The Earnings Announcement Return Cycle∗
Juhani T. Linnainmaa Conson Y. Zhang
March 2018
Abstract
Stocks earn negative abnormal returns before earnings announcements and positive returns
after them. A long-short strategy that trades on this earnings announcement return cycle
(EARC) earns a four-factor alpha of 8% per year. The EARC is unrelated to the earnings
announcement premium, and it is a feature of stocks widely covered by analysts. We show that
analysts’ forecasts follow the same pattern: analysts become less optimistic in their forecasts
before earnings announcements, and more optimistic afterwards. We attribute 55% of the EARC
return to this “optimism cycle.” Consistent with a mispricing interpretation, both the optimism
cycle and the EARC are significantly stronger among high-uncertainty stocks and stocks that
are difficult to arbitrage.
∗Juhani Linnainmaa is with the University of Southern California and NBER and Conson (Yingguang) Zhang iswith the University of Southern California. We thank Kenneth Ahern, Wayne Ferson, Gerard Hoberg, Chris Jones,Larry Harris, Christopher Parsons, Richard Sloan, K. R. Subramanyam, and the seminar participants at Universityof Southern California for helpful comments.
1. Introduction
Many return anomalies relate to earnings announcements. Stock prices tend to move in the
direction of recent earnings surprises1 and returns are higher when firms report earnings than
when they do not.2 So and Wang (2014) and Engelberg, McLean, and Pontiff (2015) find that
earnings announcements amplify anomaly returns; they are six to seven times higher on earnings
announcement days. Kim and So (2016) show that firms’ incentives to beat earnings estimates
lead to predictable price movements around earnings announcements. The competing explanations
for patterns such as these relate to risk, mispricing, and illiquidity. In this paper we present new
evidence that suggests that biases in investors’ expectations generate return predictability around
earnings announcements.
We first document a new stock return regularity, the earnings announcement return cycle
(EARC). The term “cycle” refers to the period between two consecutive quarterly earnings an-
nouncements. We show that stocks widely followed by analysts experience positive abnormal re-
turns early in the cycle and negative returns late in the cycle. This pattern is distinct from the
earnings announcement premium; the long-short strategy that we consider for capturing the EARC
is neither long nor short stocks around their earnings announcement dates.
Figure 1 illustrates our key result. In this figure we plot (1) the earnings announcement return
cycle (EARC) and (2) the percentage of analysts’ upward earnings forecast revisions. The solid line
represents average market-adjusted returns between two consecutive earnings announcements for
U.S. common stocks followed by at least five analysts. The dashed line is the percentage of upward
earnings forecast revisions for the same firms. The first vertical line at t = 0 denotes the (known)
date of the current earnings announcement; the second vertical line at t = 62.5 is the expected date
of the next earnings announcement.
Figure 1 shows that, apart from the earnings announcement premium period, which we define
as the t = −10 to 5 window, stocks continue to outperform the market by about three basis points
per day for the remainder of the first month after the earnings announcements. After this point,
they first earn the market premium for about six weeks and then underperform the market by two
1See, for example, Beaver (1968), Foster, Olsen, and Shevlin (1984), Bernard and Thomas (1989, 1990), andDaniel, Hirshleifer, and Subrahmanyam (1998).
2See, for example, Chari, Jagannathan, and Ofer (1988), Ball and Kothari (1991), Cohen, Dey, Lys, and Sunder(2007), Frazzini and Lamont (2007), Barber, De George, Lehavy, and Trueman (2013) and Savor and Wilson (2016).
1
Fig. 1. Earnings Announcement Return Cycle and Analysts’ Revision Cycle. This figure plots the averagedaily market-adjusted return and the percentage of analysts’ upward forecast revisions for U.S. common stocks tradedon the NYSE, Nasdaq and Amex, and covered by at least five analysts in the previous quarter from January 1985 toDecember 2015. A stock’s market-adjusted return is its return minus the CRSP equal-weighted index return. Thesolid line plots the three-day moving average of average market-adjusted returns from 7 trading days prior to anearnings announcement to 70 trading days after the announcement. The dashed line plots the percentage of upwardforecast revisions over the same period. The first vertical line at t = 0 denotes the (known) date of the currentearnings announcement; the second vertical line at t = 62.5 is the expected date of the next earnings announcement.
to three basis points per day for about a month as the next earnings announcement draws close.
Both the positive and negative abnormal returns in the early phase (t = 6 to 20) and the late phase
(t = 36 to 50) of the earnings cycle are statistically significant.
A long-short strategy that buys stocks in the early phase (excluding the earnings announcement
period) and sells those in the late phase earns a monthly four-factor model alpha of 68 basis
points (t-value 6.22). This alpha remains at 51 basis points (t-value 4.74) when we also include
the earnings announcement premium factor that is long stocks inside the earnings announcement
window (t = −10 to 10) and short those outside it (t = 11 to 50).
What is remarkable in Figure 1 is the synchronization between the EARC and the behavior of
analysts’ forecast revisions. During the earnings announcement periods, the majority of earnings
forecast revisions are upward revisions. This percentage, however, quickly drops below 50% and
continues to decline to 37% by t = 40. This low point coincides with the period during which
stocks earn their lowest returns in the cycle. As the next earnings announcement draws closer, the
proportion of upward revisions begins to increase.
2
To explain a periodic pattern in stock returns, such as the earnings announcement return cycle,
the underlying drivers of this pattern must also be periodic. Based on the pattern in Figure 1, we
conjecture that the predictable optimism cycle is a key driver of the EARC. Figure 1 shows that
market participants are typically the most optimistic about firms’ prospects right after earnings
announcements, and this is when stock returns are high; they are the most pessimistic around the
midpoint between two announcements, and this is when the returns are low.
We test this conjecture using a counterfactual portfolio approach. In this test we compare
the EARC alphas before and after excluding stock-days associated with any forecast revisions or
recommendation changes. That is, when a stock experiences either event, we remove it from the
sample for a three-day window around the event. The counterfactual portfolio’s monthly alpha of
30 basis points (t-value 2.65) is less than half of the original alpha of 68 basis points (t-value =
6.22), and the difference between the two is statistically significant with a t-value of 6.16. We can
therefore attribute more than 50% of the EARC strategy’s abnormal return to the event windows
around forecast revisions and recommendation changes.
Although this test does not establish causality from forecast revisions to returns—both the
returns and forecasts may respond to the same omitted variable—it is important to consider the
unconditional and cyclical nature of the earnings announcement return cycle. An investor can
capture the EARC effect by using information only on the distance from the previous earnings
announcement. Our counterfactual portfolio approach says that an investor earns more than half
of the abnormal profits exactly when analysts revise their forecasts or recommendations. These
results suggest that the optimism cycle is an important driver of the EARC.
Hirshleifer (2001) and Daniel, Hirshleifer, and Subrahmanyam (1998, 2001) suggest that be-
havioral biases should be more pronounced when uncertainty is high. Researchers thus typically
condition on the amount of uncertainty to assess whether an anomaly might be driven by behavioral
factors.3 Uncertainty about a firm’s next-quarter earnings should decrease over time as investors
acquire more information. Overoptimism, if any, should therefore be the most pronounced when
the next earnings announcement is as far in the future as possible. Figure 1 is consistent with this
prediction. Analysts tend to be the most optimistic at the beginning of the earnings cycle and
become less so over time.
3See, for example, Zhang (2006b).
3
We find that both the analysts’ overoptimism cycle and the earnings announcement return
cycle are more pronounced among high uncertainty stocks, as measured by size, age, idiosyncratic
volatility, and cash-flow volatility. The EARC strategy earns a monthly four-factor model alpha
of 140 basis points (t-value = 4.78) among firms in the top-uncertainty quintile. Both the positive
abnormal return in the early phase and the negative abnormal return in the late phase significantly
strengthen as uncertainty increases. We also find that the EARC pattern is more pronounced
among unprofitable growth firms. This finding is consistent with the results of Baker and Wurgler
(2006), who find that variation in investor sentiment has a greater effect on the prices of unprofitable
growth firms. Taken together, our estimates suggest that behavioral factors such as overoptimism
may drive the EARC phenomenon.
Can omitted systemic risk factors explain the EARC? The EARC strategy is long and short the
same stocks but at different times; it is long a stock after an earnings announcement and short as the
next announcement begins to draw close. For a risk-based explanation to apply, firms’ systematic
risks would therefore need to vary significantly based solely on the amount of time that has passed
since the previous earnings announcement. As an additional test of the risk-based explanation, we
also compare the EARC between firms with low and high analyst coverage. Under the risk story,
the EARC should not depend on the level of analyst coverage—the behavior of analysts should be
unrelated to the risk dynamics. In the data, however, the EARC pattern is absent among stocks
with low analyst coverage.
If the EARC is due to mispricing, why does it persist? One possibility is the difficulty in
arbitraging this form of mispricing. To capture the EARC in full, a trader would have to switch
between long and short positions in individual stocks on a daily basis. Moreover, the amount of
capital that would need to be committed to this trade would vary significantly as well: the number
of firms announcing their earnings ranges from 0 to over 180 per day in the sample. If a fund
has a fixed amount of capital allocated to this strategy, it might fully correct mispricing when
only a few firms announce earnings. However, when hundreds of firms announce during a week,
the fund may be unable to eliminate the mispricing due to limited capital (Shleifer and Vishny
(1997)). Conversely, if the fund has enough capital to fully correct mispricing even at the height
of the earnings season, it would have large amounts of idle capital at times when but a few firms
announce earnings; this idle capital, in turn, would lower the fund’s average return on capital.
4
This limits-to-arbitrage argument implies that abnormal return from the EARC strategy should
be higher when more firms announce their earnings on the same day. Consistent with this prediction,
we find that the abnormal returns are often 30% to 70% higher in event-time than in calendar-time,
suggesting that the average abnormal returns tend to be higher when the EARC portfolio holds
more stocks—and when would-be arbitrageurs would need to commit more capital.4
Two papers closely relate to this study. Grinblatt, Jostova, and Philipov (2016) shows that a
predictable component in analysts’ optimism helps forecast the cross section of stock returns. We
show that the dynamics of investors’ biases lead to a periodic pattern in stock returns, the earnings
announcement return cycle. Kim and So (2016) examine the link between firms’ incentives to beat
earnings estimates and stock returns around earnings announcements. Where as Kim and So (2016)
focus on the actions of firms, we examine the predictable changes in investor optimism and show
that it is associated with the predictable return pattern between two consecutive quarterly earnings
announcements.
2. Data
This study uses data from CRSP, Compustat and I/B/E/S. News data is from Ravenpack. The
main sample consists of firms with decent analyst coverage to capture stocks widely followed by
market participants. We construct the measure of active analyst coverage using I/B/E/S detail
file by counting unique analyst (analys) who make at least one annual earnings forecast in the
90 days prior to the last earnings announcement. The main sample focuses on firms with analyst
coverage of 5 or higher. The sample firms are U.S. publicly traded firms listed in NYSE, AMEX
and Nasdaq (shrcd 10 and 11, and exchcd 1, 2, 3). We drop all firm-quarter with missing quarterly
earnings announcement date (rdq). To further ensure data quality, we require firms to have at
least 4 available earnings announcement dates within the last 600 days and the distance to the
last earnings announcement to be between 30 and 200. The sample period is from January 1985
to December 2015. Prior to 1985, there are few stocks with analyst coverage of 5 or above.5 The
4Savor and Wilson (2016) find the opposite result for earnings announcement premium, where more announcingfirms on the day is associated with lower earnings announcement premium.
5All results are robust to various common stock level filters. The results reported in this version apply a pricefilter of lagged price greater than $3 (as a middle ground between the two most commonly used thresholds $1 and$5) and positive book value of equity.
5
media coverage data start in 2001.
Table 1 shows the descriptive statistics of the main sample and how it compares to the firm-
quarters with less than 5 analysts covering. The unit of observation is firm-earnings-announcement.
All numbers are yearly time-series averages. A comparison between the included and excluded
sample (Panel A) reveals that firms in the main sample are (1) much bigger by market value;
(2) valued higher by book-to-market ratio; (3) more profitable by return on book value of equity;
(4) more likely to be dividend paying firms and (5) more likely to be covered by media. These
statistics suggest that the main sample captures an economically important set of firms to which
market participants pay high attention. The main sample represents about 25% of the CRSP stock
population and this ratio increases from 1985 to 2015 due to the increasing total number of analysts.
Panel B summarizes the key variables related to analysts. “Number of analysts” is the count
of unique analyst in the previous quarter, which is used to defined “widely followed stocks.” The
average number of previous coverage is 10.6. The remaining variables are computed for the period
from one to ten weeks after earnings announcements. The typical interval between two consecutive
earnings announcements is 13 weeks with slight seasonal variations. Thus the nine-week window
considered in this paper excludes the current actual and future expected earnings announcement
periods. On average, there are 6.1 forecast revisions and 0.56 recommendation changes for a
firm-earnings-announcement during this nine-week window.6 The average number of upward and
downward revisions are 2.50 and 3.60; upgrades and downgrades are 0.27 and 0.28. We see that
downward revisions are more common than upward revisions which is consistent with existing
findings about analysts being on average too optimistic. The ratio of upgrades and downgrades
does not match with the ratio of upward and downward revisions, which is consistent with the
“two-tongues” findings from Malmendier and Shanthikumar (2014) about strategic distorters tend
to issue optimistic recommendations but less optimistic forecasts.
3. Hypotheses and Methodology
The main hypothesis in this study is that an optimism cycle by analysts and/or investors causes
the return cycle (EARC). We first document the EARC and link it to analysts’ optimism cycle
6Data on stock recommendations is not available until late 1993 and becomes reliable only after February 1994.Hence statistics reported on recommendations are based on post-1994 data.
6
using a “counterfactual portfolio approach.” We then test and exploit the relationship between
uncertainty and analysts’ optimism to further validate the mispricing interpretation. Finally, we
test the role of limits to arbitrage in the EARC return.
We do not make the distinction between analysts and investors by interpreting analysts’ forecasts
as proxies for investors’ expectations. Thereby, we leave out any analysts’ agency problems that may
produce the “optimism cycle” potentially to misguide investors. However, we argue that although
the agency problem channel may be as well at play, it may not be of first order importance compared
to the behavioral channel. Conceptually, if the “optimism cycle” is artificially created by analysts,
rational investors need to be repeatedly “fooled” for the return cycle to emerge. In addition, agency
explanation would also require that the regulatory entity fails to realize and correct the misaligned
incentives. Given that the “walking down” of analyst estimates has been known to the accounting
literature for almost two decades and there is still no evidence which shows that agency problems
substantively explain the “walking down” pattern,7 We argue that agency problem may not be of
first order importance compared to behavioral biases for the EARC. On the other hand, numerous
evidence shows that analysts’ estimates reflect investors’ expectations (see Bordalo et al. (2017)).
Thus, absent the evidence for analysts’ systematic wrongdoing, it may be fair to hypothesize that
analysts and investors share common behavioral biases as active financial market participants.
3.1. The “Counterfactual” Portfolio Approach
Identifying the causes of return anomalies is challenging, especially when the question is about
magnitude. Existing literature usually indirectly identifies the mechanism behind anomalies by
formulating theories which give unique predictions, and then conducts asset pricing tests to verify
the predictions. This standard practice is limited by the uniqueness of the theoretical predictions
and availability the observable dimensions, and is often sensitive to model specifications. This
empirical challenge is due to the lack of control experiments which produce valid counterfactual
observations. To tackle this challenge of identification, this study develops a new and simple
methodology which we call the counterfactual portfolio approach (CPA). CPA borrows the event-
7Richardson et al. (2004) links analysts’ behavior to firms’ equity issuance and insider trading. However, they donot provide quantitative estimates of how much the misaligned incentives give rise to the “walking down” pattern.Libby, Hunton, Tan, and Seybert (2015) show the importance of relationship incentives to the pattern, but the paperis unfortunately retracted. One may interpret the retraction as indirect evidence that the relationship incentives arenot there, small or hard to measure.
7
study mentality from Fama, Fisher, Jensen, and Roll (1969) but answers a different question.
Existing event-study methodologies are often adopted to examine whether certain events af-
fect stock prices and predict return anomalies (e.g. post-earnings announcement drift, earnings
announcement premium). In contrast, CPA answers the question that by how much certain events
can explain some known anomalies. This is an important question because it helps reveal the
underlying mechanism of a given anomaly. CPA also provides quantitative estimates for the im-
portance of the events. Kozak, Nagel, and Santosh (2017) address a similar question about the
causes of anomalies based on principal components. Relatedly, Engelberg, McLean, and Pontiff
(2015) examine anomaly returns on news and earnings announcement days and compare them with
normal days. The CPA complements these existing methodologies by providing a simple way to a
assess the economic and statistical significance of certain events for anomaly returns.
The central idea of the counterfactual portfolio approach is to compare portfolio abnormal re-
turns before and after replacing returns around event days by appropriate “counterfactual” returns.
It involves three steps: (1) construct anomaly portfolios and estimate abnormal returns; (2) con-
struct counterfactual portfolios by replacing returns on event days by “counterfactual” returns; (3)
compute the difference in abnormal returns between the original and counterfactual portfolios and
assess the economic and statistical significance of the difference.
The key question which one must answer when using this methodology is that what the appro-
priate “counterfactual” returns are, or equivalently, what the returns would have been absent the
events. We consider four possibilities: (1) the market return, (2) expected return from factor mod-
els, (3) regression-based residual return and (4) the average return of other stocks in the portfolio.
Each of these choices have pros and cons and have different assumptions embedded. This paper
adopts option (4), but other options all give similar results.
If we fill in market returns as the counterfactual, we explicitly impose the market model. This
option is easy to implement but suffers from its strict assumption. In particular, if the event tends
correlate with other factors or omitted events, this choice would lead to biased estimates. Using
expected returns from factor models suffers from similar problems.
The regression-residual approach provides a flexible way to account for known factors and
other events. For instance, one may attempt to remove the average effect of forecast revisions by
8
running a regression of daily return on some forecast revision variables with a set of known factors.
The residuals from the regression then can be used as a version of the “counterfactual” return.
The drawback of this approach comes from measurement error and model misspecification. When
one or both of these two issues exist, the approach may underestimate the impact of the event.
Furthermore, researchers must choose from a large number of model specifications, which creates
extra work and concerns for data mining.
The fourth option appears to strike a good balance between straightforward implementation
and reliability. By replacing the event-window returns with the cross-sectional average returns of
other stocks in the portfolio, the methodology accounts for any omitted factors affecting all stocks
in the portfolio on the same day. More importantly for this study, this choice also accounts for
omitted factors in event-time, as all stocks in the portfolio share a similar window for earnings
announcements. This paper uses the this option to construct “counterfactual” returns.
To more clearly see the mechanism of the CPA, imagine that the return generating process for
any portfolio follows a factor structure. The return on portfolio i on day t can be written as
ri,t − rf,t = αi,t + βi,jFj,t + ei,t (1)
where subscript i indexes for portfolio, t for day and j for factor; rf,t is the risk-free rate; αi,t is
the abnormal return; Fj,t is a vector of factor returns and βi,j is a vector of factor exposures for
portfolio i; ei,t is the error term.
To test the importance of certain events for the portfolio returns, we can simply take the
difference between the returns on the original and the counterfactual portfolio:
r1,t − r0,t = α1,t − α0,t + (β1,j − β0,j)Fj,t + (e1,t − e0,t) (2)
where subscript 1 and 0 denote the counterfactual and the original portfolios respectively. r1,t−r0,t
is equivalent to the return on a long-short portfolio which longs the counterfactual portfolio and
shorts the original portfolio. Therefore, we can use the conventional portfolio regression to estimate
the average α of this portfolio. If the event is important for the original abnormal return, we shall
expect that the α estimate to be significantly negative. The magnitude represents how much of the
original abnormal return can be attributed to the days around the events.
We measure abnormal returns using calendar-time portfolio alphas estimated from the CAPM,
9
the three-factor model (Fama and French (1993)) and the four-factor model (Carhart (1997)). The
counterfactual portfolio return on each day is the simple average of returns on all stocks in the
portfolio which do not fall in a three-day window of any analyst updates.
3.2. Optimism, Uncertainty and Valuation Subjectivity
The counterfactual portfolio approach helps identify the mechanism behind the EARC. The
remainder of the empirical section explores the heterogeneity within the EARC phenomenon to
further validate the behavioral channel.
3.2.1. Uncertainty in the Cross-section
Existing literature suggests that if an anomaly is driven by behavioral biases, it should be more
pronounced when uncertainty is high (e.g. Hirshleifer (2001), Daniel et al. (1998, 2001)). Ackert
and Athanassakos (1997) and Zhang (2006a) find that analysts’ optimism and underreaction pos-
itively correlates with analysts’ forecast dispersion. We first test that whether analysts’ optimism
positively correlates with uncertainty in our sample using a set of uncertainty measures similar
to Zhang (2006b). Then we test whether these measures of firm-level uncertainty such as firm
size, age, idiosyncratic volatility and cash flow volatility are positively associated with the EARC
abnormal return.
Baker and Wurgler (2006) use a similar set of uncertainty measures, and additional variables
such as book-to-market equity, profitability and dividend paying status to identify firms whose
valuations are more subjective. They find that investor sentiment negatively predicts returns on
high valuation subjectivity firms. Barberis and Shleifer (2003) and Barberis, Shleifer, and Wurgler
(2005) also argue that growth stocks are “glamour” stocks that are favored by investors. To the
extent that optimism and sentiment are related, we expect that the EARC abnormal return to be
stronger among firms with high valuation subjectivity.
3.2.2. Uncertainty in the Time-series
Uncertainty about firms’ next earnings results should decrease over time, as new information
arrives and investors continuously update their information set. Thus, information arrival, or
equivalently, uncertainty resolution may be a deeper mechanism behind analysts’ optimism cycle.
10
We examine the importance of uncertainty resolution over time using the setting of management
guidance. Consider a simple model where (1) analysts’ estimates start out being overly optimistic;
(2) the manager issues guidance when the prevailing estimate is outside some confidence interval
of the firm’s internal estimate and (3) the manager receives interim cash flow information which
makes the firm’s internal estimate more precise over time.
This model embeds uncertainty resolution over time by allowing the firm to update its internal
estimate based on interim cash flow information. The model yields predictions that (1) there are
more downward than upward guidance (by construction); (2) for reasonably low values of analysts’
optimism, there are more guidance in the late phase than in the early phase; (3) the sensitivity
of management guidance to analysts’ forecast error increases in the late phase (See Appendix C
for details of the model, proofs and implications). These predictions imply that managers are
more likely to correct analysts’ forecasts as the next earnings announcements approach by issuing
management guidance. Empirically, this means that management guidance should have power in
“explaining” the EARC especially when the next earnings announcements are close. However,
most of its effects should already be reflected by analysts’ updates as analysts duly respond to
management guidance.
3.3. Limits to Arbitrage
A behavioral factor would appear to be mispricing in the eyes of informed investors (i.e. arbi-
trageurs). Thus anomaly returns should appear to be higher for the stocks that are more costly
to trade. We examine the relation between illiquidity (Amihud (2002)) and the EARC abnormal
return. As illiquid stocks are more costly to trade, mispricing on these stock should be more
pronounced. The second measure we use for arbitrage difficulty is “event intensity” of earnings
announcements, defined as the number of announcing firms on a given day.
Event intensity may increase arbitrage difficulty. Earnings announcements arrive in waves and
the number of announcements varies from 0 to over 180 per day. Correcting mispricing requires
arbitrage capital. As the number of same-day announcing firms represents the number of trading
opportunities, the amount of capital required to fully exploit these opportunities and thus to correct
the mispricing would also fluctuate widely. In practice, arbitrageurs face leverage constrains and
11
borrowing costs. The total amount of arbitrage capital in the economy should stay relatively fixed
in the short-term due to financing frictions. Then arbitrageurs may optimally decide to under-fund
an earnings related strategy sometime to maintain a target expected return on capital. This aspect
of arbitrage difficulty predicts that the EARC should be stronger for firms announcing earnings at
the peak of the earnings seasons.
We measure event intensity in two ways, the first one by firm and the second one by day.
Specifically, the first measure (Crowdedness) is a firm level variable that counts the number of
firms announcing earnings on the same day when the firm announces earnings. The second measure
(CrowdedDay) is a day level variable of the same count. When constructing portfolios by sorting on
Crowdedness, each portfolio has the same number of stocks, but the high Crowdedness portfolio
contains fewer calendar-days; when portfolios are constructed by sorting on CrowdedDay, each
portfolio has the same number of calendar-days, but the high CrowdedDay portfolio contains
much more stocks. The two measures are complementary and should give consistent results.
4. Empirical Results
This section first establishes the EARC phenomenon and then connects it to analysts’ optimism
cycle. Then we present results on how uncertainty and limits to arbitrage individually and jointly
affect the return on the EARC strategy. Finally, we explore two alternative explanations for the
EARC: media attention and dividends.
4.1. Main Results: The EARC
This subsection establishes the earnings announcement return cycle (EARC) phenomenon. Fig-
ure 2 plots the average buy-and-hold market-adjusted return in event-time around earnings an-
nouncements, from t = −10 to t = 70. The figure first confirms that the earnings announcement
premium also exists in our sample. From t = −10 to t = 5, stock holders on average gain around 20
basis points of market-adjusted return. After the first week of the earnings announcements, stocks
continue to outperform the market index for about three weeks, until around t = 20. Then stock
prices remain flat relative to the market for about two to three weeks before starting to decline
relative to the market at around t = 33. Firms are valued about 0.65% higher at the midpoint
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Fig. 2. Earnings Announcement Return Cycle: Average Buy-and-hold market-adjusted Return. Thisfigure plots the average buy-and-hold market-adjusted return for U.S. common stocks traded in NYSE, Nasdaq andAmex covered by 5 or more analysts in the previous quarter from January 1985 to December 2015. Market-adjustedbuy-and-hold return for stock-announcement i at event-time T is defined as EXBHReti,T =
∏Tt=−10(1 + RETi,t) −∏T
t=−10(1+EWRETDi,t) where RETi,t is the daily return of the stock-announcement i at event-time t; EWRETDi,t
is the corresponding daily CRSP equal-weighted index return. T , ranging from −10 to 70, is the holding interval(from 10 trading days before to 70 trading days after the earnings announcement). The figure plots the averageof EXBHReti,T for all stock-announcement i at event-time from −10 to 70. The vertical dashed lines mark thebeginning and the end of each phase: phase 0 from t = −10 to 5, phase 1 from t = 6 to 20, phase 2 from t = 21 to35, phase 3 from t = 36 to 50 and phase 0’ (expected earnings announcement period) from t = 51 to 70.
between two earnings announcements than the week before one.
Table 2 shows calendar-time portfolio regression results of a strategy that trades on the EARC.
On each day, the strategy buys stocks that are within one to four weeks after the latest earnings
announcements (t = 6 to t = 20) and shorts stocks that are within seven to nine weeks (t = 36
to t = 50) with equal weights. The long-, short-, and long-short portfolios returns are tested
against the CAPM, the four-factor model (Carhart (1997)) and a five-factor model which includes
the earnings announcement premium factor. The results show that the alphas are significantly
different from zero in all portfolios and across all specifications. The long-short portfolio earns
alphas of about 3.4 basis points per day, or 0.68% per month.
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Fig. 3. Analyst Recommendation Change Cycle. This figure plots the percent of stock recommendationupgrades for each event-time t from 10 trading days before to 70 trading days after earnings announcements. Thevalues are computed using total number of recommendation upgrades divided by total number of recommendationchanges at each event-time.
4.2. Analysts’ Optimism Cycle
Figure 1 in reveals the synchronization between the EARC and analysts’ forecast revisions.
Figure 3 plots the percentage of upward recommendation changes in event-time. This figure shows
a similar pattern as that of the earnings forecast revision. Of all the recommendation changes in
the second half of the earnings cycle, about 44% them are upgrades, decreasing from around 50% in
the first half of the earnings cycle. This translates to a spread of over 10 percentage points between
the likelihood of stock upgrades and downgrades, given there is a recommendation change.
Although the figures are informative, they implicitly give higher weights to stocks with higher
analyst coverage by plotting the simple average across all observations. We use panel regressions
with fixed effects to formally test whether analysts tend to become less optimistic in the late phase.
As all results are consistent with the visual evidence in Figure 1 and 3 and with those in prior
studies, we report them Appendix B and provide further discussion there. Overall, the percentage
of upward forecast revisions is about 3.5 percentage points higher in the phase 1 (t = 6 to 20) than
in phase 2 (t = 21 to 35); 2.4 percentage points lower in phase 3 (t = 36 to 50) than in phase 2.
Thus the difference between phase 1 and 3 is about 5.9 percentage points. All results are highly
statistically significant. Similar results hold for recommendation changes.
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4.3. Explaining the EARC
The central question this paper addresses is how much the optimism cycle explains the EARC.
One cannot perfectly answer this question even with the counterfactual portfolio approach to the
extent that analyst updates may correlate with unobserved events that are unrelated to optimism.
As a compromise, the counterfactual portfolio methodology addresses the question that “how much
of the EARC abnormal return can be attributed to the days around analysts’ updates?” Since the
dates of analysts’ updates are quite accurately recorded in I/B/E/S, using narrow event-windows
of two or three days, we can still have some confidence in saying whether the optimism cycle causes
the EARC.
Table 3 reports portfolio regression results for the counterfactual portfolio, which replaces stock
returns within the three-day windows around analysts’ updates by the average returns of other
stocks in the portfolios. The original long-short alphas are about 3.4 basis points per day as shown
in Table 2. The counterfactual alphas decrease to below 1.5 basis points in the four-factor model as
shown in column 1 and 4. The results suggest that the three-day windows around analysts’ updates
account for about 55% of the abnormal return of the EARC strategy. Note that the optimism cycle
has much stronger explanatory power for the abnormal return in the short-portfolio than in the
long portfolio. This is potentially because analysts tend to start out having optimistic estimates
rather than adjusting them upward in the early phase.
Results from Table 3 indicate that analysts’ optimism cycle is an important driver for the EARC.
However, we need to estimate the standard errors to draw statistical inference. The counterfactual
portfolio replaces about 26% of the stock-day observations in the 30-day holding periods (t = 6 to
t = 20 and t = 36 to t = 50). It is possible that the decrease in alphas is purely by chance.
To test whether the 55% alpha reduction in the counterfactual portfolio is statistically sig-
nificant, We run portfolio regressions according to equation 2. Namely, we construct long-short
portfolios which long the counterfactual portfolios and short the original portfolios and estimate
their alphas, which represent the reduction in the EARC alphas. We repeat this test for the long-,
short- and long-short portfolios, for revisions and recommendation changes individually and jointly,
using both two-day and three-day event windows to construct the counterfactual portfolios. Table 4
reports the results.
The original alphas in column 1 are as reported in Table 2. We see from the two “Long-short”
15
rows that the alphas significantly decrease in the counterfactual portfolios with t-values typically
over 6. For instance, the CAPM panel “Long-short” row shows that the alpha reduces by 1.11
basis points by removing stock-days within three-day windows of recommendation changes. The
alpha reduction is 65 to 100% stronger in size for forecast revisions. The results on long- and
short-portfolios (first two rows in each panel) reveal that the “explanatory power” of forecast
revisions is concentrated in the short-portfolio, while recommendation changes have significant
“explanatory power” for both the long- and short-portfolios. Results in the “Short” rows indicate
that the forecast revision cycles strongly drives the negative abnormal returns in the late phase.
The reduction in negative alphas after removing days around forecast revisions exceeds 100% of
the original alpha with t-values around 10. These results strongly suggest that analysts’ optimism
cycle is a key driver for the EARC abnormal return. We also conduct a placebo test (unreported)
which randomly removes the same number of three-day windows within each stock-announcement
and estimates the bootstrapped standard errors based on the empirical distribution of alphas with
5000 trials. This test gives virtually identical results as in Table 4.
Note that the results in this section may understate the effect of the optimism cycle because
they do not account for the adding up constrain. In particular, the positive alpha in the early phase
may also decrease if the market return were adjusted for the removal of stock returns around analyst
updates. Thus, although the optimism cycle appears to only explain the abnormal return on the
short-portfolio, the adding up constrain implies that it would also explain the positive abnormal
return in the early phase at least in part. The effect of the adding up constrain may be particularly
important for this sample as they tend to be large firms. Therefore, the 55% reduction in alphas is
a conservative estimate of the effect of the optimism cycle to the EARC.
4.4. The EARC and Uncertainty
This section relates the EARC to firm-level uncertainty. Hirshleifer (2001) and Daniel, Hirsh-
leifer, and Subrahmanyam (1998, 2001) argue that mispricing due to behavioral biases should be
most pronounced among firms with high uncertainty. Ackert and Athanassakos (1997) and Zhang
(2006a) find empirical supports this conjecture and show that analysts’ dispersion is positively
correlated with analysts’ optimism and underreaction. Following Zhang (2006b), we measure un-
16
Fig. 4. Forecast Optimism by Forecast Horizon and Idiosyncratic Volatility. This figure plots the event-time cross-sectional median of quarterly earnings forecast optimism by forecast horizon (from 1 to 4 quarters ahead)and by idiosyncratic volatility quintiles, from 5 to 70 trading days after the last quarterly earnings announcement.Forecast optimism for each firm-announcement-horizon-day observation is computed as the difference between forecastand actual value scaled by closing stock price on the previous quarterly earnings announcement day and multipliedby 100 (Optimism = (forecast − actual)%/PRCpre
EA). Time-series Optimismt for a firm-announcement-horizonis constructed using the last non-missing value of Optimism. Idiosyncratic volatility (IVOL) is computed as thestandard deviation of the residuals from stock level daily 4-factor model regression (Carhart (1997)) for each stock-announcement. At the end of each March, June, September and December, IVOL is computed for each stock usingdaily return data from the prior 260 to 6 trading days. Stocks are sorted quarterly by IVOL to form 5 portfoliosfor the next quarter. IVOL increases from quintile 1 to 5 (Q1 to Q5). We align observations quarterly to have theirlast earnings announcement occuring at the vertical line to the left. The vertical lines are at t = −250, −187.5,−125, 62.5, 0, which represent actual date of the last (left) and expected date of the next (right) quarterly earningsannouncement.
certainty using market value, firm age, idiosyncratic volatility and cash flow volatility. We first
test the relation between analysts’ optimism and uncertainty in our sample. Then we show how
uncertainty affects the EARC abnormal return.
Figure 4 plots the cross-sectional median optimism in event-time by forecast periods and id-
iosyncratic volatility quintile. Note that there is no periodic pattern in this figure because each line
now chases the same quarter rather than the same forecast period. Three patterns stand out from
this figure: (1) in the time-series, analysts’ optimism decreases as the next earnings announcements
approach for all forecast periods; (2) high IVOL stocks have a much higher optimism than the full
sample and (3) as a result the optimism walk-down is much more pronounced for the high IVOL
stocks. The median optimism in earnings yield monotonically increases with IVOL, from about
17
0.02% (low IVOL) to 0.27% (high IVOL) for four-quarters-ahead forecasts. The mean and median
quarterly earnings yield for the full sample are about 0.88% and 0.91% respectively. Thus the op-
timism is economically large when the forecast period is far away and uncertainty is high. We also
see that the median quarter 1 forecast is consistently below the actually value, which is consistent
with existing findings about management’s incentives to beat estimates.
Table 5 reports the correlation coefficients (in percentage) between analysts’ next period opti-
mism and lagged measures of uncertainty. “Early optimism” is computed using one to four quarters
ahead earnings forecasts made during t = 0 to 10 relateive to the last earnings announcement. “Op-
timism Walkdown” is the difference between optimism in the early phase and the late phase (See
Appendix A for details on variable construction).
Results in Table 5 confirms that this set of uncertainty measures: size, age, idiosyncratic volatil-
ity and cash flow volatility positively correlate with both analysts’ next period optimism and op-
timism walk-down. The strongest predictors are firm size and idiosyncratic volatility, which are
about 20 percent correlated with average optimism and 7 to 9 percent correlated with optimism
walk-down. After validating the link between uncertainty and analysts’ optimism cycle, we test
whether uncertainty also predicts the EARC abnormal returns and by how much.
Table 6 presents calendar-time portfolio regression alphas for portfolios sorted at the beginning
of each quarter based on lagged uncertainty, measured as the first principle component of the
four uncertainty metrics above (calculation details are provided in Section 4.10). Uncertainty
increases from Q1 to Q5. Q5−Q1 corresponds to a long-short portfolio which longs high uncertainty
quintile and shorts the low uncertainty quintile. We apply the EARC strategy to stocks within
each uncertainty quintile to construct equal-weighted long-, short- and long-short portfolios by
buying stocks that are between t = 6 to t = 20 in earnings announcement event-time and shorting
those that are between t = 36 to t = 50. Each cell reports the four-factor alpha and its t-value in
parentheses.
The results show a clear pattern that EARC alphas increase with uncertainty. The first row
shows that abnormal returns on the long-portfolios increases from 1.82 basis points to 4.32 basis
points per day from Q1 (low uncertainty) to Q5 (high uncertainty). A strategy that longs the Q5
long-portfolio and short the Q1 long-portfolio yields an abnormal return of 2.71 basis points with
t-value=1.92. A similar pattern appears for the short-portfolios but in the opposite direction, as
18
Fig. 5. Earnings Announcement Return Cycle and Idiosyncratic Volatility. This figure plots the averagebuy-and-hold market-adjusted return for U.S. common stocks traded in NYSE, Nasdaq and Amex covered by 5 ormore analysts in the previous quarter from January 1985 to December 2015. The values are computed as in Figure 2.Idiosyncratic volatility (IVOL) is computed as the standard deviation of the residuals from stock level daily 4-factormodel regression (Carhart (1997)) for each stock-announcement. At the end of each March, June, September andDecember, IVOL is computed for each stock using daily return data from the previous 250 trading days. Stocks aresorted quarterly by IVOL to form 5 portfolios for the next quarter. IVOL increases from quintile 1 to 5 (Q1 to Q5).
the short-portfolio abnormal returns become significantly more negative as uncertainty increases.
Thus the long-short portfolio abnormal returns increase more strongly with uncertainty than the
long- or short-portfolio alone. Daily alpha increases from 1.67 to 7.02 basis points from Q1 to Q5.
These patterns hold for all four uncertainty measures individually (unreported to conserve space).
The strongest predictor is idiosyncratic volatility where in the long-short portfolio for the top IVOL
quintile earns a daily four-factor alpha of 7.25 basis points per day, significantly higher than the
1.13 basis points in low idiosyncratic volatility portfolio.
Figure 5 provides visualization for the relation between idiosyncratic volatility and the EARC.
Each line represents the average buy-and-hold market-adjusted return (as in Figure 2) for stocks
in a IVOL quintile. The clear “rainbow” pattern shows the clear relation between idiosyncratic
volatility and the EARC. The solid line (Q5) has a peak at around 1.3%, indicating that high
idiosyncratic firms are valued about 1.3% higher between two earnings announcements. This result
is consistent with Stambaugh, Yu, and Yuan (2015) which finds that the IVOL-return relation is
negative for overpriced stocks and positive for underpriced stocks. The return pattern at around t =
0 reveals that the earnings announcement premium also appears to increase with IVOL, indicating
19
its potential connection with uncertainty and/or investors’ expectations.
This subsection shows the strong positive association between the EARC strategy returns and
uncertainty, and evidence suggesting that the link is through analysts’ optimism cycle. These
results indicate that the EARC phenomenon may indeed be driven by behavioral factors such as
overoptimism.
4.5. Uncertainty Resolution over Time: the Case of Management Guidance
Conceptually, analysts’ optimism cycle may be a manifestation of uncertainty resolution over
time as new information continues to arrive. However, if uncertainty gets resolved in a linear way,
one would observe a constant negative premium, as opposed to a “sine-wave” return pattern as in
Figure 1. To generate the EARC pattern, uncertainty must be resolved at an accelerating rate,
which in turn leads analysts to revise their forecasts at an increasing rate.
To identify this feature of uncertainty resolution, we need to test whether later information is
more informative and/or arrives at a higher rate. The theoretical framework laid out in Section 3.2.2
and Appendix C provides a parsimonious way to test this hypothesis using management guidance.
If management guidance becomes increasingly informative as the next earnings announcement
approaches, the correlation between a guidance indicator variable and analysts forecast errors
should be higher in phase 3 than phase 1. The model also predicts that the total number of
guidance should be higher in the late phase. As a result, management guidance should have
significant “explanatory power” for the EARC, especially in the late phase.
We first test the behavior of management guidance according to the predictions above and then
relate it to the EARC returns. Since the results provide similar interpretations as the those related
to uncertainty in the cross-section previously discussed, we present results in Appendix C where
we discuss the role of management guidance in detail. Overall, the results are consistent with the
predictions: there are more management guidance in the late phase and these guidance are more
sensitive to prevailing forecast errors. Management guidance explains about 30% of the EARC
abnormal returns, but does not provide additional explanatory power beyond analysts’ updates.
20
4.6. Alternative Explanations
We explore two alternative explanations which may also lead to the EARC: (1) media attention
and (2) dividends, and present results and provide discussion in Appendix D. Briefly, the results
show that both media coverage and dividends exhibit clear periodicity over earnings announcement
cycles. Although stock-days around media coverage account for about 30% of unconditional EARC
abnormal return by itself, it does not add explanatory power beyond analysts’ updates. This result
suggests that analyst updates fully reflect any periodic component in media coverage that has
implications on stock returns. Dividends do not explain the EARC abnormal returns as the EARC
is stronger among non-dividend paying stocks.
4.7. Methodological Notes
So far, all asset pricing results are based on calendar-time portfolio regressions. This conven-
tional approach has many advantages but also has at least two shortcomings in the context of this
study. Firstly, calendar-time portfolio analysis weighs each day equally. This may not be appro-
priate for studies that look at events which arrive in waves. This problem is especially sever if the
event’s arrival intensity correlates with abnormal returns. Secondly, using value-weighted index
as a proxy for the market portfolio may not work well when the portfolio could hold hundreds of
stocks on a given day and most of them are large in market capitalization. Both issues may lead
to underestimation of the true magnitude of the EARC abnormal returns.
The calendar-time approach weighs each day equally and thus gives less weight to each case
when more firms are announcing on the same day. If the number of announcing firms positively
correlates with abnormal returns, the average abnormal returns by day would be lower than the
average abnormal returns by case. Depending on the convexity of the relationship between number
of announcing firms and abnormal return and the clustering density of earnings announcements,
the calendar-time approach could severely understate the extent of the mispricing.
Using value-weighted index to price portfolios of large cap stocks suffers a mechanical downward
bias in estimated alphas, especially when the portfolio holds many large cap stocks which by
construction move the “market.” This problem can have a large effect for this study as the sample
include virtually all large cap stocks and often hold hundreds of stocks on a given day.
21
To mitigate these problems about event clustering and large-cap bias, we adopt event-time port-
folio analysis and CRSP equal-weighed index as proxy for the market portfolio. Table 7 compares
market-adjusted returns between event-time and calendar-time portfolios, sorted by uncertainty
and benchmarked by equal-weighted index returns. Event-time portfolios are constructed quar-
terly using the same criteria as the calendar-time portfolios (i.e. buying stocks at t = 6 to t = 20
and selling those at t = 36 to t = 50). Each cell reports the quarterly averages of daily event-
time portfolio market-adjusted returns and their corresponding t-values. Panel A reports daily
averages of event-time portfolio market-adjusted returns and t-values. Panel B reports those for
calendar-time portfolio. Abnormal returns on both portfolios are adjusted only by subtracting the
CRSP equal-weighted index return, so any difference between the two panels solely comes from the
difference between the event-time and calendar-time methodology.
We see that the EARC abnormal returns for the long-, short- and long-short portfolios are
consistently and considerably higher in event-time than in calendar-time. For the top uncertainty
quintile (Q5), market-adjusted long-short returns is 10.76 basis points per day for event-time port-
folio, but only 6.79 for calendar-time portfolio. The calendar-time alphas from the Table 6 are
similar to results shown here on the Panel B, confirming that the additional risk factors do not
explain much of the EARC abnormal return. This is to be expected because the EARC does not
select stocks based on firm characteristics.
These results are not to say which methodology is right or better. The difference simply indicates
that the abnormal returns tend to be higher when more firms are announcing on the same day. A
strategy that scales the portfolio size (dollar value) according to the number of announcing firms
could earn considerably higher market-adjusted returns than a strategy that has a fixed portfolio
size. The two methodologies are simply answering different questions.
Table E19 in Appendix E repeats the event-time portfolio analysis using the CRSP value-
weighted index instead of the equal-weighted index as benchmark. Comparing results its results to
those in Table 6, we see that the market-adjusted returns reduce by 10 to 20% simply by changing
the benchmark from the equal-weighted index to the value-weighted index. These results suggest
that either (1) the value-weighted index captures some time-varying equity premium in sync with
the EARC which the equal-weighted index fails to capture, or (2) the mechanical relation between
the EARC portfolios and the value-weighted index is quite strong. If (2) is partly the reason,
22
these two sets of results suggest that the EARC may be a phenomenon strong enough to move the
“market.” Similarly, the EARC could also move factor returns such as SMB and HML.
This section discusses two methodological challenges suffered by the conventional calendar-time
regression approach and proposes using event-time portfolio analysis and equal-weighted index as
partial solutions. Results in Table 7 points to the arbitrage cost hypothesis which is formally
tested in the next section. Results in Table E19 suggests that the EARC may be a phenomenon
strong enough to move the market. In the following tests, we focus on event-time analysis and use
equal-weighted index as the benchmark as they seem more appropriate for this study. All results in
previous sections hold and are usually stronger in event-time and when using CRSP equal-weighted
index.
4.8. The EARC and Limits to Arbitrage
Return predictability due to behavioral factors would appear to be mispricing in the eyes of
professional asset managers. After establishing the EARC and identifying analysts’ optimism cycle
as its potential cause, the natural next question is why the EARC persists. We argue that the
persistence of the EARC may be partly due to the difficulty in arbitraging trading opportunities
that come in waves. If markets were complete, informed investors could form portfolios of stock
futures to incorporate their knowledge about the EARC into prices. The portfolio of stock futures
is in effect the event-time portfolio discussed in the previous subsection. In practice, stock futures
are virtually non-existent. Thus the EARC strategy would have widely varying number of stocks in
the portfolio over a quarter. Supposed that a fund has a fixed amount of capital, it may optimally
choose to under-fund the strategy sometime and leave some “money on the table.” Conversely, if
the fund has enough capital can fully eliminate the mispricing in the EARC, the fund would often
have most of its capital idle when few firms are announcing earnings.
This section tests the limits to arbitrage hypothesis, which predicts a positive relationship
between number of same-day announcing firms and the EARC abnormal return. Table 7 from the
last subsection has alluded to some evidence in support of this prediction as the event-time EARC
market-adjusted returns are much higher than that in calendar-time. In the next set of tests, we
construct explicit measures of “event intensity” to directly link the number of same-day announcing
firms and EARC abnormal returns.
23
We construct two ex-post measures of “event intensity” called “Crowdedness” and “Crowded
Day” as described in Section 3.3. Then we sort stocks based on the two measures. In the “Crowd-
edness” portfolio construction, each portfolio has about the same number of stocks. The “Crowded
Day” portfolios are constructed by sorting on days based on the number of announcing firms. Each
“Crowded Day” portfolio has the about the same number of days with non-zero holdings but the
high “Crowded Day” portfolios have more stocks.
Table 8 presents the results. Each cell reports the quarterly average of daily market-adjusted
returns and t-values for the EARC strategy applied to the corresponding portfolio. Results in
the first two panels show that both measures of event intensity significantly and positively cor-
relates with the EARC abnormal returns, which is consistent with the prediction from the limits
to arbitrage hypothesis. The long-short market-adjusted return increases from 2.99 to 6.97 basis
points from Quintile 1 to 5 along the “Crowdedness” measure and from -0.93 to 6.34 along the
“Crowded Day” measure. The difference between Quintile 5 and 1 are statistically significant for
both measures with t-values equal to 3.14 and 3.73. The long-portfolios have more positive and the
short-portfolios have more negative market-adjusted returns as event intensity increases.8
The third panel uses illiquidity (Amihud (2002)) as an alternative measure of arbitrage costs
and yield consistent but less clear results. We see that the short-portfolio market-adjusted return
does not decrease with illiquidity but the long-portfolio with illiquid stocks earn significantly higher
market-adjusted return. This is consistent with the illiquidity premium (Amihud (2002)) which
leads to higher expected returns on the high illiquidity quintiles for both the long- and short-
EARC portfolios. Additionally, illiquidity may negatively correlates with investors’ attention, which
dampens the EARC phenomenon.
Figure 6 provides visualization of the relation between the EARC and event intensity. It shows a
similar “rainbow” pattern as in Figure 5 where event intensity positively correlates with the strength
of the EARC. The figure shows that firms announcing earnings around the peak of earnings seasons
receive about 1% higher valuation between earnings announcements. Gilbert, Hrdlicka, and Kamara
(2016) finds that earnings announcements tend to cluster along size and book-to-market equity. The
next subsection examines this aspect of “characteristic clustering” to see how it interacts with event
8Note that results on event intensity in this table is sensitive to the choice of benchmark and the choice ofevent-time or calendar-time approach for the reasons outlined in 4.7.
24
Fig. 6. Earnings Announcement Return Cycle and Event Intensity. This figure plots the average buy-and-hold market-adjusted return for U.S. common stocks traded in NYSE, Nasdaq and Amex covered by 5 or moreanalysts in the previous quarter from January 1985 to December 2015. The values are computed as in Figure 2.Crowdedness is computed ex-post by counting the total number of firms announcing on the same day in the givenquarter. Number of same-day announcing firms (crowdedness) increases from quintile 1 to 5 (Q1 to Q5).
intensity.
Overall, results in Table 8 strongly support the limits to arbitrage hypothesis. They confirm
the conjecture that abnormal returns are positively correlated with event intensity, indicated by
the spread between event-time and calendar-time market-adjusted returns in Table 7. To further
strengthen the limits to arbitrage interpretation, we present pricing results for portfolios constructed
by sorting on both uncertainty and event intensity in Table E20 in Appendix E. The results show
that uncertainty and event intensity jointly predict the strength of the EARC. Fama-MacBeth
(Fama and MacBeth (1973)) regressions results presented later confirm that event intensity signif-
icantly correlates with EARC returns even after controlling for various firm characteristics.
This section tests the limits to arbitrage hypothesis by constructing portfolios based on event
intensity and illiquidity (Amihud (2002)). The results strongly indicate that the EARC abnormal
returns are significantly higher for firms that announce earnings around the peak of “earnings
seasons” when arbitraging may be more difficult.
25
4.9. Additional Results
This section provides additional results which further characterize the EARC phenomenon. In
particular, we examine how subjectivity in valuations and earnings announcement clustering along
the book-to-market dimension affect the EARC abnormal return.
4.9.1. Valuation Subjectivity
Existing literature suggests that prices of glamour stocks and low profitability stocks (in addition
to the high uncertainty stocks analyzed above) are likely to fluctuate with investor sentiment (e.g.
Barberis and Shleifer (2003), Barberis, Shleifer, and Wurgler (2005) and Baker and Wurgler (2006)).
To the extent that analysts’ optimism and investor sentiments are related, one would expect the
EARC to be stronger among firms with low book-to-market equity and low profitability.
Table 9 present event-time pricing results on portfolios sorted quarterly based on lagged values
of book-to-market equity and profitability. We see that the EARC abnormal returns are highest for
stocks with low book-to-market equity (growth) and low profitability. The average daily market-
adjusted return for the event-time long-short portfolios increases from 3.51 basis points per day to
7.56 when we move from value stocks to growth stocks; from 4.35 basis points per day to 8.12 when
we move from high profitability stocks to low profitability stocks. The market-adjusted returns on
both the long- and short-portfolio increase in magnitude from value to growth. Low profitability
stocks do not have higher market-adjusted returns in the long-portfolio. Similar to the results on
illiquidity, this asymmetry is likely due to the profitability premium (e.g. Novy-Marx (2013), Ball,
Gerakos, Linnainmaa, and Nikolaev (2015), Ball, Gerakos, Linnainmaa, and Nikolaev (2016)).
4.9.2. Clustering along Book-to-Market Equity
Gilbert, Hrdlicka, and Kamara (2016) finds that the SMB and HML factors help explain the
seasonal concentration in CAPM alphas in months with many earnings announcements as earnings
announcements tend to cluster along the size and book-to-market dimensions. Such “characteristic
clustering” raises concern that the results on event intensity may be driven by clustering along
book-to-market equity rather than clustering of events.9 Results from a double sort based on
9Clustering on size does not seem to matter as shown from in Table E20.
26
book-to-market equity and event intensity confirm that the two variables jointly predict the EARC
return. Results and related discussion are in Table E21 in AppendixE.
4.10. The EARC and Characteristics
All results presented above are based on univariate portfolio sorting, and results on double
sorting are in Appendix E. In this last subsection of the empirical part, we jointly examine all char-
acteristics discussed above as to summarize the findings. Specifically, we conduct Fama-MacBeth
regressions (Fama and MacBeth (1973)) of daily market-adjusted return of the event-time EARC
portfolios on uncertainty, event intensity, book-to-market equity and profitability and test their
predictive power for the EARC abnormal return individually and jointly.
We construct the uncertainty measure using the first principle component of the four measures
discussed above: size, age, IVOL and CVOL.10 We log-transform these variables and (2) normalize
them to have mean of zero and standard deviation of 1 within each quarter. Then we perform
principle component analysis to compute a rotation matrix. The weights on the four variables for
the first principle component are:
w = (wsize, wage, wIV OL, wCV OL) = (−0.532,−0.461, 0.576, 0.415) (3)
Then we compute the uncertainty measure for each firm-announcement i as the dot product of the
weight and the standardized variables obtained in the first step:
Uncertaintyi = w · (sizestdi , agestdi , IV OLstdi , CV OLstd
i ) (4)
Finally, we normalize the uncertainty measure to have mean of zero and standard deviation of 1
within each quarter. We follow similar procedure to normalize log(crowdedness), book-to-market
and profitability by standardizing them quarter by quarter. Then we conduct Fama-MacBeth
regressions using these standardized measures of uncertainty, crowdedness, book-to-market equity
and profitability.
Table 10 presents the results. Each row represents one test and each column reports the time-
series averages of quarterly coefficient estimates and the t-values of the average. Each panel, or every
10This step is mainly to conserve table space. All uncertainty measures work individually, although not jointly.IVOL largely drives out the power of the other three variables when all four variables are included. This is to beexpected as they are proxies for the same underlying variable.
27
three rows tests one of the three hypotheses outlined in the previous subsections, individually or
jointly: (1) uncertianty positively correlates with optimism cycle, and therefore should positively
predict the EARC abnormal return, (2) limits to arbitrage implies that event intensity should
positively predict the EARC abnormal return and (3) valuations of growth and low profitability
firms are more subjective and therefore book-to-market equity and profitability should negatively
predict the EARC abnormal return.
The results are consistent with all predictions. Uncertainty, event intensity, book-to-market
equity and profitability individually and jointly predict the EARC abnormal returns. The ex-
planatory power of each individual predictor is economically large and statistically significant. For
instance, in the first panel, the “Constant” column shows the baseline EARC abnormal returns are
highly significant with long-short market-adjusted return of 5.84 basis points per day, 2.14 bps for
the long-portfolio and −3.49 for the short-portfolio. The “Uncertainty” column shows that a one
standard deviation increase in the standardized uncertainty measure is associated with 0.98 bps
increase, 1.65 bps decrease and 2.93 bps increase in the long-, short- and long-short portfolios. All
other panels show similar patterns which closely conform with all predictions from the hypotheses.
Results in the last panel shows that all four variables jointly predict the EARC abnormal returns.
Table 10 provides strong evidence that uncertainty, event intensity, book-to-market equity and
profitability capture important heterogeneity in the EARC strategy along different dimensions,
while all these variables point to the same behavioral interpretation of optimism cycle. With the
counterfactual portfolio results in Table 4, an alternative explanation would need to simultaneously
explain why the EARC abnormal returns mostly occur on days around analysts’ updates, and
significantly strongly among high uncertainty firms, firms that announce earnings with many other
firms, growth firms and low profitability firms. All these results collectively suggest that the
dynamics of investors’ bias in expectations strongly affect asset price movements. The assumption
of rational expectation indeed assumes away much of the variations in asset returns.
5. Discussion and Conclusion
This paper shows new evidence that behavioral factors such as investors’ optimism cycle are
important determinants of asset returns. We establish a new and robust stock return regularity, the
earnings announcement return cycle (EARC), that stocks widely followed by analysts outperform
28
in the early phase and underperform in the late phase of the earnings announcement cycle (ex-
cluding the earnings announcement period). The EARC abnormal returns are economically large
and highly statistically significant. Then we provide strong evidence that the EARC is primarily
driven by investors’ optimism cycle using a counterfactual portfolio approach. We further vali-
date the optimism channel by testing and exploiting the relation between analysts’ optimism cycle
and uncertainty. We show that uncertainty strongly and positively correlates with both analysts’
optimism cycle and the EARC.
We argue that in the time-series, the optimism cycle may be a manifestation of uncertainty
resolution over time. Investors start out being overly optimistic, but as new information arrives
and uncertainty gets resolved, they correct their biases. Using a simple theoretical model featuring
uncertainty resolution over time and managers’ endogenous decision on when to issue guidance, we
predict and empirically verify that the informativeness and the total number of guidance increase
as the next earnings announcement approaches. Then we show that management guidance is
important for the EARC as it accounts for about 30% of its abnormal return, but its effect is fully
captured by the optimism cycle.
The last section examines the role of limits to arbitrage along the dimension of event clustering.
We show that the EARC abnormal returns are significantly higher for firms which announce earnings
on the same time as many other firms. This aspect of limits to arbitrage points to an interesting
direction about event-time efficiency and calendar-time efficiency in financial markets. Event-time
analysis weighs each case equally as opposed to weighing each day equally as in calendar-time
analysis.
Event-time efficiency is perhaps as important as calendar-time efficiency, but it is less likely to
hold up due to the limits of arbitrage caused by event clustering. Our traditional tests for market
efficiency, primarily the alphas estimated from factor models in calendar-time regressions, is a blunt
tool when it comes to testing pricing around events. In fact, even when most cases are mispriced,
they can still appear to be correctly priced most of the time. To see why, imagine if the mispriced
events, potentially hundreds of them (each one is i.i.d.) happen on the same day but very few on
any other days. In event-time, the mispricing should be highly visible as each case is weighted
equally (e.g. Figure 1). In calendar-time, however, the hundreds of event returns on the same day
collapse to a few daily average returns which are weighted equally as any other days with little
29
Fig. 7. Earnings Announcement Return Cycle and Analyst Optimism. This figure plots the three-daymoving average of average daily market-adjusted return in earnings announcement event-time from t = −7 to 70,before and after removing stock-days within three-day windows around any annual earnings forecast revisions andrecommendation changes. The sample contains all U.S. common stocks traded in NYSE, Nasdaq and Amex coveredby 5 or more analysts in the previous quarter from January 1985 to December 2015. Daily market-adjusted returnfor stock-announcement i at event-time t is defined as EXReti,t = RETi,t −EWRETDi,t where RETi,t is the dailyreturn of the stock-announcement i at event-time t; EWRETDi,t is the daily CRSP equal-weighted index returnat event-time t. The solid line is identical to that in Figure 1. The dashed line is the same value computed afterremoving observations around analyst updates.
mispricing. Thus, it is difficult for the traditional calendar-time test to detect mispricing around
such events as there are very few data points with detectable alphas. In this paper, we argue
that event-time analysis is highly important when addressing the question of market efficiency.
Zero-alpha in calendar-time is not enough to support pricing efficiency around events, especially
when the events occur in waves as earnings announcements, IPOs and M&A do. New theories and
methodologies need to be developed to better understand and assess the pricing efficiency around
events.
The earnings announcement return cycle is a new return regularity. Figure 7 provides a visu-
alization of how much the analysts’ optimism cycle could “explain” the average EARC pattern,
indicated by the wide spread between the solid line and the dashed line. Although this paper
shows that the optimism cycle may be an important factor behind the EARC, much remains un-
explored. For instance, this paper does not discuss agency issues such as management’s incentives
and analysts’ incentives. It is possible, though perhaps hard to show, that the optimism cycle is
due to agency problem from managers, analysts or both. Managers may unintentionally exert their
30
overconfidence, or knowingly overpromise during earnings announcements for private benefits and
lead analysts to form to overly optimistic expectations. Or analysts may issue high estimates to
stimulate trading, “talk-up” the firms or in fear of losing future underwriting relation as suggested
by some existing literature. Asymmetric participation and short sale constraint could also exacer-
bate the EARC. It is important to disentangle the agency, market friction and behavioral channels
and to tell apart how much of the optimism cycle is from nature, and how much is from market
imperfection and incentive misalignment. These are all interesting questions which this paper does
not have room or resource to explore. Given the economic significance of the EARC and how little
we know about the actual process of investors’ belief formation, future research may greatly benefit
from more studies in this area like those by Bordalo, Gennaioli, La Porta, and Shleifer (2017) and
Malmendier, Nagel, and Yan (2017).
31
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Table 1: Summary StatisticsThis table reports summary statistics averaged by year. The sample spans fromJanuary 1985 to December 2015. The main sample is selected as U.S. commonequities (shrcd 10, 11 and exchcd 1, 2, 3) being covered by at least 5 analysts in theprevious quarter. Each observation is a firm-announcement, identified using permnoand rdq from Compustat. All variables are defined in Appendix A. Panel A reportsfirm characteristics for the main sample and excluded sample due to low analystcoverage. Panel B reports variables related to analyst in the periods between 6 and50 trading days after the most recent earnings announcements and Panel D reportsvariables related to management guidance. Analyst recommendation data startsfrom February 1994 due to data availability.
Panel A: Fundamental Variables
Main Sample Excluded Sample
Mean SD N Mean SD N
Market Value $mil. 6527.25 13926.34 4264.68 605.95 1410.85 13902.87Book-to-Market 0.61 0.43 4264.29 1.16 2.01 13901.71Profitability 0.07 0.09 3933.58 0.02 0.14 12566.42Dividend Paying 0.54 0.48 4266.13 0.31 0.46 14014.97News 22.22 28.17 4486.13 4.27 10.14 14854.53Days with news 11.72 10.37 4486.13 2.64 5.09 14854.53
Panel B: Analyst Related Variables
Mean SD Quartile 1 Quartile 3
Number of Analysts 10.60 5.93 6.13 13.29Number of Forecasts Revisions 6.10 6.99 1.64 7.81
Number of Upward Revisions 2.50 3.94 0.10 3.03Number of Downward Revisions 3.60 5.32 0.32 4.48
Number of Recom. Changes 0.56 0.96 0 0.91Number of Upgrades 0.27 0.59 0 0.18Number of Downgrades 0.29 0.63 0 0.23
36
Table 2: Calendar-time Regression Results for the EARC StrategyThis table reports daily calendar-time regression results. The portfolios are formed by buyingstocks from t = 6 to 20 and shorting those from t = 36 to 50 relative to the most recentearnings announcements. Each stock is weighed equally. The units are in basis points. Eachcolumn reports regression results for the long-short, long, or short portfolios. The last columnreports long-short portfolio regression results using the 4 factor + earnings announcementpremium (EAP) factor model. The EAP factor is constructed as the return on the long-shortportfolio which longs stocks within 10 days around an earnings announcements (from t = −10to t = 10), and shorts stocks that are at between t = 11 and t = 50. The sample contains U.S.common stocks followed by 5 or more analysts in the previous quarter and one-day laggedprices above $3 from 1985 to 2015. Standard errors are in parentheses.
CAPM 3-Factor + Momentum EAP
Long-short Long Short Long-short Long Short Long-short
Alpha 3.338 1.917 −1.421 3.426 2.505 −0.922 2.527(0.550) (0.550) (0.574) (0.551) (0.411) (0.430) (0.533)
MKT −0.038 1.071 1.109 −0.043 1.076 1.119 −0.038(0.005) (0.005) (0.005) (0.005) (0.004) (0.004) (0.005)
SMB −0.029 0.499 0.527 −0.018(0.009) (0.007) (0.007) (0.009)
HML −0.028 −0.019 0.010 −0.023(0.010) (0.008) (0.008) (0.010)
MOM −0.013 −0.184 −0.171 −0.015(0.007) (0.005) (0.006) (0.007)
EAP 0.321(0.014)
Observations 7,794 7,794 7,794 7,794 7,794 7,794 7,784Adjusted R2 0.01 0.86 0.86 0.01 0.92 0.92 0.07
Table 3: The EARC Strategy after Removing Analyst UpdatesThis table reports daily calendar-time regression results for the counterfactual portfolios. Theportfolios are formed by buying stocks from t = 6 to 20 and shorting those from t = 36 to50 relative to the most recent earnings announcements, after removing stock-days around anyanalyst forecast revisions and recommendation changes. Each stock is weighed equally. Theunits are in basis points. Each column reports regression results for the long-short, long, orshort portfolios. The last column reports long-short portfolio regression results using the 4factor + earnings announcement premium (EAP) factor model. The EAP factor is constructedas the return on the long-short portfolio which longs stocks within 10 days around an earningsannouncements (from t = −10 to t = 10), and shorts stocks that are at between t = 11and t = 50. The sample contains U.S. common stocks followed by 5 or more analysts in theprevious quarter and one-day lagged prices above $3 from 1985 to 2015. Standard errors arein parentheses.
CAPM 3-Factor + Momentum EAP
Long-short Long Short Long-short Long Short Long-short
Alpha 1.395 1.858 0.463 1.499 2.393 0.893 0.774(0.565) (0.564) (0.591) (0.565) (0.424) (0.441) (0.555)
MKT −0.037 1.053 1.089 −0.043 1.061 1.103 −0.038(0.005) (0.005) (0.005) (0.005) (0.004) (0.004) (0.005)
SMB −0.037 0.520 0.557 −0.027(0.010) (0.007) (0.008) (0.010)
HML −0.035 −0.023 0.012 −0.031(0.011) (0.008) (0.008) (0.010)
MOM −0.015 −0.170 −0.155 −0.017(0.008) (0.006) (0.006) (0.007)
EAP 0.257(0.014)
Observations 7,793 7,793 7,793 7,793 7,793 7,793 7,783Adjusted R2 0.007 0.848 0.845 0.010 0.915 0.914 0.048
37
Table 4: Change in Alphas after Removing Analysts’ UpdatesThis table reports the difference in factor model alphas estimated before and afterremoving stock-days within three-day windows of recommendation changes (“Re-com. Change”), analyst forecast revisions (“Revision”) and both (“Total” and“Total (post-94)”). Original alphas (the first column) are as reported in Table 2.The first number in each cell in column 2 to 9 are the alphas of portfolios whichlong the counterfactual portfolios and short the original portfolios. The “Recom.Change” and “Total (post-94)” panel use only data after February 1994 due toavailability of recommendation data. Number in parentheses are t-values. Unitsare in basis points.
Original Recom.Revision Total
TotalAlpha Change (Post-94)
CAPM
Long1.97 −0.49 0.20 −0.12 −0.49
(−4.18) (1.00) (−0.55) (−2.00)
Short−1.36 0.63 2.13 1.87 2.03
(4.75) (10.17) (8.62) (7.31)
Long-short3.34 −1.11 −1.88 −1.94 −2.49
(−6.43) (−6.62) (−6.59) (−6.88)
4-Factor
Long2.51 −0.52 0.17 −0.17 −0.54
(−4.51) (0.86) (−0.80) (−2.19)
Short−0.92 0.60 2.08 1.82 1.98
(4.59) (9.95) (8.39) (7.17)
Long-short3.43 −1.12 −1.85 −1.93 −2.47
(−6.51) (−6.50) (−6.54) (−6.83)
Table 5: Analysts’ Optimism, Walkdown and UncertaintyThis table reports univariate regression coefficients (with fixed effects) and t-values which showthe relations between analysts’ optimism (dependent variables) and lagged measures of uncer-tainty. Dependent variables are log-transformed, and both independent and dependent vari-ables are normalized quarterly to have mean of zero and standard deviation of one. Thus thecoefficients represent correlations (in percentages). Each observation is a firm-announcement.Dependent variables are “Early Optimism” and “Optimism Walkdown”. “Early Optimism” iscalculated using analysts’ quarterly earnings forecasts made during t = 0 to 10 in earnings an-nouncement event-time, actual values and stock prices at t = 0. “Optimism Walkdown” is thedifference between early optimism and optimism in the late phase (see Appendix A for details).“Size”, “Age”, “IVOL” and “CVOL” are market value, firm age, idiosyncratic volatility andcash flow volatility. All regressions include industry and year-quarter fixed effects. Standarderrors are clustered by Fama-French 49 Industries and year-quarter.
Early Optimism Optimism Walkdown
Size Age IVOL CVOL Size Age IVOL CVOL
Coef. −20.38 −7.49 26.67 10.99 −7.38 −2.29 11.82 5.28S.E. (1.48) (0.88) (2.61) (1.80) (0.99) (0.63) (1.81) (1.26)Observations 80,785 80,785 80,785 65,186 80,198 80,198 80,198 64,660Adjusted R2 0.10 0.07 0.11 0.07 0.05 0.04 0.05 0.05
38
Table 6: Uncertainty and EARC 4-factor AlphaThis table reports daily 4-factor alphas on calendar-time portfolios formed accordingto the EARC strategy, sorted quarterly based on lagged uncertainty. At the beginningof each calendar-quarter (January, April, July, and October), all stocks in the sampleare sorted based on the first principle component of size, age, idiosyncratic volatility,cash flow volatility. Long-portfolio contains stocks from t = 6 to 20 and short-portfoliofrom t = 36 to 50 relative to the most recent earnings announcements. “Long-Short”panel reports the long-short strategy alphas. Uncertainty increases from Q1 to Q5.Q5−Q1 shows the long-short alphas from longing the Q5 portfolio and shorting the Q1portfolio. In parentheses are t-values. Units are in basis points.
Q1 Q2 Q3 Q4 Q5 Q5−Q1
Long1.82 1.18 2.09 4.11 4.32 2.71
(2.52) (1.81) (2.95) (4.58) (3.70) (1.92)
Short0.25 −0.44 −0.84 −2.09 −2.72 −3.13
(0.32) (−0.62) (−1.11) (−2.27) (−2.20) (−2.10)
Long-Short1.67 1.68 2.98 6.22 7.02 5.59
(1.63) (1.86) (3.03) (5.06) (4.34) (2.81)
Table 7: EARC Abnormal Return in Event-time and Calendar-timeThis table reports daily market-adjusted returns on event-time and calendar-time port-folios sorted quarterly by lagged measures of uncertainty. At the beginning of eachcalendar-quarter (January, April, July, and October), all stocks in the sample are sortedbased on the first principle component of size, age, idiosyncratic volatility, cash flowvolatility. Long-portfolio contains stocks from t = 6 to 20 and short-portfolio fromt = 36 to 50 relative to the most recent earnings announcements. “Long-Short” panelreports the long-short strategy market-adjusted returns. Uncertainty increases from Q1to Q5. Q5−Q1 shows the long-short alphas from longing the Q5 portfolio and shortingthe Q1 portfolio. In parentheses are t-values. Units are in basis points.
Panel A: Event-time EARC Abnormal Return
Q1 Q2 Q3 Q4 Q5 Q5−Q1
Long1.07 1.25 1.92 2.81 4.78 3.70
(1.24) (1.93) (2.13) (2.49) (3.73) (2.20)
Short−1.25 −2.64 −3.11 −4.25 −5.98 −4.73
(−1.39) (−3.34) (−3.22) (−3.19) (−4.07) (−2.64)
Long-Short2.32 3.89 5.03 7.05 10.76 8.44
(2.40) (3.82) (4.62) (6.02) (7.13) (4.43)
Panel B: Calendar-time EARC Abnormal Return
Q1 Q2 Q3 Q4 Q5 Q5−Q1
Long1.08 0.33 1.22 2.95 3.06 2.18
(1.26) (0.47) (1.58) (2.65) (2.10) (1.17)
Short−0.68 −1.25 −1.71 −3.15 −3.92 −3.53
(−0.74) (−1.67) (−2.03) (−2.81) (−2.42) (−1.75)
Long-Short1.64 1.60 2.96 6.09 6.79 5.40
(1.69) (1.80) (3.19) (5.11) (4.40) (2.84)
39
Table 8: The EARC and Arbitrage DifficultyThis table reports average daily market-adjusted returns on portfolios sortedby number of firms announcing earnings on the day (Crowdedness and CrowdedDay). “Crowdedness” portfolios sort on stocks: there are equal number of stocksin each portfolio. “Crowded Day” portfolios sort on days, so there are equalnumber of days in each portfolio. Units are in basis points and t-values are inparentheses. “ILLIQ” portfolios are constructed by sorting on illiquidity (Ami-hud (2002)).
Q1 Q2 Q3 Q4 Q5 Q5−Q1
Crowdedness
Long0.85 2.01 2.31 2.45 2.52 1.67
(1.57) (2.24) (3.02) (2.59) (2.60) (1.55)
Short−1.89 −2.79 −4.02 −3.58 −4.31 −2.42
(−3.22) (−3.75) (−3.83) (−3.42) (−4.04) (−2.57)
Long-Short2.99 5.13 6.59 6.17 6.97 3.98
(3.79) (4.41) (5.89) (5.49) (6.06) (3.14)
Crowded Day
Long−0.90 0.29 0.16 2.43 2.27 3.17
(−0.76) (0.35) (0.24) (3.30) (2.77) (2.13)
Short0.72 −0.56 −2.31 −2.53 −3.86 −4.58
(0.61) (−0.56) (−2.71) (−3.64) (−3.94) (−3.44)
Long-Short−0.93 1.06 2.75 5.21 6.34 7.27
(−0.57) (0.72) (2.62) (4.58) (6.20) (3.73)
ILLIQ
Long0.59 2.41 1.80 2.38 3.09 2.50
(0.52) (3.39) (2.38) (3.63) (4.49) (2.16)
Short−3.47 −3.08 −4.15 −3.05 −2.51 0.96
(−2.55) (−3.62) (−5.57) (−3.62) (−2.78) (0.59)
Long-Short4.09 5.55 6.14 5.68 6.24 2.15
(3.89) (5.14) (6.88) (5.81) (5.56) (1.65)
Table 9: The EARC, Book-to-Market and ProfitabilityThis table reports average daily market-adjusted returns on event-time portfoliossorted by lagged values of book-to-market equity and profitability. All variabledefinitions are in Appendix A. Market-adjusted returns are benchmarked againstCRSP equal-weighted index. Units are in basis points and t-values are in parentheses.
Q1 Q2 Q3 Q4 Q5 Q5−Q1
Book-to-Market
Long3.61 2.35 1.82 1.74 0.66 −2.95
(2.43) (3.02) (2.37) (2.75) (1.03) (−1.78)
Short−3.77 −4.51 −3.46 −2.18 −2.38 1.39
(−2.56) (−4.26) (−5.36) (−3.31) (−2.55) (0.83)
Long-Short7.56 7.00 5.40 4.12 3.51 −4.05
(5.37) (6.67) (5.55) (4.66) (3.15) (−2.39)
Profitability
Long1.21 1.50 1.92 2.16 3.08 1.87
(0.77) (2.33) (2.91) (2.70) (4.06) (1.12)
Short−6.10 −4.33 −3.25 −2.29 −1.16 4.94
(−3.49) (−5.08) (−5.54) (−3.25) (−1.37) (3.49)
Long-Short8.12 5.96 5.23 4.46 4.35 −3.78
(5.68) (6.63) (6.52) (4.72) (4.44) (−2.81)
40
Table 10: Fama-MacBeth Regressions: Variations in the EARC ReturnsThis table presents Fama-MacBeth (Fama and MacBeth (1973)) regression results of event-time EARC returnsregressed on uncertainty, event intensity, book-to-market equity and profitability. Each cell reports the time-seriesaverage of the coefficient estimates and the corresponding t-value in parentheses. The coefficients are estimatedquarterly from January 1985 to December 2015. The dependent variables in the first stage are average daily market-adjusted returns (in basis points) when (1) the stocks are 6 to 20 trading days, and (2) 36 to 50 trading days afterthe latest earnings announcements, and (3) the difference in average daily market-adjusted returns between the twoholding periods. Results are reported in the “Long”, “Short”, and “Long-short” rows respectively. We use CRSPequal-weighted index to proxy for the market portfolio. “Uncertainty” is the first principle component of the within-quarter standardized log-transformed values of previous quarter-end firm size, firm age, idiosyncratic volatility andcash flow volatility. “Crowdedness” is the log of number of firms announcing earnings on the day. “BM” is book-to-market equity in the previous quarter. “Profitability” is return on book equity in the previous quarter. Allexplanatory variables are winsorized at the 1st and 99th percentile, and standardized within each quarter. The firstcolumn labels the hypothesis which the regressions are testing. t-values are adjusted for time-series autocorrelationof the coefficient estimates.
Constant Uncertainty Crowdedness BM Profitability
Uncertainty and Optimism (H1)
Long2.37 1.30
(3.46) (2.11)
Short−3.45 −1.61
(−4.10) (−2.46)
Long-short5.81 2.91
(6.79) (4.30)
Limits to Arbitrage (H2)
Long2.26 0.63
(3.63) (1.96)
Short−3.27 −0.82
(−4.42) (−2.52)
Long-short5.54 1.46
(6.89) (3.55)
Valuation Subjectivity (H3)
Long2.16 −0.83 0.01
(3.27) (−1.60) (0.01)
Short−3.36 1.00 1.69
(−4.27) (1.79) (3.11)
Long-short5.53 −1.84 −1.68
(6.83) (−3.81) (−4.30)
(H1) + (H2) + (H3)
Long2.31 1.38 0.90 −0.88 0.17
(3.38) (2.36) (2.56) (−1.61) (0.37)
Short−3.49 −1.46 −1.05 0.79 1.32
(−4.15) (−2.44) (−2.66) (1.44) (2.45)
Long-short5.80 2.83 1.96 −1.67 −1.15
(6.76) (4.14) (3.74) (−3.52) (−2.89)
41
Ap
pen
dix
A.
Vari
ab
leD
efi
nit
ion
s
Tab
leA
11:
Vari
ab
leD
efin
itio
ns
Th
ista
ble
defi
nes
the
mai
nva
riab
les
use
din
this
stu
dy.
Th
efi
rst
colu
mn
show
sth
en
am
eof
the
vari
ab
les
as
refe
rred
toin
the
text.
Th
e
seco
nd
colu
mn
des
crib
eh
owth
eva
riab
les
are
con
stru
cted
.T
he
thir
dco
lum
nli
sts
rele
vant
the
vari
ab
len
am
esin
the
data
base
.T
he
fort
h
colu
mn
list
sth
eco
rres
pon
din
gd
ata
sou
rce.
Vari
ab
len
am
eD
efi
nit
ion
Data
Item
Data
Sou
rce
Mar
ket
Val
ue
Clo
sin
gst
ock
pri
cesi
xtr
ad
ing
day
s(o
rla
stqu
art
eren
d,or
last
year
end
dep
end
ing
onap
pli
cati
on)
pri
orto
earn
ings
an
nou
nce
men
tm
ult
ipli
edby
nu
mb
erof
share
s
outs
tan
din
g
prc
,sh
rou
t,rd
qC
RS
P,
Com
-
pu
stat
Book
-to-
Mar
ket
Book
valu
eof
equ
ity
div
ided
by
mark
etva
lue
at
the
end
of
pre
vio
us
year
seqq
,tx
dit
cq,
pst
kq,
prc
,
shro
ut
CR
SP
,C
om
-
pu
stat
Book
Val
ue
ofE
qu
ity
Book
valu
eof
stock
hold
ers
equ
ity,
plu
sb
ala
nce
shee
td
efer
red
taxes
an
din
vest
men
t
tax
cred
it(i
fav
aila
ble
),m
inu
sth
eb
ook
valu
eof
pre
ferr
edst
ock
(if
avail
ab
le)
seqq
,tx
dit
cq,
pst
kq
Com
pu
stat
Ass
etG
row
thT
otal
asse
td
ivid
edby
tota
lass
etin
the
pre
vio
us
qu
art
erm
inu
sone
atq
Com
pu
stat
Pro
fita
bil
ity
Rev
enu
em
inu
sco
stof
good
sold
min
us
sell
ing,gen
eralan
dad
min
istr
ati
ve
exp
ense
s
(if
avai
lab
le),
min
us
inte
rest
an
dre
late
dex
pen
se,
all
div
ided
by
lagged
book
equ
ity
revt
q,co
gsq,
xsga
q,xi
ntq
,
BE
Com
pu
stat
Div
iden
dP
ayin
gIn
dic
ator
vari
able
:1
ifth
efi
rmp
ays
at
least
on
ere
gu
lar
div
iden
d(fi
rst
3d
igit
sof
dis
trib
uti
onco
de
120,
123,
124,
125)
wit
ham
ou
nt
gre
ate
rth
an
0w
ith
inth
ela
st
200
day
sb
efor
eth
ela
stea
rnin
gs
an
nou
nce
men
t;0
oth
erw
ise
dis
tcd,
div
am
t,
rdq
CR
SP
,C
om
-
pu
stat
New
sT
he
nu
mb
erof
new
sfr
om
2to
59
day
saft
eran
earn
ings
an
nou
nce
men
t,ex
clu
d-
ing
new
sgr
oup
s:an
aly
st-r
ati
ngs,
earn
ings,
pri
ce-t
arg
ets,
stock
-pri
ces,
reve
nu
es,
tech
nic
alan
alysi
s
grou
p,
rdq
Rav
enp
ack
,
Com
pu
stat
Day
sw
ith
New
sT
he
nu
mb
erof
day
sw
ith
new
sfr
om
2to
59
day
saft
eran
earn
ings
an
nou
nce
men
tN
ews,
rdq
Rav
enp
ack
,
Com
pu
stat
42
Ear
nin
gsY
ield
(%)
Act
ual
qu
arte
rly
earn
ings
per
share
div
ided
by
stock
pri
cesi
xd
ays
bef
ore
the
earn
ings
ann
oun
cem
ent,
inp
erce
nta
ge
act
ual,
prc
CR
SP
,
I/B
/E
/S
Nu
mb
erof
An
alyst
sN
um
ber
ofu
niq
ue
analy
sts
wh
ois
sue
an
nu
alea
rnin
gs
fore
cast
sin
the
90
day
sp
rior
toth
ep
revio
us
earn
ings
an
nou
nce
men
t
an
aly
s,va
lue,
an
ndats
,rd
q
I/B
/E
/S
,
Com
pu
stat
Nu
mb
erof
For
ecas
ts
Rev
isio
ns
Th
enu
mb
erof
annu
al
earn
ings
fore
cast
mad
eby
the
sam
ean
aly
stfo
rth
esa
me
firm
and
sam
efi
scal
per
iod
wit
ha
pre
vio
us
non
-id
enti
cal
valu
ew
ith
in200
day
s.
On
lyco
nsi
der
revis
ion
sb
etw
een
6an
d50
trad
ing
day
saft
erth
ela
stea
rnin
gs
ann
oun
cem
ent
an
aly
s,va
lue,
an
ndats
,an
n-
dats
act
,rd
q
I/B
/E
/S
,
Com
pu
stat
Day
sw
ith
Rev
isio
ns
Nu
mb
erof
day
sw
ith
fore
cast
revis
ion
san
aly
s,va
lue,
an
ndats
,an
n-
dats
act
,rd
q
I/B
/E
/S
,
Com
pu
stat
Nu
mb
erof
Upw
ard
Rev
isio
ns
Nu
mb
erof
revis
ion
sw
ith
curr
ent
valu
egre
ate
rth
an
the
pre
vio
us
valu
e.P
revio
us
valu
em
ust
be
wit
hin
200
day
sb
efore
the
curr
ent
valu
ean
dfo
rth
esa
me
fisc
al
per
iod
an
aly
s,va
lue,
an
ndats
,an
n-
dats
act
,rd
q
I/B
/E
/S
,
Com
pu
stat
Nu
mb
erof
Dow
nw
ard
Rev
isio
ns
Nu
mb
erof
revis
ion
sw
ith
curr
ent
valu
egre
ate
rth
an
the
pre
vio
us
valu
e.P
revio
us
valu
em
ust
be
wit
hin
200
day
sb
efore
the
curr
ent
valu
ean
dfo
rth
esa
me
fisc
al
per
iod
an
aly
s,va
lue,
an
ndats
,an
n-
dats
act
,rd
q
I/B
/E
/S
,
Com
pu
stat
Nu
mb
erof
Rec
om.
Ch
ange
s
Th
enu
mb
erof
stock
reco
mm
end
ati
on
sm
ad
eby
the
sam
ean
aly
stfo
rth
esa
me
stock
wit
ha
pre
vio
us
non
-id
enti
cal
reco
mm
end
ati
on
wit
hin
200
day
s.O
nly
con
sid
er
reco
mm
end
atio
nch
an
ges
bet
wee
n6
an
d50
trad
ing
day
saft
erth
ela
stea
rnin
gs
ann
oun
cem
ent.
Rec
om
men
dati
on
data
start
sfr
om
Feb
ura
ry1994
irec
cd,
am
ask
cd,
an
ndats
,rd
q
I/B
/E
/S
,
Com
pu
stat
Nu
mb
erof
Up
grad
esN
um
ber
ofre
com
men
dati
on
sw
ith
curr
ent
valu
elo
wer
than
the
pre
vio
us
valu
e.
Pre
vio
us
valu
em
ust
be
wit
hin
200
day
sb
efore
the
curr
ent
valu
e
irec
cd,
am
ask
cd,
an
ndats
,rd
q
I/B
/E
/S
,
Com
pu
stat
Nu
mb
erof
dow
ngr
ades
Nu
mb
erof
reco
mm
end
ati
on
sw
ith
curr
ent
valu
eh
igh
erth
an
the
pre
vio
us
valu
e.
Pre
vio
us
valu
em
ust
be
wit
hin
200
day
sb
efore
the
curr
ent
valu
e
irec
cd,
am
ask
cd,
an
ndats
,rd
q
I/B
/E
/S
,
Com
pu
stat
43
For
ecas
tE
rror
(FE
)Q
uar
terl
yea
rnin
gsfo
reca
stva
lue
min
um
act
ualva
lue
div
ided
by
closi
ng
stco
kp
rice
onth
ela
stea
rnin
gsan
nou
nce
men
td
ay.
Th
isva
lue
isw
inso
rize
dat
the
5th
an
d
95th
per
centi
le
valu
e,act
ual,
an
ndats
,rd
q,
prc
I/B
/E
/S
,
CR
SP
,C
om
-
pu
stat
Ear
lyO
pti
mis
m
(Eop
)
Th
em
edia
nF
Efr
omt
=0
to10
inea
rnin
gs
an
nou
nce
men
tev
ent-
tim
e,av
eraged
acro
ssth
en
ext
fou
rquart
erly
fore
cast
per
iod
s.T
his
calc
ula
tion
requ
ires
non
-
mis
sin
gm
edia
nF
Efo
rall
four
qu
art
ers
ah
ead
.
FE
I/B
/E
/S
,
CR
SP
,C
om
-
pu
stat
Lat
eO
pti
mis
m(L
op
)T
he
med
ian
FE
from
t=
4to
50
inea
rnin
gs
an
nou
nce
men
tev
ent-
tim
e,av
eraged
acro
ssth
en
ext
fou
rquart
erly
fore
cast
per
iod
s.T
his
calc
ula
tion
requ
ires
non-
mis
sin
gm
edia
nF
Efo
rall
four
qu
art
ers
ah
ead
.
FE
I/B
/E
/S
,
CR
SP
,C
om
-
pu
stat
Op
tim
ism
Wal
kd
own
Th
ed
iffer
ence
bet
wee
nea
rly
op
tim
ism
(Eop
)an
dla
teop
tim
ism
(Lop
)E
op,
Lop
I/B
/E
/S
,
CR
SP
,C
om
-
pu
stat
Man
agem
ent
Gu
idan
ce
Nu
mb
erof
day
sm
an
agem
ent
issu
egu
idan
cew
ith
in6
to50
day
saft
erth
ela
st
earn
ings
ann
oun
cem
ent.
Data
start
sfr
om
Janu
rary
1993
guid
an
ceco
de,
an
ndats
,rd
q
I/B
/E
/S
,
Com
pu
stat
Gu
idan
ceA
bov
e
Con
sen
sus
Nu
mb
erof
day
sw
ith
gu
idan
ceab
ove
con
sen
sus
guid
an
ceco
de,
an
ndats
,rd
q
I/B
/E
/S
,
Com
pu
stat
Gu
idan
ceB
elow
Con
sen
sus
Nu
mb
erof
day
sw
ith
gu
idan
ceb
elow
con
sen
sus
guid
an
ceco
de,
an
ndats
,rd
q
I/B
/E
/S
,
Com
pu
stat
Gu
idan
ceM
atch
Con
sen
sus
Nu
mb
erof
day
sw
ith
gu
idan
cem
atc
hin
gco
nse
nsu
sgu
idan
ceco
de,
an
ndats
,rd
q
I/B
/E
/S
,
Com
pu
stat
IVO
LS
tan
dar
dd
evia
tion
of
4-f
act
or
mod
elre
sid
uals
ina
250-d
ayw
ind
owR
ET
CR
SP
CV
OL
Sta
nd
ard
dev
iati
onof
cash
flow
from
op
erati
on
sin
the
past
five
years
.C
FO
,T
A,
atq
Com
pu
stat
Cas
hfl
owfr
om
oper
atio
n(C
FO
)
Ear
nin
gsb
efor
eex
traord
inary
item
sm
inu
sto
tal
acc
ruals
,sc
ale
dby
aver
age
tota
l
asse
ts
ibq,
TA
Com
pu
stat
Tot
alac
cru
als
(TA
)C
han
ges
incu
rren
tass
ets
min
us
chan
ges
inca
sh,
chan
ges
incu
rren
tli
ab
ilit
ies,
an
d
dep
reci
atio
nex
pen
se,
plu
sch
an
ges
insh
ort
term
deb
t
act
q,ch
eq,
lctq
,dpq
,dlc
q
Com
pu
stat
44
Appendix B. Analysts’ Update Cycle
This appendix provide test results which formally show that analysts’ updates conform a periodic pattern.
We divide each stock-announcement observation into three stock-announcement-phases. Phase 1 spans from
t = 6 to t = 20; phase 2 from t = 21 to t = 35; phase 3 from t = 36 to t = 50. Any observations outside
phase 1, 2 and 3 are excluded. Within each stock-announcement-phase, we calculate the total number of
forecast revisions and recommendation changes and how many of them are upward or downward. Then we
run the following regression:
Updatei = β1Phase1i + β2Phase3i + β3β3β3zizizi + εi (B1)
where i indexes for firm-announcement-phase observation. Updatei includes a collection of variables describ-
ing analysts’ behaviors including: (1) percentage of upward updates (“Percent up”), (2) whether there is
at least one upward update (“Up Dummy%”), (3) whether there is at least one downward update (“Down
Dummy%”), (4) the difference between “Up Dummy%” and “Down Dummy%”. Phase1i is an indicator
variable which equals one if the observation is in phase 1, zero otherwise. Phase3i is an indicator variable
which equals one if the observation is in phase 3, zero otherwise. Phase 2 is the omitted category. zi is a set
of controls which include market value, book-to-market equity, profitability and number of analysts and fixed
effects. εi is the error term. The same specification is run for both forecast revisions and recommendation
changes. The coefficients of interest are β1 and β2. Given the pattern we see from Figure 1 and Figure 3,
we expect β1 to be positive and β2 to be negative in most specifications. We do not include many firm level
controls because all regressions are run with either firm-announcement fixed effects or firm and quarter fixed
effects. Table B12 presents the results.
The results confirm the visual evidence presented above that analysts systematically issue more downward
forecast revisions and recommendation downgrades in the late phase of the earnings cycle.11 Column 1 of
Panel A shows that the percentage of upward forecast revisions is 3.46 percentage points higher in phase
1 than in phase 2; 2.38 percentage points lower in phase 3 than in phase 2. Thus the difference between
phase 1 and 3 is about 5.84 percentage points. Both β1 and β2 are highly statistically significant and
so is their difference. Column 2 shows slightly stronger results using firm level controls and replacing firm-
announcement fixed effects by firm and year-quarter fixed effects. Column 3 and 4 show that upward revisions
are more likely both in phase 1 and phase 3. In unreported analysis, we find that the increased likelihood
11Results are also consistent with Richardson et al. (2004) and others who find the walking-down of analysts’estimates. Our emphasis here is that the walking-down appears to accelerate in the late phase.
45
of upward revision in phase 3 is due to the higher number of total revisions as earnings announcement
approaches. Column 5 and 6 show a significantly higher likelihood of around 4.74% for a firm having at least
one downward revision in phase 3 than phase 2. Column 7 and 8 show that the difference in the likelihood
of having at least one upward revision and at least one downward revisions is 4.67 percentage points higher
in phase 1 than in phase 2; the same ratio is about 3.26 percentage points lower in phase 3 than in phase 2.
Thus the difference in the spread between upward and downward revision likelihood is around 7.9 percentage
points between phase 1 and phase 3.
The same tests using recommendation changes yield similar results. Note that in column 1, none of the
coefficients are significant because there are very few firm-announcements with recommendation changes in
different phases. Column 2, 5, 6, 7 and 8 show that stock downgrades are significantly more common in
phase 3. In terms of magnitude, the unconditional probability of having any recommendation changes in
a given stock-announcement-phase is around 13.7%. Thus 0.749% in column 5 represents 5.4% difference
from the baseline. Overall the results in Table B12 strongly indicate that downward forecast revisions and
recommendation changes are significantly more likely in phase 3 than in phase 1.
46
Table B12: Analysts’ Forecast Revision and Recommendation Change CycleThis table reports panel regression results on the difference in analyst behaviors over the earnings cycle.Each observation is a firm-announcement-phase. Panel A shows results for annual earnings forecastrevisions and Panel B shows results for recommendation changes. “Phase 1” is from t = 6 to 20 relativeto earnings announcements. Phase 2 is the omitted category, which is from t = 21 to 35. “Phase 3” isfrom t = 36 to 50. All firm characteristics are as defined in Table A11. “Percent Up” is the percentageof upward revisions or upward recommendation changes. “Up Dummy%” is equal to 100 if there is atleast one upward revision or stock upgrade, zero otherwise. “Down Dummy%” is defined analogously.“Up − Down%” is equal to “Up Dummy%” minus “Down Dummy%”. Column 1, 3, 5 and 7 includefirm-quarter fixed effects. Column 2, 4, 6 and 8 include firm fixed effects and year-quarter fixed effects.Standard errors in parentheses are clustered by Fama-French 49 Industries and year-quarter.
Panel A: Earnings Forecast Revisions
Percent up Up Dummy% Down Dummy% Up − Down%
Phase 1 (t = 6 to 20) 3.460 4.218 4.533 4.308 −0.133 −0.347 4.666 4.655(0.451) (0.376) (0.973) (0.799) (0.960) (0.787) (0.539) (0.451)
Phase 3 (t = 36 to 50) −2.380 −2.654 1.478 1.221 4.739 4.417 −3.261 −3.196(0.426) (0.418) (0.828) (0.629) (0.895) (0.648) (0.615) (0.529)
log(Market Value) 0.689 3.689 3.378 0.311(0.616) (0.418) (0.446) (0.679)
Book-to-Market −9.218 −3.039 7.905 −10.944(1.170) (0.750) (0.755) (1.264)
Profitability 46.805 25.868 −27.168 53.036(5.691) (3.351) (3.712) (5.925)
Analysts −0.478 0.724 1.326 −0.602(0.076) (0.077) (0.094) (0.101)
Firm-Announcement F.E. Y Y Y YFirm F.E. Y Y Y YYear-Quarter F.E. Y Y Y YObservations 249,845 230,707 396,750 365,667 396,750 365,667 396,750 365,667Adjusted R2 0.420 0.097 0.263 0.156 0.299 0.164 0.233 0.051
Panel B: Recommendation Changes
Percent up Up Dummy% Down Dummy% Up − Down%
Phase 1 (t = 6 to 20) 0.785 2.714 0.022 −0.017 −0.783 −0.880 0.805 0.864(2.747) (1.033) (0.271) (0.226) (0.357) (0.283) (0.379) (0.305)
Phase 3 (t = 36 to 50) −2.214 −2.405 −0.044 −0.077 0.749 0.655 −0.792 −0.732(2.494) (0.999) (0.249) (0.203) (0.274) (0.228) (0.366) (0.313)
log(Market Value) −0.191 1.044 1.239 −0.195(0.726) (0.199) (0.237) (0.217)
Book-to-Market −3.892 −0.452 0.581 −1.034(1.091) (0.314) (0.423) (0.316)
Profitability −14.559 −4.008 0.498 −4.506(4.223) (1.065) (0.882) (1.043)
Analysts −0.053 0.256 0.267 −0.011(0.043) (0.033) (0.036) (0.019)
Firm-Announcement F.E. Y Y Y YFirm F.E. Y Y Y YYear-Quarter F.E. Y Y Y YObservations 42,248 39,372 289,623 268,536 289,623 268,536 289,623 268,536Adjusted R2 0.030 0.023 0.071 0.035 0.085 0.046 −0.003 0.000
47
Appendix C. A Simple Model of Uncertainty Resolution and Man-
agement Guidance
This section provides a simple model featuring resolution of uncertainty over time. The model provides
several testable implications about the role of management guidance on the EARC abnormal returns. Then
we test these implications and present results.
D1. Model Setup
1. Three periods: t = 1, 2, 3.
2. Two agents: an analyst (A) and a manager of a firm (M).
3. The firm receives random cash flow at the end of each period: x1, x2, x3.
4. Manager announces the total cash flow of the firm at the end of period 3: x = x1 + x2 + x3.
5. The analyst gives a forecast of the total earnings at the beginning of period 1: FA.
6. The manager randomly observe interim cash flow once: x1 at period 1 (t = 1) with probability p, or
x1 + x2 at period 2 (t = 2) with probability 1− p.
7. After observing the cash flow, manager computes his own unbiased forecast (FM ) and standard error
of his forecast (σM ) and decides whether to make this forecast public by issuing management guidance.
D2. Assumptions
1. Cash flows are i.i.d. and normally distributed: xi ∼ N (µ, σ2) for all i.
2. Manager is equally likely to observe cash flow x1 or x1 + x2: p = 0.5.
3. Analyst’s estimate has an exogenous bias: FA = 3µ+ b, b > 0.
4. Manager chooses whether to issue guidance G ∈ {0, 1} to minimize a loss function:
minG
a
∣∣FA(1− I(G)) + FMI(G)− FM∣∣
σM+ cI(G) (D2)
where I(G) is an indicator function equal to 1 if G = 1; a is the per unit standard deviation cost of
letting investors have biased expectation (such as probability of litigation); c is the cost of disclosing
manager’s forecast.
Uncertainty resolution over time is embedded in the manager’s information structure. When he observes
cash flow in period 2 rather than period 1, he obtains a more precise estimate of the actual total earnings
48
in period 3. In setup 6, manager only observes cash flow once and he chooses when to observe randomly by
assumption 2. This is to turn off channels other than uncertainty resolution. One can imagine this as the
CEO visiting the stores once every quarter and randomizing the time of visiting. Assumption 4 means that
the manager cares about giving accurate information to investors, but giving this information incurs some
costs. Thus, he issues guidance only when the prevailing estimation is too far off. For simplicity, the model
also assumes management guidance is the only source of information for the analyst.12
This model yields the following predictions:
1. There are more downward guidance than upward guidance
2. For sufficiently low value of bias b and/or sufficiently high disclosure threshold k, there are more
downward guidance in period 2 than in period 1
3. There are more upward guidance in period 2 than in period 1
4. Management guidance is more sensitive to expected forecast error in period 2 than in period 1
D3. Solving the Model
From equation D2, we know that the manager follows a simple decision rule: issue guidance if |FA − FM | >
kσM , where k = c/a.
Manager’s forecasts conditional on observing x1 or x1 + x2 are given by: FM,1 = E[x | x1] = x1 +
2µ; FM,2 = E[x | x1 + x2] = x1 + x2 + µ. The standard errors of the estimates are: σM,1 =√
2σ; σM,2 = σ.
Uncertainty resolution over time is shown here as the decreasing standard error for manager’s estimate from
period 1 to period 2.
Proof of prediction 1 to 4 : If manager observes cash flow at period 1 (t = 1), his probability of issuing
downward guidance is given by:
Pr(G1 = Down|t = 1) =Pr(FA − FM,1 > kσM,1) = Pr(µ+ b− x1 > k√
2σ)
=Pr(x1 − µσ
<b
σ−√
2k)
=Φz(b
σ−√
2k) (D3)
12Note that this model assumes the manager responds to optimism and pessimism symmetrically for demonstrativepurpose only. This assumption is clearly violated in the data. The relevant predictions for equation D7 still holdafter allowing for asymmetric response from manager.
49
where Φz is the cumulative distribution function of the standard normal distribution. The probability of the
manager issuing downward guidance given t = 2 is:
Pr(G2 = Down|t = 2) =Pr(2µ+ b− x1 − x2 > kσ)
=Pr(x1 + x2 − 2µ√
2σ<
b√2σ− k√
2
=Φz(b√2σ− k√
2) (D4)
When b√2σ− k√
2> b
σ −√
2k, or equivalently, b < kσ(√
2 + 1), there are more downward guidance at
period 2 is more common than period 1 (prediction 2).
Similarly, the probability of upward guidance in the two periods are:
Pr(G1 = Up|t = 1) =1− Φz(b
σ+√
2k) (D5)
Pr(G2 = Up|t = 2) =1− Φz(b√2σ
+k√2
) (D6)
Since b√2σ
+ k√2< b
σ +√
2k, there are more upward guidance in period 2 than in period 1 (prediction 3).
Because Pr(G1 = Down|t = 1) > Pr(G1 = Up|t = 1) and Pr(G2 = Down|t = 2) > Pr(G2 = Up|t = 2),
for reasonable values of b and k, there are more downward guidance than upward guidance (prediction 1).
Manager issues guidance when |FA − FM1| > k√
2σ in period 1, and when |FA − FM1| > kσ in period 2.
As it requires a smaller absolute forecast error to trigger management guidance, it follows that the sensitivity
of management guidance to expected forecast error is higher in period 2 than in period 1 (prediction 4).
D4. Discussion
These predictions provide a simple empirical specification for management guidance which includes
interaction terms of analysts’ optimism and earnings announcement event-time:
Guidei = α+ β1Phase1i + β2Phase3i + β3Optimismi
+ β4(Optimismi × Phase1i) + β5(Optimismi × Phase3i) + γizi + ei (D7)
where Guidei is an indicator variable of whether there is at least one guidance (any guidance or guidance
50
of specific type, Guidei ∈ {Upi, Downi, Anyi}) for the firm-announcement-phase. Phase1i and Phase3i are
indicator variables which equal one if the observation is in phase 1 (t = 6 to 20) or in phase 3 (t = 36 to
50), zero otherwise. Optimismi is the median value of the difference between forecast and actual earnings
during the previous phase of 15 trading days scaled lagged stock prices. If Guidei = Anyi, we take absolute
value of Optimismi. zi is a vector of firm-announcement level controls including lagged market value,
book-to-market equity, profitability and number of analysts, and fixed effects.
As a result of uncertainty resolution, managers issue more guidance in the late phase and these guidance
are more sensitive to analysts’ forecast errors. Thus when analysts respond to manager’s guidance, the
optimism cycle would emerge. That is, analysts correct their bias over time and do so at an increasing rate
(consistent with Figure 1). This model implies that information arrival such as management guidance may
be an important driver behind analysts’ revision cycle. To test this hypothesis, we estimate the model in
equation D7 and then apply the counterfactual portfolio approach to test the importance of management
guidance to the EARC abnormal return.
Existing literature in accounting suggests that managers have incentives to beat estimates and issue
downward guidance prior to earnings announcements. One can also test the strength of this incentive
channel by estimating equation D7 and compare the sensitivity to forecast error between upward guidance
and downward guidance.
D5. Empirical Results
Table D13 provides results which characterize management guidance behavior based on equation D7.
Consistent with the predictions on increasing informativeness and frequency of earnings guidance over time,
we see from column 1 and 2 that phase 1 has significantly fewer management guidance than phase 2 and
3. More importantly, from row 5 (β5 in equation D7) we see that management guidance is more strongly
correlated with lagged absolute value of optimism. The coefficient 0.451 means that one percentage point
in the absolute optimism prior to phase 3 is associated with an additional 0.451 percentage point (or about
5.6% of the unconditional mean) increase in the likelihood of the firm issuing guidance in phase 3.
Columns 3 through 8 indicate that there is a higher percentage of downward guidance in phase 3 (row
2), and an asymmetry in firms’ response to optimism and pessimism (row 6, 7 and 8). The increasing
sensitivity to forecast error is much stronger for downward guidance, which is consistent with existing
literature such as Matsumoto (2002) who shows that firms have incentives to avoid disappointment during
earnings announcements. Thus it seems that managers’ incentives to beat estimate is also an important
51
Fig. 8. Ratio of Upward and Downward Guidance in Event-time. This figure plots the ratio of upwardand downward guidance from 10 days before to 70 days after the most recent earnings announcements. Data is fromthe I/B/E/S guidance database. Although data coverage starts from 1993, the coding of guidance direction is onlyavailable after 2001. The values are computed as the ratio of all upward guidance and downward guidance on eachevent-time.
factor which helps explain the negative premium prior to earnings announcements as pointed out in Kim
and So (2016).
Results from Table D13 supports the predictions from a simple model featuring uncertainty resolution
over time. Based on the previous results on the link between uncertainty and optimism, Table D13 also
implies a connection between information arrival and analysts’ optimism cycle. Thus we expect that infor-
mative events such as management guidance should have significant power in explaining the EARC return
as they correct analysts’ estimates.
Table D14 shows the results of counterfactual portfolio test about management guidance. As expected,
we see that management guidance explains a significant fraction (about one-third) of the EARC abnormal
return as indicated by column 4 and 5. The EARC alphas decrease by about one basis points after remov-
ing stock-days around management guidance. A comparison between the “Analyst Total” panel and the
“Analyst+Guidance” panel shows that guidance does not seem to add explanatory power beyond analyst
updates, indicating that analysts fully respond to management guidance. Panel “Analyst−Guidance” shows
that management guidance accounts for about half of the explanatory power of analyst updates to the EARC
abnormal return, highlighting the importance of information arrival in correcting analysts’ biases.
Figure 8 plots the percentage of upward guidance over the sum of upward and downward guidance in
the earnings announcement event-time. It shows a similar pattern as analysts’ revisions in Figure 1 and
52
recommendation changes in Figure 3 that downward guidance is more common than upward in the late
phase. Our model where managers symmetrically respond to positive and negative forecast errors does not
predict this pattern. The figure suggests that managers’ incentives to beat estimates is also an important
factor which may help explain the negative premium in the late phase.
We examine the relative importance of the informational role of management guidance and the managers’
asymmetric response to optimism and pessimism by “debiasing” management guidance in the late phase.
Specifically, we match the number of downward guidance with the number of upward guidance by randomly
dropping downward guidance. Then we use the “debiased” sample of management guidance to perform the
contractual portfolio test. We repeat this procedure 5000 times and report the average alpha reduction and
t-values in the “Guidance Debiased” column in Table D15. Conceptually, this debiasing exercise addresses
the question that “how much management guidance could explain the EARC abnormal return if managers
were equally likely to issue upward and downward guidance?” In this hypothetical world, any explanatory
power of management guidance would come from the larger magnitude for downward guidance than upward
guidance. If managers do not systematically guide the estimates to below the actual levels, the alpha
reduction results would indicate the net effect of uncertainty resolution which lead analysts to more realistic
expectations.
There are concerns that managers may systematically “low ball” expectations to below the expected
actual level and manufacture positive surprises. If investors fail to incorporate this behavior, it may generate
the earnings announcement premium (as suggested in Kim and So (2016)). Thus it is important to distinguish
the uncertainty resolution channel from the expectation manipulation channel. If expectation manipulation
an important motive for management guidance, we would expect the subsequent earnings announcement
premium would be significantly larger among firms with management guidance. We test this hypothesis by
relating management guidance to subsequent returns during expected earnings announcement month and
present results in Table D16. Although the negative abnormal returns in phase 3 are substantial for firms that
issue guidance during that period, as shown in column 1, we find no evidence that firms which issue guidance
or downward guidance subsequently outperform other firms during expected earnings announcement month,
as indicated by the small and statistically insignificant values in the “G.−N.G.” columns. Thus it seems
that the main function of the management guidance is “debiasing” rather than “manipulating” investors’
expectations. Management guidance is better interpreted as uncertainty resolution, rather than expectation
manipulation.
53
Table D13: Management Guidance Cycle and OptimismThis table reports panel regression results about how management guidance varies over the earnings cycleand with lagged analysts’ optimism and firm characteristics. Each observation is a firm-announcement-phase. “Guidance%” an indicator variable (in percentage) which equals 100 if there is at least one guidancein for the firm-announcement-phase. “Up Guidance%” and “Down Guidance%” is equal to 100 if there isat least one guidance with guidance code equal 02 and 01 respectively in the I/B/E/S Guidance Database.”Up − Down%” is equal to “Up Guidance%” − “Down Guidance%”. “Phase 1” is from t = 6 to 20relative to earnings announcements. Phase 2 is the omitted category, which is from t = 21 to 35. ”Phase3” is from t = 36 to 50. “Optimismt−1” is the sum of one to four quarter ahead forecast errors in theprevious phase, scaled by closing price on the last earnings announcement day. Firm characteristics areas defined in Appendix A. Column 1, 3, 5 and 7 include firm-announcement fixed effects. Column 2, 4, 6and 8 include firm fixed effects and year-quarter fixed effects. Standard errors in parantheses are clusteredby Fama-French 49 Industries and year-quarter.
Guidance% Up Guidance% Down Guidance% Up − Down%
Phase 1 −1.379 −1.468 −0.649 −0.700 −0.699 −0.746 0.049 0.046(0.715) (0.624) (0.248) (0.211) (0.231) (0.195) (0.181) (0.160)
Phase 3 0.172 0.131 0.562 0.594 1.178 1.254 −0.616 −0.660(1.275) (1.111) (0.395) (0.343) (0.436) (0.376) (0.218) (0.187)
|Optimismt−1| 0.031 −0.020(0.186) (0.057)
|Optimismt−1| × Phase1 −0.148 −0.151(0.103) (0.084)
|Optimismt−1| × Phase3 0.451 0.485(0.133) (0.103)
Optimismt−1 −0.096 −0.132 0.135 0.197 −0.231 −0.328(0.080) (0.038) (0.097) (0.059) (0.114) (0.084)
Optimismt−1 × Phase1 0.067 0.069 −0.178 −0.181 0.245 0.251(0.040) (0.033) (0.074) (0.063) (0.099) (0.086)
Optimismt−1 × Phase3 −0.041 −0.035 0.214 0.217 −0.255 −0.252(0.041) (0.033) (0.072) (0.065) (0.080) (0.070)
log(Market Value) 2.536 0.395 0.894 −0.499(0.431) (0.172) (0.164) (0.240)
Book-to-market 0.985 0.057 0.769 −0.712(0.521) (0.159) (0.160) (0.198)
Profitability 4.470 1.566 1.757 −0.191(1.977) (0.923) (0.560) (1.041)
Analysts 0.075 0.011 0.033 −0.022(0.034) (0.010) (0.015) (0.017)
Firm-Announcement F.E. Y Y Y YFirm F.E. Y Y Y YYear-Quarter F.E. Y Y Y YObservations 179,317 166,090 179,317 166,090 179,317 166,090 179,317 166,090Adjusted R2 0.105 0.095 0.066 0.029 0.062 0.037 0.062 0.013
54
Table D14: Change in Alphas in Guidance Counterfactual PortfoliosThis table reports the difference in factor model alphas estimated before and after removing stock-days withintwo-day and three-day windows of analyst updates, earnings guidance and both. The sample period starts fromFebruary 1994 due to data availability of recommendation. “Original Alphas” column reports alphas for theoriginal portfolio; “Analyst Total” reports alphas for analyst counterfactual portfolio as in Table 4; “Guidance”for portfolios with returns in the three-day windows of any earnings guidance removed; “Analyst+Guidance”remove returns around both analyst updates and management guidance; “Analyst−Guidance” shows alphas ofthe portfolio which longs the analyst counterfactual portfolio and short the guidance counterfactual portfolio. Thefirst number in each cell in column 2 to 9 reports the alphas estimates for portfolios which long the counterfactualportfolios and short the original portfolios. Number in parentheses are t-values. Units are in basis points.
Original Analyst Total Guidance Analyst+Guidance Analyst−Guidance
Alpha 2-day 3-day 2-day 3-day 2-day 3-day 2-day 3-day
CAPM
Long1.98 −0.30 −0.49 0.02 0.05 −0.34 −0.55 −0.32 −0.54
(−1.47) (−2.00) (0.46) (0.82) (−1.66) (−2.22) (−1.63) (−2.24)
Short−1.49 1.76 2.03 1.07 1.15 1.84 2.01 0.63 0.83
(7.40) (7.31) (8.50) (8.48) (7.37) (6.94) (2.67) (3.00)
Long-short3.53 −2.02 −2.48 −1.05 −1.11 −2.15 −2.53 −0.92 −1.32
(−6.61) (−6.88) (−7.72) (−7.56) (−6.78) (−6.81) (−3.02) (−3.70)
4-Factor
Long2.38 −0.33 −0.54 0.01 0.03 −0.37 −0.59 −0.34 −0.57
(−1.62) (−2.19) (0.24) (0.60) (−1.81) (−2.40) (−1.73) (−2.38)
Short−1.21 1.73 1.98 1.06 1.13 1.79 1.95 0.62 0.79
(7.29) (7.16) (8.38) (8.36) (7.19) (6.76) (2.63) (2.90)
Long-short3.60 −2.02 −2.47 −1.05 −1.10 −2.13 −2.50 −0.92 −1.32
(−6.59) (−6.83) (−7.66) (−7.52) (−6.70) (−6.73) (−3.04) (−3.68)
Table D15: Debiasing Management GuidanceThis table presents counterfactual portfolio tests about management guidanceusing post-2001 sample. The “Guidance” panel remove returns around man-agement guidance. “Guidance Debiased” randomly select the same number ofdownward guidance as upward guidance, and then remove all guidance eventwindows. Therefore, the “Guidance Debiased” test removes the same numberof upward and downward guidance. The random selection is performed 5000times and averages are reported. Numbers in each cell are a factor model alphaand t-value, for a long-short portfolio which longs the counterfactual portfolioand short the original portfolio.
Original Guidance Guidance Debiased
Alpha 2-day 3-day 2-day 3-day
CAPM
Long2.06 −0.05 −0.05 −0.03 −0.04
(−0.83) (−0.76) (−0.48) (−0.68)
Short−1.12 0.83 0.86 0.38 0.35
(5.31) (5.11) (2.80) (2.45)
Long-short3.17 −0.89 −0.93 −0.41 −0.40
(−5.30) (−5.08) (−2.83) (−2.56)
4-Factor
Long1.80 −0.06 −0.06 −0.03 −0.05
(−0.85) (−0.79) (−0.51) (−0.72)
Short−1.44 0.83 0.86 0.38 0.36
(5.31) (5.11) (2.82) (2.47)
Long-short3.24 −0.89 −0.93 −0.42 −0.41
(−5.29) (−5.08) (−2.85) (−2.60)
55
Table D16: Management Guidance and Subsequent Earnings Announcement ReturnThis table shows CAPM and 4-factor alphas and standard errors in parentheses conditional on guidance status in the latephase of earnings announcement cycle. Panel A shows results related to downward guidance. Panel B shows results related toany guidance. “Phase 3” reports alphas during phase 3 (t=36 to 50) given the firm has downward guidance or any guidancein phase 3. All other columns report alphas during the expected earnings announcement period from t = 51 to t = 70.“Guide” shows the alphas for the sample firms with downward guidance (Panel A) or any guidance (Panel B) in phase 3.“N.G. Matched” reports alpha for all firms with no downward guidance (Panel A) or no guidance (Panel B) in phase 3 duringholding periods matched to the firms with guidance. “All N.G.” reports alphas for all firms with no downward guidance orany guidance at phase 3. “G−N.G.” reports the long-short portfolio alphas (long guidance firms, short non-guidance firms).
Panel A: Downward Guidance (Post-2001)
CAPM 4-Factor
Phase 3 Guide N.G. Match All N.G. G.−N.G. Phase 3 Guide N.G. Match All N.G. G−N.G.
Alpha −31.980 1.658 1.135 1.613 0.524 −32.032 1.575 0.954 1.249 0.621S.E. (2.791) (1.883) (0.814) (0.794) (1.764) (2.724) (1.793) (0.598) (0.596) (1.763)Observations 3,398 3,475 3,475 3,787 3,475 3,398 3,475 3,475 3,787 3,475Adjusted R2 0.425 0.591 0.904 0.901 0.017 0.453 0.629 0.948 0.944 0.018
Panel B: Any Guidance (Post-1993)
Phase 3 Guide N.G. Match All N.G. G.−N.G. Phase 3 Guide N.G. Match All N.G. G−N.G.
Alpha −19.051 1.570 1.726 1.680 −0.156 −18.579 2.087 1.961 1.865 0.126S.E. (2.125) (1.467) (0.703) (0.671) (1.385) (2.060) (1.395) (0.531) (0.510) (1.384)Observations 5,378 5,462 5,462 5,806 5,462 5,378 5,462 5,462 5,806 5,462Adjusted R2 0.395 0.570 0.870 0.868 0.009 0.433 0.612 0.926 0.924 0.012
56
Appendix D. Alternative Explanations
Fig. 9. Media Coverage Rate. This figure plots the percentage of firm-announcement observations which haveat least one news article on Dow Jones News Wire from t = −10 to t = 70 around earnings announcements. Newsdata is from Ravenpack and availability starts from 2001. We exclude all news with topics related to earnings andanalysts to avoid double counting analysts’ updates.
This appendix contains results and discussion about the two alternative hypotheses to the EARC phe-
nomenon: media attension and dividends. Figure 9 shows that media coverage rate spikes to above 30% on
earnings announcement days and gradually decreases until the next earnings announcements. The spread in
coverage rate is over 5 percentage points, or about 30% of the unconditional coverage rate. Existing litera-
ture indicates that media coverage has impact on demand and prices of stocks (Barber and Odean (2007)).
Thus the periodicity of media coverage may also be associated with periodicity in expected returns.
Dividends payments tend to cluster in the first month after earnings announcements. Existing literature
on dividends (e.g. Hartzmark and Solomon (2013)) shows that stock prices tend to rise around ex-dividend
days and reverse afterwards, potentially due to investors’ demand for dividends. Thus it is possible that the
positive early phase EARC return is partly due to the dividend premium.
Table D17 repeats the same panel regressions as in Table B12 but with media coverage and dividends
as dependent variables. Column 1 to 6 use different specifications for news coverage: raw count, natural
logarithm of one plus raw count and indicator variable. The results indicate that firms on average have
about two more news articles in phase 1 than in phase 3 (column 1 through 4); the probability of having
any news coverage decreases by around eight percentage points from phase 1 to phase 3. These results are
closely in line with visual evidence from Figure 9. Similarly, column 7 and 8 show that firms are about 9
57
percentage points more likely to pay dividends in phase 1 than in phase 3.
Given the periodicity of media attention and dividends, they both become potential suspects for the
EARC. Table D18 reports portfolio regression alphas for the counterfactual portfolios which remove three-
day windows around media coverage and ex-dividend days. Panel A shows results for tests related to media
coverage using the post-2001 sample; Panel B shows results related to dividends. The first row of both panels
reports the alphas for the original portfolios for comparison. The second row in Panel A shows results for the
analyst counterfactual portfolios. We see that the long-short alphas for the analyst counterfactual portofolios
are no longer significant under all three pricing models, suggesting there is not much left to explained after
removing days around analysts’ updates in the post-2001 sample. The “News Counterfactual” long-short
portfolios, however, still have significantly positive alphas of around 2.5 basis points as shown in row 3.
The results in row 3 is consistent with the notion that media coverage may on average lead to an increase
in stock price due to increased investors’ attention. after removing “news days”, both the long- and short-
portfolios have a significant decrease in alphas. However, the long-portfolios have a larger decrease in alphas
than the short-portfolios, potentially due to the higher coverage rate in phase 1. As a result, the long-short
portfolio alpha become smaller than the original alpha. The results suggest that “news days” account for
about 20% of the abnormal returns in EARC.
However, once we remove both types of events: analyst updates and media coverage, we see that media
coverage does not provide incremental explanatory power beyond analysts’ updates. The alphas in row four
are even slightly higher than the analyst counterfactual portfolios in row two.13 It seems that although
media coverage provides some explanatory power on by itself, it does not incrementally explain the EARC
alphas beyond days around analysts’ updates. This suggests the part in media coverage that explains the
EARC is already reflected in the optimism cycle.
Panel B of Table D18 shows alphas for the “Dividends counterfactual portfolios” and for the subsample of
non-dividend paying stocks. The first row shows the original alphas as reported in Table 2. The second row
shows that the three-day window around ex-dates account for a small fraction of the EARC abnormal returns:
the four-factor alpha decreases from 3.43 to 3.32, or by about 3% of the abnormal returns. The last row
shows the EARC alphas for the subsample of non-dividend paying stocks. We see that the EARC abnormal
returns are about 0.8 basis point higher for this subsample, with alphas over 4.1 basis points per day. These
results are consistent with the notion that dividend paying firms have lower cash flow uncertainty (Chay
and Suh (2009)) and subjectivity in valuations (Baker and Wurgler (2006)) and reinforce the uncertainty
13Note that we remove news types related to earnings and analysts to avoid double counting.
58
channel interpretation from earlier sections. Thus it seems safe to conclude dividends do not explain the
EARC alphas.
Table D17: Media Attention and Dividends CycleThis table reports regression results which show the difference in media coverage and dividends over theearnings announcement cycle. Each observation is a firm-announcement-phase. “Phase 1” is equal to 1if the observation is between t = 6 and 20 relative to earnings announcements. Phase 2 is the omittedcategory, which is from t = 21 to 35. ”Phase 3” is from t = 36 to 50. All firm characteristics are as definedin Appendix A. “News” is number of news. “log(1+News)” is the natural logarithm of 1 plus “News”.“News Dummy%” is equal to 100 if the stock-phase has news count of at least one, and zero otherwise.“Div. Dummy%” is equal to 100 if the firm-announcement-phase has a dividend payment, zero otherwise.Standard errors in parentheses are clustered by Fama-French 49 Industries and year-quarter.
News log(1+News) News Dummy% Div. Dummy%
Phase 1 (t = 6 to 20) 1.001 1.058 0.131 0.140 3.549 3.901 3.547 3.902(0.190) (0.160) (0.023) (0.018) (0.809) (0.589) (1.104) (0.982)
Phase 3 (t = 36 to 50) −0.957 −0.980 −0.151 −0.152 −4.842 −4.716 −5.659 −5.933(0.154) (0.127) (0.021) (0.018) (0.720) (0.586) (1.072) (0.906)
log(Market Value) 1.119 0.174 4.245 1.986(0.172) (0.021) (0.898) (0.312)
Book-to-market 0.622 0.075 1.189 0.840(0.205) (0.023) (0.950) (0.378)
Profitability −0.185 0.072 4.053 −0.692(0.414) (0.046) (2.007) (1.042)
Analysts −0.019 −0.002 −0.060 0.035(0.009) (0.001) (0.046) (0.016)
Firm-Announcement F.E. Y Y Y YFirm F.E. Y Y Y YYear-Quarter F.E. Y Y Y YObservations 201,876 187,422 201,876 187,422 201,876 187,422 396,750 365,667Adjusted R2 0.691 0.524 0.723 0.587 0.570 0.460 −0.155 0.150
59
Table D18: EARC Alphas and Media Attention and DividendsThis table reports factor model alphas on counterfactual portfolios about analysts’ updates, media coverage and dividendpayments. Panel A uses the post-2001 sample (due to data availability) to test the importance of media attention to EARCalphas. Panel B uses the full sample to test the importance of dividends. Each cell reports factor model alpha and t-value.The first row of both panels report the original alphas in the corresponding period. “Analysts” is the counterfactualportfolio which removes stock-days in three-day windows around any analyst updates. “News”, “Analysts and News”and “Dividend” are constructed analogously. “Non-dividend Stocks” row reports alphas on portfolios constructed onlyusing stocks that pay no regular dividend in the 200 days prior to the last earnings announcement. Sample contains U.S.common stocks followed by 5 or more analysts with lagged prices above $3. Standard errors are in the parentheses.
CAPM 3-Factor 3-Factor + Momentum
Panel A: Post-2001 Sample
Long-short Long Short Long-short Long Short Long-short Long Short
Original 3.174 2.056 −1.118 3.226 1.420 −1.806 3.241 1.801 −1.440(0.841) (0.807) (0.844) (0.840) (0.655) (0.673) (0.841) (0.610) (0.633)
Analysts 0.983 1.469 0.486 1.064 0.804 −0.261 1.082 1.166 0.084(0.814) (0.804) (0.865) (0.812) (0.632) (0.665) (0.813) (0.589) (0.629)
News 2.462 0.479 −1.983 2.485 −0.328 −2.813 2.480 0.076 −2.403(1.008) (0.976) (1.005) (1.009) (0.771) (0.794) (1.009) (0.728) (0.752)
Analysts and News 1.242 0.372 −0.870 1.296 −0.434 −1.730 1.301 −0.039 −1.340(1.013) (0.984) (1.029) (1.013) (0.778) (0.806) (1.013) (0.737) (0.768)
Panel B: Full Sample
Original 3.338 1.917 −1.421 3.372 1.728 −1.644 3.426 2.505 −0.922(0.550) (0.550) (0.574) (0.550) (0.439) (0.453) (0.551) (0.411) (0.430)
Dividends 3.230 1.676 −1.553 3.267 1.495 −1.772 3.323 2.278 −1.046(0.556) (0.556) (0.579) (0.555) (0.444) (0.457) (0.556) (0.416) (0.434)
Non-Dividend Stocks 4.090 1.736 −2.354 4.125 1.829 −2.296 4.163 2.736 −1.427(0.803) (0.802) (0.836) (0.803) (0.655) (0.669) (0.804) (0.630) (0.647)
60
Appendix E. Auxiliary Results
This appendix provides auxiliary results and discussion which extend the main line of argument in this
study. Table E19 shows the sensitivity of the EARC abnormal return estimates to the choice of value-
weighted versus equal-weighted index. Results in this table is to be compared with those in the left panel
of Table 7. This comparison shows that the EARC return become 10 to 20% lower simply by changing the
benchmark from CRSP equal-weighted index to value-weighted index.
Table E20 reports the quarterly averages of daily market-adjusted returns and associated t-values for
EARC portfolios sorted by uncertainty then by event intensity. Since event intensity and uncertainty operate
through different channels, one should expect that the EARC abnormal returns to increase along both
dimensions. The results strongly support this conjecture. Within each row, the high event intensity long-
short portfolios have higher market-adjusted returns, indicating that event intensity is positively associated
with the EARC market-adjusted returns even after controlling for uncertainty. In each column, the EARC
market-adjusted returns generally increase with uncertainty. These results are consistent across different
measures of uncertainty. The high event intensity and uncertainty portfolio offers up to 16.27 basis points
per day (or 3.25% monthly) in market-adjusted return, as in the high IVOL and high Crowdedness portfolio.
Table E21 presents results on portfolios sorted based on both book-to-market equity and event intensity.
It shows that the EARC abnormal return increases with event intensity even after controlling for book-to-
market equity. From left to right, the average market-adjusted return increases with crowdedness across all
book-to-market equity quintiles, but most strongly so among growth stocks. Growth stocks with earnings
announcements at the peak of earnings seasons have an average daily EARC return of 9.14 basis points or
about 1.83% monthly.
61
Table E19: Event-time EARC with Value-weighted BenchmarkThis table reports daily market-adjusted returns on event-time portfoliossorted quarterly based on lagged measures of uncertainty. At the beginningof each calendar-quarter (Janurary, April, July, and October), all stocks inthe sample are sorted based on the inverse of market value (Size), inverse ofage (Age), idiosyncratic volatility (IVOL), cashflow volatility (CVOL) (fol-lowing Zhang (2006b)). Each cell reports the quarterly time-series averageof daily market-adjusted return during the 15-day buy-and-hold period inthe early phase and the late phase of the earnings cycle. Long-portfoliois from t=6 to 20 and short-portfolio from t=36 to 50 relative to the lastearnings announcements. Long-short shows the quarterly average returndifference between the long- and short-portfolio. The benchmark is CRSPequal-weighted index. Uncertainty increases from Q1 to Q5. Q5-Q1 col-umn reports average market-adjusted returns difference between Q5 andQ1 . Units are in basis points. In parantheses are t-values computed usingtime-series standard errors adjusted for autocorrelation.
Q1 Q2 Q3 Q4 Q5 Q5-Q1
Size
Long0.79 2.10 1.47 2.77 4.13 3.34
(1.95) (3.87) (1.92) (2.97) (3.95) (2.98)
Short−0.68 −1.59 −1.80 −2.10 −2.61 −1.93
(−1.30) (−1.89) (−1.80) (−1.85) (−1.98) (−1.33)
Long-Short1.50 3.69 3.29 5.08 7.59 6.10
(2.04) (3.37) (2.55) (4.15) (5.68) (4.39)
Age
Long1.49 1.66 2.51 3.07 2.58 1.09
(2.26) (2.68) (3.21) (3.32) (2.06) (0.67)
Short−1.02 −0.81 −1.15 −2.47 −3.87 −2.84
(−1.48) (−1.01) (−1.32) (−2.10) (−2.79) (−2.16)
Long-Short2.60 2.56 3.74 5.79 7.01 4.41
(2.87) (2.85) (3.22) (4.38) (4.88) (2.97)
IVOL
Long1.39 1.69 1.35 2.42 4.31 2.92
(1.54) (2.80) (1.86) (2.43) (2.44) (1.22)
Short0.78 −0.49 −1.22 −2.53 −5.66 −6.45
(1.00) (−0.80) (−1.45) (−2.13) (−2.76) (−2.57)
Long-Short0.60 2.17 2.62 5.05 10.90 10.30
(0.72) (2.60) (2.44) (3.91) (5.61) (4.80)
CVOL
Long0.75 2.14 3.04 3.05 3.12 2.38
(0.87) (2.83) (3.29) (2.91) (3.93) (2.16)
Short0.38 −1.00 −2.09 −3.03 −2.32 −2.71
(0.72) (−1.24) (−2.18) (−2.59) (−2.21) (−2.50)
Long-Short0.44 3.34 5.14 6.23 5.67 5.23
(0.42) (3.34) (3.75) (4.30) (5.25) (3.66)
62
Tab
leE
20:
Dou
ble
Sor
ton
Un
cert
ainty
and
Cro
wd
edn
ess
This
table
rep
orts
aver
age
dai
lym
arke
t-ad
just
edre
turn
son
por
tfol
ios
sort
edquar
terl
ybas
edon
mea
sure
sof
unce
rtai
nty
and
num
ber
offirm
san
nou
nci
ng
earn
ings
onth
esa
me
day
.A
tth
eb
egin
nin
gof
each
quar
ter,
firm
sar
eso
rted
into
five
quin
tile
sbas
edon
lagg
edm
easu
res
of
unce
rtia
nty
:in
vese
ofm
arke
tva
lue
(Siz
e),
inve
rse
ofag
e(A
ge),
idio
syncr
atic
vola
tility
(IV
OL
)an
dca
shflow
vol
atilit
y(C
VO
L).
Then
wit
hin
each
quin
tile
,firm
sar
eso
rted
bas
edon
two
crow
ded
nes
sm
easu
res.
The
firs
tm
easr
ue
(pan
elA
)so
rtfirm
sbas
edon
the
num
ber
offirm
san
nou
nci
ng
onth
esa
me
day
.T
he
seco
nd
mea
sure
(Pan
elB
)so
rts
onday
s.T
her
ear
eth
esa
me
num
ber
offirm
sin
each
crow
ded
nes
squin
tile
inpan
elA
and
sam
enum
ber
ofday
sin
each
quin
tile
inpan
elB
.U
nit
sar
ein
bas
isp
oints
andt-
valu
esar
ein
par
enth
eses
.Sta
ndar
der
rors
are
adju
sted
for
auto
corr
elat
ion.
Siz
eA
geIV
OL
CV
OL
Un
cert
ain
ty\C
row
ded
ness
Q1
Q5
Q5−
Q1
Q1
Q5
Q5−
Q1
Q1
Q5
Q5−
Q1
Q1
Q5
Q5−
Q1
Q1
Lon
g0.
241.
130.8
90.
981.
930.9
51.0
91.
73
0.6
40.6
00.
640.0
4(0.2
6)(0.9
3)(0.7
8)(1.3
3)(2.4
2)(1.0
3)(0.9
5)(1.6
9)(0.6
6)(0.7
4)(0.7
1)(0.0
4)
Shor
t−
0.37
−3.
01−
2.6
4−
1.73
−3.
90−
2.1
6−
0.8
1−
0.23
0.5
7−
0.0
9−
2.69
−2.
59(−
0.27
)(−
2.04
)(−
1.7
4)(−
1.86
)(−
4.18
)(−
1.8
5)(−
0.8
9)(−
0.19
)(0.4
8)(−
0.0
9)(−
2.33
)(−
1.85
)
Lon
g-Shor
t0.
624.
143.5
22.
885.
943.0
61.8
91.
96
0.0
70.7
43.
332.5
8(0.6
2)(2.5
7)(1.7
4)(2.8
4)(5.3
1)(2.1
0)(1.9
8)(1.3
9)(0.0
4)(0.7
2)(2.2
5)(1.5
0)
Q3
Lon
g0.
971.
760.8
00.
643.
242.6
00.7
02.
06
1.3
50.2
53.
172.9
2(1.1
7)(1.5
4)(0.6
6)(0.6
8)(2.6
5)(2.0
4)(0.7
9)(2.0
1)(1.1
4)(0.2
6)(2.6
1)(1.9
9)
Shor
t−
1.46
−3.
97−
2.5
1−
1.83
−3.
64−
1.8
1−
2.8
4−
3.99
−1.1
5−
2.0
5−
4.75
−2.
69(−
1.73
)(−
3.36
)(−
2.5
9)(−
1.43
)(−
3.12
)(−
1.1
7)(−
3.4
4)(−
4.39
)(−
1.0
4)(−
1.9
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)(−
1.85
)
Lon
g-Shor
t2.
505.
673.1
72.
576.
944.3
73.6
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05
2.3
82.4
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865.4
3(2.1
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0)(1.8
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7)(1.8
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3)(5.5
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8)(1.8
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9)(2.7
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Q5
Lon
g1.
983.
151.1
7−
1.06
3.37
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65.
43
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33.
312.2
8(1.7
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)(1.5
6)(1.8
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1)(1.8
9)(1.1
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0)(2.2
3)(0.9
9)
Shor
t−
2.97
−7.
19−
4.2
3−
2.84
−7.
83−
4.9
9−
1.2
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1−
8.9
50.1
8−
7.24
−7.4
2(−
2.11
)(−
3.98
)(−
1.7
8)(−
1.97
)(−
3.34
)(−
1.8
1)(−
0.5
3)(−
2.76
)(−
1.9
1)(0.1
6)(−
2.68
)(−
3.0
1)
Lon
g-Shor
t5.
8311.0
75.2
32.
5111.6
09.0
93.6
716.2
712.6
00.9
710.6
89.7
1(3.2
7)(4.9
2)(1.5
7)(1.0
6)(5.0
4)(2.3
7)(1.0
3)(4.4
9)(1.9
5)(0.6
3)(4.0
4)(3.3
0)
63
Table E21: The EARC, Book-to-Market and Event IntensityThis table reports daily market-adjusted returns on event-time portfolios sortedquarterly based on lagged values of book-to-market equity and crowdedness. At thebeginning of each calendar-quarter (January, April, July, and October), stocks aresorted first based on book-to-market equity and then by the number of announcingfirms on the same day. Each cell reports the quarterly time-series average of dailymarket-adjusted return during the 15-day buy-and-hold period in the early phaseand the late phase of the earnings cycle. Long-portfolio is from t = 6 to 20 and short-portfolio from t = 36 to 50 relative to the last earnings announcements. Long-shortshows the quarterly average return difference between the long- and short-portfolio.The benchmark is CRSP equal-weighted index. Uncertainty increases from Q1 toQ5. Q5−Q1 column reports average market-adjusted returns difference between Q5and Q1 . Units are in basis points. In parentheses are t-values computed usingtime-series standard errors adjusted for autocorrelation.
Book-to-Market\ Crowdedness Q1 Q2 Q3 Q4 Q5 Q5−Q1
Q1
Long0.67 4.40 4.73 4.72 3.61 2.94
(0.55) (2.21) (2.38) (3.01) (1.82) (1.68)
Short−2.16 −3.28 −4.34 −3.88 −5.35 −3.19
(−1.71) (−2.05) (−2.22) (−1.87) (−2.39) (−1.80)
Long-Short2.96 7.88 9.28 8.69 9.14 6.18
(2.53) (3.15) (3.98) (4.31) (4.13) (2.61)
Q3
Long0.47 2.05 1.46 2.64 2.54 2.08
(0.61) (1.57) (1.34) (2.29) (2.18) (1.55)
Short−2.11 −3.00 −3.43 −3.77 −4.53 −2.43
(−2.21) (−3.50) (−3.13) (−2.86) (−4.45) (−2.05)
Long-Short2.66 5.22 4.96 6.50 7.28 4.61
(2.29) (2.99) (3.48) (4.07) (4.13) (2.49)
Q5
Long1.07 0.59 0.57 0.40 0.98 −0.09
(1.08) (0.60) (0.63) (0.38) (0.71) (−0.06)
Short−1.88 −2.06 −2.47 −1.59 −3.50 −1.62
(−1.40) (−1.86) (−2.08) (−1.08) (−2.89) (−1.07)
Long-Short3.49 3.03 3.45 2.39 4.97 1.48
(2.04) (2.48) (2.46) (1.57) (2.77) (0.68)
64
Fig. 10. Bootstrap Distribution of 4-Factor Alpha. This figure plots the bootstrap distribution of 4-factoralpha on long-short portfolios constructed based on earnings announcement event-time. The total number of trials is10000. In each trial, the strategy randomly picks 15 days (from the 45-day interval of t=6 to 50) without replacementto construct the long-portfolio, and another 15 days for the short-portfolio. Therefore, the strategy is long, short andneutral on each stock for 15 random trading days in each quarter. Then we compute the 4-factor alpha for each ofthe 10000 randomly generated strategies and plot it density distribution. The original EARC strategy buys stocksthat are from 6 to 20 trading days after the last earnings announcement and shorts stocks that are from 36 to 50trading days after the last earnings announcement. Its 4-factor alpha is 3.426 basis points per day as shown by thevertical line.
65