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Expectation dynamics and stock returns
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Expectation dynamics and stock returns
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University of Southern California
Doctoral Dissertation
Expectation Dynamics and Stock Returns
Author:
Yingguang Zhang
Advisors:
Gerard Hoberg (co-chair)
Juhani Linnainmaa (co-chair)
Christoper Jones
Cary Frydman
Richard Sloan
A dissertation submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy in Business Administration
USC Graduate School
Marshall School of Business
Department of Finance and Business Economics
May 2019
ii
c
2019 Yingguang Zhang
All rights reserved
iii
Abstract
This dissertation consists of two papers that study expectation dynamics and stock returns. I show
that sell-side analysts’ earnings expectations behave in predictable ways and drive two new stock
return patterns in the cross-section. The first chapter examines the effect of attention boundary on
forecast accuracy and price efficiency. Using the term structure of analysts’ earnings expectations,
I find that two-quarter-ahead expected growth negatively predicts stock returns. Three-quarter-
ahead expected growth does not immediately predict stock returns, but does so with a one-quarter
delay. My results suggest that analysts and investors underreact to information beyond the one-
quarter horizon. The resulting mispricings do not correct until the underlying biased expectations
approach the one-quarter horizon. I estimate that while investors pay full attention to one-quarter
ahead earnings information, they are only 25% as attentive to earnings information beyond the
one-quarter horizon. In the second chapter, we document the “earnings announcement return cy-
cle” (EARC) phenomenon: stocks earn significantly negative abnormal returns before earnings
announcements and positive after them. Analysts’ forecasts follow the same pattern as returns,
exhibiting an optimism cycle. We attribute one-half of the earnings announcement return cycle
to analysts’ optimism cycle. The EARC may stem from mispricing: both the return and opti-
mism patterns are stronger among high-uncertainty and difficult-to-arbitrage stocks. This thesis
highlights the importance of understanding investors’ expectation dynamics when studying asset
prices.
iv
Acknowledgements
I am grateful to my advisors, Gerard Hoberg (co-chair), Juhani Linnainmaa (co-chair), Cary Fryd-
man, Christopher Jones, and Richard Sloan for their support, advice, and encouragement over the
years. I thank Pavel Savor (discussant), David Solomon (discussant), conference participants at the
AFA2019andtheSFSCavalcade2018,KennethAhern,RonAlquist,SarahJiang,TobyMoskowitz,
Marina Niessner, K.R. Subramanyam, and seminar participants at the USC finance brownbag, and
at AQR Capital Management for their valuable comments and suggestions. I thank Wayne Fer-
son, Arthur Korteweg, Anthony Marino, John Matsusaka, Kevin Murphy, Oguzhan Ozbas, Selale
Tuzel and Fernando Zapatero for their advice and support throughout the Ph.D. program. I thank
Georgios Magkotsios, Yuan (Bruce) Li, Louis Yang and Chong Shu for invaluable peer support.
v
Contents
Abstract iii
Acknowledgements iv
1 Attention Boundary, Expectation Term Structure, and Delayed Alpha 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 The setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 Measuring investors’ attention using price correction . . . . . . . . . . . . . 9
1.3 Data and empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Sample construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.2 Empirical strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.3 Measuring expected earnings growth . . . . . . . . . . . . . . . . . . . . . . 13
1.3.4 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.1 Expected change in growth and stock returns . . . . . . . . . . . . . . . . . 15
1.4.2 Decomposing expected change in earnings growth . . . . . . . . . . . . . . . 17
1.4.3 Delayed alpha . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4.4 The efficient horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.4.5 Testing the mechanism: Inattention to long-horizon forecast errors . . . . . 23
1.4.6 Underreaction to bad news . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.4.7 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.5 Discussion and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
A1.1 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
vi
A1.2 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
A1.3 Structural shift in information environment around earnings announcements . . . . 51
A1.4 Additional tables and figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2 The Earnings Announcement Return Cycle 59
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.3 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.3.1 The earnings announcement return cycle . . . . . . . . . . . . . . . . . . . . 68
2.3.2 Analysts’ optimism cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.3.3 Measuring the association between the EARC and optimism: The counter-
factual portfolio methodology . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.3.4 Forecast revisions, recommendation changes, and stock returns after and be-
fore earnings announcements . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.3.5 Cross-sectional variation in the earnings announcement return cycle . . . . 78
2.3.6 Earnings announcement return cycle and limits to arbitrage . . . . . . . . 83
2.3.7 Earnings announcement return cycle in Fama-MacBeth regressions . . . . . 87
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
A2.1 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
A2.2 Supplementary analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
vii
List of Figures
1.1 Historical and expected quarterly earnings: Apple Inc. . . . . . . . . . . . . . . . . 4
1.2 Expected growth and average returns . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.3 Expected growth and alphas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.4 Expected next-quarter growth and buy-and-hold returns . . . . . . . . . . . . . . . 35
1.5 Expected two-quarter-ahead growth and buy-and-hold returns . . . . . . . . . . . . 36
1.6 Expected three-quarter-ahead growth and buy-and-hold returns . . . . . . . . . . . 37
1.7 The term structure of earnings expectations . . . . . . . . . . . . . . . . . . . . . . 38
1.8 Betting against expected growth: strategy performance . . . . . . . . . . . . . . . . 39
1.9 Earnings announcement with guidance . . . . . . . . . . . . . . . . . . . . . . . . . 51
1.10 Two-quarter-ahead expected growth and average returns by year . . . . . . . . . . 53
1.11 Sample firms size distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.1 Earnings announcement return cycle and analysts’ revision cycle . . . . . . . . . . 61
2.2 Buy-and-hold earnings announcement return cycle . . . . . . . . . . . . . . . . . . 69
2.3 The return cycle among firms with low or no analyst coverage . . . . . . . . . . . . 71
2.4 Bootstrapped distribution of t-values . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.5 Recommendation upgrades around earnings announcements . . . . . . . . . . . . . 73
2.6 Forecast optimism by forecast horizon and idiosyncratic volatility . . . . . . . . . . 79
2.7 Earnings announcement return cycle and idiosyncratic volatility . . . . . . . . . . . 82
2.8 Earnings announcement return cycle and event intensity . . . . . . . . . . . . . . . 85
2.9 The return cycle with and without analyst updates . . . . . . . . . . . . . . . . . . 89
ix
List of Tables
1.1 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.2 Expected change in growth and stock returns . . . . . . . . . . . . . . . . . . . . . 42
1.3 Expected change in growth at different horizons and stock returns . . . . . . . . . 43
1.4 Lagged expected change in growth and average return in Fama-MacBeth regressions 44
1.5 Expected change in growth and delayed alpha . . . . . . . . . . . . . . . . . . . . . 45
1.6 Expected change in growth and forecast errors . . . . . . . . . . . . . . . . . . . . . 46
1.7 Alphas and events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
1.8 Earnings announcement returns and surprises at different horizons . . . . . . . . . 48
1.9 Expected change in growth and earnings announcement returns . . . . . . . . . . . 49
1.10 Double-sort portfolio alphas by past return and expected change in growth . . . . . 50
1.11 Robustness: Fama-MacBeth regressions with alternative specifications . . . . . . . 55
1.12 Expected change in growth and revision momentum . . . . . . . . . . . . . . . . . 56
1.13 Expected change in growth and average returns: Fama-MacBeth regressions . . . . 57
1.14 Double-sort portfolio alphas by forecast dispersion and expected change in growth . 58
2.1 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
2.2 Earnings announcement return cycle: Daily time-series regressions . . . . . . . . . 92
2.3 Analysts’forecastrevisionsandrecommendationchangesaroundearningsannounce-
ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.4 Measuring the contribution of analyst-update days to the earnings announcement
return cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
2.5 Analysts’ optimism, walkdown, and firm-level uncertainty . . . . . . . . . . . . . . 96
2.6 Firm-level uncertainty and the earnings announcement return cycle . . . . . . . . . 97
x
2.7 Earnings announcement return cycle, book-to-market, and profitability . . . . . . . 98
2.8 Arbitrage difficulty and the earnings announcement return cycle . . . . . . . . . . . 99
2.9 Returns on the earnings announcement return cycle in event- and calendar-time . . 100
2.10 Earnings announcement return cycle in Fama-MacBeth regressions . . . . . . . . . 101
2.11 Measuring the contribution of management guidance to the earnings announcement
return cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
xi
Dedicated to my colleagues, my family, and my love.
1
Chapter 1
Attention Boundary, Expectation Term
Structure, and Delayed Alpha
Yingguang Zhang
Abstract
The term structure of analysts’ earnings expectations and its dynamics predict the cross-section
of stock returns. Stocks with the most positive expected change in earnings growth underper-
form those with the most negative expected change by over 8% per year. I decompose growth
expectations by forecast horizon and find that the return predictability almost entirely stems from
errors in two-quarter-ahead earnings forecasts, as opposed to one- or three-quarter-ahead forecasts.
Strategies that trade against growth forecasts beyond the two-quarter horizon experience “delayed
alpha:” they do not earn alpha immediately but with a delay. Behavioral models with bounded
rationality can explain both the return predictability and the delayed alpha through inattention
to long-horizon earnings news. I estimate that while investors pay full attention to one-quarter-
ahead earnings information, they are only 25% as attentive to earnings information beyond the
one-quarter horizon.
2 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
1.1 Introduction
Thispaperexaminestherelationbetweeninformationhorizonandinformationalefficiencyofprices.
I define “information horizon” as the distance between now and the future period during which the
information becomes realized. For example, a forecast of a firm’s two-quarter-ahead earnings has
an information horizon of two quarters; a projection of the world’s average temperature in ten years
has an information horizon of ten years. In most rational asset pricing models, information horizon
plays little role for price efficiency. The efficient market hypothesis, for example, only distinguishes
between public and private information. On the other hand, behavioral models, such as those with
bounded rationality, suggest that investors may overweight information at shorter horizons.
Boundedly rational investors process only a subset of all available information. They ratio-
nally choose which information to process by weighing the value of the information against the
costs of acquiring and processing it, subject to monetary and cognitive budget constraints.
1
To
the extent that long-horizon information adds less value, and costs more to acquire and process,
investors are less likely to include long-horizon information in their information set. Therefore,
models with bounded rationality predict that investors may misprice long-horizon information due
to inattention.
Models with bounded rationality provide a unique yet untested prediction about when the
mispricing associated with long-horizon information resolves: when the mispriced long-horizon
information enters investors’ information set, or crosses their “boundary of rationality.” To see how
boundedrationalitypredictsthetimingofpricecorrection, imagineamarketinwhichinvestorsonly
consider how news affects the firm’s next quarterly earnings. Suppose that an unexpected negative
shock hits the firm. Investors immediately trade based on their updated beliefs about the firm’s
next quarterly earnings, pushing the stock price down to a new equilibrium. This equilibrium price,
which is efficient with respect to one-quarter-ahead earnings information, is inefficient with respect
to two-quarter-ahead information. Fully rational investors could, therefore, profit by trading on
the two-quarter-ahead implications of the shock. However, a small mass of the rational investors
with budget constraints would not expect to profit immediately from the trade, but to profit only
1
Gabaix (2014) provides a sparsity-based model for bounded rationality. See also Gabaix (2017) for a review on
inattention.
1.1. Introduction 3
when the boundedly rational investors realize the pricing error. Bounded rationality predicts that
the price corrects around the next earnings announcement when the two-quarter-ahead earnings
become one-quarter-ahead and thus enters investors’ focal information set.
The thought experiment above describes the main findings of this paper. Analysts not only
issue earnings forecasts for the next quarter, but also for the following quarter, the quarter after
that, and so forth. I call analysts’ consensus earnings forecasts over different horizons the “term
structure of earnings expectations.” I measure analysts’ forecasts of earnings growth in the next
quarter, in the second quarter, and in the third quarter. I first show that analysts’ earnings growth
forecasts negatively predict stock returns. A strategy that buys stocks with low earnings growth
forecasts for the subsequent three quarters and shorts those with high earnings growth forecasts
earns a value-weighted six-factor model (Fama and French (2015b) augmented with momentum)
alpha of over 8% per year with a t-value of 3.57.
2
I find that the profit from this strategy almost
entirely stems from errors in two-quarter-ahead earnings forecasts. The strategy that trades against
one-quarter-ahead forecasts is unprofitable. The strategy that trades against three-quarter-ahead
forecasts earns a “delayed alpha:” if we form the portfolio immediately upon receiving the signal, it
does not generate alpha; however, if we hold on to the portfolio for a quarter, it starts generating
significant alpha.
Profits from typical trading strategies decay as the return predictors become stale. Di Mascio,
Lines, and Naik (2017) call this phenomenon the “alpha decay.” In contrast, this paper shows that
alpha can come with a delay when investors trade on long-horizon information. I find that investors
appear to systematically misprice long-horizon information due to inattention, and correct such
mispricing only when the mispriced information becomes imminent. My results are consistent with
models with bounded rationality in which investors consider only a salient subset of all information,
such as those with short horizons.
As a case in point, many popular financial websites, such as the Wall Street Journal, Yahoo
Finance, CNN Business, and MarketWatch.com, provide analysts’ quarterly earnings forecasts, but
only for the current and the next quarter (see Figure 1.1). Therefore, investors who rely only on
2
La Porta (1996), Dechow and Sloan (1997) and Bordalo, Gennaioli, La Porta, and Shleifer (2017) show that
analysts’ extreme long-term growth forecasts negatively predict stock returns. My paper focuses on short-term
forecasts over different horizons to examine the effect of information horizon on price efficiency.
4 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
these websites to gather information do not see analysts’ three-quarter-ahead forecasts, until they
become two-quarter-ahead.
Figure 1.1: Actual and estimated quarterly earnings for Apple Inc. on the Wall Street
Journal website. Wall Street Journal reports actual and estimated earnings for the prior four
quarters and the estimated earnings for the next two quarters. Source: https://quotes.wsj.com/
AAPL (November 15, 2018).
Following the analytical framework by Gabaix (2014), I construct a model in which investors
pay different levels of attention to analysts’ forecast errors at different horizons. I then estimate the
attention parameters by calculating how much of the long-horizon strategy’s alpha accrues when
the underlying mispriced information moves across different horizons. I find that investors pay full
attention to one-quarter-ahead earnings forecasts, as the mispricings associated with erroneous two-
quarter-ahead forecasts fully vanish after these forecasts enter the one-quarter horizon. However,
investors are only 25% as attentive to two-quarter-ahead forecasts. My results show that about
25% of the total alpha from a strategy that trades against three-quarter-ahead growth forecasts
accrues within the first quarter, and hence about 75% of the alpha from this strategy is delayed by
over a quarter.
3
3
My results are also consistent with other models such as those with hyperbolic discounting, conservatism, and
myopia. I do not distinguish among these models in this paper; they give observationally equivalent predictions in
my setting. I discuss the results under the bounded rationality framework, but the other interpretations are equally
valid.
1.1. Introduction 5
I call the information horizon at which some news becomes correctly priced the “informationally
efficient horizon” for that news. In the model, the efficient horizon corresponds to the longest
horizon at which investors retain full attention to earnings information. Existing papers show
that stock prices of larger firms are more informationally efficient because larger firms enjoy better
information environment and their stocks are more actively traded. Therefore, we expect that
larger stocks have longer efficient horizons than smaller firms. Consistent with this prediction, I
find that the strategy that trades against three-quarter-ahead earnings forecasts starts to profit
one month earlier among large firms than among small firms, and the price correction also finishes
one month earlier.
Except for the timing of the price correction, bounded rationality gives similar predictions as
other models of market underreaction. Therefore, we expect the strategy to correlate positively
with various momentum-type factors that capture market underreaction, such as price momentum
(Jegadeesh and Titman (1993)), earnings momentum (Ball and Brown (1968)), and momentum
in analysts’ revisions (Chan, Jegadeesh, and Lakonishok (1996)). The results from factor model
regressions show that a strategy that bets against analysts’ two-quarter-ahead growth forecasts
has a 0.15 loading on the UMD factor (with an alpha of 0.58% per month and a t-value of 3.15).
Thus, although the strategy seemingly resembles a contrarian strategy as it shorts stocks with the
highest expected earnings growth, it behaves more a like a momentum-type strategy that bets
against analysts’ slow adjustments to longer-term expectations. If we examine the characteristics
of the stocks that the strategy shorts, they often have poor past performance. Therefore, the
strategy tends to short stocks for which analysts maintain high growth expectations despite their
poor recent performance, or stocks whose performance analysts expect to rebound. The strategy
performs better when applied to losers. A strategy that trades against analysts’ two-quarter-ahead
growth forecasts among stocks at the bottom tercile of past-quarter returns generates a six-factor
value-weighted (equal-weighted) alpha of 12.2% (10.7%) per year with a t-value of 4.06 (5.89).
This strategy only earns a value-weighted (equal-weighted) alpha of 1.1% (4.2%) per year with
a t-value of 0.47 (2.98) when applied to stocks at the top tercile of past-quarter performance.
This asymmetry between winners and losers is consistent with the market underreacting more to
negative news.
6 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
If the strategies’ profits stem from errors in analysts’ earnings forecasts, we expect that (1)
the return predictors also predict analysts’ ex-post forecast errors, and (2) most of the alpha ac-
crue on days around analysts’ forecast revisions. The evidence supports both conjectures. High
expected change in earnings growth significantly predicts overly optimistic forecasts at the corre-
sponding horizons. Returns on days around analysts’ forecast revisions, recommendation changes,
and earnings announcements account for about 90% of the alpha for a strategy that trades against
two-quarter-ahead forecasts.
4
These results suggest that the profits from the strategies likely stem
from expectation errors rather than omitted risk factors.
To test the mechanism whether investors underreact to long-horizon information relative to
short-term information, I exploit shifts in the entire term structure of earnings expectations around
earnings announcements. An earnings announcement shifts the entire term structure of earnings
expectations. I estimate the return sensitivities to analysts’ forecast revisions at the one-quarter,
two-quarter, and three-quarter horizons. I find that while earnings announcement returns strongly
respond to forecast revisions at all three horizons, returns are more than twice as sensitive to one-
quarter-ahead forecast revisions as to two-quarter- or three-quarter-ahead revisions. The difference
in return sensitivities suggests that investors respond less to long-horizon information even when
they can expect to receive both the short- and long-horizon information at the same time, which
is consistent with what bounded rationality predicts. These results also indicate that the profits
from the trading strategies may stem not only from analysts’ forecast errors at the long horizon as
discussed above, but also from investors’ underreaction to analysts’ long-horizon revisions.
Myresultsrelatetotheliteratureoninvestors’shortforward-lookinghorizonsuchasDellaVigna
andPollet(2007)andDaandWarachka(2011). ThisliteraturedatesbacktoatleastKeynes(1936),
who writes:
“For most of these [professional investors and speculators] are, in fact, largely concerned, not
with making superior long-term forecasts of the probable yield of an investment over its whole
life, but with foreseeing changes in the conventional basis of valuation a short time ahead of
the general public. They are concerned, not with what an investment is really worth to a man
who buys it “for keeps”, but with what the market will value it at, under the influence of mass
psychology, three months or a year hence.” (emphasis added)
This quote echoes with another well-known quote by Keynes, “the market can remain irrational
4
This result is consistent with Engelberg, McLean, and Pontiff (2017) who find that many return anomalies are
much stronger around earnings announcements and days with corporate news.
1.2. Model 7
longer than you can remain solvent.” Keynes recognizes that investors focus on short-term price
movements and stock prices can persistently deviate from fair values. In this paper, I show that
even in the present market environment, investors’ short-term focus can cause predictable and
persistent deviations between stock price and fair value. Price correction may only occur when the
mispriced information enters an imminent horizon.
This paper contributes to the current debate about corporate short-termism in America. Cor-
porate short-termism may have caused the slow growth in some businesses as managers choose
to boost the firms’ short-term financial performance at the expense of their long-term prospects.
In June 2018, Jamie Dimon and Warren Buffett urged companies to consider ending the practice
of providing earnings guidance because they believed earnings guidance may have encouraged an
“unhealthy focus” on short-term profits.
5
This same argument has also been raised by the CFA
Institute and the consulting company McKinsey, and it has been subject to much academic debate
in the accounting literature (e.g., Kim, Su, and Zhu (2017) and Houston, Lev, and Tucker (2010)).
Managers need to trade off between short-term profits and long-term growth, but the evidence in
this paper suggests that investors may see only one side of this tradeoff.
MostrelatedtothispaperisDaandWarachka(2011)andDellaVignaandPollet(2007). Daand
Warachka (2011) find that stocks with high long-term growth forecasts but low short-term growth
forecasts tend to underperform. DellaVigna and Pollet (2007) find that investors underreact to
predictable long-term demographic changes. They reach similar conclusions as this paper that
investors seem to be inattentive to information about the far future. This paper contributes to
the literature by measuring the efficient horizon for earnings information, estimating how much
attention investors pay to earnings information at different horizons, and showing how trading
strategies can earn delayed alphas.
1.2 Model
I construct a simple model of inattention to provide some structure to the intuition behind delayed
alpha. In the model, investors pay different levels of attention to analysts’ earnings forecasts errors
5
https://www.wsj.com/articles/buffett-dimon-team-up-to-curb-unhealthy-focus-on-quarterly-earnings-
1528387431.
8 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
at different horizons. The model contains parameters that describe investors’ different levels of
attention. I estimate these attention parameters empirically in Section 1.4.
1.2.1 The setup
Themodelhasthreeperiods. Investorsarerisk-neutral. Theeconomyhasonestockwithexogenous
pricingerror(
P
)causedbyerroneousthree-quarter-aheadearningsforecast(
3
E
). Existingresearch
suggestsseveralpotentialcausesofexpectationerrorsthatleadtomispricings, suchasextrapolative
or diagnostic beliefs, investors overweighting analysts’ biased signals, and sticky expectations (see
La Porta (1996), Dechow and Sloan (1997), Barberis, Greenwood, Jin, and Shleifer (2015), Bordalo,
Gennaioli, La Porta, and Shleifer (2017), Chan, Jegadeesh, and Lakonishok (1996) and Bouchaud,
Krueger, Landier, and Thesmar (2016)). I do not model the origin of the expectation errors but
focus on the correction of such errors.
The stock price at time 0 is:
P
0
=
P +
P
; (1.1)
where
P denotes the fair value of the stock. We can also write the term structure of earnings
expectation at time 0 as:
f
^
E
1
;
^
E
2
;
^
E
3
g
t=0
=f
E
1
;
E
2
;
E
3
+
3
E
g
t=0
; (1.2)
where
^
E
i
denotes the observed consensus earnings forecast for quarter i (i2f1; 2; 3g).
E
i
denotes
thetrueexpectedearningsforquarteri. Withoutlossofgenerality, Iassumethatquarterlyearnings
are independent and identically distributed, so
E
i
=
E for all i. As time passes, the forecast error
moves from three-quarter-ahead, to two-quarter- and then to one-quarter-ahead forecast. I assume
risk-free rate to be zero, so the price does not vary when the forecast error moves along the
expectation term structure, unless the forecast error itself varies over time.
1.2. Model 9
Investors are boundedly rational. They rationally allocate their limited attention to important
information. Thissetupfollowsthesparsity-basedboundedrationalityframeworkinGabaix(2014).
Following the notation in Gabaix (2014), I denotem
i
2 [0; 1] as the attention level which investors
allocate to quarter i forecast errors, with 0 being no attention, and 1 being full attention. I do not
attempt to model how investors choose m
i
, but only to measure m
i
empirically.
1.2.2 Measuring investors’ attention using price correction
An intuitive way to connect the attention parameter m
i
to price correction is via an identify link.
That is, I let m
i
equal to the fraction of mispricing that is corrected when the erroneous forecast
move from i + 1 to i quarters ahead. For example, if investors pay half attention to two-quarter-
ahead earnings forecasts errors, or m
2
= 0:5, then half of the mispricing (
P
) disappears when the
erroneous earnings forecast moves from the three-quarter horizon to the two-quarter horizon. We
can also interpret the attention level m
i
in a probabilistic sense. An m
2
= 0:5 means that the
mispricing (
P
) has a 50% chance of disappearing when the underlying forecast error enters the
two-quarter horizon. Hence, at t = 1, or one quarter after the model starts, expected stock price
is P
1
=
P + (1m
2
)
P
=
P + 0:5
P
. Generally, stock price at time t is equal to:
P
t
=
P +
P
2
Y
i=3t
(1m
i
): (1.3)
This equation means that as long as m
i
> 0, the mispricing decreases over time. Similarly, the
forecast error shrinks as it moves closer to the short end of the expectation term structure ifm
i
> 0.
At time t, the forecast error becomes:
t
E
=
3
E
2
Y
i=3t
(1m
i
): (1.4)
Using equation 1.3 and 1.4, we can then empirically measurem
1
andm
2
by tracing an expectation
error over time and estimate how its associated pricing error is corrected. Equation 1.3 implies
that abnormal returns on the stock in period 1 and 2 are:
10 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
r
1
=
P
1
P
0
P
0
=
m
2
P
P
0
; (1.5)
r
2
=
P
2
P
1
P
1
=
(1m
2
)m
1
P
P
1
: (1.6)
In period 3, the true earnings is announced and hence all remaining mispricing must be corrected,
leading to a final period return of:
r
3
=
PP
2
P
2
=
(1m
2
)(1m
1
)
P
P
2
: (1.7)
Wecanempiricallymeasurethetotalmispricing(
P
)andallholdingperiodreturns({r
1
;r
2
;r
3
}).
Therefore, we can obtain estimates for m
1
and m
2
.
We see from the equations above that the holding period returns in period 1 and 2 are pro-
portional to the remaining mispricing at the beginning of the period, and to the attention level
investors pay to the forecast error. Therefore, if the mispricing has been fully corrected at time
i because, say, m
i
= 1, then m
i1
cannot be identified because no mispricing is left. Hence I
assume a monotonicity condition: m
1
m
2
, which means that investors always pay equal or more
attention to information that is more imminent.
Delayed alpha emerges if investors pay little attention to analysts’ forecast errors until the
errors enter the one-quarter horizon (i.e., m
2
0 and m
1
1). If investors pay half attention
to two-quarter-ahead forecast errors and full attention to one-quarter-ahead errors (m
2
0:5 and
m
1
1), the mispricing is corrected by an equal amount in period 1 and 2, and hence leading
to a constant alpha. In an efficient market, investors always pay full attention (m
2
= m
1
= 1),
which means that all mispricing is corrected within one period after it arises. I provide empirical
estimates of m
1
and m
2
in Section 1.4.
1.3. Data and empirical strategy 11
1.3 Data and empirical strategy
1.3.1 Sample construction
This paper uses data from three standard databases: monthly and daily stock-level data from
CRSP, quarterly firm-level data from Compustat and analyst-related data from IBES Unadjusted
Detail File. To enter the final sample, the firm-announcement observations must (1) have non-
missing earnings announcement dates (rdq), (2) have regular earnings announcements in the past
year,
6
(3) have stock price above five dollars three days before rdq, (4) have positive total asset and
book value of equity, (5) be covered by at least five analysts in the 120 days prior to rdq, (6) have
outstanding quarterly forecasts for the current quarter (Q0) and the three subsequent quarters (Q1,
Q2 and Q3) three days before rdq. At the security level, the stocks must be the primary shares
of the firms, identified as having the highest dollar volume in the previous month. The primary
exchange must be NYSE, NASDAQ or AMEX. In all asset pricing tests, shares with prices below
five dollars in the previous month are dropped. Delisting returns are set to be30% when missing.
I start my sample from January 2002 because recent research indicates that there is a struc-
tural break in the information environment around earnings announcements in the early 2000’s.
Beaver, McNichols, and Wang (2018) show that the amount of information released during earnings
announcements, measured as the ratio of price variation around earnings announcements to price
variation during normal periods, has increased substantially after 2001. This phenomenon is likely
caused by Regulation Fair Disclosure, which was enacted in October of 2000. Since then, managers
increasingly provide forward-looking guidance during earnings announcements. In my sample, the
percentage of firms that provide earnings guidance during earnings announcements increases from
below 10% in 2000 to above 70% in 2004. Many argue that earnings guidance may affect investors’
forward-looking horizon by shifting their focus toward short-term earnings performance. Consis-
tent with this hypothesis, my results are much stronger in the post-2002 period. Appendix A1.3
provides comparison between the pre- and post-2002 periods.
6
The last earnings announcement must be between 60 to 120 calendar days before the current one. The earnings
announcement in the previous year for the same quarter must be between 395 to 335 days before the current one.
12 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
1.3.2 Empirical strategy
To estimate investors’ attention to forecast errors at different horizons, m
1
and m
2
, we need to
track how the mispricings associated with forecast errors correct over time. To do so, we first need
a plausible ex-ante measure of forecast error that can be computed for each horizon. La Porta
(1996), Dechow and Sloan (1997) and Bordalo, Gennaioli, La Porta, and Shleifer (2017) find that
extreme analysts’ growth forecasts tend to be too extreme. They show that stocks with the highest
analysts’long-termgrowthforecastsunderperformthosewiththelowestlong-termgrowthforecasts.
Following their work, I construct measures of analysts’ expected quarterly earnings growth, which
I expect to negatively predict stock returns.
I first confirm that analysts’ expected earnings growth over the next three quarters predicts
stockreturnswithanegativesign. ThenIseparatelymeasureexpectedearningsgrowthforthefirst,
second, and third subsequent quarter, and test which of these growth expectations predict returns.
If investors pay full attention to two-quarter-ahead earnings forecasts, or m
2
= 1, we expect that
the alpha should entirely stem from the strategy that trades against three-quarter-ahead growth
forecasts, because all pricing error would be corrected when three-quarter-ahead forecasts become
two-quarter-ahead. That is, r
1
> 0;r
2
= 0;r
3
= 0. If investors only pay attention to one-quarter-
ahead forecasts (m
2
= 0 and m
1
= 1), we expect that the alpha comes from trading against
two-quarter-ahead growth forecasts, or r
1
= 0;r
2
> 0;r
3
= 0. Ifm
2
> 0 andm
1
= 1, we would see
strategies that trade against two-quarter- and three-quarter-ahead forecasts both generate alphas,
or r
1
> 0;r
2
> 0;r
3
= 0. Delayed alpha emerges if m
1
m
2
0, which means investors pay high
attention to one-quarter-ahead forecast errors, but much less to two-quarter-ahead forecast errors.
I call the estimation procedure above the “cross-sectional measure” because it uses the entire
cross-section of two-quarter- and three-quarter-ahead growth to measure m
1
and m
2
. Another
way of measuring m
1
and m
2
is a “time-series measure,” which is to trace the three-quarter-ahead
earnings forecasts over time and test when errors in expectations and mispricings correct. Oper-
ationally, I test whether lagged values of three-quarter-ahead growth predict stock returns. The
cross-sectional measure is more appropriate if forecast errors arise randomly at different horizons.
The time-series measure is more appropriate if forecasts errors usually arise in long-horizon fore-
casts, and then move toward the near-term as time passes. I provide more details about both
1.3. Data and empirical strategy 13
methods when I present the results in Section 1.4.
1.3.3 Measuring expected earnings growth
The key variables in this paper are measures of expected quarterly earnings growth. Quarterly
earnings contain a large seasonal component that is quite difficult to correct (Chang, Hartzmark,
Solomon, and Soltes (2016)). If we ignore earnings seasonality, we may confuse a seasonal effect
with true expected earnings growth and hence make the expected growth measures noisy. To
mitigate the impact of earnings seasonality, I first subtract analysts’ consensus earnings forecasts
by the same-quarter actual earnings in the prior year to obtain “year-over-year earnings growth
forecasts.” I then measure expected quarterly earnings growth as the difference between the year-
over-year earnings growth forecasts in adjacent quarters. Thus, the earnings growth forecasts I
construct are technically “expected change in year-over-year earnings growth” or expected change
in growth (ECG) for short. Conceptually, the ECG is a measure of expected growth acceleration:
how much analysts expect the year-over-year growth in one quarter to exceed its preceding quarter.
If we consider that each firm has an equilibrium growth rate that leads to zero risk-adjusted return,
the ECG can remove this equilibrium growth and help identify firms that are expected to enter a
new growth state.
Computing the ECG requires two steps: (1) calculate the expected year-over-year earnings
growth (g
yoy
i
) for quarteri and (2) calculate the quarter-over-quarter difference ing
yoy
i
. I construct
allanalysts’forecastvariablesoneweekafterearningsannouncements. Specifically, att = 5relative
to the last earnings announcement, I compute g
yoy
0
=
E
0
E
4
MV
, ^ g
yoy
1
=
^
E
1
E
3
MV
, ^ g
yoy
2
=
^
E
2
E
2
MV
,
^ g
yoy
3
=
^
E
3
E
1
MV
, where
^
E
i
is analysts’ consensus (median) earnings forecasts for quarteri;E
j
is the
actual earnings for a past quarter j; MV is the market value of equity three trading days before
the last earnings announcement. A symbol with a hat means that the value is based on analysts’
forecasts. g
yoy
0
is computed using actual values and thus has no “
^
” attached. The expected change
in growth over the subsequent three quarters (b cg) are calculated as the slope of the linear time-
trend fitted to g
yoy
0
, ^ g
yoy
1
, ^ g
yoy
2
and ^ g
yoy
3
. The unit of b cg is in dollar earnings per quarter scaled by
lagged market capitalization (or earnings yield per quarter).
14 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Using the slope of a linear time-trend makes the expected growth measures robust to issues with
small and negative earnings levels. Namely, if we calculate the growth rate as the ratio between two
earnings levels, the rate can be close to infinity when the denominator is close to zero. Negative
earnings levels also make the growth rate ratio hard to interpret. Another advantage of using the
slope of the fitted time-trend is that it weights forecasts at different horizons equally, and therefore
avoid overweighting the first and last earnings estimates as the growth rates ratio does. My growth
measure is similar to how Dechow and Sloan (1997) calculate past earnings growth in one of their
specifications.
Then I compute the single-period expected change in growth for the subsequent three quarters
as b cg
1
= ^ g
yoy
1
g
yoy
0
, b cg
2
= ^ g
yoy
2
^ g
yoy
1
and b cg
3
= ^ g
yoy
3
^ g
yoy
2
. I omit the superscriptsyoy henceforth
to make the notations cleaner. These four variables of expected change in earnings growth, b cg, b cg
1
,
b cg
2
and b cg
3
are the main variables of interest in this paper.
All expected growth measures are updated once per quarter, on the fifth trading day after
earnings announcements. Hence, each stock in monthly rebalanced portfolio maintains the same
growth expectation throughout a quarter, including the month when the next earnings announce-
ment occurs. This quarterly updating allows us to estimate investors’ response to growth forecasts
throughout the quarter, including when the forecasts cross between horizons. My results are not
sensitive to the rebalancing frequency.
1.3.4 Descriptive statistics
Table 1.1 provides descriptive statistics for the main sample. Panel A overviews the firm char-
acteristics. ME is market value of equity; BM is the ratio of book value of equity to ME; OP is
operating profitability; AG is asset growth; SUE is earnings surprise relative to analysts’ consensus
forecasts, scaled by stock price prior to the earnings announcement. We see that this sample tilts
toward large cap (see Figure 1.11 in Appendix A1.4 for the size distribution), high valuation and
profitable firms due to the analyst coverage filter. The mean and median of SUE are positive,
which is consistent with previous findings that most firms beat earnings forecasts. The mean and
median realized year-over-year earnings growth (g
0
) (in terms of earnings yield) are0:02% and
0:12% in the sample period.
1.4. Empirical results 15
PanelBshowsthesummarystatisticsforanalysts’earningsexpectationsoverdifferenthorizons.
We see that analysts expect the typical firm to grow at a growing rate: the mean and median of
^ g
i
increases with i. The expected change in year-over-year earnings growth for the next quarter
(b cg
1
= ^ g
1
g
0
) has an average of zero and a median of0.04%, which means that analysts do
not expect the firms’ earnings growth to increase in the next quarter. However, analysts typically
hold optimistic outlook beyond the one-quarter horizon, as b cg
2
and b cg
3
average at 0.15% and
0.11% respectively. This pattern is consistent with the “walk-down” of analysts’ earnings forecasts
(Richardson, Teoh, and Wysocki (2004)).
Panel C shows the quarterly time-series average correlations between the ECG variables and
firmcharacteristics. Weseealargenegativecorrelationof0:38between b cg andSUE.Thisnegative
correlation suggests that analysts expect the current earnings shock to be in part transient and
future earnings tend to revert toward the mean. We also see that earnings are expected to grow
faster for smaller firms, less profitable firms and firms with lower past asset growth. Surprisingly,
the ECG variables correlate positively with book-to-market, suggesting that it is value firms, not
growth firms, whose earnings growth are expected to increase faster.
7
The ECG variables also have
slightly negative correlations with analysts’ long-term growth forecasts (LTG), suggesting ECG is
an economically different quantity than the traditional measures of growth expectations.
1.4 Empirical results
1.4.1 Expected change in growth and stock returns
I first confirm that my measure of analysts’ growth expectations (b cg) negatively predicts stocks
returns. While existing papers mostly measure growth expectations using analysts’ long-term
growth forecasts, my measure is based on quarterly earnings forecasts within one year. Figure 1.2
shows the average excess return (raw return 3-month T-bill return) for stocks in each b cg decile.
We see a nearly monotonic pattern that stocks with lower expectations tend to earn higher returns.
7
ThisresultisconsistentwithDoukas, Kim, andPantzalis(2002)whofindthatanalystsaremoreoverlyoptimistic
about value stocks, rather than growth stocks. They interpret their results as evidence against the expectation error
explanation for the value premium.
16 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Stocks in the bottom expected growth deciles earn around 0.9% per month in excess of the risk-
free rate while stocks in the top decile of expected growth earn less than 0.4%. Figure 1.3 shows
a similar pattern with six-factor model (Fama and French (2015b) augmented with momentum)
alphas and 95% confidence intervals. Stocks with low expectations significantly outperform those
with high expectations both in terms of excess return and risk-adjusted return.
Table1.2showsthefactormodelregressionresults. Atthebeginningofeachmonth,Isortstocks
into five quintiles based on expected earnings growth (b cg). Then I form value-weighted portfolios
using stocks in the top and bottom quintiles. Stocks in the bottom quintile has low expected
growth and stocks in the top quintile has high expected growth. The hedged portfolio buys stocks
in the bottom quintile and shorts those in the top quintile. Column 1 through 3 in Table 1.2 show
that stocks with low expectations earn significantly higher excess returns. Stocks in the bottom
expected growth quintile earns an average of 0.87% excess return per month, while stocks in the
top quintile earn only 0.25% per month. The difference of 0.61% is economically large and has a
t-value of 2.73. The return spread between the low and high expectation portfolios become even
larger after controlling for various factors. Column 4 shows that the low expectation portfolio earns
a CAPM alpha of 0.24%, while in column 5, we see that the high expectation portfolio earns a
0:52% alpha per month. The hedged strategy that buys stocks with low expectations and shorts
those with high expectations earns a CAPM alpha of 0.77% per month (over 9% per year) with a
t-value of 3.71. Column 7 to 9 show that some of the most well-known factors do not explain the
alpha. The long-short strategy earns a six-factor model alpha of 0.68% per month with a t-value
of 3.57.
The results in Figure 1.2, Figure 1.3 and Table 1.2 illustrate a negative association between
earnings growth expectations and stock returns. While these results are consistent with existing
findings using analysts’ long-term growth forecasts, I show that analysts’ growth forecasts within
one year also negatively predict stock returns. Next, I examine growth expectations at each forecast
horizon to test how investors respond differently to forecast errors at different distances, and how
such difference in response can generate delayed alpha.
1.4. Empirical results 17
1.4.2 Decomposing expected change in earnings growth
At the beginning of each month, I sort stocks into quintiles by their expected change in growth
in the first, the second, and the third subsequent quarter (b cg
1
, b cg
2
, and b cg
3
). Then I form value-
weighted portfolios that buy stocks in the bottom quintile and short those in the top quintile
for each horizon. If investors pay full attention to two-quarter-ahead forecasts, we expect the
b cg
3
portfolio to generate significant alpha because investors and analysts would start correcting
the forecast and pricing errors when the three-quarter-ahead forecasts approach the two-quarter
horizon. If investors pay full attention to one-quarter-ahead forecasts, we expect to see a significant
alpha from the b cg
2
portfolio. If investors only correct the pricing error when the actual earnings
are announced, the b cg
1
portfolio should generate significantly positive alpha.
Table 1.3 provides portfolio regression results for the b cg
1
, b cg
2
, and b cg
3
portfolios using a six-
factor model. From column 3, 6 and 9, we see that the only significantly positive long-short alpha
arises from the b cg
2
portfolio. This strategy that trades against analysts’ two-quarter-ahead growth
forecasts earns a value-weighted six-factor long-short alpha of 0.58% per month with a t-value of
3.15. The long-leg of this strategy earns a six-factor model alpha of 0.27% per month with a t-value
of 2.11, and short-leg earns an alpha of0:31% with a t-value of2:26.
It is unprofitable to trade against analysts’ one-quarter-ahead forecasts, as column 3 shows that
the strategy incurs a negative alpha of0:38%, which means that trading against one-quarter-
ahead forecasts contributes negatively, if anything, to the alpha in Table 1.2. Column 9 shows
that the strategy that trades against three-quarter-ahead growth forecasts earn an insignificant
alpha of 0.23% per month. These results indicate that almost all the return predictability from
the strategy discussed in the previous subsection stems from trading against analysts’ two-quarter-
ahead forecasts.
The significantly positive alpha from the b cg
2
strategy suggests that investors pay high attention
to one-quarter-ahead earnings forecasts, as investors tend to correct the pricing errors associated
with extreme growth forecasts when these forecasts move from the two-quarter-ahead horizon to
one-quarter-ahead. This implies a high value for m
1
. The b cg
1
strategy is unprofitable, suggesting
there is little mispricing left after the forecasts enter the one-quarter horizon. The profitability of
the b cg
2
strategy and the unprofitability of the b cg
1
together suggest that a reasonable estimate for
18 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
m
1
is m
1
= 1, which means that investors pay full attention to one-quarter-ahead forecasts.
The b cg
3
strategy generates an alpha that is statistically indistinguishable from 0, which means
that either the three-quarter-ahead growth forecasts are correctly priced, or investors do not pay
sufficient attention to the errors in these forecasts. We already see that two-quarter-ahead fore-
casts negatively predict stock returns, and three-quarter-ahead forecasts should theoretically be
less accurate than two-quarter-ahead forecasts. Therefore, the only plausible explanation for this
insignificant alpha is investors’ lack of attention. If we assume any remaining mispricing in the
b cg
3
portfolio is corrected in the subsequent quarter in the b cg
2
portfolio, based on the alpha point
estimates of 0.23% for the b cg
3
portfolio and 0.58% for the b cg
2
portfolio, we can estimate investors’
attention level to two-quarter-ahead earnings forecasts as m
2
= 0:23=(023 + 0:58) 0:284. Thus,
results in Table 1.3 suggest that investors pay full attention to one-quarter-ahead earnings forecasts
(m
1
= 1), and about 28.4% attention to two-quarter-ahead earnings (m
2
= 0:284). I provide more
measurements for m
2
in later sections.
1.4.3 Delayed alpha
This subsection demonstrates the delayed alpha using event-study plots, Fama and MacBeth (1973)
regressions, and portfolio regressions.
Event-study figures
If investors are inattentive to analysts’ forecast errors before the forecasts approach the one-quarter
horizon, we expect that (1) the strategy that trades against one-quarter-ahead expectations is
unprofitable; (2) the strategy that trades against two-quarter-ahead expectations is profitable;
(3) the strategy that trades against three-quarter-ahead expectations is unprofitable initially, but
becomes profitable after a quarter, and therefore earns a delayed alpha. Event-study figures are
well suited to examine these predictions, because they show whether the strategies are profitable
and if so, when they earn the profits.
Figure 1.4, 1.5 and 1.6 plot the market-adjusted buy-and-hold returns on portfolios sorted by
growth expectations at the one-quarter, two-quarter, and three-quarter horizon (b cg
1
, b cg
2
and b cg
3
).
The black lines show the return on the low-expectation portfolios (quintile 1), and the red lines
1.4. Empirical results 19
show the return on the high-expectation portfolios (quintile 5). The gray dotted lines correspond
to portfolios that consist of stock in quintile 2, 3 and 4. The vertical solid lines are at the expected
days of subsequent earnings announcements.
InFigure1.4,weseenovisibleseparationbetweenthecumulativereturnsonthefiveexpectation-
sorted portfolios, indicating that stocks with different one-quarter-ahead growth forecasts do not
perform significantly differently. In Figure 1.5, however, we see large spreads between the return
paths of the high- and low-expectation portfolios. The low-expectation portfolio (black) starts to
outperform the high-expectation portfolio (red) at around one and a half months after the earnings
announcements. The spread continues to widen to about 2% at around month 4, and remains at
2% thereafter. The visual evidence in Figure 1.4 and 1.5 confirms the results in Table 1.3: it is
profitable to trade against two-quarter-ahead earnings forecasts, but not against one-quarter-ahead
forecasts. Figure 1.4 and 1.5 suggest that investors pay full attention to one-quarter-ahead earnings
forecasts, or m
1
= 1.
Figure 1.6 plots the market-adjusted buy-and-hold returns on portfolios sorted by b cg
3
. We
see that the low-expectation portfolio (black) performs similarly as the high-expectation portfolio
(red) in the first quarter following portfolio construction. The two lines slightly diverge around the
first subsequent earnings announcement, generating a spread of around 0.4% which persists over
the second quarter. When the second subsequent earnings announcement approaches, or when
the three-quarter-ahead earnings forecasts are about to enter investors’ one-quarter horizon (at
between month 5 and month 6), the return spread starts to substantially widen. After the second
earnings announcement, the spread reaches around 1.5%.
Figure 1.6 suggests that the market partially corrects the mispricings induced by three-quarter-
ahead forecast errors in the first quarter, but most of the price correction occurs in the second
quarter. The fraction of price correction in the first quarter, which I interpret as investors’ attention
level for two-quarter-ahead forecast errors is m
2
= 0:4=1:5 0:267.
Evidence from Fama and MacBeth (1973) regressions
One concern with univariate portfolio sorting is that it does not control for known predictors of
stock returns. I address this concern here using Fama and MacBeth (1973) regressions. Table 1.4
20 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
shows the average slopes and time-series t-values from Fama and MacBeth (1973) regressions that
predict monthly stock returns with lagged values of one-quarter-, two-quarter-, and three-quarter-
ahead expected change in growth (b cg
tk
1
, b cg
tk
2
, and b cg
tk
3
) and a set of firm-level control variables,
8
where k denotes the number of months by which the expectation measures are lagged. I present
results for the full sample, and the small and large firm subsamples splitted by the 50
th
NYSE
market capitalization percentile. I omit the slope estimates for the control variables in this table
to conserve space and report them in Table 1.13 in Appendix A1.4.
In the full sample, we see that one-quarter-ahead expected change in growth (b cg
tk
1
) does not
predict stock returns. The slope estimates in row 1 are statistically indistinguishable from zero
at any lag k. In contrast, two-quarter-ahead growth forecast (b cg
tk
2
) negatively predicts stock
return with an average slope of0:27 and a t-value of4:49 at k = 0. This estimate means
that a one percentage point increase in analysts’ two-quarter-ahead expected change in growth is
associated with a 0:27% decrease in monthly expected return. The standard deviation of b cg
2
is
about 0.85 percentage point (see Table 1.1), which implies that a long-short strategy that buys
stocks whose two-quarter-ahead growth forecasts are one standard deviation below the average,
and shorts those that are one standard deviation above the average would earn a monthly return
spread of (0:86 2 0:27 =) 0:464%. This return spread is orthogonal to the effects from growth
expectations at other horizons and the control variables. The predictive power of b cg
2
completely
disappears once the variable is lagged by more than three months (k 3), which means that the
price correction about b cg
2
completes within one quarter.
Results in row 3 show that lagged three-quarter-ahead forecasts predict stock returns. In the
full sample, the average slope of b cg
tk
3
becomes increasingly negative from0:05 (t-value =0:85)
to0:24 (t-value =3:94) as the number of lags k increases from 0 to 4. This result means that
three-quarter-ahead growth forecasts predict stock returns not in the current quarter, but in the
subsequent quarter.
The results are similar across small and large firms. b cg
tk
1
never predicts returns; b cg
tk
2
predicts
returns at the current quarter; b cg
tk
3
predicts returns mostly in the next quarter. The consistency
8
These control variables are: last earnings surprise, last earnings announcement return, market value, book-to-
market equity, asset growth, profitability, past returns, long-term growth, past forecast revisions, number of analysts,
and earnings forecast dispersion.
1.4. Empirical results 21
between the small and large firm results suggests that the analysts’ long-horizon forecast errors
and investors’ inattention to them are common across big and small firms. We see that the average
slopes for b cg
tk
2
and b cg
tk
3
for big firms are somewhat larger in magnitude and sometimes more
statistically significant than those of small firms. This difference in the point estimates could be
because bigger stocks are usually followed by more analysts, which makes my expectation measures
less noisy for bigger firms and thus increases the statistical power of the tests.
The results in Table 1.4 suggest that m
1
= 1 is a good approximation for investors’ attention
to one-quarter-ahead earnings forecasts, as the pricing errors associated with two-quarter-ahead
earnings forecasts completely vanish after three months. We can estimate m
2
using the slope
estimates for b cg
t0
3
, b cg
t3
3
, and b cg
t4
3
: m
2
=0:05=(0:05 +
0:190:24
2
) = 0:189.
Evidence from factor model regressions
Factor model regressions allow us to directly estimate the abnormal returns from the strategies
after controlling for well-known factors. Table 1.5 shows the six-factor model alphas on portfolios
constructed based on lagged values of one-quarter-, two-quarter-, and three-quarter-ahead expected
change in growth (b cg
tk
1
, b cg
tk
2
, and b cg
tk
3
), where k denotes the number of months lagged. Panel
A shows results for value-weighted portfolios and Panel B for equal-weighted portfolios. The first
row in Panel A shows that the b cg
2
portfolio earns alpha immediately, and the alpha decays with
the number of lags. The strategy’s alpha steadily decreases from 0.58% (t-value = 3.15) per month
at k = 0 to essentially 0% at k 3.
The alpha for the b cg
3
portfolio, however, increases over time as shown in row 2 of Panel A. At
k = 0, the alpha is 0.23% and statistically indistinguishable from 0. At k = 2; 3; and 4, the alpha
increases to 0.33%, 0.43%, 0.37% and becomes significantly different from 0 at the 5% or 1% level.
These results suggest that most of the pricing errors associated with three-quarter-ahead growth
forecasts do not get corrected immediately, but with a delay of about a quarter. Subsample results
for the small and big firms show that while the alpha of the strategy is larger among small firms,
the delayed alpha results are similar across small and large firms, suggesting that inattention to
earnings forecasts beyond the one-quarter horizon is a common phenomenon.
22 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
The results are stronger with equal-weighted portfolios as shown in Panel B. In the full sample,
the alpha on the b cg
3
portfolio increases from 0.11 at k = 0 to 0.55% (t-value = 4.11) for the full
sample. The alpha at k = 4 is 0.58% (t-value = 3.48) for small firms, and 0.43% (t-value = 3.45)
for big firms at k = 4.
We can estimate m
2
again with the results in Table 1.5. Using the alpha estimates at k = 0; 3
and 4 in row 2 of Panel A, I compute m
2
= 0:23=(0:23 +
0:43+0:37
2
) = 0:365. The equal-weighted
results (row 2 of Panel B) suggest a m
2
= 0:11=(0:11 +
0:47+0:55
2
) = 0:177.
1.4.4 The efficient horizon
I call the horizon at which some news becomes efficiently priced the “informationally efficient
horizon” for that news. In my model with inattention, the efficient horizon corresponds to the
horizon at which investors’ attention reaches 1 for the first time. Existing research indicates that
prices of larger stocks tend to be more informationally efficient, because these stocks enjoy better
information environment and have more active trading. Therefore, given that the strategy that
trades against three-quarter-ahead growth forecasts generates delayed alpha, one may expect that
the alpha comes with a shorter delay and the price correction completes earlier among large firms.
In other words, we expect larger firms to have a longer informationally efficient horizon for earnings
forecasts.
We indeed see that larger firms have longer efficient horizons in Table 1.4. At k = 2, three-
quarter-ahead growth forecast (b cg
t2
3
) does not significantly predict returns among small firms
(slope =0:06 and t-value =1:02), but predicts returns among large firms (slope =0:21 and
t-value =2:66). At k = 5, three-quarter-ahead forecasts (b cg
t5
3
) predict stock returns among
small firms (slope =0:18 and t-value =2:54) while its predictive power among large firms
disappears (slope =0:02 and t-value =0:26). These results mean that prices of large stocks
start to correct about one month before small stocks, and the price corrections among large stocks
also finish one month before those among small stocks. This one month difference implies that large
firms on average have an efficient horizon that is one month longer than small firms for earnings
forecasts. We can see the same general pattern in the subsample results in Table 1.5 with factor
model alphas. This result that larger firms have longer efficient horizons is consistent with existing
1.4. Empirical results 23
findings that large stocks tend to be more efficiently priced. However, I show that even among
large stocks, price correction can come a with a significant delay, making a strategy that trades on
long-horizon information experience delayed alpha.
Them
2
estimated using the value-weighted alphas (m
2
= 0:365) in Table 1.5 is about twice as
large as the m
2
estimated using equal-weighted alphas (m
2
= 0:177). This is consistent with the
idea that investors generally pay more attention to larger stocks, which makes larger stocks have
longer efficient horizons. Averaging all them
2
estimates so far, I estimate investors’ attention level
totwo-quarter-aheadearningsforecaststobem
2
=
1
5
(0:284+0:267+0:189+0:365+0:177) 0:256,
or about a quarter of full attention.
1.4.5 Testing the mechanism: Inattention to long-horizon forecast errors
In this section, I test the mechanism behind the alpha and delayed alpha documented in the
previous sections by examining the link between the return predictability and analysts’ forecast
errors.
Forecast errors and growth expectations
If my measures of growth expectations predict returns through analysts’ forecast errors, we expect
that b cg
2
and b cg
3
also predict analysts’ ex-post forecast errors at the corresponding horizons. Ta-
ble 1.6 presents the results from panel regressions that regress ex-post forecast errors on growth
expectations and firm characteristics. The dependent variables are the actual earnings one-quarter-
, two-quarter-, and three-quarter-ahead, minus the consensus (median) earnings forecasts for the
corresponding quarter measured one week after the last earnings announcements, scaled by the
market value of equity three days before the last earnings announcements. All regressions include
industry (Fama-French 48 industries) and year-quarter fixed effects. Standard errors are clustered
by industry and year-quarter. The variables of interest are the two-quarter- and three-quarter-
ahead earnings growth expectations (b cg
2
and b cg
3
). If high expectations predict overly optimistic
forecasts, we expect the coefficients on these two variables to be negative.
We see from row 2 that b cg
2
consistently predicts forecast errors with a negative sign across
all horizons. Its predictive power is strongest when predicting two-quarter-ahead forecast errors.
24 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
The coefficients are0:21 (t-value =4:36) without firm controls and0:16 (t-value =3:77)
with controls. These coefficients mean that a one percentage point increase in expected earnings
growth in the second quarter (in terms of earnings yield) is associated with earnings forecasts
that are about 0.21 or 0.16 percentage point too high. Column 1 and 2 show that two-quarter-
ahead growth forecasts also significantly predict forecast errors in the current quarter even after
controllingforthecurrentquartergrowthforecasts(b cg
1
)andobservablefirmcharacteristics, though
the magnitudes are small (0:09 and0:05). b cg
2
also predicts three-quarter-ahead forecast errors
(with coefficients of0:18 and0:13 and t-values of3:46 and2:75), which is not surprising
because if analysts are overly optimistic about the firm’s second-quarter growth, they would also
likely overestimate the firm’s third-quarter earnings.
Results in row 3 show that three-quarter-ahead growth forecasts predict three-quarter-ahead
forecast errors with coefficients of0:18 (t-value =3:13) and0:13 (t-value =2:56), but do
not significantly predict one-quarter- or two-quarter-ahead forecast errors. This result is consis-
tent with the delayed alpha: strategies that trade against three-quarter-ahead earnings growth
forecasts do not profit until a quarter later. Overall, coefficient estimates in row 2 and 3 show
that two-quarter- and three-quarter-ahead growth forecasts most strongly predict forecast errors
at their corresponding horizons. These results suggest that the alpha and delayed alpha from these
strategies that trade against these growth forecasts stem from investors’ inattention to predictable
forecast errors.
Results in Table 1.6 demonstrates the relation between analysts’ growth forecasts and ex-post
forecast errors, and thus suggest that investors’ inattention to long-horizon forecasts errors as a
likely explanation for the return predictability. However, the results do not establish a direct link
between forecast errors and return predictability. While analysts’ growth forecasts at different
horizons simultaneously predict forecast errors and stock returns at the matching horizons, the
relation between the forecast errors and the return predictability is still unclear because correlations
are non-transitive. That is, a variable being able to predict both forecast errors and stock returns
does not necessarily mean that the variable predicts returns through predicting forecast errors.
Hence, the evidence in Table 1.6 is necessary, but not sufficient to establish a direct link between
investors’ inattention to long-horizon forecast errors and the (delayed) alpha.
1.4. Empirical results 25
Analysts’ belief revisions and delayed alpha
To draw a more direct link between forecast errors and the (delayed) alphas from the strategies,
I follow the counterfactual portfolio approach in Linnainmaa and Zhang (2018) to estimate how
much of the alphas from the strategies are accrued over days when analysts revise their beliefs.
Specifically, I compare the alpha of the strategies before and after removing stock-days within the
three-day windows around any analysts’ forecast revisions, recommendation changes, and earnings
announcements. We call this event-free portfolio the “counterfactual portfolio” because it approx-
imates what the portfolio would have performed if one could perfectly skip these events. Among
the events I study, investors do not know in advance when forecast revisions or recommendation
changes occur, but most likely do know when earnings announcements arrive. Hence, I separately
test the alpha contribution from earnings announcements. Overall, about 33.6% of the sample fall
in the three-day windows of at least one of these events, and 4.3% of the sample fall in the three-day
windows around earnings announcements.
Table 1.7 presents the results from the counterfactual portfolio tests using daily rebalanced
equal-weighted portfolios. To avoid overly emphasizing small stocks, I include only stocks above
the 20
th
percentile of the NYSE market capitalization distribution in the previous month. The
results are qualitatively similar when using value-weighted portfolios or including micro-cap stocks.
The first four columns of Table 1.7 show results for a strategy that buys stocks in the bottom
quintile of two-quarter-ahead growth expectations (b cg
2
) and short those in the top quintile. P
0
is
the actual portfolio; P
NEA
is the portfolio with no earnings announcements; P
NE
is the portfolio
with no events (forecast revisions, recommendation changes and earnings announcements); P
0
P
NE
is the difference portfolio. If these events are important for the strategy’s alpha, we expect to
see small alphas for P
NEA
and P
NE
, and a large alpha for P
0
P
NE
.
Column 1 shows that the actual portfolio P
0
earns a six-factor model alpha of 2.46 basis points
per day (or about 0.54% per month) with a t-value of 4.24. This alpha estimate using daily data is
in line with results in Table 1.3. Column 2 shows that after removing stock-days around earnings
announcements, the strategy’s alpha drops to 1.81 basis points per day, which represents a 26.4%
decrease in alpha relative to the original portfolio. After removing all events, the alpha becomes
0.24 basis points, which is not significantly different from 0 as shown in column 3. The alpha for
26 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
the difference portfolio (P
0
P
NE
) is 2.22 basis points per day with a t-value of 6.30, which means
that about (2.22/2.46 =) 90% of the alpha of the strategy is attributable to this set of events about
belief revisions.
Results in column 5 to 8 show a similar pattern for the strategy that trades against analysts’
three-quarter-ahead earnings growth expectations measured one quarter ago: most of the delayed
alpha is accrued on days when analysts update their beliefs. We see that the strategy earns a
daily (delayed) alpha of 2.33 basis points per day with a t-value of 4.04. After removing earnings
announcements, the alpha decreases to 1.94, and down to 0.94 after removing all events. The alpha
for the difference portfolio is 1.38 (t-value = 3.87), which means that about (1:38=2:33 =) 59%
of the delayed alpha is attributable to days around analysts’ belief updates. Overall, results in
Table 1.7 indicate that the alpha and delayed alpha from the strategies that trade against analysts’
growth expectations mostly accrue when analysts update their beliefs. This evidence suggests that
the (delayed) alphas most likely represent mispricings due to expectations errors, and not likely
stem from other reasons such as omitted risk factors.
Earnings announcement returns and expectation term strucuture shifts
This subsection provides evidence on investors’ underreaction to long-horizon information by ex-
ploitingshiftsintheentiretermstructureofearningsexpectationsaroundearningsannouncements.
During earnings announcements, cash flow information over different horizons arrives simultane-
ously, shifting the entire term structure of expectations. If investors pay less attention to earnings
forecasts beyond the one-quarter horizon, we expect to see that stock prices respond less to shifts
in the two-quarter- and three-quarter-ahead earnings expectations. I call the changes in earnings
expectations immediately following earnings announcements the “forward earnings surprises” to
contrast them with the current earnings surprise.
I regress three-day cumulative abnormal returns around earnings announcements on current
surprise (SUE) and forward surprises at the one-quarter, two-quarter, and three-quarter horizons
(FSUE1, FSUE2, FSUE3). I measure forward surprises as the change in analysts’ consensus (me-
dian) earnings forecasts within one week after the earnings announcements relative to their consen-
sus three days before these earnings announcements (for the same fiscal quarter, as opposed to for
1.4. Empirical results 27
the same forecast horizon), scaled by market value of equity three days before the announcements.
I also include a set of firm-level controls, industry (Fama-French 48 industries) and year-quarter
fixed effects.
9
Table 1.8 column 1 shows results for a baseline regression in which I only include the standard
variables on the right-hand-side. We see in the first row that current earning surprise explain
earnings announcement returns with a coefficient of 3.64 and a t-value of 3.79. The magnitude
means that a one percentage point increase in current earnings surprise (in terms of earnings yield)
is associated with an average of 3.64% increase in cumulative abnormal returns in the three days
around earnings announcements. The R-squared of this baseline regression is 0.05. Once I include
the one-quarter-ahead forward surprise (FSUE1) to the regression, the R-square jumps to 0.12.
FSUE1 explains earnings announcement return with a coefficient of 6.56 and a t-value of 9.88.
This strong explanatory power of FSUE1 suggests that investors pay high attention to forward-
looking information around earnings announcements. The coefficient on SUE decreases from 3.64
to 2.36 after including FSUE1 to the regression, suggesting this coefficient in baseline specification
suffers from an omitted variable bias. Similar results hold for FSUE2 and FSUE3, indicating that
forward surprises significantly explain earnings announcement returns.
Once we include forward surprises at different horizons simultaneously, we see that investors
mostly react to one-quarter-ahead earnings information and much less so to two-quarter- and three-
quarter-ahead information. In column 5 and 6, the coefficients on FSUE1 are 4.30 (t-value = 10.25)
without firm controls and 4.83 (t-value = 10.02) with controls. However, the coefficients on the
two-quarter- and three-quarter-ahead forward surprises (FSUE2 and FSUE3) are over 50% smaller
than the coefficient on FSUE1. The coefficients on FSUE2 are 1.69 (t-value = 4.24) and 1.96
(t-value = 4.52) without and with firm-level controls; the coefficients for FSUE3 are 1.97 (t-value
= 6.70) and 2.25 (t-value = 7.48).
These results suggest that while investors respond to shifts in the entire expectation term
structure around earnings announcements, they respond to one-quarter-ahead earnings information
more than twice as strongly as they do to two-quarter- or three-quarter-ahead information. If we
interprettheresponsecoefficientsasaproxyforinvestors’attention, theysuggestthatinvestorspay
9
Control variables include pre-announcement return (So and Wang (2014)), firm size, book-to-market equity,
profitability, asset growth, past stockreturns, long-termgrowthforecasts, numberofanalystsand forecastdispersion.
28 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
more than twice as much attention to one-quarter-ahead earnings forecasts than to two-quarter-
or three-quarter-ahead forecasts. This conclusion is in line with our earlier attention estimate of
m
2
0:25.
Growth expectations and earnings announcement returns
In this subsection, I examine the relations between analysts’ growth expectations, earnings an-
nouncement returns, and forward earnings surprises. If analysts’ two-quarter-ahead growth fore-
casts predict stocks returns through predicting forecast errors, we expect that b cg
2
negatively pre-
dicts both earnings announcement return and one-quarter-ahead forward surprise. Similarly, if the
delayed alpha from the b cg
3
portfolio is due to expectation errors, we expect that b cg
lag1Q
3
negatively
predicts both announcement return and one-quarter-ahead forward surprise.
I regress the three-day cumulative abnormal returns around earnings announcements on an-
alysts’ expected change in growth over different horizons (b cg
1
, b cg
2
, b cg
lag1Q
3
, and b cg
3
), with and
without firm-level controls.
10
Table 1.9 column 1 to 4 present the results. We see that both b cg
2
and b cg
lag1Q
3
negatively predict earnings announcement returns. The coefficients on b cg
2
are0:24
(t-value =6:91) without firm-level controls and0:21 (t-value = 5.13) with firm-level controls.
The magnitude means that a one percentage point increase in two-quarter-ahead expected change
in growth (in terms of earning yield) is associated with an approximately 0.2% decrease in earnings
announcement return. The results are similar for b cg
lag1Q
3
. The coefficients estimates are0:19
(t-value =3:80) and0:16 (t-value =3:33). In column 5 and 6, I regress one-quarter-ahead
forward surprises (FSUE1) on the same set of variables. We see that b cg
2
and b cg
lag1Q
3
significantly
predict FSUE1, with coefficients of4:67 (t-value =6.81) and1:75 (t-value =3.24).
Table 1.9 shows that analysts’ growth forecasts negatively predict both earnings announcement
returns and forward earnings surprises. This is consistent with the results shown in Table 1.7
that earnings announcement returns contribute significantly to the overall (delayed) alpha from
the strategies. Results in Table 1.9 support the hypothesis that the growth expectations predict
returns through predicting expectation errors, and thereby suggesting a mispricing interpretation
10
In these regressions, I measure analysts’ expectations one week prior to the earnings announcement to ensure
the variables are up-to-date.
1.4. Empirical results 29
of the (delayed) alphas. They also show that the predictive power of the growth expectations
persists after including a set of firm-level control variables.
1.4.6 Underreaction to bad news
Prior research such as Chan, Jegadeesh, and Lakonishok (1996) and Hong, Lim, and Stein (2000)
find that investors underreact more to negatively news. Models with bounded rationality and
limited attention predict underreaction to long-horizon information. Therefore, we may expect
the (delayed) alpha to be more pronounced among firms with poor recent performance. To test
this hypothesis, I sort stocks into terciles based on their returns in the past quarter. Following the
literatureonmomentumstrategies,Iskipthemostrecentmonthwhenconsideringpastperformance
to mitigate the effects of short-term reversal. Then I examine the performance of the strategies
that trade against b cg
2
and b cg
lag1Q
3
within each tercile.
Table 1.10 presents value-weighted and equal-weighted monthly six-factor model alphas from
portfolios constructed by three-by-three conditional double sort on past quarter return (r
4;2
) and
analysts’ growth forecasts (b cg
2
or b cg
lag1Q
3
). The T1T3 portfolios represent strategies that buy
stocks with low growth expectations and short those with high expectations within a past return
tercile. If the alpha and the delay alpha from trading against b cg
2
and b cg
lag1Q
3
come from investors’
underreaction due to inattention, we expect the alphas to be larger among stocks in the bottom
past return tercile (T1).
Indeed we see from the T1T3 rows in the b cg
2
and b cg
lag1Q
3
panel that the (delayed) alphas of
the strategies are largest among loser stocks. The strategy that trades against b cg
2
among stocks
in the bottom past return tercile earn a value-weighted six-factor model alpha of 1.02% per month
(t-value = 4.06), and an equal-weighted alpha of 0.89% (t-value = 5.89). The same strategy applied
to past winners earns a value-weighted alpha of 0.09% (t-value = 0.47) per month and an equal-
weighted alpha of 0.35% (t-value = 2.98) per month. The same pattern holds for strategies that
trade against b cg
lag1Q
3
. These results are consistent with the underreaction interpretation in which
investors’ inattention to long-horizon forecast errors causes the alpha and delayed alpha of the
strategies.
30 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
1.4.7 Robustness
My results are robust to different ways of measuring growth expectations and controlling for other
momentum type factors. I suppress the results from these robustness tests to Appendix A1.4 for
conciseness but provide some brief discussions here. My main measures of growth expectations use
earnings to measure growth and use market value of equity as the scaling variable (i.e.,
Earnings
Price
).
Table 1.11 provides the results from Fama and MacBeth (1973) regressions using four alternative
definitions for expected growth: (1) revenue scaled by market value of equity, (2) earnings scaled
by total asset, (3) earnings scaled by book value of equity, and (4) earnings scaled by revenue.
The results for each variable definition is shown in each column. Row 2 shows that lagged values
of three-quarter-ahead growth measured in all four ways significantly predict stock returns with
negative slopes, which means that the results about delayed alpha are robust to these alternative
measures of growth. Results for two-quarter-ahead forecasts are always stronger, so I only show
results with lagged three-quarter-ahead forecasts.
The (delayed) alpha from my strategies arises from analysts’ systematic forecast errors and
investors’ inattention to them. Prior research shows that analysts’ revision exhibits momentum
(e.g., Chan et al. (1996)). One concern is that whether momentum in analysts’ revision can
subsume my results. To address this concern, I conduct a factor spanning test between factor
mimicking portfolios constructed based on analysts’ forecast revisions and analysts’ two-quarter-
ahead growth forecasts. I construct the forecast revision portfolio by sorting stocks monthly into
quintiles based on their one-quarter-ahead earnings forecast revisions in the past three months. The
portfolio buys stocks in the top forecast revision quintile and shorts those in the bottom quintile.
Then I construct the b cg
2
portfolio similarly by buying stocks with low two-quarter-ahead growth
expectations and shorting those with high expectations. Then I regress the returns on these two
portfolios on each other to test whether one factor is spanned by the other.
Table 1.12 presents the results for the spanning tests with value-weighted portfolios. Column
1 shows that the forecast revision portfolio has a marginally significant CAPM alpha of 0.43% per
month (t-value = 1.70). After including the b cg
2
factor, alpha decreases by over 50% to 0.20 and
becomes statistically insignificant. The b cg
2
portfolio, on the other hand, has a CAPM alpha of
0.66% per month (t-value = 3.57). After including the revision factor, its CAPM alpha decreases
1.5. Discussion and conclusion 31
slightlyto0.58%(t-value=3.20). Thetwostrategiesarecorrelated, asonefactorloadssignificantly
on the other factor (row 3 and 4). However, the significant alpha in on the b cg
2
portfolio (column 4)
suggests that the b cg
2
factor contains significant pricing power that is independent of the revision
factor. Column 5 to 8 show similar results using the six-factor model. These results suggest
that the strategy that trades against analysts’ two-quarter-ahead growth forecasts is different from
the revision momentum strategy. The results from Fama and MacBeth (1973) regressions shown
in Table 1.4 also suggest that the predictive power of my expectation measures are robust to
momentum in analysts’ revisions, as those regressions include analysts’ past revisions as one of the
control variables (see Table 1.13 for complete regression results).
1.5 Discussion and conclusion
The term structure of analysts’ earnings expectations and its dynamics predict the cross-section of
stock returns. A strategy that trades against analysts’ two-quarter-ahead growth forecasts earns
a value-weighted six-factor model alpha of 0.58% per month (t-value = 3.15); a strategy that
trades against analysts’ three-quarter-ahead growth forecasts experiences a delayed alpha. Models
with bounded rationality can explain both the return predictability and the delayed alpha through
inattention to long-horizon information. While investors pay full attention to one-quarter-ahead
earnings information, I estimate that they are only about 25% as attentive to earnings information
beyond the one-quarter horizon. My results suggest that information horizon is an important
determinant of informational efficiency of prices. Long-horizon information is less likely to be
efficiently priced, and the mispricings associated with long-horizon information may correct with
significant delay. The efficient horizon for earnings information is about one quarter. Larger firms
have longer efficient horizons than smaller firms.
While this paper shows that the term structure of earnings expectations has significant power
to predict the cross-section of stock returns, much about this term structure remains unexplored.
Figure 1.7 plots the cross-sectional median earnings expectation term structure (before and after
earnings announcements) and the actual median earnings at the corresponding horizons. This fig-
ure reveals some potentially interesting regularities that can be fruitful for future research. Most
existing papers about earnings announcements focus on actual earnings surprises. In this paper, I
32 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
introduce the concept of “forward earnings surprises” by focusing on the shifts in the entire expecta-
tion term structure around earnings announcements. My results suggest that earnings announce-
ment returns respond strongly to forward earnings surprises. Investors can benefit from future
studies on the determinants of the expectation term structure, and by extension, the determinants
of term structure of forecast errors and alphas.
On a cognitive level, why should the efficient horizon be one quarter, instead of two or three
quarters? The literature on level-k thinking offers a potential answer. Camerer, Ho, and Chong
(2004) show that k = 1:5 fits the average steps of thinking in many games. If we imagine that
considering the next quarterly earnings represents the first step of thinking, a 1.5-step thinking
implies an efficient horizon between one and two quarters, which is consistent with my results.
If level-k thinking is indeed the psychological root of investors’ short-termism, reducing the re-
porting frequency may potentially lead investors to consider information at longer horizons.
11
An
experimental study seems natural to test this hypothesis.
Figure 1.8 plots the cumulative returns on simple long-short strategies that capture the return
predictability and delayed alpha documented in this paper. The value-weighted strategies have
Sharpe ratios around 0.7 and the equal-weighted strategies (not shown) have Sharpe ratios around
1. The market seems to reward investors who can see just beyond the one-quarter horizon. In real
life, we may also benefit from lengthening our forward-looking horizon when considering important
issues such as climate change, plastic pollution, and energy sustainability.
11
The SEC has been investigating the effects of changing the earnings reporting frequency from quarterly to
semi-annual (https://www.nytimes.com/2018/08/17/business/dealbook/trump-quarterly-earnings.html).
A1.1. Figures 33
A1.1 Figures
Monthly excess return (%)
Expected change in growth decile
1 (Low) 2 3 4 5 6 7 8 9 10 (High)
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Figure 1.2: Average excess returns by expected change in growth deciles. Stocks are
sorted into equal-weighted deciles by their expected change in earnings growth (b cg) each month.
This figure plots the average excess returns for each decile. Expected change in growth increases
from decile one to ten. The sample period is from January 2002 to December 2016.
34 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Monthly six-factor alpha (%)
Expected change in growth decile
1 (Low) 2 3 4 5 6 7 8 9 10 (High)
- 0.6 - 0.4 - 0.2 0.2 0.4 0.0
Figure 1.3: Six-factor model alphas by expected change in growth deciles. Stocks are
sorted into deciles by their expected change in growth (b cg) each month. This figure plots the equal-
weighted six-factor model alpha and 95% confidence interval for each decile. The six-factor model
is the five-factor model from Fama and French (2015b) augmented with the UMD factor of Carhart
(1997). Expected change in growth increases from decile one to ten. The sample period is from
January 2002 to December 2016.
A1.1. Figures 35
Cumulative market-adjusted return (%)
1 2 3 4 5 6 7 8 9 10 11 12
Number of months since the last earnings announcement
0.0 0.5 1.0 1.5 2.0 - 0.5
cg
1
Q1 (Low)
cg
1
Q2
cg
1
Q3
cg
1
Q4
cg
1
Q5 (High)
Quarter 1 Quarter 2 Quarter 3 Quarter 4
cg
1
revealed cg
2
revealed cg
3
revealed
Figure 1.4: Event-time portfolio returns and one-quarter-ahead expected change in
growth (b cg
1
). This figure plots the average market-adjusted buy-and-hold returns on stocks sorted
into quintile portfolios by their one-quarter-ahead expected changes in growth (b cg
1
). I first compute
the buy-and-hold return for each stock in the portfolio. Then I subtract each buy-and-hold return
by the contemporaneous buy-and-hold return from the CRSP value-weighted index. This figure
shows the average of the resulting market-adjusted buy-and-hold returns for each portfolio in event-
time relative to the last earnings announcement, from t = 10 to 255. The horizontal axis labels
the number of months after the last earnings announcement. Each month has 21 trading days. b cg
1
is measured on the fifth trading day (t = 5) after the last earnings announcement. I assign each
stock-announcement observation to a quintile on t = 9 based on the cross-section of b cg
1
on that
date.
36 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Cumulative market-adjusted return (%)
1 2 3 4 5 6 7 8 9 10 11 12
Number of months since the last earnings announcement
0.0 0.5 1.0 1.5 2.0 - 0.5
cg
2
Q1 (Low)
cg
2
Q2
cg
2
Q3
cg
2
Q4
cg
2
Q5 (High)
Quarter 1 Quarter 2 Quarter 3 Quarter 4
cg
1
revealed cg
2
revealed cg
3
revealed
Figure 1.5: Event-time portfolio returns and two-quarter-ahead expected change in
growth (b cg
2
). This figure plots the average market-adjusted buy-and-hold returns on stocks sorted
into quintile portfolios by their two-quarter-ahead expected changes in growth (b cg
2
). I first compute
the buy-and-hold return for each stock in the portfolio. Then I subtract each buy-and-hold return
by the contemporaneous buy-and-hold return from the CRSP value-weighted index. This figure
shows the average of the resulting market-adjusted buy-and-hold returns for each portfolio in event-
time relative to the last earnings announcement, from t = 10 to 255. The horizontal axis labels
the number of months after the last earnings announcement. Each month has 21 trading days. b cg
2
is measured on the fifth trading day (t = 5) after the last earnings announcement. I assign each
stock-announcement observation to a quintile on t = 9 based on the cross-section of b cg
2
on that
date.
A1.1. Figures 37
Cumulative market-adjusted return (%)
1 2 3 4 5 6 7 8 9 10 11 12
Number of months since the last earnings announcement
0.0 0.5 1.0 1.5 2.0 - 0.5
cg
3
Q1 (Low)
cg
3
Q2
cg
3
Q3
cg
3
Q4
cg
3
Q5 (High)
Quarter 1 Quarter 2 Quarter 3 Quarter 4
cg
1
revealed cg
2
revealed cg
3
revealed
Figure 1.6: Event-time portfolio returns and three-quarter-ahead expected change
in growth (b cg
3
). This figure plots the average market-adjusted buy-and-hold returns on stocks
sorted into quintile portfolios by their three-quarter-ahead expected changes in growth (b cg
3
). I first
compute the buy-and-hold return for each stock in the portfolio. Then I subtract each buy-and-hold
return by the contemporaneous buy-and-hold return from the CRSP value-weighted index. This
figure shows the average of the resulting market-adjusted buy-and-hold returns for each portfolio
in event-time relative to the last earnings announcement, from t = 10 to 255. The horizontal axis
labels the number of months after the last earnings announcement. Each month has 21 trading
days. b cg
3
is measured on the fifth trading day (t = 5) after the last earnings announcement. I
assign each stock-announcement observation to a quintile on t = 9 based on the cross-section of b cg
3
on that date.
38 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
1.25 1.30 1.35 1.40 1.45 1.50
Earnings yield (%)
Quarter(s) ahead
Q0 Q1 Q2 Q3 Q4
Pre-EA expectation
Post-EA expectation
Actual earnings yield
Figure1.7: The term structure of earnings expectations and actual earnings. This figure
plots the cross-sectional median analysts’ consensus (median) earnings per share forecasts over the
subsequent quarters, before and after the current earnings announcement at Q0. The red line
shows the median actual earnings per share for the same sample. All EPS estimates are scaled by
stock prices three trading days before the Q0 announcement. The pre-EA expectations (black), are
measured three trading days before the Q0 announcement, and the post-EA expectations (blue) are
measured five trading days after the Q0 announcement. The sample is from the intersection between
IBES and Compustat, and contains firms-announcements between January 2002 to December 2016.
I require the firms to have non-missing forecasts from Q0 to Q4, a stock price above $5 three trading
days before the Q0 announcement, and at least five analysts following in the 120 days before the
Q0 announcement. I also apply the filters described in Section 1.3.
A1.1. Figures 39
Cumulative return
2002 2004 2006 2008 2010 2012 2014 2016 2018
1.0 1.5 2.0 2.5 3.0
cg
2
VW
cg
3
lag1Q
VW
Year
Figure 1.8: Cumulative returns on value-weighted long-short portfolios formed based
on b cg
2
and b cg
lag1Q
3
. This figure plots the cumulative returns on the value-weigthed long-short
portfolios that buy stocks in the bottom b cg
2
or b cg
lag1Q
3
quintile and short those in the top quintile.
b cg
2
is analysts’ two-quarter-ahead expected change in growth. b cg
lag1Q
3
is analysts’ three-quarter-
aheadexpectedchangeingrowthmeasuredinthepreviousquarter. Thesolidlineplotsthereturnon
the b cg
2
portfolio; the dashed line plots return on the b cg
lag1Q
3
portfolio. The portfolios are rebalanced
monthly.
40 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
A1.2 Tables
A1.2. Tables 41
Table 1.1: Descriptive statistics
This table reports summary statistics of key variables and correlations among them. Each obser-
vation is a firm-announcement. The sample period is from January 2002 to December 2016. Panel
A and B show the time-series average quarterly summary statistics and Panel C shows the quar-
terly time-series average correlations. ME is the market value of equity at the end of the previous
calendar quarter (March, June, September, and December). BM is the ratio of lagged book value
of equity to ME. OP is lagged profitability. AG is lagged asset growth. SUE is actual earnings
per share minus analysts’ consensus (median) forecast, scaled by market value three trading days
before the earnings announcement (P
t=3
). g
yoy
0
is the most recent year-over-year quarterly earn-
ings growth (i.e., current quarter earnings minus the earnings four quarters ago) scaled by P
t=3
.
Panel B reports variables about analysts’ expectations over different horizons. The “hat” means the
variables are constructed based on analysts’ forecasts. ^ g
yoy
i
is equal to the expected year-over-year
earnings growthi quarter(s) ahead, scaled byP
t=3
wherei2f1; 2; 3g. b cg
i
is the expected change
in growth over quarteri, defined as b cg
i
= ^ g
yoy
i
^ g
yoy
i1
fori2f2; 3g and b cg
1
= ^ g
yoy
1
g
yoy
0
. b cg is the
average expected change in earnings growth over the subsequent three quarters, computed as the
slope of the linear trend fitted tog
yoy
0
, ^ g
yoy
1
, ^ g
yoy
2
and ^ g
yoy
3
. Panel C reports the correlations between
growth expectations and firm characteristics. r
12;2
is the buy-and-hold return from twelve to
two months before the earnings announcement.
Panel A: Firm Characteristics (N=1,306)
Variable Mean SD 1
st
25
th
Median 75
th
99
th
ME ($billion) 9:09 26:71 0:17 0:88 2:16 6:27 129:09
BM 0:52 0:36 0:05 0:27 0:43 0:69 1:95
OP 0:07 0:08 0:19 0:04 0:06 0:09 0:45
AG 0:03 0:09 0:15 0:01 0:01 0:04 0:56
SUE 0:05 0:46 2:27 0:03 0:05 0:18 1:53
g
yoy
0
0:02 1:20 5:78 0:24 0:12 0:40 3:62
Panel B: Analysts’ Expectation Term Structure (N=1,306)
^ g
yoy
1
0:03 0:94 4:18 0:23 0:08 0:30 3:11
^ g
yoy
2
0:12 0:82 3:10 0:08 0:13 0:34 3:45
^ g
yoy
3
0:23 0:76 2:28 0:01 0:17 0:37 3:93
b cg
1
0:00 1:02 2:88 0:28 0:04 0:19 3:71
b cg
2
0:15 0:86 2:23 0:10 0:05 0:30 3:28
b cg
3
0:11 0:83 2:25 0:11 0:03 0:25 3:15
Panel C: Correlations between Expectations and Firm Characteristics
b cg b cg
1
b cg
2
b cg
3
SUE ln(ME) ln(BM) OP AG r
12;2
LTG
b cg 1:00 0:38 0:13 0:15 0:22 0:10 0:30 0:04
b cg
1
0:54 1:00 0:41 0:04 0:05 0:10 0:04 0:11 0:02
b cg
2
0:53 0:13 1:00 0:09 0:09 0:10 0:11 0:04 0:19 0:03
b cg
3
0:40 0:03 0:16 1:00 0:09 0:08 0:09 0:14 0:08 0:18 0:02
42 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Table 1.2: Expected change in growth and stock returns
This table reports average excess returns, CAPM and six-factor model (Fama and French (2015b)
augmented with momentum) alphas and factor loadings for monthly rebalanced value-weighted
portfoliosthatcontainstocksinthetoporbottomquintilesofanalysts’expectedchangeinearnings
growth (b cg). The Low (High) portfolio consists of stocks in the bottom (top) b cg quintile at the end
of the previous month. LoHi is the return difference between the Low and the High portfolios.
b cg is the slope of the linear trend fitted to the current year-over-year earnings growth and the
expected year-over-year earnings growth in the subsequent three quarters (see Section 1.3.3 for
details). Returns are in percentages per month. t-values are in square brackets and standard errors
are in parentheses. The sample period is from January 2002 to December 2016.
Excess Return CAPM Six-factor
Low High LoHi Low High LoHi Low High LoHi
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Alpha 0:87 0:26 0:61 0:24 0:52 0:77 0:20 0:47 0:68
[2:37] [0:58] [2:73] [1:80] [3:37] [3:71] [1:44] [3:37] [3:57]
MKT 1:08 1:36 0:28 1:12 1:24 0:12
(0:03) (0:04) (0:05) (0:04) (0:04) (0:05)
SMB 0:06 0:12 0:06
(0:06) (0:06) (0:08)
HML 0:08 0:21 0:28
(0:06) (0:06) (0:09)
RMW 0:00 0:26 0:26
(0:10) (0:10) (0:13)
CMA 0:04 0:09 0:05
(0:08) (0:08) (0:11)
UMD 0:06 0:20 0:26
(0:03) (0:03) (0:04)
N 180 180 180 180 180 180 180 180 180
Adj. R
2
0:00 0:00 0:00 0:87 0:89 0:15 0:87 0:92 0:35
A1.2. Tables 43
Table 1.3: Expected change in growth at different horizons and stock returns
This table reports six-factor model (Fama and French (2015b) augmented with momentum) alphas
and factor loadings for monthly rebalanced value-weighted portfolios that contain stocks in the
top or bottom quintiles of analysts’ expected change in year-over-year earnings growth at the one-,
two-, or three-quarter horizon (b cg
1
, b cg
2
, and b cg
3
). Please see Section 1.3.3 for details about variable
construction. The Low (High) portfolios contain stocks whose b cg
i
(i2f1; 2; 3g) are in the bottom
(top) quintile at the end of the previous month. LoHi is the return difference between the Low
and High portfolios. Returns are in percentages per month. t-values are in square brackets and
standard errors are in parentheses. The sample period is from January 2002 to December 2016.
One-quarter-ahead Two-quarter-ahead Three-quarter-ahead
expected growth (b cg
1
) expected growth (b cg
2
) expected growth (b cg
3
)
Low High LoHi Low High LoHi Low High LoHi
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Alpha 0:32 0:06 0:38 0:27 0:31 0:58 0:03 0:26 0:23
[2:61] [0:47] [2:16] [2:11] [2:26] [3:15] [0:23] [1:78] [1:17]
MKT 1:16 1:13 0:04 1:13 1:16 0:02 1:06 1:17 0:11
(0:04) (0:03) (0:05) (0:04) (0:04) (0:05) (0:04) (0:04) (0:06)
SMB 0:06 0:02 0:04 0:03 0:08 0:11 0:06 0:13 0:06
(0:05) (0:05) (0:08) (0:06) (0:06) (0:08) (0:06) (0:06) (0:08)
HML 0:03 0:05 0:08 0:04 0:09 0:13 0:04 0:02 0:02
(0:06) (0:06) (0:08) (0:06) (0:06) (0:08) (0:06) (0:07) (0:09)
RMW 0:01 0:02 0:02 0:10 0:20 0:30 0:15 0:20 0:05
(0:08) (0:08) (0:12) (0:09) (0:09) (0:13) (0:10) (0:10) (0:13)
CMA 0:14 0:04 0:17 0:06 0:08 0:02 0:05 0:14 0:09
(0:07) (0:07) (0:10) (0:07) (0:08) (0:11) (0:08) (0:08) (0:11)
UMD 0:04 0:11 0:07 0:02 0:13 0:15 0:09 0:23 0:32
(0:03) (0:03) (0:04) (0:03) (0:03) (0:04) (0:03) (0:03) (0:05)
N 180 180 180 180 180 180 180 180 180
Adj. R
2
0:91 0:92 0:03 0:89 0:90 0:12 0:86 0:90 0:31
44 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Table 1.4: Lagged expected change in growth and average return in Fama-
MacBeth regressions
This table reports average Fama and MacBeth (1973) regression slopes and t-values (in square
brackets) for b cg
tk
1
, b cg
tk
2
and b cg
tk
3
from cross-sectional regressions that predict monthly stock
returns. b cg
tk
1
, b cg
tk
2
and b cg
tk
3
are the one-, two- and three-quarter-ahead expected change in
growth lagged by k months. Control variables include earnings surprise, earnings announcement
return, firm size, book-to-market equity, profitability, asset growth, past return, long-term growth
forecasts, analysts’ forecast revisions, number of analysts, and forecast dispersion. This table shows
results for the full sample, small firms and big firms. Small firms and big firms are divided using
the 50
th
percentile of the NYSE market capitalization distribution at the end of the prior month.
Complete results including the estimates for the control variables are in Table 1.13. The sample
period is from January 2002 to December 2016.
Number of months lagged
k = 0 1 2 3 4 5 6
Full Sample
b cg
tk
1
0:05 0:03 0:01 0:01 0:03 0:04 0:02
[0:84] [0:58] [0:24] [0:32] [0:67] [0:98] [0:38]
b cg
tk
2
0:27 0:26 0:19 0:06 0:01 0:03 0:01
[4:49] [4:47] [2:92] [0:96] [0:26] [0:57] [0:20]
b cg
tk
3
0:05 0:06 0:11 0:19 0:24 0:14 0:02
[0:85] [1:14] [2:06] [3:45] [3:94] [2:30] [0:40]
Avg. N 1207:32 1203:76 1200:22 1197:28 1188:46 1178:50 1172:08
Avg. Adj. R
2
0:08 0:08 0:08 0:08 0:08 0:08 0:08
Small (< 50
th
)
b cg
tk
1
0:05 0:04 0:00 0:01 0:04 0:04 0:02
[0:81] [0:68] [0:06] [0:22] [0:70] [0:69] [0:28]
b cg
tk
2
0:22 0:23 0:21 0:07 0:03 0:05 0:01
[3:43] [3:38] [2:87] [0:96] [0:48] [0:73] [0:21]
b cg
tk
3
0:02 0:04 0:06 0:17 0:24 0:18 0:01
[0:31] [0:74] [1:02] [2:65] [3:54] [2:54] [0:11]
Avg. N 542:89 541:22 539:49 537:81 532:52 526:42 521:94
Avg. Adj. R
2
0:06 0:06 0:06 0:06 0:06 0:06 0:06
Big ( 50
th
)
b cg
tk
1
0:04 0:01 0:02 0:02 0:01 0:02 0:00
[0:62] [0:22] [0:33] [0:35] [0:12] [0:40] [0:07]
b cg
tk
2
0:36 0:31 0:13 0:02 0:01 0:02 0:01
[4:25] [3:73] [1:53] [0:28] [0:17] [0:22] [0:12]
b cg
tk
3
0:03 0:09 0:21 0:26 0:21 0:02 0:14
[0:43] [1:10] [2:66] [3:42] [2:62] [0:26] [1:66]
Avg. N 664:43 662:54 660:73 659:47 655:93 652:08 650:14
Avg. Adj. R
2
0:10 0:10 0:10 0:10 0:10 0:10 0:10
A1.2. Tables 45
Table 1.5: Expected change in growth and delayed alpha
This table reports six-factor model (Fama and French (2015b) augmented with momentum) alphas
and t-values (in square brackets) for portfolios that buy stocks in the bottom b cg
tk
i
quintile and
short those in the top quintile. b cg
tk
i
is the expected change in year-over-year earnings growth from
quarteri 1 toi lagged by k months, wherei2f2; 3g. Panel A reports results for value-weighted
portfolios and Panel B reports results for equal-weighted portfolios. Within each panel, results for
the full sample, small firms, and big firms are presented. Small and big firms are divided using the
50
th
percentile of the NYSE market capitalization distribution at the end of the previous month.
The sample period is from January 2002 to December 2016.
Panel A: Value-weighted portfolio alphas
Number of months lagged
k = 0 1 2 3 4 5 6
Full Sample
b cg
tk
2
0:58 0:39 0:36 0:08 0:04 0:06 0:05
[3:15] [2:04] [1:95] [0:48] [0:27] [0:41] [0:33]
b cg
tk
3
0:23 0:16 0:33 0:43 0:37 0:19 0:15
[1:17] [0:89] [1:77] [2:38] [1:94] [0:99] [0:93]
Small (<50
th
)
b cg
tk
2
0:71 0:71 0:57 0:08 0:06 0:14 0:16
[4:05] [3:94] [3:30] [0:55] [0:40] [0:86] [1:05]
b cg
tk
3
0:07 0:13 0:24 0:38 0:47 0:37 0:12
[0:35] [0:73] [1:29] [2:28] [2:80] [2:34] [0:77]
Big (50
th
)
b cg
tk
2
0:55 0:31 0:24 0:07 0:03 0:11 0:04
[3:34] [1:71] [1:34] [0:44] [0:19] [0:73] [0:24]
b cg
tk
3
0:08 0:00 0:19 0:28 0:32 0:06 0:20
[0:43] [0:00] [1:12] [1:59] [1:85] [0:35] [1:31]
Panel B: Equal-weighted portfolio alphas
Full Sample
b cg
tk
2
0:71 0:71 0:47 0:18 0:08 0:01 0:03
[5:76] [5:58] [3:73] [1:67] [0:79] [0:11] [0:27]
b cg
tk
3
0:11 0:15 0:35 0:47 0:55 0:40 0:09
[0:81] [1:23] [2:71] [3:80] [4:11] [3:06] [0:76]
Small (<50
th
)
b cg
tk
2
0:71 0:74 0:61 0:20 0:07 0:14 0:10
[4:20] [4:39] [3:80] [1:49] [0:51] [0:99] [0:71]
b cg
tk
3
0:11 0:19 0:24 0:39 0:58 0:50 0:17
[0:65] [1:13] [1:43] [2:42] [3:48] [3:26] [1:20]
Big (50
th
)
b cg
tk
2
0:61 0:59 0:29 0:08 0:14 0:19 0:06
[5:06] [4:75] [2:24] [0:68] [1:24] [1:63] [0:56]
b cg
tk
3
0:04 0:05 0:34 0:38 0:46 0:19 0:01
[0:33] [0:35] [2:57] [2:94] [3:45] [1:37] [0:11]
46 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Table 1.6: Expected change in growth and forecast errors
This table reports coefficient estimates and t-values (in square brackets) from panel regressions
that predict forecast errors at different horizons using analysts’ growth expectations and firm char-
acteristics. The dependent variables are actual earnings i quarters ahead (i2f1; 2; 3g) minus the
median earnings forecast for that quarter measured one week after the last earnings announce-
ment, scaled by the market value of equity three days before the last earnings announcement.
Control variables include earnings surprise (SUE), earnings announcement return (CAR3), firm
size (ln(ME)), book-to-market equity (ln(BM)), profitability (OP), asset growth (AG), past return
(r
12;2
), long-term growth forecast (LTG), number of analysts and forecast dispersion. All regres-
sions include industry (Fama-French 48 industries) and year-quarter fixed effects. Standard errors
are clustered by industry and year-quarter. The sample period is from January 2002 to December
2016.
Actual minus forecasted earnings in quarter q
q = 1 q = 2 q = 3
(1) (2) (3) (4) (5) (6)
b cg
1
0:11 0:04 0:10 0:05 0:09 0:04
[3:72] [1:92] [2:52] [1:29] [2:21] [1:06]
b cg
2
0:09 0:05 0:21 0:16 0:18 0:13
[3:58] [3:07] [4:36] [3:77] [3:46] [2:75]
b cg
3
0:04 0:01 0:06 0:02 0:18 0:13
[1:74] [0:49] [1:80] [0:65] [3:13] [2:56]
SUE 0:27 0:17 0:17
[3:04] [2:19] [2:43]
CAR3 0:24 0:57 0:72
[2:43] [5:38] [5:46]
ln(ME) 0:02 0:07 0:09
[2:25] [4:62] [5:59]
ln(BM) 0:01 0:07 0:10
[1:24] [3:30] [3:62]
OP 0:08 0:09 0:33
[1:48] [1:12] [2:43]
AG 0:04 0:08 0:07
[1:33] [1:58] [1:59]
r
12;2
0:12 0:22 0:24
[4:23] [5:11] [5:29]
LTG 0:12 0:31 0:42
[1:85] [3:60] [4:34]
ln(No. of analysts) 0:01 0:01 0:00
[0:83] [0:28] [0:06]
ln(Dispersion) 0:02 0:05 0:06
[2:50] [4:01] [5:26]
Industry F.E. Y Y Y Y Y Y
Year-quarter F.E. Y Y Y Y Y Y
N 69,063 69,063 69,063 69,063 69,063 69,063
Adj. R
2
0:07 0:11 0:10 0:12 0:10 0:13
A1.2. Tables 47
Table 1.7: Alphas and events
This table reports equal-weighted daily six-factor model (Fama and French (2015b) augmented
with momentum) alphas and factor loadings for portfolios that buy stocks in the bottom quintiles
of analysts’ growth expectations and short those in the top quintiles, before and after removing
stock-days around events. The set of events includes earnings announcements, analysts’ forecast
revisions, and recommendation changes. Portfolios are formed by sorting stocks daily by their
two-quarter-ahead expected change in growth (b cg
2
) or three-quarter-ahead expected change in
growth measured one quarter ago (b cg
lag1Q
3
). P
0
is the actual portfolio. P
NEA
is the portfolio
with no earnings announcements. P
NE
is the portfolio with no events (i.e., analysts’ revisions,
recommendation changes, and earnings announcements). P
0
P
NE
is the difference between the
actual portfolio and the no-event portfolio. Returns are in basis points per day. t-values are in
square brackets and standard errors are in parentheses. The sample consists of stocks above the
20
th
NYSE market capitalization percentile in the month prior to the last earnings announcement.
The sample period is from January 2002 to December 2016.
Two-quarter-ahead Lagged three-quarter-ahead
expected growth (b cg
2
) expected growth (b cg
lag1Q
3
)
P
0
P
NEA
P
NE
P
0
P
NE
P
0
P
NEA
P
NE
P
0
P
NE
(1) (2) (3) (4) (5) (6) (7) (8)
Alpha 2:46 1:81 0:24 2:22 2:33 1:94 0:94 1:38
[4:24] [3:20] [0:45] [6:30] [4:04] [3:46] [1:79] [3:87]
MKT 0:03 0:03 0:02 0:01 0:02 0:02 0:00 0:02
(0:01) (0:01) (0:01) (0:00) (0:01) (0:01) (0:01) (0:00)
SMB 0:06 0:06 0:03 0:03 0:03 0:03 0:01 0:03
(0:01) (0:01) (0:01) (0:01) (0:01) (0:01) (0:01) (0:01)
HML 0:06 0:06 0:02 0:04 0:01 0:01 0:03 0:04
(0:01) (0:01) (0:01) (0:01) (0:01) (0:01) (0:01) (0:01)
RMW 0:10 0:11 0:12 0:01 0:16 0:15 0:15 0:01
(0:02) (0:02) (0:01) (0:01) (0:02) (0:02) (0:01) (0:01)
CMA 0:02 0:02 0:02 0:05 0:00 0:00 0:04 0:04
(0:02) (0:02) (0:02) (0:01) (0:02) (0:02) (0:02) (0:01)
UMD 0:10 0:11 0:11 0:01 0:07 0:07 0:07 0:00
(0:01) (0:01) (0:01) (0:00) (0:01) (0:01) (0:01) (0:00)
N 3,777 3,777 3,777 3,777 3,777 3,777 3,777 3,777
Adj. R
2
0:13 0:14 0:14 0:02 0:08 0:09 0:09 0:03
48 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Table 1.8: Earnings announcement returns and surprises at different horizons
This table reports coefficient estimates and t-values (in square brackets) from panel regressions
that explain three-day cumulative abnormal returns around earnings announcements using current
and forward earnings surprises, and lagged firm characteristics. SUE is the earnings surprise,
measured as the actual earnings minus consensus (median) forecast, scaled by the market value
of equity three days before the earnings announcement. FSUE1 is the one-quarter-ahead “forward
earnings surprise,” measured as analysts’ earnings forecast revision for the subsequent quarter
within one week after the earnings announcement, scaled by the market value of equity three
days before the earnings announcement. FSUE2 and FSUE3 are the two-quarter- and three-
quarter-ahead forward surprises, defined analogously to FSUE1. Control variables include pre-
announcement return (PAR) (So and Wang (2014)), firm size (ln(ME)), book-to-market equity
(ln(BM)), profitability (OP), asset growth (AG), past return (r
12;2
), long-term growth forecast
(LTG), number of analysts and forecast dispersion. All regressions include industry (Fama-French
48 industries) and year-quarter fixed effects. Standard errors are clustered by industry and year-
quarter.
(1) (2) (3) (4) (5) (6)
SUE 3:64 2:36 2:77 3:02 2:23 2:20
[3:79] [3:47] [3:42] [3:47] [3:21] [3:29]
FSUE1 6:56 4:30 4:83
[9:88] [10:25] [10:02]
FSUE2 6:29 1:69 1:96
[8:76] [4:24] [4:52]
FSUE3 6:06 1:97 2:25
[8:58] [6:70] [7:48]
PAR 0:07 0:11 0:10 0:10 0:11
[3:38] [5:39] [4:62] [4:11] [5:59]
ln(ME) 0:08 0:25 0:14 0:07 0:29
[1:79] [4:26] [2:94] [1:56] [4:92]
ln(BM) 0:00 0:27 0:16 0:10 0:29
[0:04] [3:69] [2:32] [1:37] [3:74]
OP 1:02 0:03 0:45 0:54 0:06
[1:86] [0:04] [0:69] [0:92] [0:09]
AG 0:33 0:40 0:22 0:35 0:35
[0:57] [0:76] [0:43] [0:63] [0:69]
r
12;2
0:47 1:66 1:41 1:26 1:93
[2:02] [5:80] [5:07] [4:56] [6:53]
LTG 0:03 0:16 0:15 0:17 0:23
[0:03] [0:17] [0:17] [0:20] [0:27]
ln(No. of analysts) 0:13 0:03 0:06 0:07 0:01
[1:46] [0:27] [0:60] [0:68] [0:08]
ln(Dispersion) 0:06 0:14 0:07 0:03 0:16
[1:49] [3:15] [1:88] [0:86] [3:65]
Industry F.E. Y Y Y Y Y Y
Year-quarter F.E. Y Y Y Y Y Y
N 69,794 69,794 69,794 69,794 69,794 69,794
Adj. R
2
0:05 0:12 0:10 0:09 0:12 0:13
A1.2. Tables 49
Table 1.9: Expected change in growth and earnings announcement returns
This table reports coefficient estimates and t-values (in square brackets) from panel regressions that
predict three-day cumulative abnormal returns around earnings announcements (column 1 through
4), and one-quarter-ahead forward earnings surprises (column 5 and 6) using analysts’ growth fore-
castsatdifferenthorizonsandfirmcharacteristics. b cg
i
isanalysts’expectedchangeinyear-over-year
earnings growth from quarteri1 to quarteri. b cg
lag1Q
3
is the three-quarter-ahead expected change
in growth measured one quarter ago. Control variables include pre-announcement return (PAR)
(So and Wang (2014)), firm size (ln(ME)), book-to-market equity (ln(BM)), profitability (OP),
asset growth (AG), past return (r
12;2
), long-term growth forecast (LTG), number of analysts
and forecast dispersion. All regressions include industry (Fama-French 48 industries) fixed effects
and year-quarter fixed effects. Standard errors are clustered by industry and year-quarter.
Earnings announcement return Forward surprise
(1) (2) (3) (4) (5) (6)
b cg
1
0:18 0:20 0:94 1:50
[4:33] [4:68] [1:44] [2:33]
b cg
2
0:24 0:21 4:67
[6:91] [5:13] [6:81]
b cg
lag1Q
3
0:19 0:16 1:75
[3:80] [3:33] [3:24]
b cg
3
0:02 0:01 2:21 1:71
[0:35] [0:12] [3:05] [2:48]
PAR 0:06 0:06 0:55 0:58
[2:92] [2:87] [9:65] [10:10]
ln(ME) 0:09 0:10 4:66 4:97
[1:86] [2:05] [10:14] [10:41]
ln(BM) 0:12 0:12 3:69 3:53
[1:50] [1:52] [4:90] [4:64]
OP 0:35 0:48 13:43 8:51
[0:55] [0:73] [2:45] [1:46]
AG 0:43 0:45 1:23 0:66
[0:73] [0:75] [0:63] [0:34]
r
12;2
0:04 0:01 18:22 19:75
[0:18] [0:03] [8:80] [8:85]
LTG 0:10 0:08 4:94 3:71
[0:12] [0:09] [1:39] [1:01]
ln(No. of analysts) 0:09 0:09 1:36 1:35
[1:01] [1:00] [2:51] [2:29]
ln(Dispersion) 0:08 0:08 2:78 3:04
[2:27] [2:58] [6:97] [7:30]
Industry F.E. Y Y Y Y Y Y
Year-quarter F.E. Y Y Y Y Y Y
N 69,794 69,794 69,794 69,794 69,794 69,794
Adj. R
2
0:00 0:00 0:00 0:00 0:16 0:15
50 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Table 1.10: Double-sort portfolio alphas by past return and expected change
in growth
This table reports the six-factor model (Fama and French (2015b) augmented with momentum)
alphas from value- and equal-weighted portfolios constructed by three-by-three monthly conditional
double sorts. Stocks are first sorted into terciles by their returns in the past quarter, skipping the
most recent month (r
4;2
). Within each return tercile, stocks are sorted by their two-quarter-
ahead expected change in growth (b cg
2
) or three-quarter-ahead expected change in growth measured
in the last quarter (b cg
lag1Q
3
). Values increase from T1 to T3, so T1 is the bottom tercile. T1T3
corresponds to the long-short strategy that buys the T1 portfolio and shorts the T3 portfolio.
Returns are in percentages per month. t-values are in square brackets. The sample period is from
January 2002 through December 2016.
Return in the past quarter (r
4;2
)
Value-weighted Equal-weighted
T1 T2 T3 T1 T2 T3
b cg
2
T1
0:59 0:18 0:04 0:40 0:20 0:16
[3:13] [1:65] [0:28] [2:81] [2:44] [1:38]
T2
0:04 0:02 0:01 0:21 0:04 0:06
[0:23] [0:22] [0:10] [1:59] [0:57] [0:60]
T3
0:43 0:31 0:04 0:49 0:19 0:19
[2:09] [2:53] [0:22] [3:24] [2:10] [1:45]
T1T3
1:02 0:49 0:09 0:89 0:39 0:35
[4:06] [3:25] [0:47] [5:89] [3:63] [2:98]
b cg
lag1Q
3
T1
0:31 0:16 0:04 0:23 0:11 0:12
[1:72] [1:38] [0:24] [1:58] [1:33] [1:06]
T2
0:17 0:05 0:05 0:28 0:05 0:04
[1:06] [0:62] [0:35] [2:11] [0:69] [0:32]
T3
0:26 0:19 0:14 0:35 0:10 0:13
[1:31] [1:42] [0:69] [2:33] [1:08] [0:94]
T1T3
0:57 0:35 0:10 0:57 0:21 0:25
[2:39] [2:16] [0:48] [3:81] [1:82] [1:92]
A1.3. Structural shift in information environment around earnings announcements 51
A1.3 Structural shift in information environment around earnings
announcements
0 20 40 60 80
Earnings announcements with guidance (%)
Year
1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
10 30 50 70
Main sample
starts
Regulation FD
enacted
Figure 1.9: Percentage of earnings announcements with management guidance. This
figure plots the percentage of quarterly earnings announcements that contain management guidance
from 1994 to 2017. Earnings guidance data is from the IBES Guidance database. The sample
includes firms that satisfy filters specified in Section 1.3. Regulation Fair Disclosure was enacted in
October 2000. The main sample for this study starts from 2002. I match a management guidance
with an earnings announcement if the guidance is within a five-trading-day window (t2 [2; 2])
around an earnings announcement. I include all guidance types identified by IBES.
This section examines how the main results vary in the pre- and post-2002 period, and provides
analysis on why earnings guidance may have important effects. Beaver, McNichols, and Wang
(2018) shows that the information environment around earnings announcements shifted dramati-
callyintheearly2000’s. ThisshiftislikelycausedbyRegulationFairDisclosure, whichwasenacted
in October 2000. Since 2001, firms increasingly provide forward-looking guidance during earnings
announcements. Figure 1.9 plots the percentage of firms in my sample that provides management
guidance during earnings announcements from 1994 to 2017. We see that before 2001, less than
10% of the firms provide management guidance during earnings announcements. After 2001, this
percentage jumps to 30% and continues to rise rapidly to over 70% in 2004.
52 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Recent research in accounting argues that the practice of providing earnings guidance may
in part have caused corporate short-termism (Kim, Su, and Zhu (2017)). In June 2018, Warren
BuffettandJamieDimonjointlyproposedthattopexecutivesshouldstopissuingquarterlyearnings
guidance because they believed that earnings guidance leads to “an unhealthy focus on short-term
profits at the expense of long-term strategy, growth, and sustainability.”
The argument that earnings guidance alters investors’ forward-looking horizon is coherent with
bounded rationality. Quarterly earnings guidance provides an important piece of information at
a low cost. This information subsidy can crowd out private information generation because the
guidance lowers the incentives for conducting costly private research. As a result, boundedly
rationalinvestorsmayoptimallychoosetostopconductingcostlyprivateresearchandrelysolelyon
management’s guidance for stock valuation.
12
When guidance becomes available, investors’ welfare
generally increases, but errors in asset prices become more systematic because the information that
underlies price discovery becomes more correlated. This reasoning also implies that returns would
become more predictable using long-horizon information because investors’ information set now
has a shorter average information horizon.
If earnings guidance shortens investors’ forward-looking horizon, investors may underreact to
long-horizon earnings information more in the post-2002 period. Therefore, we expect strategies
that trade against analysts’ earnings growth forecasts beyond one quarter to be more profitable
in the post-2002 period. Figure 1.10 shows the Fama and MacBeth (1973) regression slopes for
two-quarter-ahead expected change in growth (b cg
2
) by year. The regression specification is as in
Table 1.4. The dependent variable is monthly stock return. The independent variables include
the expected change in growth at the one-quarter, two-quarter, and three-quarter horizon, as well
as firm characteristics. We see that the yearly slopes for b cg
2
in the post-2002 period (black) are
consistently negative. In the pre-2002 period, there is no clear pattern. This difference in return
predictability is consistent with the hypothesis that earnings guidance affects investors’ forward-
looking horizon.
12
To see why, suppose that investors can collect information (I) that allows them to form earnings forecasts for
the subsequent four quarters (FE1, FE2, FE3, FE4) at some fixed cost c. Now suppose the firm starts to issue
earnings guidance for the next quarter, which makes FE1 freely available, and as a result, makes the information
I less valuable. If the cost of acquiring information I remains the same, investors may rationally choose to stop
forming their own forecasts for the subsequent quarters, but rely on management’s guidance only.
A1.3. Structural shift in information environment around earnings announcements 53
cg
2
slope
1987 1990 1993 1996 1999 2002 2005 2008 2011 2014
Year
0.0 0.2 - 0.6 - 0.4 - 0.2
Figure1.10: FamaandMacBeth(1973)regressionslopesfortwo-quarter-aheadgrowth
forecasts (b cg
2
) by year. This figure plots the Fama and MacBeth (1973) regression slopes for
b cg
2
by year from 1987 to 2016. The regression specification is as in Table 1.4. The dependent
variable is monthly stock return. The independent variables include one-quarter-, two-quarter-, and
three-quarter-ahead expected change in growth (b cg
1
, b cg
2
, b cg
3
), earnings surprise (SUE), earnings
announcement return (CAR3), market value of equity (ln(ME)), book-to-market equity (ln(BM)),
profitability (OP), asset growth (AG), past returns (r
1
,r
4;2
,r
12;5
), long-term growth forecast
(LTG), forecast revision, number of analysts and forecast dispersion.
54 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
A1.4 Additional tables and figures
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Percent of sample (%)
0 1 2 3 4 5 6
NYSE market capitalization percentile
Figure 1.11: Sample distribution in monthly NYSE size percentiles
A1.4. Additional tables and figures 55
Table 1.11: Robustness: Fama-MacBeth regressions with alternative specifi-
cations
This table reports average Fama and MacBeth (1973) regression slopes and t-values (in square
brackets) from cross-sectional regressions that predict monthly stock returns. Each column uses
an alternative definition of growth. The main definition of growth in this paper is the change
in earnings scaled by the market value of equity (
Earnings
ME
). Column 1 uses revenue instead of
earnings. Column 2, 3, and 4 use lagged total asset, lagged book value, and revenue as the scaling
variable.
Definition of growth:
Revenue
ME
Earnings
AT
Earnings
BE
Earnings
Revenue
(1) (2) (3) (4)
Constant 0:19 0:21 0:21 0:18
[0:35] [0:39] [0:39] [0:35]
b cg
lag1Q
3
0:03 0:13 0:06 0:02
[2:35] [2:51] [2:72] [3:16]
ln(ME) 0:02 0:01 0:01 0:02
[0:24] [0:13] [0:14] [0:25]
ln(BM) 0:11 0:08 0:08 0:09
[1:12] [0:91] [0:90] [1:05]
OP 1:99 1:73 1:79 1:65
[2:05] [2:13] [2:19] [1:95]
AG 0:91 0:96 0:96 0:92
[2:49] [2:81] [2:79] [2:64]
r
12;2
0:01 0:02 0:00 0:06
[0:04] [0:05] [0:01] [0:17]
LTG 0:81 0:65 0:68 0:56
[0:99] [0:77] [0:80] [0:68]
Revision 0:95 1:08 1:07 1:10
[2:86] [3:46] [3:43] [3:45]
ln(No. of analysts) 0:03 0:02 0:03 0:04
[0:27] [0:20] [0:23] [0:32]
ln(Dispersion) 0:08 0:08 0:07 0:08
[1:70] [1:68] [1:64] [1:75]
Avg. N 1,124.9 1,197.7 1,197.7 1,179.1
Adj. R
2
0:06 0:06 0:06 0:06
56 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Table 1.12: Expected change in growth and revision momentum
This table reports the results from factor spanning tests between the b cg
2
portfolio and the portfolio
that captures momentum in analysts’ revisions. The “Revision” factor is constructed as the return
on a long-short strategy that buys stocks at the top analysts’ revision quintile and shorts those in
the bottom quintile. I compute analysts’ revisions using the three-month moving average change of
one-quarter-ahead earnings forecasts scaled by the market value of equity in the previous month.
The b cg
2
portfolio buys stocks at the bottom b cg
2
quintile and shorts those in the top quintile. The
portfolios are value-weighted. t-value are in square brackets.
CAPM Six-factor
Revision b cg
2
Revision b cg
2
(1) (2) (3) (4) (5) (6) (7) (8)
Alpha 0:43 0:20 0:66 0:58 0:48 0:39 0:58 0:52
[1:70] [0:80] [3:57] [3:20] [2:33] [1:85] [3:15] [2:80]
MKT 0:31 0:27 0:12 0:07 0:16 0:16 0:02 0:00
[5:17] [4:48] [2:86] [1:49] [2:70] [2:66] [0:42] [0:05]
b cg
2
0:35 0:16
[3:48] [1:84]
Revision 0:18 0:12
[3:48] [1:84]
SMB 0:02 0:00 0:11 0:11
[0:18] [0:02] [1:38] [1:36]
HML 0:08 0:06 0:13 0:12
[0:89] [0:68] [1:52] [1:40]
RMW 0:36 0:36 0:02 0:02
[3:03] [3:03] [0:19] [0:23]
CMA 0:29 0:34 0:30 0:33
[2:05] [2:36] [2:34] [2:61]
UMD 0:47 0:45 0:15 0:09
[9:78] [9:05] [3:46] [1:70]
N 180 180 180 180 180 180 180 180
Adj. R
2
0:13 0:18 0:04 0:10 0:47 0:48 0:12 0:13
A1.4. Additional tables and figures 57
Table 1.13: Expected change in growth and average returns: Fama-MacBeth
regressions
This table reports the complete results from the Fama and MacBeth (1973) regressions performed
in Table 1.4 for the full sample. The estimates are average slopes from monthly cross-sectional
regressions that predict returns. Time-series t-values are in square brackets.
No. of months lagged k = 0 1 2 3 4 5 6
Constant 0:75 0:72 0:72 0:65 0:63 0:66 0:60
[1:45] [1:38] [1:37] [1:23] [1:20] [1:23] [1:12]
b cg
tk
1
0:05 0:03 0:01 0:01 0:03 0:04 0:02
[0:84] [0:58] [0:24] [0:32] [0:67] [0:98] [0:38]
b cg
tk
2
0:27 0:26 0:19 0:06 0:01 0:03 0:01
[4:49] [4:47] [2:92] [0:96] [0:26] [0:57] [0:20]
b cg
tk
3
0:05 0:06 0:11 0:19 0:24 0:14 0:02
[0:85] [1:14] [2:06] [3:45] [3:94] [2:30] [0:40]
SUE 0:29 0:22 0:21 0:21 0:23 0:25 0:28
[2:65] [2:08] [2:02] [2:15] [2:28] [2:33] [2:60]
CAR3 0:35 0:36 0:33 0:31 0:26 0:38 0:42
[0:73] [0:72] [0:67] [0:64] [0:54] [0:77] [0:85]
ln(ME) 0:05 0:04 0:04 0:03 0:03 0:03 0:03
[0:63] [0:56] [0:52] [0:41] [0:35] [0:44] [0:34]
ln(BM) 0:13 0:13 0:14 0:13 0:11 0:11 0:12
[1:39] [1:41] [1:50] [1:39] [1:23] [1:18] [1:27]
OP 1:90 1:90 1:90 1:91 1:78 1:91 2:07
[2:35] [2:37] [2:40] [2:41] [2:25] [2:43] [2:57]
AG 0:93 0:92 0:91 1:00 1:01 0:96 0:87
[2:80] [2:73] [2:71] [2:99] [2:98] [2:82] [2:61]
r
1
1:85 1:84 1:86 1:92 1:89 1:84 1:89
[2:49] [2:49] [2:51] [2:60] [2:56] [2:48] [2:54]
r
4;2
0:56 0:57 0:58 0:61 0:62 0:70 0:70
[1:03] [1:06] [1:06] [1:13] [1:15] [1:30] [1:29]
r
12;5
0:36 0:34 0:33 0:33 0:36 0:37 0:30
[0:93] [0:88] [0:84] [0:85] [0:94] [0:94] [0:78]
LTG 0:01 0:01 0:01 0:01 0:01 0:01 0:01
[1:03] [1:06] [0:99] [0:92] [1:00] [1:02] [0:98]
Revision 1:11 1:13 1:28 1:42 1:42 1:46 1:56
[3:51] [3:66] [4:12] [4:66] [4:55] [4:64] [4:91]
ln(No. of analysts) 0:02 0:02 0:01 0:00 0:00 0:01 0:00
[0:16] [0:14] [0:05] [0:02] [0:02] [0:06] [0:01]
ln(Dispersion) 0:04 0:05 0:05 0:05 0:06 0:05 0:06
[0:96] [1:07] [1:11] [1:24] [1:36] [1:30] [1:38]
Avg. N 1207.3 1203.8 1200.2 1197.2 1188.5 1,178.5 1172.0
Avg. Adj. R
2
0:08 0:08 0:08 0:08 0:08 0:08 0:08
58 Chapter 1. Attention Boundary, Expectation Term Structure, and Delayed Alpha
Table 1.14: Double-sort portfolio alphas by forecast dispersion and expected
change in growth
This table reports the six-factor model (Fama and French (2015b) augmented with momentum)
alphas from value- and equal-weighted portfolios constructed by three-by-three monthly conditional
double sorts. Stocks are first sorted into terciles by their two-quarter-ahead forecast dispersion
(Diether et al. (2002)). Within each dispersion tercile, stocks are sorted by their two-quarter-
ahead expected change in growth (b cg
2
). Values increase from T1 to T3, so T1 is the bottom
tercile. T1T3 corresponds to the long-short strategy that buys the T1 portfolio and shorts the
T3 portfolio. Returns are in percentages per month. t-values are in square brackets. The sample
period is from January 2002 through December 2016.
Two-quarter-ahead forecast dispersion
Value-weighted Equal-weighted
T1 T2 T3 T1 T2 T3
b cg
2
T1
0:06 0:32 0:20 0:26 0:23 0:24
[0:61] [2:61] [0:96] [3:44] [2:46] [1:78]
T2
0:02 0:05 0:08 0:12 0:07 0:06
[0:22] [0:46] [0:46] [1:67] [0:88] [0:53]
T3
0:16 0:20 0:38 0:11 0:13 0:68
[1:51] [1:41] [1:95] [1:25] [1:29] [5:56]
T1T3
0:22 0:52 0:57 0:15 0:35 0:92
[1:55] [2:81] [2:27] [1:61] [2:88] [5:77]
59
Chapter 2
The Earnings Announcement Return
Cycle
Juhani Linnainmaa
Yingguang Zhang
Abstract
Stocks earn significantly negative abnormal returns before earnings announcements and positive
after them. This “earnings announcement return cycle” (EARC) is unrelated to the earnings an-
nouncement premium, and it is a feature of stocks widely covered by analysts. Analysts’ forecasts
follow the same pattern as returns: analysts’ forecasts become more optimistic after an earnings an-
nouncement and more pessimistic as the next one draws near. We attribute one-half of the earnings
announcement return cycle to this optimism cycle. The EARC may stem from mispricing: both
the return and optimism patterns are stronger among high-uncertainty and difficult-to-arbitrage
stocks, and the EARC strategy is more profitable on days when it would accommodate larger
amounts of arbitrage capital.
60 Chapter 2. The Earnings Announcement Return Cycle
2.1 Introduction
Manyreturnanomaliesrelatetoearningsannouncements. Stockpricestendtomoveinthedirection
of recent earnings surprises
1
and returns are higher in the months in which firms report earnings
than in those they do not.
2
So and Wang (2014) and Engelberg, McLean, and Pontiff (2018b) find
that earnings announcements amplify anomaly returns by a factor of six or seven. Kim and So
(2018) show that firms earn low returns before, and high returns during, earnings announcements
because firms typically manage expectations down before the announcements. The competing
explanations for price 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 earn positive abnormal returns
early in the cycle and negative returns late in the cycle. This pattern is distinct from the earn-
ings announcement premium, that is, the tendency of stocks to earn high returns around their
earnings announcements. Our trading rule is neither long nor short stocks around the earnings
announcement dates themselves.
Figure 2.1 illustrates our key result. We center the graph around a quarterly earnings an-
nouncement and plot (1) the average market-adjusted returns (solid line) and (2) the percentage of
positive forecast revisions by analysts (dashed line) for a six-month period around this date. The
sample includes U.S. common stocks followed by at least five analysts. The x-axis counts trading
days. The vertical line at t =63 is the typical date of the previous earnings announcement; the
line at t = 0 is the current announcement; and the line at t = 63 is the expected date of the next
announcement.
Figure 2.1 shows that, apart from the earnings announcement premium period, which we define
asrunningfromtwoweeksbeforeanannouncementtoaweekafterit, stockscontinuetooutperform
1
See, for example, Ball and Brown (1968), Beaver (1968), Foster, Olsen, and Shevlin (1984), Bernard and Thomas
(1989, 1990), and Daniel, Hirshleifer, and Subrahmanyam (1998).
2
See, 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).
2.1. Introduction 61
Average daily return (%)
- 70 - 60 - 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50 60 70
0.00 0.02 0.04 0.06 - 0.04 - 0.02
Trading day relative to current earnings announcement
Current
announcement
Expected next
announcement
Typical previous
announcement
40 42 44 46 48 50 52
Upward revision (%)
Stock return
Upward revision (%)
Figure 2.1: Earnings announcement return cycle and analyst optimism. This figure plots
the average daily market-adjusted return (solid line) and the percentage of positive forecast revisions
by analysts (dashed line) for common stocks traded on the NYSE, Nasdaq and Amex for a six-month
period centered around a firm’s quarterly earnings announcement. The sample begins in January
1985 and ends in December 2016 and includes stocks covered by at least five analysts over the
previous quarter. A stock’s market-adjusted return is its return minus the equal-weighted market
return; we report three-day moving averages of these returns. The vertical line at t =63 is the
typical date of the previous earnings announcement; the line at t = 0 is the current announcement;
and the line at t = 63 is the expected date of the next announcement.
themarketbyaboutthreebasispointsperdayfortheremainderofthefirstmonth. Afterthispoint,
they go on to earn the market premium for about six weeks before beginning to underperform the
market by two to three basis points per day for about a month as the next earnings announcement
draws close.
3
Both the positive returns in the early phase and the negative returns in the late phase 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 71 basis points (t-value = 6.02). This alpha remains at 68 basis points (t-value = 5.89)
when we also include the earnings announcement premium factor that is long stocks inside the
earnings announcement window and short those outside it.
3
The two cycles in Figure 2.1—the one before the current announcement at date t = 0 and the one after it—are
not identical because we have a limited number of earnings announcements for each firm and because firms do not
always announce their earnings exactly every 63 trading days. The two cycles in the figure slightly differ because
each firm’s first quarterly announcement in the sample can only appear on the left-hand side of the graph and the
last one can only appear on its right-hand side.
62 Chapter 2. The Earnings Announcement Return Cycle
We apply a bootstrapping procedure in the spirit of White (2000) and Stambaugh, Yu, and
Yuan (2014) to verify that the earnings announcement return cycle is unlikely an artifact of data-
mining. The actual EARC strategy is long stocks in the early part of the cycle and short those in
the late part. We generate 100,000 strategies that resample the positions of this strategy without
replacement. That is, whereas the original strategy has positions L;L;L;:::;S;S;S over a com-
bined30-dayperiodovertheearningscycle—whereLandS standforlongandshortpositions—one
of the randomized strategies might take positions L;S;S;:::;L;S;L. By bootstrapping without
replacement, both the actual and bootstrapped strategies are long and short each stock the same
number of days in the cycle. If the earnings announcement return cycle was an artifact of data-
mining, we would expect a number of the randomized trading rules to outperform the actual rule.
The data do not support to this view; only 0.004% of the randomized strategies outperform the
actual EARC strategy.
What is remarkable in Figure 2.1 is the synchronization between the average returns and an-
alysts’ forecast revisions. During the earnings announcement periods, the majority of earnings
forecast revisions are positive. This percentage, however, promptly falls below 50% and reaches a
low point of 37% eight weeks after the announcement. This low point coincides with the period
during which stocks earn their lowest returns during the cycle. As the next earnings announcement
draws closer, the proportion of positive forecast revisions begins to increase.
To explain a periodic pattern in stock returns, such as the earnings announcement return cycle,
the drivers of this pattern must also be periodic. Figure 2.1 suggests that the analyst optimism
cycle may be a key driver of the pattern in average returns. We measure the connection between the
patterns in average returns and forecast revisions using a counterfactual portfolio approach. In this
test we contrast the EARC strategy with a modified strategy that excludes stock-days associated
with analyst forecast revisions or recommendation changes. That is, when an analyst revises his
forecast or recommendation, we remove the target stock from the long and short portfolios for
a three-day window around this event. The counterfactual portfolio’s monthly alpha of 38 basis
points(t-value=3.22)is55%oftheoriginalalphaof68basispoints(t-value=6.10). Thedifference
between the two is statistically significant with a t-value of 5.81. The EARC strategy therefore
earns approximately one-half of its returns by being long or short in stocks when analysts revise
2.1. Introduction 63
their forecasts or recommendations.
This test does not establish causality from forecast revisions to returns; both the returns and
forecasts may respond to the same omitted variable.
4
An unusual property of the earnings an-
nouncement return cycle, however, is important to bear in mind. An investor can capture the
EARC effect by using information only on the distance from the previous earnings announcement;
it uses no information on realized earnings or analyst forecasts. Our counterfactual portfolio ap-
proach shows that, whatever mechanism generates the profits of the EARC strategy, an investor
earns one-half of these profits exactly when analysts revise their forecasts or recommendations. We
interpret these results as suggesting that the optimism cycle is an important factor of the earn-
ings announcement return cycle. This statement holds without taking any stance on the causality
between analyst actions and returns.
Our results confirm the key findings of Kim and So (2018). Stock returns are low before
announcements, and these low returns seem to stem from changes in expectations. The actual
EARC strategy earns a daily alpha of0:73 basis points before an earnings announcement, but
the counterfactual strategy that excludes analyst-days has an alpha of 0.63 basis points. The
difference between the two alphas has at-value of7:44, indicating that the forecast-revision days
explain all of the low pre-announcement returns. This difference is consistent with Kim and So’s
(2018) suggestion that firms guide market expectations down before announcements. Our estimates
showthatwhenfirmsdonotdoso, andanalystsdonotrevisetheirforecasts, firmsearnhighreturns
before announcements.
Although forecast revisions explain all of the negative returns before announcements, they
do not explain why returns are high after firms have announced their earnings. Analyst actions
explain only between 4% and 14% of the high post-announcement returns. That is, analysts
explain all of the low returns before announcements but almost none of the high returns after
announcements. The mechanism that drives stock prices up for weeks after announcements must
therefore be different from the one that drives them down before the announcements. If this part
of the cycle is about changing expectations, analysts do not appear to share the same expectations
4
Bradley, Clarke, Lee, and Ornthanalai (2014) use intraday data on analyst forecast revisions to suggest that the
association between revisions and stock returns is causal; they show that stock returns move in response to forecast
revisions.
64 Chapter 2. The Earnings Announcement Return Cycle
as those who set the prices. Moreover, the fact that stocks earn significantly positive abnormal
returns for a long time after firms have announced their earnings casts some uncertainty on the
risk-based explanations
5
for this part of the cycle. Because these firms have already announced
their earnings, these returns cannot be due to non-announcing firms being riskier at times they are
expected to announce their earnings.
If the earnings announcement return cycle is about mispricing, the literature provides guidance
on when this pattern should be weaker or stronger. Hirshleifer (2001) and Daniel, Hirshleifer,
and Subrahmanyam (1998, 2001), for example, suggest that behavioral biases should be more pro-
nounced when uncertainty is high. Uncertainty, in the context of the earnings announcement return
cycle, should change almost deterministically; market participants’ 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 2.1 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.
Both the earnings announcement return cycle and the pattern in analysts’ forecasts 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 147 basis
points (t-value = 4.34) among firms in the top-uncertainty quintile; among the low-uncertainty
stocks, this strategy’s alpha is 35 basis points is not statistically different from zero. We also
find that the EARC pattern is more pronounced among unprofitable growth firms. This finding is
consistent with Baker and Wurgler (2006), who suggest that variation in investor sentiment has a
greater effect on the prices of unprofitable growth firms. Taken together, our results suggest that
the cyclical pattern in returns around earnings announcements may stem from mispricing.
The earnings announcement return cycle is unlikely to emanate from systematic risk factors.
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 draws 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 after the previous earnings announcement. An analysis of
5
See, for example, Savor and Wilson (2016).
2.1. Introduction 65
how the EARC varies between firms with low and high analyst coverage also provides a test of the
risk-based explanation. 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 it not arbitraged away? One possibility is the difficulty
in arbitraging away this form of mispricing. To capture the abnormal returns associated with the
earnings announcement cycle, an investor would have to switch between long and short positions
in individual stocks on almost a daily basis. Moreover, the amount of capital that this trade could
accommodate varies significantly as well: the number of firms announcing their earnings ranges
from 0 to over 180 per day over our 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, the fund may have no meaningful impact on mispricing due
to limited capital (Shleifer and Vishny, 1997). Conversely, if the fund has enough capital to fully
eliminate mispricing even at the height of the earnings season, it would have large amounts of idle
capital at times when only a few firms announce earnings; this idle capital, in turn, would lower
the fund’s average return on capital and render the trade unattractive.
Thislimits-to-arbitrageargumentimpliesthattheabnormalreturnassociatedwiththeearnings
announcement cycle strategy should be higher among firms that announce their earnings on days
when many others do so as well. Consistent with this prediction, we show that the abnormal
returns are 30% to 70% higher in event-time than in calendar-time. That is, the average returns
are higher when the strategy holds more stocks—but these are also the days when the would-be
arbitrageurs would need to commit more capital.
6
Two studies closely relate to ours. Grinblatt, Jostova, and Philipov (2016) show that a pre-
dictable component in analysts’ optimism forecasts the cross-section of stock returns. Our results
suggest that the dynamics of investors’ biases lead to a cyclical pattern in stock returns, the earn-
ings announcement return cycle. An investor can capture the return associated with the earnings
announcement cycle without directly conditioning on, for example, analyst optimism—they only
6
Savor and Wilson (2016) find the opposite result for the earnings announcement premium: the earnings an-
nouncement premium is lower when more firms announce their earnings. This discrepancy further suggests that the
earnings announcement premium is disconnected from the earnings announcement return cycle.
66 Chapter 2. The Earnings Announcement Return Cycle
need to condition on the amount of time that has elapsed since the previous earnings announce-
ment. Kim and So (2018) examine the link between stock returns and management guidance.
Our results are consistent with their findings on low returns before firms announce their earnings,
and the fact that these returns seem to stem from managers guiding market expectations down.
We show that firms earn significantly positive abnormal returns for weeks after announcing their
earnings, and that analyst actions cannot explain this part of the pattern.
2.2 Data
We use data from four sources:
1. Monthly and daily CRSP: monthly and daily stocks returns, industry classifications, and
the number of shares outstanding.
2. Annual and quarterly Compustat: book value of equity, operating profitability, and
quarterly earnings announcement dates.
3. Thomson Reuters I/B/E/S: analyst coverage, annual earnings forecasts, quarterly earn-
ings forecasts at one- to four-quarter horizons, and recommendations.
4. Ravenpack: news and media coverage data.
In our main tests we include firms covered by at least five analysts. We measure analyst coverage
at the time of each earnings announcement by counting the number of analysts in the I/B/E/S
detail file who issued at least one annual earnings forecast over the three-month period prior to the
earnings announcement.
We limit the sample to the common stock of U.S. firms listed on the NYSE, AMEX, and
Nasdaq. We drop all firm-quarters with missing quarterly earnings announcement dates. We
identify earnings announcement dates using the rdq variable in the quarterly Compustat. We also
requirefirmstohave, atthetimeofanearningsannouncement, atleastfourearningsannouncement
dates over the prior 400-calendar day period and the gap to the last earnings announcement to be
between 70 and 110 calendar days. These screens ensure that our sample includes firms that have
followed, up to the current announcement, regular schedules in reporting quarterly earnings. Our
2.2. Data 67
sample period runs from January 1985 to December 2016. Data limitations determine the starting
data; analyst coverage is sparse before 1985. The media coverage data start in 2001.
Table 2.1 shows the descriptive statistics for the main sample and compares this sample to firms
not widely covered by analysts. The unit of observation is a firm-earnings announcement pair. The
statistics we report are time-series averages of quarterly cross-sectional statistics; the average size
of $7.4 billion, for example, is the size of the average firm in the average quarter.
A comparison between the main sample and the excluded firms shows that the sample firms
(1) are significantly larger by market value; (2) have lower book-to-market ratios; (3) are more
profitable; (4) are more likely to pay dividends; and (5) receive greater amounts of media coverage.
The main sample includes approximately 25% of the total number of CRSP stocks and 74% of the
total market capitalization.
Panel B summarizes the key variables related to analysts’ forecasts and recommendations.
“Number of analysts” is the number of analysts that issued forecasts in the previous quarter; the
sample includes firms covered by at least five analysts. The average firm in the sample is covered
by 10.6 analysts. We compute the other analyst variables using data between two consecutive earn-
ings announcements; we exclude the earnings announcement period itself and consider forecasts
and recommendations issued between two and ten weeks after the most recent quarterly earnings
announcement. Analysts issue 6.1 forecast revisions and 0.6 recommendation changes for the aver-
age firm during this period.
7
A breakdown into positive and negative changes shows that downward
forecast revisions outnumber upward revisions at 3.6 to 2.5. This pattern is consistent with ana-
lysts being, on average, initially too optimistic (Ertimur et al., 2011). Analysts’ recommendation
changes, by contrast, are evenly split between upgrades and downgrades.
7
The data on stock recommendations become available in late 1993; Malmendier and Shanthikumar (2014),
however, show that these data are not reliable prior to February 1994. We therefore use post-February 1994 data to
compute the statistics associated with analyst recommendations.
68 Chapter 2. The Earnings Announcement Return Cycle
2.3 Empirical results
2.3.1 The earnings announcement return cycle
We use the term “earnings announcement return cycle” to refer to the pattern in average stock
returns between two consecutive quarterly earnings announcements, excluding the periods imme-
diately around earnings announcements. Figure 2.2 illustrates this cycle by plotting the average
market-adjusted buy-and-hold returns around earnings announcements. These estimates corre-
spond to those reported in Figure 2.1 except that here we measure cumulative returns. We begin
computing returns two weeks before an earnings announcement and end the computation 13 weeks
after the announcement. This period covers the expected gap between consecutive earnings an-
nouncements; the typical gap is t = 63 trading days.
Figure 2.2 shows the earnings announcement premium. The average stock outperforms the
market by 20 basis points over the period from two weeks prior to an earnings announcement to
a week after it. Following this earnings announcement period, stocks continue to outperform the
market for three more weeks. At the peak between two consecutive earnings announcements, firms
are valued 0.65% higher relative to the week before the earnings announcement. After this point,
stock prices remain flat relative to the market for about two to three weeks before starting their
decline relative to the market.
Table 2.2 examines the performance of a long-short strategy that captures the earnings an-
nouncement return cycle. This strategy is long stocks that announced their earnings one to four
weeks ago; we label this period as “Phase 1” in Figure 2.2. It is short stocks that announced
their earnings seven to ten weeks ago; this period is “Phase 3” in the figure. We consider an
equal-weighted strategy that is rebalanced daily; we later partition the sample by firm size.
We regress the excess returns of the long- and short-portfolios and those of the long-short
strategy against the CAPM, the four-factor model (Carhart, 1997), and a five-factor model that
adds the earnings announcement premium (EAP) factor to the four-factor model. The earnings
announcement premium factor is long stocks from two weeks before an earnings announcement
to a week after it—this period is labeled “Phase 0” in Figure 2.2—and short stocks outside this
window. In constructing this factor, we either forecast the date of the next earnings announcement
2.3. Empirical results 69
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Cumulative return (%)
-10 0 10 20 30 40 50 60 70
Trading day relative to earnings announcement
Phase 0 Phase 1 Phase 2 Phase 3 Phase 0'
Figure 2.2: Earnings announcement return cycle: Cumulative market-adjusted re-
turns. This figure shows the average cumulative market-adjusted buy-and-hold returns between
two consecutive quarterly earnings announcements. The sample includes common stocks traded on
the NYSE, Nasdaq and Amex. A stock is included if it is covered by at least five analysts over
a three-month period prior to the current earnings announcement. The sample begins in January
1985 and ends in December 2016. We begin computing returns two weeks (t =10) before an
earnings announcement and end the computation 13 weeks (t = 70) after the announcement. A
stock’s market-adjusted buy-and-hold return for a stock-earnings announcement pair i at timeT is
Buy-and-hold return
i;T
=
T
Y
t=10
(1 +r
i;t
)
T
Y
t=10
(1 +r
m;t
);
where r
i;t
is stock i’s return on day t relative to the announcement and r
m;t
is the equal-weighted
market return on the same day.
(“real-time EAP”) or assume that investors know the date of the next earnings announcement at
least two weeks prior to it (“perfect-foresight EAP”). In forecast the next earnings announcement,
we expect firms to announce their quarterly earnings on the same weekday as they did a year ago.
The results in Table 2.2 show that the alphas are significantly different from zero in all factor
models. The long-short portfolio earns a CAPM alpha of 3.3 basis points (t-value = 5.95) per day;
the four-factor model alpha is 3.4 basis points (t-value = 6.12). Because the earnings announcement
return cycle strategy takes long and short positions in stocks outside the earnings announcement
period, its correlation with the earnings announcement premium is economically small. In the
five-factor models that include one of the earnings announcement premium factors, the t-values
associated with alphas are 6.04 (real-time EAP) and 5.89 (perfect-foresight EAP).
70 Chapter 2. The Earnings Announcement Return Cycle
Limited analyst coverage and the earnings announcement return cycle
Our main sample consists of firms covered by at least five analysts over a 30-day period before the
current earnings announcement. Figure 2.3 shows the earnings announcement return cycle for firms
with limited analyst coverage. We retain all the other filters—such as those relating to the number
of earnings announcements over the prior 400-calendar day period—but limit the sample to firms
that were covered by at least one but no more than four analysts over the prior quarter (Panel A)
or those that were not covered by any analyst (Panel B). Figure 2.3 is the same as Figure 2.1 except
for changing this analyst-coverage requirement.
Figure 2.3 shows that the earnings announcement return cycle is largely absent among low-
coverage firms and firms with no analyst coverage. These findings show that the earnings an-
nouncement return cycle behaves differently from many other anomalies, such as momentum, which
are stronger for firms with low analyst coverage Hong et al. (2000). At the same time, these re-
sults appear to support the mispricing interpretation. Engelberg, McLean, and Pontiff (2018a),
for example, suggest that investors who follow analysts’ price targets and recommendations may
contribute to mispricing. If so, the earnings announcement return cycle may be stronger among
stocks widely covered by analysts because a larger number of analysts reaches a larger pool of
investors.
Data-mining and the earnings announcement return cycle
The actual earnings announcement return cycle strategy is long each stock for a 15-day period
from one week after an earnings announcement to four weeks after it; it is short the same stock for
another 15-day period from seven weeks after the announcement to ten weeks after it. A concern
about the profitability of this trading rule is that it might be due to luck; if we were to try enough
many trading rules similar to this strategy, we might expect to find many others that display
comparable or even better performance. In Figure 2.4 we address this concern by comparing the
performance of the actual strategy to a large number of alternative trading rules.
We construct 100,000 trading rules that randomly choose when to be long and short each
stock. We can characterize the actual strategy as a 30-element sequence L;L;L;:::;S;S;S over
the earnings cycle, whereL andS stand for long and short positions. We generate each randomized
2.3. Empirical results 71
Panel A: Low analyst coverage
Average daily return (%)
- 70 - 60 - 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50 60 70
0.00 0.02 0.04 0.06 0.08 - 0.02
Trading day relative to current earnings announcement
Current
announcement
Expected next
announcement
Typical previous
announcement
40 45 50
Upward revision (%)
Stock return
Upward revision (%)
Panel B: No analyst coverage
Average daily return (%)
- 70 - 60 - 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50 60 70
0.00 0.02 0.04 0.06 - 0.04 - 0.02
Trading day relative to current earnings announcement
Current
announcement
Expected next
announcement
Typical previous
announcement
Figure 2.3: Earnings announcement return cycle for firms with limited or no analyst
coverage. This figure plots the average daily market-adjusted return (solid line) and the percentage
of positive forecast revisions by analysts (dashed line) for common stocks traded on the NYSE,
NasdaqandAmexforasix-monthperiodcenteredaroundafirm’squarterlyearningsannouncement.
This figure is the same as Figure 2.1 except that it only includes stocks covered by at least one but
no more than four analysts (Panel A) or those not covered by any analyst (Panel B); the sample in
Figure 2.1 consists of stocks covered by at least five analysts.
strategy by reordering this sequence so that the strategy is still short and long each stock for 15
days each. We compute the daily return series associated with each randomized strategy, estimate
the four-factor model regression, and record the t-value associated with the alpha. A comparison
oft-values is appropriate; theset-values are proportional to the strategies’ information ratios, that
is, their alphas divided by the standard deviation of the residuals.
Figure 2.4 shows the bootstrapped distribution of thet-values. By the virtues of randomization
72 Chapter 2. The Earnings Announcement Return Cycle
Figure 2.4: Bootstrapped distribution of t-values associated with four-factor model
alphas. The actual earnings announcement return cycle strategy is long stocks that announced
quarterly earnings between one and four weeks ago and short stocks that announced earnings be-
tween seven and ten weeks ago. The strategy is therefore long each stock for 15 days and short
another 15 days. In this figure we construct 100,000 strategies that randomly choose which days,
over the combined 30-day window, to be long or short. We estimate the daily four-factor model
regression for each strategy and record the t-values associated with the alphas. This figure plots
the distribution of these bootstrappedt-values. The red arrow att-value = 6.22 denotes thet-value
associated with the actual earnings announcement return cycle strategy.
and for being long and short each stock for the same number of days, the mean of this distribution
is close to zero att-value =0:01. The actual strategy’st-value of 6.22 stands out as an outlier; the
99.9th percentile of the bootstrapped distribution, for example, lies at 5.19. Indeed, just 0.004% of
the 100,000 bootstrapped strategies return t-values that exceed that of the actual strategy. This
estimate of 0.004% is also the bootstrappedp-value associated with the actual strategy; it suggests
that it would improbable to identify a trading rule as profitable as the earnings announcement
return cycle by luck.
2.3.2 Analysts’ optimism cycle
The pattern in average returns around earnings announcements aligns with those in analysts’
forecast revisions and recommendation changes. Figure 2.1 shows that, as measured by the fraction
of positive forecast revisions, analysts are the most optimistic around and immediately following an
2.3. Empirical results 73
0 20 40 60
42 44 46 48 50 52
Percent of upgrades (%)
-10 0 10 20 30 40 50 60 70
Trading day relative to earnings announcement
Figure 2.5: The proportion of analyst recommendation upgrades around earnings an-
nouncements. This figure shows the average proportion of analysts’ stock recommendation up-
grades from two weeks before an earnings announcement to 13 weeks after it. The proportion of
upgrades is the total number of upgrades across all stocks divided by the total number of recom-
mendation changes.
earnings announcement; they are the most pessimistic close to the midpoint between two earnings
announcements. Figure 2.5 is similar to Figure 2.1 except that it shows the fraction of analyst
recommendation upgrades. The resulting pattern is similar to that in forecast revisions. After an
earnings announcement, approximately 50% of all recommendation changes are upgrades; before
the next earnings announcement, this fraction is just 44%. Figures 2.1 and 2.5 show that there is
a predictable unconditional difference in analyst behavior that depends only on the distance from
the firm’s previous earnings announcement, and that this pattern aligns with a similar pattern in
average returns.
In Table 2.3 we report estimates from panel regressions to assess the economic magnitude of the
patterns shown in Figures 2.1 and 2.5. The dependent variable is either the proportion of positive
forecast changes or recommendation upgrades (“Proportion”) or an indicator variable that takes
the value of one if the number of positive changes exceeds the number of negative changes and zero
otherwise (“Up Down”). We again exclude from the analysis all forecasts and recommendations
issued around earnings announcement, and consider the period that runs from one week after an
74 Chapter 2. The Earnings Announcement Return Cycle
announcement to 13 weeks after it. The main regressors in Table 2.3 are indicator variables for
Phases 1 and 3. Phase 1 is the three-week period from one week after an earnings announcement
to four weeks after it; Phase 3 is the three-week period from seven weeks after an announcement to
ten weeks after it. The period in the middle, Phase 2, is the omitted category. We include in the
regressions firm-earnings announcement fixed effects; we therefore identify differences in analyst
behavior from within-earnings announcement time-series variation alone.
Table 2.3 shows that, relative to the period in the middle of two earnings announcements,
the proportion of positive forecast revisions is 3.5% higher (t-value = 7.67) immediately after
earnings announcements and 2:4% lower (t-value =5:59) as the next earnings announcement
draws close. The results for recommendation changes are similar albeit weaker. In the regression in
with indicator variables, thet-values associated with the two indicator variables are 2.12 and2:16.
Both the average return (Table 2.2) and optimism patterns (Table 2.3) are therefore statistically
significant.
2.3.3 Measuring the association between the EARC and optimism: The coun-
terfactual portfolio methodology
We use a counterfactual portfolio methodology to measure the association between the earnings
announcement return cycle and the analyst optimism pattern. This methodology measures how
much of the earnings announcement return cycle can be attributed to days surrounding analyst
actions. In this analysis we create an alternative (counterfactual) strategy that removes all stock-
days in the vicinity of analysts’ forecast revisions and recommendation changes. If the actual
strategy is long or short a stock in the vicinity of an analyst event, we remove this position from the
portfolios. We then measure the return difference between the actual and counterfactual strategies.
If this difference is small, the excluded set of events are not important in generating the profits of
the anomaly; if the difference is large, a large proportion of the anomaly profits derives from these
events.
8
8
This analysis is similar to that in Engelberg, McLean, and Pontiff (2018b), who measure differences in anomaly
returns between news and no-news days. Our methodology is the same in spirit, but we implement it by comparing
the returns on two strategies.
2.3. Empirical results 75
This methodology is well-suited for assessing the extent to which a strategy derives its alpha
from the excluded set of events. Suppose that the strategy’s alpha is unrelated to the analyst
events, and that the strategy derives its alpha from the differential exposures that the long and
short legs have to some factors. In our computation, we, in effect, replace an excluded stock’s
actual return with the cross-sectional average of the other stocks. If the events do not correlate
with risk exposures—that is, that a stock’s HML beta, for example, is not higher or lower on days
analysts issue revised forecasts—then the excluded stock’s expected return is equal to this average
plus measurement error. The actual strategy’s average return should then be close to that of the
counterfactual strategy; after all, under the null, we merely drop a handful of random stocks from
the portfolios that still remain well-diversified.
Assuming that the returns on the actual and counterfactual strategies follow factor structures,
these processes can be written as:
r
actual
t
=
actual
t
+
actual
F
t
+e
actual
t
; (2.1)
r
cf
t
=
cf
t
+
cf
F
t
+e
cf
t
; (2.2)
where
actual
and
cf
are 1K vectors of factor loadings andF
t
is aK1 vector of factor returns.
Our tests are about the difference in the strategy returns,
r
actual
t
r
cf
t
=
actual
t
cf
t
+
actual
cf
F
t
+
e
actual
t
e
cf
t
: (2.3)
Under the null hypothesis that the strategy’s alpha is unrelated to the excluded events,
actual
t
cf
t
0. Moreover, if the factor loadings also are unrelated to the events—that is, they are not
different on analyst and non-analyst days—thenj
actual
cf
j0. A time-series regression of the
difference between the actual and counterfactual strategy returns against factors therefore measures
the extent to which the actual strategy’s alpha stems from the excluded events, and the extent to
which factor loadings vary between days when analysts revise their forecasts and non-analyst days.
Table 2.4 reports estimates from time-series regressions that compare the actual strategy to
the counterfactual strategy. We estimate five-factor model regressions that include the earnings
announcement premium factor. Panel A defines an analyst event as a forecast change; that is,
76 Chapter 2. The Earnings Announcement Return Cycle
when an analyst revises his forecast, we remove the stock from the long and short portfolios, when
applicable, for a three-day window around this event. If an analyst, for example, issues a forecast
revision about a stock in the long-portfolio on May 5, 2005, we replace this stock’s return from May
4 to May 6, 2005 with the average return on the other stocks in the long portfolio on these three
days. We use a three-day window to ensure that the window captures the effects of the forecast
revision even if the forecast is issued after-hours. One-fifth of stocks that are either on the long or
short side of the actual strategy experience at least one forecast revision on a typical day.
PanelAshowsthattheactuallong-shortstrategythattradestheearningsannouncementreturn
cycle earns a daily alpha of 3.2 basis points (t-value = 5.89). The estimates for the “counterfactual”
long-short strategy show that this alpha falls to 1.8 basis points (t-value = 3.22) when we remove
stocks from the portfolios around analyst forecast revisions. This reduction of 45% in the point
estimates is statistically significant; the rightmost column shows that the alpha of the difference
between the actual and counterfactual long-short strategies has a t-value of 5.81.
The decomposition of the long-short strategy in the other columns shows that the removal of
analyst events alters the returns on the short side significantly more than those on the long side.
Whereas the alphas of the actual and counterfactual strategies are almost the same for the long
portfolio—the difference of 0.08 basis points is less than one standard error away from zero—the
alpha of the short side increases from0:73 basis points per day to 0.63 basis points when we
remove the analyst events. The earnings announcement return cycle strategy therefore derives a
disproportionate amount of its profits by being short stocks on days when analysts lower their
forecasts.
Panel B of Table 2.4 uses the post-1994 to examine the roles of both analyst forecast revisions
and recommendation changes. When an analyst issues a revised forecast or a recommendation,
we again remove the stock from the portfolios for a three-day window around this event. In this
analysis the alpha associated with the long-short strategy falls from 3.4 basis points per day to 1.4,
and this reduction of 58% is significant with at-value of 6.34. Almost all of the reduction in alphas
is again concentrated on the short side.
Table2.4providesnoevidencetosuggestthatstocks’factorexposuresvarysignificantlybetween
days when analysts revise their forecasts and no-analyst days. The factor loadings in the three
2.3. Empirical results 77
rightmost columns, both in Panel A and B, are all close to zero. Although analyst event contribute
significant to alphas, they do not meaningfully alter the factor exposures.
2.3.4 Forecast revisions, recommendation changes, and stock returns after and
before earnings announcements
Table2.4showsthatanalyst-days—thatis,analysts’forecastrevisionsandrecommendationchanges—
explain between 45% and 58% of the total earnings announcement return cycle. The importance of
this mechanism, however, differs significant between the early and late parts of the cycle. Because
the EARC strategy is long stocks that have recently announced their earnings and short those that
are expected to announce their earnings, we can compare the long and short legs in Table 2.4 to
assess the importance of analyst days.
Panel A of Table 2.4 shows that the actual EARC strategy earns a daily alpha of0:73 ba-
sis points before an earnings announcement (column “short”). The counterfactual strategy that
excludes analyst-days, however, has an alpha of 0.63 basis points, and the difference between the
two alphas has a t-value of7:44. The forecast-revision days therefore explain all of the low
pre-announcement returns. This finding is consistent with the analysis of Kim and So (2018):
stock returns are low before announcements, and these low returns seem to stem from changes in
expectations.
Neither forecast revisions nor recommendation changes, however, explain why firms earn high
returnswellaftertheyhaveannouncedtheirearnings. Acomparisonofthe“long” columninPanelA
of Table 2.4 shows that analyst forecast revisions explain only 4% of the high post-announcement
returns; Panel B, which also excludes days with recommendation changes, moves this estimate up,
but only to 14%. That is, the comparison of the “long” and “short” columns shows that analyst
actions fully explain the low returns before firms announce earnings—but almost none of the high
returns after they have done so.
In a supplementary analysis (Table 2.11 in the appendix), we follow Kim and So (2018) and,
instead of measuring the analysts’ effect of the earnings announcement return cycle, we examine
the role of management guidance. Similar to Table 2.4, we construct a counterfactual strategy that
excludes a three-day window for each stock around a day when the management issues guidance.
78 Chapter 2. The Earnings Announcement Return Cycle
The sample period in this analysis begins in January 2002, which is the start date of the guidance
data. Consistent with Kim and So (2018), we find that management guidance alone explains a
significant part of the returns in late part of the cycle. The alpha increases from1:39 basis points
per day to0:58 when we exclude these days, and this change is statistically significant with a
t-value of 4.64. At the same time, management guidance is unrelated to the significantly positive
returns that firms earn in the early part of the cycle. The alpha falls from 1.56 to 1.49, and this
change within one standard error from zero. Taken together, Tables 2.4 and 2.11 show that the
actions taken neither by analysts nor the management can explain why stock prices drift up well
after firms have disclosed their earnings to the public.
2.3.5 Cross-sectional variation in the earnings announcement return cycle
Analyst optimism by uncertainty and forecast horizon
Hirshleifer (2001) and Daniel, Hirshleifer, and Subrahmanyam (1998, 2001) suggest that if an
anomaly stems from mispricing, it should be stronger in a high-uncertainty environment. Ackert
and Athanassakos (1997) and Zhang (2006a) find empirical support for this conjecture; they show
that the dispersion in analysts’ forecasts positively correlates with analysts’ optimism and under-
reaction to new information. We first test whether analyst optimism correlates with firm size, age,
idiosyncratic volatility, and cash-flow volatility, which are the uncertainty measures used in Zhang
(2006b). We then test whether these measures positively correlate with the earnings announcement
return cycle.
Figure 2.6 shows that analyst optimism significantly varies by the amount of idiosyncratic
volatility. We consider analysts’ one- to four-quarter ahead forecasts. We report the cross-sectional
median forecast error, which is defined as the difference between the analyst forecast and the
actual quarterly earnings, divided by the closing stock price on the day of the previous earnings
announcement. We assign firms into quintiles based on the standard deviation of the residuals from
the four-factor model (Carhart, 1997). We divide the graph into four regions to delineate between
the four forecast horizons. The leftmost region, labeled “4 quarters ahead,” shows how analysts’
forecasts of quarter q + 4 earnings change between quarter q and q + 1 earnings announcements.
2.3. Empirical results 79
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Forecast error (%)
-260 -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0
High IVOL (Q5)
Q4
Q3
Q2
Low IVOL (Q1)
Trading day relative to earnings announcement
4 quarters ahead
3 quarters ahead
2 quarters ahead
1 quarter ahead
Figure 2.6: Forecast optimism by forecast horizon and idiosyncratic volatility. This
figure plots median analyst forecast errors in event time around earnings announcements. We parti-
tion analysts’ forecasts by forecast horizon (one to four quarters ahead) and stocks by idiosyncratic
volatility quintile. Forecast error is the difference between the forecasted and actual quarterly earn-
ings divided by the closing stock price on the day of the previous earnings announcement. Firm i’s
forecast error on dayt is the last non-missing forecast error. Idiosyncratic volatility is the standard
deviation of the residuals from the four-factor model (Carhart, 1997). We compute idiosyncratic
volatility using one year of daily data. We update the idiosyncratic volatility measures and rebal-
ance the corresponding quintiles at the end of each quarter. The vertical lines denote the dates of
earnings announcement. The line to the left from each point is the date of the previous earnings
announcement; the line to the right is the expected date of the next announcement. We assume
that the gap between two consecutive quarterly earnings announcements is 63 trading days.
Two patterns stand out in Figure 2.6. First, analysts’ optimism decreases from one earnings an-
nouncement to the next. Analysts are the most optimistic about quarterq +4 earnings, then about
q+3 earnings, and so forth, and the amount of optimism decreases monotonically between earnings
announcements. Second, analysts are significantly more optimistic about high-idiosyncratic volatil-
ity firms that those of low volatility. It is also among the high-idiosyncratic volatility firms that
the analysts walk down their forecasts the most. Whereas analysts overestimate the four-quarters
ahead earnings yield by over 0.25% among the high-idiosyncratic volatility firms, the median fore-
cast error at this horizon is 0.02% among low-volatility firms. The average actual earnings yield in
the sample is 0.88%, and so an error of 0.25% corresponds, in percentage terms, to analysts being
overly optimistic about the earnings yield by 28%. Analysts are therefore excessively optimistic
about these firms’ future prospects by an economically significant margin. As the date of the
80 Chapter 2. The Earnings Announcement Return Cycle
actual earnings draws close—this is the “1 quarter ahead” region in Figure 2.6—analysts’ median
forecasts are consistently below the actual value. This reversal in expectations is consistent with
the finding that management has incentives guide analysts down so that they can beat analyst
estimates (Richardson et al., 2004; Kim and So, 2018).
Table 2.5 reports the correlation coefficients between analysts’ next period optimism and lagged
measures of uncertainty. We define two measures of analyst optimism. “Early optimism” is the
difference between the analyst forecast of quarterly earnings and the actual earnings, divided by
the closing stock price at the time of the previous earnings announcement. We average across
the one to four quarters ahead forecasts, and measure optimism over the two-week period after the
previous quarterly earnings announcement. “Optimism Walkdown” is the difference between “Early
optimism” and “Late optimism,” where late optimism is defined the same way as early optimism
except that it is measured over a period from seven to ten weeks after the previous quarterly
earnings announcement.
Table 2.5 shows that firm size, firm age, idiosyncratic volatility and cash-flow volatility all
positively correlate with both early optimism and optimism walkdown. Firm size and idiosyn-
cratic volatility are the strongest predictors; their correlations with early optimism and optimism
walkdown are approximately 20 percent and 10 percent, respectively.
Uncertainty and the earnings announcement return cycle
Table 2.6 partitions the sample by firm-level uncertainty and reports daily four-factor model alphas
for portfolios associated with the earnings announcement return cycle. We measure uncertainty
either by firm size or by the first principal component of the four measures examined in Table 2.5:
firm size, firm age, idiosyncratic volatility, and cash-flow volatility. We cross-sectionally standardize
these four variables each quarter to be mean-zero with unit standard deviations before extracting
the first principal component. The resulting principal component’s weights on these four variables
are:
w = (w
firm size
;w
firm age
;w
ivol
;w
cvol
) = (0:532;0:461; 0:576; 0:415): (2.4)
We compute this composite uncertainty measure for each firm-earnings announcement observation
as the product of these weights and the standardized variables.
2.3. Empirical results 81
We sort stocks into quintiles at the end of each quarter and hold the assignments fixed over
the following quarter. The long-portfolio again consists of stocks that announced their quarterly
earnings between one and four weeks ago; those in the short-portfolio announced earnings between
seven and ten weeks ago.
The alpha estimates in Table 2.6 show that the earnings announcement return cycle is stronger
among high-uncertainty stocks. Using the first principal component to measure uncertainty, the
first row shows that the alpha of the long-portfolio increases from 1.8 to 4.3 basis points from the
bottom to the top quintile. A strategy that is long the top-uncertainty long-portfolio and short
the bottom-uncertainty long-portfolio returns 2.7 basis points (t-value = 1.92). Short-portfolios
display the same pattern. The alpha decreases from a statistically insignificant 0.3 basis points to
2:7 basis points from the low- to the high-uncertainty quintile, and the difference has a t-value
of2:10. The estimates for the long and short portfolios imply that the alpha associated with the
long-short strategy must increase significantly as well; indeed, the “hedge” row shows that while the
earnings announcement return cycle strategy has an alpha of 1.7 basis points (t-value = 1.63) per
day among low-uncertainty stocks, this alpha is 7.0 basis points (t-value = 4.34) among the high-
uncertainty stocks. The difference between the high- and low-uncertainty strategies is statistically
significant with a t-value of 2.81.
The lower part of Table 2.6 sorts stocks into portfolios by the inverse of firm size. The estimates
on the hedge-row show that the earnings announcement return cycle is more pronounced among the
smaller stocks in the sample. In the two highest quintiles—which correspond to smaller firms—the
alphas of the earnings announcement return cycle strategy have t-values of 4.56 and 5.61; among
larger firms, the t-values range from 0.75 to 1.56. These estimates do not imply that the earnings
announcement return cycle exists only among tiny stocks—our sample, after all, excludes stocks
not widely covered by analysts. The descriptive statistics in Table 2.1 show that even the firm at
the 25th percentile in our sample has a market value of $0.7 billion.
Figure 2.7 illustrates the relation between idiosyncratic volatility and the earnings announce-
ment return cycle. Each line in this figure represents the average market-adjusted buy-and-hold
return for an earnings announcement return cycle strategy. We assign stocks into quintiles at the
end of each quarter based on idiosyncratic volatility, and held these assignment constant over the
82 Chapter 2. The Earnings Announcement Return Cycle
0.0 0.5 1.0
Cumulative return (%)
-10 0 10 20 30 40 50 60 70
High IVOL (Q5)
Q4
Q3
Q2
Low IVOL (Q1)
Trading day relative to earnings announcement
Figure 2.7: Earnings announcement return cycle and idiosyncratic volatility. This fig-
ure shows the average cumulative market-adjusted buy-and-hold returns between two consecutive
quarterly earnings announcements. The sample includes U.S. common stocks traded on the NYSE,
Nasdaq and Amex. A firm is included if it was covered by at least five analysts over the three-month
period prior to the previous earnings announcement. The sample begins in January 1985 and ends
in December 2016. We assign stocks into quintiles at the end of each quarter by idiosyncratic
volatility; these portfolios are held constant over the following quarter. Idiosyncratic volatility is
measured as the standard deviation of residuals from the four-factor model regression that uses
daily returns over the prior year. We begin computing returns two weeks (t =10) before an
earnings announcement and end the computation 13 weeks (t = 70) after the announcement. A
stock’s market-adjusted buy-and-hold return for a stock-earnings announcement pair i at timeT is
Buy-and-hold return
i;T
=
T
Y
t=10
(1 +r
i;t
)
T
Y
t=10
(1 +r
m;t
);
where r
i;t
is the daily stock return on day t relative to the announcement and r
m;t
is the equal-
weighted market return on the same day.
following quarter. Figure 2.2 is the unconditional version of this figure; it does not partition the
sample by idiosyncratic volatility.
As suggested by the alpha estimates in Table 2.6, the earnings announcement return cycle
is more pronounced among high-uncertainty firms. Among the firms in the highest idiosyncratic
volatility quintiles, cumulative returns peak at approximately 1.3%. That is, the firms in this top
quintile are typically priced 1.3% higher four weeks after the earnings announcement relative to
one week before it. Among the firms in the lowest quintile, the cumulative return at the four-week
mark is just 0.2%. The results in Table 2.6 and Figure 2.7 are consistent with those in Stambaugh,
2.3. Empirical results 83
Yu, and Yuan (2015) on asset pricing anomalies being stronger among high-idiosyncratic volatility
stocks.
Valuation subjectivity
Barberis and Shleifer (2003), Barberis, Shleifer, and Wurgler (2005), Baker and Wurgler (2006),
and others suggest that the prices of unprofitable growth (or “glamour”) stocks likely fluctuate more
with investor sentiment than those of profitable value firms. If the earnings announcement return
cycle relates to analyst optimism, and analyst optimism, in turn, relates to investor sentiment, we
would expect to find a stronger effect among unprofitable growth stocks.
Table 2.7 partitions stocks by book-to-market and profitability, and reports average abnormal
returns for long- and short-portfolios based on the earnings announcement return cycle. Abnormal
returnsarethehighestforstockswithlowbook-to-marketratiosandforthosewithlowprofitability.
The average daily market-adjusted return for the long-short portfolios increases from 3.5 basis
points per day to 7.6 when we move from value stocks to growth stocks. Similarly, the return
increases from 4.4 basis points to 8.1 basis points when we move from high- to low-profitability
stocks. These differences are statistically significant with t-values of 2.39 and 2.81.
The results in Table 2.7 are consistent with the view of that investor sentiment affects the prices
of unprofitable stocks with low book-to-market more than those of profitable stocks with high book-
to-market ratios (Baker and Wurgler, 2006). If the cycle in optimism contributes to the earnings
announcement return cycle, then this variation in optimism should have a disproportionate effect
on the returns of unprofitable growth stocks.
2.3.6 Earnings announcement return cycle and limits to arbitrage
If the earnings announcement return cycle stems from mispricing, its persistence points to severe
limits to arbitrage. We examine the association between the earnings announcement return cycle
and limits to arbitrage in both the cross-section and time series. First, in our cross-sectional
analysis we measure and sort stocks by illiquidity. We expect the EARC to be stronger among
stocks that are more expensive to trade; rational arbitrageurs will trade against the EARC only
up to the point where it is profitable to do so. Second, in our time-series analysis, we measure how
84 Chapter 2. The Earnings Announcement Return Cycle
the strength of the EARC varies by the intensity of the earnings season. When only a handful of
companies announce earnings, arbitrageurs would require relatively little capital to trade against
the EARC; but far more capital would be needed when hundreds of companies announced their
earnings at the same time. Event intensity is important if a fund’s amount of arbitrage capital
is fixed. If a fund has enough capital to eliminate mispricing even at the height of the earnings
season, it will have large amounts of idle capital at times when only a few firms announce earnings.
The optimal amount of capital allocated to this trade, to maximize the return on capital, would
therefore be such that it leaves some arbitrage profits on the table towards the peak of the earnings
season.
Table 2.8 presents the results. The first block of numbers sort stocks into quintiles based on
Amihud’s (2002) illiquidity measure. The average return on the long-portfolio is significantly higher
for illiquid stocks. The 2.5 basis point difference per day between the top and bottom quintiles
is significant with a t-value of 2.16. The average return on the short-portfolio, by contrast, does
not vary as greatly based on stock-level illiquidity; the difference between the top and the bottom
quintiles is within one standard error from zero. As a consequence, the average return on the
long-short portfolio increases modestly in illiquidity.
The second block of numbers in Table 2.8 sorts trading days into quintiles based on event
intensity. We define event intensity as a firm-level variable that counts the number of firms that
announced their earnings on the same day. Each quintile therefore has the same number of trading
days in it; but, because the days are partitioned by event intensity, the portfolios in the top quintile
contain many more stocks than those in the bottom quintile.
The average return estimates in Table 2.8 show that the earnings announcement return cycle
significantly correlates with event intensity. The average return on the long-portfolio increases by
3.2 basis points per day (t-value = 2.13) from the bottom to the top quintile, and that on the
short-portfolio decreases by 4.6 basis points (t-value =3:44). As a consequence, the long-short
strategy yields 7.3 basis points more per day (t-value = 3.73) in the top quintile. In the bottom
quintile, which represents times when arbitrage capital would be spread out over a small number
stocks, the average return on the earnings announcement return cycle strategy is negative at1
basis points per day and statistically insignificant. These estimates are consistent with the earnings
2.3. Empirical results 85
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
Cumulative return (%)
-10 0 10 20 30 40 50 60 70
High Event Intensity (Q5)
Q4
Q3
Q2
Low Event Intensity (Q1)
Trading day relative to earnings announcement
Figure 2.8: Earnings announcement return cycle and event intensity. This figure plots
the average buy-and-hold market-adjusted returns in event time between two consecutive quarterly
earnings announcements. The sample includes U.S. common stocks traded on the NYSE, Nasdaq
and Amex. A firm is included if it was covered by at least five analysts over the three-month
period prior to the previous earnings announcement. The sample begins in January 1985 and ends
in December 2016. Event intensity is a firm-level measure that counts the number of firms that
announce their quarterly earnings on the same day. We first assign stocks into portfolios based
on event intensity and then construct the long-short earnings announcement return cycle strategies
within each quintile. The top quintile includes those stocks that announced their earnings on days
when many others did so as well.
announcement return cycle stemming from mispricing; when the number of arbitrage opportunities
is greater, more of the mispricing persists.
Figure 2.8 assign stocks into quintiles by event intensity—for example, a stock is assigned into
the top quintile if many other stocks announced their earnings on the same day it did—and plots
the average returns on the earnings announcement return cycle strategies within each quintile.
The resulting pattern is similar to that in Figure 2.7 for idiosyncratic volatility. This figure shows
that the firms announcing earnings close to the peak of the earnings season have approximately
1% higher valuations a month after an earnings announcement relative to their valuations a week
before it. Among firms that announce their earnings when relatively few others do, the average
difference between the pre- and post-announcement valuations is less than 0.4%.
The estimates in Table 2.8 and Figure 2.8 support the limits to arbitrage hypothesis. Abnormal
86 Chapter 2. The Earnings Announcement Return Cycle
returns positively correlate with event intensity and, to a lesser extent, with stock-level illiquidity.
The earnings announcement return cycle is more pronounced for firms that announce their earnings
close to the peak of the earnings season, that is, at times when arbitrage capital would be spread
out more thinly.
The results on the correlation between event intensity and the earnings announcement return
cycle relate to the event-time versus calendar-time measurement of returns on the long-term per-
formance of initial public offerings. The long-term performance of IPOs is significantly worse when
measured in event time because a greater number of IPOs occur at times of high valuations Schultz
(2003)—similar to earnings (although at a different frequency), IPOs come in waves. The event-
intensity results in Table 2.8 and Figure 2.8 are similar: the returns on the earnings announcement
return cycle are higher when a greater number of firms announce their earnings. We can there-
fore alternatively quantify the association between event intensity and the earnings announcement
return cycle by comparing event- and calendar-time returns.
Table 2.9 compares market-adjusted returns between event- and calendar-time portfolios. We
sort stocks into portfolios by firm-level uncertainty—we use the same first-principal component
measure as in Table 2.6—and then measure average returns over equal-weighted market returns.
The event-time portfolios, similar to the calendar-time portfolios, are long stocks that announced
their quarterly earnings between one and four weeks ago, and short stocks that announced their
earnings between seven and ten weeks ago. The two event- and calendar-time computations are
therefore the same in every dimension except in how they weight the data.
The estimates in Table 2.9 show that the abnormal returns associated with the earnings an-
nouncement return cycle are significantly higher in event-time than in calendar-time. For the
top-uncertainty quintile, the average market-adjusted long-short return is 10.8 basis points per day
(t-value = 7.13) in event time; in calendar time, this average return is 6.8 basis points (t-value
= 4.40). This difference between two measures is consistent with the event-intensity results. An
arbitrageur who invests the same amount of capital into each stock would earn significantly higher
returns than one who commits the same amount of capital to the earnings announcement return
cycle each day.
2.3. Empirical results 87
2.3.7 Earnings announcement return cycle in Fama-MacBeth regressions
Our results on the earnings announcement return cycle above are based on univariate portfolio
sorts; we have sorted, in turn, by firm-level uncertainty, valuation subjectivity (as measured by
book-to-market and profitability), and measures of limits to arbitrage. In this section we estimate
Fama and MacBeth (1973) regressions that predict the cross-section of quarterly stock returns
using these three measures at the same time.
We define the dependent variable in three ways. First, the long-return component in quarter q
is the stock’s average “phase 1” return, that is, its average return from one week after the quarterly
earnings announcement to four weeks after it. Second, the short-return component is the stock’s
average “phase 3” return, that is, its average return from seven weeks after the announcement to ten
weeks after it. Third, the long-short return is the difference between these two components. Every
stock in the sample has both long- and short-return components each quarter. We use Fama-
MacBeth regressions to examine the extent to which firm characteristics explain cross-sectional
variation in these return components.
The explanatory variables represent the same factors we examine above. Each is defined for
firmi at the start of quarter q. The first is firm-level uncertainty, which is the same first principal
component of firm size, firm age, idiosyncratic volatility, and cash-flow volatility examined in
Table 2.6. The second is event intensity, which is defined as the log-number of firms that announced
earnings on the same day as firm i. We cross-sectionally standardize both of these variables each
quarter so that they have a mean of zero and a standard deviation of one. The third and fourth
are similarly cross-sectionally standardized book-to-market ratios and profitability.
Because we standardize the explanatory variables to be mean-zero, the intercepts in these
regressionsmeasuretheaveragelong-andshort-returncomponentsovertheearningsannouncement
returncycleforthe“average” firm, thatis, forthefirmthatisofaverageuncertainty, eventintensity,
book-to-market, andprofitability. Because theexplanatoryvariables have unitstandarddeviations,
the slopes in the Fama-MacBeth regressions measure the changes in average returns when the
explanatory variables move by one standard deviation in the distribution.
Table 2.10 presents the results. Each row represents estimates from one set of Fama-MacBeth
regressions. Both the univariate and multivariate regressions are consistent with the patterns
88 Chapter 2. The Earnings Announcement Return Cycle
documented above. First, uncertainty positively correlates with analyst optimism, and therefore
the long-return components increase and the short-return components decrease in uncertainty. The
point estimate for the difference between the long and short return components (row 9) shows that
a one-standard deviation increase in uncertainty increases the earnings announcement return cycle
by 50%.
Second, event intensity, which plausibly measures limits to arbitrage, also amplifies the earnings
announcement return cycle. The point estimate of 1.46 on row 10 indicates that a one-standard
deviation shock to event intensity strengthens the return pattern by approximately one-third.
Third, the earnings announcement return cycle significantly decreases in both book-to-market
and profitability. A simultaneous one-standard deviation shock to both, on row 11, amplifies the
earnings announcement return cycle by approximately 50%. The last regression shows that all
these effects coexist. While the “average” firm earns a return of 5.80 basis points per day over the
earnings announcement return cycle—this is the average daily return from being long a stock in
weeks two through four after an earnings announcement and short in weeks seven through ten—this
return effect is more than twice as high for stocks that lie one standard deviation above or below
the average firm in terms of uncertainty, event intensity, book-to-market, and profitability.
Table 2.10 shows that uncertainty, event intensity, book-to-market, and profitability each cap-
ture cross-sectional variation in the earnings announcement return cycle strategy. Moreover, each
of these variables point to the same behavioral explanation for the earnings announcement return
cycle. The pattern in average returns is stronger in high-uncertainty stocks, at times when more
capital would be required to eliminate mispricing, and among stocks whose prices we would expect
to be more swayed by variation in investor sentiment.
2.4 Conclusions
In this paper we document a new regularity in stock returns, the earnings announcement return cy-
cle. Weshowthatstockswidelyfollowedbyanalystsearnhighreturnsintheweeksafterannouncing
their quarterly earnings and low returns during the period leading up the next announcement. This
pattern in average returns coincides with that in analyst optimism. Analysts become increasingly
optimistic about firms’ prospects after earnings announcements, and they revise their forecasts
2.4. Conclusions 89
-0.04 -0.02 0.00 0.02 0.04 0.06
Daily return (%)
-10 0 10 20 30 40 50 60 70
Original return
No analysts updates
Trading day relative to earnings announcement
Return cycle
explained by
analysts' updates
Figure 2.9: Earnings announcement return cycle and analyst optimism. This figure
plots the three-day moving average of average daily market-adjusted return from seven trading days
before a quarterly earnings announcement to 70 trading days after it. The sample contains all
common stocks traded on the NYSE, Nasdaq, or Amex; a stock must have been covered by at least
five analysts in the previous quarter. The sample begins in January 1985 and ends in December
2016. The solid line in this figure represents the return on the actual earnings announcement return
cycle strategy; it is identical to that in Figure 2.1. The dashed line represents the return on the
counterfactual strategy; it removes a stock from a portfolio for a three-day window around each
analyst forecast revision. The shaded gap between the two lines represents the amount of the
earnings announcement return cycle that is due to being long or short on stocks around analyst
forecast revisions.
downwards as the next announcement draws close. The optimism cycle accounts for approximately
one-half of the earnings announcement return cycle. Firm-level uncertainty positively correlates
with both the analysts’ optimism cycle and the earnings announcement return cycle.
Figure2.9illustratestheconnectionbetweentheoptimismcycleandtheearningsannouncement
return cycle. As in Section 2.3.3 we compare the returns of the actual earnings announcement
return cycle strategy against a counterfactual strategy; this counterfactual strategy removes stocks
from portfolios for three-day windows around analyst forecast revisions. The shaded area in the
figure denotes the amount of the earnings announcement return cycle that accrues around the days
revise their forecasts. The estimates in Table 2.4 show approximately one-half of the profits to the
earnings announcement return cycle disappear when the strategy does not take positions in stocks
around analyst forecast revisions.
90 Chapter 2. The Earnings Announcement Return Cycle
The explanatory power of analysts concentrates in the latter part of the cycle. By excluding
analyst days, we can fully explain why firms earn low returns before earnings announcements. The
result in this part of the cycle is consistent with guide-down mechanism of Kim and So (2018).
At the same time, neither the actions of analysts nor management guidance can explain the high
returns that firms earn well after they have announced earnings. In Figure 2.9, the shaded area
shows up mostly in the period leading up to the next announcement. Why do stock prices drift
upwards for weeks even after the uncertainty about their earnings has been resolved, and when at
least analysts do not revise their expectations of these firms’ prospects higher?
Ourestimatesofhowmuchtheoptimismcyclecontributestotheearningsannouncementreturn
cycle are plausibly conservative. Insofar as analyst forecast revisions do not perfectly correlate with
changes in investor sentiment, our estimates of the role of investor sentiment are biased downwards.
Indeed,whenweconsiderbothanalystforecastrevisionsandrecommendationchanges,ourestimate
of how much analyst events contribute to the return cycle increases by 13 percentage points. When
available, it would be valuable to consider other measures of firm-level sentiment to revisit this
computation. The investors who set the prices after earnings announcements, for example, may
not share the same beliefs as analysts, and that may explain why the exclusion of analyst days
does not explain away this part of cycle in average stock returns.
Our results on the connection between returns and sentiment could also be read in reverse. If
one subscribes to our interpretation of these results—that the majority of the earnings announce-
ment return cycle likely derives from predictable variation in sentiment—one could use the earnings
announcement return cycle itself as a proxy for within-firm time-series variation in investor senti-
ment. The market participants who set prices are seemingly the most optimistic after a firm has
released its earnings and the most pessimistic as the next announcement draws near.
A2.1. Tables 91
A2.1 Tables
Table 2.1: Summary statistics
This table reports summary statistics for U.S. common equities traded on the NYSE, Amex, and
Nasdaq. Each observation is a firm-earnings announcement pair. In this table we report time-series
averages of cross-sectional statistics. Panel A reports firm characteristics for the main sample and
excluded sample due to low analyst coverage. The main sample includes firms covered by at least
five analysts during the previous quarter; the excluded sample includes firms with a lower level of
coverage. Panel B reports variables related to analysts for a period from 50 trading days prior to
6 trading days prior to each earnings announcement. The data begin in January 1985 and end in
December 2016 except for the analyst recommendations in Panel B, for which the data begin in
February 1994.
Main sample (N =1,066) Excluded firms (N =3,476)
Percentiles Percentiles
Variable Mean 25th 50th 75th Mean 25th 50th 75th
Fundamental variables
Market value, $ billions 7:43 0:67 1:83 5:62 0:79 0:04 0:14 0:50
Book-to-market 0:61 0:32 0:52 0:79 1:16 0:41 0:70 1:12
Profitability 6:8% 3:5% 6:4% 9:8% 2:3% 0:2% 3:9% 7:7%
Dividend payer 54:2% 3:2% 51:6% 100:0% 31:4% 0:0% 0:0% 95:2%
No. of news articles 22:51 6:70 14:09 27:50 4:25 0:00 0:00 5:09
Analyst forecasts and recommendations
Number of analysts 10:57 6:14 8:68 13:16
Forecast revisions 6:10 1:74 3:94 7:87
Upward 2:51 0:15 1:29 3:07
Downward 3:60 0:38 1:81 4:53
Recommendation changes 0:56 0:00 0:06 0:90
Upgrade 0:27 0:00 0:00 0:25
Downgrade 0:29 0:00 0:01 0:32
92 Chapter 2. The Earnings Announcement Return Cycle
Table 2.2: Earnings announcement return cycle: Daily time-series regressions
This table reports alphas and factor loadings from daily time-series regressions in which the depen-
dent variable is a return associated with a strategy that trades the earnings announcement return
cycle. The long-portfolio holds stocks from one week after an earnings announcement to four weeks
after it; the short-portfolio holds stocks from seven weeks after an earnings announcement to ten
weeks after it; and the hedge-portfolio is the return difference between the long and short portfolios.
The portfolios are equal-weighted and rebalanced daily. The returns are in basis points per day.
The two rightmost columns add an earnings announcement premium (EAP) factor to Carhart’s
(1997) four-factor model. This factor is long stocks from two weeks before an earnings announce-
ment to one week after it and short all other stocks. The real-time factor uses the predicted date of
the next earnings announcement; the perfect-foresight factor assumes that investors know the date
of the next earnings announcement two weeks prior to it. We reportt-values associated with alphas
in parentheses and the standard errors associated with the factor loadings in square brackets. The
sample period begins in January 1985 and ends in December 2016.
+ EAP factor
Perfect
CAPM Four-factor model Real-time foresight
Regressor Long Short Hedge Long Short Hedge Hedge Hedge
Daily alpha (basis points)
Constant 1:92 1:36 3:27 2:47 0:90 3:37 3:33 3:24
(3:48) (2:36) (5:95) (6:02) (2:09) (6:12) (6:04) (5:89)
Factor loadings
Market 1:07 1:11 0:04 1:08 1:12 0:04 0:04 0:04
[0:01] [0:01] [0:01] [0:00] [0:00] [0:01] [0:01] [0:01]
SMB 0:50 0:53 0:03 0:03 0:03
[0:01] [0:01] [0:01] [0:01] [0:01]
HML 0:02 0:01 0:03 0:03 0:03
[0:01] [0:01] [0:01] [0:01] [0:01]
UMD 0:19 0:17 0:02 0:01 0:01
[0:01] [0:01] [0:01] [0:01] [0:01]
EAP 0:02 0:07
[0:01] [0:01]
N 7,779 7,779 7,779 7,779 7,779 7,779 7,779 7,779
Adj. R
2
85:9% 85:7% 0:7% 92:2% 92:0% 0:9% 0:9% 1:2%
A2.1. Tables 93
Table 2.3: Analysts’ forecast revisions and recommendation changes around
earnings announcements
This table reports estimates from panel regressions that explain optimism in analyst behavior
between two consecutive quarterly earnings announcements. The dependent variable is either the
proportion of positive forecast changes or recommendation upgrades (“Proportion”) or an indicator
variablethattakesthevalueofoneifthenumberofpositivechangesexceedsthenumberofnegative
changes and zero otherwise (“Up Down”). “Phase 1” is an indicator variable that takes the value
of one if the firm announced its earnings between one and four weeks ago and zero otherwise; “Phase
3” is an indicator variables that takes the value of one if the firm announced its earnings between
seven and ten weeks ago and zero otherwise. “Phase 2,” which identifies the period in the middle, is
the omitted category. The sample excludes firms from two weeks before an earnings announcement
to one week after it. The sample in the first two columns begins in January 1985 and ends in
December 2016; in columns three and four, it begins in February 1994. We cluster standard errors
by quarter and industry and report t-values in parentheses; we use the 49 Fama-French industries.
Forecast Recommendation
Explanatory revisions changes
variable Proportion Up Down Proportion Up Down
Phase 1 3:46 5:32 0:79 2:36
(6t 20) (7:67) (8:82) (0:29) (2:16)
Phase 2 : : : :
(21t 35) : : : :
Phase 3 2:38 3:72 2:21 2:33
(36t 50) (5:59) (5:24) (0:89) (2:18)
Firm-announcement FEs Y Y Y Y
YYYYYYYY YYYYYYYY YYYYYYYY YYYYYYYY
N 249,845 348,225 42,248 98,652
Adj. R
2
42:0% 23:3% 3:0% 0:2%
94 Chapter 2. The Earnings Announcement Return Cycle
Table 2.4: Measuring the contribution of analyst-update days to the earnings
announcement return cycle
This table reports alphas and factor loadings from daily time-series regressions in which the depen-
dent variable is a return associated with a strategy that trades the earnings announcement return
cycle. The long-portfolio holds stocks from one week after an earnings announcement to four weeks
after it; the short-portfolio holds stocks from seven weeks after an earnings announcement to ten
weeks after it; the hedge-portfolio is the return difference between the long and short portfolios.
The portfolios are equal-weighted and rebalanced daily. The returns are in basis points per day.
The “actual strategy” in columns one through three is the same as that examined in Table 2.2.
The “counterfactual strategy” in columns four through six removes a stock from a portfolio for a
three-day window around each analyst event. The dependent variable in columns seven through
nine is the difference between the actual and counterfactual strategies. Panel A defines an analyst
event as a forecast revision; Panel B defines an analyst event as a forecast revision or recommen-
dation change. The earnings announcement premium (EAP) factor is long stocks from two weeks
before the announcement to one week after and short all other stocks. This factor is computed by
assuming that investors know the date of the next earnings announcement at least two weeks prior
to it. We report t-values associated with alphas in parentheses and the standard errors associated
with the factor loadings in square brackets. The sample period in Panel A begins in January 1985
and ends in December 2016; that in Panel B begins in February 1994.
Panel A: Removing stocks around analyst forecast revisions
Actual Counterfactual Actual
strategy strategy Counterfactual
Regressor Long Short Hedge Long Short Hedge Long Short Hedge
Daily alpha (basis points)
Constant 2:51 0:73 3:24 2:42 0:63 1:79 0:08 1:36 1:45
(6:10) (1:71) (5:89) (5:82) (1:44) (3:22) (0:48) (7:44) (5:81)
Factor loadings
Market 1:08 1:12 0:04 1:07 1:11 0:04 0:01 0:01 0:00
[0:00] [0:00] [0:01] [0:00] [0:00] [0:01] [0:00] [0:00] [0:00]
SMB 0:50 0:53 0:03 0:52 0:55 0:03 0:02 0:02 0:01
[0:01] [0:01] [0:01] [0:01] [0:01] [0:01] [0:00] [0:00] [0:00]
HML 0:02 0:01 0:03 0:02 0:01 0:03 0:00 0:00 0:01
[0:01] [0:01] [0:01] [0:01] [0:01] [0:01] [0:00] [0:00] [0:01]
UMD 0:19 0:17 0:01 0:18 0:16 0:01 0:01 0:01 0:00
[0:01] [0:01] [0:01] [0:01] [0:01] [0:01] [0:00] [0:00] [0:00]
EAP 0:02 0:09 0:07 0:02 0:06 0:04 0:00 0:03 0:03
[0:01] [0:01] [0:01] [0:01] [0:01] [0:01] [0:00] [0:00] [0:01]
N 7,779 7,779 7,779 7,779 7,779 7,779 7,779 7,779 7,779
Adj. R
2
92:2% 92:1% 1:2% 91:8% 91:7% 1:1% 1:4% 1:8% 0:2%
A2.1. Tables 95
Panel B: Removing stocks around analyst forecast revisions and recommendation changes
Actual Counterfactual Actual
strategy strategy Counterfactual
Regressor Long Short Hedge Long Short Hedge Long Short Hedge
Daily alpha (basis points)
Constant 2:41 0:95 3:36 2:08 0:67 1:41 0:33 1:61 1:95
(4:54) (1:71) (4:72) (3:97) (1:20) (2:03) (1:65) (6:81) (6:34)
Factor loadings
Market 1:07 1:10 0:04 1:05 1:09 0:04 0:01 0:01 0:00
[0:01] [0:01] [0:01] [0:01] [0:01] [0:01] [0:00] [0:00] [0:00]
SMB 0:50 0:53 0:03 0:52 0:55 0:03 0:02 0:02 0:00
[0:01] [0:01] [0:01] [0:01] [0:01] [0:01] [0:00] [0:00] [0:01]
HML 0:01 0:02 0:03 0:02 0:02 0:04 0:01 0:00 0:01
[0:01] [0:01] [0:01] [0:01] [0:01] [0:01] [0:00] [0:00] [0:01]
UMD 0:20 0:19 0:01 0:19 0:18 0:01 0:01 0:01 0:00
[0:01] [0:01] [0:01] [0:01] [0:01] [0:01] [0:00] [0:00] [0:00]
EAP 0:00 0:08 0:08 0:00 0:05 0:05 0:00 0:03 0:03
[0:01] [0:01] [0:02] [0:01] [0:01] [0:02] [0:00] [0:01] [0:01]
N 5,463 5,463 5,463 5,463 5,463 5,463 5,463 5,463 5,463
Adj. R
2
92:4% 92:2% 1:2% 92:4% 92:1% 1:0% 1:6% 1:8% 0:3%
96 Chapter 2. The Earnings Announcement Return Cycle
Table 2.5: Analysts’ optimism, walkdown, and firm-level uncertainty
This table reports regression-based estimates of the correlations between analyst optimism and four
firm-level measures uncertainty. The unit of observation is a firm-quarterly earnings announcement
pair. The dependent variable is either Early Optimism or Optimism Walkdown. Early Optimism
is the analyst forecast minus the actual quarterly earnings divided by the closing stock price on
the day of the previous earnings announcement. We average over the one- to four-quarter ahead
forecasts, and measure optimism over a two-week period after the previous earnings announcement.
Optimism Walkdown is the difference between Late Optimism and Early Optimism, where Late
Optimism is defined the same way as Early Optimism except that it is measured from seven weeks
after an announcement to ten weeks after it. The explanatory variables are firm size, firm age,
idiosyncratic volatility, and cash-flow volatility. We standardize the dependent and explanatory
variables each quarter to be mean-zero with unit standard deviations. The regressions include
industry and year-quarter fixed effects, where the industries are the 49 Fama-French industries.
The standard errors, which are reported in parentehses, also cluster by industry and year-quarter.
Firm Firm Idiosyncratic Cash-flow
size age volatility volatility
Dependent variable: Early Optimism
Coefficient 20:38 7:49 26:67 10:99
S.E. 1:48 0:88 2:61 1:80
YYYYYYY YYYYYYY YYYYYYY YYYYYYY
N 80,785 80,785 80,785 65,186
Adj. R
2
10.0% 7.0% 11.0% 7.0%
Dependent variable: Optimism Walkdown
Coefficient 7:38 2:29 11:82 5:28
S.E. 0:99 0:63 1:81 1:26
N 80,198 80,198 80,198 64,660
Adj. R
2
5.0% 4.0% 5.0% 5.0%
A2.1. Tables 97
Table2.6: Firm-level uncertainty and the earnings announcement return cycle
Thistablereportsfour-factormodelalphasforlongandshortportfoliosassociatedwiththeearnings
announcement return cycle. The alphas are reported in basis points per day. Stocks are assigned
into quintiles at the end of each quarter by either the first principal component of uncertainty or
the inverse of firm size. Uncertainty increases from the low to the high quintile. The rightmost
column shows the alphas associated with the strategy that is long the high-uncertainty portfolio
and short the low-uncertainty strategy. The first principal component of uncertainty is that of
cross-sectionally standardized firm size, firm age, idiosyncratic volatility, and cash-flow volatility.
The long-portfolio contains stocks that announced their quarterly earnings between one and four
weeks ago; the short portfolio contains stocks that announced their earnings seven to ten weeks
ago; and the hedge portfolio is the difference between the two. We report t-values in parentheses.
Quintile High
Portfolio Low Q2 Q3 Q4 High Low
Uncertainty measure: First principal component
Long 1:82 1:18 2:09 4:11 4:32 2:71
(2:52) (1:81) (2:95) (4:58) (3:70) (1:92)
Short 0:25 0:44 0:84 2:09 2:72 3:13
(0:32) (0:62) (1:11) (2:27) (2:20) (2:10)
Hedge 1:67 1:68 2:98 6:22 7:02 5:59
(1:63) (1:86) (3:03) (5:06) (4:34) (2:81)
Uncertainty measure: 1/Firm size
Long 1:43 2:05 1:36 2:43 4:61 3:15
(2:20) (2:84) (1:86) (3:24) (5:13) (2:88)
Short 0:64 0:28 0:23 2:24 2:30 3:01
(0:90) (0:29) (0:29) (2:84) (2:44) (2:58)
Hedge 0:73 1:72 1:62 4:69 6:96 6:21
(0:75) (1:45) (1:56) (4:56) (5:61) (3:96)
98 Chapter 2. The Earnings Announcement Return Cycle
Table 2.7: Earnings announcement return cycle, book-to-market, and prof-
itability
This table reports average daily market-adjusted returns for long and short portfolios associated
with the earnings announcement return cycle. The average returns are reported in basis points
per day. The long-portfolio contains stocks that announced quarterly earnings between one and
four weeks ago; the short portfolio contains stocks that announced quarterly earnings seven to ten
weeks ago; and the hedge portfolio is the difference between the two. We compute returns over the
equal-weighted market portfolio. We sort stocks into quintiles either by book-to-market ratio or
profitability. Profitability is the operating profitability of Fama and French (2015a); it is defined
as the sales minus the cost of good sold minus selling, general and administrative expenses (if
available), minus interest and related expense, all divided by the lagged book value of equity. We
report t-values in parentheses.
Quintile High
Portfolio Low Q2 Q3 Q4 High Low
Book-to-market
Long 3:61 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)
Hedge 7:56 7:00 5:40 4:12 3:51 4:05
(5:37) (6:67) (5:55) (4:66) (3:15) (2:39)
Profitability
Long 1:21 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)
Hedge 8:12 5:96 5:23 4:46 4:35 3:78
(5:68) (6:63) (6:52) (4:72) (4:44) (2:81)
A2.1. Tables 99
Table 2.8: Arbitrage difficulty and the earnings announcement return cycle
This table reports average daily market-adjusted returns for long and short portfolios associated
with the earnings announcement return cycle. The average returns are reported in basis points per
day. The long-portfolio contains stocks that announced quarterly earnings between one and four
weeks ago; the short portfolio contains stocks that announced earnings seven to ten weeks ago.
The first block of numbers assigns stocks into quintiles by Amihud’s (2002) illiquidity measure;
each quintile therefore contains the same number of stocks. The second block of numbers assigns
trading days into quintiles based on event intensity; each quintile therefore contains the same
number of trading days. Event intensity of stock i in quarter q is defined as the number of firms
that announced their quarter q 1 earnings on the same day as stock i. We report t-values in
parentheses.
Quintile High
Portfolio Low Q2 Q3 Q4 High Low
Sort stocks by Amihud’s (2002) illiquidity
Long 0:59 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)
Hedge 4:09 5:55 6:14 5:68 6:24 2:15
(3:89) (5:14) (6:88) (5:81) (5:56) (1:65)
Sort days by event intensity
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)
Short 0:72 0:56 2:31 2:53 3:86 4:58
(0:61) (0:56) (2:71) (3:64) (3:94) (3:44)
Hedge 0:93 1:06 2:75 5:21 6:34 7:27
(0:57) (0:72) (2:62) (4:58) (6:20) (3:73)
100 Chapter 2. The Earnings Announcement Return Cycle
Table 2.9: Returns on the earnings announcement return cycle in event- and
calendar-time
This table reports daily market-adjusted returns for long- and short-portfolios associated with the
earnings announcement return cycle. The long-portfolio contains stocks that announced quarterly
earnings between one and four weeks ago; the short-portfolio contains those that announced earn-
ings between seven and ten weeks ago. We sort stocks into quintiles based on firm-level uncertainty,
measured as of the end of the previous quarter. Uncertainty is the first principal component of
cross-sectionally standardized firm size, firm age, idiosyncratic volatility, and cash-flow volatility.
This table reports average returns computed in event- and calendar-time. The event-time averages
are weighted towards stocks that announce their earnings at times when many other firms do so
as well; the calendar-time averages weigh all days the same. We report t-values in parentheses.
Uncertainty quintile High
Portfolio Low Q2 Q3 Q4 High Low
Event-time abnormal returns
Long 1:07 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)
Hedge 2:32 3:89 5:03 7:05 10:76 8:44
(2:40) (3:82) (4:62) (6:02) (7:13) (4:43)
Calendar-time abnormal returns
Long 1:08 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)
Hedge 1:64 1:60 2:96 6:09 6:79 5:40
(1:69) (1:80) (3:19) (5:11) (4:40) (2:84)
A2.1. Tables 101
Table2.10: EarningsannouncementreturncycleinFama-MacBethregressions
This table reports average coefficients and t-values from Fama and MacBeth (1973) regressions
that predict the cross-section of quarterly stock returns. A stock’s long-return component, r
long
,
in quarter q is its cumulative return over the equal-weighted market portfolio from one week after
its quarterly earnings announcement to four weeks after it; the short-return component, r
short
, is
the stock’s cumulative return over the equal-weighted market portfolio from seven weeks after the
announcement to ten weeks after it; and r
long
r
short
is the difference between these two return
components. The four explanatory variables for stock i in quarter q are defined as follows: (1)
uncertainty is the first principal component of cross-sectionally standardized firm size, firm age,
idiosyncratic volatility, and cash-flow volatility at the beginning of quarter q; (2) event intensity
is the log-number of firms that announced their quarter q 1 earnings on the same day as firm i;
(3) book-to-market ratio; and (4) profitability. Profitability is the operating profitability of Fama
and French (2015a); it is defined as the sales minus the cost of good sold minus selling, general and
administrative expenses (if available), minus interest and related expense, all divided by the lagged
book value of equity. All explanatory variables are cross-sectionally standardized each quarter to
be mean-zero and with unit standard deviations; they are also winsorized at the 1st and 99th
percentiles. We reportt-values in parentheses. Theset-values are Newey-West-adjusted using four
quarterly lags.
Event
Dep. Constant Uncertainty intensity BE/ME Profitability
variable #
^
b t
^
b t
^
b t
^
b t
^
b t
r
long
1 2:37 3:46 1:30 2:11
2 2:26 3:63 0:63 1:96
3 2:16 3:27 0:83 1:60 0:01 0:01
4 2:31 3:38 1:38 2:36 0:90 2:56 0:88 1:61 0:17 0:37
r
short
5 3:45 4:10 1:61 2:46
6 3:27 4:42 0:82 2:52
7 3:36 4:27 1:00 1:79 1:69 1:68
8 3:49 4:15 1:46 2:44 1:05 2:66 0:79 1:44 1:32 2:45
r
long
r
short
9 5:81 6:79 2:91 4:30
10 5:54 6:89 1:46 3:55
11 5:53 6:83 1:84 3:81 1:68 4:30
12 5:80 6:76 2:83 4:14 1:96 3:74 1:67 3:52 1:15 2:89
102 Chapter 2. The Earnings Announcement Return Cycle
A2.2 Supplementary analysis
A2.2. Supplementary analysis 103
Table 2.11: Measuring the contribution of management guidance to the earn-
ings announcement return cycle
This table reports alphas and factor loadings from daily time-series regressions in which the depen-
dent variable is a return associated with a strategy that trades the earnings announcement return
cycle. The long-portfolio holds stocks from one week after an earnings announcement to four weeks
after it; the short-portfolio holds stocks from seven weeks after an earnings announcement to ten
weeks after it; the hedge-portfolio is the return difference between the long and short portfolios.
The portfolios are equal-weighted and rebalanced daily. The analysis in this table is the same as
that in Table 2.4 except that, instead of removing events relating to analysts, it conditions on
management guidance. The “actual strategy” in columns one through three is the same as that
examined in Table 2.2. The “counterfactual strategy” in columns four through six removes a stock
from a portfolio for a three-day window around each day when management issues guidance. We
report t-values associated with alphas in parentheses and the standard errors associated with the
factorloadingsinsquarebrackets. ThesampleperiodbeginsinJanuary2002andendsinDecember
2016.
Actual Counterfactual Actual
strategy strategy Counterfactual
Regressor Long Short Hedge Long Short Hedge Long Short Hedge
Daily alpha (basis points)
Constant 1:56 1:39 2:94 1:49 0:58 2:07 0:07 0:80 0:87
(2:61) (2:19) (3:51) (2:51) (0:96) (2:53) (0:93) (4:64) (4:67)
Factor loadings
Market 1:06 1:10 0:04 1:07 1:11 0:04 0:00 0:00 0:00
[0:01] [0:01] [0:01] [0:01] [0:01] [0:01] [0:00] [0:00] [0:00]
SMB 0:54 0:56 0:02 0:54 0:56 0:02 0:00 0:01 0:01
[0:01] [0:01] [0:02] [0:01] [0:01] [0:02] [0:00] [0:00] [0:00]
HML 0:02 0:01 0:03 0:02 0:01 0:03 0:00 0:00 0:00
[0:01] [0:01] [0:02] [0:01] [0:01] [0:02] [0:00] [0:00] [0:00]
UMD 0:16 0:15 0:02 0:16 0:15 0:02 0:00 0:00 0:00
[0:01] [0:01] [0:01] [0:01] [0:01] [0:01] [0:00] [0:00] [0:00]
EAP 0:02 0:10 0:08 0:02 0:10 0:09 0:00 0:00 0:00
[0:01] [0:01] [0:02] [0:01] [0:01] [0:02] [0:00] [0:00] [0:00]
N 3,525 3,525 3,525 3,525 3,525 3,525 3,525 3,525 3,525
Adj. R
2
94.6% 94.3% 1.8% 94.6% 94.7% 1.8% 0.5% 0.0% 0.1%
105
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Expectation dynamics and stock returns
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