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Journal of Behavioral Finance

ISSN: 1542-7560 (Print) 1542-7579 (Online) Journal homepage: http://www.tandfonline.com/loi/hbhf20

How (Over) Confident Are Financial Analysts?

Ning Du & David V. Budescu

To cite this article: Ning Du & David V. Budescu (2017): How (Over) Confident Are Financial

Analysts?, Journal of Behavioral Finance, DOI: 10.1080/15427560.2018.1405004

To link to this article: https://doi.org/10.1080/15427560.2018.1405004

Published online: 15 Dec 2017.

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How (Over) Conﬁdent Are Financial Analysts?

Ning Du

a

and David V. Budescu

b

a

DePaul University;

b

Fordham University

ABSTRACT

Extensive research has been devoted to the quality of analysts’earnings forecasts. The common

ﬁnding is that analysts’forecasts are not very accurate. Prior studies have tended to focus on the

mean of forecasts and measure accuracy using various summaries of forecast errors. The present

study sheds new light on the accuracy of analysts’forecasts, by measuring how well calibrated

these forecasts are. The authors follow the tradition of calibration studies in psychological literature

and measure the degree of calibration by the hit rate. They analyze a year’s worth of data from the

Institutional Brokers Estimate System database, which includes over 200,000 annual earnings

forecasts made by over 6,000 analysts for over 5,000 companies. By using different ways to convert

analysts’point estimates of earnings into a range of values, the authors establish the bounds that

are necessary to determine the hit rates, and examine to what extent the actual earnings

announced by the companies are bracketed by these intervals. These hit rates provide a more

complete picture of the accuracy of the forecasts.

KEYWORDS

Financial analyst; Earning

forecasts; Overconﬁdence;

Judgment and decision

making; Calibration

Introduction

Financial analysts are important information

intermediaries in the capital market. Analysts receive

and transfer ﬁnancial accounting information, research

macroeconomic and microeconomic conditions, analyze

company fundamentals and private information, and

help investors and other market participants make sound

investment decisions. Two key outputs of their research

activities are earnings forecasts and stock recommenda-

tions. Analyst earnings forecasts are inputs to stock rec-

ommendation and serve as the basis for some investors’

trading decisions. Analysts usually predict companies’

future earnings 1 or 2 years ahead of the actual earnings

are announced, and may also predict a company’s annual

or quarterly earnings. Prior research has shown that ana-

lyst forecasts affect stock prices and are often used as a

proxy for investors’expectation and differences in opin-

ions (Friesen and Weller [2006]). Naturally, researchers

have been interested in the quality of analyst forecast.

Forecast accuracy is usually deﬁned as the absolute dif-

ference between the forecast and the actual earnings, and

is found to be affected by factors such as frequency and

timeliness of forecasts, experience, industry specializa-

tion, number of companies an analyst follows, and bro-

kerage house characteristics (Jacobs, Lys, and Neale

[1999]). Studies have also found that analyst earnings

forecasts are often inaccurate, as analysts tend to issue

optimistic estimates that are systematically higher than

the actual realized earnings are (Brown [1997], Ramnath

et al. [2008]). In addition to measurement errors, incen-

tive (intentional bias) and unintentional cognitive biases

have been proposed to explain the inaccuracy (Easter-

wood and Nutt [1999], Lin and McNichols [1998], Libby

et al. [2006]).

The incentive explanation suggests that analysts are

motivated to generate biased earnings forecasts to con-

vince investors to follow their recommendations. For

example, analysts might forecast higher earnings when

they offer “buy”recommendation and forecast lower

earnings when their recommendation is “sell.”In addi-

tion, analysts may try to positively affect companies’

stock prices for the sake of maintaining a good relation-

ship with managers and gain access to more private

information from managers. Analysts may also feel pres-

sure from their employers to generate biased forecasts

(Stickel [1990], Easterwood and Nutt [1999], Lin and

McNichols [1998], Libby et al. [2006]).

Other researchers have invoked cognitive biases, such

as overconﬁdence, representativeness, or self-attribution

to explain inaccuracy in an analyst’s forecast. In these

studies, overconﬁdence has been used as overarching

explanation for forecast inaccuracy. These studies have

CONTACT Ning Du ndu1@depaul.edu School of Accountancy and Management Information Systems, DePaul University, One East Jackson Boulevard,

Chicago, IL 60604.

© 2018 The Institute of Behavioral Finance

JOURNAL OF BEHAVIORAL FINANCE

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utilized large samples of analysts’forecast data to search

for overconﬁdence in the analysts’forecasts. Consistent

with theories in behavioral ﬁnance (Gervais and Odean

[2001], Daniel et al. [1998]), they have deﬁned an over-

conﬁdent analyst as one who overestimates her ability

and attaches excessive weight to private, relative to pub-

lic, information (Daniel et al. [1998]). For example, Frie-

sen and Weller [2006] developed a formal rational

(Bayesian) model and empirically test whether analysts

deviate from rational Bayesian updating by examining

errors from analyst forecasts. They found that analysts

place twice as much weight on their private information

as justiﬁed by rational Bayesian updating. They con-

cluded that when analysts incorporate new information

into their forecasts, the new information does not receive

the rational Bayesian weight due to overconﬁdence.

Hilary and Menzly [2006] used past forecast accuracy to

predict the overconﬁdence of a given analyst. They

showed that after a short series of good predictions, ana-

lysts are more likely to be inaccurate as they often take

additional risks by deviating from the consensus. They

interpreted this pattern to be consistent with overconﬁ-

dence as past successes, through the mechanism of self-

attribution bias, exacerbate overconﬁdence (Gervais and

Odean [2001], Daniel et al. [1998]). Bessiere and Elke-

mali [2014] focused on forecast revisions and forecast

errors to test the notion that overconﬁdence leads to an

overreaction to private information followed by an

underreaction when the information becomes public.

They showed that preceding an earnings announcement,

analysts excessively integrate information in their revi-

sions (i.e., overreact) and revise their forecasts too

strongly, but this overreaction disappears in the period

following the announcement.

One problem with these studies is that they do not

measure directly overconﬁdence. Instead, they rely on

proxies to infer overconﬁdence from abnormal forecast

error or excessive forecast revision after benchmarking

against some rational expectations. The use of indirect

proxies makes it difﬁcult to know whether overconﬁ-

dence is the real, or primary, source of earnings forecast

inaccuracy. Overconﬁdence is a well-deﬁned term in the

psychological literature, and is most closely related to the

probability judgment research. Overconﬁdence has been

deﬁned as a particular form of miscalibration observed

when the judged probability that the answers given or

selected are correct, exceeds the actual rate of occurrence

of the target events. For example, Oskamp [1965]deﬁned

overconﬁdence as an excess of conﬁdence in expressed

judgment over accuracy of this judgment. Fischhoff et al.

[1977] suggested that appropriate calibration takes place

“if over the long run, for all propositions assigned a given

probability, the proportion that is true is equal to the

probability assigned”(p. 552). Following this tradition,

we suggest that a well-calibrated analyst is one who is

able to correctly asses his or her accuracy, whereas an

overconﬁdent analyst is one who overestimate his or her

accuracy in earnings forecasts.

We believe the ﬁrst step is to establish the level of con-

ﬁdence among ﬁnancial analysts is to determine how

accurate, or well calibrated, they are. Our goal is to estab-

lish a baseline of analysts’forecast conﬁdence, to calcu-

late their degree of overconﬁdence. To avoid problems

such as nonrepresentative sampling and small sample

size, we rely on large sample of analysts’data. We ran-

domly selected a year’s worth of data from the Institu-

tional Brokers Estimate System (IBES) database, which

includes over 200,000 annual earnings forecasts made by

over 6,000 analysts for over 5,000 companies. Based on

this dataset, we calculated the accuracy of analysts’fore-

casts and empirically established the degree of conﬁ-

dence associated with these forecasts.

Literature review

Overconﬁdence in the psychological literature

Moore and Healy [2008] discussed 3 prevalent deﬁni-

tions of overconﬁdence in the psychological literature:

(1) overestimation of one’s actual performance, (2) over-

placement of one’s performance relative to others, and

(3) excessive precision in one’s beliefs. Extensive research

has focused primarily on 1 facet of judgment quality, cal-

ibration—the match between subjective probabilities

with the corresponding fraction of actual realizations of

the target events (Gigerenzer et al. [1991], Lichtenstein

et al. [1982], Von Winterfeldt and Edwards [1986]).

Most studies have shown that people are systematically

overconﬁdent about the accuracy of their knowledge and

judgments, because their subjective probabilities are fre-

quently more extreme than corresponding accuracy rates

are. For example, when people express 95% conﬁdence,

they may be correct only about 80% of the time. These

studies also have found that the amount of overconﬁ-

dence depends on the difﬁculty of the task. The so-called

hard-easy effect implies that overconﬁdence is higher in

hard tasks, but attenuated, or even eliminated, in easy

tasks (Lichtenstein et al. [1982], Keren 1991]), although

the reality of this effect was questioned (Juslin et al.

[2000]).

Calibration studies use 2 types of response modes:

probability intervals or direct probability estimates.

Probability intervals require estimation of quantiles

(sometimes referred to as fractiles) of probability func-

tions of continuous variables, as well as probabilistic

judgments about discrete propositions (Keren [1991]).

2N. DU AND D. V. BUDESCU

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Estimates of the quantiles of probability distributions are

used for uncertain continuous quantities. Judges are

required to provide values that correspond to prestated

probabilities (Juslin et al. [2000], Keren [1991]), and one

can use them to derive probability intervals (e.g., a sub-

jective 50% probability interval spans the range from the

25th to 75th quantiles). Typically, over- or underconﬁ-

dence is measured by the rate of surprises across multiple

judgments (i.e., the percentage of true values falling out-

side the subjective intervals). For example, consider an

investor who provides 90% intervals for the values of a

variety of stocks at the end of the year. If the investor is

perfectly calibrated, 90% of bounds he or she provided

should bracket the actual values (and 10% of the values

should fall outside the stated intervals). If the percentage

of surprises is higher than 10%, and the proportion of

values in the intervals is lower than the prestated proba-

bility (e.g., only 40% of true values fall within the 90%

intervals), it is inferred that the judge is overconﬁdent.

Conversely, underconﬁdence is inferred when the pro-

portion of true values in the interval is higher than the

prestated probability. The common ﬁnding is that the

empirical intervals are far too narrow. Hit rates in many

studies using 90–99% conﬁdence intervals are less than

50%, leading to surprise rates of 50% or higher instead of

the 1–10% expected from well-calibrated judges (Alpert

and Raiffa [1982], Klayman et al. [1999], Lichtenstein

et al. [1982]). However, there is literature challenging

this approach (for review, see Park and Budescu [2015]).

Essentially, the claim is that people cannot tell the differ-

ence among 50%, 70%, and 90% intervals and they

respond similarly regardless of the conﬁdence level pre-

scribed. Thus, if one compares their answers to the 50%

standard, they look underconﬁdent, but if one compares

them to 90% the same people look overconﬁdent.

Direct probability estimates of binary events ask

judges to assess the probability that various statements

are true (or that certain events will occur) on a scale

ranging from 0 (certainly false)to1(certainly true). For

example, one could ask investors to estimate the proba-

bility that the stock price for Google will be higher than

$160 at the end of the year (and other similar questions

about other stocks). Judges are considered well cali-

brated if the relative frequencies of true statements

match the stated probabilities (e.g., 90% of all events

assigned probability 0.9 should be correct). The calibra-

tion curve plots the proportion of true (correct) items

as a function of the judges’probabilities. The 45line

represents perfect calibration, and points below (above)

this line reﬂect over- (under-) conﬁdence (Lichtenstein

et al. [1982]). Most studies have found overconﬁdence

(e.g., Lichtenstein et al. [1982]), but conservatism

(underconﬁdence) was also observed (Budescu and Du

[2007], Du and Budescu [2005]). Winman et al. [2004]

suggested that probability estimates and conﬁdence

intervals are formally equivalent because high (low)

uncertainties can be expressed either by low (high)

probability judgments or by wide (narrow) interval esti-

mates. Empirically, however, different elicitation meth-

ods have produced systematically different judgments

(Rottenstreich and Tversky [1997]). For example

Budescu and Du [2007] and Du and Budescu [2005]

investigated the 2 response modes using different meas-

ures of miscalibration. They asked decision makers

(DMs) to make judgments about a random sample of

stocks (accompanied by identical information to facili-

tate comparison between the 2 judgment methods).

DMs judged the probabilities that the stocks will reach

a certain threshold, provided lower and upper bounds

of these forecasts, and estimated median, 50%, 70%,

and 90% conﬁdence intervals of their future prices.

They found that the direct probability method induced

overconﬁdence as DMs’subjective probabilities were

higher than the observed relative frequencies, but the

conﬁdence interval method generated a mixed pattern:

underconﬁdence at the 50% level, perfect calibration at

the 70% level, and overconﬁdence at the 90% level.

Yaniv and Foster [1995,1997] challenged the use of

probabilistic calibration as “the normative”standard for

accuracy. They suggest the communication of judgment

estimates, such as forecasts of future outcomes, is part of

the interaction between information senders and

receivers; the choice of the information precision, such

as the width of an interval estimate, not only reﬂects the

level of uncertainty judged by the senders, but also infor-

mation receivers’preferences. Stating an enormous pre-

diction range would be perceived as uninformative in

many real-life decisions. For example, consider a ﬁnan-

cial analyst who can issue 1 of 3 annual forecasts for

earnings per share: (a) $5, (b) $4–6, and (c) $0–10. The

third option with its wide interval is highly likely to be

accurate (i.e., to include the real future earnings), but it

is not very informative (some would call it useless) for

investors who seek guidance about the ﬁrm’s proﬁtabil-

ity. Yaniv and Foster [1995,1997] studied this conﬂict

between the accuracy (deﬁned as the hit rate) and the

informativeness of a range estimate in a series of studies.

They argued that the choice of the graininess of estima-

tion under uncertainty involves a tradeoff between these

2 conﬂicting objectives and proposed a simple additive

(i.e., compensatory) model that weights differentially

accuracy and informativeness, and showed that people

are willing to accept errors in the interest of securing

more informative judgments. This line of work provides

a sensible explanation for the inaccuracy in analyst

forecasts.

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Overconﬁdence in the behavioral ﬁnance literature

Researchers in behavioral ﬁnance have used overconﬁ-

dence to explain market anomalies for decades and

explored this topic through experiments, surveys, theo-

retical modeling, and analysis of ﬁnancial market data.

Overconﬁdence is usually deﬁned as an overestimation

of one’s knowledge or precision of their information

(sometimes more speciﬁcally: overestimating the impact

of private signals and underestimating the relevance or

diagnosticity of public ones). Incorporating the notion of

overconﬁdence in an economic theory allows researchers

to explain puzzles in the ﬁnancial markets such as securi-

ties misvaluations, excessive trading volumes, and the

disposition effect (i.e., a tendency to sell well-performing

stocks too quickly and to hold on to losing ones for too

long; Odean [1998], Daniel et al. [2001], Chuang and

Lee [2006]). Chuang and Lee [2006] developed a com-

plex theoretical model of major ﬁndings on overconﬁ-

dence in behavioral ﬁnance and evaluated it empirically.

They provided both theoretical and empirical evidence

for 4 hypotheses: (1) overconﬁdence causes investors to

overreact to private information, and underreact to pub-

lic information (see Daniel et al. [1998], Odean [1998]),

(2) experienced market gains result in increasingly

aggressive trading (e.g., Gervais and Odean [2001], De

Long et al. [1991], Kyle and Wang [1997], Benos

[1998]), (3) excessive trading of overconﬁdent traders

induce persistent excessive volatility (Benos [1998], Dan-

iel et al. [1998], Odean [1998], Gervais and Odean

[2001]), and (4) overconﬁdent traders underestimate

risk (Hirshleifer and Luo [2001]).

To understand abnormal returns, excessive trading

volume, or extreme volatility, some researchers analyzed

ﬁnancial market data to establish the link between over-

conﬁdence and the trading behavior (Odean [2001], Bar-

ber and Odean [2000,2001]). Other researchers

attempted to establish a direct link. For example, De

Bondt [1998] surveyed investors and conﬁrmed the prev-

alence of overconﬁdence: He found that investors were

overly optimistic about the performance of shares they

own but not about the level of the stock index in general.

Investors were miscalibrated and their probability inter-

vals were consistently too narrow (De Bondt [1998]). In

an experimental study, Glaser and Weber [2007] docu-

mented a direct relation between investor overconﬁdence

and trading volume. Their results also supported miscali-

bration as participants underestimated price volatilities

and their judgments reﬂected tight probability distribu-

tions. Analyzing survey results of German ﬁnancial mar-

ket participants, Deaves et al. [2010] documented

overconﬁdence among participants, and found that

learning occurred as participants widened or narrowed

conﬁdence intervals to correct judgment errors, but years

of working experience did not appear to moderate misca-

libration. Similarly, Gort et al. [2008] focused on institu-

tional investors in Switzerland by surveying the decision

makers of Swiss pension plans. They found that these

managers and members of investment committees pro-

vided too narrow conﬁdence intervals when asked to

estimate past returns of various assets as well as to fore-

cast future returns but their overconﬁdence is less severe

compared with laypeople. They also found that people

with more education and working experience are more

overconﬁdent.

The present study

In this study, we ﬁrst calculate the accuracy of analysts’

annual forecasts and then we determine hit rates of these

forecasts to examine the degree of calibration. The meth-

odological novelty of our approach is the use of a very

large multicompany and multianalysts database that

allows us to examine empirical probability distributions

of forecasts and use them to infer interval predictions.

This approach allows us to examine to what extent the

actual earnings announced by the companies are brack-

eted by these intervals and calculate hit rates at various

levels (analyst, time period, industry, etc.). These hit rates

provide a more complete picture of the accuracy of the

forecasts.

Data analysis

We use data from the IBES database that is maintained

by Thomson Financial and contains comprehensive

global information on analyst estimates of earnings per

share (EPS) including individual forecasts and consensus

data. The database currently covers over 69,000 compa-

nies in 90 countries. We selected all 205,664 individual

forecasts related to the ﬁscal year 2014 in the United

States. The earliest forecast was made 488 days before

the actual EPS announcement date, and the average lag

between the forecast date and the actual EPS announce-

ment is 204 days. This 2014 dataset contains 205,664

forecasts issued by 5,197 analysts for 6,010 companies.

An analyst may issue multiple forecasts for one com-

pany, or for multiple companies. For example, there are

65 analysts who follow Apple, Inc. Table 1 shows the dis-

tribution of analysts following a company. Two compa-

nies are followed by more than 60 analysts and, at the

other extreme, 3,332 companies are followed by fewer

than 10 analysts (The mode and the median of the distri-

bution are in this category). Table 2 shows the distribu-

tion of the number of companies followed by various

4N. DU AND D. V. BUDESCU

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analysts. For example, one analyst follows 83 different

companies, and a total of 3,903 analysts follow fewer

than 10 companies.

We start by calculating the 4 different measures of

accuracy of the analysts’earnings forecasts: individual

error, relative individual error, absolute error, and rela-

tive absolute error. Individual error is the difference

between each individual forecast and the actual EPS

announced by the company and is not signiﬁcantly dif-

ferent from zero (tD¡0.76, df D205,663, p>0.05). As

the positive and negative errors tend to cancel out, we

also analyze the absolute errors. The mean absolute error

is 0.69 with a standard deviation of 7.10, and is signiﬁ-

cantly higher than 0 (tD44.19, df D205,663, p<0.05).

Because of the large variability in EPSs, we calculated rel-

ative values by dividing the individual error and absolute

error by the actual EPS announced by the company. As

some companies have negative EPS value, we use the

absolute value of the actual EPS as the denominator to

ensure that all relative absolute errors are positive. The

mean relative absolute error is 0.47 with a standard devi-

ation of 12.51, not signiﬁcantly different from 0 (tD

1.18, df D205,515, pD0.24). Table 3 presents the details

of forecast errors.

Naturally, we expect that forecasts will become more

accurate as a function of how close they are to the actual

EPS announcement date. For example, there are 112

forecasts made by 34 different ﬁnancial analysts for Star-

bucks in 2014 (ﬁscal year ending 9/30/2014). These fore-

casts are made on 25 different dates and the actual EPS

is announced on 10/30/2014. The forecast horizon, the

time lag between each forecast date and the earnings

announcement date (10/30/2014), ranges from 17 to

364 days with a mean lag of 203.80 days (SD D105.29).

To examine how forecast accuracy changes as a func-

tion of time, we ran 4 different regressions using the 4

measures of error (i.e., individual errors, relative individual

errors, absolute error, and relative absolute error) as

dependent variables. We used the same predictors—time

lag, market capitalization, and several dummy variables for

the various classes of industries. We matched the company

code with a different database Capital to match companies

with industries. We rely on SIC industry code (Standard

Industrial Classiﬁcation by U.S. Department of Labor)

and divide the companies into 9 industries: agriculture,

forestry and ﬁshing, mining, construction, manufacturing,

transportation, communications, electric, gas and sanitary

Table 1. Distribution of analysts following speciﬁc companies.

# of Analysts Following a Company Frequency

More than 60 2

Between 50 and 60 12

Between 40 and 50 42

Between 30 and 40 168

Between 20 and 30 470

Between 10 and 20 1,171

Less than 10 3,332

Total 5,197

Table 2. Distributions of companies followed by speciﬁc analysts.

# of Companies Followed by the Analysts Frequency

Above 80 1

Between 70 and 80 2

Between 60 and 70 1

Between 50 and 60 5

Between 40 and 50 18

Between 30 and 40 88

Between 20 and 30 587

Between 10 and 20 1,405

Less than 10 3,903

Total 6,010

Table 3. Descriptive statistics of four measures of analyst forecast error.

Measure of Accuracy

Statistic Individual Error Relative Individual Error Absolute Error Relative Absolute Error

Mean ¡0.01 ¡0.02 0.69 0.47

95% conﬁdence interval for mean ¡0.04 to 0.02 ¡0.07 to 0.04 0.66 to 0.72 0.41 to 0.52

5% Trimmed Mean 0.04 ¡0.01 0.27 0.18

Median 0.00 ¡0.01 0.14 0.08

Variance 50.87 156.56 50.39 156.34

Std. Deviation 7.13 12.51 7.10 12.53

Minimum ¡921.00 ¡842.00 0.00 0

Maximum 541.39 5,204.00 921.00 5,204

Range 1,462.39 6,046.00 921.00 5,204

Interquartile range 0.29 0.15 0.34 0.22

Skewness ¡46.27 349.42 65.46 356.29

Kurtosis 6,361.01 145,861.81 6,457.14 146,216

Number of forecasts 205,564 205,516 205,564 205,516

Note: Individual error is the difference between each individual forecast and the actual earnings per share (EPS) announced by the company. Relative individual

error is calculated by dividing individual error with the actual EPS. Absolute error is the absolute value of individual error. We calculate relative individual error

by dividing the individual error with the actual EPS value. The relative absolute error is calculated by dividing the absolute error with the absolute value of

actual EPS.

JOURNAL OF BEHAVIORAL FINANCE 5

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service, wholesale trade, ﬁnance, insurance and real estate,

and services. We excluded from the analysis 990 compa-

nies that do not have a matching SIC industry code. Com-

panies in the regression analysis are mostly from the

manufacturing, ﬁnance, and services industries. Market

capitalization is the aggregate valuation of the company

based on its current share price and the total number of

outstanding stocks. Table 4 shows the coefﬁcients for the

regressions.

Errors Db1timelag Cb2market capitalization

Cb3industry dummy variablesðÞ

Most coefﬁcients are not signiﬁcant and the adjusted

R

2

for the models is zero. Time lag and size have signiﬁ-

cant coefﬁcients for all errors except for the relative

error. The positive coefﬁcients for time lag indicate that

short (long) horizons forecasts are more (less) accurate

but, as indicated previously, the effect size is miniscule.

In addition, we examined forecast errors in different

time periods. We use 2 methods to stratify the forecast

horizons into different time periods. The ﬁrst method

(we refer it as DAY1 method) divides them into 4 differ-

ent horizons using intervals of 100 days: (1) less than

100 days (from the actual EPS days), …and (4) more

than 300 days. For example, Starbucks has 26 forecasts

that were issued less than 100 days before the actual

earnings days; 28 forecasts were issued between 101 and

200 days, 33 were made between 201 and 300 days, and

25 made more than 300 days before the actual EPS

announcement. The second grouping method (DAY2

method) divides the forecast horizon into 9 time periods

of size 50 days: (1) less than 50 days, …(9) more than

400 days. By this grouping, Starbucks has 3 forecasts in

group 2 (between 0 and 49 days), 23 in group 3, 4 in

group 4, 24 in group 5, 5 in group 6, 28 in group 7, 6 in

group 8, and 19 in group 9.

First, we focus on the DAY1 grouping with 4 time

periods. Table 5 shows the relative absolute errors for

each of the 4 time periods. A 1-way analysis of variance

(ANOVA) suggests that the means are signiﬁcantly dif-

ferent from each other (FD3.54, p<0.05, df D3,

205,512), and the mean relative absolute errors increase

as the time lag increases. Note that the distribution of

the forecasts in this time period is also skewed, where

skewness D[mean –median)/SD] positively.

Then, we use the more reﬁned DAY2 grouping, which

divides the forecasts into 10 time period groups. Table 6

shows the means for all 10 periods. In general, the values

increase as a function of duration (see, especially the

high value for the last category), but the 1-way ANOVA

suggests that means are not signiﬁcantly different from

each other.

The error analysis conﬁrms prior ﬁndings that ana-

lysts’forecasts are not accurate, and we ﬁnd only weak

evidence that longer forecasting horizons are associated

with larger errors. Next, we follow the tradition in the

judgment and decision making literature, and rely on the

hit rate to measure forecast accuracy. We deﬁne hit rate

as the relative frequency that the actual earnings number

(EPS) announced by each company is bracketed by the

Table 4. Coefﬁcients for the regression (Errors Db1timelag C

b2market capitalization Cb3industry (dummy variables)).

Predictor

Individual

Error

Relative

Error

Absolute

Error

Relative Absolute

Error

Timelag 0.02

*

0.00 0.04

*

0.00

*

Size 0.01

*

0.00 ¡0.01

*

¡0.21

*

Agriculture 0.00 0.00 0.00 0.00

Mining 0.00 ¡0.01 0.01 0.31

*

Construction 0.00 0.00 0.00 0.00

Manufacture ¡0.04 0.01 ¡0.02 0.00

Transportation ¡0.01 0.00 ¡0.01 0.71

*

Wholesale ¡0.01 0.00 ¡0.01 ¡0.09

Retail ¡0.01 0.00 ¡0.02 ¡0.05

Finance ¡0.04 0.00 ¡0.01 ¡0.06

Service ¡0.07

*

0.00 0.02 0.05

Adj. R square 0.00 0.00 0.00 0.00

N 186,118 185,978 186,118 185,978

Note: Individual error is the difference between each individual forecast and

the actual earnings per share (EPS) announced by the company. Relative

individual error is calculated by dividing individual error with the actual EPS.

Absolute error is the absolute value of individual error. We calculate relative

individual error by dividing the individual error with the actual EPS value.

The relative absolute error is calculated by dividing the absolute error with

the absolute value of actual EPS. We rely on SIC industry code (Standard

Industrial Classiﬁcation by U.S. Department of Labor and divide the compa-

nies into 9 industries. Market capitalization is the aggregate valuation of the

company based on its current share price and the total number of outstand-

ing stocks.

p<0.05.

Table 5. Relative absolute error for each of the 4 periods.

Period (Days) Mean SD Skewness n

Less than 100 0.32 5.99 73.58 41,467

100–200 0.45 21.58 228.12 61,903

200–300 0.51 5.09 77.22 58,323

Over 300 0.59 2.63 17.845 43,826

Table 6. Relative absolute error for each of the 10 periods.

Period (Days) Mean SD Skewness N

Under 49 0.75 11.63 13.311 15,940

50–99 0.30 6.84 83.222 25,527

100–149 0.36 5.28 62.813 32,127

150–199 0.53 5.89 112.648 29,775

200–249 0.51 30.51 166.986 23,161

250–299 0.51 4.32 83.385 35,161

300–349 0.63 5.54 73.329 17,297

350–399 0.55 2.71 18.554 26,409

Over 400 1.70 2.58 17.408 119

6N. DU AND D. V. BUDESCU

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forecasted range. To calculate hit rate, we must ﬁrst

establish a relevant range of values. We rely on different

methods to obtain these bounds and we aggregate fore-

casts in different ways—across forecast horizons, compa-

nies, or analysts.

First, we use the DAY1 grouping scheme to examine

the hit rate within each category. For each company, we

aggregated the forecasts made by different analysts in the

same time period to establish the relevant bounds. For

example, Starbucks’112 forecasts from 34 different ana-

lysts were classiﬁed into 4 unique time period groups

and, for each time period, we aggregated the Starbucks’

forecasts and found their minimal and maximal forecasts

for each period. Thus, we create 4 unique time-speciﬁc

records with minimum and maximum values for Star-

bucks. We calculated the hit rate by matching the actual

EPS with each record and determined whether the actual

EPS falls into the time-speciﬁc bounds. For Starbucks,

for example, the ranges for the 4 time periods are

1.33–1.36, 1.32–1.36, 1.30–1.35, and 1.30–1.37. The

actual EPS is 1.33, so this constitutes “a hit”for all time

periods.

When we aggregate across different companies over

the 4 different time periods in DAY1 grouping scheme,

we have 17,515 sets of forecasts. Table 7 shows the fore-

casts are quite evenly distributed across the time (ranging

from 4,042 made less than 100 days before the actual EPS

date to 4,653 made between 100 and 199 days). Across

the 17,515 distribution of forecasts, the hit rate is around

45%, with 30% of the cases falling below the minimum

and 25% above the maximal value, suggesting a slight

tendency to overestimate the EPS. We examined the hit

rates across time periods to see whether it is time sensi-

tive. The hit rate appears to be the highest between 100

and 199 days, and it decreases to 37% when the forecasts

are made 300 days ahead. We also examined the width

of these intervals. Wider intervals reﬂect higher uncer-

tainty in, and variably between, the forecasts. The mean

width is quite low, except for the time period of 200–

299 days, where it is considerably higher (23.82). Post

Table 7. Hit rates across the 4 periods (using DAY1 grouping).

Classiﬁcation Less Than 100 Days 100–199 Days 200–299 Days More Than 300 Days Total

Below minimum 887 1,154 1,398 1,581 5,020

22% 25% 32% 38% 30%

Hit 1,945 2,437 1,960 1,522 7,864

48% 52% 44% 37% 45%

Above maximum 1,208 1,062 1,078 1,037 4,355

30% 23% 24% 25% 25%

Total 4,040 4,653 4,436 4,140 17,269

Mean width (SD) 1.06 (9.45) 1.23 (14.84) 23.81 (3,002.41) 1.14 (17.70) 6.97 (761.10)

Table 8. Hit rates across the 4 periods using the 90% quasi-range (using DAY1 grouping).

Classiﬁcation Less than 100 days 100–199 days 200–299 More than 300 Total

Below minimum 717 1,006 1,257 1,433 4,413

21% 24% 31% 38% 28%

Hit 1,757 2,238 1,794 1,400 7,189

50% 53% 44% 37% 46%

Above maximum 1,016 984 985 961 (3,946)

29% 23% 24% 25% 25%

Total 3,490 4,228 4,036 3,794 15,548

Mean width (SD) 0.29 (0.43) 0.38 (0.47) 0.41 (0.48) 0.40 (0.46) 0.37 (0.46)

Table 9. Hit rates across the 10 periods (using DAY2 grouping).

Number of days before EPS announcement

Classiﬁcation Under 49 50–99 s 100–149 150–199 200–249 250–299 300–349 350–399 Over 400 Total

Below minimum 893 927 1,131 1,203 1,402 1,402 1,506 1,460 14 9,949

27% 27% 28% 32% 38% 36% 44% 40% 64% 34%

Hit 1,135 1,392 1,800 1,418 1,379 1,379 849 1,127 3 10,289

35% 40% 44% 38% 32% 35% 25% 31% 14% 35%

Above maximum 1,265 1,175 1,177 1,119 1,112 1,112 1,055 1,032 5 9,057

38% 34% 29% 30% 30% 29% 31% 29% 23% 31%

Total 3,293 3,494 4,108 3,716 3,893 3,893 3,410 3,619 22 29,295

Mean width (SD) 0.75 (0.78) 0.75 (8.05) 1.10 (15.10) 0.67 (6.12) 0.76 (11.81) 1.02 (15.43) 1.01 (17.15) 0.91 (17.97) 0.34 (0.48) 0.87 (13.18)

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hoc tests using Fisher’s Least Signiﬁcant Difference

(LSD) test show none of the means is signiﬁcantly differ-

ent from the others.

We used a very liberal deﬁnition of the intervals in the

initial analysis (range Dmax –min). Next, we used a

stricter 90% quasi-range, which is obtained by eliminating

the highest 5% and the lowest 5%. Using this measure, the

hit rate increases slightly from 45% to 46%, as shown in

Table 6, so the previous results cannot be attributed to a

minority of extreme and highly inﬂuential outlying fore-

casts. The mean width of the quasi-ranges is quite low (all

are less than 0.5). This indicates that the unusually wide

interval in one of the periods in Table 8 is due to a small

minority of aberrant responses. Post hoc tests using LSD

shows most of the mean widths are not signiﬁcantly differ-

ent from the other, except for the period less than 100 days,

which has intervals that are signiﬁcantly narrower than the

other time periods (p<0.05).

Next, we break the forecasts by DAY2 grouping. For

each company we calculated the minimum and maxi-

mum forecast value across these 10 periods. This gives

us a total of 29,542 distributions of forecasts. We can see

from Table 9 that the highest number of forecasts are

issued in the third period (100–149 days before the target

event), with a total of 4,108 forecasts. The mean widths

of the forecast intervals are quite narrow, ranging from

0.07 to 1.10. A 1-way ANOVA suggests their widths are

not signiﬁcantly different. It appears the forecasts are

evenly distributed in terms of accuracy. About one third

(34%) fall below the minimum forecasts, 31% above the

maximum with a hit rate of 35%. The hit rate is highest

during the third period (100–149 days prior to

announcement). Post hoc tests using LSD show that the

mean widths are not signiﬁcantly different from the

other. Table 10 shows the results using 90% quasi-ranges

by trimming the extreme values. The hit rate changes

only slightly but the mean width shrinks signiﬁcantly.

The most consistent forecasts (narrowest intervals) are

issued in the second period (50–100 days before

announcement).

Next, we aggregated the forecasts for each com-

pany and calculated its hit rate (each company should

have one actual annual earnings for 2014). We have

4,729 companies that are valid for our calculation (we

have a total of 5,221, but 492 have missing values).

Table 11 shows the mean hit rate is around 68%.

Table 12 shows that the hit rate increases to 70%

when we use the 90% quasi-ranges by trimming the

extreme values.

There are 6,011 analysts in the database. On aver-

age each analyst made 35 forecasts across different

companies. One analyst made a total of 1,110 fore-

casts. Two analysts made over 500 forecasts. Many

analysts (a total of 565) only made 1 forecast in

2014! Multiple analysts may follow the same compa-

nies, but the company has only 1 actual earnings for

2014. Thus, some analysts have multiple hit rates

depending on the number of companies they follow.

For example, Starbucks have 34 analysts following the

company, and each analyst made multiple forecasts

for Starbucks related to the 2014 ﬁscal year. For each

analyst, we take the minimum and maximum values

he/she made for Starbucks, so this gives us 34 unique

records containing minimum and maximum values

Table 10. Hit rates across the 10 periods using the 90% quasi-range (using DAY2 grouping).

Number of days before EPS announcement

Classiﬁcation Under 49 50–99 100–149 150–199 200–249 250–299 300–349 350–399 Over 400 Total

Below minimum 775 803 1,012 1,085 1,286 1,270 1,364 1,337 12 8.944

34% 26% 27% 32% 38% 36% 45% 40% 60% 34%

Hit 1,000 1,254 1,629 1,287 1,070 1,235 748 1,021 3 9,247

26% 40% 44% 38% 32% 35% 25% 31% 15% 35%

Above maximum 550 1,056 1,085 1,013 1,011 1,009 943 961 5 8,183

42% 34% 29% 30% 30% 29% 31% 29% 25% 31%

Total 2,875 3,113 3,726 3,385 3,367 3,514 3,055 3,319 20 26,374

Mean width (SD) 0.18 (0.32) 0.21 (0.32) 0.26 (0.35) 0.26 (0.35) 0.26 (0.35) 0.30 (0.37) 0.25 (0.35) 0.31 (0.36) 0.37 (0.49) 0.26 (0.35)

Table 11. Hit rates for forecasts for individual companies (nD

5,221).

Classiﬁcation Percentage

Below minimum 11%

Hit 68%

Above maximum 11%

Missing 9%

Total 100%

Table 12. Hit rates for individual companies using the 90% quasi-

range (nD4,699).

Classiﬁcation Percentage

Below minimum 11%

Hit 70%

Above maximum 11%

Total 8%

Total 100%

8N. DU AND D. V. BUDESCU

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for Starbucks. We calculate the hit rate by counting

the frequencies when the actual earnings fall within

each minimum and maximum record, and ﬁnd a hit

rate of 59% for Starbucks. We use this procedure and

create a dataset of 49,475 unique analyst-company

dataset (1,764 records are invalid due to missing

actual EPS numbers). Table 13 shows a hit rate of

39%, 27% of the forecast are lower than the minimal

value and 31% are higher than the maximal one, and

3% with missing values. Table 14 shows the result

does not change much when we rely on the quasi-

range (see Table 12).

Last, we investigated the analysts’forecasts by each

industry. Of the total of 49,475 records, 6,454 cannot be

matched with the industry code. Deleting the missing

values, we are left with a dataset of 43,021 records.

Table 15 shows the hit rates are the highest when ana-

lysts’forecasts the retail industry and agriculture, for-

estry, and ﬁshing industries, with a 48% hit rate.

Conclusions

Extensive research has been devoted to the quality of

analysts’earnings forecasts. The common ﬁnding is that

analysts’forecasts are not very accurate. Prior studies

tend to focus on the mean of forecasts and measure accu-

racy using various forecast errors. By examining the fore-

cast error, the distance between actual earnings from the

company and estimates made by analysts, these studies

tell us how inaccurate the analysts’earnings estimates

are. Depending on the metric of inaccuracy one chooses

(see Table 3), the answer is in $ (errors and absolute

errors) or as fraction of the actual values (for the relative

measures). It is not surprising that analysts’forecasts are

not very accurate, because earnings forecasts are always

issued in the form of a point estimate, almost impossible

to match the actual realized earnings. In fact work on

investors’perceptions of these estimates (Du et al.

[2011]) has shown that they preferred forecasts that

include some margin of error, and judged them to be

more informative and credible than their precise (point)

counterparts.

Our study takes a different approach to and sheds light

on the accuracy of analysts’forecasts, by measuring how

well calibrated these forecasts are. We follow the tradition

of calibration studies in psychological literature and mea-

sure the degree of calibration by the hit rate. By using differ-

ent ways to convert analysts’point estimates of earnings

into a range of values, we established the bounds that are

necessary to determine the hit rate, and examined to what

extent the actual earnings announced by the companies are

bracketed by these intervals. These hit rates provide a more

complete picture of the accuracy of the forecasts.

We used a very large multicompany and multianalysts

database to examine empirical probability distributions

of forecasts and use them to infer interval predictions.

We used different procedures to collapse data to estab-

lish upper and lower bounds and calculated hit rates at

various levels (analyst, time period, industry, etc.). The

procedure is very ﬂexible as we can use different levels to

determine the calibration, and allows us to investigate

different facets of the quality of analysts’earnings. We

believe this method potentially may be useful for invest-

ors as they evaluate analyst performance and decide to

what degree to use analysts’forecasts as inputs to their

investment decision. For example, none of Starbucks’

112 forecasts from 34 different analysts exactly matches

Table 13. Hit rates of individual ﬁnancial analysts for each com-

pany (nD49,475).

Classiﬁcation Percentage

Below minimum 27%

Hit 39%

Above maximum 31%

Missing 3%

Total 100%

Table 14. Hit rates of individual ﬁnancial analysts for each com-

pany using the 90% quasi-range (nD44,529).

Classiﬁcation Percentage

Below minimum 26%

Hit 39%

Above maximum 31%

Missing 4%

Total 100%

Table 15. Hit rate for individual ﬁnancial analysts across industry.

Industry

Below

minimum Hit

Above

maximum Total

Agriculture, forestry, and ﬁshing 7 30 26 63

11% 48% 41%

Mining 1,526 1,994 705 4,225

36% 47% 17%

Construction 177 198 153 34

34% 37% 29%

Manufacturing 3,617 6,370 5,042 15,030

24% 42% 30%

Transportation, communications,

electric, gas, and sanitary service

1,386 1,863 1,405 4,654

30% 40% 30%

Wholesale trade 377 301 235 913

41% 33% 26%

Retail trade 898 1,506 739 3,143

29% 48% 24%

Finance, insurance, and real estate 1,891 2,859 2,351 7,101

27% 40% 33%

Services 1,321 2,546 2,920 6,787

20% 37% 43%

Nonclassiﬁed 9 22 3 34

26% 65% 9%

Total 11,209 17,689 13,580 4,2479

26% 42% 32%

JOURNAL OF BEHAVIORAL FINANCE 9

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the actual EPS; thus, these forecasts will be determined as

inaccurate based on most conventional metrics. How-

ever, when we aggregated the Starbucks’forecasts and

established time-speciﬁc bounds (1.33–1.36, 1.32–1.36,

1.30–1.35, and 1.30–1.37 for the 4 time periods), the

actual EPS of 1.33 constitutes “a hit”for all time periods.

In addition, when we focus on these 34 analysts, we ﬁnd

a hit rate of 59%, suggesting that forecasts for Starbucks

are relatively well calibrated. Moreover, as 32% of the

forecasts are below the minimal value and only 9% are

higher than the maximal value it appears that the typical

error in this case is to underestimate.

Prior studies have relied on proxies to infer overconﬁ-

dence from abnormal forecast error or excessive forecast

revision without directly measuring overconﬁdence. The

use of indirect proxies makes it difﬁcult to know whether

overconﬁdence is the real, or primary, source of earnings

forecast inaccuracy. The analysis of hit rate suggests that

analysts are not very accurate. When aggregated across

different time periods, the forecasts by different analysts

include the actual EPS number less than 50%, as the hit

rate ranges from 35% to 45%. The hit rate increases

somewhat when we use different aggregation levels. Our

results establish an empirical baseline for analyst conﬁ-

dence, and can be used as an effective way to evaluate or

select some ﬁnancial analysts based on the degree of cali-

bration and, similarly, learn to put more trust in forecasts

provided for some companies, and ignore analysts’pro-

jections for other companies. A possible explanation for

the low hit rates documented in this study is that analysts

may trade accuracy for informativeness when making

forecasts, as suggested by Yaniv and Foster [1995,1997],

and thus, it is almost impossible for forecasts to be per-

fectly calibrated. To test this claim, we artiﬁcially

increased the widths of the original range forecasts by

50%, 100%, 300%, 500%, and calculated the hit rate for

each of the new “inﬂated”intervals (see also Du et al.

[2011]). We ﬁnd the hit rates increase to 79.3%, 82.4%,

84.6%, and 85.4%. However, to achieve a hit rate of 90%,

we must increase the range width 100-fold. This suggests

that analysts might have deliberately chosen narrow

widths so they could keep range forecasts sufﬁciently

informative, even though this reduces their accuracy.

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