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ESSAYS ON THE PROPERTIES
OF FINANCIAL ANALYSTS’ FORECASTS

by
Dmitri Kantsyrev

______________________________________________________________________

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ECONOMICS)

May 2007

Copyright 2007 Dmitri Kantsyrev

ii

For My Mom and Dad

iii

ACKNOWLEDGMENTS

I would first like to thank my thesis committee members, Professor Michael
Magill, Mendel Fygenson, and Fernando Zapatero, for their helpful discussions and
suggestions. I am grateful for the insightful comments from Jaksa Cvitanic,
Christopher Jones, Cheng Hsiao, and Lloyd Levitin. I appreciate comments received
from participants of the 2006 European Financial Management Association
Conference.
I extend my gratitude to all professors and colleagues at Moscow State
University, the University of Michigan and the University of Southern California
whose wisdom sharpened my mind and helped me to gain knowledge. Finally, I give
my sincerest thanks to my family for their love, support, and encouragement. Thank
you.
iv

TABLE OF CONTENTS

Dedication………….........….………………………………………….…………..
Acknowledgements..........….…………………………………………………........
List of Tables……………………………………………………………………….
List of Figures……….......…………………………………………………………
Abstract……………………………………………………………………….……
Introduction……….………………………………………………………………..
Chapter I: Does Adaptive EPS Forecasting Make Analysts’ Forecasts Redundant?
I.1 Experimental Design…..……………………………………………….…
I.2 Estimation and Model Selection……………………………….................
I.3 Empirical Results …….……………………………………….………….
Chapter II: Systematic Optimism in Financial Analysts Earnings Forecasts…........
II.1 Experimental Design…..………………………………………………...
II.2 Evidence of the Financial Analysts’ Forecast Optimism……...….……..
II.3 Properties of the Financial Analysts’ Forecast Error …….……………..
Chapter III: Macroeconomic Activity and Financial Analysts’ Forecast Error……
III.1 Financial Analysts’ Forecast Bias and the Overall Economic activity…
III.2 Disagreement among Analysts and the Overall Economic Activity........
III.3 Financial Analysts’ Forecast Bias and the Macroeconomic Variables…
Chapter IV: Conclusion…………………………………………………………….
Bibliography………………………..………………………………………………

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vii
viii
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6
6
16
21
39
39
48
68
84
84
91
98
105
109

v
LIST OF TABLES

Table 1:

Table 2:

Table 3:

Table 4:

Table 5:

Table 6:

Table 7:

Table 8a:

Table 8b:

Table 8c:

Table 9a:

Table 9b:

Table 9c:

Rank orders of financial analysts and time-series models forecasting
one-year-ahead EPS at the beginning of a fiscal year

Rank orders of financial analysts and time-series models forecasting
two-year-ahead EPS at the beginning of a fiscal year

Prediction matrixes of financial analysts and time-series models
forecasting one- and two-year-ahead EPS at the beginning of a fiscal
year

Informational content of forecasts

Relative forecast accuracy and the number of analysts issuing
forecasts, standard deviation of individual forecasts used to construct
consensus forecasts

Forecast bias for financial analysts, random walk with drift and
quarterly neural networks one- and two-year-ahead EPS forecasts
made at the beginning of a fiscal year

Number of firms for which at least one forecast exists during the
specified six-year period

Biases for analysts’ EPS forecasts made at the beginning of a fiscal
year (1987 - 1992)

Biases for analysts’ EPS forecasts made at the beginning of a fiscal
year (1993 - 1998)

Biases for analysts’ EPS forecasts made at the beginning of a fiscal
year (1999 - 2004)

Biases for analysts’ EPS forecasts made at the middle of a fiscal year
(1987 - 1992)

Biases for analysts’ EPS forecasts made at the middle of a fiscal year
(1993 - 1998)

Biases for analysts’ EPS forecasts made at the middle of a fiscal year
(1999 - 2004)

26

26

26

35

35

35

49

57

58

59

61

62

63

vi
Table 10:

Table 11:

Table 12:

Table 13:

Table 14:

Table 15:

Table 16:

Table 17

Percentage decrease in the financial analysts’ forecast bias at the
middle of a fiscal year relative to the beginning of a year

Number of individual financial analysts’ one-year-ahead EPS
forecasts made at the beginning and the middle of a fiscal year

Financial analysts’ forecast revisions for the Most Volatile, Middle,
and the Steadiest category firms prior to the earnings announcement
date

Financial analysts’ forecast errors for the Most Volatile, Middle, and
the Steadiest category firms prior to the earnings announcement date

Financial analysts’ median forecast error at the beginning of a fiscal
year in the case of one- (two)-year-ahead forecast horizon and the
economic activity

Standard deviation among financial analysts’ individual forecasts and
the average number of analysts issuing forecasts in and around
economic recessions at the beginning and the middle of a fiscal year in
the case of the one- and two-year-ahead forecast horizon

Pearson correlation matrices for economic innovations and corporate
earnings

Financial analysts’ one-year-ahead median forecast error and
macroeconomic innovations

64

67

81

82

94

95

104

104

vii
LIST OF FIGURES

Figure1:

Figure 2:

Figure 3:

Figure 4:

Figure 5:

Figure 6:

Figure 7:
EPS before Extraordinary Items (1973-1985)/EPS from Operations
(1986-2002) of Alcoa Inc., Avery Dennison, and the S&P500 index

Average EPS before Extraordinary Items (1973-1985)/EPS from
Operations (1986-2002) of the Volatile, Steady category firms, and the
S&P500 index

EPS from Operations (1987-2004) for four extreme groups of firms

Financial analysts’ forecast bias at the beginning of a fiscal year in the
case of the one- (two)-year-ahead forecast horizon

Financial analysts’ median forecast error for the Most Volatile,
Middle, and the Steadiest category firms prior to the earnings
announcement date

Financial analysts’ median forecast error for the Most Volatile
category firms at the beginning and the middle of a fiscal year in the
case of the one- (two)-year-ahead forecast horizon and the economic
activity

Financial analysts’ median forecast error for the Steady category firms
at the beginning and the middle of a fiscal year in the case of the one-
(two)-year-ahead forecast horizon and the economic activity

11

23

49

60

73

96

97

viii
ABSTRACT
This work examines forecast errors in financial analysts’ earnings forecasts.
First, the relative accuracy of financial analysts’ and adaptive time-series forecasts is
considered. The central question is whether financial analysts efficiently utilize
available information and produce forecasts that are more accurate than predictions of
statistical models. The study employs a novel forecasting approach - artificial neural
networks and identifies cognitive anomalies that influence the analysts’ forecasting
behavior. Financial analysts exhibit systematic optimism for a specific subset of
companies. The magnitude of the analysts’ optimistic forecast bias increases with the
difficulty of the forecasting task, which is represented by statistical characteristics of a
firm’s earnings as well as the overall economic activity. Both the mean and median
forecast errors are largest for companies with the most volatile earnings that move
against or independently of the market earnings. The study also presents a model of
the analysts’ forecasting behavior and provides evidence that the analysts’ optimistic
forecast error somewhat slowly decreases throughout the forecast horizon. Financial
analysts on average are found to overreact to positive earnings releases and underreact
to negative. In addition, they tend to ignore the expected economic activity when
making earnings forecasts and, furthermore, fail to adjust their forecasts appropriately
in periods of economic downturns. It leads to the inverse relationship between the
optimistic forecast bias and the overall economic activity. The evidence presented
contributes to the understanding of the formation and value of analysts’ predictions.

1
INTRODUCTION
While earnings are the basic accounting-based measure of a firm’s
performance, earnings expectations are one of the strongest signals about its future
prospects. Over the years, two methods of earnings predictions have been exploited:
the use of financial analysts and non-adaptive time-series models. The latter are often
simple statistical techniques, whereas financial analysts are viewed as a more reliable
source of forecasts for all companies and at all forecast horizons. On the other hand,
financial analysts may not always issue objective forecasts for a number of reasons.
Their forecasts may be influenced by personal career concerns, incentive problems, or
behavioral biases. However, there have been few attempts to find alternative methods
of forecasting in the literature since the 1980s, when the view of analysts’ superiority
prevailed. Therefore, it seems natural to come back to the issue of forecasting
accuracy from the current perspective. This work compares the relative accuracy of
financial analysts’ forecasts to adaptive time-series models predictions and provides
quantitative analysis of analysts’ forecast errors. It demonstrates the importance of
statistical characteristics of a firm’s earnings as well as macroeconomic factors for
assessing the analysts’ forecasting behavior. The foremost result is that the greater the
difficulty of the forecasting task faced by analysts, the bigger their optimism and the
poorer relative forecast accuracy.
The first chapter of this study considers IBES earnings forecasts and employs
adaptive forecasting techniques, in particular, a novel approach: artificial neural
networks. Neural networks can detect systematic patterns, learn, and adapt to

2
underlying relationships. They are data driven and therefore useful where one does not
have particular beliefs about functional forms. This study provides evidence of the
superiority of adaptive time-series models forecasts over financial analysts’ forecasts
made at the beginning of a fiscal year for companies with highly volatile earnings that
are relatively harder to predict. In addition, financial analysts are found to produce less
accurate two-year-ahead forecasts made at the beginning of a fiscal year than any
other adaptive time-series model. It leaves in question the existence of analysts’ two-
year-ahead forecasts as a reliable measure of a firm’s expected performance. Next, the
study examines whether additional information processed by analysts is constructive
or if it is a noise that hinders the discovery of systematic patterns. The relative
informational content of forecasts is considered and time-series models are shown to
contain information missing in analysts’ predictions. This result suggests that financial
analysts either underestimate the importance of information contained in histories of
earnings or cannot properly filter the extensive set of all available information. It
points at the existence of some distortions that affect the analysts’ forecasting
behavior.
The rest of the study is concerned with identifying sources of these distortions.
The objective is to advance our understanding of the financial analysts’ forecasting
behavior by investigating determinants of cross-sectional and time-series differences
in the analysts’ forecast error. This work distinguishes itself from most of the existing
literature by analyzing all available data on analysts’ annual consensuses as well as
timely constructed forecasts for the 1987-2004 period. It leaves a sampling issue out

3
of the scope of the study and suggests that behavioral anomalies have an extensive
presence in the process of earnings predictions. Analysts’ forecasts are fraught with
cognitive failures, while neural networks better organize the data by identifying
nonlinear patterns.
The evidence of systematic optimism in financial analysts’ earnings forecasts
is presented in Chapter II. The magnitude of the analysts’ optimistic forecast bias is
found to depend on statistical characteristics of a firm’s earnings: the coefficient of
variation of the first difference of earnings and the coefficient of correlation of a
firm’s earnings with the S&P500 earnings. Forecasts are not optimistically biased only
for companies, whose earnings are strongly correlated with the market earnings or
have the smallest variation of the change in earnings. In addition, the analysts’ forecast
optimism is found to increase with the forecast horizon. In the case of the two-year-
ahead forecast horizon, the analysts’ forecast error is two, three, or even eight times
greater than that in the case of the one-year-ahead forecast horizon.
To investigate the properties of the financial analysts’ optimism as a fiscal year
progresses, changes in the analysts’ forecast error are traced over the forecast horizon.
Analysts’ forecast optimism decreases as the announcement date approaches.
However, the rate of the decrease is relatively slow. Three months prior to a fiscal year
end, the financial analysts’ optimistic bias is on average only 33-46% and 6-24%
smaller than that at the beginning of a fiscal year in the case of the one- and two-year-
ahead forecast horizon. In addition, statistical characteristics of a firm’s earnings
continue to play an imperative role for its observed magnitude. The more uncertainty

4
exists about the future prospects of a company, the slower the rate of the analysts’
optimistic forecast bias decrease. It suggests that the difficulty of the forecasting task
is the determinant factor for the financial analysts’ forecast optimism not only at a
fixed point in time, but also as a fiscal year advances.
Whatever is the explanation of the analysts’ forecast bias in the literature,
incentive or cognitive based, none of the studies, to our knowledge, explicitly
confronts the analysts’ forecasting behavior models with the empirical data. Here, the
dynamics of the analysts’ forecast error over the two-year forecast horizon is
examined in the extensive model where the analysts’ forecasting behavior is
characterized by their reactions to actual earnings releases. Overall, the results are
consistent with the hypothesis that financial analysts on average overreact to positive
earnings releases and underreact to negative.
While there were numerous attempts to analyze cross sectional characteristics
of financial analysts’ forecasts in the literature, only a few have studied how the
financial analysts’ accuracy is related to the macroeconomic activity. Chapter III
examines the temporal variation in the analysts’ forecast optimism. The central
question is how the analysts’ forecast error depends on the expected and historical
economic activity that represents the difficulty of the forecasting task at the macro
economy-wide level. It is evidently harder to predict earnings in a period of economic
recession than in a period of stable performance and expectations. Accordingly, the
analysts’ optimistic forecast bias and the economic activity are negatively related.
Throughout the years of strong economic growth, the analysts’ forecast bias

5
diminishes, and during the years of stagnation, it becomes relatively large. Financial
analysts seem to ignore the future economic activity when making earnings forecasts
and extrapolate the positive, but not the negative historical economic growth into the
future. This result is also supported by the finding that the disagreement among
financial analysts regarding the future prospects of companies increases only during
recession periods, but not before the recessions. Furthermore, we observe in the data
that financial analysts not only fail to anticipate weaknesses in the economic condition
before an economic downturn, but they also fail to adjust their forecasts sufficiently
after the downturn settles.
Finally, the relationship between the analysts’ forecast error and
macroeconomic factors is analyzed. The results suggest that the change in the term
spread has much descriptive power over the temporal variations in the analysts’
forecast error. Term spread increases after business peaks, when it is low, preceding
sluggish economy, and decreases after troughs, when it is high, preceding strong
growth rates in production during phases of business expansions. As a result, an
increase in the term spread over the year horizon is associated with a reduction in the
corporate earnings and an increase in the forecast error produced by financial analysts
at the beginning of that year. The finding that forecast error varies systematically with
the business cycle suggests that analysts may focus too much on firm-specific issues
and not enough on the overall macroeconomic condition.

6
CHAPTER I
DOES ADAPTIVE EPS FORECATING MAKE ANALYSTS’
FORECASTS REDUNDANT?
The organization of this chapter is as follows. Section I.1 describes the related
literature, data used, and a sample selection process. It also illustrates differences
between the suggested adaptive statistical approach and the non-adaptive one that has
been continuously exploited in the past. Section I.2 discusses estimation methodology,
while the empirical findings are presented in Section I.3.

I.1 Experimental Design

A. This work versus the related literature.
Underlying this research is abundant theoretical and empirical literature on the
subject of time-series of earnings. Earlier studies, such as Ball and Watts (1972),
Albrecht et al. (1977), Watts and Leftwich (1977), argue that histories of past annual
earnings per share contain almost no information about future earnings, and conclude
that earnings are best described as random processes. On the other hand, works by
Brown and Roseff (1979), Collins and Hopwood (1980), Hopwood et al. (1982)
consider quarterly earnings as inputs to forecasting models and state that quarterly
EPS have appeared to yield the predictions of future annual earnings that often
compete in accuracy with the random walk model.
Empirical tests comparing the accuracy of financial analysts’ earnings
forecasts to the accuracy of non-adaptive time-series models predictions claim
analysts’ superiority. Brown and Roseff (1978) analyze fifty firms followed by a

7
single analyst, Value Line Investment Survey, and provide evidence of Value Line’s
superiority over the Box and Jenkins and naive models. Fried and Givoly (1982) note
that the broadness of the information set employed by analysts and their reliance on
information released after the end of a fiscal year appear to be important contributing
factors to the analysts’ superior performance. Similarly, Brown et al. (1987) attribute
the analysts’ superiority to a timing advantage and an information advantage
1
. They
also show a positive association between the firm size and the advantage of financial
analysts’ forecasts over time-series based forecasts.
However, note that most empirical works have studied the accuracy of non-
adaptive statistical models, specifications of which are fixed through time. This
approach neglects the changing nature of data generating processes and may not
provide the most accurate forecasts. Our approach is to consider the use of adaptive
time-series models as a tool for forecasting earnings. In contrast to non-adaptive
statistical models, the main feature of this method is the assumption that the
underlying relationship between past and future earnings may be evolving over time.
As approximate means by which we hope to capture this phenomenon, we not only re-
estimate parameters of statistical models, but also choose a new specification each
time new data become available.

1
Timing advantage - more information is available after the earnings announcement; information
advantage - more information is used by analysts than historical earnings.

8
B. Data and the sample selection.
We use consensus forecast data from the Institutional Brokers Estimate System
Summary file. In the IBES database, consensus forecasts of firms’ earnings are the
means or medians of all analysts’ estimates outstanding as of the Thursday before the
third Friday of each month. The choice of consensus forecasts in favor of individual
analysts’ forecasts is not arbitrary. Investors often rely on consensus forecasts of
earnings as measures of a firm’s future performance. In firm valuation models, the
intrinsic value of a company also depends on consensus expectations of future
earnings. In testing such models, consensus forecasts are the appropriate proxies to be
used, and an ex-post accuracy is not a key motive for using consensus measures.
The IBES earnings forecasts database covers approximately 14,500 companies
for different periods starting in 1977. We restrict attention to the December year-end
firms. In addition, for a firm to be included in the sample there should exist one- and
two-year-ahead forecasts by at least one analyst in March of each year starting in
1993. Because most calendar-year-end firms announce their annual earnings between
January and March, we use analysts’ forecasts from the month of March. It ensures
that analysts’ as well as statistical models forecasts are conditioned on the same
knowledge of previous years earnings
2
.
The selection procedure results in a sample of 539 firms with ten-year histories
of annual forecasts (1993-2002). The ten-year forecast comparison window is chosen
because of the following consideration: time-series models in this study require

2
The requirement of annual earnings releases by the middle of March is checked manually.

9
histories of actual earnings to estimate parameters of the models and to generate
forecasts. Therefore, there is a tradeoff between the number of years used to compare
forecast errors and the selection bias that increases with extending histories of actual
earnings farther in the past. The selected twenty-year earnings histories requirement
reduces the set to 218 firms
3
. Note that the common criticism of most published
studies is that, by dealing with only a few forecast comparison dates, they report
results that may be specific to relatively short time intervals. For example, Brown and
Roseff (1978) compare forecasts for only four years.
To analyze all 218 firms does not look feasible due to the extensive time
requirement. As discussed later, in a real-time forecasting approach, parameters of
statistical models should be re-estimated each year and for each company a new. Thus,
with 218 firms we would need to produce 2,180 estimates by means of several time-
series models. To reduce the set to a manageable size, we finalize the selection
procedure by randomly choosing forty-eight firms
4
. We admit that it is possible that
there exist some sample bias. This bias is towards a greater coverage of large and
somewhat older firms, which have forecast data reported by the IBES in March for ten
consecutive years and actual earnings available for thirty years. For this reason,
extrapolations to larger populations should be made with care.

3
We take actual earnings (1973-1992) from the Compustat database. Note that both analysts’ forecasts
and actual earnings series are Earnings per Share before Extraordinary Items and Earnings from
Operations as soon as the latter became available around 1986. All data are adjusted for stock splits and
stock dividends.
4
We believe that this sample is representative of the 218 firms set. In fact, we first randomly choose
twenty-four companies and produce forecasts; then, we repeat the exercise with another twenty-four
firms. The results in both sub-samples are similar.

10
C. Time-series models.
In this section, we discuss the adaptive time-series models that are used to
forecast future earnings. By an adaptive model, we mean that a new specification is
chosen before each new rolling forecast is constructed. The notion of adaptability or
real-time forecasting constitutes a key difference between the current research and the
existing literature, which conditions the analysis on a fixed, non-adaptive forecasting
model assumed to be in effect throughout an entire sample period. The latter approach
misses the important detail that a time-series model, which reasonably describes an
earnings-generating process in one period, may be inappropriate in another. For
example, an earnings-generating process may alter due to changes in general
economic factors such as cyclical changes, which represent economy-wide
fluctuations caused by a business cycle, or structural changes like changes in the
demographic structure or technologies. Shifts in an industry’s position as well as
transformations in the political situation may also change a company’s fortune over
time. To illustrate the idea, earnings per share of two companies are presented in
Figure 1. In the first graph, earnings are highly cyclical, indicating that the company’s
performance is very sensitive to the overall market condition. Whereas in the second
graph, earnings follow the market quite closely, suggesting that we are dealing with a
typical market firm.
By estimating adaptive linear and non-linear models, we address the following
question: “Is there evidence that adaptive models are valuable in forecasting
earnings?” If so, we have a clear alternative to often expensive financial analysts’

11
-0.50
0.00
0.50
1.00
1.50
2.00
2.50
3.00
1972 1976 1980 1984 1 988 1992 1996 2000 2004
EPS
0
10
20
30
40
50
60

-0.50
0.00
0.50
1.00
1.50
2.00
2.50
3.00
1972 1976 1980 1984 1 988 1992 1996 2000 2004
EPS
0
10
20
30
40
50
60

Figure 1. EPS before Extraordinary Items (1973-1985)/EPS from Operations (1986-2002) of Alcoa
Inc., Avery Dennison (presented by the solid line, left scale), and the S&P500 index (presented by the
dotted line, right scale).

earnings forecasts. Swanson and White (1995, 1997) find that such models are useful
when the variable of interest is the spot-forward rate differential: they show that
adaptive linear vector autoregression models often outperform professionally available
survey predictions, as well as no-change and non-adaptive linear models of key
macroeconomic variables.
The class of non-linear time-series models is presented by artificial neural
networks that are known to be universal function approximators and are capable of
exploiting non-linear relationships between variables
5
. Neural Networks are applied
across a wide range of disciplines: medicine, engineering, geology, and physics. In
contrast, for many years, linear modeling has been a commonly used technique in
economics and finance since linear models have well-known optimization strategies.
Where the linear approximation was not valid, the models suffered accordingly. Only
recently, artificial neural networks became the focus of attention as a possible vehicle

5
For further discussions see, for example, Bishop (1995), Fausett (1994), Hornik et al. (1989).

12
for forecasting economic and financial variables. Kuan et al. (1995) consider exchange
rate forecasting and conclude that neural networks have significant market timing
ability and significantly lower out-of-sample mean square prediction error relative to
the random walk model. Tkacz (2001) finds that neural networks yield statistically
lower forecasts errors for the growth rate of real Canadian GDP relative to linear
models.
An artificial neural network is a sophisticated information processing
technique that is inspired by the way the human brain processes information. The
major element of this mechanism is a novel structure of the information processing
system that is composed of highly interconnected processing elements. These
elements, or units, are organized in layers. It is customary to distinguish the input
layer, which supplies input data, hidden layers, and the output layer. The greater the
number of hidden layers, the greater the complexity of the system, and as a result,
more cases are required to estimate the model. Due to the small number of cases
available in this study, the networks we consider contain only one hidden layer and,
therefore, can be represented by a simple functional form:








+












+ =
∑∑
=
h
j
out
n
i
j i ji j out j ji j h
a
1
) , , , ( ξ ξ ω ψ ω ψ ξ ξ ω ω ϕ , (1)
where ω
ji
denotes the weight for the connection between input i (total n inputs) and the
processing unit j in the hidden layer (total h units in the hidden layer), ω
j
denotes the
weight between unit j in the hidden layer and the output unit, ξ
j
and ξ
out
are the

13
threshold values and ψ is a given non-linear activation function; in this case, it is the
logistic cumulative distribution function )) exp( 1 /( 1 ) ( z z − + = ψ .
The network interpretation of Equation (1) is as follows. The input units send
signals (a
1,
…, a
n
), which represent historical earnings in this study, over the
connections to the units in the hidden layer. Each connection can amplify or reduce the
signal by weight, ω
ji
, which controls the strength and the polarity of the relationship.
The modified signals that arrive at the intermediate hidden units are first summed and
after the addition of a threshold, ξ
j
, converted to a hidden unit activation, ψ( ). The
operation of the next level is similar when hidden unit activations are sent through the
connections to the output unit. The output unit performs a biased weighted sum of its
inputs and passes the activation level through the transfer function to produce the
output. Thus, the network has a simple interpretation as a form of input-output model
with weights and thresholds as free parameters of this model. Barron (1991)
demonstrates that a feedforward neural network can achieve an approximation rate
O(1/h) by using a number of parameters O(hn) that grows linearly in h, whereas
traditional polynomial and trigonometric expansions require exponentially O(h
n
) terms
to achieve the same approximation rate. Consequently, neural networks are relatively
more parsimonious than the series expansions in approximating unknown functions.
This property makes neural networks an attractive econometric tool in nonparametric
applications.
The neural network is data driven in that it learns only from the data presented
to it and has no underlying parametric model. The greater the number of units in the

14
hidden layers, the more the network is able to cope with non-linear relationships, but
the danger of overfitting increases. The network is only trained on a training set and it
is not the same as minimizing error on the error surface of the underlying and
unknown model. Thus, a major flaw in the approach outlined above is that it does not
minimize the error we are interested in: the error that the network will make when it
encounters new and unseen cases. For this reason, some fraction of the data set must
be reserved for cross-verification. The verification data are taken out from the training
data and not, in fact, used for training in the back propagation. Instead, they are kept
for use in an independent check on the progress of the algorithm. As the training
progresses, the training error essentially drops and verification error drops as well.
However, if the verification error starts to rise, it indicates that the network starts to
overfit and training should cease. A larger verification set is likely to be more
representative. However, it does take the data away from the training set. It is,
therefore, necessary to strike a balance between the training and verification data sets.
Experimentally, we find that the optimal size of the verification set is about 25-30% of
the total number of available data points and that verification cases should be shifted
more to the end of the data sample
6
.
The linear models considered in this paper are represented by the
ARIMA(p,d,q) specification:
() ( )
t
q
q t
d p
p
L L L c a L L L L ε θ θ θ φ φ φ ) ... 1 ( 1 ... 1
2
2 1
2
2 1
+ + + + + = − − − − − , (2)

6
It is important that independent data, unrelated to the test companies, were used in the
experimentation.

15
where a
t
denotes annual earnings per share and d is equal to zero if the earnings
generating process is stationary and equal to one or two if there is evidence of
nonstationarity. To find a suitable model specification and to estimate the parameters,
we adopt the Box and Jenkins (1970) modeling technique
7
. The procedure is repeated
every time a new data point becomes available. This technique certainly captures the
spirit of real-time forecasting and, therefore, enables us to select the most appropriate
linear time-series specification that is consistent with each firm’s earnings generating
process at a specific point in time. Consequently, forecasts obtained by this method
should be superior to forecasts of ad hoc time-series models applied to all firms’ time-
series data.
Another linear time-series model, which plays the role of a benchmark is a
random walk with drift:
t t t
a f ε δ + + =
−1
, (3)
where the drift parameter, δ, is specific for each firm and period of time. It is
estimated as the average earnings change from one year to the next using two to
fifteen years of annual earnings data preceding the year for which a forecast is desired:
1
1
−
−
=
− −
n
a a
n t t
δ , (4)
where n is a firm and time specific lag parameter. This is a main attribute of the
proposed random walk process. It transforms the model into the framework of
adaptability. To evaluate lags, the following procedure is implemented. First, starting

7
First, patterns of autocorrelation and partial autocorrelation functions are considered to identify the
specification of the model. Then, parameters are estimated by OLS with the Schwarz information
criterion as a guide to model selection, and diagnostic checks on residuals are performed.

16
in 1987, for each company using (3) and (4) with n ranging from two to fifteen, a
sequence of one-year-ahead ex post forecasts for 1988-1992 is generated. Next, the
value of n is chosen that results in the smallest MSE over this period. Finally, (3) and
(4) are used with the found value of n to predict earnings for 1993-1997. The
procedure is then repeated in 1997 to find new firm specific values of n and predict
1997-2002 earnings. Values of n decrease with the decline in earnings volatility. If a
company’s earnings are steady, only recent earnings are important for forecasting, and
n is small. On the contrary, if earnings are volatile, the value of n becomes relatively
large. It tends to incorporate a relatively long-term trend in forecasting.

I.2 Estimation and Model Selection

A. Estimation.
In this section, we discuss the estimation of two classes of models described
above. The parameters of all non-linear and linear models are estimated using only a
finite window of past data rather than all of the previously available data. By pursuing
this strategy, we assume that the underlying earnings generating process may be
evolving through time. Annual and quarterly earnings data are used as inputs to neural
networks and annual data as inputs to linear models. Accordingly, throughout the
paper, by an annual/quarterly neural networks model, we mean that the model exploits
and predicts annual/quarterly data. Annual models are estimated using twenty years
and quarterly models using eighty quarters of earnings data immediately preceding the
year for which a forecast is desired. As a result, one-, two-year-ahead and one-, two-,

17
… , seven-, eight-quarter-ahead forecasts are obtained for each firm, year and model.
Then, quarterly forecasts are added to find a forecast of annual earnings for a given
firm by a given model. We re-estimate the configuration of neural networks, the
specification of the ARIMA model, and the parameters of these models each year
during the period of 1993-2002.
The type of linear econometric models used and their underlying assumptions
are standard. Therefore, we now turn to the discussion of non-linear neural networks
estimation. In practice, there are mainly two tasks in building neural networks: a
suitable network structure (the number of hidden units) must be determined, and
unknown network parameters must be estimated. The main feature of neural networks
is that they learn the input/output relationship through training. The training data
contain examples of inputs together with the corresponding outputs, and the network
learns to infer the relationship between the two. The training proceeds by back
propagation developed by Rumelhert et al. (1986), which uses data to adjust the
network weights, ω, and thresholds, ξ, so as to minimize the error in its predictions:
( )
2
*
, , min arg ξ ω ϕ θ a y E
h h
− = . (5)
The estimation is performed through iterations. Each iteration of the training
process proceeds as follows: first, the network is presented with a set of training
examples from which weight and threshold adjustments are made. As a result, the
training algorithm incrementally seeks for the global minimum by calculating a
gradient vector of the multidimensional error surface and making a downhill move.
Then, the network is tested using independent verification data to find the ability of

18
the network to generalize on the unseen data. Training stops at the iteration where the
MSE for the verification set starts to rise indicating overfitting.
The second task in practice is to establish a suitable network structure. As the
activation function, ψ, can be chosen quite arbitrarily, this task reduces to determining
the network complexity, i.e. the number of lagged variables, the number of hidden
layers and the number of units in these layers. Although back propagation can be
applied to networks with any number of layers, Cybenko (1989) shows that only one
layer of hidden units suffices to approximate a large class of functions to arbitrary
precision, provided that the number of hidden units, h, is adequately large and the
activation functions, ψ, are non-linear. On the other hand, while a simple network (few
hidden units) may not be able to approximate well, an excessively complex network
(many hidden units) may overfit the data. For this reason, one should find a balance
between the network complexity and the ability to predict unseen data.
For each firm and year, we estimate networks with different number of lags:
three and five for the annual data and four, eight, and twelve for the quarterly data. It
means that if, for example, the lag is equal to four in the case of quarterly forecasts,
then the inputs to neural networks consist of quartets (x
t-1
, x
t-2
, x
t-3
, x
t-4
) and the output
is a single earnings number x
t
. Accordingly, the first annual rolling sample consists of
seventy-six inputs (x
1
, x
2
, x
3
, x
4
), (x
2
, x
3
, x
4
, x
5
),…, (x
76
, x
77
, x
78
, x
79
) and their
corresponding outputs x
5
, x
6
,…, x
80
. Thus, we produce forecasts that one could make
with the model as time progresses. We also test different numbers of units in the

19
hidden layer for each lag value
8
. Neural networks are found to perform the best with
the next number of units: two units (h=2) for lags equal to three and four, three units
(h=3) for lags equal to five, and four units (h=4) for eight and twelve.

B. Measurements of the forecast accuracy.
To assess the out-of-sample predictive abilities of alternative forecasting
models, we compute the following statistics for each company and forecast horizon.
The first is the mean-squared error, since it is the most frequently quoted measure in
the forecasting literature:
() ,
1
2
∑
− =
t
ki k ki
f a
T
MSE (6)
where a
k
denotes actual earnings of firm k, and f
ki
denotes the predicted earnings of
firm k by model i. However, if forecast errors are measured in terms of levels of
earnings, as the level of earnings increases in absolute magnitude, so will the absolute
magnitude of the forecast errors. In addition, Dacco and Satchell (1999) argue that
MSE measure may be not quite appropriate for the non-linear models since this
measure may imply that a non-linear model is less accurate than a linear one when it is
not actually true. Accordingly, we calculate a second scale invariant measure of
accuracy - MSPE:
.
1
2
∑







 −
=
t k
ki k
ki
a
f a
T
MSPE (7)

8
We use two companies to find the most appropriate specifications of neural networks for this study.
These companies are not from the sample of forty-eight firms considered in the results.

20
In order to compare the MSE and MSPE error measures from different models,
we use the asymptotic loss differential test proposed by Diebold and Mariano (1995).
The test considers a sample path { }
T
t t
d
1 =
of a loss-differential series and tests the null
hypothesis of equal forecast accuracy between two alternative models by exercising
the next statistic:
() 1 , 0 ~
) 0 (
ˆ
2
N
T f
d
S
d
π
= , (8)
where d is the sample mean loss differential:
() () []
∑
=
− =
T
t
jt t it t
y y g y y g
T
d
1
ˆ , ˆ ,
1
, (9)
and ) 0 (
ˆ
d
f is a consistent estimator of the spectral density at frequency 0. It is
computed as a weighted sum of the available sample autocovariences:
() () ( )
∑ ∑
+ =
−
−
− − =
− −








=
T
t
t t
T
T
d
d d d d
T T S
I f
1
) 1 (
) 1 (
1
) ( 2
1
0
ˆ
τ
τ
τ
τ
π
, (10)
where the uniform lag window I( ) is given by:
1
) (
1
) (
≤ =








T S
for
T S
I
τ τ
(11)
= 0 otherwise.
The truncation lag, S(T), is equal to zero for one-year-ahead forecasts and equal to one
for two-year-ahead-forecasts. It follows from the familiar fact that k-step-ahead
forecast errors are at most (k-1) dependent. We define the loss differential series to be
() ( )
jt t it t t
f a f a d − − − = for the MSE test and ( ) ( )
t jt t it t
a f a f d − − − = 1 1 for the MSPE

21
test, where a
t
denotes actual earnings at time t, while f
it
and f
jt
are predicted earnings
by models i and j, respectively. The formula indicates that due to the cumulation of
autocovarience terms, the correction for serial correlation may be substantial even if
the loss differential is only weakly correlated.

I.3 Empirical Results

A. Comparison of the forecast accuracy.
Some companies’ earnings may be steady and, therefore, relatively easier to
predict. In contrast, earnings of other firms may be very volatile that poses a challenge
for their forecasting. As a result, we divide companies into two categories according to
the difficulty of the forecasting task. We call these groups the Steady and the Volatile
categories, respectively. To describe the earnings volatility quantitatively, we employ
the following measure - the coefficient of variation of the first difference of earnings:
( ) ( )
() const a Q
a d Q a d Q
CV
k
k k
k
+
−
=
2
1 3
) ( ) (
, (12)
where Q
3
( ) - Q
1
( ) denotes the interquartile range of changes in earnings of firm k,
()
k
a Q
2
is the median earnings of firm k, and const is some integer necessary to avoid
the division by a number close to zero. We use const = 1, which makes the
denominator greater than one. This coefficient demonstrates the variation of the

22
change in earnings scaled by the level of earnings
9
. The greater the coefficient, the
more volatile changes in earnings, and therefore, the harder the task of forecasting.
The Steady and the Volatile categories consist of firms with values of the
coefficient that are smaller and larger than its median value, respectively. Each
category contains twenty-four companies. The majority of companies in the Volatile
category represent the manufacturing (eleven firms) and the transportation (eight
firms) industries, whereas the Steady category is composed of companies in the
manufacturing (eleven firms), finance, insurance, real estate, and the trade (twelve
firms) industries. Furthermore, while manufacturing companies in the Volatile
category are mostly metal, chemicals, and lumber producers, in the Steady category,
manufacturing firms represent pharmaceutical, electronics, food, packaging, and
printing sectors. The average earnings of the Volatile and Steady category firms are
presented in Figure 2. While average earnings are highly volatile and cyclical in the
first graph, they are steady and grow remarkably in line with the S&P500 earnings in
the second graph.
First, using forecasting models described above, we generate forecasts for the
1993-2002 period and calculate the MSE and the MSPE for each company, model, and
forecast horizon. Then, we carry out the Diebold and Mariano test of equal forecasting
accuracy and assign ranks from one to five to each of the five models in
consideration
10
. Finally, we sum the ranks of each forecasting method i across N firms:

9
The rational for scaling is that the same variation of change in earnings results in the larger volatility,
the smaller the level of earnings.
10
Note that if the hypothesis of equal forecasting accuracy between models i and j cannot be rejected at
the 5% significance level, both models get the same rank. As a result, the average across models ranks
are not equal to three.

23
-0.50
0.00
0.50
1.00
1.50
2.00
2.50
3.00
1972 1976 1980 1984 1988 1992 1996 2000 2004
EPS
0
10
20
30
40
50
60
-0.50
0.00
0.50
1.00
1.50
2.00
2.50
3.00
1972 1976 1980 1984 1988 1992 1996 2000 2004
EPS
0
10
20
30
40
50
60

Figure 2. Average EPS before Extraordinary Items (1973-1985)/EPS from Operations (1986-2002) of
the Volatile, Steady category firms (presented by the solid line, left scale) and the S&P500 index
(presented by the dotted line, right scale). Each group consists of twenty-four firms.

∑
=
=
N
k
ki i
rank N rank
1
1 . (13)
The idea behind this average rank measure is that the model that produces more
accurate forecasts for a greater number of companies and, therefore, obtains a smaller
rank should be preferred
11
.
The results for the one- and two-year-ahead forecast horizon cases are
presented in Table 1 and Table 2, respectively. The main result in Table 1 is that
artificial neural networks that make use of quarterly data (QNN) outperform the other
time-series methods in consideration and produce the performance comparable to
financial analysts. Average ranks of QNN based on the MSE and MSPE error
measures are 1.40 and 1.47, while financial analysts’ ranks are 1.69 and 1.91,

11
Consider the next example: ten firms, two alternative forecasting models, model 1 produces no error
for firm one and produces error x for each of the other nine companies. This error x is larger than the
error y produced by model 2 for each of the ten firms, but the total error produced by model 1 is equal to
the total error produced by model 2. The proposed rank order procedure ensures that model 2 is
preferred since it obtains a better forecasting accuracy for nine out of ten companies.

24
respectively. Financial analysts generate a better accuracy than the random walk with
drift model (RW) based on the MSE measure, 1.69 versus 2.23, and comparable
accuracy based on the MSPE measure, 1.91 versus 2.03. On the other hand, artificial
neural networks that exploit annual data (ANN) and their linear analog, the Box and
Jenkins procedure (BJ), fail to produce a better accuracy than the random walk. We
link the poor performance of the ANN relative to the QNN model to the insufficient
number of data points used for its training. In contrast, we explain the success of QNN
by the two factors: the desegregation effect that results from higher data frequency and
the ability to avoid significant outlier quarters in training without radically reducing
the training set.
Table 2 presents the results for the two-year-ahead forecast horizon. The QNN
modeling technique continues to be a leader in forecasting accuracy based on both the
MSE and the MSPE error measures. Its ranks are the smallest and equal to 1.73 and
1.77, respectively. Taking into account that in order to produce a two-year-ahead
forecast, one needs to obtain one- to eight-quarters-ahead forecasts and the fact that
the forecast accuracy decreases with the forecast horizon, the QNN superior accuracy
is a prominent result. On the contrary, financial analysts produce worse accuracy two-
year-ahead forecasts made at the beginning of a fiscal year than any other model in
consideration; even the linear BJ procedure and the adaptive random walk supply
more accurate forecasts. This fact sheds significant doubt on the credibility of
financial analysts as providers of accurate two-year-ahead forecasts.

25
By looking at the Volatile and Steady categories, we can draw the following
conclusions. For the one-year-ahead forecast horizon, analysts’ forecasts have the
accuracy comparable to the random walk forecast accuracy for the Volatile category
companies and have better accuracy for the Steady category firms. For the two-year-
ahead forecast horizon, the analysts’ forecast accuracy is inferior to all models for the
Volatile category companies and only comparable to the BJ model accuracy for the
Steady category companies. Next, for both forecast horizons, the advantage of
quarterly neural networks is greater for the Volatile type firms. According to both
error measures, a gap between the QNN and the analysts’ accuracy widens as we
move from the Steady to the Volatile category companies. The average rank of the
QNN model for the Volatile category is about 36% (49%) smaller for the one- (two)-
year-ahead forecast horizon than that of financial analysts
12
. This is a focal result. It
shows that neural networks are the most valuable in forecasting earnings of companies
with volatile earnings. It is apparently caused by their superior ability to extract
nonlinear systematic patterns from series of past earnings. On the other hand, financial
analysts consider larger information sets that often consist of contradictory signals
about companies’ future prospects. As a result, they may underestimate the importance
of historical earnings when making predictions for the Volatile type firms.

12
Note that we perform an ex ante division of companies between the Volatile and the Steady groups.
The coefficient of variation (12) is evaluated only using the 1973-1992 earnings data. To verify the
results using an ex post measure of variation, we reclassify companies between groups according to the
coefficient of variation that is estimated using the 1983-2002 earnings data. In this case, the quarterly
neural networks accuracy advantage is even greater for the Volatile group companies as compared to
the Steady group firms.

26
Average Rank based on MSE Average Rank based on MSPE
Model Volatile
firms
Steady
firms
Total
Volatile
firms
Steady
firms
Total

Financial Analysts
RW with drift
QNN (Quarterly EPS)
ANN (Annual EPS)
BJ

2.08
2.08
1.29
2.33
2.29

1.29
2.38
1.50
2.08
2.92

1.69
2.23
1.40
2.20
2.60

2.12
1.93
1.38
2.04
1.98

1.70
2.13
1.55
2.60
2.66

1.91
2.03
1.47
2.32
2.32
Average across models 2.01 2.03 2.02 1.89 2.13 2.01
Table 1. Rank orders of financial analysts and time-series models forecasting one-year-ahead EPS at
the beginning of a fiscal year. Forecast accuracy is measured by MSE and MSPE. The Diebold-Mariano
predictive accuracy test is applied to MSE and MSPE loss differentials. The ranks are assigned
according to the 5% significance level. Each group consists of twenty-four firms.

Average Rank based on MSE Average Rank based on MSPE
Model Volatile
firms
Steady
firms
Total
Volatile
firms
Steady
firms
Total

Financial Analysts
RW with drift
QNN (Quarterly EPS)
ANN (Annual EPS)
BJ

3.33
2.21
1.63
2.17
1.96

2.63
2.58
1.83
2.25
3.04

2.98
2.40
1.73
2.21
2.50

3.29
2.21
1.75
1.92
1.88

2.75
2.33
1.79
2.34
2.54

3.02
2.27
1.77
2.13
2.21
Average across models 2.26 2.47 2.37 2.21 2.35 2.28
Table 2. Rank orders of financial analysts and time-series models forecasting two-year-ahead EPS at
the beginning of a fiscal year. Forecast accuracy is measured by MSE and MSPE. The Diebold-Mariano
predictive accuracy test is applied to MSE and MSPE loss differentials. The ranks are assigned
according to the 5% significance level. Each group consists of twenty-four firms.

One-year-ahead Two-year-ahead
Prediction matrixes Prediction matrixes

Model
Up Down

HM
p

Up Down

HM
p

Financial Analysts
RW with drift
QNN (Quarterly EPS)
ANN (Annual EPS)
BJ

318, 12
267, 63
228, 102
238, 92
228, 102

110, 40
117, 33
54, 96
69, 81
107, 43

0.00
0.20
0.00
0.00
0.82

295, 5
244, 56
224, 76
223, 77
238, 62

116, 16
110, 22
52, 80
61, 71
95, 37

0.00
0.06
0.00
0.00
0.06
Total 330 150 300 132
Table 3. Prediction matrixes of financial analysts and time-series models forecasting one- and two-
year-ahead EPS at the beginning of a fiscal year. The first entry corresponds to correctly predicted up
moves, second to actual up/predicted down, third to actual down/predicted up and fourth to correctly
predicted down moves. HM p-values for the rejection of the hypothesis of no forecasting skills. Each
group consists of twenty-four firms.

27
To summarize, according to the rank orders forecast comparison procedure,
neural networks utilizing quarterly data appear to be the method with the best accuracy
of one- and two-year-ahead EPS forecasts made at the beginning of a fiscal year. The
advantage of neural networks is the most evident for high volatility companies whose
earnings regularly deviate from the market earnings. On the contrary, financial
analysts predict relatively well earnings of companies whose earnings are steady and,
therefore, move in line with the market earnings. This result suggests that financial
analysts have a lack of ability or incentives to extract patterns from histories of
volatile earnings. Do they fail to predict the upward or downward deviations, or both?
The next section provides an insight into this interesting question.

B. The direction of change measure.
A slightly different approach to assess the forecast accuracy and to get an
insight into sources driving statistical models and financial analysts’ forecasting
abilities is to utilize the direction of change measure. This measure is related to
forecasts interpreted only in terms of whether a firm’s earnings will increase or
decrease. We demonstrate the performances of models in terms of prediction matrixes
in Table 3. They portray forecasts as the numbers of correct and incorrect predictions
of the direction of change
13
.
As it is evident from the results, financial analysts produce fewer mistakes in
predicting upward movements (actual up/predicted down is equal to twelve and five

13
The first entry corresponds to correctly predicted up moves, second to actual up/predicted down, third
to actual down/predicted up and fourth to correctly predicted down moves.

28
for the one- and two-year-ahead forecast horizon), but more mistakes in predicting
downward movements (actual down/predicted up is equal to 110 and 116 for the one-
and two-year-ahead forecast horizon) as compared to neural networks. In fact, analysts
correctly predict 96% (98%) of one- (two)-year-ahead up moves and only 27% (12%)
of one- (two)-year-ahead down moves, whereas similar statistics for quarterly neural
networks are 69% (75%) and 64% (61%). Quarterly neural networks possess the best
skills for predicting down moves (96 out of 150 and 80 out of 132 for the one- and
two-year-ahead forecast horizon, respectively). It apparently leads to their superior
performance observed in terms of the rank orders. On the contrary, financial analysts
often miss the correct prediction of downward movements, which are the most
important deviations to predict in the environment of rising earnings. Financial
analysts have a tendency to produce upward predictions and, thus, to some extent,
ignore histories of earnings. In the case of the Volatile group firms, these histories may
contain a number of long lasting downturns pointing at a great potential for downward
deviations in the future.
Next, note that there are some similarities between financial analysts and the
random walk and linear BJ models. Namely, in the case of the one-year ahead forecast
horizon, the number of correctly predicted down moves by analysts is only slightly
higher than that by the random walk, 40 versus 33 out of 150 (and similar to the BJ
model predictions, 43.) For the two-year-ahead forecast horizon, analysts correctly
predict 16 out of 132 down moves, while the random walk model correctly predicts
22. This suggests that financial analysts incorporate trends into their forecasts that

29
shadow drift components of the random walk model. This behavior is similar to the
behavior of the naive investor, who extrapolates the past performance into the future
14
.
Finally, there is the question of whether the least confusing models are the
models that we would choose based on the MSE and MSPE forecast measures in the
setting of real-time forecasting. To provide an answer, we perform the nonparametric
test given by Hendrickson and Merton (1981) and compute HM p-values for the
rejection of hypothesis of no forecasting skills. As a result, we reject the hypothesis of
no forecasting skills for financial analysts and neural networks models for both
forecast horizons at the 1% significance level. These models are found to be useful as
predictors of the sign of change in earnings. On the contrary, the random walk model,
which demonstrates a solid performance based on the MSE and MSPE measures, has
no forecasting skills for the direction of change.

C. Relative informational content of forecasts.
The adaptive statistical models used to forecast earnings exploit only series of
past earnings, whereas financial analysts make use of a considerably broader
information set. It constitutes the information advantage. Then, how should we
interpret the differences in forecasts? Does each model have strength of its own, or do
financial analysts’ forecasts dominate in the sense of incorporating all information in
the other model plus sum? We examine this question by considering the regression of
actual changes in earnings on changes forecasted by financial analysts and statistical

14
See, for example, Lakonishok, Shleifer and Vishny (1994). They argue that value strategies yield
higher returns because these strategies exploit the suboptimal behavior of the typical investor, who
extrapolates past growth too far into the future.

30
models. This procedure may comprise advantages over the direct comparison of MSE
or MSPE error measures. For example, if the MSE are close for two forecasts, and
performing the Diebold and Mariano test, we cannot reject the hypothesis of equal
forecasting accuracy; little can be concluded about the relative merits of the two.
Furthermore, even if the MSE of one model is bigger than the other, it may still be the
case that its forecasts contain additional information. There is no way to test for this
using the MSE framework. Therefore, we consider the following regression equation:
kt s t k kt s t k kt s t k kt
a f a f a a ε β β α + − + − + = −
− − −
) ( ) (
) (
2
2 ) (
1
1 ) (
(14)
where a
k
denotes actual earnings of firm k, f
k
1
and f
k
2
are predicted earnings by models
one and two, while s = 1, 2 is the forecast horizon. If neither model contains useful
information for s-period-ahead forecasts, then estimates of β
1
and β
2
should both be
zero, and α would be the average s-period-ahead change in earnings. If forecasts are
not perfectly correlated, and both models contain independent information, then β
1
and
β
2
should both be nonzero. Finally, if the model two is completely contained in the
model one, and the model one contains further relevant information as well, then β
2

but not β
1
should be nonzero.
We focus on the performance of financial analysts (model 1) versus the
quarterly neural networks (model 2), which were shown to have superior predictive
abilities in terms of rank orders, and the random walk model, which represents a
sufficiently simple forecasting technique. The procedure consists of estimating
Equation (14) first, and then, testing the hypotheses: H0: β
1
= 0 that analysts’ forecasts
contain no information, which is not incorporated in a constant term and in statistical

31
models forecasts, and H0: β
2
= 0 that the statistical models contain no information,
which is not included in a constant term and in analysts’ forecasts. Note that it does
not seem reasonable to estimate Equation (14) for each company or each year
separately
15
. Therefore, we consider the pooled data set that produces 480 (432) data
points in the case of the one- (two)-year-ahead forecast horizon. The OLS estimator is
not the best linear unbiased estimator in this case. Therefore, we consider the feasible
generalized least square estimator, which is the weighted average of between- and
within-group estimators given in Maddala (1971):
w k b GLS
I β β β
ˆ
) (
ˆ ˆ
∆ − + ∆ = , (15)
where consistent estimators of unknown
2
θ
σ and
2
ν
σ are used to determine the weight
∆. This is called the random effect model, where ε
it
= θ
i
+ ν
it
, and ν
it
are treated as
random variables.
Table 4 presents the estimated coefficients of Equation (14) for the one- and
two-year-ahead forecast horizon. With respect to the one-year-ahead forecast horizon,
the coefficient estimates for financial analysts’ and RW/QNN forecasts are both
nonzero and statistically significant for the Volatile category companies. It indicates
that there is some information in RW/QNN forecasts that is not in analysts’ forecasts.
This result suggests that financial analysts process the information in histories of
earnings differently than the time-series models or that they neglect this information at
all. It contradicts the common view that analysts make use of all available information
in constructing their forecasts.

15
The sample consists of ten forecast dates and twenty-four companies in each group.

32
Now, consider two-year-ahead forecasts. For the Volatile category firms,
random walk model has independent information; its coefficient estimate is nonzero
and statistically significant. Moreover, while the coefficient estimate for quarterly
neural networks forecasts is nonzero and statistically significant, the coefficient
estimate for financial analysts’ forecasts is not significantly different from zero at the
5% level. It reveals that analysts’ forecasts contain no information, which is not
incorporated in a constant term and in QNN forecasts, for companies with volatile
earnings. This result demonstrates that quarterly neural networks forecasts are not
collinear with financial analysts’ forecasts and that the difference between the QNN
and financial analysts’ accuracy is meaningful.
To summarize, quarterly neural networks as well as the adaptive random walk
with drift model contain information not in a constant term and in analysts’ forecasts
for high change in earnings volatility companies. In contrast, neither coefficient
estimate for the Time-Series variable in Table 4 is significant for the low change in
earnings volatility companies indicating that all information is already included in
financial analysts’ forecasts. Overall, without considering conventional measures of
accuracy, results support the hypothesis that financial analysts have relatively good
predictive abilities for companies with steady earnings that follow the market
earnings, whereas quarterly neural networks carry useful information that is not in
financial analysts’ forecasts for companies with volatile earnings. It poses a challenge
to the previously acclaimed notion of financial analysts’ informational superiority.

33
D. The number of analysts, deviation of individual forecasts, and the forecast
accuracy.

While some companies may be followed by over than thirty financial analysts,
others are covered by only few. For some companies, the standard deviation of
individual analysts’ forecasts may be small indicating that the majority of analysts
agree on estimates, for others, it may be large pointing at disagreement among
financial analysts and uncertainty about companies’ future prospects. Note that even
though the number of analysts issuing forecasts and the standard deviation of
individual forecasts for a specific company often change from year to year, it is very
persistent.
One would logically expect consensus forecasts to have better accuracy
relative to time-series models as the number of individual analysts’ forecasts used to
construct consensus increases. This view can be explained by widening the
information set with each additional analyst or by portfolio benefits of averaging. Note
that there is a positive relationship between the number of analysts issuing forecasts
and the size of a company. The larger the size of a company, the greater the
dimensionality of its information set. Then, if each additional analyst processes
information available to other analysts plus some new information, the consensuses
should become more accurate.
Similarly, the more disperse individual analysts’ forecasts used to construct
consensus forecasts, the more likely there is to be substantial uncertainty about future
earnings. It may be a sign that different analysts receive different signals about future
prospects, or that they process the information flow differently. As a result, we can

34
anticipate the relative accuracy of financial analysts’ consensus forecasts to increase as
more analysts follow the company and as the standard deviation of individual
forecasts decreases.
To test these hypotheses, we calculate the mean number of forecasts and the
mean standard deviation of forecasts for each company and forecast horizon over a
ten- (nine)-year period
16
. The next question is which measure of the relative accuracy
to employ. While subtracting the MSPE error measures of two alternative models can
produce meaningless values, subtracting the MSE measures does not look practical as
well
17
. Therefore, we suggest the following measure of the relative forecast accuracy.
First, we take differences of RMSE calculated over the 1993-2002 period and then,
scale it by the standard deviation of the first difference in earnings over the same
period, )) ( ( ) (
. .
A d RMSE RMSE
Series Time An Fin
σ
−
− . The idea is that differences in RMSE
should be discounted more as earnings are less predictable. The proposed measure
should allow revealing effects of the number of analysts and the standard deviation of
individual forecasts on the relative forecast accuracy without distorting the results by
the difficulty of the forecasting task. Finally, we exclude outlier observations and
regress the constructed accuracy measure on the number of analysts or the standard
deviation of individual forecasts. Table 5 presents the results.

16
The number of analysts who issue one- (two)-year-ahead forecasts in our sample is as many as thirty-
four (twenty-one), and as few as five (two). Therefore, to control for possible problems with the
standard deviation as a proxy for the uncertainty when only few analysts follow a company, we exclude
two companies for which the mean number of analysts is less than three.
17
In the case of the MSPE error measure: if the denominator value is close to zero, one of the MSPEs
can be quite large. In the case of the MSE error measure: similar resulting differences in errors are not
the same for companies with different volatilities of earnings.

35
One-year-ahead
Volatile firms Steady firms

Time-Series Model

Const FA Time-Series Const FA Time-Series

RW with drift

QNN

-0.14
(3.15)
-0.17
(4.25)

0.78
(10.3)
0.69
(9.37)

-0.93
(3.30)
0.57
(5.90)

-0.05
(1.35)
-0.01
(0.43)

0.80
(9.91)
0.75
(8.67)

0.35
(1.76)
0.13
(1.53)
Two-year-ahead

RW with drift

QNN

-0.10
(1.09)
-0.10
(1.13)

0.43
(4.04)
0.23
(1.88)

-0.63
(2.75)
0.53
(5.26)

0.04
(0.61)
0.04
(0.58)

0.46
(4.38)
0.47
(3.95)

0.15
(1.41)
0.21
(1.87)
Table 4. Informational content of forecasts. Financial analysts versus the adaptive time-series models:
Estimation of Equation (14). FA is financial analysts’ predictions minus actually realized values. Time-
Series is random walk with drift/quarterly neural networks predictions minus actually realized values.
Heteroskedasticity-robust t-statistics in absolute value are in parentheses.
One-year-ahead Two-year-ahead

Model

Const Number
FA
SD
FA
Const Number
FA
SD
FA

FA – RW

-0.12
(1.00)
0.04
(1.01)

0.01
(0.53)

0.70
(5.12)

0.04
(0.35)
-0.12
(1.38)

0.00
(0.55)

0.85
(1.56)

FA – QNN

-0.08
(1.55)
-0.18
(2.40)

0.01
(0.79)

1.26
(1.86)

0.01
(0.09)
-0.18
(1.89)

0.01
(0.58)

2.04
(3.50)
Table 5. Relative forecast accuracy and the number of analysts issuing forecasts, standard deviation of
individual forecasts used to construct consensus forecasts. FA-RW, FA-QNN are the differences in the
RMSE of financial analysts and the random walk with drift/quarterly neural networks models scaled by
the standard deviation of the change in earnings over the 1993-2002. Number
FA
is the mean number of
financial analysts issuing forecasts, SD
FA
is the mean standard deviation of individual forecasts over the
1993-2002. Heteroskedasticity-robust t-statistics in absolute value are in parentheses.
One-year-ahead Two-year-ahead
Volatile firms Steady firms Volatile firms Steady firms

Model
Const Const Const Const

Fin. Analysts

RW with drift

QNN

0.27
(4.07)
0.02
(0.31)
-0.05
(0.75)

0.05
(1.74)
-0.07
(2.15)
-0.06
(1.70)

0.53
(4.51)
0.05
(0.64)
-0.03
(0.29)

0.15
(2.86)
-0.06
(1.53)
-0.12
(2.18)
Table 6. Forecast bias for financial analysts, random walk with drift and quarterly neural networks one-
and two-year-ahead EPS forecasts made at the beginning of a fiscal year.

36
Conversely to intuition, the relative accuracy of financial analysts’ consensus
forecasts does not depend on the number of forecasts used to construct them. Instead
of being negative as expected, the estimates of coefficients are not significantly
different from zero for both time-series models and both forecast horizons. We do not
observe benefits of aggregating a large number of individual analysts’ forecasts on the
relative performance of financial analysts. It implies that analysts make use of
identical sets of information in the construction of forecasts.
With respect to the standard deviation of individual analysts’ forecasts, as
expected, the relative accuracy of financial analysts tends to increase as the dispersion
of individual forecasts decreases. The estimates of coefficients are always positive and
statistically significant for the random walk model in the case of the one-year-ahead
forecast horizon and for quarterly neural networks in the case of the two-year-ahead
forecast horizon. It indicates that the value of adaptive time-series models forecasts
increases with the standard deviation of individual analysts’ forecasts and, as a result,
with the degree of uncertainty about a company’s future prospects.
To conclude, the relative accuracy of financial analysts is not related to the
dimensionality of a company’s information set as measured by the mean number of
analysts issuing forecasts. Instead, it is linked to the quality of this set as measured by
the mean standard deviation of individual analysts’ forecasts. Quarterly neural
networks perform relatively better for companies with the high dispersion of

37
individual analysts’ forecasts, that is, for companies with highly volatile earnings
18
.
Furthermore, the estimate of the coefficient, 2.04, is greater for the two-year-ahead
forecast horizon than that, 1.26, for the one-year-ahead forecast horizon indicating that
the neural networks relative accuracy increases faster for longer forecast horizons.
These results are absolutely in line with our prior findings.

E. Financial analysts’ relative forecast accuracy and the forecast bias.
Next, to get an insight into the properties of financial analysts’ relative forecast
accuracy, we compute the forecast bias for financial analysts and RW/QNN
forecasting methods. We employ a modification of Equation (14) and regress the
predicted minus the actual change in earnings on a constant. Table 6 presents the
results. With respect to the Steady category companies, financial analysts produce a
positive (5 cents optimistic) but not statistically significant bias for the one-year-ahead
forecast horizon, and a positive (15 cents optimistic) and significant bias for the two-
year-ahead forecast horizon. The random walk and quarterly neural networks models
have negative (6-12 cents pessimistic) and in two instances statistically significant
biases, which are apparently caused by the relatively flat earnings plateau in the
beginning of the 1990s and the consecutive shift to the drastic growth as demonstrated
in Figure 2.
For the Volatile category firms, financial analysts generate large optimistic
biases: 27 cents for the one-year-ahead and 53 cents for the two-year-ahead forecast

18
As the standard deviation of the change in earnings increases, the standard deviation of individual
analysts’ forecasts grows too. The coefficient of correlation between the two is high and statistically
significant.

38
horizon. These estimates are significantly different from zero and more than three
times larger than those for the Steady category firms. It once again suggests that
financial analysts tend to predict the upward growth for all types of companies, which
results in the large optimistic biases for the Volatile category firms. On the contrary,
quarterly neural networks and the random walk model predictions are not biased for
the Volatile category companies. This result helps to explain the observed time-series
accuracy advantage.
Overall, the analysts’ optimistic forecast bias is found to increase with the
volatility of earnings. To our knowledge, this observation is a new result in the
literature examining the analysts’ forecast rationality, and it deserves further attention
in a separate chapter.

39
CHAPTER II
SYSTEMATIC OPTIMISM IN FINANCIAL ANALYSTS’
EARNINGS FORECASTS
Chapter II is organized as follows. Section II.1 describes data and the
experimental design. Section II.2 presents evidence of financial analysts’ forecast
optimism and addresses the analysts’ self-selection issue. Section II.3 introduces the
model of the analysts’ forecasting behavior. It also demonstrates the dynamics of the
analysts’ forecast bias throughout the forecast horizon.

II.1 Experimental Design

A. This work versus the related literature.
When financial analysts’ forecasts first picked up the interest of researchers in
the 1980s, the main subject of empirical tests was the comparison of the predictive
accuracy of financial analysts’ forecasts and time-series models. Later, the literature
on financial analysts developed in the three major directions. The first direction is
concerned with locating and explaining incentives that may govern financial analysts
in producing their earnings forecasts, while the second one looks for cognitive based
explanations of the analysts’ forecasting behavior
19
. Apparently, incentive and

19
Research on systematic errors in analysts’ earnings forecasts has produced a diverse set of incentive-
based explanations intended to account for them. Francis and Philbrick (1993) find that analysts
incorporate optimism into their forecasts to repair management relationships, following sell
recommendations. Lin and McNichols (1998) find that co-underwriter analysts’ earnings forecasts are
more favorable than those made by unaffiliated analysts. Dugar and Nathan (1995) find that analysts
exhibit greater optimism for firms that are investment-banking clients. McNichols and O’Brien (1997)
suggest that the observed bias is a result of the selection process when analysts with relatively
unfavorable information decide to exit the pool of forecasters. H. Hong et al. (2000) provide evidence
that the analysts’ behavior is consistent with career-concern-motivated herding theories.

40
cognitive based approaches overlap. In this study, we do not make any effort to
measure the relative strength of them. In contrast, we follow the third line of inquiry:
are financial analysts’ earnings forecasts rational? Namely, we address the existing
dilemma on whether analysts’ forecasts are biased. To achieve that, we pay close
attention to statistical properties of forecasted earnings rather than provide an ex-ante
search for incentive based explanations.
Academic research on the quality of financial analysts’ forecasts is divided.
Crichfield et al. (1978) find no evidence of systematic bias in analysts’ forecasts by
analyzing fifty analysts issuing forecasts for only forty-six firms for 1967-1976.
Moreover, they admit: “Due to the nature of the available data, the firms used in this
study could not be selected in a truly random fashion”. Givoly (1985) considers sixty-
eight analysts and 424 firms for the 1969-1979 period and states: “Earnings
expectations of financial analysts to be formed in a rational manner. Their forecasts
are generally unbiased.” However, his study also introduces restrictive constraints on
the sample
20
. These or similar sampling techniques make the results of the existing
studies less pronounced. In contrast, the key feature of the current study is that it does
not employ any sampling procedures. It analyzes all available analysts’ annual
earnings forecasts in the IBES database for the 1987-2004 period.
Next, note two influential studies by DeBondt and Thaler (1990) and
Abarbanell and Bernard (1992). DeBondt and Thaler analyze IBES consensus

20
Actual earnings exist for ten preceding years, NYSE listing, no negative earnings firms, more than
four analysts issue forecasts.

41
forecasts for 1976-1984 and have a minimal set of restrictions so far.
21
They conclude
that financial analysts are too optimistic: “Forecasted changes are simply too extreme
to be considered rational”. Similar findings are reported in Abarbanell and Bernard,
who consider individual Value Line forecasts for 178 firms for 1976-1986
22
. They
consider quarterly earnings and find that analysts’ forecasts are upward biased, but
only before the first quarter reports are released.
A conflicting opinion is presented in O’Brien (1988). O’Brien tests for
unbiasedness using 1975-1981 IBES quarterly data and econometric technique that
adjusts for time-period-specific aggregate shocks. She finds the means of analysts’
forecasts exhibit optimism, whereas median forecasts appear to be unbiased.
23
Finally,
Keane and Runkle (1998) analyze quarterly IBES forecasts for 1983-1991. They note
that most of the previous studies fail to account properly for the covariance structure
of forecast errors and argue that financial analysts are rational. However, their
conclusions are based on examination of only twenty-one companies.
Among the most recent studies, first note Lim (2001) who argues that financial
analysts trade off bias to ease their access to the management and improve the forecast
accuracy. He concludes that the positive bias may be a rational property of optimal
earnings forecasts. Gu and Wu (2003) argue that financial analysts minimize the mean

21
Actual earnings exist for ten preceding years, and returns exist for three preceding years.
22
The sample consists of 178 firms: 100 large size firms, 100 small size firms; after the “sixteen
consecutive quarter forecasts” restriction it is down to 178. Note that the study does not find substantial
differences between the large and small size firms groups.
23
The study suggests that the means of analysts’ forecasts are biased for all one- to five-quarter-ahead
forecasts, and median analysts forecasts are only biased for three-quarter-ahead forecasts at the 5%
significance level. These findings contradict Abarbanell and Bernard (1992). Yet, the sample size is
also small: it consists of only 184 firms.

42
absolute error and that median analysts’ forecasts are unbiased. However, the results
of this study do not fully support either of the above hypotheses. We show that the
analysts’ forecast optimism decreases at a somewhat slow rate as a fiscal year
progresses. Similarly, we determine that while the median forecast error is smaller
than the mean, it is still significant.
To summarize, a substantial literature exists in accounting and finance that
examines properties of financial analysts. However, the results are often controversial.
Depending on the sample (individual versus consensus forecasts, analysts used,
number of analysts, firms, years considered, time periods or econometric techniques
employed), researchers either find evidence of financial analysts’ forecast optimism or
do not The observed division in opinions stresses the importance of the current
research.

B. Predictability of earnings.
Predicting future earnings, financial analysts use a combination of quantitative
techniques as time-series models that use historical earnings to project the future or
financial analysis that extracts information from accounting statements. In addition,
analysts undertake qualitative assessment of related public news as well as information
obtained from private sources. One of the common methods in financial valuation is
known as the bottom-up approach, when a company’s performance is projected first
and then corrected for the industry and economy prospects. Therefore, the difficulty of
the forecasting task consists of factors such as the volatility of historical earnings,

43
transparency of financial statements, trend in the industry or market earnings, and
uncertainty about the overall economic activity
24
.
Accordingly, the primary factor that is considered in this study with respect to
the analysts’ forecasting performance is the volatility of change in earnings. Let us
emphasize that we are interested in the volatility of change in earnings, not the
volatility of earnings.
25
Next, there exist aggregate shocks to the economy, industries,
and sectors that cause companies’ earnings to be correlated. Systematic risk factors as
economic business cycles, transformations in technologies, political or demographic
structure may affect companies’ earnings in a similar way. Then, if a company’s
earnings are correlated with the market earnings, the uncertainty about its future
prospects can be reduced by adding information about the market behavior and thus
extending the firm’s information set
26
. Consequently, it should be easier to predict
prospects of companies whose earnings move in line with the market earnings, relative
to companies whose earnings are unrelated to the market pattern. As a result, the

24
Financial statements transparency is one of the determinants of the earnings forecasting difficulty.
However, constructing a measure of transparency is not trivial. While some shenanigans can be easily
identified and corrected, others can be discovered only by management interviews and sophisticated
investigations. In this study, we leave this step out and only consider statistical characteristics of firms’
earnings as well as the overall economic activity.
25
Consider the next simple example. EPS of the first company continually increase by twenty cents
from $0 to $1 in five years, whereas EPS of the second company increase by fifty cents and
subsequently drop by twenty-five cents in the alternating manner. As a result, EPS of both companies
are equal in five years. Now, while the average EPS of both companies are also equal, the standard
deviation of the second company’s EPS is smaller than of the first. However, there is no doubt it is
harder to predict the oscillating earnings of the second company. Therefore, the proposed measure of
the difficulty of the forecasting task is the volatility of change in earnings.
26
Consider the next example. Earnings of some company are highly correlated with the earnings of the
firm’s sector. Then, even if one may possess only scarce information specific to the company, he/she
can consider peer firms, come up with some aggregate estimate for them, and finally adjust that
estimate for the considered company. In contrast, it would be worthless to apply this relative analysis to
a company whose earnings move independently of the peers.

44
second determinant of the difficulty of the forecasting task in this study is the
correlation of a firm’s earnings with the market earnings
27
.
Finally, it is necessary to determine how the macroeconomic activity affects
the difficulty of the forecasting task and, thus, the analysts’ forecast errors. Evidently,
it is harder to predict earnings in a period of economic downturn than during an
economic expansion. The duration of a recession, its magnitude and impact on a
specific firm’s performance are usually hard to estimate in advance. Therefore, we
may expect the analysts’ forecast error patterns to differ among common periods of
economic growth and times of accidental downturns.
In the previous chapter, we saw that the analysts’ relative forecast accuracy is
determined by the nature of data generating processes or namely by the difficulty of
their forecasting. The main hypothesis here is that the analysts’ forecast error is
systematically related to the predictability of earnings as well. While the relationship
between statistical characteristics of firms’ earnings and analysts’ forecast errors is
examined in the current chapter, the analysts’ accuracy with respect to the difficulty of
the forecasting task at the macro economy level is studied in the following chapter.
In the literature, a few relevant studies examine the properties of financial
analysts’ forecasts with respect to companies’ characteristics. The size of the company
has received the most attention. Among others, Brown et al. (1987) find that the
financial analysts’ superiority relative to time-series models is positively related to a
firm’s size, and it is not related to the number of lines of business. Similarly, Das et al.

27
Note that a more refined measure can be obtained by considering the correlation of a firm’s earnings
with the aggregate earnings in its industry or a sector.

45
(1998) argue that the forecast optimism is smaller for larger firms with rich
information sets, since market participants can better assess their future performance.
However, factors like a firm’s capitalization or measures of its price performance
seem to be inferior to statistical characteristics of earnings that unambiguously
determine the difficulty of the forecasting task. For instance, earnings of a large
capitalization company may be extremely volatile and thus hardly predictable, while
earnings of a small firm may be smooth and easily forecasted. Therefore, the
predictability of a firm’s earnings and as a result the analysts’ forecasting performance
depend on a concrete environment the firm operates in. This environment determines
the earnings generating process, and it can be only understood through a careful
examination of its statistical characteristics.

C. Data and the construction of variables.
We use consensus forecast data from the Institutional Brokers Estimate System
Summary file and create timely forecasts by using the Detail file. The construction of
timely forecasts will be discussed later. We restrict the attention to December year-end
firms and the 1987-2004 period. Because most calendar-year-end firms announce their
annual earnings between January and March, and their second quarter earnings
between July and September, we choose to use analysts’ forecasts from the month of
March and September to represent the beginning and middle of year forecasts. The
release of 10K (10Q) for each firm and date is checked to ensure that analysts’

46
forecasts are conditioned on the knowledge of previous year (second quarter)
earnings
28
.
We define the analysts’ forecast error as the difference between the mean of
analysts’ estimates and actual earnings per share, f
t+i
- a
t+i
, where i = 1, 2 denotes the
one- and two-year-ahead forecast horizon. Thus, a forecast is perceived to be
optimistic if it is higher than subsequently released actual earnings. We choose not to
scale the forecast error by the share price as it is commonly done in the literature,
since the deflator can introduce spurious effects if price-earnings ratios systematically
change over time. Furthermore, the unscaled approach allows representing forecast
errors in cents and makes the discussion more descriptive. Similarly, the difficulty of
the forecasting task is determined by statistical characteristics of earnings and it is not
related to any scales
29
.
To describe the difficulty of the forecasting task quantitatively, we employ the
coefficient of variation of the first difference of earnings given by (12). As changes in
earnings become more volatile and the task of forecasting gets harder, the value of the
constructed coefficient increases appropriately. The next measure is the coefficient of
correlation of a firm’s earnings with the S&P500 earnings, ( )
500 &
,
P S k
a a ρ , where the

28
Note that both analysts’ forecasts and actual earnings series are Earnings per Share before
Extraordinary Items and Earnings from Operations as soon as the latter become available. Earnings
from Operations are not distorted by one-time occurrences as restructuring charges, inventory write-
offs, or gains and losses on investments and merges. All data are adjusted for stock splits and stock
dividends.
29
Yet, we recognize that the same value of the forecast error have different consequences for
companies whose shares are traded at different prices. For this reason, we replicate the results discussed
in this chapter by scaling the forecast error by the price of a firm’s stock. Forecast bias patterns remain
unchanged. To conserve space, we do not report the results of the scaled version. They are available
upon request.

47
S&P500 earnings serve as a proxy for the market earnings. While both measures
represent the difficulty of the forecasting task, the first one puts accent on a specific
firm factors that determine its earnings volatility, whereas the second measure
demonstrates the strength and the direction of the relationship between a firm’s
earnings and the market earnings
30
.
Next, we break the 1987-2004 data in three six-year periods. As we can see in
Figure 3, the first one (1987-1992) is the period of relatively flat market earning that
includes a major recession, whereas two subsequent periods (1993-1998, 1999-2004)
represent times of substantial growth. The idea is to separate different market patterns
and determine if a bias pattern produced by analysts in one market environment
translates to another, or if bias patterns are alike if no significant changes in the market
environment are noticeable. For each period, we filter out companies whose earnings
are extreme: a company is excluded if its earnings are in the one percent of the lowest
or the highest earnings during a considered period. It allows avoiding the influence of
unusual earnings firms. Then, we compute coefficients of variation and correlation for
each firm using the considered period data. Thus, the only sampling requirement here
is that a company’s annual earnings are available in the Compustat database for six
consecutive years. Table 7 presents the number of firms that satisfy the above
requirements and the average number of years for which at least one forecast exists
during the six-year periods. The number of firms varies from 916 to 2,275. It increases

30
A company’s earnings behavior depends on the variety of factors as macroeconomic condition (some
industries are more sensitive to the business cycle than others), nature (competition, operational
leverage) or diversification of the business (geographic location, number of lines of business),
management’s choice for the capital structure, competitive strategy or accounting practices.

48
in September relative to March and decreases for the two-year-ahead relative to the
one-year-ahead forecast horizon. Finally, companies are divided in twenty-five
groups, and analysts’ forecast biases are estimated in each group by regressions of
predicted minus actual changes in earnings on a constant. These calculations are
performed by using ninety-five percent of observations.

II.2 Evidence of the Financial Analysts’ Forecast Optimism

A. Financial analysts’ forecast bias as a function of statistical characteristics of
earnings.

Tables 8a, 8b, and 8c present analysts’ forecast biases produced at the
beginning of a fiscal year in 1987-1992, 1993-1998, and 1999-2004 periods
respectively. The Most Volatile category consists of firms with the most volatile
changes in earnings. In contrast, companies in the Steadiest category attain the lowest
values of the coefficient of variation of the change in earnings. Similarly, earnings of
companies in the Against the Market category are negatively correlated with the
market earnings, whereas companies in the With the Market category have positive
and statistically significant coefficient of correlation at least at the 10% level. Figure 3
illustrates earnings of representative companies from the four extreme groups
31
. While
changes in earnings are highly volatile in the top graphs, in the top-right graph,

31
The four extreme groups are: Most Volatile/Against the Market (changes in earnings are the most
volatile, earnings move against or independently of the market earnings), Most Volatile/With the Market
(changes in earnings are the most volatile, earnings are highly correlated with the market earnings),
Steadiest/Against the Market (changes in earnings are the least volatile, earnings move against or
independently of the market earnings), and Steadiest/With the Market (changes in earnings are the least
volatile, earnings are highly correlated with the market earnings).

49
One-year-ahead Two-year-ahead

Time Period
March September March September
1987-1992
1993-1998
1999-2004
1,152
1,820
2,159
(4.6)
(4.4)
(4.3)
1,246
1,940
2,275
(4.8)
(4.6)
(4.6)
916
1,566
1,950
(4.0)
(3.9)
(3.9)
1,217
1,861
2,215
(4.6)
(4.4)
(4.4)
Table 7. Number of firms for which at least one forecast exists during the specified six-year period.
Average number of years for which at least one forecast exists is in parentheses.

0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
1985 1989 1993 1997 2001 2005
EPS
0
10
20
30
40
50
60
70

0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
1985 1989 1993 1997 2001 2005
EPS
0
10
20
30
40
50
60
70

0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
1985 1989 1993 1997 2001 2005
EPS
0
10
20
30
40
50
60
70

0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
1985 1989 1993 1997 2001 2005
EPS
0
10
20
30
40
50
60
70

Figure 3. EPS from Operations (1987-2004) for four extreme groups of firms. EPS are presented by the
solid line, left scale: top-left graph - high coefficient of variation, low coefficient of correlation; top-
right graph - high coefficient of variation, high coefficient of correlation; bottom-left graph - low
coefficient of variation, low coefficient of correlation; bottom-right graph - low coefficient of variation,
high coefficient of correlation. S&P500 earnings are presented by the dotted line, right scale. (The
coefficient of variation of the change in earnings is defined by (12), the coefficient of correlation of a
firm’s earnings with the S&P500 earnings.)

50
earnings are also correlated with the market earnings indicating that a company’s
performance is very sensitive to the overall market condition. In the bottom graphs,
changes in earnings are relatively steady. In addition, while in the bottom-left graph,
earnings are unsusceptible to the market upturns or downturns; in the bottom-right
graph, they follow the market quite closely, suggesting that we deal with a typical
market firm.
Table 8c reports the results for the latest 1999-2004 period. Financial analysts’
forecast biases for the one-year-ahead forecast horizon are presented in the upper
panel. The difficulty of the forecasting task increases as we move from the
Steadiest/With the Market (bottom-right) group to the Most Volatile/Against the
Market (top-left) group. Amazingly, the analysts’ optimism increases right in the same
direction. The analysts’ forecast bias increases from a pessimistic 2 cents for the
steadiest change in earnings companies, whose earnings move with the market
earnings, to an optimistic 66 cents for the most volatile change in earnings companies
whose earnings move against or independently of the market earnings.
For With the Market category companies, financial analysts produce no bias
regardless of the volatility pattern. While the mean forecast bias for this category
denoted by Mean is not significantly different from zero, the median forecast error
denoted by Median is a pessimistic 4 cents. Similarly, the mean forecast bias for the
Steadiest category companies is not significantly different from zero, and the median
forecast error is a pessimistic 2 cents. With the exception of the Steadiest and With the
Market categories, we observe that the forecast bias has a relatively lower rate of

51
increase with the coefficient of correlation than with the coefficient of variation.
Namely, as we fix the volatility category and move across the market pattern
categories, the forecast bias increases from 7 to 14 cents for the Steady category
companies and from 24 to 66 cents for the Most Volatile category firms. On the other
hand, if we move across the volatility categories, it increases from 7 to 24 cents and
from 14 to 66 cents for the Weakly Correlated and Against the Market category firms.
Therefore, we can conclude that the volatility of change in earnings plays a primary
role for the magnitude of financial analysts’ forecast optimism, whereas the earnings
pattern relative to the market earnings is important but at a somewhat lesser extent.
Financial analysts’ forecast biases for the 1993-1998 period are presented in
Table 8b. In general, the results are similar to the 1999-2004 period. The only
difference is that a greater number of groups in the Weakly Correlated category have
zero or statistically insignificant forecast biases. It is caused by the fact that
companies’ earnings had generally higher correlations with the market earnings during
the 1993-1998 than 1999-2004 period. Overall, the similarity of results suggests that if
there are no significant changes in the market environment, the analysts’ bias pattern
may remain unchanged for a relatively long period.
Table 8a presents the results for the first 1987-1992 period that embraces a
major economic recession in July 1990 - March 1991. In this recession period, the
analysts’ mean and median forecast biases are greater than biases for corresponding
groups and categories in the subsequent periods. It suggests that analysts overlooked
the approaching recession and did not adjust their forecasts downward adequately. The

52
second difference is that the analysts’ forecast bias appears to be not related to the
correlation coefficient. The values of the forecast error are similar in each volatility
category. We suggest the next explanation. As the correlation coefficient decreases,
the more uncertainty exists about a firm’s future prospects, and analysts tend to exhibit
higher forecast optimism. On the other hand, as the correlation increases, a firm’s
earnings decline to a greater extent with the market earnings. Analysts fail to foresee
the economic downturn that causes the optimistic forecast error to increase. As a
result, the analysts’ forecast bias does not depend on the correlation of a firm’s
earnings with the market earnings in the 1987-1992 economic recession period
32
.
However, the analysts’ forecast optimism continues to vary greatly with the volatility
of change in earnings. It increases from a few cents for the Steadiest category
companies to almost a dollar for the Most Volatile category firms. Overall, by
comparing forecast errors among categories, we observe that the magnitude of the
analysts’ forecast optimism is similar in the 1993-1998 and 1999-2004 periods, but it
is somewhat higher in the 1987-1992 recession period (for example, median forecast
errors are twice bigger for four out of five volatility categories). This result implies
that the overall economic activity is an important factor for the magnitude of the
analysts’ forecast error.

32
The additional support for this explanation can be obtained by scrutinizing analysts’ forecast biases
for the With the Market/Steady and With the Market /Steadiest group firms. They are two to ten times
higher than biases for other groups in the same volatility categories: 13(22) and 10(21) cents in the case
of the one- (two)-year-ahead forecast horizon. If a company’s earnings are correlated with the market
earnings, during a recession, they decrease by a greater amount than earnings of firms that move
independently of the market. If analysts do not adjust their forecasts downward sufficiently, it causes
the analysts’ forecast bias to increase for these groups.

53
The results for the two-year-ahead forecast horizon are presented in the bottom
panels of Table 8. The financial analysts’ two-year-ahead forecast error exhibits a
similar escalation pattern as the one-year-ahead, but the magnitude of this error is
bigger. In the 1993-1998 and 1999-2004 periods, as the forecast horizon doubles, the
optimistic bias on average doubles as well. However, for some groups, it is three, four
or even eight times greater than the corresponding group bias in the case of the one-
year-ahead forecast horizon. It means that when analysts are optimistic about a
company’s performance in the short term, they are even more optimistic about its
longer term prospects. In contrast, in the 1987-1992 period, the financial analysts’
forecast bias increases only by a factor of two or less. Thus, the analysts’ forecast
optimism grows in the accelerating fashion with the forecast horizon in periods of
economic growth and in less than a proportionate manner during economic downturns.
It suggests that financial analysts are more sensible in producing longer forecast
horizon forecasts during the recession period with the enlarged uncertainty about
future economic prospects.
Finally, we would like to address the study by O’Brian (1988), who considers
quarterly analysts’ forecasts and finds that median consensus forecasts appear to be
unbiased, whereas mean forecasts are. We replicate Table 8 using medians of
individual analysts’ forecasts instead of means and find no significant differences. The
estimated values of biases vary from the presented numbers by no more than 2 cents.
To summarize, the observed results are entirely consistent with the hypothesis
that the analysts’ forecast bias increases with the difficulty of the forecasting task. The

54
mean and median forecast errors approximately double with each category of firms.
Overall, at the beginning of a fiscal year financial analysts’ produce optimistic
forecasts for the majority of companies. Their forecasts are not optimistically biased
only for companies, whose earnings are strongly correlated with the market earnings
or have the smallest variation of the change in earnings. Figure 4 illustrates the
analysts’ forecast errors graphically.

B. Financial analysts’ forecast bias at the middle of a year relative to the beginning.
In this section, we analyze financial analysts’ forecast errors produced at the
middle of a year given the knowledge of the first and second quarter earnings. Table 9
reports the results. Not surprisingly, the analysts’ forecast error exhibits a similar
dependence on the statistical characteristics of earnings as it does at the beginning of a
fiscal year. Furthermore, in most instances, proportions among biases for different
groups of companies remain unchanged. Therefore, here we are only concerned with
explaining the relative magnitude of the analysts’ forecast error in the middle of a year
relative to the beginning of a year.
At the middle of a year, financial analysts exploit larger information sets. As a
result, their forecasts become more accurate, and forecast biases decrease. In the
month of September relative to March, the mean and median forecast errors reduce by
approximately 15 cents for the Most Volatile and Against the Market category firms
and by 5 cents for other categories companies. In the relative terms, a percentage

55
reduction in the analysts’ forecast bias is presented in Table 10
33
. In the combined
1993-2004 period, the forecast bias on average decreases by 46% in the one-year-
ahead and by 15-24% in the two-year-ahead forecast horizon case. However, the rates
of the decline are not uniform. The more uncertainty exists about the future prospects
of a company, the smaller the rate of the decrease. While the forecast bias reduces by
64-66% for the Steady category companies, it decreases only by 36-43% for the Most
Volatile category firms in the case of the one-year-ahead forecast horizon. It suggests
that the difficulty of the forecasting task is the determinant factor for the financial
analysts’ forecast optimism not only at a fixed point in time, but also as a fiscal year
progresses.
In the 1987-1992 period, the direction of the more rapid decline is inversed:
the analysts’ forecast bias decreases by 24% for the Steady category companies and by
greater 35% for the Most Volatile category firms. The reason for this change is the
different market condition. In the 1993-2004 period, the market earnings are generally
growing. As a result, for the Most Volatile category firms whose earnings usually go
up or down by more than the market earnings, financial analysts are more likely to
assign a greater likelihood to the increase than to decrease in earnings. Consequently,
the forecast optimism dies out relatively slowly for the volatile earnings companies. In
contrast, in the 1987-1992 recession period, the likelihood of a down movement seems
greater, and the optimistic forecast bias dies out relatively faster.

33
To find the relative decrease in the forecast error for each category of firms, we first, calculate
relative decreases for all groups in each category and then weight them by the average number of firm-
years in those groups.

56
Finally, note that the forecast bias averaged across all categories reduces more slowly
in the 1987-1992 period than in subsequent 1993-2004 economic growth period. It
decreases by 33% (6%) relative to 46% (24%) in the case of the one- (two)-year-ahead
forecast horizon, respectively. This result once again reveals that the greater the
uncertainty and the harder the forecasting task (in this case due to the overall
economic condition), the slower the rate of the analysts’ optimism decay Overall, at
the middle of a fiscal year, the financial analysts’ forecast bias is on average only 33-
46% (6-24%) smaller in the case of the one- (two)-year-ahead forecast horizon than
that at the beginning of a fiscal year. This result is not consistent with the somewhat
conventional hypothesis in the literature that financial analysts produce optimistic
forecasts only at the beginning of a year in order to maintain good relationships with
the management and gain access to its private information
34
. For this hypothesis to be
entirely valid, the analysts’ optimism should disappear at a somewhat faster rate than
we detect in the data. With the observed slow rates, this hypothesis becomes a closed
loop. Analysts produce optimistically biased forecasts in March in order to improve
accuracy later on. Yet, later in September, they still exhibit significant optimism. On
the other hand, the value of accurate forecasts decreases as the announcement date
approaches. Thus, the release of optimistic forecasts throughout the major part of a
fiscal year in order to improve the forecast accuracy just before actual earnings are
announced does not look logical. Therefore, the access to the management hypothesis
cannot be viewed as an universal explanation of the analysts’ forecast optimism.

34
See, for example, Lim (2001).

57
One-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

0.90
(9.2)

0.36
(9.4)

0.09
(5.1)

0.04
(3.3)

0.04
(5.5)

0.82
(9.4)

0.34
(7.1)

0.15
(5.6)

0.06
(3.4)

0.01
(2.8)

0.87
(8.9)

0.36
(5.9)

0.25
(7.5)

0.08
(5.7)

0.03
(5.9)

0.86
(10.1)

0.39
(12.4)

0.19
(7.2)

0.04
(2.8)

0.04
(4.7)

0.72
(7.8)

0.29
(7.9)

0.17
(10.0)

0.13
(11.2)

0.10
(3.8)

0.84

0.36

0.17

0.07

0.03

0.48

0.23

0.10

0.04

0.01
Mean
Median
0.29
0.10
0.21
0.02
0.24
0.04
0.34
0.11
0.31
0.12

Two-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

1.44
(10.6)

0.57
(9.6)

0.20
(5.9)

0.08
(4.8)

0.13
(6.8)

1.18
(10.9)

0.57
(9.0)

0.21
(4.7)

0.12
(4.2)

0.03
(4.3)

1.42
(10.2)

0.48
(7.2)

0.45
(11.3)

0.12
(4.9)

0.07
(6.3)

1.37
(11.3)

0.67
(13.0)

0.26
(6.5)

0.09
(2.2)

0.06
(3.7)

1.18
(8.0)

0.43
(6.7)

0.36
(10.4)

0.22
(11.4)

0.21
(4.5)

1.34

0.57

0.31

0.14

0.07

1.02

0.44

0.23

0.10

0.03
Mean
Median
0.51
0.23
0.31
0.08
0.43
0.12
0.58
0.27
0.56
0.30

Table 8a, (1987 - 1992). Biases for analysts’ EPS forecasts made at the beginning of a fiscal year.
Biases are estimated by the regression of the predicted minus the actual change in earnings on a
constant. (t-statistics in absolute value are in parentheses.) Mean (Median) is the mean (median)
forecast error estimated within each category of firms. Asterisks denote insignificance at the 1% level
according to the t-test (sign test). Companies are divided in groups according to the coefficient of
variation of the change in earnings (vertical axis) and the coefficient of correlation of their earnings
with the S&P500 earnings (horizontal axis). Positive values denote forecast optimism.

58
One-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

0.78
(19.9)

0.39
(16.1)

0.28
(12.4)

0.24
(9.6)

0.11
(3.1)

0.48
(11.7)

0.22
(9.4)

0.12
(7.9)

0.10
(8.6)

0.00*
(0.3)

0.28
(4.2)

0.09
(3.7)

0.04
(2.7)

0.04
(4.1)

0.02
(2.0)

0.33
(4.1)

0.09
(2.1)

0.02*
(1.3)

-0.00*
(0.5)

-0.01
(4.0)

0.19*
(1.2)

0.07*
(1.5)

0.00*
(0.2)

0.01*
(1.7)

0.01*
(1.7)

0.58

0.22

0.09

0.05

0.00

0.35

0.13

0.04

0.00*

-0.01
Mean
Median
0.51
0.30
0.26
0.11
0.09
0.02
0.03
-0.01
0.02
-0.01

Two-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

1.21
(20.3)

0.74
(19.6)

0.60
(14.5)

0.47
(9.6)

0.25
(5.6)

0.86
(11.8)

0.37
(11.2)

0.23
(9.1)

0.24
(11.8)

0.00*
(1.4)

0.74
(6.3)

0.18
(4.4)

0.14
(6.0)

0.07
(5.3)

0.03
(2.0)

0.64
(4.1)

0.16
(2.1)

0.09
(3.1)

0.00*
(0.2)

-0.02
(3.2)

0.56*
(1.7)

0.22
(3.0)

0.04*
(1.2)

0.05
(3.0)

0.02
(3.1)

1.00

0.42

0.20

0.10

0.01*

0.76

0.35

0.12

0.06

-0.02
Mean
Median
0.88
0.62
0.47
0.27
0.22
0.10
0.06
-0.02
0.07
0.00*

Table 8b, (1993 - 1998). Biases for analysts’ EPS forecasts made at the beginning of a fiscal year.
Biases are estimated by the regression of the predicted minus the actual change in earnings on a
constant. (t-statistics in absolute value are in parentheses.) Mean (Median) is the mean (median)
forecast error estimated within each category of firms. Asterisks denote insignificance at the 1% level
according to the t-test (sign test). Companies are divided in groups according to the coefficient of
variation of the change in earnings (vertical axis) and the coefficient of correlation of their earnings
with the S&P500 earnings (horizontal axis). Positive values denote forecast optimism.

59
One-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

0.66
(11.6)

0.29
(10.8)

0.28
(14.6)

0.14
(10.5)

0.16
(9.2)

0.49
(11.7)

0.25
(9.8)

0.13
(6.9)

0.08
(5.8)

0.07
(5.3)

0.43
(10.4)

0.15
(5.4)

0.09
(5.0)

0.09
(5.2)

0.00*
(0.0)

0.24
(3.7)

0.16
(4.6)

0.07
(3.2)

0.07
(3.7)

0.00*
(0.4)

0.14*
(1.2)

0.08*
(0.8)

-0.02*
(0.9)

-0.02*
(1.1)

-0.02
(4.1)

0.44

0.19

0.13

0.07

0.01*

0.23

0.11

0.07

0.02

-0.02
Mean
Median
0.31
0.18
0.27
0.11
0.19
0.05
0.08
-0.01
-0.01*
-0.04

Two-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

1.33
(14.7)

0.68
(14.8)

0.62
(18.7)

0.38
(15.9)

0.34
(10.7)

0.96
(14.0)

0.62
(13.8)

0.39
(12.3)

0.27
(10.6)

0.24
(9.2)

0.93
(13.6)

0.45
(10.0)

0.30
(7.9)

0.23
(8.2)

0.13
(5.1)

0.55
(5.2)

0.30
(4.6)

0.28
(6.3)

0.16
(5.4)

0.04
(3.3)

0.49
(2.6)

0.09*
(0.6)

0.09
(2.2)

0.03*
(1.3)

-0.01*
(0.6)

0.94

0.48

0.37

0.21

0.06

0.68

0.39

0.30

0.16

0.01
Mean
Median
0.71
0.49
0.61
0.38
0.48
0.24
0.21
0.06
0.07
0.00*

Table 8c, (1999 - 2004). Biases for analysts’ EPS forecasts made at the beginning of a fiscal year.
Biases are estimated by the regression of the predicted minus the actual change in earnings on a
constant. (t-statistics in absolute value are in parentheses.) Mean (Median) is the mean (median)
forecast error estimated within each category of firms. Asterisks denote insignificance at the 1% level
according to the t-test (sign test). Companies are divided in groups according to the coefficient of
variation of the change in earnings (vertical axis) and the coefficient of correlation of their earnings
with the S&P500 earnings (horizontal axis). Positive values denote forecast optimism.

60
FA 1-year-ahead for. Bias (1987-1992)
FA 2-year-ahead for. Bias (1987-1992)

FA 1-year-ahead for. Bias (1993-1998) FA 2-year-ahead for. Bias (1993-1998)

FA 1-year-ahead for. Bias (1999-2004) FA 2-year-ahead for. Bias (1999-2004)

Figure 4. Financial analysts’ forecast bias at the beginning of a fiscal year in the case of the one- (two)-
year-ahead forecast horizon. The bias is estimated by the regression of the predicted minus the actual
change in earnings on a constant. Companies are divided in 100 groups according to the coefficient of
correlation of their earnings with the S&P500 earnings, Corr; and the coefficient of variation of the
change in earnings, Coeff Var. 3D-surfaces are plotted using the bicubic spline smoothing procedure.

61
One-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

0.60
(9.7)

0.21
(6.8)

0.07
(5.7)

0.02
(2.4)

0.02
(3.5)

0.63
(10.0)

0.24
(7.8)

0.08
(4.4)

0.05
(3.9)

0.00*
(0.8)

0.58
(9.3)

0.25
(5.5)

0.12
(6.1)

0.05
(5.7)

0.02
(6.5)

0.49
(8.4)

0.26
(11.6)

0.12
(5.6)

0.04
(2.8)

0.04
(5.6)

0.44
(7.7)

0.17
(7.1)

0.10
(8.6)

0.08
(9.5)

0.07
(3.7)

0.57

0.23

0.10

0.05

0.02

0.25

0.12

0.05

0.02

0.00*
Mean
Median
0.20
0.04
0.16
0.01
0.19
0.02
0.20
0.06
0.18
0.06

Two-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

1.10
(11.0)

0.56
(12.0)

0.18
(7.6)

0.06
(4.9)

0.06
(7.2)

1.14
(12.9)

0.49
(9.8)

0.21
(6.3)

0.12
(5.7)

0.02
(3.1)

1.38
(12.3)

0.49
(7.9)

0.34
(10.0)

0.15
(8.3)

0.06
(9.3)

1.03
(11.0)

0.58
(14.6)

0.31
(9.7)

0.07
(3.2)

0.07
(6.6)

1.02
(8.7)

0.53
(10.0)

0.30
(12.5)

0.19
(13.0)

0.12
(5.5)

1.15

0.56

0.28

0.13

0.05

0.81

0.43

0.20

0.08

0.02
Mean
Median
0.41
0.16
0.32
0.05
0.39
0.11
0.47
0.19
0.47
0.23

Table 9a, (1987 - 1992). Biases for analysts’ EPS forecasts made at the middle of a fiscal year. Biases
are estimated by the regression of the predicted minus the actual change in earnings on a constant. (t-
statistics in absolute value are in parentheses.) Mean (Median) is the mean (median) forecast error
estimated within each category of firms. Asterisks denote insignificance at the 1% level according to
the t-test (sign test). Companies are divided in groups according to the coefficient of variation of the
change in earnings (vertical axis) and the coefficient of correlation of their earnings with the S&P500
earnings (horizontal axis). Positive values denote forecast optimism.

62
One-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

0.51
(16.5)

0.22
(13.1)

0.19
(10.7)

0.13
(8.4)

0.07
(3.2)

0.32
(10.7)

0.14
(8.4)

0.05
(5.3)

0.05
(5.4)

0.00*
(0.8)

0.06*
(1.3)

0.05
(3.1)

0.02*
(1.9)

0.01*
(1.2)

0.01*
(1.8)

0.25
(4.5)

-0.01*
(0.4)

-0.01*
(1.3)

0.00*
(0.5)

-0.01
(5.8)

0.25
(2.1)

0.02*
(0.6)

-0.01*
(0.9)

-0.01
(2.8)

0.00*
(1.1)

0.36

0.12

0.05

0.01

0.00*

0.13

0.05

0.01

-0.01

-0.01
Mean
Median
0.33
0.14
0.16
0.04
0.03
0.00*
0.00*
-0.01
0.00*
-0.01

Two-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

1.10
(23.4)

0.60
(19.9)

0.47
(16.0)

0.35
(11.6)

0.24
(5.8)

0.75
(13.9)

0.38
(12.9)

0.20
(10.8)

0.14
(9.8)

0.03
(2.0)

0.37
(4.2)

0.23
(7.4)

0.11
(6.0)

0.07
(6.1)

0.05
(3.6)

0.62
(5.3)

0.12
(2.2)

0.03*
(1.7)

0.02*
(1.5)

0.01
(3.1)

0.60
(2.8)

0.19
(2.9)

0.07
(2.6)

0.03
(2.5)

0.01*
(1.8)

0.84

0.38

0.17

0.08

0.01

0.60

0.28

0.10

0.03

-0.01
Mean
Median
0.75
0.53
0.42
0.19
0.17
0.08
0.05
-0.01
0.06
-0.01

Table 9b, (1993 - 1998). Biases for analysts’ EPS forecasts made at the middle of a fiscal year. Biases
are estimated by the regression of the predicted minus the actual change in earnings on a constant. (t-
statistics in absolute value are in parentheses.) Mean (Median) is the mean (median) forecast error
estimated within each category of firms. Asterisks denote insignificance at the 1% level according to
the t-test (sign test). Companies are divided in groups according to the coefficient of variation of the
change in earnings (vertical axis) and the coefficient of correlation of their earnings with the S&P500
earnings (horizontal axis). Positive values denote forecast optimism.

63
One-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

0.39
(10.3)

0.12
(7.7)

0.14
(11.4)

0.05
(6.6)

0.06
(5.0)

0.28
(10.7)

0.12
(7.8)

0.04
(3.1)

0.02
(2.1)

0.02
(2.6)

0.27
(9.1)

0.09
(5.1)

0.05
(3.8)

0.04
(3.9)

0.01
(3.8)

0.21
(5.1)

0.18
(7.2)

0.06
(4.0)

0.03
(2.3)

0.00*
(0.5)

0.08
(2.0)

0.12
(4.6)

0.02*
(1.1)

-0.01*
(0.9)

-0.01*
(2.0)

0.28

0.13

0.07

0.03

0.00*

0.10

0.04

0.02

0.00*

-0.02
Mean
Median
0.16
0.05
0.14
0.04
0.11
0.01
0.07
-0.01
0.03
-0.03

Two-year-ahead

Earnings Pattern

Against the
Market
(_1)
Independent
(_2)
Independent
(_3)
Weakly
corr-ed
(_4)
With the
Market
(_5)

Mean

Medi
an

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

1.02
(14.3)

0.51
(15.7)

0.48
(19.4)

0.28
(17.3)

0.27
(12.6)

0.78
(15.2)

0.43
(13.1)

0.28
(10.7)

0.17
(8.6)

0.14
(7.1)

0.73
(13.3)

0.30
(8.2)

0.19
(7.7)

0.17
(7.8)

0.08
(4.7)

0.41
(5.0)

0.32
(7.0)

0.23
(6.7)

0.14
(3.1)

0.03
(2.6)

0.37
(2.6)

0.07*
(1.1)

0.07
(2.4)

0.03*
(1.3)

0.00*
(0.6)

0.74

0.36

0.27

0.16

0.05

0.48

0.28

0.20

0.11

0.00*
Mean
Median
0.52
0.34
0.47
0.25
0.35
0.15
0.18
0.04
0.06
-0.01

Table 9c, (1999 - 2004). Biases for analysts’ EPS forecasts made at the middle of a fiscal year. Biases
are estimated by the regression of the predicted minus the actual change in earnings on a constant. (t-
statistics in absolute value are in parentheses.) Mean (Median) is the mean (median) forecast error
estimated within each category of firms. Asterisks denote insignificance at the 1% level according to
the t-test (sign test). Companies are divided in groups according to the coefficient of variation of the
change in earnings (vertical axis) and the coefficient of correlation of their earnings with the S&P500
earnings (horizontal axis). Positive values denote forecast optimism.

64
1987-1992 1993-1998 1999-2004

Time Period
One-year Two-year One-year Two-year One-year Two-year
Most Volatile (1)
Steady (4)
35%
24%
14%
4%
43%
66%
17%
19%
36%
64%
21%
25%
All 33% 6% 46% 15% 46% 24%
Table 10. Percentage decrease in the financial analysts’ forecast bias at the middle of a fiscal year
relative to the beginning of a year. Rows 1-4 and columns 1-4 in Table 8 and Table 9 are used for the
comparison (the Steadiest and With the Market categories, for which the forecast bias is either
statistically insignificant or relatively small, are excluded; in the 1993-1998 period, group 4_4 with no
forecast bias is also excluded). Relative decreases in the forecast bias for each group are calculated first
and then weighted by the average number of firm-years in those groups (the average number of firm-
years is taken between the month of March and September).

In contrast, many of the presented findings point at the behavioral biases in the
analysts’ forecasting behavior.

C. Predicting median earnings versus mean earnings.
In a recent study, Gu and Wu (2003) argue that the optimal earnings forecast is
the median rather than the mean forecast, and that the median forecast error is not
significantly different from zero. In this section, we test if this hypothesis stands after
the division of companies according to the difficulty of the forecasting task. We
calculate the median forecast error at the beginning and the middle of a fiscal year for
each volatility and market correlation category and report it as Median in Table 8 and
Table 9, respectively.
The median forecast error is on average about 60% (40%) smaller than the
mean forecast error for the market correlation categories and about 50% (25%) smaller
for the volatility categories in the case of the one- (two)-year-ahead forecast horizon.
However, it is subject to the same regularity as the mean forecast error - it
approximately doubles with each volatility category for all periods and with each

65
market correlation category for the 1993-1998 and 1999-2004 periods. Next, the
median forecast error is optimistic for most categories - its values change from a few
cents to 48 (102) cents in the case of the one- (two)-year-ahead forecast horizon. It is
pessimistic only for companies whose earnings are steady or move with the market
earnings. The magnitude of the pessimism does not exceed 2 cents. Thus, the support
for the contention that analysts predict median earnings is at best weak.

D. Self-selection by financial analysts.
An analyst chooses to cover a company if it is in interests of a firm he/she is
employed by. The pool of covered firms usually consists of companies that appear to
have an investment interest. It may be bigger market capitalization firms, well-
publicized firms, or firms in a specific sector of the economy. Yet, there is some
flexibility with the choice of firms for whom to produce forecasts and for whom do
not.
35
. Therefore, it is interesting to investigate if there exists the self-selection by
financial analysts based on the difficulty of the forecasting task.
Remember that a company is included in our data set if at least one forecast is
present during a specified six-year period. It is reasonable to assume that if a company
picks up the interest of analysts at least once in a six-year period, it is a big enough
and well-known company, whose earnings are the subject of analysts’ interest. We
divide companies in categories according to the statistical characteristics of earnings,
so that the number of firms is each category is equal. Then, we calculate the number of

35
For instance, one of the most prominent companies in the investment research, Value Line, covers
about 8,000 companies, but it does not cover all of the S&P500 firms.

66
individual analysts’ forecasts made for the one- and two-year-ahead forecast horizon
as:
∑∑
==
=
N
kt
t k
n n
1
6
1
,
, (16)
where N is the number of firms in each category and n
k,t
is the number of individual
analysts’ forecasts for a firm k in a year t; it is equal to zero if no forecasts for a firm’s
earnings exist in a given year and the specified forecast horizon.
The results for the one-year-ahead forecast horizon case are presented in Table
11. In the 1987-1992 and 1993-1998 periods, the number of individual analysts’
forecasts is 76% and 53% greater for companies whose earnings are highly correlated
with the market earnings, than for companies whose earnings move against the market
earnings. With respect to the volatility categories, the numbers of individual analysts’
forecasts increases by 50%-67% at the beginning of a year and by an even greater
71%-75% at the middle of a year for companies whose changes in earnings are the
least volatile relative to firms with the most volatile changes in earnings. In the latest
1999-2004 period, the increase rates are relatively smaller: between the With the
Market to the Against the Market category, the number of forecasts increases only by
50%, and between the Most Volatile to the Steadiest category by 16%-17%. Thus, the
self-selection effect is weaker in the latest 1999-2004 period. Accordingly, we find
that the analysts’ optimistic forecast bias is smaller in this recent period too.
To conclude, at the first stage that consists of choosing companies to predict
financial analysts seem to differentiate firms according to their statistical

67

Number of forecasts made at the Beginning of a fiscal year

Time Period
1987-
1992
1993-
1998
1999-
2004

Time Period
1987-
1992
1993-
1998
1999-
2004

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

9,235

11,082

10,481

11,737

13,827

10,561

11,216

13,149

14,066

17,611

13,227

12,267

12,512

14,491

15,461

Against the Market (_1)

Independent (_2)

Independent (_3)

Weakly correlated (_4)

With the Market (_5)

7,857

10,642

11,233

12,815

13,815

9,980

11,299

15,441

14,594

15,289

12,076

11,856

11,832

14,111

18,083
% increase 50% 67% 17% % increase 76% 53% 50%
Slope 984
(3.9)
1,695
(6.1)
669*
(2.2)
Slope 1,409
(7.5)
1,391
(3.1)
1,427
(2.7)
Number of firms in
each category
230 364 431
Number of firms in each
category
230 364 431

Number of forecasts made at the Middle of a fiscal year

Time Period
1987-
1992
1993-
1998
1999-
2004

Time Period
1987-
1992
1993-
1998
1999-
2004

Most Volatile (1)

Volatile (2)

Middle (3)

Steady (4)

Steadiest (5)

8,780

11,015

11,281

12,608

14,975

10,594

11,822

14,005

15,236

18,500

14,115

12,964

13,475

14,680

16,367

Against the Market (_1)

Independent (_2)

Independent (_3)

Weakly correlated (_4)

With the Market (_5)

7,982

11,285

12,146

13,208

14,038

10,224

11,667

16,232

15,558

16,476

12,574

12,411

12,645

15,150

18,821
% increase 71% 75% 16% % increase 76% 61% 50%
Slope 1,398
(7.1)
1,923
(9.8)
622*
(2.0)
Slope 1,403
(5.2)
1,640
(3.6)
1,523
(3.1)
Number of firms in
each category
249 388 455
Number of firms in each
category
249 388 455
Table 11. Number of individual financial analysts’ one-year-ahead EPS forecasts made at the
beginning and the middle of a fiscal year. The number of firms is equal among categories. % increase is
the percentage increase in the number of forecasts between the Most Volatile, (1), and the Steadiest, (5),
(Against the Market and With the Market) categories. Slope is the slope coefficient in the regression of
the number of forecasts in a category on the numerical number of that category. (t-statistics are in
parentheses. Asterisks denote insignificance at the 10% level.) Companies are divided in categories
according to the coefficient of variation of the change in earnings (left panel) and the coefficient of
correlation of their earnings with the S&P500 earnings (right panel).

68
characteristics of earnings. Many of those analysts, who may have negative
information about prospects of volatile earnings companies and thus do not share the
same sentiment as the majority, have little choice as to not to produce forecasts and
exit the pool of forecasters (or they will be risking reputation betting against the
crowd)
36
. Then, once the selection is made, many of those analysts who stay may
either have positive information or fail to distinguish among subsets of firms. In the
environment of generally rising earnings, they tend to predict the upward growth. It
augments the optimistic forecast bias for firms with volatile earnings or earnings that
move against or independently of the market earnings.

II.3 Properties of the Financial Analysts’ Forecast Error

A. Tracking the financial analysts’ optimism over time.
In the previous section, we established that the analysts’ forecast error is
optimistic for the majority of volatility and market correlation categories at the
beginning and the middle of a fiscal year. In contrast, the business press often alleges
that companies deliberately pressure analysts into making beatable forecasts. A classic
illustration is the next citation from the CNNMoney “Everybody knew business was
good in the fourth quarter, and everybody knew that companies and analysts alike
were low balling what earnings would look like”
37
. Thus, it is interesting to look at the

36
This result is in line with the previous literature that finds that analysts choose to produce forecasts
based on their incentives. See, for example, McNichols and O’Brien (1997). They suggest that the
observed bias is a result of the selection process when analysts with relatively unfavorable information
decide to exit the pool of forecasters. Note that the results for the two-year-ahead forecast horizon are
similar and available form the authors upon request.
37
CNNMoney, January 22, 2004, “Seven earnings reports that matter.”

69
discrepancy between the alleged pessimism by the media and the evidence of
optimism in this study and the academic literature. In this section, we examine the
dynamic behavior of the analysts’ forecast error over the two-year forecast horizon
prior to annual earnings announcements. It allows us to consider the continuity in the
analysts’ forecast optimism reduction as well as to determine if the decline patterns are
alike for different categories of companies.
Consensus forecasts used in the analysis above consist of all analysts’
estimates outstanding as of the Thursday before the third Friday of each month.
However, not all analysts update their forecasts promptly after the quarterly earning
figures and interim news are released. Thus, IBES consensus forecasts include both
current and stale forecasts. Brown and Kim (1991) argue that the earnings forecast
accuracy can be improved by discarding the stale forecasts. For this reason, we
consider earnings forecasts produced by individual analysts employed by over 200
brokerage firms in the IBES Detail file. Each observation in that file represents the
individual forecast value, broker and analyst identifiers, company ticker, forecast
horizon, and the date of the forecast. We define the timely forecasts as medians of all
analysts’ latest estimates in each calendar month submitted within that month
38
.
Accordingly, errors estimated by using consensus and timely forecasts are called the
consensus and timely forecast errors.
Figure 5 reports the consensus as well as timely forecasts errors for the three
volatility categories defined above. Panel A presents graphs for the Most Volatile

38
Note, that it is often the case that some analysts issue multiple forecasts for the same company and
the forecast horizon within the same month. We choose to use the latest forecast available in each
month.

70
category firms. First, the timely forecast error is typically smaller than the consensus
forecast error. The average difference between the two is 25% of the latter in the
relative terms or 9 cents in the absolute values. It varies from 19 cents in earlier
months to 4 cents in months just prior to earnings releases. These numbers are uniform
among different periods. Second, for the Most Volatile category companies, both
consensus and timely forecast errors are smaller in the 1993-1998 and 1999-2004
periods than in the 1987-1992 period. For example in 1987-1992, the timely forecast
error is statistically different from zero at the 5% level at all months prior to earnings
releases, while in 1999-2004, it is not in October and November. Furthermore, the
error becomes pessimistic in December and January. Overall, we observe a decline in
the analysts’ forecast optimism for the Most Volatile category firms over the
considered periods.
The dynamics of the forecast error for the Middle category firms is similar.
The optimistic timely forecast error reduces as the announcement date approaches. It
becomes statistically insignificant from zero in the month of September and even
pessimistic thereafter. The only significant difference with the Most Volatile category
is that while the one-year-ahead forecast error is smaller in the 1999-2004 period
relative to the 1987-1992 period, it is about the same or even larger at the two-year-
ahead forecast horizon. Thus, we do not observe a clear reduction of the analysts’
forecast error over periods as in the case of the Most Volatile firms. For the Steadiest
category firms, the timely forecast error declines from 2 to 0 cents in the 1987-1992

71

Panel A: The Most Volatile category firms
Financial Analysts' Median Forecast Error prior to the announcement date
Consensus forecasts
The Most Volatile category firms
-0.1 0
0.00
0.1 0
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1. 00
1. 10
2_2 3_2 4_2 5_2 6_2 7_2 8_2 9_2 1 0_2 1 1 _2 1 2_2 1 _2 2_1 3_1 4_1 5_1 6_1 7_1 8_1 9_1 1 0_1 1 1 _1 1 2_1 1 _1
Calendar month_forecast horizon
Forecast Error, $
19 8 7 -1 9 9 2
19 9 3 -1 9 9 8
19 9 9 -2 0 0 4

Financial Analysts' Median Forecast Error prior to the announcement date
Timely forecasts
The Most Volatile category firms
-0.1 0
0.00
0.1 0
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1. 00
1. 10
2_2 3_2 4_2 5_2 6_2 7_2 8_2 9_2 1 0_2 1 1 _2 1 2_2 1 _2 2_1 3_1 4_1 5_1 6_1 7_1 8_1 9_1 1 0_1 1 1 _1 1 2_1 1 _1
Calendar month_forecast horizon
Forecast Error, $
19 8 7 -1 9 9 2
19 9 3 -1 9 9 8
1 999-2004

72

Panel B: The Middle category firms
Financial Analysts' Median Forecast Error prior to the announcement date
Consensus forecasts
The Middle category firms
-0.04
0.00
0.04
0.08
0.1 2
0.1 6
0.20
0.24
0.28
0.32
0.36
0.40
0.44
2_2 3_2 4_2 5_2 6_2 7_2 8_2 9_2 1 0_2 1 1 _2 1 2_2 1 _2 2_1 3_1 4_1 5_1 6_1 7_1 8_1 9_1 1 0_1 1 1 _1 1 2_1 1 _1
Calendar month_forecast horizon
Forecast Error, $
19 8 7 -1 9 9 2
19 9 3 -1 9 9 8
1 999-2004

Financial Analysts' Median Forecast Error prior to the announcement date
Timely forecasts
The Middle category firms
-0.04
0.00
0.04
0.08
0.1 2
0.1 6
0.20
0.24
0.28
0.32
0.36
0.40
0.44
2_2 3_2 4_2 5_2 6_2 7_2 8_2 9_2 1 0_2 1 1 _2 1 2_2 1 _2 2_1 3_1 4_1 5_1 6_1 7_1 8_1 9_1 1 0_1 1 1 _1 1 2_1 1 _1
Calendar month_forecast horizon
Forecast Error, $
19 8 7 -1 9 9 2
19 9 3 -1 9 9 8
1 999-2004

73
Panel C: The Steadiest category firms
Financial Analysts' Median Forecast Error prior to the announcement date
Consensus forecasts
The Steadiest category firms
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
2_2 3_2 4_2 5_2 6_2 7_2 8_2 9_2 1 0_2 1 1 _2 1 2_2 1 _2 2_1 3_1 4_1 5_1 6_1 7_1 8_1 9_1 1 0_1 1 1 _1 1 2_1 1 _1
Month_forecast horizon
Forecast Error, $
19 8 7 -1 9 9 2
19 9 3 -1 9 9 8
1 999-2004

Financial Analysts' Median Forecast Error prior to the announcement date
Timely forecasts
The Steadiest category firms
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
2_2 3_2 4_2 5_2 6_2 7_2 8_2 9_2 1 0_2 1 1 _2 1 2_2 1 _2 2_1 3_1 4_1 5_1 6_1 7_1 8_1 9_1 1 0_1 1 1 _1 1 2_1 1 _1
Calendar month_forecast horizon
Forecast Error, $
19 8 7 -1 9 9 2
19 9 3 -1 9 9 8
19 9 9 -2 0 0 4

Figure 5. Financial analysts’ median forecast error for the Most Volatile, Middle, and the Steadiest
category firms prior to the earnings announcement date. Consensus forecasts are from the IBES
Summary file. Timely forecast are constructed from the IBES Detail file. Forecast error is the median
forecast error in $; Calendar month_forecast horizon denotes the calendar month when forecasts are
made and the forecast horizon. For instance, data points at 2_2, …, 1_2 correspond to two-year-ahead
forecasts that are produced in February of year t-1, …, January of year t, and 2_1, …, 1_1 correspond to
one-year-ahead forecasts that are produced in February of year t, …, January of year t+1. Data points at
1_2 and 1_1 correspond to two- and one-year-ahead forecasts that are made in January when previous
year earnings have not been released yet. Points with unfilled background represent data points that are
not significantly different from zero at the 5% level.

74
period. In the 1999-2004 period, it is about 2 - 3 cents pessimistic starting fifteen
months prior to a fiscal year end.
Finally, note a drop in the forecast error in the month of February in the second
year of the forecasting. This decline is more visible in the case of the consensus
forecasts for the Most Volatile category firms. It is caused by the fact that forecast
errors in that month are calculated only over the forecasts produced for companies
whose prior year actual earnings have already been released. As a result, the amount
of uncertainty about those companies is reduced that causes the analysts’ forecast
optimism to decline.
To summarize, the analysts’ forecast optimism reduces as the announcement
date approaches across volatility categories and time intervals. The timely analysts’
forecast errors for companies with volatile earnings are optimistic for the entire two
year forecasting period in 1987-1992 and for up to three month prior to the fiscal year
end in the most recent 1999-2004 period. In contrast, for the firms with the least
volatile earnings, the timely forecast error is only slightly optimistic in the 1987-1992
period, and pessimistic throughout the forecast horizon in the 1993-1998 and 1999-
2004 periods.

B. Model of financial analysts’ forecasting behavior.
Here, we propose a simple model that depicts changes in analysts’ forecasts
throughout the two-year forecast horizon. In this model, the forecasting behavior of
analysts is characterized by their reactions to actual earnings releases. First, analysts
observe actual annual earnings, a
-2
, and produce two-year-ahead forecasts by

75
multiplying these earnings by some factor. This multiplication factor may differ if the
released earnings are positive or negative. Then, analysts revise their forecasts each
month, m
-2
= [1, …, 11]. In the second stage, the next year actual earnings, a
-1
, become
available. In response, financial analysts adjust their forecasts by some multiple of the
realized difference in earnings, a
-1
- a
-2
. Since analysts may react differently to the
growth or decline in actual earnings, we should consider positive and negative changes
in earnings separately. In addition, subsequent monthly revisions of forecasts, m

= [12,
…, 23], may also depend on the sign of the change in actual earnings, and therefore
they are modeled independently. The next linear relationship is employed to describe
the model:
ε γ β γ β + + + + =
− −
pos pos
m
m a d m a f
1 1 2 0 2 0
) ( (17)
ε γ β + + +
neg neg
m a d
'
1
'
1
)(,
where a
-2
is actual earnings two years prior to the announcement date, m
-2
and m are
the calendar months when the two- and one-year-ahead forecasts are made (m
-2
takes
values from zero in February
t-1
to eleven in January
t
, m - from twelve in February
t
to
twenty-three in January
t+1
), d(a) is the change in actual EPS from year t-2 to t-1,
23 ..., 12, m if EPS - EPS ) (
2 - t 1 - t
= = a d ,
11 ..., 0, m if 0 = = ,
and superscripts pos and neg denote situations when d(a)>0 and d(a)<0, respectively,
0 , 0 ) ( = =
pos pos
m a d if (EPS
t-1
- EPS
t-2
) < 0
0 , 0 ) ( = =
neg neg
m a d if (EPS
t-1
- EPS
t-2
) > 0.

76
Note that the Month variables, m
-2
and m, are multiplied by the actual earnings two
years prior to the fiscal year end, a
-2
, so that the coefficients γ
0
and γ
1
represent the
percentage change in monthly analysts’ forecasts relative to initial actual earnings.
Cases when the initial earnings are positive, a
-2
> 0, and negative, a
-2
< 0 are
considered separately.
As we observed in Figure 5, the analysts’ forecasting behavior differs over
time and volatility categories. Therefore, we estimate the regression coefficients
separately for companies with different volatilities and for different periods. In
addition, a modification of the Chow test is also performed to test the hypotheses

'
1 1
β β = and
'
1 1
γ γ = for each period and volatility category. The former hypothesis is
uniformly rejected at the 5% level, while the latter is rejected with the exception of
two cases
39
. The results are presented in Table 12.
First, let us consider the a
-2
> 0 case. In the most recent 1999-2004 period,
predicting two-year-ahead earnings, financial analysts on average multiply actual
earnings of the Most Volatile, Middle and the Steadiest category firms by 1.08, 1.22,
and 1.21, respectively. Then, these initial forecasts are perceived to be high and
revised downward each month by about 3%, 1%, and 0.1%, respectively. When the
next year actual earnings, a
-1
, become available, financial analysts adjust their
forecasts again to account for the newly revealed information. If the change in annual
earnings is positive, d(a)>0, depending on the volatility category, analysts inflate their
forecasts on average by 0.83, 1.05, and 1.30 of the change in earnings in the case of

39
See G. Chow (1960) or F. Fisher (1970) for the discussion of the test. The exceptions are the Middle
and the Steadiest category cases in the 1999-2004 period.

77
the Most Volatile, Middle, and the Steadiest category companies. If the change is
negative, d(a)<0, they deflate their forecasts but by the relatively smaller factors: 0.34,
0.67, and 0.78. Thus, the greater the volatility of earnings, the smaller the
multiplication parameters, β
0
and β
1
40
. That is analysts exhibit the regression, which is
consistent with the theory of forecasting. On the other hand, we observe asymmetric
responses to changes in earnings with a different sign. A negative change has much
smaller impact (0.34-0.78) on the analysts’ forecast revisions than a positive one
(0.83-1.30). As we are going to show in the next section, it leads to an increase in the
analysts’ forecast bias when a negative change in earnings is realized.
Then, once again, monthly downward reductions in forecasts continue. They
are the largest for the Most Volatile category firms: depending on the period 1.2% -
1.3% in the positive and 2.2% - 2.6% in the negative change in earnings cases. The
corresponding decreases for Steadiest category firms are smaller: 0.05% - 0.09% and
0.02% – 0.09%, respectively. Therefore, as the volatility of earnings increases,
monthly adjustments become greater. It implies that financial analysts tend to
overreact to positive and under-react to negative changes in earnings more as the
uncertainty about a company’s future prospects enlarges. To improve the forecast
accuracy, they should react less to positive changes in earnings (inflate forecasts by a
smaller coefficient) and in contrast, respond more to negative changes in earnings
(deflate forecasts by a greater coefficient).

40
In the 1987-1992 period, the pattern is similar with the exception that the monthly deflation
coefficients are relatively smaller. It helps to explain the observed higher optimistic forecast biases in
this period.

78
The next step is to analyze the negative initial earnings case, a
-2
<0. In the
1987-1992 period, observing negative annual earnings, financial analysts produced
positive earnings forecasts, on average equal to 0.30, 0.39 and 0.83 of actual earnings
absolute values in the case of the Most Volatile, Middle and the Steadiest category
firms, respectively. It may be explained by analysts viewing these negative earnings as
temporary deviations due to the weak macroeconomic situation in that period. In
contrast, in the 1999-2004 period, analysts’ initial forecasts are negative: they are on
average equal to 0.11, 0.29, and 0.30 of the actual negative earnings for the Most
Volatile, Middle and the Steadiest category firms, respectively.
Comparing the results for two periods, we detect that the amount of initial
optimism in analysts’ forecasts has decreased over time. It is completely in line with
our prior findings that the analysts’ optimistic forecast error is smaller in the 1999-
2004 than in the 1987-1992 period. On the other hand, in both periods, the greater the
volatility of earnings, the closer the analysts’ forecasts to zero. It suggests that
negative earnings of a company with volatile earnings are viewed by analysts only as a
temporary deviation due to the explosive nature of the earnings generating process.
This behavior is apparently a significant contribution to the analysts’ large optimistic
forecast bias for this category of firms in the two-year-ahead forecast horizon.
Then, financial analysts monthly increase their estimates for the Steadiest
category firms on average by 1.7% - 3.8%, and leave the projections almost
unchanged for the Middle and Most Volatile category companies. Thus, there are no
downward monthly reductions as in the positive initial earnings case. On average,

79
analysts take status quo and wait for more information to arrive. The rest is similar to
the positive earnings case. When a
-1
earnings are released, analysts increase their
forecasts if the change in earnings is positive: on average by 0.68 - 0.69, 0.76 - 0.92,
and 0.79 - 1.05 of the change for the Most Volatile, Middle and the Steadiest category
firms, respectively. If the change in earnings is negative, they decrease their forecasts
but by the relatively smaller amounts: 0.00 - 0.12, 0.36 - 0.59, and 0.83 - 1.30. Finally,
in the last twelve months prior to the announcement date, analysts decrease their
forecasts by 2.2% - 9.4% per month depending on the volatility category and the
period considered. Overall, the magnitude of analysts’ monthly downward revisions is
much larger than in the case of positive initial earnings. It once again points at the
greater analysts’ optimism for companies with negative earnings. Thus, to improve the
forecast accuracy, observing negative earnings, analysts should produce lower initial
forecasts. In other words, there exists more information in negative earnings about the
future than analysts originally think.
To conclude, the results suggest that financial analysts generally overreact to
positive earnings releases and under-react to negative. When a positive earnings figure
is released, financial analysts on average inflate it by such a number that later on they
are required to make monthly downward adjustments. It is overreaction. Similarly, if
actual earnings are negative, analysts also produce a forecast that is too high, so that
there is a need for subsequent downward revisions. This is underreaction.

80
C. Actual earnings and the analysts’ forecast bias.
In this section, we examine implications of the analysts’ forecasting behavior
for the dynamics of the forecast bias. We employ a modification of Equation (17) with
the independent variable being the analysts’ forecast error. The results for the positive
initial earnings case, a
-2
> 0, are presented in Table 13, panel A, and for the negative
case, a
-2
< 0 in Panel B. In the 1999-2004 period, when financial analysts are first
called upon producing earnings forecasts, they on average generate the optimistic
forecast error that is equal to 0.40 and 0.19 of actual positive earnings for the Most
Volatile and the Middle category firms, respectively; whereas they produce no bias for
the Steadiest category companies. If actual earnings are negative, the bias is about
0.20 of their absolute values for all categories of firms. In the 1987-1992 period, initial
forecast errors are higher in relative terms for both, positive and negative earnings
cases.
In the case of positive initial earnings, the optimistic forecast error is then
reduced each month by 1.7% - 2%, 0.7% - 1.1%, and 0.0% - 0.1% depending on the
period for the Most Volatile, Middle and the Steadiest category firms, respectively. In
the final forecasting year, the forecast error continues to decrease by 1.8% - 2.1%,
0.8% - 1.0%, and 0.1% - 0.2% per month for each category firms, respectively. Thus,
the greater the volatility of earnings, the greater the initial optimism and the larger its
monthly downward reductions.
When the interim annual earnings, a
-1
, are released, the optimistic forecast
error reduces by 1% - 13% in the 1999-2004 period and by 0% - 5% in the 1987-1992

81

Panel A: EPS two years prior to the announcement date are positive, a
-2
>0
1987-1992 1999-2004
Earning pattern
a
-2
m
-2
da m a
-2
m
-2
da m

1.07 -0.018 1.07 -0.013 1.08 -0.030 0.83 -0.012 da>0
Most Volatile
(1)
0.19 -0.026 0.34 -0.022 da<0
1.18 -0.008 1.26 -0.011 1.22 -0.010 1.05 -0.011 da>0
Middle
(3)
0.34 -0.013 0.67 -0.012 da<0
1.17 -0.000* 1.32 -0.005 1.21 -0.001 1.30 -0.009 da>0
Steadiest
(5)
0.58 -0.002 0.78 -0.009 da<0

Panel B: EPS two years prior to the announcement date are negative, a
-2
<0
1987-1992 1999-2004
Earning pattern
a
-2
m
-2
d(a) m a
-2
m
-2
d(a) m

-0.30 0.002* 0.68 -0.041 0.11 0.009 0.69 -0.022 da>0
Most Volatile
(1)
0.12 -0.024 0.01* -0.032 da<0
-0.39 -0.003* 0.76 -0.043 0.29 -0.001* 0.92 -0.025 da>0
Middle
(3)
0.36 -0.039 0.59 -0.038 da<0
-0.83 -0.038 0.79 -0.069 0.30 -0.017 1.05 -0.028 da>0
Steadiest (5)
1.30 -0.094 0.83 -0.040 da<0
Table 12. Financial analysts’ forecast revisions for the Most Volatile, Middle, and the Steadiest
category firms prior to the earnings announcement date. EPS forecasts produced in each calendar month
are regressed on a
-2
- earnings two years prior to the announcement date, m
-2
- the calendar month when
the two-year-ahead forecasts are made (February
t-1
– January
t
), da = EPS
t-2
-EPS
t-1
, - change in the
actual EPS from year t-2 to t-1, and m - the calendar month when the one-year-ahead forecasts are made
(February
t
– January
t+1
). da>0 and da<0 -denote positive and negative changes in earnings from year t-
2 to t-1, respectively. m
-2
and m are multiplied by the absolute value of a
-2
, so that all monthly revisions
are in percentage terms (a negative sign at m
-2
or m denotes a downward revision and a positive sign -
an upward revision). Companies are divided in categories according to the coefficient of variation of the
change in earnings defined by (12). Asterisks denote insignificance at the 5% level.

82

Panel A: EPS two years prior to the announcement date are positive, a
-2
>0
1987-1992 1999-2004
Earning pattern
a
-2
m
-2
d(a) m a
-2
m
-2
d(a) m

0.53 -0.017 -0.00* -0.021 0.40 -0.020 -0.02 -0.018 da>0
Most Volatile
(1)
-0.06 -0.020 -0.00* -0.018 da<0
0.17 -0.007 -0.01* -0.008 0.19 -0.011 -0.05 -0.010 da>0
Middle
(3)
-0.10 -0.007 -0.07 -0.010 da<0
0.05 -0.001 -0.02 -0.002 0.00* -0.000* -0.13 -0.001 da>0
Steadiest
(5)
-0.04 -0.002 -0.07 -0.00* da<0

Panel B: EPS two years prior to the announcement date are negative, a
-2
<0
1987-1992 1999-2004
Earning pattern
a
-2
m
-2
d(a) m a
-2
m
-2
d(a) m

-0.35 -0.012 0.03* -0.013 -0.17 -0.010 -0.01 -0.007 da>0
Most Volatile
(1)
-0.22 -0.014 -0.08 -0.009 da<0
-0.30 -0.010 -0.05 -0.010 -0.20 -0.009 -0.03 -0.008 da>0
Middle
(3)
-0.14 -0.010 -0.12 -0.010 da<0
-0.08 -0.003 -0.04* 0.000* -0.19 -0.009 -0.07 -0.008 da>0
Steadiest
(5)
-0.17* -0.006* -0.13 -0.009 da<0
Table 13. Financial analysts’ forecast errors for the Most Volatile, Middle, and the Steadiest category
firms prior to the earnings announcement date. Median forecast errors, FE = actual EPS – predicted
EPS, produced in each calendar month are regressed on a
-2
- earnings two years prior to the
announcement date, m
-2
- the calendar month when the two-year-ahead forecasts are made (February
t-1
– January
t
), d(a) =EPS
t-1
-EPS
t-2
, - change in the actual EPS from year t-2 to t-1, and m - the calendar
month when the one-year-ahead forecasts are made (February
t
– January
t+1
). da>0 and da<0 - denote
positive and negative changes in earnings from year t-2 to t-1, respectively. m
-2
and m are multiplied by
the absolute value of a
-2
, so that all monthly revisions are in percentage terms (a negative sign at m
-2
or
m denotes a downward revision and a positive sign - an upward revision). Companies are divided in
categories according to the coefficient of variation of the change in earnings defined by (12). Asterisks
denote insignificance at the 5% level.

83
period if the change in earnings is positive. On the contrary, if the change is negative,
it increases by up to 13% in the 1999-2004 and up to 22% in the 1987-1992 period.
Thus, analysts exhibit an excessive optimism for companies whose earnings decline.
To conclude, the analysts’ systematic optimism observed in forecast errors is at
least partially caused by the next reason. Analysts are too bullish in their reactions to
actual earnings releases, especially if changes in earnings are negative. The degree of
the analysts’ optimism generally increases with the difficulty of the forecasting task.
The more uncertainty exists about future earnings of a company, the greater the
analysts’ optimistic forecast error. The explanation for this behavior is offered in the
cognitive psychology literature, which shows that people commonly over-predict in
highly uncertain situations. For example, Kahneman and Tversky (1973) report that
subjects confidently predict academic performance of an individual based on scare
personality information, even when this information is attributed to an unreliable
source.

84
CHAPTER III
MACROECONOMIC ACTIVITY AND FINANCIAL ANALYSTS’
FORECAST ERROR
In contrast to the above crossectional investigation, this chapter examines
temporal variations in the analysts’ forecast error. Section III.1 considers two major
hypotheses: the financial analysts’ optimistic forecast bias is a function of the
expected economic performance, and that it is a function of the historical economic
activity. The disagreement among financial analysts during and around economic
recessions is analyzed in Section III.2, while Section III.3 studies the relationship
between the analysts’ forecast error and macroeconomic variables.

III.1 Financial Analysts’ Forecast Bias and the Overall Economic
Activity

The first hypothesis examined in this section is that producing earnings
forecasts, financial analysts consider future macroeconomic performance. The rational
behind this idea is that analysts as professionals should collect and interpret
information at all stages of the bottom-up or top-down financial analysis: firm
specific, industry and the overall economy. However, evidence from the 2000 internet
stock bubble burst indicates that financial analysts did not pay proper attention or
incorrectly foresaw the industry’s prospects. They were believed by the exuberant
market and subsequently often blamed for the bubble and astonishing losses
41
. Then, it
is interesting to see if financial analysts take into account the expected overall

41
According to First Call, more than 70% of the 27,000 recommendations outstanding on some 6,000
stocks in November 2000 were strong buys or buys, while less than 1% were sells. “The rating game”,
Money, January 2001.

85
economic activity when making earnings forecasts as classical valuation approaches
suggest.
The implication of the first hypothesis is that the forecast bias is expected to
stay unchanged throughout different macroeconomic scenarios since the future
economic activity is already incorporated into earnings forecasts. To demonstrate,
suppose financial analysts produce some bias, b , caused by some other factors than
the economic activity for a specific category of firms. Then, in the case of a positive or
negative change in the GDP growth prediction, analysts may adjust their forecasts
upward or downward, respectively, so that the initial bias, b , stays approximately
unchanged. We can even go a step further and suppose that financial analysts may
overreact to macroeconomic predictions. In this scenario, the forecast bias is expected
to increase in the case of a positive change prediction and decrease in the case of a
negative change prediction in the GDP growth. In either case, analysts are assumed to
respond to forecasts of the macroeconomic condition. Accordingly, the coefficient in
the regression of time-series of the analysts’ median forecast error on the predicted
change in the nominal GDP growth is expected to be zero or positive. As a source of
expectations about future prospects of the overall economy, financial analysts can
utilize predictions of macroeconomic forecasters or produce their own forecasts by,
for example, examining the yield spread
42
.

42
Several studies investigate the relationship between the slope of the yield curve and the future
economic activity. Among others, Estrella and Hardouvelis (1991), Bernard and Gerlach (1998), Ang,
Piazzesi and Wei (2005).

86
In contrast to the just described model, an alternative hypothesis is that
financial analysts do not take the forecasted macroeconomic condition into account. In
this model, analysts hold to their previous expectations. It leads to an increase in the
optimistic forecast bias if a negative change in the GDP growth is realized or to a
decrease in bias if a change in the GDP growth is positive. Among others, reasons for
the analysts’ refusal to lower their earning expectations in times of weak anticipated
economic performance may include the following: analysts cannot foresee economic
downturns and do not trust macroeconomic forecasters; they may naively believe that
a macroeconomic situation has no lasting effects on firms’ earnings, or that
macroeconomic downturns are very short-lived. The empirical prediction of this
hypothesis is that the analysts’ forecast bias increases during recessions and decreases
in economic expansions.
The results for the Most Volatile and the Steady category firms are presented in
Panel A of Table 14. The analysts’ median forecast error produced at the beginning of
a fiscal year (in the month of March) is regressed on the change in the GDP growth
predicted by the Survey of Professional Forecasters
43
. It is calculated as Predicted ∆ =
forecasted g
t
– g
t-1
for the one-year-ahead forecast horizon and Predicted ∆ =
2×(forecasted g
t-1
– g
t-2
) for the two-year-ahead forecast horizon, where g
t
is the
growth in the nominal GDP in a year t. For example, the nominal GDP growth in 1986
is 5.8%, while the predicted growth for 1987 is 6.7% and the actually realized is 6.2%.

43
The source of the data is the Federal Reserve Bank of Philadelphia. Note that the correlation between
predicted and subsequently realized changes in the GDP growth is equal to 0.5 and statistically
significant at the 1% level.

87
Then, the predicted change for 1987 is 0.9% and the actual change is 0.4%. Note that
predicted changes are observed by financial analysts at the time of earnings
forecasting.
As a contradiction to the first proposed model, the relationship between the
analysts’ forecast error and the predicted change in the GDP growth is negative. For
the Most Volatile category companies, the optimistic forecast bias on overage
increases by about 13 - 14 cents per 1% predicted decline in the overall economic
output. It suggests that financial analysts do not fully exploit information about future
prospects of the economy when making their earnings forecasts for individual
companies. Note that while coefficients for the Volatile and Middle category firms
generally lie between the coefficients of the two categories presented in Table 14,
coefficients for the Steadiest category companies are mostly statistically insignificant
at the 5% level. They are not reported to conserve space.
Next, to determine the outcome of disregard for the future economic activity,
we regress the analysts’ median forecast error on the actually realized change in the
nominal GDP growth and present the results in Panel B of Table 14. The key result is
that the analysts’ forecast error and the macroeconomic activity are negatively related.
On average, the forecast error increases by 17 (24) cents for the Most Volatile and by
1.4 (2.8) cents for the Steady category firms in the case of one- (two)-year-ahead
forecast horizon per 1% decline in the nominal GDP growth.
To facilitate the further discussion, we present the data for the Most Volatile
and the Steady category firms in Figure 6 and 7, respectively. The inverse relationship

88
between the analysts’ optimistic forecast bias produced at the beginning as well as at
the middle of a fiscal year and the GDP growth can be clearly detected. In recession
periods like 1990-1991 or 2001, the optimistic forecast bias increases and reaches
historical maximums. In contrast, in years of the strong economic growth like 1988 or
2004, the optimistic forecast bias becomes minimal. As graphs suggest, financial
analysts did not foresee approaching declines in the economic activity in either 1990
or 2001, and apparently extrapolated the historical GDP growth into the future. The
overall economic output declined that led to larger optimistic forecast biases in these
periods. Furthermore, producing forecasts for the 1991 earnings, financial analysts
have already observed the economic decline in 1990 and had the knowledge of
downward economic growth predictions. However, they failed to reduce their earnings
estimates appropriately. The median forecast error produced in March and September
increased by 10 and 5 cents in the case of the Most Volatile category firms and by 2
and 1 cents in the case of the Steady category firms. The extreme optimism persisted
even after the overall economic activity declined in 1990. Consequently, escalations in
the analysts’ optimistic forecast bias cannot be explained by the idea that economic
declines happen unexpectedly to financial analysts. We observe that financial analysts
not only fail to anticipate weaknesses in the economic condition before a downturn,
but they also fail to sufficiently adjust their forecasts after the downturn settles.
As we have just determined, financial analysts do not fully utilize information
about the future economic activity when making earnings forecasts. Then, the question

89
left to answer is whether analysts extrapolate the historical GDP growth rates into the
future. To check this proposition, we construct the following ratios:
r = (g
t
– g
t-1
)/(g
t-1
-g
t-2
) for the one-year-ahead forecast horizon and
(18)
r = (g
t
– g
t-2
)/[2·(g
t-2
-g
t-3
)] for the two-year-ahead forecast horizon,
where g
t
is the growth in the nominal GDP in a year t. Next, we consider two
situations: first, when the economic activity grows before the one- (two)-year-ahead
forecasts are produced, g
t-1
- g
t-2
> 0 at t-1 (g
t-2
- g
t-3
> 0 at t-2), and when it declines,
g
t-1
- g
t-2
< 0 (g
t-2
- g
t-3
< 0). We call these cases the positive and negative economic
base growth, respectively.
First, suppose the base economic growth is positive. Then, if the ratio is equal
to one, r = 1, the change in the realized GDP growth is equal to the previous period
change, and the initial bias, b , is assumed to remain unchanged. If the ratio is greater
than one, r > 1, the actual growth is greater than the one predicted by the
extrapolation, and the forecast bias decreases. Similarly, if the ratio is less than one, r
< 1, the forecast bias increases. Furthermore, the forecast bias is expected to increase
in an accelerating manner as the economic activity declines, and r becomes negative, r
< 0. Finally, the largest increase in the optimistic forecast error is expected as the
economic growth rates decline by a greater amount than they increased in the
preceding year, which corresponds to the r < -1 case. Note that just the reverse is true
for the negative economic base growth case.
If financial analysts are found to extrapolate the historical economic
performance into the future, we should expect an inverse nonlinear relationship

90
between the analysts’ forecast bias and the modified ratio, (r-1), in the case of the
positive economic base growth, and a direct nonlinear relationship in the case of the
negative. The results of the quadratic fit are presented in Panel C of Table 14. The
upper section demonstrates the results for the positive economic base growth case,
when financial analysts observe an increase in the economic growth at the time of
forecasting. In the lower section, the results for the symmetric case of negative
economic base growth are presented.
First, if the change in the realized economic growth rates is positive and equal
to the historical one (g
t
- g
t-1
= g
t-1
- g
t-2
, and > 0) the financial analysts’ bias is equal to
18 (54) cents for the Most Volatile category firms in the case of the one- (two)-year-
ahead forecast horizon. If the change is equal and negative (g
t
- g
t-1
= g
t-1
- g
t-2
, and <
0), the corresponding bias is 73 (114) cents. We call these bias values the default
biases. The observed inequality between the default biases suggests that financial
analysts do not anticipate negative changes in the economic growth to continue. They
do not extrapolate down.
Second, in accordance with the model, the analysts’ optimistic forecast error
changes as the economic activity fluctuates. In the case of the positive base growth, if
the GDP growth accelerates enough for r to become greater than one, the analysts’
forecast bias reduces. In contrast, if the GDP growth stay unchanged (r = 0), the
forecast bias increases: for the Most Volatile category firms, it grows to 29 (85) cents
in the case of one- (two)-year-ahead forecast horizon, which is 11 (31) cents higher
than the default bias. Furthermore, if the GDP growth declines (r < 0), the forecast

91
bias growth accelerates. When r = -1, the analysts’ forecast bias is 42 (122) cents,
which is already 13 (37) cents higher than in the previous r = 0 state. Similarly, in the
negative base growth case, as the growth in the GDP increases the analysts’ forecast
bias decreases. For the Most Volatile category firms, when r changes from one to zero,
the forecast error declines by 21 (39) cents; when r goes from zero to minus one, it
declines by greater 29 (45) cents. Overall, the quadratic fit explains 62% - 83% of
variability in the time-series of financial analysts’ median forecast error in the case of
the Most Volatile category firms, and 22% - 64% in the case of the Steady category
companies.
To conclude, financial analysts seem to ignore predictions of the future
economic activity when making their earnings forecasts and extrapolate the positive
but not the negative economic growth rates into the future. It leads to the inverse
relationship between the optimistic forecast bias and the overall economic activity.
Throughout the years of strong economic growth, the analysts’ forecast bias
diminishes, and during the years of stagnation, it becomes relatively large.

III.2 Disagreement among financial analysts and the overall
economic activity

Another way to check the hypotheses discussed in the previous section is to
examine the divergence of analysts’ opinions in different macroeconomic scenarios.
The overall economic uncertainty augments during or even before economic
downturns, causing future prospects of companies to be more indecisive. If analysts
take the expected economic activity into consideration when making their earnings

92
forecasts, there should be a greater divergence of individual opinions before economic
recessions. On the contrary, if analysts are found to ignore the economic activity, the
divergence among analysts’ opinions is expected to stay nearly unchanged.
We consider two recession periods: July of 1990 - March of 1991 and March -
November of 2001. The interest in these recession periods stems from their very
definition as periods with the increased uncertainty and poorer corporate performance.
First, analysts’ forecasts made after the onset of recessions are separated from those
made prior (1988-1989 and 1999-2000) and right after the recessions (1992-1993 and
2002-2004). Then, the divergence among analysts’ opinions is measured by the
standard deviation of their individual forecasts. In addition, the number of analysts
issuing forecasts is calculated in the recession periods relative to the surrounding
years. Table 15 presents the results.
Standard deviations of analysts’ one- and two-year-ahead forecasts (0.27 and
0.42 respectively) produced in March of 1990, (that is just before the onset of the
1990-1991 recession) are not statistically greater than those in the surrounding
years(0.25 and 0.40). On the other hand, the divergence among analysts’ individual
forecasts produced during the recession (September of 1990 and March of 1991) and
right after it (September of 1991) is greater than in the adjoining years and statistically
significant in most cases
44
. For instance, the standard deviation of one-year-ahead
analysts’ forecasts produced in March of 1991 increases from the average value of

44
Note that the NBER announce official dates of a recession with a significant time lag. Thus, in
September of 1991, financial analysts did not have the official recognition of the recession end in
March of 1991.

93
0.25 in the surrounding years to 0.33 and from 0.06 to 0.09 in the case of the Most
Volatile and Steady category firms, respectively. For the two-year-ahead forecast
horizon, we observe a similar picture: forecasts produced from September of 1990 to
September of 1991 for the 1991 and 1992 fiscal years exhibit higher divergence of
analysts’ opinions (though increases are not statistically significant for the Steady
category firms).
The above results are fully replicated by the data from the second recession in
our sample. Namely, one- and two-year-ahead forecasts produced during the 2001
recession exhibit a higher divergence in analysts’ opinions. For example, for the Most
Volatile category firms, the standard deviation of forecasts produced in March of 2001
increases from the average value of 0.17 (0.24) in the surrounding years to 0.19 (0.30)
in the case of the one- (two)-year-ahead forecast horizon.
The results in the bottom section of Table 15 show that the average number of
analysts issuing forecasts, with the exception of two-year-ahead forecasts for 2002
earnings, do not decrease before or during recessions. It suggests that financial
analysts do not self-select to produce forecasts on the basis of the macroeconomic
condition as they do based on the statistical characteristics of earnings.
To summarize, the disagreement among financial analysts regarding future
prospects of companies increases only during the recession periods, but not before
them. This result entirely supports our previous conclusion that financial analysts tend
to ignore future prospects of the overall economy when making their earnings
forecasts.

94
Panel A
Earnings pattern One-year-ahead Two-year-ahead
Const Predicted ∆ R
2
Const Predicted ∆ R
2

Most volatile (1)

Steady (4)
0.38
(5.6)
0.027
(2.8)
-0.14
(2.5)
-0.004*
(0.5)
28%

1%
0.80
(7.2)
0.102
(4.3)
-0.13
(2.9)
-0.010*
(1.0)

35%

7%
Panel B
Const Actual ∆ R
2
Const Actual ∆ R
2

Most volatile (1)

Steady (4)

0.43
(8.5)
0.028
(3.6)
-0.17
(4.8)
-0.014
(2.7)
59%

31%
0.84
(13.8)
0.107
(5.8)
-0.24
(7.4)
-0.028
(2.8)
77%

33%
Panel C Positive change in g
GDP
, ∆
-t

Const r-1 (r-1)
2
R
2
Const r-1 ( r-1)
2
R
2

Most volatile (1)

Steady (4)
0.18

0.005
-0.10

-0.006
0.01

0.001
62%
22%
0.54

0.031
-0.28

-0.053
0.03

0.007
70%

60%
Negative change in g
GDP
, ∆
-t

Most volatile (1)

Steady (4)
0.73

0.056
0.19

0.019
-0.02

-0.003
78%

58%
1.14

0.099
0.36

0.017
-0.03

-0.000
83%

64%
Table 14. Financial analysts’ median forecast error at the beginning of a fiscal year in the case of one-
(two)-year-ahead forecast horizon and the economic activity. Companies are divided in categories
according to the coefficient of variation of the change in earnings defined by (12). t-statistics in absolute
value are in parentheses. Asterisks denote insignificance at the 5% level.
Panel A: Median forecast errors for the Most Volatile and Steady category firms are regressed on the
change in the nominal GDP growth predicted by the Survey of Professional Forecasters and For the
one-year-ahead forecast horizon: Predicted ∆ = forecasted g
t
– g
t-1
, Actual ∆ = realized g
t
– g
t-1
; for the
two-year-ahead forecast horizon: Predicted ∆ =2*(forecasted g
t-1
– g
t-2
), Actual ∆ = realized g
t
– g
t-2.

Panel B: Median forecast errors for the Most Volatile and Steady category firms are regressed on the
actually realized change in the nominal GDP growth.
Panel C: Quadratic fit for the analysts’ median forecast errors for the Most Volatile and Steady category
firms; r is defined as the realized change in the nominal GDP growth over the previous year growth. For
the one-year-ahead forecast horizon: r = (g
t
– g
t-1
)/(g
t-1
- g
t-2
), and for the two-year-ahead forecast
horizon: r = (g
t
– g
t-2
)/[2·(g
t-2
- g
t-3
)]. Positive (Negative) change in g
GDP
, ∆
- t
,denotes that the change in
the nominal GDP observed by analysts at t-1 or t-2, when making one- or two-year-ahead predictions
for year t or t+1, is greater (less) than zero, g
t-1
- g
t-2
>0 (<0),or g
t-2
- g
t-3
>0 (<0).

95
Panel A: standard deviation among financial analysts’ individual forecasts
The Most Volatile category firms The Steady category firms

One-year-ahead Two-year-ahead One-year-ahead Two-year-ahead
Time period, t March September March September March September March September
Average around
recession,
σ

1990

1991

1992
0.25
0.27*
(-0.9)
0.33
(-5.4)
0.20
0.25
(-2.5)
0.27
(-3.5)
0.40
0.42*
(-0.9)
0.38*
(0.7)
0.48
(-2.9)
0.28
0.29*
(-1.5)
0.30
(-2.4)
0.29*
(-1.0)
0.06
0.06*
(1.7)
0.09
(-55.0)
0.05
0.06
(-4.2)
0.06
(-4.0)
0.10
0.11*
(-0.8)
0.09*
(5.0)
0.11*
(-1.4)
0.08
0.09*
(-0.8)
0.09*
(-0.3)
0.09*
(-0.4)
Average around
recession,
σ

2001

2002
0.17
0.19
(-3.4)
0.12
0.15
(-3.6)
0.24
0.22*
(0.8)
0.30
(-2.4)
0.23
0.21*
(1.1)
0.28
(-2.5)
0.06
0.06*
(-0.8)
0.05
0.05*
(-1.0)
0.09
0.07*
(1.9)
0.09*
(-0.2)
0.08
0.07*
(2.2)
0.09*
(-2.2)
Panel B: number of financial analysts issuing forecasts
The Most Volatile category firms The Steady category firms

One-year-ahead Two-year-ahead One-year-ahead Two-year-ahead
Time period, t March September March September March September March September
Average around
recession, n
1990

1991

1992
9.1
9.4*
(-0.8)
9.7*
(-1.6)
7.9
8.5*
(-2.3)
8.5*
(-2.3)
4.6
3.9*
(1.3)
4.0*
(1.1)
5.2*
(-1.2)
7.1
7.6*
(-3.2)
8.2*
(-7.4)
8.1*
(-6.5)
10.3
10.6*
(-1.2)
10.8*
(-2.1)
9.9
10.2*
(-0.8)
10.3*
(-1.1)
4.7
3.9*
(1.3)
3.9*
(1.3)
4.7*
(-0.1)
9.0
9.7*
(-3.4)
9.5*
(-2.4)
9.7*
(-3.2)
Average around
recession, n
2001

2002
7.3
7.3*
(-0.3)
6.8
6.9*
(-0.3)
5.2
5.6*
(-2.5)
4.7
(2.5)
6.7
6.8*
(-1.1)
6.7*
(0.2)
7.5
7.4*
(0.2)
7.0
6.5
(4.2)
5.7
5.5*
(0.8)
4.8
(3.2)
7.1
6.8*
(1.7)
6.6
(2.9)
Table 15. Standard deviation among financial analysts’ individual forecasts (Panel A) and the average
number of analysts issuing forecasts (Panel B) in and around economic recessions at the beginning and
the middle of a fiscal year in the case of the one- and two-year-ahead forecast horizon. Average around
recession numbers,
σ
and n , are calculated using two years before and two years after the official
recession periods determined by the NBER. Data that correspond to forecasts made after the onset of a
recession are in italic. Companies are divided in categories according to the coefficient of variation of
the change in earnings defined by (12). t-statistics are in parentheses. Asterisks denote insignificance at
the 5% level for the hypothesis H0:
t
σ σ ≥
(Panel A) and H0:
t
n n ≤
(Panel B).

96
Financial Analysts' Forecast Error and Economic Activity
Firms with the Most Volatile earnings, one-year-ahead forecasts
-0.25
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005
Forecast Error, $
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
g
GDP
, %
Media n FE, M arch
Media n FE, S eptem ber
GDP growth fo reca st
GDP gro wth

Financial Analysts' Forecast Error and Economic Activity
Firms with the Most Volatile earnings, two-year-ahead forecasts
-0.25
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005
Forecast Error, $
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
g
GDP
, %
Median F E, March
Median F E, Septem ber
GDP gro wth fo recas t
GDP gro wth
Figure 6. Financial analysts’ median forecast error for the Most Volatile category firms at the beginning
and the middle of a fiscal year in the case of the one- (two)-year-ahead forecast horizon and the
economic activity. Median FE is the median forecast error in $, left scale; GDP growth is the growth in
the nominal GDP in %, GDP growth forecast is the forecasted growth in the nominal GDP in %
(Survey of Professional Forecasters, compounded growth of median quarterly growth forecasts), right
scale. Companies are divided in categories according to the coefficient of variation of the change in
earnings defined by (12).

97
Financial Analysts' Forecast Error and Economic Activity
Firms with the Steady earnings, one-year-ahead forecasts
-0.04
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.36
0.40
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005
Forecast Error, $
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
g
GDP
, %
Median FE, Marc h
Median FE, Septembe r
GDP gro wth fo recas t
GDP gro wth

Financial Analysts' Forecast Error and Economic Activity
Firms with the Steady earnings, two-year-ahead forecasts
-0.04
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.36
0.40
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005
Forecast Error, $
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
g
GDP
, %
Me dia n F E, M a rc h
Me dian FE, Septembe r
GDP gro wth fo recas t
GDP gro wth
Figure 7. Financial analysts’ median forecast error for the Steady category firms at the beginning and
the middle of a fiscal year in the case of the one- (two)-year-ahead forecast horizon and the economic
activity. Median FE is the median forecast error in $, left scale; GDP growth is the growth in the
nominal GDP in %, GDP growth forecast is the forecasted growth in the nominal GDP in % (Survey of
Professional Forecasters, compounded growth of median quarterly growth forecasts), right scale.
Companies are divided in categories according to the coefficient of variation of the change in earnings
defined by (12).

98

III.3 Financial Analysts’ Forecast Bias and Macroeconomic
Variables

The analysis above shows that some fraction of the analysts’ forecast bias may
be attributed to unanticipated macroeconomic events. Here, we test this conjecture by
examining the relationship between the analysts’ forecast bias and macroeconomic
factors similar to those produced by Chen, Roll and Ross (1986)
45
. For the simplicity
of discussion, we chose to measure economic innovations only over the one-year
forecast horizon and consider analysts’ forecasts produced at the beginning of a fiscal
year (in the month of March). Thus, financial analysts make their earnings predictions
observing the previous year values of macroeconomic variables that are normally
released in the middle of January
46
. Changes in macroeconomic variables are
calculated over the January - December period that corresponds to the calendar fiscal
year of companies analyzed in this study.
The first macroeconomic variable we choose to consider is the Unanticipated
Inflation. It is defined as:
) (
1 t t t t
I E I UI
−
− = , (19)
where I
t
is the realized inflation in year t calculated as the percentage change in the
Consumer Price Index over that year. For series of the expected inflation, we use two
proxies. First, we compute it by compounding the predicted quarterly growth rates of

45
They study whether economic forces other than the systematic risk may explain stock returns.
46
The source of macroeconomic data is the Federal Reserve System.

99
the CPI Index that come from the Survey of Professional Forecasters. As an
alternative way to estimate it, we employ the Fisher’s equation:
) ( ) (
, 1 , 1 1 t t t t t t
R E TB I E
− − −
− = , (20)
where the expected inflation for year t is equal to the return on the one-year T-bill,
known at the end of the t-1 period, minus the expected real return on that T-bill at the
end of t-1. The expected real return series are constructed by looking at the ex post real
returns, ( )
t t t
I TB −
− , 1
, and detecting that this series follows the ARIMA(1,1,1) process
with parameters (0.60,1,0.85)
47
. The impact of the unanticipated inflation on a firm’s
earnings depends on prices of inputs and outputs and the firm’s inventory method
(LIFO or FIFO). Overall, the use of the historical cost accounting in US implies a
positive correlation between a company’s earnings and the unanticipated inflation.
Therefore, as the unanticipated inflation increases, firms’ earnings raise and the
analysts’ forecast bias is expected to decrease.
The second macroeconomic variable is the Growth in the Industrial
Production:
1
1
−
−
−
=
t
t t
t
IP
IP IP
GIP , (21)
where IP
t
is the seasonally adjusted industrial production in December of year t. Note
that we do not find it is necessary to decompose this variable into the expected and
unexpected components, since as shown in the previous section financial analysts

47
To find a suitable model specification and to estimate parameters, we adopt the Box and Jenkins
(1970) modeling technique. Parameters are estimated by OLS with the Schwarz information criterion as
a guide to the model selection.

100
appear not to take the expected economic activity into consideration. Growth in the
industrial production denotes growth in companies’ sales. With the assumption of
constant earnings margin, it leads to the growth in actual corporate earnings.
Therefore, we may expect a positive relationship between the GIP and corporate
earnings and as a result, a negative relationship between the GIP and the analysts’
optimistic forecast bias.
Next, we consider the Change in the Default Spread:
1 10 10
) ( ) (
−
− − − =
t Baa t Baa
r r r r CDS , (22)
where r
Baa
and r
10
are the returns on portfolios of Baa rating bonds and ten-year to
maturity Treasury notes. The agents’ risk aversion increases in periods of economic
uncertainty. As a result, the required rate of return on corporate bonds raises, and the
change in the default spread increases. Thus, the change in the default spread over the
year horizon may be viewed as a signal of deteriorating macroeconomic situation and
decreasing corporate earnings. We anticipate a negative relationship between the
change in the default spread and the corporate earnings and a positive relationship
between the CDS and the analysts’ forecast bias.
To capture effects caused by changes in the shape of the term structure of
interest rates, we employ another interest rate variable - Change in the Term Spread:
1 3 10 3 10
) ( ) (
−
− − − =
t m t m
r r r r CTS , (23)
where r
10
and r
3m
are the rates on ten-year and three-month to maturity Treasury notes
and bills, respectively. This measure gives us a change in forward-looking estimates of
interest rates faced by corporations. The term spread increases in periods of economic

101
downturns as future interest rates and the economic activity are expected to increase,
and current corporate earnings decline. In contrast, when the term spread decreases,
the economy is in the expansionary phase, and the corporate earnings grow. Therefore,
we can expect a negative relationship of the change in the term spread with the
corporate earnings and a positive relationship with the analysts’ optimistic bias.
Series of macroeconomic variables discussed above, despite their potential
value, cannot capture all information available to market participants. In contrast,
stock prices react quickly to news releases and, therefore, should reflect all
innovations in the macroeconomic factors. Accordingly, stock returns reveal market
expectations about the future firms’ performance far beyond the one-year horizon. On
the other hand, corporate earnings disclose the current year performance and thus, may
be partially included in stock returns. Consequently, we can expect a positive
correlation of market returns with corporate earnings, and a negative correlation with
the analysts’ optimistic forecast bias. To examine the described relationship, the
Change in the Market Risk Premium variable is constructed:
1 1 1
) ( ) (
−
− − − =
t M t M
r R r R CMRP , (24)
where R
M
and r
1
are the annual value-weighted returns on all stocks traded on NYSE
and AMEX obtained from CRSP database and the one-year to maturity Treasury note
rate.
Table 16 presents correlation coefficients among the macroeconomic variables
and corporate earnings. Indeed, for the Most Volatile category firms, we find a
positive correlation of corporate earnings with the growth in the industrial production,

102
the unexpected inflation computed using the Survey of Professional Forecasters
method and the change in the market risk premium, and a negative correlation with the
change in the default and term spreads. However, the correlation coefficients for the
unexpected inflation and the change in the market risk premium are not statistically
significant. In the case of the Middle and Steadiest category firms, whose earnings
exhibit a smaller variability, correlation coefficients are also not statistically
significant. Table 17 presents the results for the regression of analysts’ one-year-ahead
median forecast error on the macroeconomic innovations:
ε β β β β β α + + + + + + = CMRP CTS CDS UI GIP FE
PF 5 4 3 2 1
, (25)
Note that all dependent and independent variables in this regression represent the
flows in a given year. The results are presented in.
For the Most Volatile category companies, all coefficients have the anticipated
signs. As the growth in the industrial production and the unanticipated inflation
decrease and changes in the term and default spread increase, the analysts’ optimistic
error augments. Yet, due to the apparent multicolinearity, only the change in the term
spread coefficient is statistically significant. Next, the forecast error is regressed on the
two most influential macroeconomic factors, which are the changes in the term and
default spreads in the case of the Most Volatile category firms. Seventy-four percent of
the temporal variability in the analysts’ forecast error is explained by changes in these
two variables. In the absence of any macroeconomic innovations, the analysts’
forecast error is about 42 cents. As the term and default spreads increase by one

103
percent, the analysts’ forecast error on average increases by 21 and 20 cents,
respectively.
For the Middle category analysts’ forecast error, the growth in the industrial
production and the term spread play the most important roles: a one percent decrease
in the industrial production growth and a one percent increase in the term spread are
associated with 0.5 and 1.8 cents escalations in the analysts’ optimistic forecast error.
The adjusted R
2
of the regression is 63%. In contrast, in the case of the Steadiest
category firms, none of the macroeconomic variables appear to be related to the
analysts’ forecast error, and the percent of its explained variation is close to zero. It is
caused by the absence of significant variations in the forecast error itself.
In summary, the change in the term spread has much descriptive power over the
analysts’ one-year-ahead forecast error. Term spread increases after business peaks,
when it is low, preceding sluggish economy and decreases after troughs, when it is
high, preceding strong growth rates in production during phases of business
expansions. As a result, an increase in the term spread over the year horizon is
associated with a reduction in the corporate earnings and an increase in the forecast
error produced by financial analysts at the beginning of that year. The results on the
association of the analysts’ forecast error with the growth in the industrial production,
the unexpected inflation, changes in the default spread, and the market risk premium
are mixed. Overall, the results shows that optimism is a prevailing sentiment among
analysts since the median forecast error is consistently optimistic even after
controlling for the macroeconomic innovations.

104
Variable GIP UI
TS
UI
PF
CDS CTS CMRP
A
v

A
m
A
s
0.45
0.07*
0.06*
-0.05*
0.01*
0.03*
0.33*
0.17*
0.09*
-0.31*
-0.06*
0.06*
-0.67
-0.10*
-0.08*
0.07*
0.06*
0.12*
Table 16. Pearson correlation matrices for economic innovations and corporate earnings. A
v
, A
m
, and A
s

are the aggregate actual earnings for the Most Volatile, Middle and the Steadiest categories companies.
GIP is the growth in the industrial production, UI
PF
is the unanticipated inflation computed using the
Survey of Professional Forecasters, UI
TS
is the unexpected inflation computed using the time-series
modeling, CDS, CTS, and CMRP are the annual changes in the default spread, the term structure spread,
and the market risk premium. Companies are divided in categories according to the coefficient of
variation of the change in earnings defined by (12). Asterisks denote insignificance at the 5% level.

Variable const GIP UI
PF
CDS CTS CMRP R
2
Adj.
FE, Most Volatile

FE, Most Volatile
0.495
(7.2)
0.422
(10.7)
-0.024*
(1.3)

-0.071*
(1.11)

0.134*
(1.6)
0.204
(3.0)
0.161
(3.4)
0.207
(6.1)
-0.003*
(1.2)

73%

74%
FE, Middle

FE, Middle
0.050
(5.7)
0.042
(4.8)
-0.007
(3.1)
-0.005
(2.2)
-0.017*
(2.1)

- 0.011*
(1.0)

0.012*
(2.0)
0.018
(2.9)
-0.001
(2.6)

71%

63%
FE, Steadiest

FE, Steadiest
-0.010*
(1.3)
-0.011
(4.8)
-0.000*
(0.2)

-0.003*
(0.5)

- 0.003*
(0.6)

0.003*
(0.3)
0.004*
(1.3)
-0.0003*
(1.0)
-0.0002*
(1.0)
0%

3%
Table 17. Financial analysts’ one-year-ahead median forecast error, FE, and macroeconomic
innovations. GIP is the growth in the industrial production, UI
PF
is the unanticipated inflation
computed using the Survey of Professional Forecasters, UI
TS
is the unexpected inflation computed using
the time-series modeling, CDS, CTS, and CMRP are the annual changes in the default spread, the term
structure spread, and the market risk premium. Companies are divided in categories according to the
coefficient of variation of the change in earnings defined by (12). OLS regressions. t-statistics in
absolute value are in parentheses. Asterisks denote insignificance at the 5% level.

105
CHAPTER IV
CONCLUSION
According to the rank orders procedure that utilizes the MSE and MSPE error
measures, neural networks exploiting quarterly data produce forecasts that are
comparable in accuracy to analysts’ predictions in the case of the one-year-ahead
forecast horizon or even superior in the case of the two-year-ahead forecast horizon. In
fact, financial analysts produce less accurate two-year-ahead forecasts made at the
beginning of a fiscal year than any other adaptive time-series model in consideration;
even the linear random walk with drift model supplies more accurate forecasts. These
facts shed a significant doubt on the credibility of financial analysts as providers of
accurate annual earnings forecasts. Furthermore, the study demonstrates that the
accuracy advantage of artificial neural networks is more pronounced for companies
with volatile and, therefore, hardly predictable earnings. In contrast, financial analysts
produce forecasts of a relatively good accuracy for companies with steady earnings
that generally move in line with the market earnings. It implies that financial analysts
have either inferior abilities relative to artificial neural networks to extract nonlinear
systematic patterns from histories of volatile earnings due to cognitive biases affecting
their forecasting behavior or a lack of incentives to extract it properly, or both.
As it is evident from the direction of change measure, both financial analysts
and neural networks are found to be useful predictors of the sign of change in
earnings. However, the structure of predictions differs. Financial analysts have the
advantage in recognizing upward movements, while quarterly neural networks possess

106
the best skills to identify downward moves. The financial analysts’ tendency to
produce mostly positive sign predictions is consistent with the generally growing
earnings in the 1990s, but hides a potential danger to underestimate the importance of
historical earnings, which may contain frequent downturns in the case of companies
with volatile earnings. On the other hand, the better ability of quarterly neural
networks to predict downward movements lead to their superior performance observed
in terms of rank orders.
Next, without considering conventional measures of accuracy, this work
presents evidence suggesting that adaptive statistical models that only utilize series of
past earnings contain information not in a constant term and in analysts’ forecasts
made at the beginning of a fiscal year for companies with volatile earnings. It yet
again suggests that analysts overlook the information in histories of earnings. This
result contradicts the widely accepted hypothesis that financial analysts use all
available information in constructing forecasts and poses a challenge to the previously
acclaimed notion of analysts’ informational superiority. The related question is how
the number of analysts issuing forecasts and the standard deviation of individual
forecasts influence the relative accuracy of financial analysts’ consensuses. The results
suggest that not the size and the amount of available information, but the type of the
company is a main determinant of financial analysts’ relative forecast accuracy. Thus,
the deterioration in the relative accuracy of analysts’ forecasts is linked to the
difficulty of the forecasting task as measured by the volatility of change in earnings or
by the analysts’ disagreement. Overall, if financial analysts acted more like statistical

107
models and less like humans with conflicting objectives and behavioral anomalies,
then they would do a better job of earnings forecasting.
The second chapter of this study looks for explanations of the documented
relatively poor analysts’ forecast accuracy. It provides evidence that analysts’
forecasts exhibit systematic optimism for companies with hardly predictable earnings.
In the latest 1999-2004 period, the financial analysts’ mean forecast bias increases
from a pessimistic 2 (0) cents for companies, whose earnings are the least volatile and
move with the market earnings, to an optimistic 66 (133) cents for companies, whose
earnings are the most volatile and move against or independently of the market
earnings, in the case of one- (two)-year-ahead forecast horizon. If analysts are
optimistic about a company’s performance in the short term, they are even more
optimistic about its longer-term prospects. While the median forecast error is smaller
than the mean, it is still significant. In addition, the study finds that the difficulty of the
forecasting task plays a role in the analyst’s decision to follow a company. Analysts
almost twice more often produce earnings forecasts for companies whose earnings are
the least volatile or highly correlated with the market earnings than for firms whose
earnings are the hardest to predict.
Next, the study proposes a simple model of the analysts’ forecasting behavior
over the two-year forecast horizon. As the volatility of the change in earnings
increases, the analysts’ reactions to actual earnings get smaller, but the following
monthly adjustments increase in the magnitude. Financial analysts on average are
found to overreact to positive earnings releases and underreact to negative. The

108
strength of this statement increases with the difficulty of the forecasting task, which is
once again found to be an important factor for the pattern of analysts’ forecast
revisions. The constructed model has a practical application: with some refinements, it
can be applied to de-bias analysts’ forecasts at any month throughout the two-year
forecast horizon.
Analyzing temporal variations in the analysts’ forecast error, we can conclude
that financial analysts seem to ignore the future economic activity when making
earnings forecasts and extrapolate the positive, but not the negative historical
economic growth into the future. It leads to the inverse relationship between the
analysts’ optimistic forecast bias and the overall economic activity. During economic
recessions like 1990-1991 or 2001, the optimistic forecast bias reaches historical
maximums, whereas in years of the strong economic growth like 1988 or 2004, it
becomes minimal. What makes it even more unsettling is the persistence of large
optimistic errors even after the onset of a recession. Analysts after failing to anticipate
deteriorating economic conditions, still refuse to learn from macro economic events.
The last statement as well as many other results discussed throughout the study are
consistent with the behavioral explanation of analysts’ forecast error. Cognitive biases
are likely to aggravate during uncertain macroeconomic situations and for companies
whose earnings are relatively hard to predict, as more human judgment is needed to
produce forecasts. In contrast, there is no convincing reason to believe that incentive
concerns would escalate during recession periods.

109
Overall, the difficulty of the forecasting task, which is measured at either an
individual firm level or the overall macro economy level, is found to be a key
determinant for the analysts’ forecasting behavior. The explanation for this
phenomenon should be sought in the judgment under uncertainty literature in
cognitive psychology, and it is a subject for the promising future research.

BIBLIOGRAPHY
Abarbanell, J., and Bernard, V., 1992, Tests of analysts’ overreaction/underreaction to
earnings information as an explanation for anomalous stock price behavior,
The Journal of Finance, 47, 1181-1207.

Albrecht, W., Lookabill, L., and McKeown, J., 1977, The time-series properties of
annual earnings, Journal of Accounting Research, 15, 226-44.

Ang, A., Piazzesi, M., and Wei, M., 2005, What does the yield curve tell us about
GDP growth?, Journal of Econometrics, forthcoming.

Ball, R., and Watts, R., 1972, Some time-series properties of accounting income,
Journal of Finance, 27, 663-81.

Barron, A., 1991, Universal approximation bounds for superpositions of sigmoidal
function, Report No. 58, Department of Statistics, University of Illinois,
Urbana-Champaign.

Bernard, H., and Gerlach, S., 1998, Does the term structure predict recessions? The
international evidence, International Journal of Finance and Economics, 3,
195-215.

Bishop, C., 1995, Neural Networks for Pattern Recognition, Oxford: University Press.

Box, G., and Jenkins, G., 1970, Time Series Analysis, Forecasting and Control, San
Francisco: Holden-Day, Inc.

Brown, L., and Roseff, M., 1978, The superiority of analysts forecasts as measures of
expectations: evidence from earnings, Journal of Finance, 33, 1-16.

110
Brown, L., and Roseff, M., 1979, Univariate time series models of quarterly
accounting earnings per share: a proposed model, Journal of Accounting
Research, 17, 178-189.

Brown, L., Richardson, G., and Schwager, G., 1987, An information interpretation of
financial analysts superiority in forecasting earnings, Journal of Accounting
Research, 25, 49-67.

Chen, N., Roll, R., and Ross, S., 1986, Economic forces and stock market, Journal of
Business, 59, 383-403.

Chow, G., 1960, Tests of equality between sets of coefficients in two linear
regressions, Econometrica, 28, 591-605.

Collins, W., and Hopwood, S., 1980, A multivariate analysis of annual earnings
forecasts generated from quarterly forecasts of financial analysis and univariate
time series models, Journal of Accounting Research, 1980, 18, 390-406.

Crichfield, T., Dyckman, T., and Lakonishok, J., 1978, An evaluation of security
analysts’ forecasts, The Accounting Review, 53, 651-668.

Cybenko, G., 1989, Approximation by superpositions of a sigmoidal function,
Mathematics of Control, Signals, and Systems, 2, 303-314.

Dacco, R., and Satchell, S., 1990, Why do regime-switching models forecast so badly,
Journal of Forecasting, 18, 1-16.

Das, S., Levine, C., and Sivaramakrishnan, K., 1998, Earnings predictability and bias
in analysts’ earnings forecasts, The Accounting Review, 73, 277-294.

DeBondt, W., and Thaler, R., 1990, Do security analysts overreact?, American
Economic Review, 80, 52-57.

Diebold, F., and Mariano, R., 1995, Comparing predictive accuracy, Journal of
Business and Economic Statistics, 13, 253-263.

Dugar, A., and Nathan, S., 1995, The effects of investment banking relationships on
financial analysts’ earnings forecasts and investment recommendations,
Contemporary Accounting Research, 12, 131-660.

Elliott, G., Komunjer, I., and Timmermann, A., 2005, Estimation and testing of
forecast rationality under flexible loss, The Review of Economic Studies, 72,
1107-1125.

111
Estrella, A., and Hardouvelis, G., 1991, The term structure as a predictor of real
economic activity, The Journal of Finance, 46, 555-576.

Fausett, L., 1994, Fundamentals of Neural Networks, New York: Prentice Hall.

Fisher F., 1970, Tests of equality between sets of coefficients in two linear
regressions: an expository note, Econometrica, 38, 361-366.

Francis, J., and Philbrick, D., 1993, Analysts’ decisions as products of a multi-task
environment, Journal of Accounting Research, 31, 216-230.

Fried, D., and Givoly, D., 1982, Financial analysts’ forecasts of earnings: a better
surrogate for earnings expectations, Journal of Accounting and Economics, 4,
85-107.

Givoly, D., 1985, The formation of earnings expectations, The Accounting Review, 60,
372-386.

Gu, Z., and Wu, J., 2003, Earnings skewness and analyst forecast bias, Journal of
Accounting and Economics, 35, 5-29.

Henriksson, R., and Merton, R., 1981, On market timing and investment performance.
II. Statistical procedures for evaluating forecasting skills, The Journal of
Business, 54, 513-533.

Hong, H., Kubik, J., and Solomon, A., 2000, Security analysts’ career concerns and
herding of earnings forecasts, RAND Journal of Economics, 31, 121-144.

Hopwood, W., McKeown, J., and Newbold, P., 1982, The additional information
content of quarterly earnings reports: intertemporal disaggregation, Journal of
Accounting Research, 20, 343-349.

Hornik, K., Stinchcombe, S., and White, H., 1989, Multilayer feedworward networks
are universal approximators, Neural Networks, 2, 359-366.

Kahneman, D., and Tversky, A., 1973, On the psychology of prediction,
Psychological Review,80, 237-251.

Keane, M., and Runkle, D., 1998, Are financial analysts’ forecasts of corporate profits
rational?, Journal of Political Economy, 106, 768-805.

Kuan, C., and Liu, T., 1995, Forecasting exchange rates using feedforward and
recurrent neural networks, Journal of Applied Econometrics, 10, 347-364.

112
Lakonishok, J., Shleifer, A., and Vishny, R., 1994, Contrarian investment,
extrapolation, and risk, Journal of Finance, 49, 1541-1578.

Lim, T., 2001, Rationality and analysts’ forecast bias, Journal of Finance, 56, 369-
385.

Lin, H., and McNichols, M., 1998, Underwriting relationships, analysts’ earnings
forecasts and investment recommendations, Journal of Accounting and
Economics, 25, 101-127.

Maddala, G., 1971, The likelihood approach to pooling cross-section and time series
data, Econometrica, 39, 939-953.

McNichols, M., and O’Brian, P., 1997, Self selection and analyst coverage, Journal of
Accounting Research, 35, 167-199.

O’Brien, P., 1988, Analysts’ forecasts as earnings expectations, Journal of Accounting
and Economics, 10, 53-83.

Rumelhart, D., and McClelland, J., 1986, Parallel Distributed Processing, Vol. 1,
Cambridge, MA: MIT Press.

Swanson, N., and White, H., 1995, A model selection approach to assessing the
information in the term structure using linear models and artificial neural
networks, Journal of Business and Economic Statistics, 13, 265-275.

Swanson, N., and White, H., 1997, A model selection approach to real-time
macroeconomic forecasting using linear models and artificial neural networks,
The Review of Economics and Statistics, 79, 540-550.

Tkacz, G., 2001, Neural network forecasting of Canadian GDP growth, International
Journal of Forecasting, 17, 57-69.

Watts, R., and Leftwich, R., 1977, The time series of annual accounting earnings,
Journal of Accounting Research, 15, 253-71.

Abstract (if available)

Abstract This work examines forecast errors in financial analysts' earnings forecasts. First, the relative accuracy of financial analysts' and adaptive time-series forecasts is considered. The central question is whether financial analysts efficiently utilize available information and produce forecasts that are more accurate than predictions of statistical models. The study employs a novel forecasting approach -- artificial neural networks and identifies cognitive anomalies that influence the analysts' forecasting behavior. Financial analysts exhibit systematic optimism for a specific subset of companies. The magnitude of the analysts' optimistic forecast bias increases with the difficulty of the forecasting task, which is represented by statistical characteristics of a firm's earnings as well as the overall economic activity. Both the mean and median forecast errors are largest for companies with the most volatile earnings that move against or independently of the market earnings. The study also presents a model of the analysts' forecasting behavior and provides evidence that the analysts' optimistic forecast error somewhat slowly decreases throughout the forecast horizon. Financial analysts on average are found to overreact to positive earnings releases and underreact to negative. In addition, they tend to ignore the expected economic activity when making earnings forecasts and, furthermore, fail to adjust their forecasts appropriately in periods of economic downturns. It leads to the inverse relationship between the optimistic forecast bias and the overall economic activity. The evidence presented contributes to the understanding of the formation and value of analysts' predictions.

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Asset Metadata

Creator Kantsyrev, Dmitri (author)

Core Title Essays on the properties of financial analysts' forecasts

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 04/06/2009

Defense Date 03/27/2007

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag financial analysts' forecast bias,forecast optimism,neural networks,OAI-PMH Harvest

Language English

Advisor Magill, Michael J.P. (committee chair), Fygenson, Mendel (committee member), Zapatero, Fernando (committee member)

Creator Email kantsyre@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m354

Unique identifier UC1181644

Identifier etd-Kantsyrev-20070406 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-322869 (legacy record id),usctheses-m354 (legacy record id)

Legacy Identifier etd-Kantsyrev-20070406.pdf

Dmrecord 322869

Document Type Dissertation

Rights Kantsyrev, Dmitri

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu