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).

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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).

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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.

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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.

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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.

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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

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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,

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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.

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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

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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,

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-

pu

stat

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-to-

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ket

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valu

eof

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ity

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ided

by

mark

etva

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at

the

end

of

pre

vio

us

year

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cq,

pst

kq,

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shro

ut

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SP

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om

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pu

stat

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valu

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taxes

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din

vest

men

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),m

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eb

ook

valu

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pre

ferr

edst

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(if

avail

ab

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kq

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pu

stat

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etG

row

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otal

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td

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edby

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us

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art

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pu

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d(fi

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3d

igit

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trib

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120,

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125)

wit

ham

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nt

gre

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rth

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0w

ith

inth

ela

st

200

day

sb

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rnin

gs

an

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t;0

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rdq

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SP

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sT

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t,ex

clu

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sgr

oup

s:an

aly

st-r

ati

ngs,

earn

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arg

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stock

-pri

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nic

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grou

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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

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ge

act

ual,

prc

CR

SP

,

I/B

/E

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mb

erof

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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

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,

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pu

stat

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mb

erof

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ecas

ts

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enu

mb

erof

annu

al

earn

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mad

eby

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sam

ean

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stfo

rth

esa

me

firm

and

sam

efi

scal

per

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pre

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non

-id

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ith

in200

day

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lyco

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revis

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6an

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trad

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s,va

lue,

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pu

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sw

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pu

stat

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mb

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ard

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mb

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the

pre

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us

valu

e.P

revio

us

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em

ust

be

wit

hin

200

day

sb

efore

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curr

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valu

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rth

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me

fisc

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per

iod

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pu

stat

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mb

erof

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om.

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ange

s

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enu

mb

erof

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reco

mm

end

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stfo

rth

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stock

wit

ha

pre

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non

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reco

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day

s.O

nly

con

sid

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reco

mm

end

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d50

trad

ing

day

saft

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ela

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rnin

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ann

oun

cem

ent.

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om

men

dati

on

data

start

sfr

om

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ura

ry1994

irec

cd,

am

ask

cd,

an

ndats

,rd

q

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pu

stat

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mb

erof

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grad

esN

um

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ofre

com

men

dati

on

sw

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valu

elo

wer

than

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pre

vio

us

valu

e.

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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

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,

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pu

stat

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mb

erof

dow

ngr

ades

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mb

erof

reco

mm

end

ati

on

sw

ith

curr

ent

valu

eh

igh

erth

an

the

pre

vio

us

valu

e.

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vio

us

valu

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ust

be

wit

hin

200

day

sb

efore

the

curr

ent

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e

irec

cd,

am

ask

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an

ndats

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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

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,

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

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s.T

his

calc

ula

tion

requ

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non

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mis

sin

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rall

four

qu

art

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ah

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from

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rnin

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tim

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kd

own

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rly

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tim

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(Eop

)an

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teop

tim

ism

(Lop

)E

op,

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pu

stat

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agem

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ce

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mb

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day

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to50

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start

sfr

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rary

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guid

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ceA

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gu

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years

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pu

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oper

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FO

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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

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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)

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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

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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

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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