases will ensue.
Somewhat surprisingly, this is not the current explanation offered in the literature to explain
the observed findings. Rather, as discussed in more detail below, prior literature has relied on
prospect theory for a preference-based explanation of 52-week high induced behavior. While not
1
See Tversky and Kahneman (1974) for an introduction to the psychological motives behind anchoring.
This is true even after controlling for past returns and the disposition effect.
3
Poteshman and Serbin (2003) find similar behavior among retail traders, noting that retail traders irrationally
exercise stock options when the price exceeds the past 52-week high.
2
1
ruling out a preference-based explanation, the evidence presented in this paper suggests that a
belief-based explanation offers a much more intuitive rationale for the previously documented
findings.
I denote the anchoring hypothesis as the hypothesis that investors utilize the 52-week high
as an anchor when forming expectations, and when interpreting the potential impact of new
information. Specifically, the anchoring hypothesis predicts that the 52-week high serves as a
psychological barrier, representing an upper bound for prices in investors’ minds.4 Two specific
predictions arise from the anchoring hypothesis.
First, the anchoring hypothesis predicts that nearness of a stock’s price to its 52-week high
induces expectational errors among investors. Because investors are hesitant to believe that
subsequent upward movements in price above a 52-week high will be justified, expectations for
stocks trading near a 52-week high will be overly pessimistic. Meanwhile, for stocks trading far
from a 52-week high, investors tend to think that subsequent downward movements in price will
be unlikely, resulting in upward biased expectations for stocks trading far from a 52-week high.
Second, there are implications for how new information is impounded into prices. For example, if good news arrives for a stock that is already trading close to its 52-week high, investors
will initially be hesitant to push the stock above this psychological price barrier, resulting in an
underreaction to the good news. Eventually, however, the good news will prevail and the price
will continue its increase beyond the 52-week high. Similarly, if a stock is far from its 52-week
high, investors will be less willing to push the stock price lower. In this case, stocks trading far
from a 52-week high will initially underreact to negative news.
These two hypotheses are the focus of this paper. To be clear, the two hypotheses tested
here are separate, distinct hypotheses that are related only in that both arise from investor
anchoring on the 52-week high. The first hypothesis, that nearness to a 52-week induces expectational errors, is a new hypothesis, that to my knowledge has not been posited before. The
second hypothesis, that nearness to a 52-week high induces underreaction to news, is offered by
George and Hwang (2004) as a potential explanation for their findings. While this hypothesis
4
The anchoring hypothesis is in line with the idea of resistance and support levels in technical analysis, in
which the resistance level serves as a price level above which investors believe it difficult for a stock price to rise
and the support level reflects a price level below which investors believe it unlikely for a stock to fall. See Brock,
Lakonishok, and LeBaron (1992) for additional discussion of resistance and support levels and implications for
stock returns.
2
is consistent with their findings, it is not the only explanation that is consistent with their findings, and it cannot be tested in their setting. For instance, another potential explanation for
their findings is the following. There is widespread evidence in the literature, that in general,
stocks underreact to news. Stocks near a 52-week high have on average experienced recent good
news, while stocks far from a 52-week high have on average experienced negative recent news.
Therefore, in the future, stocks near (far from) a 52-week high will have higher (lower) returns
as this recent news is eventually incorporated into prices. This alternative hypothesis suggests
that the 52-week predicts future returns because it is a proxy for the sign of the recent past news
about the firm, but not that the 52-week high itself is the cause of the return predictability.
This paper adds to the extant literature in the following ways. To my knowledge, this paper
is the first to hypothesize that the 52-week high induces expectational errors, and the first to
document this effect empirically. This paper is also the first to provide direct empirical evidence
that the 52-week high induces underreaction to news. Furthermore, I document the presence
of expectational errors not just among relatively unsophisticated individual investors, but also
among analysts, a subset of market participants believed to be more sophisticated than the
average investor.
Importantly, the paper also adds to the literature by shedding light on the exact mechanism
through which the 52-week high affects investor behavior. The previous literature typically appeals to prospect theory arguments of Kahneman and Tversky (1979) to explain the mechanism
through which the 52-week high affects investor behavior.5 Specifically, according to prospect
theory, investors become more risk averse when prices exceed a reference point.6 Under the
assumption that the 52-week high serves as a reference point from which investors evaluate
gains and losses, prospect theory implies that investors will become more risk averse when
prices exceed the 52-week high. The evidence I document indicating that nearness to a 52-week
high induces overly pessimistic expectations provides an alternative explanation for these past
findings. In contrast to a utility-based explanation, I argue that the belief-based explanation
may more accurately explain the mechanism driving the previously observed findings.
In addition to the previously discussed literature on the 52-week high, the results are also
5
George and Hwang (2004) is an exception, as they do not rely on prospect theory.
In more recent work, Barberis and Xiong (2012) show that realization utility can also explain the previously
documented irrational investor behavior around the 52-week high.
6
3
related to the price barrier findings of Donaldson and Kim (1993). They document that Dow
Index movements are restrained near index multiples of 100, and that this restraint disappears
upon breaking through a barrier. Driessen, Lin, and Van Hemert (2012) document similar behavior around the 52-week high, as they find that option implied volatility increases after prices
rise above the 52-week high. Huddart, Lang, and Yetman (2009) document volume spikes in
the stock market when a stock passes a 52-week high. The results also shed light on the specific
mechanism driving the predictive ability of the 52-week high for future returns as documented
by George and Hwang (2004) in the cross-section of stocks, and Li and Yu (2012) in the time
series of index returns.
The paper proceeds as follows. Section 2 discusses the main hypotheses. Section 3 discusses
the data and descriptive statistics. Section 4 presents evidence of anchoring-induced expectational errors. Section 5 examines underreaction to earnings news. Section 6 concludes.
2. Hypothesis Development
To explore the implications of nearness to a 52-week high, I primarily examine the behavior of
stock prices around earnings announcements. Earnings announcements provide a fertile setting
for exploring these hypotheses. First, they provide a setting in which there is a standardized
news announcement for which price reactions can be easily identified. Second, one can clearly
infer expectations of market participants and document how the earnings realization differs
from expectation. This environment facilitates exploration of two straightforward predictions
of the hypothesis that investors believe subsequent price movements above the 52-week high to
be unlikely. Formally, the two predictions of the anchoring hypothesis that I focus on are the
following:
Hypothesis 1 (H1: Expectational Errors): Expectations will be overly
pessimistic for stocks near a 52-week high and overly optimistic for stocks far
from a 52-week high.
4
Nearness to a 52-week high induces expectational errors. Specifically, investor expectations
will be downward biased for stocks near a 52-week high. Intuitively, when a stock is trading at or
near its one-year maximum, investors will believe it unlikely that new information will suggest
that the price should rise even farther still. On the other hand, when a stock’s price has fallen
far from its 52-week high, investors will believe it unlikely that further bad news will suggest
that the price should drop even farther still. I test two predictions of this hypothesis. First,
earnings surprises will be systematically positive for firms near a 52-week high and systematically
negative for firms far from a 52-week high; on average expectations of earnings will be too low
for stocks near a 52-week high, and too high for stocks trading far from a 52-week high. Second,
analyst expectations of price appreciation will be more pessimistic for stocks near a 52-week
high than for stocks far from a 52-week high.
The first testable prediction arises naturally. Investors may set low earnings expectations
in order to validate not setting a price above the 52-week high. Alternatively, taking price as
given, investors may set expectations of earnings low to justify the continued belief that the
price is unlikely to rise above its 52-week high price barrier. The second testable prediction
arises naturally from the belief that further price increases are less likely for stocks near a 52week high than for those far from a 52-week high. That analysts anchor on a 52-week high
when forming beliefs is particularly compelling evidence of the ability of the 52-week high to
induce expectational errors in light of the fact that analysts are in general thought to be more
sophisticated than the average investor, and in particular should be among the most informed
in the market with regards to the specific stocks they cover.
Hypothesis 2 (H2: Underreaction to news): Stocks near a 52-week high
will underreact to positive earnings surprises, while stocks far from a 52-week
high will underreact to negative earnings surprises.
The general idea is the following. Prices near a 52-week high will hinder the immediate
incorporation of information into positive surprise stocks. This is because investors are irrationally hesitant to push prices beyond the 52-week high. Conversely, prices near a one-year
maximum facilitate the immediate impounding of information into negative surprise stocks as
investors exhibit no hesitance to push prices away from the 52-week high in the downward
5
direction. Trading far from a maximum has the opposite effect; it facilitates the immediate
impounding of positive surprise information and hinders the speed of incorporation of negative
news into prices.
H1 and H2 are two distinct hypotheses. H1 does not imply H2, nor does H2 imply H1.
For instance, if an investor is overly pessimistic, it certainly need not be the case that she underreacts to subsequent positive news. Similarly, there are many reasons why investors might
underreact to news. Underreaction to good news does not imply ex-ante overly pessimistic
beliefs.
I find strong support for both H1 and H2. First, nearness to a 52-week high, measured as of
the end of the previous month, is a strong and significant predictor of both earnings surprises
and analyst forecasts of price appreciation. Consistent with nearness to a 52-week high inducing
overly pessimistic expectations, earnings surprises (measured either by analyst forecast surprises
or by stock price reactions) are systematically positive for stocks trading near a 52-week high
and systematically negative for stocks trading far from a 52-week high. Stocks in the top decile
of nearness to a 52-week high outperform stocks in the bottom decile of nearness to a 52-week
high by more than 80 basis points over a three-day window around the earnings announcement. A long-short strategy that exploits biased investor expectations in the days around the
announcement generates a daily alpha of nearly 23 basis points. The results are similar when
using analyst-based measures of surprise; in fact, in 96% of the sample quarters (107 out of
112), surprises measured relative to median analyst forecasts are larger for the decile of stocks
nearest a 52-week high than for the decile of stocks farthest from a 52-week high. Importantly,
the predictive ability of the 52-week high is robust to, and arguably dominates, price momentum and earnings momentum explanations. Further consistent with nearness to a 52-week high
inducing overly pessimistic expectations, one-year-ahead forecasts of price appreciation are substantially higher for stocks far from a 52-week high than for stocks near a 52-week high. Of
course, this may not reflect biased expectations if stocks far from a 52-week high do tend to
experience greater price appreciation; however, this is not the case. Comparing the one-year
ahead forecasts to the ex-post realized one-year ahead price reveals that the forecasts for stocks
far from a 52-week high are indeed substantially overestimated relative to those near a 52-week
6
high.
Second, nearness to a 52-week high does in fact induce underreaction to news, as it is a
strong predictor of both post-earnings announcement drift and announcement date price reaction. Stocks trading near a 52-week high underreact to positive surprises, while those trading
far from a 52-week high underreact to negative surprises. Stocks near a 52-week high that experience positive surprises have weaker announcement date price reactions to their own earnings
news as compared to positive surprise firms far from a 52-week high, and this is followed by a
larger post-earnings announcement drift for stocks near a 52-week high. Double-sorts on earnings surprise and nearness to a 52-week high reveal a difference in benchmark-adjusted returns
to portfolios that maximally exploit underreaction - specifically, good news stocks nearest to
a 52-week high minus bad news stocks farthest from a 52-week high - of over 7% over the 60
trading days following announcement of earnings news. A long-short calendar-time portfolio exploiting 52-week high induced underreaction to news generates a monthly alpha of over 150 basis
points. The findings are not driven by liquidity, momentum, or the disposition effect. Rather,
nearness to a 52-week high dominates momentum and capital gains in explaining underreaction.
3. Data and Descriptive Statistics
3.1 Data
Quarterly earnings announcement data is obtained from IBES and Compustat covering a
sample period of 1984 to 2011. Price target data is from the IBES unadjusted detail history
dataset and begins in 1999. Price targets are adjusted for splits using CRSP data. Stock return
data is from CRSP. Earnings analysis is conducted as in Livnat and Mendenhall (2006). Following Livnat and Mendenhall (2006), I exclude observations for which market value of equity
at the fiscal quarter end is missing or less than $5 million, and I also require that assets and
sales are both greater than 0. I also exclude stocks under $5 and require that the announcement
date is available on both Compustat and IBES and that the dates are within five days of one
another. In the event that the dates are not equal, I use the earlier of the dates, as DellaVigna
and Pollet (2009) find that the earlier of the two dates is almost always the correct one when
7
the Compustat and IBES dates differ. When available, I also utilize information on the time
of the day of the announcement from IBES. For announcements occurring after market closing,
the date of announcement is assigned to the following trading day.
I follow the literature and define earnings surprise as the standardized unexpected earnings
(SUE). This is equal to the difference between realized earnings and the median analyst forecast
normalized by the end of quarter stock price. Only the most recent forecast for each analyst
is used, and only forecasts made in the 90 days prior to the announcement date are included.
The earnings surprise measure as defined for firm i in quarter q is
SU Ei,q =
EP Si,q −F orecasti,q
.
Pi,q
I conservatively define the 52-week high as the highest daily closing price in the 12 month
period ending at the end of the previous month. For any given month, nearness to a 52-week
high is defined as the ratio of the closing price at the end of month t − 1 to the highest stock
price in the 12 month period ending in month t − 1. Specifically, M axi,t is defined as
M axi,t =
Pi,t−1
Highi,t−1
where Pi,t−1 is the price of stock i as of the end of month t − 1, and Highi,t−1 is the highest
price of stock i in the 12 month period ending at the end of month t − 1.
3.2 Descriptive Statistics
In much of the following analysis I rely on cumulative abnormal returns (CAR) to provide
insight into the effects of psychological price barriers. CARs are measured relative to size and
book-to-market matched portfolios. In addition to SU Ei,q , I also analyze the CAR in the three
days around an announcement as a further measure of earnings surprise. CAR(-1,1) is the
return in the three days around the announcement, defined as
8
CAR(−1, 1)i,q =
t+1
Y
(1 + Ri,k ) −
k=t−1
t+1
Y
(1 + Rp,k )
k=t−1
where t is the announcement date of firm i’s earnings, Ri,k is the daily return of firm i, and
Rp,k is the daily return to the size-B/M matched portfolio. I use the Fama-French 25 size-B/M
portfolios as benchmark returns. Firms are matched based on their market capitalization as
of the end of June and book-to-market value at the end of the last calendar year, where book
equity is from the last fiscal year end in the previous calendar year and market capitalization
is from the end of December of the previous calendar year.
Table 1 provides summary statistics by M ax decile for the main control variables used
throughout the analysis. Variable definitions follow. Number of analysts is the number of analyst estimates used to create the median forecast. Reporting lag is the number of days between
quarter end and announcement of earnings. Turnover is the average monthly stock turnover
over the previous 12 months. Market cap is defined as of the end of month t − 1. B/M is
book equity from the last fiscal year end in the previous calendar year and market value as of
December of the last calendar year. Earnings persistence is the first-order autocorrelation of
quarterly earnings over the past four years. Earnings volatility is the volatility of deviations of
quarterly earnings from one-year-ago earnings over the past four years. I require at least four
observations to calculate earnings persistence and earnings volatility. All regression variables
are winsorized at 1% and 99% throughout the analysis.
4. Expectational Errors
4.1 Predicting Earnings Surprises
I first test H1. Specifically, the anchoring hypothesis predicts that investors believe it unlikely that a stock near a 52-week high will increase further in value, as a result investors will
discount the probability that earnings will be good enough to justify a large upward movement
in stock price. In other words, for stocks near a 52-week high, investors’ expectations of earnings
will be too pessimistic. On the other hand, stocks trading far from a 52-week high will be seen as
9
being unlikely to fall farther in value, leading investors to have expectations of future earnings
that are overly optimistic. The anchoring hypothesis therefore makes a clear prediction about
earnings surprises: specifically, stocks trading near a 52-week high will on average see earnings
that are better than expected (positive surprises), while stocks trading far from a 52-week high
will on average realize earnings that are worse than expected (negative surprises).
Table 2 shows the results of a simple univariate sort. Each quarter stocks are sorted into
deciles based on nearness to a 52-week high (M ax). Earnings surprises are measured by standardized unexpected earnings based on analyst forecasts (SUE), and also based on the returns
in the three days around the earnings announcements (CAR (-1,1)). Table 2 shows that firms
near a 52-week high have systematically positive surprises, while those far from a 52-week high
have systematically negative surprises.
The pattern is generally increasing with more variation coming in the bottom deciles than
the top deciles of the sort. This is not surprising as the summary stats in Table 1 show that
M ax exhibits substantial variation in the lower deciles, while exhibiting far less variation in
the upper deciles where a large fraction of the observations take values between 0.9 and 1. For
example, the mean value of M ax in decile 10 is 0.987 which is only slightly larger than the
mean value of 0.953 in decile 9. On the other hand, the mean of M ax is 0.462 in decile 1 as
compared to 0.622 in decile 2.
The results of the univariate sorts are consistent with the 52-week high acting as a price
barrier in the manner hypothesized. The magnitude of the effect is quite large. The difference
in three day returns between the top and bottom deciles of portfolios sorted on nearness to a
52-week high is 80 basis points and statistically significant.
Chan, Jegadeesh, and Lakonishok (1996) document that past returns and pasts surprises
each have independent power in predicting future surprises. Specifically, they find a positive
relationship between past returns and future surprises and a positive relationship between past
surprises and future surprises. The evidence they provide is consistent with investor underreaction to the informativeness of past news. Because nearness to a 52-week high is likely to be
correlated with both past returns and past surprises, I next examine whether the predictive
ability of M ax can be explained by price momentum or earnings momentum.
10
Table 3 takes a first step in addressing this question, and displays 3x3 double sorts of M ax
and price momentum and M ax and earnings momentum. Price momentum is measured as
the return from t − 12 to t − 1 and earnings momentum is measured by one period lagged
earnings (SU Et−1 ).7 Panel A asks whether, after controlling for earnings momentum or price
momentum, nearness to a 52-week high has any independent explanatory power in predicting
surprises. Conversely, the analysis in Panel B asks whether, after controlling for nearness to a
52-week high, earnings momentum or price momentum has any independent incremental ability
to predict surprises.
Table 3 shows that the results are quite favorable for M ax. M ax retains its ability to
predict surprises within loser, middle, and winner groups as sorted by momentum or earnings
surprise. The same is not always the case for the predictive ability of earnings or momentum
after sorting into groups by nearness to a 52-week high. Furthermore, the magnitude of the
difference between winners and losers sorted within groups assigned by the first ranking criteria
is substantially larger when sorting based on M ax than when sorting based on momentum or
past earnings. In fact, the magnitude of 5 of the 6 winner minus loser portfolios within groups
first sorted by momentum and then by M ax is larger than that within groups first sorted by
M ax and then by momentum. The same is true for 5 of the 6 winner minus loser portfolios
first sorted by earnings and then by M ax as compared to those first sorted by M ax and then
earnings. In other words, the predictive ability of M ax seems to be at least as good, and arguably better, than that of momentum or past earnings in predicting future surprises. Given
that there is also some predictive ability of momentum or past earnings after first sorting on
M ax, the results also suggest that the driver of surprise predictability for M ax is likely distinct
from that of momentum or past earnings.
The next step is to examine whether the predictive ability of M ax holds while simultaneously
controlling for multiple determinants of earnings surprises. While the 3x3 sorts are quite informative, sorting on more than two variables is not practical. To examine whether the predictive
ability of M ax is in fact distinct from previously discovered determinants of earnings surprises,
I next turn to a multivariate regression framework. Panel C examines whether M ax continues
7
The results here and throughout the analysis are similiar if 6 month momentum is used in place of 12 month
momentum.
11
to predict earnings surprises after controlling for momentum, past earnings, and a host of other
variables. Specifically, I follow Hirshleifer et al. (2009) and include controls for the number of
analysts, reporting lag, average monthly stock turnover, market cap, book-to-market, earnings
persistence, and earnings volatility, and I also control for the firm’s dividend to price ratio.
I also include industry, year, month, and day-of-week fixed effects. The first three columns
confirm that M ax, momentum, and past earnings each have univariate predictive ability. The
specification in column 4 includes all three variables together, while column 5 also includes the
additional control variables. The results show that while the predictive ability of momentum
is substantially weakened - the point estimate decreases by nearly 80% - the predictive ability
of M ax and past earnings are quite robust to the other controls. The coefficient of M ax continues to be economically significant, as it only decreases by about 35% when all variables are
included, while the coefficient on past earnings decreases by about 13%. The regression results
confirm that nearness to a yearly max is an economically and statistically significant predictor
of earnings surprises.
In an effort to shed further light on the economic magnitude of the results, I examine the
returns that accrue to an implementable calendar portfolio strategy. On each day I identify
stocks that are within a three day window of an earnings announcement, day t − 1 to t + 1.
Stocks are then sorted into deciles by M ax. I then examine the returns to a strategy that on
each day holds stocks closest to the 52-week high and sells stocks farthest from the 52-week
high. If there are no stocks in a bucket on a particular day, the strategy invests in the riskfree asset for that day. Of course, in practice, implementing such a strategy would incur large
transactions costs arising from daily rebalancing; however, the objective of this analysis is to
measure the economic magnitude of the effect.
Daily alphas are calculated from a time-series regression of daily returns on the daily FamaFrench three factors along with the Carhart (1997) momentum factor. The results are displayed
in Table 4. The portfolio returns are increasing in nearness to a 52-week high. A long-short
portfolio strategy that buys stocks near a 52-week high and sells those far from a 52-week high
delivers a statistically significant daily alpha of about 23 basis points. The large alpha again
indicates the sizable economic magnitude of the effect.
12
4.2 Analyst Price Targets
I next turn to a second, separate test of the hypothesis that nearness to a maximum induces
expectational errors. Expectational errors induced by nearness to a 52-week high should manifest itself in the forward price targets that analysts set. Specifically, the anchoring hypothesis
predicts that all else equal, analyst expectations of price appreciation will be more pessimistic
for stocks near a 52-week high than for stocks far from a 52-week high.
Utilizing price target data from IBES, I find evidence which strongly supports the anchoring
hypothesis. I use target price forecasts from the IBES unadjusted detail history price target
dataset and use data from CRSP to adjust estimates for splits. For each stock, I keep only
the latest analyst forecast in each month and calculate the monthly consensus analyst expected
price appreciation by taking the mean across all analyst expected price appreciation forecasts
in that month. IBES target price forecast data starts in 1999; however, there are relatively
few observation in the first three months of 1999, so I begin the sample in April of 1999. The
sample ends in December of 2012. I focus only on 12 month horizon forecasts as these are by
far the most popular, however the results are unchanged if I instead focus on other horizons.
Expected price appreciation is defined as the difference between the analyst price target
forecast and the closing price of the stock on the day prior to the forecast, normalized by the
price at the close of the day prior to the forecast. I also examine the difference between analyst
expectations and the true ex-post stock price appreciation. Forecast error is the analyst price
appreciation minus the true stock price appreciation measured on the trading date closest to,
but not prior to, 365 days subsequent to the forecast. Table 5 examines the univariate relationship between price appreciation expectations and nearness to a max. As before, nearness to a
52-week high is defined as of the end of the previous month.
The results are clear. Price appreciation expectations monotonically decrease as price nears
a 52-week high. Stocks nearest a 52-week high have the smallest price appreciation expectations,
while those farthest from a 52-week high have the highest price appreciation expectations. The
same is true of forecast errors, indicating that analyst forecasts are not capturing rationally
expected differences in price appreciation. The differences are also quite large in magnitude.
13
Stocks farthest from a 52-week high have an expected price appreciation of nearly 50%, while
those nearest a 52-week high have an expected price appreciation of 15.7%. While analyst price
target forecasts are well known to be overly optimistic in general, they are particularly overly
optimistic for stocks farthest from a 52-week high, as they overestimate price appreciation by
over 38% on average, while only doing so by 6% for stocks nearest a 52-week high.
Table 6 undertakes monthly cross-sectional Fama-MacBeth regressions to explore the relationship between price appreciation expectations and M ax in a multivariate setting. The first
two columns use price appreciation as the dependent variable, while the last two examine the
relationship between forecast errors and M ax. Brav, Lehavy, and Michaely (2005) find that
analyst price targets are affected by beta, size, book-to-market, and prior returns. I therefore
include all of these variables, as well as the dividend yield from the previous year as a proxy for
expected dividend yield.
Again, consistent with the univariate sort, the results support the hypothesis that nearness
to a 52-week high leads to lower expectations of price growth from analysts. The coefficients
of the control variables are also consistent with the results of Brav et al. (2005). The average
cross-sectional standard deviation of the M ax variable within this sample is 0.186; from column
2, this implies that a one-standard deviation increase in nearness to a 52-week high is associated
with a decrease in one-year forecasted price appreciation of 8.1% (0.186 x -0.437). The results
provide further evidence that nearness to a 52-week high induces expectational errors. Stocks
far from a 52-week high elicit overly optimistic expectations relative to stocks near a 52-week
high.
4.3 Robustness
The evidence thus far indicates that stock market participants anchor on the 52-week high
and as a result form biased expectations. An alternative interpretation is that nearness to a
52-week high appears to affect expectations because it is correlated with a notion of an overly
high valuation, but that the 52-week high itself is not actually an explicit anchor for market
participants. While the regressions do control for measures of valuation such as market-to-book,
I nevertheless explore this alternative hypothesis more robustly. To evaluate this alternative
14
explanation I examine the predictive ability of the 52-week high relative to other values that
also capture high valuations. I focus on the 13-week high, 26-week high, and 104-week high.
I first construct analogous versions of the M ax variable for the current price relative to the
13, 26, and 104-week high. I then examine the explanatory power of these alternative M ax
variables relative to the variable measured relative to the 52-week high. To do so, I run a horse
race for the four M ax variables to examine their ability to explain SUE, Price Appreciation, and
Forecast Error. Specifically, I examine the coefficients from regressions containing all four of
the M ax variables together, along with the full controls from the main regression specifications
(Table 3, Panel C, Column 5; Table 6, Column 2; and Table 6, Column 4). Figure 1 displays
the absolute value of the coefficient estimates from these three regressions. In order to make
the coefficients directly comparable across variables, all M ax variables are standardized to have
zero mean and unit variance. The version of the M ax variable defined relative to the 52-week
high clearly dominates the other frequencies. The results indicate that the effects observed are
specific to the 52-week high price in particular, and not other price values, consistent with the
52-week high serving as a specific price from which individuals form expectations.
In unreported analyses, I also examine whether the 52-week low has predictive ability. While
there is some evidence of predictive ability for the 52-week low, it is much weaker than the 52week high. There are many potential explanations for why the 52-week low is likely a far less
salient value than the 52-week high. For instance, since long positions are far more common
than short positions, if investors naturally care more about the upside potential of a stock
then they are more likely to focus on the 52-week high than the low. When assessing best or
worst case scenarios for future price movements, the 52-week high likely serves as a natural
“best-case scenario”, while a natural lower bound representing the worst-case scenario is likely
$0, rather than the 52-week low. Further insight regarding the relative salience of these two
values is gathered from a simple count of the relative occurrence in the Wall Street Journal’s
widely read “Abreast of the Market” column, which serves as a summary of the most recent day
of market activity.8 Utilizing online records for the column from the period 1984-2014, I find
that the phrase “52-week high” appears more than 1.5 times more often than “52-week low.”
8
See Tetlock (2007) and Dougal, Engelberg, Garcı́a, and Parsons (2012) for a more detailed discussion of the
influence of the “Abreast of the Market” column.
15
The discrepancy between the two becomes far more stark when examining the usage in more
relevant contexts; for example, searching for phrasing which captures distance from a 52-week
high or 52-week low results in the 52-week high occurring with 3.6 times more frequency than
the 52-week low.9
An extensive array of additional robustness tests is reported in the Appendix. The results
of the robustness tests are consistent with the main results of the paper. Appendix A displays
results using two alternative measures of SUE that use earnings volatility rather than stock
price as the scaling variable. Appendix B displays results using an alternative definition of
M ax that takes into account the price path of the stock. Specifically, the alternately defined
M ax variable distinguishes between cases in which a stock has seen large movements in price
over the prior 52-weeks and cases in which a stock has experienced very little price movement
over the past 52-weeks and therefore may mechanically be near a 52-week high. All of the main
results are robust to using these alternative definitions of SUE and to using the alternative
measure of M ax. The Appendix further discusses the alternative variable definitions and the
findings.
5. Underreaction to News
5.1 Calendar Portfolios
Having examined the predictive ability of nearness to a 52-week high for earnings surprises,
I next test H2. As a first step in exploring whether nearness to a 52-week high induces underreaction to news, I examine the returns to a calendar portfolio strategy in the post-announcement
period. I follow Jegadeesh and Titman (1993) and Fama (1998) and use a rolling portfolio
strategy to calculate abnormal returns. At the beginning of each month, stocks are sorted into
5 x 5 portfolios based on nearness to a 52-week high and their most recent earnings surprise
(conditional on the earnings surprise occurring in the last 3 months). The portfolios are then
held for 1, 2, or 3 months. The resulting returns can be interpreted as the returns to a strategy
that in any given month holds a portfolio of stocks selected at the beginning of the current
9
Specifically, phrases where “from” or “off” precedes 52-week high or 52-week low.
16
month as well as stocks chosen in the previous k − 1 months, where k is the holding period
(equal to either 1, 2, or 3).
The time-series of excess returns are regressed on the Fama and French (1993) factors in
order to calculate monthly alphas. The monthly alphas to an equal-weighted strategy are displayed in Table 7. Appendix C displays value-weighted results. The one, two and three month
strategies each tell the same story. For instance, the three month portfolio strategy in Panel C
shows that for the quintile of stocks experiencing the most positive surprises, stocks in the top
quintile of M ax outperform stocks in the bottom quintile of M ax by a statistically significant
128 basis points per month. This is consistent with stocks near a 52-week high underreacting
to good news. In the bottom quintile of SUE, stocks in the bottom M ax quintile underperform
stocks in the top M ax quintile by 81 basis points per month, consistent with stocks farther
from a 52-week high underreacting to negative news.
Within surprise quintiles, post-announcement alphas increase with nearness to a 52-week
high. That is, within each surprise quintile, stocks nearest to a 52-week high substantially
outperform stocks farthest from a 52-week high over the period subsequent to the earnings announcement. The difference in returns between the top and bottom quintile of stocks sorted on
nearness to a 52-week high is positive in each of the earnings surprise quintiles for each of the
one, two and three month strategies. These differences in returns are statistically significant in
13 of the 15 instances.
One can maximally exploit this underreaction via a strategy that takes a long position in
stocks near a 52-week high in the top surprise quintile and short stocks far from a 52-week
high in the lowest surprise quintile. This strategy proves quite profitable, providing an alpha of
nearly 150 basis points per month for the three month holding period sample. The magnitudes
are quite similar for the one and two month holding periods.
Additionally, one can form a portfolio that goes long in the positive surprise stocks farthest
from the maximum and short in the negative surprise stocks closest to their 52-week high that
actually earns a negative alpha. In other words, one can identify a portfolio of negative surprise
stocks that outperforms a portfolio of positive surprise stocks in the months after an earnings
announcement. In fact, for all holding periods statistically significant negative abnormal returns
17
accrue to positive surprise stocks that are farthest from a 52-week high, potentially consistent
with an initial overreaction to good news for those stocks farthest from a 52-week high. For the
two and three month holding period portfolios, the portfolio of negative surprise stocks closest
to a 52-week high outperforms positive surprise stocks farthest from the 52-week high by over
50 basis points, and this difference is statistically significant. The results support the hypothesis
that nearness to a 52-week high induces underreaction to news.
5.2 Double Sorts
The calendar portfolio results showing that stocks near a 52-week high have larger drift than
stocks far from a 52-week high are consistent with the hypothesis that nearness to a 52-week
high induces underreaction to news. Specifically, that stocks near a 52-week high underreact to
good news while stocks far from a 52-week high underreact to bad news. Before declaring the
case closed, however, there is a subtle concern that arises. Because nearness to a 52-week high
also predicts earnings surprises, it is possible that even within the surprise quintiles, sorting
by 52-week high is performing a further sort on surprise. For example, within the top surprise
quintile it is possible that those stocks nearest to the 52-week high have the most positive surprises. In this case, post-earnings announcement drift predicts that because these stocks have
the largest surprises they will have the largest drift. The concern is that the observed results
may be partly driven by the 52-week high serving as a second sort on earnings surprises, and not
fully by the 52-week high inducing underreaction to news. Fortunately for the underreaction
story, the magnitude of the differences in observed alphas in Table 7 between top and bottom
M ax portfolios within the same surprise quintile is too large to be purely driven by relatively
small within quintile differences in surprises, however, it nevertheless could be contributing to
part of the results. I investigate whether this is the case by calculating portfolio returns to
double-sorts on earnings surprises and M ax. This also allows for a further test of H2: underreaction to news should show up not just as larger post-event drift, but also as a smaller
announcement date return response.
To examine the post-earnings returns, I follow the earnings announcement literature and
focus on the 60 trading days after the announcement (Bernard and Thomas (1989), Livnat
18
and Mendenhall (2006), Hirshleifer, Lim, and Teoh (2009)).10 I define the post-announcement
period to start on day t + 2. The 60-day post-announcement CAR is defined as
CAR(2, 61)i,q =
t+61
Y
(1 + Ri,k ) −
k=t+2
t+61
Y
(1 + Rp,k )
k=t+2
where t is the announcement date of firm i’s earnings, Ri,k is the daily return of firm i, and
Rp,k is the daily return to the size-B/M matched portfolio. I use the Fama-French 25 size-B/M
portfolios as benchmark returns. Firms are matched based on their market capitalization as
of the end of June and book-to-market value at the end of the last calendar year, where book
equity is from the last fiscal year end in the previous calendar year and market capitalization
is from the end of December of the previous calendar year.
To examine the immediate response to the earnings announcement I focus on the t − 1 to
t + 1 window. Panel A of Table 8 shows results from 5x5 portfolio sorts on earnings surprise
and M ax. The table reports mean cumulative abnormal returns over t − 1, t + 1 and t + 2,
t + 61. Earnings surprises are also reported. Results from the top and bottom M ax quintile
are shown for each earnings surprise quintile.
The last three columns report the 60 day post-earnings announcement returns. Consistent
with the calendar portfolios, in each of the surprise quintiles the quintile nearest the 52-week
high realizes significantly larger returns in the post-event period than the quintile farthest from
the 52-week high. Within the highest earnings surprise quintile, stocks in the top quintile of
M ax outperform those in the bottom quintile of M ax by 3.29% over the 60 trading days following the announcement. In the bottom quintile of SUE, the spread between top and bottom
M ax quintiles is a statistically significant 1.47%.
The second three columns report the returns accruing over the (-1,1) window. The results
are again consistent with stocks near a 52-week high underreacting to good news. The top quintile sorted on M ax earns lower returns than the bottom quintile sorted on M ax in four of the
five surprise quintiles. For stocks experiencing the most positive surprises, those stocks nearest
the 52-week high see an immediate reaction that is 72 basis points lower than those stocks
10
All of the results also hold if I instead require that the window end at least two days prior to the next earnings
announcement.
19
farthest from the 52-week high. This pattern holds for all surprise quintiles, except the firms
experiencing the lowest surprises. The first three columns shed light on the anomalous (-1,1)
returns for the low surprise quintile. Within the lowest surprise quintile, there is still substantial heterogeneity in SUE, and indeed M ax does serve as a further sort on surprise within this
quintile. Within the lowest quintile, stocks farthest from the 52-week high do see substantially
more negative surprises than stocks nearest the 52-week high. This explains the (-1,1) returns
that appear to go the opposite direction as H2 predicts within the lowest surprise quintile it also potentially explains the post-event drift results that do go in the predicted direction.
Within the other surprise quintiles, the concern of further sorting on surprise through the M ax
sorts does not seem to be an issue as the difference in surprise between top and bottom M ax
quintiles is often economically small.
However, while not statistically significant, this difference is somewhat large economically
for the highest surprise quintile. The difference in surprise is not concerning for the (2,61)
window returns, as it would predict the opposite result, however, it could potentially explain
part of the (-1,1) window difference that we see. To further rule out this possiblity, I sort
surprises even more finely with the hope that finer sorts will leave little within bucket variation
in surprises that can be identified by M ax. To this end, Panel B reports results for surprise
sorted by decile.
As the first columns of Panel B show, sorting surprises into deciles eliminates the concern of
M ax serving as a further sort on surprise for all deciles except the lowest surprise decile. It is
still the case that within the low surprise decile there is substantial variation in surprises, and
sorting on M ax does indeed capture this. The remainder of the rows however show economically tiny differences in surprises between top and bottom M ax quintiles. As before, the results
suggest that high M ax stocks underreact to positive news, and low M ax stocks underreact to
negative news. In the top surprise decile there is virtually no difference in surprise for the top
and bottom M ax quintile, however the bottom M ax quintile sees a three-day announcement
reaction that is nearly 86 basis points larger than stocks in the top quintile of M ax. This initial
underreaction to the good earnings news by stocks in the top M ax quintile is followed by a
post-announcement drift for these stocks that is 4.47% larger than that for stocks in the bottom
20
M ax quintile. As a whole, the results strongly support the hypothesis that nearness to a max
induces underreaction to news. Specifically, stocks trading near a high underreact to positive
news, while stocks trading far from a high underreact to negative news.
5.3 Robustness: Momentum and the Disposition Effect
I next address alternative explanations for the observed relationship between nearness to
the 52-week high and the post-announcement underreaction to news. There are two alternative
variables that are likely to be correlated with nearness to the 52-week high. The first variable
that I focus on is momentum. Momentum predicts that within surprise quintiles, those stocks
with the largest past returns will have the largest future returns.
The second alternative explanation focuses on the disposition effect. Grinblatt and Han
(2005) propose a theory in which the disposition effect induces underreaction to news. Frazzini
(2006) examines this hypothesis in the context of post-earnings announcement drift and documents evidence consistent with the hypothesis that selling pressure for positive surprise stocks
by disposition investors seeking to lock in a gain will hinder the incorporation of the good news.
Conversely, for negative surprises, disposition investors who are reluctant to realize a loss will
be less likely to sell. This restriction of supply will hinder the incorporation of negative news,
resulting in low future returns as the information is gradually incorporated into the stock’s
price. Therefore, the disposition effect predicts that within surprise quintiles, those stocks with
the largest capital gains will underreact the most to positive surprises, while those with capital
losses will underreact the most to negative surprises.11
To identify the effect of momentum I calculate M omentum as the return from month t − 12
to t − 1. To identify the effect of the disposition effect, I calculate the Grinblatt Han (2005)
measure of capital gains as Gaint =
Rt =
60
X
n=1
Vt−n
n−1
Y
Pt−1 −Rt−1
.
Pt−1
Where
!
[1 − Vt−n+τ ] Pt−n .
τ =1
11
Note that the disposition effect does not make the prediction that earnings surprises themselves are predictable. Therefore, the ability of nearness to a 52-week high to predict subsequent surprises as documented in
the first part of the analysis, is consistent only with the anchoring story and not with a disposition effect-based
explanation.
21
Vt is the stock’s turnover ratio at time t, and n is measured in months. The weight on Pt−n
represents the probability that a stock purchased at time t − n has not been sold by time t. The
reference price thus represents an estimate of investors’ aggregate cost basis for the stock.12
To pinpoint the driver of post-announcement underreaction, I regress benchmark-adjusted
returns on M ax as well as M omentum and Gain and a host of controls, discussed below. Table
9 displays the results to the portfolio regressions that are run separately for each SU E quintile.
In the first five columns of Panel A I display results from univariate regressions of CAR(2,61)
on Gain, with a separate regression run for each surprise quintile. The next five columns of
Panel A repeat the same univariate analysis for the M omentum variable. The univariate results
indicate that each has explanatory power in predicting post-announcement returns, especially
amongst stocks with larger earnings surprises. In the first five columns of the bottom half of
Panel A I repeat the analysis with M ax. Consistent with the earlier results, M ax is a strong
predictor of post-announcement drift.
Each of the univariate regressions documents the relationship between post-earnings announcement drift and the predictive variable in the absence of additional controls or fixed
effects. In the final five columns of the bottom half of Panel A I include all three variables
together, M ax, M omentum, and Gain, as well as controls for the number of other earnings
announcements occurring on the same day, number of analysts, reporting lag, average monthly
stock turnover, market cap, book-to-market, earnings persistence, and earnings volatility, along
with year, month, day-of-week, and industry fixed effects. The results show that neither Gain
nor M omentum predict returns with the correct sign after M ax is included. Table 8 showed
that the results to the lowest surprise quintile are not informative regarding underreaction to
news, as they will be biased by the fact that M ax proxies for surprise within this quintile;
however, after including the controls, M ax as well as Gain and M omentum fail to explain
returns in this quintile, so the bias becomes immaterial. The sign of the coefficient on M ax is
however correct in the other four earnings surprise quintiles and is significant at the 5% level
in all four of these quintiles. The inclusion of these additional controls does little to affect
12
All prices used in the reference price calculation are corrected for splits.
22
the statistical or economic significance of M ax in predicting post-announcement returns, while
Gain and M omentum no longer predict returns in the correct direction.
In Panel B of Table 9 I repeat the regression analysis for the immediate reaction (CAR
(-1,1)). Consistent with the results in Panel A, M ax continues to predict underreaction in the
expected direction for all but the lowest quintile of surpsises, even in the presence of controls
and variables to capture momentum and the disposition effect. While not reported, the results from regressions within SUE deciles rather than quintiles are qualitatively similar. For
all but the most negative surprise stocks, the results are again consistent with the hypothesis
that nearness to a 52-week high induces underreaction to news, and importantly that the underreaction due to the 52-week high can not be explained by momentum or the disposition effect.
6. Conclusion
This research utilizes the 52-week high to shed light on the role of psychological price barriers in financial markets. The 52-week high serves as a salient reference price for investors, and
importantly is a reference price which is common across investors. Recent work has shown that
the 52-week high affects financial choices ranging from investor portfolio decisions (Heath, Huddart, and Lang (1999); Poteshman and Serbin (2003)) to offer prices in mergers (Baker, Pan,
and Wurgler (2012)). This paper adds to this recent line of literature by providing evidence
that the 52-week high serves as a psychological price barrier that induces expectational errors
and induces underreaction to news.
The evidence provided supports the hypothesis that nearness to a 52-week high induces
expectational errors. Stocks trading near a 52-week high see systematically positive earnings
surprises, while those trading far from a 52-week high experience systematically negative earnings surprises. Analyst price target forecasts also indicate that expected price appreciation is
substantially lower for stocks near a 52-week high than for stocks far from a 52-week high. The
evidence is consistent with the view that investors perceive stocks near a 52-week high to be
unlikely to appreciate in price and those far from a 52-week high to be unlikely to fall in price.
Further, the evidence here sheds light on the precise mechanism through which the 52-week
23
high influences investor actions, and casts doubt on the previously proposed mechanism offered
in the literature. While the previous literature highlights prospect theory as the mechanism
through which the 52-week high influences investors, the evidence presented here offers a more
intuitive explanation: the 52-week high can influence investors through its effect on beliefs.
Further, the behavior of prices around earnings announcements supports the hypothesis that
nearness to a 52-week high induces underreaction to news. Stocks near a 52-week high initially
underreact to positive surprises and then, consistent with an initial underreaction, experience
larger than average post-earnings announcement drift. This evidence is consistent with investors
being hesitant to push the price higher for a stock near a 52-week high, even in the face of good
news.
24
Appendix
A. Alternative SUE Measures
Appendix A examines whether the main results hold when using alternative measures of analyst earnings surprise. Tables A1 and A2 examine whether the results are robust to definining
SUE for firm i in quarter q as
EP Si,q −F orecasti,q
,
σ
where σ is earnings volatility, defined as the volatility of deviations of quarterly earnings from
one-year-ago earnings over the past four years. Tables A3 and A4 examine whether the results
are robust to defining SUE for firm i in quarter q as
EP Si,q −EP Si,q−4
.
σ
Tables A1 and A3 replicate the SUE predictability regressions of Table 4 Panel C using the
alternative measures. Tables A2 and A4 replicate the post-earnings announcement drift regressions of Table 9 using the alternative measures. In all cases the main results hold for the
alternative measures of SUE.
25
EP S
−F orecasti,q
i,q
Table A1: SUE defined as
σ
Earnings Surprise Regressions
This table displays regression results from a regression of SU Et on M ax, SU Et−1 , momentum, and the control variables
from Table 1. The regressions are the same as Panel C of Table 4 except that SU Et is now defined as
EP Si,q −F orecasti,q
σ
.
Year, month, day of week, and industry fixed effects are included in all regressions. Heteroskedastic standard errors
clustered by day of announcement are in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% level,
respectively.
Dependent Variable: SUEt
1
2
3
Max
2.238*** 0.879*** 1.031***
(0.073)
(0.083)
(0.099)
SUE (t-1)
0.265*** 0.263***
(0.010)
(0.010)
Momentum
0.347*** 0.281***
(0.031)
(0.032)
Controls
N
N
Y
FE
R2
N
Y
0.0109
197,319
26
Y
0.0885
161,110
Y
0.08937
160,919
EP S
−F orecasti,q
i,q
Table A2: SUE defined as
σ
Horse Race by SUE Quintile
This table reports results from regressions of characteristic-adjusted cumulative abnormal returns on predictive variables.
The regressions are the same as in Table 9 except that SU Et is now defined as
EP Si,q −F orecasti,q
σ
. Regressions are
run separately by earnings surprise quintile. Panel A reports results for univariate regressions of CAR (2,61) on M ax,
Gain, or M omentum, as well multivariate regressions that also control for # earnings announcements on the same
day, # analysts, reporting lag, average monthly share turnover, log market cap, book-to-market, earnings persistence,
and earnings volatility. Year, month, day of week, and industry fixed effects are included where denoted. Panel B
reports results for regressions where the dependent variable is CAR(-1,1).
Heteroskedastic standard errors clustered
by the day of announcement are in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively.
Panel A: Dependent Variable: CAR (2,61)
1
2
3
4
Max
-1.327
2.575**
1.039
3.983***
(1.180)
(1.053)
(1.115)
(1.138)
Gain
-0.973** -1.331*** -1.228*** -2.484***
(0.417)
(0.369)
(0.378)
(0.429)
Momentum
0.422
-0.930***
-0.446
0.2
(0.401)
(0.361)
(0.337)
(0.355)
Controls
Y
Y
Y
Y
FE
Y
Y
Y
Y
R2
0.02958
0.02546
0.01577
0.01421
N
32,595
33,773
31,672
32,671
Max
Gain
Momentum
Controls
FE
R2
N
Panel B: Dependent Variable: CAR (-1,1)
1
2
3
4
1.953***
-0.962** -2.039*** -2.281***
(0.460)
(0.424)
(0.436)
(0.460)
-0.245
0.137
-0.427*** -0.968***
(0.157)
(0.143)
(0.153)
(0.170)
-0.835*** -0.569*** -0.343**
0.154
(0.161)
(0.148)
(0.135)
(0.132)
Y
Y
Y
Y
Y
Y
Y
Y
0.045
0.01897
0.01602
0.02201
32,595
33,773
31,672
32,671
27
5
2.746**
(1.156)
-1.091**
(0.529)
0.640*
(0.331)
Y
Y
0.01736
32,649
5
-2.704***
(0.479)
-0.534***
(0.195)
0.278**
(0.126)
Y
Y
0.0411
32,649
EP S
−EP Si,q−4
i,q
Table A3: SUE defined as
σ
Earnings Surprise Regressions
This table displays regression results from a regression of SU Et on M ax, SU Et−1 , momentum, and the control variables
from Table 1. The regressions are the same as Panel C of Table 4 except that SU Et is now defined as
EP Si,q −EP Si,q−4
.
σ
Year, month, day of week, and industry fixed effects are included in all regressions. Heteroskedastic standard errors
clustered by day of announcement are in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% level,
respectively.
Dependent Variable: SUEt
1
2
3
Max
3.509*** 1.339*** 1.374***
(0.050)
(0.040)
(0.047)
SUE (t-1)
0.546*** 0.539***
(0.006)
(0.006)
Momentum
0.325*** 0.297***
(0.015)
(0.015)
Controls
N
N
Y
FE
R2
N
Y
0.093
169,246
28
Y
0.406
131,077
Y
0.407
130,958
EP S
−EP Si,q−4
i,q
Table A4: SUE defined as
σ
Horse Race by SUE Quintile
This table reports results from regressions of characteristic-adjusted cumulative abnormal returns on predictive variables.
The regressions are the same as in Table 9 except that SU Et is now defined as
EP Si,q −EP Si,q−4
.Regressions
σ
are run
separately by earnings surprise quintile. Panel A reports results for univariate regressions of CAR (2,61) on M ax, Gain,
or M omentum, as well multivariate regressions that also control for # analysts, reporting lag, average monthly share
turnover, log market cap, book-to-market, earnings persistence, and earnings volatility. Year, month, day of week, and
industry fixed effects are included where denoted. Panel B reports results for regressions where the dependent variable
is CAR(-1,1). Heteroskedastic standard errors clustered by the day of announcement are in parentheses. ***, **, and *
denote significance at the 1%, 5%, and 10% level, respectively.
Panel A: Dependent Variable: CAR (2,61)
1
2
3
4
Max
-3.173**
-0.766
1.929
6.656***
(1.265)
(1.193)
(1.266)
(1.266)
Gain
-1.398*** -0.549 -1.494*** -2.929***
(0.422)
(0.370)
(0.441)
(0.521)
Momentum
0.596
-0.765*
0.136
-0.912**
(0.546)
(0.428)
(0.415)
(0.384)
Controls
Y
Y
Y
Y
FE
Y
Y
Y
Y
R2
0.023
0.023
0.020
0.021
N
28,210
28,307
28,279
28,285
Max
Gain
Momentum
Controls
FE
R2
N
Panel B: Dependent Variable: CAR (-1,1)
1
2
3
4
-0.297
-1.008
-2.063*** -2.596***
(0.481)
-(2.010)
(0.510)
(0.580)
0.027
-0.228
-0.438** -0.710***
(0.158)
(0.146)
(0.172)
(0.218)
-0.609*** -0.642*** -0.495*** -0.453***
(0.212)
(0.202)
(0.166)
(0.149)
Y
Y
Y
Y
Y
Y
Y
Y
0.016
0.011
0.013
0.020
28,210
28,307
28,279
28,285
29
5
3.723***
(1.356)
-0.95
(0.590)
0.205
(0.343)
Y
Y
0.017
28,245
5
-2.025***
(0.592)
-0.35
(0.238)
0.171
(0.139)
Y
Y
0.020
28,245
B. Alternative M ax Definition
Appendix B examines whether the main results are robust to an alternative definition of
M ax that takes into account the price path process of the stock. M axi,t is defined as
M axi,t =
Highi,t−1 −P ricei,t−1
Highi,t−1 −Lowi,t−1 ,
where Highi,t−1 (Lowi,t−1 ) is the highest (lowest) price of stock i in the 12 month period ending
at the end of month t-1. Defining the variable in this way distinguishes between stocks that
have seen large price movements over the year and are now close to the 52-week high and stocks
that may be near the 52-week high simply because the stock has seen very little price movement
over the past year. Using this alternative definition of M ax, low values of M ax correspond to
stocks near a 52-week high. As a result, coefficients on M ax are expected to take the opposite
sign as in the main regressions.
Table B1 replicates Table 4 Panel C using the new measure of M ax. Consistent with the
earlier results, stocks nearest a M ax see the largest earnings surprises. Table B2 replicates
the price target regressions of Table 6 using the new M ax variable. Consistent with Table 6,
stocks nearest the 52-week high have the lowest price appreciation forecasts and have the most
negative forecast errors. Table B3 replicates Table 9 using the new M ax variable. Consistent
with Table 9, stocks nearest the 52-week high see the greatest underreaction to positive earnings
news. In all cases the main results are robust to the use of the alternative measure of M ax.
30
High
−P rice
i,t−1
Table B1: Max defined as Highi,t−1
i,t−1 −Lowi,t−1
Earnings Surprise Regressions
This table displays regression results from a regression of SU Et on M ax, SU Et−1 , momentum, and the control variables
from Table 1. The regressions are the same as Panel C of Table 4 except that M ax is now defined as
Highi,t−1 −P ricei,t−1
.
Highi,t−1 −Lowi,t−1
Year, month, day of week, and industry fixed effects are included in all regressions. Heteroskedastic standard errors
clustered by day of announcement are in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% level,
respectively.
Dependent Variable: SUEt
1
2
Max
-0.368*** -0.243***
(0.008)
(0.009)
SUE (t-1)
0.198***
(0.006)
Momentum
0.033***
(0.004)
Controls
N
N
FE
R2
N
Y
0.040
221,350
Y
0.074
185,557
31
3
-0.200***
(0.009)
0.193***
(0.007)
0.044***
(0.005)
Y
Y
0.080
170,007
High
−P rice
i,t−1
Table B2: Max defined as Highi,t−1
i,t−1 −Lowi,t−1
Price Appreciation Expectations by Nearness to 52-Week High
This table presents the results of Fama-MacBeth monthly cross-sectional regressions. The regressions are the same as in
Table 6 except that M ax is now defined as
Highi,t−1 −P ricei,t−1
.
Highi,t−1 −Lowi,t−1
In columns 1 and 2, the dependent variable is analyst
price appreciation expectation. Price appreciation is defined as the 12-month horizon analyst target-price forecast minus
the stock price on the day prior to the forecast, all divided by the price on the day prior to forecast. In columns 3 and
4 the dependent variable is forecast error. Forecast error is the difference between expected price appreciation and true
ex-post stock price appreciation. Price appreciation and forecast error reflect the average values for a stock in a given
month. Momentum is the past 12 month return. Beta is calculated using the past 60 months of data, with a minimum of
24 months of data required for calculation. Dividend yield is the annual dividend yield in year t − 1. Standard errors are
Newey-West adjusted with 11 lags. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively.
Dependent Variable:
Max
Momentum
Beta
B/M
log(mkt cap)
Div Yield
N (months)
Avg N per month
Avg R2
Price Appreciation
1
2
0.275*** 0.180***
(0.041)
(0.022)
0.009**
(0.005)
0.045***
(0.008)
-0.026***
(0.007)
-0.039***
(0.003)
-2.404***
(0.137)
165
165
1,620
1,515
0.069
0.181
32
Forecast Error
3
4
0.272*** 0.254***
(0.072)
(0.035)
0.052***
(0.019)
0.045879
(0.028)
-0.040***
(0.011)
-0.024***
(0.005)
-1.017***
(0.337)
165
165
1,502
1,409
0.051
0.118
High
−P rice
i,t−1
Table B3: Max defined as Highi,t−1
i,t−1 −Lowi,t−1
Horse Race by SUE Quintile
This table reports results from regressions of characteristic-adjusted cumulative abnormal returns on predictive variables.
Regressions are run separately by earnings surprise quintile. Panel A reports results for univariate regressions of CAR
(2,61) on M ax, Gain, or M omentum, as well multivariate regressions that also control for # earnings announcements
on the same day, # analysts, reporting lag, average monthly share turnover, log market cap, book-to-market, earnings
persistence, and earnings volatility. Year, month, day of week, and industry fixed effects are included where denoted. Panel
B reports results for regressions where the dependent variable is CAR(-1,1). Heteroskedastic standard errors clustered
by the day of announcement are in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively.
Max
Gain
Momentum
Controls
FE
R2
N
Panel A: Dependent Variable: CAR (2,61)
1
2
3
4
-0.258
-1.119** -1.433*** -2.027***
(0.493)
(0.432)
(0.448)
(0.450)
-1.424*** -1.496*** -1.064**
-0.745*
(0.348)
(0.438)
(0.524)
(0.441)
-0.230
-0.44325
-0.11924
-0.50091
(0.404)
(0.394)
(0.425)
(0.351)
Y
Y
Y
Y
Y
Y
Y
Y
0.030
0.023
0.017
0.016
32,386
33,862
31,845
32,770
Panel B: Dependent Variable: CAR (-1,1)
1
2
3
4
Max
-0.147
0.495*** 0.963*** 0.897***
(0.191)
(0.172)
(0.173)
(0.180)
Gain
-0.145
-0.344**
0.444**
0.789***
(0.125)
(0.170)
(0.204)
(0.161)
Momentum -0.542*** -0.697*** -0.576*** -0.339**
(0.163)
(0.168)
(0.153)
(0.141)
Controls
Y
Y
Y
Y
FE
Y
Y
Y
Y
R2
0.037
0.024
0.014
0.020
N
32,386
33,862
31,845
32,770
33
5
-2.671***
(0.473)
-0.54698
(0.346)
-0.14613
(0.317)
Y
Y
0.015
32,515
5
0.471**
(0.186)
-0.282**
(0.137)
0.336***
(0.130)
Y
Y
0.034
32,515
C. Post-Earnings Announcement Drift: Value-Weighted Calendar Portfolios
Table C1
Post-Earnings Announcement Drift Calendar Portfolios: Value-Weighted
This table reports Fama-French alphas of value-weighted post-earnings announcement drift portfolios. At the beginning of
each month stocks are sorted into 5 x 5 portfolios based on their most recent earnings surprise (conditional on the earnings
surprise occurring in the last 3 months) and nearness to the 52-week high as of the end of the last month. Portfolios are
held for 1, 2, or 3 months. The resulting returns can be interpreted as the return to a strategy that in any given month
holds a portfolio of stocks selected at the beginning of the current month as well as stocks chosen in the previous k − 1
months, where k is the holding period (equal to either 1, 2, or 3). Alphas are in monthly percent. Panels A, B, and C
display calendar returns to 1, 2, and 3 month strategies, respectively. Standard errors are in parentheses. ***, **, and *
denote significance at the 1%, 5%, and 10% level, respectively.
Max
1
2
3
4
5
(5-1)
1
-1.052
(0.302)
-0.400
(0.188)
-0.006
(0.173)
0.150
(0.172)
-0.044
(0.193)
1.008***
(0.358)
Panel A: 1 Month Strategy
SUE Quintile
2
3
4
-0.377
-0.314
-0.279
(0.272) (0.301) (0.312)
0.094
0.019
0.192
(0.175) (0.195) (0.205)
-0.067
0.073
0.332
(0.130) (0.139) (0.147)
-0.092
0.165
0.148
(0.114) (0.103) (0.139)
-0.306
-0.028
0.232
(0.122) (0.134) (0.131)
0.071
0.286
0.511
(0.298) (0.330) (0.338)
34
5
-0.685
(0.304)
-0.054
(0.194)
0.158
(0.157)
0.365
(0.143)
0.072
(0.163)
0.757**
(0.345)
Table C1 (Continued)
Max
1
2
3
4
5
Max
1
2
3
4
5
1
-1.071
(0.296)
-0.402
(0.183)
-0.129
(0.152)
0.241
(0.143)
0.155
(0.172)
1.226***
(0.342)
Panel B: 2 Month Strategy
SUE Quintile
2
3
4
-0.525
-0.494
-0.323
(0.256) (0.284) (0.303)
-0.087
-0.004
0.126
(0.156) (0.177) (0.196)
-0.004
0.169
0.285
(0.118) (0.117) (0.122)
-0.071
0.116
0.162
(0.096) (0.084) (0.109)
-0.225
0.096
0.241
(0.105) (0.122) (0.125)
0.300
0.590*
0.564*
(0.277) (0.309) (0.328)
5
-0.851
(0.281)
-0.080
(0.168)
-0.090
(0.132)
0.174
(0.122)
0.150
(0.145)
1.001***
(0.316)
1
-1.061
(0.291)
-0.393
(0.176)
-0.190
(0.140)
0.296
(0.126)
0.060
(0.157)
1.121***
(0.331)
Panel C: 3 Month Strategy
SUE Quintile
2
3
4
-0.519
-0.581
-0.256
(0.249) (0.274) (0.300)
-0.070
-0.155
0.064
(0.148) (0.168) (0.182)
-0.036
0.157
0.237
(0.108) (0.107) (0.111)
-0.023
0.105
0.151
(0.093) (0.076) (0.095)
-0.255
0.186
0.233
(0.100) (0.116) (0.118)
0.264 0.767*** 0.489
(0.268) (0.298) (0.323)
5
-0.742
(0.273)
-0.175
(0.162)
-0.163
(0.121)
0.124
(0.108)
0.067
(0.136)
0.809***
(0.305)
35
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38
Figure 1: Coefficients for Various Weekly Highs
This figure displays absolute values of coefficient estimates from regressions of the dependent
variable (SUE, Price Appreciation, or Forecast Error) on four M ax variables defined relative
to the noted weekly highs. The regressions include all controls and fixed effects from the main
specifications (specifically, Table 3, Panel C, Column 5; Table 6, Column 2; and Table 6,
Column 4). In order to make the coefficients directly comparable across variables, all M ax
variables are standardized to have zero mean and unit variance.
39
40
Max
Decile
1
2
3
4
5
6
7
8
9
10
Max
0.462
0.622
0.707
0.768
0.815
0.854
0.889
0.921
0.953
0.987
# Analysts
4.856
4.720
4.828
4.901
4.886
4.969
5.029
5.013
5.092
4.932
Report
Lag
31.652
30.714
29.878
28.963
28.503
28.060
27.657
27.434
27.139
27.609
Turnover
0.249
0.182
0.157
0.139
0.129
0.121
0.116
0.114
0.113
0.122
log(mkt cap)
19.393
19.769
20.053
20.270
20.443
20.599
20.739
20.822
20.926
20.813
the volatility of deviations of quarterly earnings from one-year-ago earnings over the past four years.
B/M
0.536
0.604
0.636
0.646
0.655
0.660
0.654
0.650
0.662
0.670
Earnings
Persistence
0.317
0.309
0.310
0.315
0.315
0.323
0.326
0.330
0.326
0.338
Earnings
Volatility
1.331
0.925
0.755
0.631
0.614
0.535
0.475
0.469
0.433
0.444
N
22,081
22,144
22,153
22,142
22,127
22,170
22,141
22,152
21,904
22,336
market value is as of December of the last calendar year. Earnings persistence is the first-order autocorrelation of quarterly earnings over the past four years. Earnings volatility is
stock turnover over the previous 12 months. Market cap is defined as of the end of month t − 1. B/M is book equity from the last fiscal year end in the previous calendar year and
analyst estimates used to create the median forecast. Reporting lag is the number of days between quarter end and announcement of earnings. Turnover is the average monthly
M ax is defined as the ratio of the stock price at the end month t − 1 to the maximum stock price in the 12 months ending in month t − 1. # analysts is equal to the number of
This table gives summary statistics for 52-week high deciles for stocks. Each quarter stocks announcing earnings are sorted into deciles based on nearness to their 52-week high.
Table 1
Summary Stats
Table 2
Earnings Surprises by Nearness to 52-Week High
This table shows earnings surprises as defined by SUE and CAR(-1,1) sorted by M ax decile. M ax is defined as the ratio
of the stock price at the end month t − 1 to the maximum stock price in the 12 months ending in month t − 1. Earnings
surprise and CAR are in percent. Standard errors are in parentheses. ***, **, and * denote significance at the 1%, 5%,
and 10% level, respectively.
Max Decile
1
2
3
4
5
6
7
8
9
10
(10-1)
SUE (%)
-0.73
-0.30
-0.11
-0.23
-0.01
0.02
0.05
0.03
0.18
0.08
0.81***
(0.05)
41
CAR(-1,1)
-0.46
-0.09
0.14
0.15
0.31
0.19
0.28
0.22
0.23
0.35
0.80***
(0.12)
N
22,081
22,144
22,153
22,142
22,127
22,170
22,141
22,152
21,904
22,336
42
Classified By
Max
Winner
Loser
Winner-Loser
Winner
Loser
Winner-Loser
Winner
Loser
Winner-Loser
Classified By
Momentum
Winner
Loser
Winner-Loser
Winner
Loser
Winner-Loser
Winner
Loser
Winner-Loser
Classified By
Momentum
Loser
Middle
Winner
Classified By
Max
Loser
Middle
Winner
Sue (%)
0.02
-0.46
0.47***
(0.05)
0.09
-0.07
0.16***
(0.02)
0.08
0.03
0.05**
(0.02)
Sue (%)
0.03
-0.46
0.48***
(0.04)
0.11
-0.48
0.59*
(0.34)
0.08
0.02
0.06**
(0.03)
Panel B
CAR
Classified By
(-1,1)
Max
-0.11
Loser
-0.10
-0.01
(0.14)
0.32
Middle
0.11
0.21***
(0.08)
0.31
Winner
0.16
0.16
(0.11)
Panel A
CAR
Classified By
(-1,1)
Earnings
0.16
Loser
-0.10
0.26**
(0.11)
0.19
Middle
0.02
0.17*
(0.10)
0.31
Winner
-0.11
0.43***
(0.14)
Winner
Loser
Winner-Loser
Winner
Loser
Winner-Loser
Classified By
Earnings
Winner
Loser
Winner-Loser
Winner
Loser
Winner-Loser
Winner
Loser
Winner-Loser
Classified By
Max
Winner
Loser
Winner-Loser
of announcement are in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively.
Sue (%)
-0.14
-0.60
0.46***
(0.06)
0.12
-0.13
0.25***
(0.03)
0.16
0.03
0.13**
(0.05)
Sue (%)
0.03
-0.60
0.63***
(0.06)
0.03
-0.33
0.36
(0.24)
0.16
-0.14
0.31***
(0.05)
CAR
(-1,1)
-0.22
-0.12
-0.11
(0.10)
0.30
0.14
0.16**
(0.08)
0.29
0.19
0.11
(0.07)
CAR
(-1,1)
0.19
-0.12
0.30***
(0.08)
0.24
0.11
0.13
(0.10)
0.29
-0.22
0.52***
(0.10)
ratio, and the control variables from Table 1. Year, month, day of week, and industry fixed effects are included in all regressions. Heteroskedastic standard errors clustered by day
month t − 12 to t − 1. Earnings surprise and returns are in percent. Panel C displays regression results from a regression of SU Et on M ax, SU Et−1 , momentum, price dividend
This table shows earnings surprises based on double sorts. The variables used to sort are M ax, SU Et−1 , and price momentum. Price momentum is defined as the return from
Table 3
Earnings Surprise Double Sorts
43
Controls
FE
R2
N
Momentum
SUEt−1
Max
Panel C
Dependent Variable: SUEt
1
2
3
4
0.736***
0.515***
0.019
0.020
0.218***
0.194***
0.006
0.006
0.161*** 0.033***
0.005
0.004
N
N
N
N
Y
Y
Y
Y
0.042
0.062
0.032
0.076
221,350
185,572
221,350
185,557
Table 3 (Continued)
5
0.482***
0.022
0.189***
0.006
0.037***
0.005
Y
Y
0.082
170,007
Table 4
Surprise Alphas
This table reports daily Carhart four-factor alphas of surprise portfolios. On each day, stocks within a three day window of
an earnings announcement (-1,1) are ranked by nearness to a 52-week high as of the end of the previous month. Alphas are
reported for a strategy that buys stocks closest to the 52-week high and sells stocks farthest from the 52-week high. Daily
alphas are calculated from a time-series regression of daily returns on the daily Fama-French three factors and the Carhart
momentum factor. Alphas are in daily percent. Standard errors are in parentheses. ***, **, and * denote significance at
the 1%, 5%, and 10% level, respectively.
Max
1
2
3
4
5
6
7
8
9
10
(10-1)
Alpha (%)
-0.112
-0.007
0.049
0.049
0.075
0.079
0.102
0.142
0.068
0.116
0.228***
(0.045)
44
Raw (%)
-0.087
0.025
0.090
0.093
0.120
0.127
0.151
0.189
0.118
0.162
0.249***
(0.048)
Table 5
Price Appreciation Expectations by Nearness to 52-Week High
This table shows analyst price appreciation expectations sorted by M ax decile. Each month stocks are sorted into deciles
by M ax. Price appreciation is defined as the 12 month horizon analyst target price forecast minus the stock price on the
day prior to the forecast, all divided by the price on the day prior to forecast. Forecast error is the difference between
expected price appreciation and true ex-post stock price appreciation. M ax is defined as the ratio of the stock price at the
end month t − 1 to the maximum stock price in the 12 months ending in month t − 1. ***, **, and * denote significance
at the 1%, 5%, and 10% level, respectively.
Max Decile
1
2
3
4
5
6
7
8
9
10
(10-1)
Price Appreciation
0.486
0.384
0.326
0.276
0.238
0.215
0.195
0.175
0.161
0.157
-0.329***
(0.004)
45
Forecast Error
0.386
0.295
0.237
0.176
0.137
0.112
0.095
0.076
0.064
0.061
-0.325***
(0.006)
Table 6
Price Appreciation Expectations by Nearness to 52-Week High
This table presents the results of Fama-MacBeth monthly cross-sectional regressions. In columns 1 and 2, the dependent
variable is analyst price appreciation expectation.
Price appreciation is defined as the 12-month horizon analyst
target-price forecast minus the stock price on the day prior to the forecast, all divided by the price on the day prior to
forecast. In columns 3 and 4 the dependent variable is forecast error. Forecast error is the difference between expected
price appreciation and true ex-post stock price appreciation. Price appreciation and forecast error reflect the average
values for a stock in a given month. M ax is defined as the ratio of the stock price at the end month t − 1 to the maximum
stock price in the 12 months ending in month t − 1. Momentum is the past 12 month return. Beta is calculated using
the past 60 months of data, with a minimum of 24 months of data required for calculation. Dividend yield is the annual
dividend yield in year t − 1. Standard errors are Newey-West adjusted with 11 lags. ***, **, and * denote significance at
the 1%, 5%, and 10% level, respectively.
Dependent Variable:
Max
Momentum
Beta
B/M
log(mkt cap)
Div Yield
N (months)
Avg N per month
Avg R2
Price Appreciation
1
2
-0.571*** -0.437***
(0.048)
(0.034)
0.037***
(0.006)
0.023***
(0.006)
-0.027***
(0.007)
-0.032***
(0.002)
-2.037***
(0.125)
165
165
1,620
1,515
0.128
0.197
46
Forecast Error
3
4
-0.603*** -0.534***
(0.122)
(0.050)
0.056**
(0.022)
0.024
(0.024)
-0.039***
(0.010)
-0.018***
(0.005)
-0.533
(0.350)
165
165
1,502
1,409
0.083
0.127
Table 7
Post-Earnings Announcement Drift Calendar Portfolios
This table reports Fama-French alphas of post-earnings announcement drift portfolios. At the beginning of each month
stocks are sorted into 5 x 5 portfolios based on their most recent earnings surprise (conditional on the earnings surprise
occurring in the last 3 months) and nearness to the 52-week high as of the end of the last month. Portfolios are held for
1, 2, or 3 months. The resulting returns can be interpreted as the return to a strategy that in any given month holds a
portfolio of stocks selected at the beginning of the current month as well as stocks chosen in the previous k − 1 months,
where k is the holding period (equal to either 1, 2, or 3). Alphas are in monthly percent. Panels A, B, and C display
calendar returns to 1, 2, and 3 month strategies, respectively. Standard errors are in parentheses. ***, **, and * denote
significance at the 1%, 5%, and 10% level, respectively.
Max
1
2
3
4
5
(5-1)
1
-0.872
(0.208)
-0.614
(0.124)
-0.481
(0.101)
-0.294
(0.124)
-0.315
(0.151)
0.557**
(0.271)
Panel A: 1 Month Strategy
SUE Quintile
2
3
4
-0.519
-0.629
-0.328
(0.224) (0.246)
(0.239)
-0.468
-0.279
0.132
(0.130) (0.147)
(0.139)
-0.253
0.016
0.497
(0.096) (0.106)
(0.110)
-0.145
0.103
0.366
(0.089) (0.091)
(0.099)
-0.402
-0.043
0.163
(0.120) (0.118)
(0.121)
0.117 0.586*** 0.491**
(1.026) (0.202)
(0.246)
47
5
-0.351
(0.227)
0.214
(0.131)
0.588
(0.115)
0.905
(0.110)
0.789
(0.128)
1.140***
(0.112)
Table 7 (Continued)
Max
1
2
3
4
5
(5-1)
Max
1
2
3
4
5
(5-1)
1
-0.859
(0.204)
-0.541
(0.116)
-0.319
(0.085)
-0.139
(0.106)
-0.108
(0.146)
0.751***
(0.251)
Panel B: 2 Month Strategy
SUE Quintile
2
3
4
-0.614
-0.779
-0.485
(0.214)
(0.239)
(0.238)
-0.422
-0.233
0.017
(0.123)
(0.138)
(0.130)
-0.149
0.045
0.345
(0.090)
(0.096)
(0.097)
-0.071
0.110
0.324
(0.081)
(0.087)
(0.089)
-0.228
0.097
0.244
(0.109)
(0.111)
(0.112)
0.386
0.876*** 0.729***
(0.24)
(0.263)
(0.263)
5
-0.618
(0.215)
0.112
(0.117)
0.479
(0.099)
0.724
(0.101)
0.742
(0.120)
1.360***
(0.247)
1
-0.893
(0.203)
-0.443
(0.110)
-0.238
(0.081)
-0.063
(0.099)
-0.076
(0.133)
0.811***
(0.243)
Panel C: 3 Month Strategy
SUE Quintile
2
3
4
-0.643
-0.851
-0.571
(0.208)
(0.233)
(0.234)
-0.314
-0.247
-0.047
(0.117)
(0.134)
(0.123)
-0.127
0.035
0.273
(0.085)
(0.093)
(0.089)
-0.017
0.167
0.301
(0.079)
(0.084)
(0.085)
-0.163
0.144
0.278
(0.101)
(0.106)
(0.105)
0.480** 0.995*** 0.849***
(0.231)
(0.256)
(0.256)
5
-0.663
(0.212)
0.018
(0.111)
0.374
(0.090)
0.592
(0.092)
0.622
(0.110)
1.285***
(0.239)
48
Table 8
CARs by SUE and 52-Week High
This table reports characteristic-adjusted cumulative abnormal returns for portfolios formed from sorts on earnings
surprise (SUE) and M ax. Each quarter firms are sorted into independent quintiles (or deciles) based on their earnings
surprise and nearness to 52-week high. Cumulative abnormal returns are reported for the 3 trading days around the
earnings announcement beginning on day t-1 and ending on day t+1 (-1,1), and 60 trading days following the earnings
announcement beginning on day t+2 and ending on day t+61 (2,61). Returns are in percent. ***, **, and * denote
significance at the 1%, 5%, and 10% level, respectively.
Panel A
SUE Quintile
CAR (-1,1)
SUE (%)
SUE
Rank
1
2
3
4
5
Max 1
-2.36
-0.08
0.03
0.15
1.24
Max 5
-0.91
-0.06
0.03
0.14
1.02
(5-1)
1.45***
0.02***
0.00
-0.01***
-0.22
Max 1
-3.56
-0.37
-0.16
-0.03
0.00
0.05
0.10
0.18
0.35
1.86
Max 5
-1.95
-0.30
-0.11
-0.03
0.01
0.05
0.10
0.18
0.33
1.87
Max 5
-2.28
-1.38
-0.08
1.35
2.66
(5-1)
1.08***
-0.42***
-0.48***
-0.35**
-0.72***
Max 1
-4.08
-3.17
-2.74
-2.11
-1.78
Panel B
SUE Decile
CAR (-1,1)
SUE (%)
SUE
Rank
1
2
3
4
5
6
7
8
9
10
Max 1
-3.36
-0.96
0.40
1.70
3.38
CAR (2,61)
(5-1)
1.61***
0.07***
0.05***
0.00**
0.01***
0.00***
0.00***
0.00
-0.02***
0.01
Max 1
-3.92
-2.43
-1.55
-0.53
0.21
0.56
1.43
1.93
2.47
4.01
49
Max 5
-2.44
-2.19
-1.76
-1.10
-0.39
0.21
1.19
1.53
2.26
3.14
(5-1)
1.49***
0.24
-0.21
-0.57***
-0.59***
-0.35*
-0.25
-0.40**
-0.21
-0.86***
Max 5
-2.60
-2.18
-0.84
-0.15
1.51
(5-1)
1.47***
0.99***
1.91***
1.96***
3.29***
CAR (2,61)
Max 1
-4.57
-3.25
-2.99
-3.31
-3.34
-2.25
-2.20
-2.04
-1.71
-1.83
Max 5
-2.63
-2.58
-2.39
-2.03
-1.15
-0.54
-0.09
-0.21
0.59
2.64
(5-1)
1.94***
0.66
0.60
1.28***
2.19***
1.71***
2.10***
1.83***
2.30***
4.47***
50
N
N
0.000
35,380
N
N
0.001
33,154
N
N
0.002
34,249
N
N
0.002
34,211
Controls
FE
R2
N
N
N
0.000
34,177
Max
Controls
FE
R2
N
5
4.970***
(0.716)
Controls
FE
R2
N
Momentum
Gain
Momentum
4
4.593***
(0.739)
N
N
0.002
34,211
1.328***
(0.254)
Momentum
Max
3
3.508***
(0.800)
N
N
0.001
34,249
1.345***
(0.306)
1
-2.229*
(1.149)
-1.062***
(0.361)
0.141
(0.390)
Y
Y
0.030
32,386
0.265
(0.278)
N
N
0.000
34,177
Panel A: Dependent Variable: CAR (2,61)
4
5
1
Max
Gain
2
1.936***
(0.714)
1
1.739**
(0.720)
N
N
0.001
33,154
1.103***
(0.365)
3
Gain
N
N
0.000
35,380
0.078
(0.318)
N
N
0.000
34,177
0.426
(0.264)
2
Controls
FE
R2
N
Momentum
Gain
Max
1
2
2.228**
(1.125)
-1.653***
(0.452)
-0.238
(0.380)
Y
Y
0.023
33,862
-0.269
(0.267)
N
N
0.000
35,380
2
3
2.765**
(1.208)
-1.178**
(0.541)
0.052
(0.409)
Y
Y
0.017
31,845
0.425
(0.295)
N
N
0.000
33,154
3
standard errors clustered by the day of announcement are in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively.
4
3.878***
(1.108)
-0.817*
(0.456)
-0.328
(0.337)
Y
Y
0.016
32,770
0.106
(0.246)
N
N
0.000
34,249
4
5
2.967***
(1.060)
-0.550
(0.353)
0.281
(0.303)
Y
Y
0.014
32,515
0.865***
(0.225)
N
N
0.001
34,211
5
month, day of week, and industry fixed effects are included where denoted. Panel B reports results for regressions where the dependent variable is CAR(-1,1). Heteroskedastic
the same day, # analysts, reporting lag, average monthly share turnover, log market cap, book-to-market, price-dividend ratio, earnings persistence, and earnings volatility. Year,
Panel A reports results for univariate regressions of CAR (2,61) on M ax, Gain, or M omentum, as well multivariate regressions that also control for # earnings announcements on
This table reports results from regressions of characteristic-adjusted cumulative abnormal returns on predictive variables. Regressions are run separately by earnings surprise quintile.
Table 9
Horse Race by SUE Quintile
51
Gain
N
N
0.001
35,380
N
N
0.002
33,154
N
N
0.002
34,249
N
N
0.003
34,211
Controls
FE
R2
N
N
N
0.002
34,177
Max
Controls
FE
R2
N
5
-2.041***
(0.309)
Momentum
4
-1.818***
(0.311)
Momentum
3
-2.020***
(0.328)
Gain
2
-0.971***
(0.284)
1
1.776***
(0.268)
N
N
0.002
34,211
-0.527***
(0.104)
Gain
Max
N
N
0.000
34,249
0.028
(0.121)
Controls
FE
R2
N
N
N
0.001
35,380
N
N
0.001
34,177
N
N
0.000
33,154
-0.347**
(0.145)
1
1
1.753***
(0.443)
-0.324**
(0.134)
-0.754***
(0.156)
Y
Y
0.037
32,386
-0.417***
(0.110)
N
N
0.001
34,177
Panel B: Dependent Variable: CAR (-1,1)
4
5
Max
Controls
FE
R2
N
-0.502***
(0.120)
3
Momentum
0.322***
(0.095)
2
Momentum
Gain
Max
1
Table 9 (Continued)
2
-1.101**
(0.444)
-0.238
(0.178)
-0.747***
(0.158)
Y
Y
0.024
33,862
-0.976***
(0.111)
N
N
0.005
35,380
2
3
-2.491***
(0.474)
0.635***
(0.207)
-0.640***
(0.145)
Y
Y
0.014
31,845
-0.707***
(0.110)
N
N
0.003
33,154
3
4
-1.818***
(0.461)
0.903***
(0.170)
-0.426***
(0.133)
Y
Y
0.020
32,770
-0.402***
(0.100)
N
N
0.001
34,249
4
5
-1.643***
(0.450)
-0.110
(0.143)
0.355***
(0.124)
Y
Y
0.034
32,515
0.001
(0.096)
N
N
0.000
34,211
5