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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
https://doi.org/10.1080/15427560.2018.1405004
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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)
JOURNAL OF BEHAVIORAL FINANCE 7
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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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