Robust Measures of Earnings Surprises

• Date: 01 April 2019
• Author: JUN TU,WEI DAI,CHIN‐HAN CHIANG,HARRISON HONG,JIANQING FAN
• Published date: 01 April 2019
• DOI: http://doi.org/10.1111/jofi.12746

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 2 •APRIL 2019

Robust Measures of Earnings Surprises

CHIN-HAN CHIANG, WEI DAI, JIANQING FAN, HARRISON HONG, and JUN TU∗

ABSTRACT

Event studies of market efficiency measure earnings surprises using the consensus

error (CE), given as actual earnings minus the average professional forecast. If a sub-

set of forecasts can be biased, the ideal but difficult to estimate parameter-dependent

alternative to CE is a nonlinear filter of individual errors that adjusts for bias. We

show that CE is a poor parameter-free approximation of this ideal measure. The frac-

tion of misses on the same side (FOM), which discards the magnitude of misses, offers

a far better approximation. FOM performs particularly well against CE in predicting

the returns of U.S. stocks, where bias is potentially large.

ECONOMISTS HISTORICALLY MEASURE THE DEGREE to which the market is surprised

by an earnings announcement using the consensus error, a simple parameter-

free measure given as the difference between actual earnings and the consensus

forecast, where the consensus is calculated as the mean of the available pro-

fessional forecasts. The consensus error is widely used in financial markets.

For instance, commentaries frequently refer to the extent to which earnings

missed the consensus forecast in explaining significant stock price movements.

The consensus error is also a commonly used component of event studies on the

efficiency with which markets react to earnings news (see MacKinlay (1997),

Lyon, Barber, and Tsai (1999), Kothari and Warner (2007)).

A canonical specification in such event studies regresses the cumulative ab-

normal return of a stock around the earnings announcement date (CAR)or

subsequent to the announcement date (POSTCAR) on the consensus error

(CE): the more positive is the consensus error CE, the higher are CAR and

POSTCAR (see, e.g., Bernard and Thomas (1990)). These regressions indicate

∗Chin-Han Chiang is with World Bank Group. Wei Dai is with Princeton University. Jianqing

Fan is with Princeton University and International School of Economics and Management, Capital

University of Economics and Business. Harrison Hong is with Columbia University and NBER.

Jun Tu is with Singapore Management University. The authors thank Ken Singleton (Editor) and

anonymous referees for many helpful comments. They also thank Bruce Grundy; Hongjun Yan;

and seminar participants at the European Finance Association Meetings 2015, Western Finance

Association 2015 Meetings, China International Finance Conference 2015, Financial Management

Association 2015 Meetings, Singapore Management University, Seoul National University, and

Emory University. Jun Tu acknowledges support from Sim Kee Boon Institute of Financial Eco-

nomics. This paper was previously titled “When Everyone Misses on the Same Side: Debiased

Earnings Surprises and Stock Returns.” The authors have no material financial or nonfinancial

interests related to this research, as identified in the Journal of Finance’s disclosure policy.

DOI: 10.1111/jofi.12746

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944 The Journal of Finance R

that markets react to earnings news gradually and have become a linchpin in

the debate on market efficiency (see Fama (1998)).

The widespread use of this measure is premised on the consensus forecast

being an unbiased measure of the market’s expectation of earnings. But it is

well known that a subset of professional earnings forecasts can be biased. One

important reason relates to analysts’ conflicts of interest. A large literature

shows that a number of firms and analysts engage in an earnings guidance

game whereby analysts make optimistic forecasts at the start of the year and

then walk their estimates down to a level the firm can beat by the end of the

year (see, e.g., Richardson, Teoh, and Wysocki (2004)).1These biases in earn-

ings forecasts tend to be stronger in the U.S. stock market, where firm issuance

incentives are more likely to distort earnings forecasts, than in international

markets (see, e.g., Chan, Karceski, and Lakonishok (2007)). Moreover, it may

be optimal for analysts to strategically shade their forecasts, whether positively

or negatively, away from their unbiased signal if the rewards to the forecast-

ing tournament are sufficiently convex (see, e.g., Laster, Bennett, and Geoum

(1999), Hong, Kubik, and Solomon (2000), Ottaviani and Sørensen (2006)). In

short, some fraction of individual forecasts can be significantly biased depend-

ing on analysts’ exposure to different incentives.

Since many investors—particularly institutions, which comprise a signifi-

cant fraction of the market—attempt to adjust for these strategic forecast bi-

ases in forming their earnings expectations (see, e.g., Iskoz (2003), Malmendier

and Shanthikumar (2007), Mikhail, Walther, and Willis (2007)), the end re-

sult is that the consensus forecast is no longer an unbiased measure of the

market’s expectation of earnings. In other words, by averaging biased analyst

forecasts, the consensus forecast systematically diverges from the true expec-

tation of the market. In the context of the CAR and POSTCAR regressions,

we ideally want an accurate and unbiased measure of the true market sur-

prise as the explanatory variable on the right-hand side. If CE as a proxy

for the true market surprise has substantial measurement error, this would

translate into poor explanatory power for CAR or POSTCAR in these canonical

regressions, and thereby leave room for a better measure of the true market

surprise.

The challenge from the econometrician’s point of view is how to construct this

better measure, such that, like the CE, it has the advantage of being parameter-

free but at the same time it takes as given the fact that the econometrician does

not have the same information set as institutional investors. The usual robust

statistics such as medians or winsorization cannot help as these statistics are

meant to deal with outliers, not the systematic bias of forecasts.

To address this problem, we first articulate a tractable and empirically sensi-

ble model of earnings and forecasts where some fraction of individual forecasts

1See also Brown (2001); Bartov, Givoly, and Hayn (2002); and Kasznik and McNichols (2002)

for studies on biases in earnings surprises and the returns to firms beating analyst expectations.

Complementary evidence on the importance of career concerns for analyst forecast bias includes

Hong and Kubik (2003).

Robust Measures of Earnings Surprises 945

can be biased. This bias has an aggregate component that can have a nonzero

mean and variance. We then derive the ideal measure of the true earnings sur-

prise, using the filter of individual forecast errors that is maximally correlated

with the true surprise assuming that the parameters governing the individ-

ual forecasts are known. In general, this nonlinear filter of individual forecast

errors accounts for biases and precision. We show that this nonlinear filter

optimally downweights extreme misses of individual forecasts when there is

potential for bias. Even if the bias has zero mean, the optimal filter will down-

weight extreme misses if there is ex-ante uncertainty or variance in the size of

the aggregate bias. However, it is difficult to estimate the underlying param-

eters of individual forecasts to implement this filter in practice, as we show

below. This is no doubt an important reason why the literature continues to

use CE, which is parameter-free, in the face of extensive evidence of individual

forecast biases.

We next develop a robustness criterion whereby the robustness of a

parameter-free measure of earnings surprise, be it CE or some other mea-

sure, is evaluated by how well it approximates this ideal measure. We show

that the efficiency of CE relative to this full-information benchmark is close

to zero when the potential bias is large, that is, CE is not a robust earnings

surprise measure.

We prove that the ideal earnings surprise measure is much better approxi-

mated by the fraction of forecasts that miss on the same side (FOM). Suppose

that there are Nforecasts, Kis the number of forecasts that are lower than

actual announced earnings A,andMis the number of forecasts that are higher

than A. Then the fraction of misses on the same side is given by

FOM =K

N−M

N,

which takes values between −1 and 1. The higher is FOM, the more posi-

tive the earnings surprise. Consider the case in which K=M. Then FOM =0

and there are equal misses on both sides. When K=Nand M=0, then

FOM =1 and actual lies above the range of forecasts, which we denote by

IAct ual >All =1 (0 otherwise). When K=0andM=N,FOM =−1 and everyone

misses above the actual, which we denote by IAc tua l<Al l =1 (0 otherwise). In the

case in which N=1, FOM equals either 1, 0, or −1.

The fraction of misses is equivalent to taking the average of the signs (either

−1, 0, or 1) of individual forecast errors. As a result, it discards information

on the magnitude of misses much in the same way that the ideal filter would

downweight large misses when potential bias is significant. We provide a the-

oretical lower bound on the efficiency of FOM relative to this full-information

benchmark. The lower bound on the relative efficiency of FOM can be as high

as 50% using plausible parameter values. Thus, FOM shares the advantage of

CE of being parameter-free but is less sensitive to biased forecasts and hence

is potentially superior to CE. While we use earnings forecasts to frame our

model and motivate our empirical analysis, the methodology and idea can be