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LIBRARY

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This is to certify that the

dissertation entitled

AN EMPIRICAL INVESTIGATION OF BIAS
IN ANALYSTS' EARNINGS FORECASTS

presented by

Hakan Saraoglu

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Bus . Adm.

 

 

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MSU leAn Nflrrnetlve Action/EM Opportunity Inetttulon

1

 

AN EMPIRICAL INVESTIGATION OF BIAS IN ANALYSTS’ EARNINGS
FORECASTS

By

Hakan Saraoglu

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Finance and Insurance
Eli Broad Graduate School of Management

1996

ABSTRACT

AN EMPIRICAL INVESTIGATION OF BIAS IN ANALYSTS’ EARNINGS
FORECASTS

By

Hakan Saraoglu

This study investigates bias in security analysts’ earnings forecasts using samples
of firms in the United States. Methods to identify bias and to improve the accuracy of
analyst forecasts are suggested and tested. Samples of forecasts in Japan, the UK. and
Germany are also examined for bias.

The results in the US. sample of 1984-91 show that (1) forecasts are on average
optimistic, (2) biases in negative forecasts and in negative earnings are more obvious than
those in positive forecasts and earnings, (3) positive forecasts that overestimate negative
earnings are the biggest source of forecast error, (4) optimistic bias in forecasts seems to
be driven by firms with negative earnings.

Based on these observations, methods to improve the accuracy of negative
earnings forecasts are suggested and tested. Results show that adjustments of up to 1% of
share price yield improved forecast accuracy, an increased probability of beating the
consensus forecast, and little increase in the probability of underestimating actual

earnings.

Multiple Discriminant Analysis and Logistic Regression are utilized to predict the
sign of earnings before the announcement date using firm-specific information together
with earnings forecasts. The sum of the first three quarterly earnings, the magnitude of
the consensus forecast, and the percentage change in share price from the previous year
are found to be good predictors of the sign of earnings. Using this methodology in a hold-
out sample, optimistic positive forecasts of negative earnings are identified and adjusted.
Test period results indicate that this methodology outperforms security analysts’
consensus forecasts in predicting negative earnings outcomes. Mean square forecast error
is greatly reduced through forecast adjustments in all but one test period.

An investigation of the accuracy of security analysts' median consensus forecasts
in Japan, the UK, and Germany for the 1987-94 the period finds that analysts’ forecasts
contain an optimistic bias in all three countries. A majority of negative forecasts are
overoptimistic in Japan and Germany, where analysts rarely report negative forecasts for
earnings that turn out to be positive. In contrast, negative earnings forecasts in the UK.
are on average pessimistic. Tests of symmetry suggest that the average forecast error is
negative and its magnitude is symmetric regardless of the size of forecasts in Japan and
the United Kingdom. On the other hand, the forecast errors become larger and more

negative as the forecasts become smaller in Germany.

Copyright by
HAKAN SARAOGLU
1 996

DEDICATION

To the memory of my father, Kemal Saraoglu.

ACKNOWLEDGMENTS

I wish to express my appreciation to my dissertation committee members: Dr. Kirt
Butler, Dr. John Gilster, Dr. Kathy Petroni and Dr. Peter Schmidt. Dr. Gilster and Dr.
Petroni have been a diligent source of insight throughout my research. Dr. Schmidt’s
thorough and constructive reviews of my dissertation went far beyond the call of duty.

I am grateful to Dr. Kirt Butler, my dissertation committee chairperson. With his
sound advice and encouragement, Dr. Butler has been a valuable mentor and a constant
source of inspiration to me throughout my doctoral program.

I would like to express my gratitude to Dr. Richard Simonds for his confidence in
my capabilities and for his nominating me to a highly visible and challenging teaching
position. I am also thankful to Dr. John O’Donnell, who recruited me to the doctoral
program.

I am indebted to Dr. Tamer Cavusgil, who has been a constant source of support
and encouragement during my years in East Lansing. Thanks are also extended to the
Michigan State University Center for International Business Education and Research for
generously funding my research.

Most of all, I wish to thank my mother, Aysel Saraoglu, and my wife, Poh-Lin

Yeoh Saraoglu, for their unconditional support and love.

vi

TABLE OF CONTENTS

LIST OF TABLES
LIST OF FIGURES
INTRODUCTION

CHAPTER 1

LITERATURE REVIEW
The Association of Earnings and Earnings Forecasts to Stock Prices
Superiority of Analysts’ Forecasts to Time-Series Models
Bias in Analysts’ Earnings Forecasts

CHAPTER 2
DO ANALYSTS FORECAST NEGATIVE EARNINGS OUTCOMES
DIF F ERENTLY THAN POSITIVE EARNINGS OUTCOMES?
Forecast Bias
Forecast Bias and Firm Size
Is the Forecast Bias Symmetric?
A Test of Structural Change in the Forecasts
Forecast Bias and the Sign of Forecasts
Summary

CHAPTER 3
IMPROVING THE ACCURACY OF NEGATIVE EARNINGS FORECASTS
The Earnings Forecast Adjustment
Measures of Analyst Forecast Performance
Relative Forecast Accuracy
Beating the Consensus
Probability of Under-Estimating Earnings
Summary

vii

ix

xi

ONUIM

15
15
18
20
21
24
27

43
44
44
45
47
49
51

CHAPTER 4

PREDICTING THE SIGN OF EARNINGS 56
Predicting the Sign of Earnings Using Multiple Discriminant Analysis
(MDA) 57
Predicting the Sign of Earnings Using Logistic Regression (LR) 66
Summary 68

CHAPTER 5

IMPROVING THE ACCURACY OF POSITIVE EARNINGS FORECASTS 78
Estimation Period 78
Test Period 82
Summary 85

CHAPTER 6

A COMPARATIVE ANALYSIS OF ANALYSTS’ EARNINGS FORECASTS IN

INTERNATIONAL EQUITY MARKETS 92
Data 95
Forecast Bias 96
Are Forecast Errors Symmetric? 98
Forecast Bias and the Sign of Forecasts 100
Summary 104

CHAPTER 7

CONCLUSION AND DIRECTIONS FOR FUTURE RESEARCH 124

APPENDIX

DECOMPOSITION OF THE FORECAST ERROR 131

BIBLIOGRAPHY 134

viii

Table 2.1

Table 2.2
Table 2.3
Table 2.4

Table 2.5
Table 2.6
Table 2.7

Table 2.8

Table 4.1
Table 4.2
Table 4.3
Table 4.4

Table 4.5
Table 4.6

Table 4.7
Table 4.8
Table 5.1
Table 5.2
Table 5.3

Table 5.4

LIST OF TABLES

Descriptive Statistics: Actual Earnings (EPS) and Analysts’
Forecasts of Earnings (F EPS)

Predictions of Earnings Per Share

Predictions of Earnings Per Share For Relatively Large Firms
Predictions of Earnings Per Share For Relatively Medium-Size
Firms

Predictions of Earnings Per Share For Relatively Small Firms
Matched Pair Test of Symmetry in Forecast Errors

OLS Regressions of EPS Against F EPS (Categorized by the Sign of
FEPS)

OLS Regressions of EPS Against FEPS With a Zero-Intercept
Restriction (Categorized by the Sign of F EPS)

Mean and Standard Deviation of Variables in Analysis

Correlation Matrix of Variables in Analysis

Multiple Discriminant Analysis (Forced Entry Method)

Multiple Discriminant Analysis Classification Summary (Forced
Entry Method)

Multiple Discriminant Analysis (Stepwise Selection Method)
Multiple Discriminant Analysis Classification Summary (Stepwise
Selection Method)

Logistic Regression (Forced Entry Method)

Logistic Regression Classification Summary (Forced Entry Method)
Multiple Discriminant Analysis (Estimation of Function Parameters)
Multiple Discriminant Analysis Classification Summary (Estimation
Period) ' ,

OLS Regression of Forecast Errors Against Discriminant Scores for
the Negative Earnings Classification (Estimation Period)

OLS Regression of Forecast Errors Against Discriminant Scores for
the Positive Earnings Classification (Estimation Period)

ix

35
36
37

38
39
4O

41
42
7O
71
72

73
74

75
76
77
86
87
88

89

Table 5.5
Table 5.6
Table 6.1
Table 6.2
Table 6.3
Table 6.4
Table 6.5
Table 6.6
Table 6.7
Table 6.8

Table 6.9

Table 6.10
Table 6.11
Table 6.12

Multiple Discriminant Analysis Classification Summary (Test
Period)

Improvement in Forecast Accuracy of Adjusted Positive Forecasts
(Test Period)

Descriptive Statistics: Actual Earnings and Analysts’ Forecasts of
Earnings (Japan)

Descriptive Statistics: Actual Earnings and Analysts’ Forecasts of
Earnings (The United Kingdom)

Descriptive Statistics: Actual Earnings and Analysts’ Forecasts of
Earnings (Germany)

Predictions of Earnings Per Share (Japan)

Predictions of Earnings Per Share (The United Kingdom)
Predictions of Earnings Per Share (Germany)

Matched Pair Test of Symmetry in Forecast Errors (Japan)
Matched Pair Test of Symmetry in Forecast Errors (The United
Kingdom)

Matched Pair Test of Symmetry in Forecast Errors (Germany)
OLS Regressions of EPS Against FEPS (Japan)

OLS Regressions of EPS Against FEPS (The United Kingdom)
OLS Regressions of EPS Against F EPS (Germany)

90

91

112

113

114
115
116
117
118

119
120
121
122
123

Figure 1

Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 3.1
Figure 3.2
Figure 3.3
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.1
Figure 6.2
Figure 6.3
Figure A.1

LIST OF FIGURES

Earnings Per Share (EPS) Vs. Forecasts of Earnings Per Share
(FEPS)

EPS Versus F EPS For Relatively Large Firms

EPS Versus FEPS For Relatively Medium-Size Firms

EPS Versus F EPS For Relatively Small Firms

Obtaining the Point of Structural Change in Forecasts
Structural Change in Forecasts Represented by a Linear Spline
Relative Forecast Accuracy

Probability of Beating the Consensus

Probability of Overestimating Earnings

EPS Versus FEPS in Japan

EPS Versus FEPS in the United Kingdom

EPS Versus F EPS in Germany

EPS Versus FEPS in Japan (Larger Scale Graph)

EPS Versus FEPS in the United Kingdom (Larger Scale Graph)
EPS Versus FEPS in Germany (Larger Scale Graph)
Decomposition of Mean Square Forecast Error of EPS Forecasts

xi

3O
31
32
33
34
53
54
55
106
107
108
109
110
111
133

INTRODUCTION

The market value of equity is often estimated by finding the present value of its
future cash flows discounted at a rate of return appropriate for its risk. Faced with the task
of estimating a stock's future cash flows, investors frequently rely on security analysts'
forecasts of earnings per share. Investors' reliance on earnings forecasts is evident in the
association between earnings surprises and stock prices changes (Brown (1978) and
Rendleman, Jones and Latane (1982)). Since investors use analysts' earnings forecasts to
form their expectations of future earnings and cash flow, accuracy of the forecasts is of
paramount importance.

Various research studies have evaluated the accuracy of analysts’ earnings
forecasts. Brown and Rozeff (1979), Brown, Hagerman, Griffin and Zmijewski (1987),
Collins and Hopwood (1980) showed that analysts produce significantly better forecasts
than time series models. However, research has also shown that analysts’ forecasts of
earnings per share tend to be optimistically biased (Dowen (1989), O’Brien (1994),
Dreman and Berry (1995)). If investors in the market do not discount the forecast bias
when forming their expectations, it may be possible to develop profitable trading rules
based on the association of earnings surprises to stock price changes. Thus, an

understanding of the nature of forecast bias gains additional importance for investors.

This study investigates bias in security analysts’ earnings forecasts using samples
of firms in the United States. Methods to identify bias and to improve the accuracy of
analyst forecasts are suggested and tested. Samples of forecasts in Japan, the UK. and
Germany are also examined for bias.

Figure 1 plots actual against expected annual earnings based on median consensus
forecasts reported during November for a sample of 4250 observations over the period
1984-1991. A casual inspection of Figure 1 suggests that positive earnings outcomes tend
to be clustered around a 45-degree line through the origin as one would expect of rational
forecasts. The forecasts associated with negative earnings outcomes, on the other hand,
appear to be over-optimistic. Indeed, rarely do negative earnings outcomes exceed the
consensus forecast and fall above the 45-degree line. Based on this observation, the
following research issues emerge: (1) Are analysts’ consensus forecasts biased and/or
inefficient in a systematic manner? (2) If they are, is the bias in the overall sample driven
by forecasts of earnings that turn out to be negative? (3) Do negative earnings forecasts
differ from positive earnings forecasts? (4) Can the accuracy of forecasts be improved
based on observation of systematic biases such as over-optimism in forecasts of negative
earnings?

To answer these questions the following related null hypotheses are formed: (1)
analysts’ forecasts are unbiased and efficient, (2) the rationality of forecasts is
independent of the forecasts’ magnitude and sign.

Chapter 1 discusses the relevant literature and highlights the research issues.

Chapter 2 investigates analysts’ consensus forecasts of annual earnings in the US. and

tests null hypotheses (l) and (2). Chapter 3 suggests and tests methods to improve the
accuracy of negative earnings forecasts, and evaluates the implications of forecast
adjustments from the standpoint of both investors and analysts. Chapter 4 develops a
methodology for predicting the sign of earnings per share before the announcement date
using firm-specific information together with earnings forecasts. Significance of various
measures of pre-announcement information is tested using Multiple Discriminant
Analysis and Logistic Regressions. Chapter 5 uses the methodology suggested in Chapter
4 to identify and adjust optimistic forecasts of negative earnings in the sample. Out-of-
sample tests are performed to assess the power of the model in predicting the negative
earnings outcomes. The significance of forecast improvement is evaluated using the same
out-of-sample tests. Chapter 6 investigates the accuracy of analysts’ earnings forecasts in
samples from Japan, the United Kingdom, and Germany. Chapter 7 summarizes the

results of the study and suggests directions for future research.

Figure 1. Earnings Per Share (EPS) Vs. Forecasts of Earnings Per Share (FEPS)

Annual earnings per share (EPS) are plotted against analysts’ forecasts of annual earnings per
share (FEPS) for the US. companies in a pooled sample between 1984 and 1991.

 

 

FEPS

 

 

 

 

 

 

 

 

Chapter 1

LITERATURE REVIEW

This chapter presents a discussion of the relevant literature and highlights the
research issues regarding the importance of earnings numbers and forecasts of earnings

per share as well as the accuracy of earnings forecasts.

The Association of Earnings and Earnings Forecasts to Stock Prices

Valuation of a share of common stock requires estimation of the share’s future
cash flow stream. The expectations of market participants on company fundamentals,
which serve as measures of future performance, play an important role in driving the
market values of stocks. Research studies show that firms’ earnings per share numbers
and analysts’ forecasts of earnings per share are proxies for investors’ expectations of
firms' future prospects. In a seminal study that introduced the concept of post-eamings
announcement drift (or, the literature on standardized unexpected earnings) Ball and
Brown (1968) show that changes in annual earnings are associated with changes in stock
prices of the same directions. Using data for nine years, 1957-65, the study shows that:
(1) annual earnings capture approximately one-half of the information that becomes

available during the year; and (2) approximately 85 to 90 percent of stock price

movements occurs in the 12 months prior to the month in which the annual earnings
number is reported. This study also shows that, after annual earnings are announced,
stock prices continue to move in the same direction as the annual earnings change. The
Ball and Brown study is considered as the pioneer study of the quarterly reporting
literature; studies that focused on the magnitude of the earnings change rather than simply
the direction; the use of cash flows numbers in lieu of earnings numbers; and the use of
more sophisticated earnings forecasting models than simply earnings changes.

Empirically examining the extent to which common stock investors perceive
earnings to possess informational value, Beaver (1968) supports the findings of Ball and
Brown (1968) on the information content of earnings reports.

Givoly and Lakonishok (1979) evaluate the information content of analysts’
earnings forecast revisions by analyzing the relationship between stock price behavior
and the direction and magnitude of the revision. Their results show that revisions in
earnings forecasts convey information to the stock market or reflect variables that
determine stock prices.

In an empirical test of the theory that expectations about a firm’s characteristics
are reflected in security prices, Elton, Gruber and Gultekin (1981) examine data from a
monthly file of one and two-year earnings forecasts prepared in the period 1973-75. Their
finding support the theory. Their results indicate that large excess returns can be earned if
the investor can determine stocks for which analysts have underestimated earnings; the

larger the underestimation, the larger the return. Elton, et a]. conclude that with any

amount of forecasting ability, investor can earn best returns by acting on the difference
between their forecasts and consensus forecasts.

Niederhoffer and Regan (1972) show that earnings changes have a significant
impact on stock prices, implying that an accurate earnings forecast is of paramount
importance in stock selection models. Focusing on 100 case histories, this study provides
evidence that stock price changes are positively associated with forecasts of moderately
increased earnings and realized earnings far in excess of analysts’ expectations. The
worst-perforrning stocks, on the other hand, are characterized by severe earnings declines
in combination with unusually optimistic forecasts.

Benesh and Peterson (1986) examine the importance of unexpected and actual
earnings changes on the market’s determination of stock prices. In an earnings sample of
1980-1981, their results indicate that unexpected earnings changes have a major impact
on share price. Firms with high return performance generally have substantial earnings
increases and earnings that surpass analysts’ expectations. Over time, forecasts become
more optimistic for top-performing firms. Furthermore, earnings announcements may
play a major role in forecast revisions, and securities that experience significant revisions

tend to have substantial excess returns for the remainder of the year.

Superiority of Analysts’ Forecasts to Time-Series Models
Evaluating the predictive power of security analysts’ earnings forecasts, various

research studies have compared forecasts produced by analysts to those generated by

statistical models. Results suggest that analysts’ forecasts of earnings per share are more
accurate than those of time-series models.

According to Brown and Rozeff (1978), basic economic theory and the
equilibrium employment of analysts imply that analysts must produce better forecasts
than time series models. Their results show that Box-Jenkins models consistently produce
significantly better earnings forecasts than martingale and sub-martingale models. Also,
earnings forecasts of Value Line Investment Survey consistently outperform the Box-
Jenkins and naive time-series models. Brown and Rozeff conclude that, if market
earnings expectations are rational, the best available forecasts should be used to measure
market earnings expectations. They also suggest that analysts’ forecasts should be used in
studies of firm valuation, cost of capital, and the relationship between unanticipated
earnings and stock price changes until forecasts superior to those of analysts are
discovered.

Fried and Givoly (1982) assess the quality of financial analysts’ forecasts as
proxies for the market expectation of earnings, compare them with other prediction
models, and analyze the factors that contribute to analysts’ forecasts having information
content. In a forecast sample between 1969 and 1979, the results indicate that analysts’
prediction errors provide a better proxy for market expectations than forecasts generated
by time-series models. Fried and Givoly suggest that analysts show better performance
due to their ability to utilize a much broader set of information than that used by the
univariate time-series models. The study also provides evidence that the analysts

efficiently exploit the extrapolative power of the earnings series itself.

Based on a multivariate analysis of variance design (MAN OVA), Collins and
Hopwood (1980) compare the relative accuracy of annual earnings forecasts generated
from the quarterly forecasts of financial analysts and from four univariate time-series
models. Results indicate that the performance comparison of univariate time-series
models to the financial analyst model favor the financial analysts. Analysis of the list of
outliers show that the financial analysts also generate fewer outliers than the univariate
models. Collins and Hopwood conclude that the financial analysts are more capable of
incorporating the effects of the economic events that are the underlying causes of the
outliers.

Crichfield, Dyckman and Lakonishok (1978) show that financial analysts’
predictions of earnings per share based on accounting information improve as the
reporting date approaches, and that, generally, the financial analysts are better able to
predict earnings per share compared to the statistical models.

Brown, Hagerman, Griffin and Zmijewski (1987) provide evidence that security
analysts’ are superior to univariate time-series models in predicting firms’ quarterly
earnings numbers. Similar to the conclusion of Fried and Givoly (1982), they attribute
this superiority to: (1) better use of information that exists on the date that time-series
models can be initiated (a contemporaneous advantage), and (2) use of information
acquired between the date of initiation of time series model forecasts and the date when
security analysts’ forecasts are published (a timing advantage).

Several articles in the literature investigate the possible improvement in forecast

accuracy by combining analysts’ forecasts with those generated by time series models.

10

Consensus results of such studies indicate that a forecast synergy can be achieved when
analysts forecasts are combined with forecasts from time-series models. Covering a
diversified sample of 261 firms with a 1980-1982 post-sample estimation period, Guerard
(1987) shows that security analysts’ forecasts can be improved when combined with
time-series forecasts. Results indicate that the mean square error of analysts’ forecasts
may be decreased by combining analyst and univariate time-series model forecasts in
constrained and unconstrained OLS regression models. In a sample of four forecast
horizons, Lobo (1992) investigates the effects of disagreement in financial analysts’
earnings forecasts on the accuracy of analysts’ forecasts, forecasts generated by time-
series models, and the combined forecasts. The empirical results indicate that, while
analysts do better than any of the three other time-series models studied, simple
combinations of analysts’ and time series forecasts are superior to forecasts from either

source in every horizon.

Bias in Analysts’ Earnings Forecasts

In spite of the relative accuracy of analysts’ earnings forecasts compared to those
generated by statistical models, numerous research studies suggest that analysts’ forecasts
of earnings per share tend to be optimistically biased. An understanding of the nature of
bias in analysts’ eamings forecasts is crucial due to the widely documented relationship
between earnings surprises and stock price changes.

Affleck-Graves, Davis and Mendenhall (1990) provide an explanation for

analysts’ superiority as well as possible reason for bias. According to Affleck-Graves, et

11

a]. (1) analysts use more recent information, (2) analysts use information not included in
the time series of past earnings, and (3) the analyst bias observed may be due to the use of
judgmental heuristics.

In an analysis based on ten years of data, Dowen (1989) finds that analysts
systematically overestimate firms’ future earnings per share. The study shows that (1) the
number of analysts following a firm is positively correlated with firm size and forecast
error, and (2) firm size is positively correlated with forecast error.

According to the cognitive bias theory, the market should form overly pessimistic
(optimistic) expectations of future earnings for those stocks that have experienced sharp
share price declines (increases). Klein (1990) examines revisions and errors in analysts’
forecasts during and after the portfolio formation period in order to distinguish between
the cognitive bias theory and a rational expectations hypothesis. The evidence does not
support the cognitive bias theory. Klein concludes that analysts do not underpredict
earnings following large stock price declines. Rather, they remain overly optimistic about
future earnings.

Various studies have focused on specific circumstances where an optimistic bias
is observed. Francis and Philbrick (1993) examine analysts’ earnings forecasts as
products of an environment in which analysts forecast earnings and maintain
management relations. Their study finds that analysts’ earnings forecasts are optimistic,
on average, and are more optimistic for stocks with sell or hold recommendations than for

those with buy recommendations.

12

Dugar and Nathan (1995) present evidence that financial analysts employed by
brokerage firms that provide investment banking services to a company are optimistic,
relative to other analysts, in their earnings forecasts and investment recommendations.1
The authors hypothesize that market participants rely relatively less on forecasts of the
investment banker analysts in forming their expectations if information regarding the
investment banking relationship of brokerage firms is publicly available.

From a different perspective, Francis and Philbrick (1992) conclude that Value
Line analysts make over—optimistic forecasts although they are not on the supply side.
They explain this evidence by suggesting that analysts are pressured by the managers to
produce optimistic forecasts in order to continue to share management's asymmetric
information. Interpreting the finding that analysts' earnings estimates are overly
optimistic after stock price declines, Klein (1990) provides a similar interpretation that
managers whose firms face adverse conditions pressure analysts to make overly
optimistic forecasts.

Huberts and Fuller (1995) find that current forecasts of earnings are excessively
optimistic for companies whose earnings have been hard to predict in the past.

Trueman (1990) suggests that analysts may be reluctant to revise their forecasts
upon receipt of new information because of the negative signal such a revision provides
concerning the accuracy of their prior forecasts. As a result, the accuracy of analysts’
observed forecasts may understate the precision of their actual information. In a different

study, Trueman (1994) provides evidence on a tendency for analysts to release

 

1 Popular press frequently reports cases of overoptimism by sell-side analysts (see
Dorfman (1991) and Sicinolfi (1992, 1995)).

13

information close to prior expectations than is appropriate, given their information.
Trueman also argues that analysts exhibit herding behavior, whereby they release
forecasts similar to those previously announced by other analysts, even when this is not
justified by their information.

Chapter 2 is motivated by the research findings that (1) analysts outperform time-
series models due to their ability to use a much broader set of information not included in
the time series of past earnings, a human advantage, and (2) although they generate
superior forecasts than the time-series models, analysts consistently overestimate earnings
per share. In light of these findings, it can be argued that if analysts use their advantage
selectively depending on their incentive structure and neglect certain negative
information while forming their expectations, this might result in systematic optimistic
biases that are reflected in their forecasts. For example, a sell-side analyst or an analyst
who wants to maintain good management relations may report optimistic forecasts even
though he has access to information that shows the Opposite. Chapter 2 further
investigates the nature of bias in analysts’ consensus forecasts of earnings per share.

Recent research studies suggest that models combining analysts’ forecasts with
time-series models result in better forecast accuracy. These findings and results of
Chapter 2 that analysts systematically over-estimate negative earnings motivate Chapter 4
where analysts forecasts are combined with firm-specific pre-announcement information
to better estimate the sign of actual earnings.

Chapter 3 and 5 develop methods of forecast adjustment motivated by findings in

research that (1) earnings and earnings forecasts are closely associated with stock price

14

changes, (2) the accuracy of forecasts is of paramount importance because, if detected,
systematic biases in forecasts can be utilized to devise trading rules to earn abnormal

I'CIUITIS.

Chapter 2
DO ANALYSTS FORECAST NEGATIVE EARNINGS OUTCOMES
DIFFERENTLY THAN POSITIVE EARNINGS OUTCOMES?

Forecast Bias

In his review of the academic research on security analysts’ forecasts of earnings,
Brown (1993) concludes that analysts’ earnings forecasts are positively biased.l Brown
leaves open the question of whether or not this forecast bias is intentional. In search of an
explanation for this over-optimism, researchers have focused on those companies that: 1)
use the analyst’s employer to underwrite their securities (Lin and McNichols (1991)), 2)
use the analyst’s employer as an investment banker (Dugar and Nathan (1995)), and 3)
are in financial distress (Moses (1990) and Klein (1990)). Each of these studies finds that
analysts’ forecasts for these firms are positively biased. An important aspect of such
studies is that they pool the forecast data assuming that the forecast error is orthogonal to
the forecasts. With few exceptions, research on forecast bias has treated the negative and
positive forecasts within the same pool. One exception is the Francis and Philbrick (1993)
study, in which the authors conclude that analysts’ earnings forecasts are more optimistic
for sell and for bold stocks than for buy stocks. Motivated by the anomaly manifested in

Figure 1, this chapter investigates whether or not analysts forecast negative earnings

 

1 Brown (1996) points out that on average, analysts’ forecasts have been negatively
biased in recent quarters.

15

16

differently from positive earnings. This inquiry has a potentially important contribution to
the literature, since the previous findings of forecast optimism may be driven by the
positive bias in forecasts of negative earnings.

This study uses Lynch, Jones and Ryan’s Institutional Brokers Estimate System
(I/B/E/S) data base of individual security analysts’ annual earnings forecasts for the
period 1984-1991. The I/B/E/S detail tape contains individual forecasts of annual primary
earnings per share before extraordinary items. These earnings forecasts were matched
with the corresponding earnings figures from Standard & Poor’s Compustat Full-
Coverage database.‘ Observations were kept if the following conditions were satisfied:

three or more forecasts of primary EPS reported to I/B/E/S during November
for December fiscal year-end companies,

share price greater than two dollars from the previous December on
Compustat.

F orecasted and actual earnings per share for each firm were divided by beginning-
of-year share price in order to scale for cross-sectional differences in the level of earnings
and share price. Hereafter, “earnings” and “EPS” refer to the earnings/price ratio.

Median consensus forecasts for each sample firm and year were constructed from
the November forecasts. Median consensus forecasts were chosen over mean forecasts

because of O’Brien’s (1988) finding that median earnings forecasts exhibit the smallest

 

1To the extent that analysts do not report “earnings before extraordinary items” to
I/B/E/S, there is an empirical problem with matching earnings from Compustat with
forecasts from I/B/E/S. Discussion of this errors-in-variables problem is beyond the scope
of this paper.

l7

bias of competing consensus forecast measures. The filter on share price (> $2/share)
eliminated 22 observations (about one—half of one percent of the sample). A large
proportion of these were firms in financial distress with depressed stock prices and large
negative earnings outcomes, for which earnings/price ratios are not meaningful. Table 2.1
shows the descriptive statistics of earnings per share and forecasts of earnings per share
for each sample year from 1984 to 1991, as well as for the pooled sample period of 1984-
91.

Figure 1 plots actual against expected annual earnings based on median consensus
forecasts reported during November for a sample of 4250 observations over the period
1984-1991. A casual inspection of Figure 1 suggests that positive earnings outcomes tend
to be clustered around a 45-degree line through the origin as one would expect of rational
forecasts. The forecasts associated with negative earnings outcomes, on the other hand,
are clearly over-optimistic. Indeed, rarely do negative earnings outcomes exceed the
consensus forecast and fall above the 45-degree line.

Table 2.2 presents the percentage of cases where forecasts overestimate actual
earnings on a year-by-year basis and categorized according to the sign of actual earnings
(EPS) and the sign of the consensus forecast (FEPS). While forecasts of positive earnings
outcomes do not appear to be inaccurate in any systematic way, forecasts of negative
earnings over-estimate actual earnings in each of the sample years in Table 2.2. The
northeast quadrant of Figure 1 corresponds to the positive-earnings, positive-forecast
category (EPS > 0 and FEPS > 0) in the center of Table 2.2. The forecasts in this

quadrant appear to be unbiased and efficient. In contrast, over 75% of forecasts in the

18

southwest quadrant (EPS < 0 and FEPS < 0) are over-optimistic. The ray of observations
scattered along the y-axis in the southeast quadrant of Figure 1 reflects a tendency of
analysts to report positive forecasts even when actual earnings are negative.

The northwest and southeast quadrants of Figure 1 are also asymmetric. In only a
handful of cases do analysts make the error of reporting negative forecasts when actual
earnings turn out to be positive as in the northwest quadrant. Of the 258 negative
forecasts, only fourteen earnings outcomes (or about 5% of the sample) are positive.
Many more analysts make the opposite error of forecasting positive earnings when actual
earnings turn out to be negative. As many as 206 of the 450 forecasts associated with
negative earnings outcomes are positive and about 87% of these forecasts are higher than
actual earnings. Negative forecasts as a whole over-estimate actual earnings 71.71% of

the time.

Forecast Bias and Firm Size

In this section I investigate whether firm size (proxied by the market value of
equity) is a factor in forecast bias. The sample is divided into three size groups following
the methodology of Atiase (1985). The first size group (relatively large companies)
includes companies with market values ranging between $300 million-$95,697 million.
Market values of the second (relatively medium size companies) and third size (relatively
small companies) groups range between $50 million-$300 million and $3 million-$50
million, respectively. Figures 2.1 through 2.3 plot actual earnings against the median

consensus forecasts for each size group. Tables 2.3 through 2.5, which are divided into

l9

quadrants according to the signs of EPS and F EPS, show the percentage of earnings
overestimated, average bias, and average earnings per share in each quadrant for each size
group.

Regardless of the firm size forecasts of negative earnings appear to be over-
optimistic in these figures and tables. Analysts overestimate negative earnings 88.76% of
the time for larger firms that constitute the first size group. In the second size group, the
percentage of forecasts overestimating the negative earnings is 82.79%. Analysts do a
relatively better job forecasting the positive earnings of firms in the first and second size
groups. When the forecasts and actual earnings are both positive (northeast quadrant),
forecasts are clustered around the 45-degree line and the percentage of optimistic
forecasts is close to 50% (48.88% for the first size group and 53.40% for the second size
group). These results suggest that the phenomenon of over-optimism in forecasting
negative earnings is true for larger firms. Analysts also overestimate the negative
earnings of the smallest firms in the sample that constitute the third size group. The
percentage of earnings over—estimated is 86.15% in this case. The northeast quadrant of
Figure 4 reveals that analysts also appear to be more optimistic when they forecast
positive earnings of the small firms. For the pooled sample of 1984-91 , the percentage of
forecasts overestimating the actual earnings in this quadrant is 60% for small firms,
which is significantly larger than for the other size groups. This finding is consistent with
previous research documenting a correlation between size and forecast error (Dowen

(1989)).

20

Is the Forecast Bias Symmetric?

To examine symmetry in negative and positive earnings forecasts the following
null hypothesis is formed: “Given that there exists a forecasts error, this error is
independent of the size of forecasts” To test this hypothesis, the pooled sample of 1984-
91 is divided into deciles with respect to the size of the earnings forecasts.2 Forecast error
and the percentage of forecasts that overestimate actual earnings are calculated for each
decile. Then, forecast error and mean square forecast error for corresponding top and
bottom deciles are compared using a paired sample t-test and analysis of variance. Results
of the analysis are presented in Table 2.6.

As is evident in Table 2.6, there is a clear asymmetry in forecast errors. Forecasts
that are larger in magnitude have smaller error. The bottom decile has the largest forecast
error (-.050159) and the forecast error is significantly different from zero. The percentage
of forecasts that overestimate actual earnings is also the largest (65.73%) in the bottom
decile of forecasts. A binomial test rejects the null hypothesis that the proportion of
optimistic forecasts is 50%. The percentage of forecasts overestimating actual earnings
monotonically decreases to 56.67% as the bottom category is widened to include the next
four deciles. Mean forecast error in the bottom half of forecasts (-.019323) is smaller than
in the bottom decile but still statistically significant at 5%. The negative sign of the error
indicates that average forecast exceeds actual earnings. The proportion of optimistic
forecasts is close to 50% in the top decile. In fact, the null hypothesis that the proportion

is equal to 50% cannot be rejected. Although significantly different from zero, the mean

 

2 Size of the forecasts instead of the actual earnings is used in forming the decile groups
because the actual earnings numbers are not known ex ante.

21

forecast error is smaller than that of the bottom decile. A paired sample t-test test rejects
the null hypothesis (with 5% significance) that the difference between mean errors in the
top and the bottom deciles are equal. In each paired sample the mean error of the bottom
group of forecasts is significantly greater than that of the top group. Also, mean square
errors in the bottom groups are significantly greater than mean square error in the top
groups. Analysis of variance rejects the null hypothesis (with 5% significance) that the
mean square errors are equal.

In summary: (1) analysts’ forecast errors are asymmetric with respect to the size
of the forecasts, (2) the magnitude of the forecast error increases as the magnitude of the
forecast decreases, and (3) the percentage of optimistic forecasts increases as the forecasts

fall below the average.

A Test of Structural Change in the Forecasts

This section investigates whether the evidence of asymmetry in forecast bias is an
indication of structural change in the analysts’ prediction of earnings per share. In a broad
interpretation, Poirier (1976) states that structural change occurs whenever the parameters
of an economic model change a “small” number of times in response to forces within or
outside the model. In formulating this concept of structural change, Poirier advocates the
use of spline functions as an alternative to dummy variable representations. His focus on
spline functions is based on an assumption of continuity in economic models. A spline

function is a piecewise function in which pieces are joined together in a smooth fashion.

22

Pieces of the spline are commonly chosen to be polynomials. A smoothness condition is
assumed for the spline function and its derivative.

My attempt to fit a spline function to the relationship of eamings forecasts and
actual earnings is motivated by the previous section’s finding that forecasts become more
accurate as their magnitude increases. If, in fact, analysts shy away from predicting poor
performance, their forecasts are expected to reflect this as a structural change. Thus, the
objective of this section is to test the existence of structural change empirically with a
linear spline model.

The mathematical formulation of a linear spline is as follows:3
Let the set A = {x I < E 2 < < 12“} of abscissa values be referred to as a mesh and the

k-l individual points in = 1, 2, k - 1} as interior knots or simply knots. Then the
dependent variable y is a linear spline S A(x) over A if and only if y is a continuous
piecewise linear function in x consisting of k segments defined over k intervals (-00, x1],
[32 1, i2], ..., DIM, 00), respectively.

In order to formulate the model, I use the following parametrization suggested by

Poirier and referred to as an elementary spline fimction by Barrondale and Young (1966):

SAX) = 50+ I31 “’1 + 32 W2 + + Bk Wk

where
wl = x
~31 = (x- x ,--.). =max(x- x j-.. 0)
X“ = j- l’th interior knot
51 = slope of the spline over the first interval

 

3 This formulation and its discussion is taken from pages 9-11 of Poirier’s 1976 book
entitled “The Econometrics of Structural Change

23

Bj = the change in slope from interval (j-l) toj,j = 2, 3, 4, ..., k

The first derivative of the above linear spline is a step function with jump discontinuities
equal to 13; (i = 2, 3, 4, ..., k) at the knots. The slope in the jth segment is (B, + [32 + [3]).
The t-statistic corresponding to Bj (i = 2, 3, 4, ..., k) indicates the statistical significance of

the change in slope over intervals (H) and j. If BJ- is statistically nonzero, then this

implies structural change occurring at x H
In order to formulate the relationship of forecasts to actual earnings as a linear

spline function, I use the following representation:

SAFEPS) = 130+ Bl -W1 + 52 - “’2
where

w, = FEPS (forecast of earnings per share)
wz = max(FEPS - FEPS ,, 0)
F EPS 1: the interior knot (point of structural change)

[3, slope of the spline over the first interval
[32 the change in slope from interval 1 to 2

 

Estimating the parameters of this spline function involves applying the method of linear
multiple regression. However, the exact location of the interior knot is not known a
priori. Thus, the above spline model is not defined unless the values of the transformed
variable wz are known. In order to address this issue, I apply the following methodology.

Starting with an initial value of -2.0 (which is the minimum value of the forecast sample)
for F EPS 1, the above regression is iteratively run by adding an infinitesimal incremental

a term of 0.0025 to the initial value of FEPS, after each iteration. The value of F EPS 1

that maximizes the r2 of the regression is taken as the point of structural change. Figure

24

2.4 plots r2 values of regressions against the values of FEPS 1. The value of r2 is

maximized (0.7148) when the magnitude of FEPS, is -0.8625. This point, which yields
the best fit for the spline function, is a good candidate for the point of structural change.

Parameter estimates of the regression equation are as follows:

SA(FEPS) = -0.685223 + 0.415010 . wl + 0.762667 . w2
(-15.26) (9.24) (14.84)

where

w, = FEPS (forecast of earnings per share)
wz max (F EPS - (-0.8625), 0)

As the t-statistics in parentheses indicate, the coefficients of w, and wz are both
significant at a 5% level. The coefficient of WI which represents the slope before the
interior knot has a value of 0.415010. The slope then changes significantly at the interior
knot by an amount 0.762667, as indicated by the coefficient of wz. Figure 2.5 presents a
graphical representation of the spline function. Although this suggests a point of
structural change in the forecasts, this point lacks a clear-cut economic rationale. This
may be attributed to the existence of a bimodal distribution, possibly with multiple

variances.

Forecast Bias and the Sign of Forecasts
This section investigates my initial question of whether or not predictions of
negative earnings are different from predictions of positive earnings. The null hypothesis

is that analysts’ earnings forecasts are accurate and rational, and therefore should lie on a

25

45-degree line drawn through the origin. In order to test this hypothesis, the following

OLS regressions are run:

EPS“ = a, + bt . FEPSit + en V FEPS
EPS“ = a, + bt . FEPS“ + e“ V FEPS < O
EPS“ = a1 + bt . FEPSit + e" V FEPS > 0
where
EPS,t = actual earnings per share for firm i and fiscal year t
FEPS,t = earnings forecast per share for firm i and fiscal year t

The first regression uses all observations. The second and third regressions use
observations from the negative FEPS sample and the positive FEPS sample separately in
order to further examine whether predictions of negative earnings are different than those
of positive earnings.

The results are summarized in Table 2.7. The regression that uses the sample of
all observations yields a negative intercept that is significantly different from zero
(-.018979) using a two-tailed t-test and a slope that is greater than one (1.064125). This
suggests that forecasts are biased, inefficient, or both.4

For the pooled sample of 1984-91, the intercept term for the negative F EPS
sample is significantly different from zero (-0.082138) and the slope is less than one
(0.953991). The intercept term is negative in each year and is statistically significant in

five of the eight annual samples. This finding of a negative intercept points to an

 

4 Appendix presents a discussion of decomposition of mean square forecast errors into
bias and inefficiency components.

26

optimistic bias in negative forecasts. The slope term is significantly different from one in
four out of eight sample years.

In the case of positive F EPS, the sample pooled over 1984 to 1991 has a slope that
is less than one (.958910). The intercept term is close to, but significantly different from,
zero (-.007279). This shows that positive forecasts are also optimistic, although this
optimism may be driven by the positive forecasts of negative earnings in the southeast
quadrant of Figure 1. An investigation of the annual samples reveals that the negative
intercept term is significantly different from zero in only three of the eight years.

To summarize, for the positive earnings sample, the regression line of actual
earnings versus earnings forecasts is found to have an intercept different from zero and a
slope different from one. The intercept term is significantly non-zero for the negative
forecasts sample. These results indicate that negative earnings forecasts are optimistically
biased and that positive forecasts are biased and inefficient in the pooled sample.
Regression parameters in the negative and positive FEPS samples differ from each other,
as well as from the theoretical relationship between actual EPS and forecast EPS that is
characterized by a 45-degree line passing through the origin.

Regressions are also run by imposing a no-intercept restriction using each year

from 1984 to 1991 as well as the pooled sample of 1984-91. The regressions are:

EPSit = b, . FEPS“ + eit v FEPS
EPSit = b, . FEPS" + eit v FEPS < 0
EPSit = b, . FEPS" + eit v FEPS > 0

where

EPS" = actual earnings per share for firm i and fiscal year t

27

F EPS,t = earnings forecast per share for firm i and fiscal year t

The motive behind this inquiry is simply to compare the empirical regression line with
the theoretical (or ideal) line that passes through the origin at a 45-degree angle. Results
of these regressions are summarized in Table 2.8. The slope term for the negative FEPS
sample is greater than one (1.088715) and statistically significant in the pooled sample of
1994-91. Regressions using the annual samples of negative FEPS result in slope terms
that are greater than one in six of the eight sample years. In comparison to the theoretical
line passing through the origin, this is a further indication of overoptimism in the
negative earnings forecasts. On the other hand the regression slope for the positive FEPS
sample is less than one (.890330) in the pooled sample as well as in each of the individual

years. Results of these regressions further support my finding that predictions of negative

EPS and positive EPS differ from each other.

Summary

In this chapter, analysts median consensus forecasts of earnings per share are
evaluated for forecast bias in a sample drawn from 1984 through 1994. Negative forecasts
of earnings per share are found to be over-optimistic. Analysts overestimate earnings
71.71% of the time when they report negative forecasts. Out of the 258 negative
forecasts, only 14 correspond to a positive earnings outcome (.0036% of all the positive
earnings sample). Positive forecasts of earnings per share paint a different picture.
Positive forecasts overestimate actual earnings 54.19% of the time. In the case of positive

forecasts of positive earnings, analysts are over-optimistic only 50.50% of the time. Only

28

5.16% of these positive forecasts are associated with earnings outcomes that turn out
negative.

Negative earnings forecasts are more optimistic than positive forecasts, with an
average bias of (-0.0741 76) in the pooled sample of 1984-91. Positive forecasts have an
average bias of (-0.010772) in the same sample. Bias is statistically significant and
reflects optimism in every year from 1984 to 1991 for both negative and positive forecast
samples.

The empirical relationship of forecasts and actual earnings deviates from the
theoretical relation of a 45-degree line. This deviation is most apparent in the form of
large optimistic biases for the negative forecast sample. Regressions using the positive
forecast sample result in parameter estimates that reflect bias and inefficiency.

The findings in this chapter suggest that the over-optimism is mostly driven by
forecasts of companies with negative earnings. The percentage of earnings overestimated
is 50.32% and average bias is (-0.002439) in the positive earnings sample. In the negative
earnings sample, analysts are overoptimistic 86.69% of the time with an average bias of
(-0.1 17492).

The main conclusions of the chapter are that (1) forecasts are on average
optimistic, (2) bias in negative forecasts is more pronounced than bias in positive
forecasts, (3) optimistic bias in forecasts seem to be driven by firms with negative
earnings, and (4) positive forecasts that overestimate negative earnings are a major source

of forecast error.

29

These observations form the motivation for the remaining chapters. In particular
Chapter 3 investigates methods to improve the accuracy of negative earnings forecasts.
Chapters 4 develops a methodology to predict the sign of actual earnings. Chapter 5

corrects positive earnings forecasts that are likely to be associated with negative earnings.

30

Figure 2.1. EPS Versus FEPS For Relatively Large Firms

The group of “relatively large firms” (first size group) includes firms with market values
greater than $300 million in the pooled sample period of 1984-91.

 

 

 

 

 

 

 

 

 

 

 

 

 

31

Figure 2.2. EPS Versus FEPS For Relatively Medium-Size Firms

The group of “relatively medium-size firms” (second size group) includes firms with
market values greater than $50 and less than $300 million in the pooled sample period of
1984-91.

 

 

 

 

 

 

 

-lj

 

 

 

 

 

 

 

 

 

32

Figure 2.3. EPS Versus FEPS For Relatively Small Firms

The group of “relatively small firms” (third size group) includes firms with market values
less than $50 million in the pooled sample period of 1984-91.

 

FEPS
0. 50

 

 

-2.00 -l.80 -l.60 -l.40 -l.20 -l.00 -O.80 -O_60 -O.4O

 

 

 

 

 

33

Figure 2.4. Obtaining the Point of Structural Change in Forecasts

The following regression is run iteratively. FEPSI is assigned an initial value of -2.0, and
an infinitesimal a term of 0.0025 is added to its value at each iteration:
SAFEPS) = 50+ 131 - W1 + 132 - W2

where

 

w, = FEPS (forecast of earnings per share)

w2 = max(FEPS - FEPS ,, 0)

FEPSI = the interior knot (point of structural change)
[31 = slope of the spline over the first interval

[32 = the change in slope from interval 1 to 2

 

 

 

 

 

point of structural change

 

-2.00 0.50

34

Figure 2.5. Structural Change in Forecasts Represented by a Linear Spline

Parameter estimates of the linear spline function are as follows:

SA(FEPS) = -0.685223 + 0.415010 . w, + 0.762667 . wz

where

w, = FEPS (forecast of earnings per share)
max (FEPS - (-0.8625), 0)

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Chapter 3

IMPROVING THE ACCURACY OF NEGATIVE EARNINGS FORECASTS

Given a consensus forecast is negative in Table 2.2 the forecast is overoptimistic
71.71% of the time. This raises the possibility that the accuracy of negative forecasts can
be improved by adjusting for forecast bias. This chapter investigates gain in forecast
performance arising from adjusting forecasts of negative earnings for analyst
overoptimism. Forecast adjustments of varying magnitudes are evaluated using the
following three measures of forecast performance: (1) the change in forecast accuracy
relative to the consensus as measured by mean square forecast error, (2) the probability of
being closer to actual earnings than the consensus forecast, and (3) the probability that
adjusted forecasts overshoot the mark and underestimate actual earnings. Forecast
performance is evaluated along each of these dimensions so that both producers and
consumers of earnings forecasts can make an informed decision regarding their own
optimal adjustment of consensus earnings forecasts.

Results indicate that relative forecast accuracy as well as the probability of
beating the consensus forecast can be improved by adjusting negative forecasts
downward by a small amount without an inordinate increase in the probability of

underestimating earnings. Because the costs and benefits of overadjusting or

43

44

underadjustrnent differ depending on one’s perspective, the choice of how far to diverge

from the consensus forecast is best left to the individual.

The Earnings Forecast Adjustment

Overoptimism in negative earnings forecasts (F EPS < O) manifests itself in Table
2.2 as a negative bias (where BIAS = EPS - FEPS) ranging from 4.35% to 15.35% of
share price for annual samples and averaging 7.42% of share price over the pooled
sample. Both consumers and producers of earnings forecasts should be able to obtain
better forecasts by lowering the negative consensus forecasts even further. I perform the
following adjustment:

AFEPS“: FEPS“ ' ADJ"

where
AFEPSit — adjusted forecast for firm i and fiscal year t,
FEPS,t — unadjusted earnings forecast for firm i and fiscal year t,
ADJ it = adjustment factor (ADJ,t > O) as a percentage of share price

for firm i and fiscal year t.
If the penalties associated with forecast errors are not symmetric around actual earnings,
then individuals will want to adjust consensus forecasts by an amount that varies from the

expected bias.

Measures of Analyst Forecast Performance
In this section, forecast adjustments of varying magnitudes are evaluated using the

following three measures of forecast performance: (1) the change in forecast accuracy

45

relative to the consensus as measured by mean square forecast error, (2) the probability of
being closer to actual earnings than the consensus forecast, and (3) the probability that

adjusted forecasts overshoot the mark and underestimate actual earnings.

Relative Forecast Accuracy

Consumers of earnings forecasts such as individual investors and fimd managers
use forecasts of current and future earnings as inputs into valuation models designed to
identify mispriced securities. Consequently, consumers of earnings forecasts are
concerned with the magnitude of actual earnings and would like their earnings forecasts
to be unbiased and efficient. Unbiased and efficient forecasts are neither systematically
too high nor too low and are distributed as tightly as possible around actual earnings. A
good measure of forecast performance for consumers of earnings forecasts is the mean
squared forecast error.

In order to measure the accuracy of adjusted earnings forecasts relative to
unadjusted consensus forecasts, mean squared forecast errors before and after adjustment

are computed according to:

n
MSE = (yn ;(EPSit — FEPSit)2 t=1984,....,1991

and

n
AMSE = (yn 2(EPSit — AFEPSit)2 t=1984,....,199l
i=l

46

where n is the number of negative forecasts in a particular sample. The performance of

adjusted forecasts relative to unadjusted forecasts is measured by the ratio:

Relative forecast accuracy = AMSE / MSE

This measure of forecast performance will be of interest to both producers and consumers
of earnings forecasts.

Figure 3.1 plots the observed improvement in MSE against the magnitude of the
forecast adjustment over each of the years 1984-91 and over the pooled 1984-91 sample
(the dark line in the figure). A bias adjustment of about 6% of share price results in the
best forecast accuracy in the negative forecast sample pooled across all sample years.
This corresponds to an earnings forecast adjustment of $6 on a $100 share of stock. Not
surprisingly this is fairly close to the mean bias of 7.4% of share price in the negative
forecast sample of Table 2.2. With this adjustment, the squared errors of the adjusted
forecasts are 85.7% of unadjusted forecast squared errors. Adjusted forecast accuracy
begins to deteriorate in the overall sample beyond an adjustment of about 6% of share
price. By the time forecasts have been reduced by 12% of share price, adjusted and
unadjusted forecasts have nearly equal forecast accuracy in the pooled sample. At this
level, adjusted forecasts are about as far below actual earnings as unadjusted forecasts are
above earnings.

Within each sample year, relative forecast accuracy improves monotonically for

adjustments of up to 4% of share price. Beyond this point, the magnitude of the optimal

47

adjustment exhibits a good deal of year-to-year variation. Those years with the largest ex
post bias in the negative forecast sample of Table 2.2 (1985 and 1990) benefit the most
from large forecast adjustments in Figure 3.1. Improvement in forecast accuracy during
those years with the smallest bias (1988 and 1989) is correspondingly smaller. The
magnitude of the forecast bias in the negative forecast samples is about 4.1% of share
price in 1988 and 1989 and adjustments of more than this amount begin to lose their
effectiveness. Nevertheless, relative forecast accuracy is improved over unadjusted
forecasts for adjustments of up to 8% of share price in these two years. The forecast
accuracy of adjusted forecasts is superior to that of unadjusted forecasts for adjustments

of up to 11% of share price in the remaining six years.

Beating the Consensus

Forecast accuracy as measured in the previous section is most prized by
consumers of earnings forecasts such as individuals and fund managers using earnings
forecasts in valuation models. In contrast to consumers of earnings forecasts, the forecasts
of earnings forecast producers are primarily judged not on forecast accuracy but on
whether their forecasts are closer to actual earnings than those of other analysts. A
successful security analyst is one whose forecasts are consistently closer to actual
earnings than competing forecasts. Given the observed overoptimism in the negative
forecast samples, analysts should be able to consistently beat consensus forecasts simply

by adjusting consensus forecasts downward by an arbitrarily small amount. More

48

aggressive analysts can attempt larger adjustments in an effort to further improve their
forecast accuracy relative to the consensus.

The measure of relative forecast accuracy in the following equation is based on a
squared error criterion. Forecast accuracy can alternatively be measured as the probability
that adjusted forecasts lie closer to actual earnings than the consensus. This frequency can

be used to estimate the probability of an analyst beating the consensus forecast:

P[beating the consensus] = P[ | EPS“ - F EPS" | > | EPSit - AFEPS,t | ].

For the negative forecast sample, arbitrarily small downward adjustments will beat the
consensus forecast by the amount shown in the “% over” column under “TOTALS” in
Table 2.2. For example, since 71.71% of the total sample of negative forecast
observations overestimate actual earnings, small downward adjustments to the consensus
forecasts will be closer to actual earnings 71.71% of the time across the entire sample.
Relative forecast accuracy will improve as progressively larger downward adjustments
are made, but the probability of beating the consensus forecast will be less than the initial
level of 71.71%. As succesively larger adjustments are made, relative forecast accuracy
will begin to deteriorate and the probability of beating the consensus will fall below 50%.
Figure 3.2 plots the probability of beating the consensus forecast for progressively
larger downward adjustments for the yearly samples and for the pooled sample. For

arbitrarily small downward adjustments ADJ i > 0, these probabilities emerge from the y-

axis in Figure 3.2 according to the “% over” probabilities in Table 2.2. The overall

49

sample as well as each of the yearly samples begin at probabilities well over 50%, so it is
a good bet that small downward adjustments will beat the consensus. As the size of the
downward adjustment is increased, the probability of beating the consensus falls. In the
pooled sample, downward adjustments of up to 4.75% of stock price continue to yield a
greater than 50% probability of beating the consensus. Downward adjustments of up to
2.2% of stock price yield a greater than 50% probability of beating the consensus in each
of the yearly samples. Adjusted forecasts of up to 10% of share price continued to beat
the consensus over 50% of the time in half of the sample years. The years in which
forecast bias is smallest tend also to be the years in which the probability of beating the
consensus falls most rapidly, although the relation between these two variables is not as
pronounced as the relation between forecast bias and changes in relative forecast accuracy

in Figure 3.1.

Probability of Underestimating Earnings

Klein (1990) suggests that managers are most likely to exert pressure on security
analysts when their firm is in financial distress. It is at these times when managers are
most sensitive to negative publicity and a negative earnings forecast is most likely to sour
an analyst’s relation with management. If good relations with management are more
important than an unbiased forecast, then a ‘politically correct’ forecast will be more
generous than is warranted by the facts.

An analyst adjusting negative consensus forecasts downward will want an

estimate of the probability of being exposed to this kind of scrutiny by management. One

50

measure of the analysts’ exposure to negative criticism from management is the
probability that a forecast adjustment of a given size results in earnings underestimates.

Analysts can use the probability P[EPSi>AFEPSi] as an estimate of their exposure to this

risk. Conversely, the probability of overestimating earnings is given by:

P [overestimating earnings] = P[EPS“ < AFEPSit ]

where P [overestimating earnings] = 1 - P[underestimating earnings]. As an example,
unadjusted forecasts over-estimate actual earnings 71.7% of the time in the pooled
sample (see Table 2.2), so the risk of underestimating earnings is 28.3%. Progressively
larger adjustments for overoptimism increase the probability of underestimating earnings.
At a probability of 0.5, adjusted forecasts are as likely to be too high as too low.

Figure 3.3 plots changes in the probability of overestimating earnings for
incremental adjustments of zero to 15% of share price. In the pooled sample, the
probability of overestimating earnings falls to 50% for downward forecast adjustments of
about 2.2% of share price. The yearly samples fall to a 50% probability for adjustments
of between 1.2% (1986 and 1991) and 5.5% (1984 and 1990) of share price. Beyond
5.5% of share price, the probability of underestimating earnings exceeds that of

overestimating earnings in each yearly sample.

51

Summary

Summarizing the results in Figures 3.1 through 3.3, I find that adjustments of up
to 1% of share price result in improved forecast accuracy, a high probability of beating
the consensus forecast, and little increase in the probability of underestimating actual
earnings. Forecast adjustments of between 1% and 2% of share price consistently beat
consensus forecasts and continue to improve forecast accuracy, although there is an
increasing risk of underestimating earnings. Relative forecast accuracy continues to
improve for adjustments of up to 5% of share price. While the probability of beating the
consensus is still on average greater than half for adjustments of up to 5% of share price,
the extent to which forecasts can be adjusted and still beat the consensus more than half
the time exhibits a good deal of year-to-year variation. The maximum adjustment before
the probability of beating the consensus falls below one-half in the yearly samples ranged
from 2% to 11% of share price. Beyond an adjustment of 2% of share price there is
substantial risk of underestimating earnings. Forecast adjustments of up to 11% of share
price are still likely to be superior to unadjusted forecasts on relative forecast accuracy,
although by this point one has probably overshot the mark; the probability of beating the
consensus and the probability of underestimating earnings are both unacceptably high.

Each analyst must make an individual decision on how much to adjust negative
earnings forecasts according to the incentives and penalties they face in their individual
circumstance. Small downward adjustments can improve forecast accuracy as well as the

probability of beating the consensus forecast. Larger adjustments continue to improve

52

forecast accuracy at the expense of an increasing probability of underestimating earnings
and a lower probability of beating the consensus forecast.

If forecast accuracy is paramount, then adjustments of about 5% of share price are
likely to prove optimal. If beating the consensus forecast is prized, then adjustments of up
to 2% of share price will capture gains in forecast accuracy while providing the analyst
with bragging rights over consensus forecasts. To the extent that a security analyst is
penalized for underestimating earnings, attempting to adjust for the full extent of the bias
will expose the analyst to undue criticism. Adjustments of up to 1% of share price are
likely to keep the analyst’s probability of underestimating earnings below 50%, although
the management of individual companies might still find room to complain. Adjustments
of 1% do not take full advantage of the potential gain in forecast accuracy, but do provide
a high probability of beating the consensus forecast.

If all analysts adjust their forecasts by the average forecast bias reported in Table
2.2, then forecasts will on average underestimate actual earnings by the amount of the
current forecast overestimate. Since the institutional incentive (and penalty) structure
faced by security analysts is unlikely to change overnight, a possible prediction is that
analysts will be slow to adopt the recommendations in this chapter. There will still be
room for improvement in forecast performance so long as analysts make only incremental

rather than complete adjustments to their negative earnings forecasts.

53

Figure 3.]. Relative Forecast Accuracy

(Adjusted MSE) / (Unadjusted MSE)

 

 

 

 

 

 

 

2.00
1.80 ..
1989
1.60 4 1988
L40 4-
[/4
M5” ’
100 M; 1986
0.80 4»- I984
1985
0.60 + 1990
0.40 ~»
0.20
0.“) . ‘ T * 4 t " ‘ i A l L 1 4 r 'r Ar - i L

0.00% 1.50% 3.00% 4.50% 6.00% 7.50% 9.00% l0.50% 12.00% 13.50% 15.00%
Size of Forecast Adjustment as a % of stock price

54

Figure 3.2. Probability of Beating the Consensus

P [IEPS - FEPSI > IEPS - AFEPSI]
0.90

 

0.80 .

 

0.70 l

 

 

060 ..

 

 

0.50 l

 

 

0.40 .

 

030 ~

 

 

 

 

0.20 ..

0.101.

 

 

0.00 f ‘v ' ¢ # L .L f t T ; i 4 * ‘. : f 4 1 4 A, a 1 4 4 4 4
0.00% 1.50% 3.00% 4.50% 6.00% 7.50% 9.00% 10.50% 12.00% 13.50% 15.00%

 

Size of Forecast Adjustment as a % of Stock Price

55

Figure 3.3. Probability of Overestimating Earnings

P [EPS < AFEPS]
0.90

 

0.80

0.70 1

0.60 ..

0.50 .2

 

0.40 ..

 

0.30 4~

 

 

 

0.20 i.

 

 

1988

0.10 4

 

I \

\
0.00 + ' . : ~ 4 . : A. 4 ¢ ‘ : : 4 4% . #4
0.00% 1.50% 3.00% 4.50% 6.00% 7.50% 9.00% 10.50% 12.00% 13.50% 15.00%
Size of Forecast Adjustment as a % of Stock Price

 

 

 

 

Chapter 4

PREDICTING THE SIGN OF EARNINGS

The methodology in the previous chapter serves as a tool to correct the
overoptimism in negative forecasts of earnings. Most of the earnings outcomes
corresponding to these negative forecasts indeed turn out to be negative. On the other
hand, positive forecasts that correspond to negative earnings outcomes result in an even
bigger overestimation problem. Knowing that the sign of a forecast is negative implies a
.7171 probability of overestimating earnings. In contrast, a positive forecast may
correspond to a positive earnings outcome where it is quite accurate (50.50% chance of
overestimation in Table 2.2), or to a negative earnings outcome where it is grossly
overoptimistic. This raises the possibility that the accuracy of positive earnings forecasts
can be improved if the sign of actual earnings can be predicted using predisclosure
information.

This section uses Multiple Discriminant Analysis (MDA) and Logistic
Regressions (LR) based on a predisclosure estimation period to identify those company-
specific variables that help predict the sign of actual earnings for the sample of positive
forecasts. Multiple discriminant analysis, using a linear set of input variables also called
discriminating variables, provides an index (discriminant score) that allows classification

of an observation into one of several a priori groupings (Weston and Copeland (1986)).

56

57

Logistic regression is a conditional probability model that uses the coefficients of the
independent variables to predict the probability of occurrence of a dichotomous (or

polytomous) dependent variable (Zavgren (1983)).

Predicting the Sign of Earnings Using Multiple Discriminant Analysis (MDA)

Despite a debate on its applicability in finance and accounting, (see Eisenbeis
(1977), Joy and Tollefson (1975, 1978), Altman and Eisenbeis (1978)), discriminant
analysis has been a valuable tool in areas that require predictive model building (Altman
(1968), Altman, Haldeman and Narayanan (1977)).

Discriminant analysis is a statistical technique that allows the researcher to study
the differences between two or more groups of objects with respect to several variables
simultaneously. In order to be able to use the discriminant analysis on a particular
sample, certain assumptions must be satisfied: (1) there must be two or more groups, (2)
there must be at least two cases per group, (3) there can be any number of discriminating
variables, provided that it is less than the total number of cases minus two, (4)
discriminating variables are measured at the interval level, (5) discriminating variables
must be linearly independent, (6) the covariance matrices for each group must be
approximately equal (unless special formulas are used), and (7) each group has been
drawn from a population with a multivariate normal distribution on the discriminating
variables (Klecka [1980]). The most important of these assumptions are numbers (6) and
(7), and debate on the applicability of discriminant analysis to finance research focuses on

the argument that samples of finance and accounting numbers are most likely to violate

58

these assumptions. However, Klecka [1980] states that: "F or the researcher whose main
interest is in a mathematical model which can predict well or serve as a reasonable
description of the real world, the best guide is the percentage of correct classifications. If
this percentage is high, the violation of assumptions was not very harmful. Efforts to
improve the data or use alternative formulas can give only marginal improvements. When
the percentage of correct classifications is low, however, we cannot tell whether this is
due to violating the assumptions or using weak discriminating variables."

The following equation is fit to the positive forecast sample for each year in the
period 1985-1991. For each year, positive forecasts are reclassified in-sample as negative
if the dependent variable Dt is less than the MDA cut-off score. The performance of the
analysts is then compared to the performance of the MDA in predicting the sign of
earnings. This methodology is extended to an out-of-sample test period (that is predicting

the sign of earnings in the following year with current year’s parameters) in Chapter 5:

D, = a + b.EPS,_, + c.FEPS, + e.OVEREST,,, + f.FOLLCHGt + g.SUM3QEPS,

+ h.MVt + i.PRICECHGt V FEPSt > O t =1985,....,1991

where

Dt = the value of the discriminant function

EPSH = previous year’s earnings per share

F EPS, = current year's median earnings forecast

OVERESTH = the magnitude of previous year's EPS overestimation‘

F OLLCHGt = percentage change in number of analysts following the firm

SUM3QEPSt = sum of first three quarters’ earnings per share

 

1 OVEREST is calculated by subtracting EPS from F EPS in order to assign positive
values to cases where forecasts are greater than the actual earnings. Note that elsewhere
in this study forecast errors are calculated by subtracting F EPS from EPS reflecting
optimism with a negative sign in the error.

59

MVt = natural logarithm of the market value of the firm
PRICECHGt percentage price change

Each of these variables is discussed in the paragraph that follow."-

In line with the findings of a study by Ali, Klein and Rosenfeld (1992), previous
year’s earnings per share (EPSH) is included in the analysis with the hypothesis that
earnings in one year can be used to predict the sign of earnings in the following year if
company performance persists over time. Ali, et al. examine whether analysts properly
recognize the time-series properties of annual earnings when setting their annual earnings
per share. The study documents an optimistic forecast bias that is most pronounced in
firms that previously reported negative earnings.

Analysts’ positive forecasts are fairly accurate in the northeast quadrant of Figure
2.2. However, the southeast quadrant contains an apparent ray of observations that extend
close to the y-axis. These observations represent overoptimistic negative forecasts of
positive earnings. This indicates that analysts are issuing slightly positive or zero
forecasts for negative earnings outcomes, perhaps because of pressure by management. If
this is the case, the magnitude of the current year’s forecasts (F EPSJ may be useful in
predicting the sign of actual earnings.

The magnitude of the previous year’s forecasts optimism (OVERESTH), which is

the difference between the previous year’s forecast minus the previous year’s actual

 

2 In addition to these variables, the timing of annual earnings announcements (Chambers
and Penman (1984), Damodaran (1987)), earnings predictability (Pincus (1983), Lipe
(1990)), institutional ownership (Potter (1992)), exchange listing (Grant (1980)),
systematic risk and earnings growth (Collins and Kothari (1989)), and factors relating to
life cycle stage (Anthony and Ramesh (1992)) could also be included in the analysis due
to insights provided by the cited research work.

60

earnings, may be a good predictor if analysts are consistently overestimating the earnings
of particular companies. This is in line with the management pressure (Francis and
Philbrick (1992)) and investment banking relationship (Lin and McNichols (1991), Dugar
and Nathan (1995)) arguments that are cited in the literature as cases where optimistic
biases are most prominent. Furthermore, Ali, et al. document significantly positive serial
correlations in 8-month and one-month forecast errors, a result that is consistent with the
hypothesis that analysts consistently underestimate the permanence of the last year’s
forecast error.

FOLLCHGt is calculated as the percentage change from the previous year in the
number of analysts following the company. The null hypothesis regarding the inclusion
of F OLLCHGt is that the sign of earnings is independent of the number of analysts
following a firm. Several studies use the number of analysts’ following a firm as a
measure of the amount of prior information available about a firm (Lobo and Mahmoud
(1989), Bhardwaj and Brooks (1992)). Brennan and Hughes (1991) show that the number
of analysts following a firm is inversely related to its share price in a sample covering the
period of 1976-1987. Bhushan (1989) analyzes relationship of a firm’s analyst following
to such firm characteristics as ownership structure, firm size, retum variability, number of
lines of business, and the correlation between market return and firm return. Bhushan
suggests that these factors have a significant impact on the aggregate demand for, or
supply of, analysts’ services for the firm. In line with these studies, if analyst following of
a company is related to firm characteristics such as performance, then analysts may

choose to neglect a poorly performing company rather than forecasting negative earnings.

61

The change in the number of analysts following a company (FOLLCHGJ may be useful
in predicting the sign of earnings per share.3

Atiase (1980, 1985) and Freeman (1987) use firm size as a proxy for the amount
of predisclosure information. Atiase (1987) suggests that the greater the predisclosure
information the less the surprise element in earnings announcements. My analysis in
Chapter 2 documents that the forecasts of smaller firms are optimistic, both in the case of
positive and negative forecasts. In line with this finding, market value (MVt defined as
the natural log of the market value of equity at the beginning of the year) is included in
the analysis to test whether it can predict the sign of earnings.

When analysts report their November forecasts they already possess information
regarding earnings performance in the first three quarters. Previous research has shown
that analysts follow an adaptive behavior to new information releases. Nevertheless, if
analyst optimism towards negative earnings is intentional, then one would expect them to
disregard the information revealed in quarterly earnings. In this case, the sum of the first
three quarters’ earnings (SUM3QEPS,) may predict negative earnings.

The percentage change in the stock price from the previous year (PRICECHGJ
may itself contain information regarding the sign of annual earnings. Abarbanell (1991)
suggests a positive relationship between earnings forecasts and prior price changes
whether or not price changes are combined with analysts’ private signals as they

formulate their earnings forecasts. This suggests that, if information in price changes is

 

3 Number of analysts following the company during the year was not a significant factor
in predicting the sign of EPS in Multiple Discriminant Analysis. To measure a possible
performance-related neglect or drop-out effect, the percentage change in the number of
analysts following a firm is included in the analysis.

62

omitted from analysts’ forecasts, these price changes will help predict the sign of forecast
errors. This result is contrary to the hypothesis that analysts’ forecasts fully incorporate
prior price changes. Abarbanell offers two possible explanations for this result: (1)
analysts are inefficient in collecting and interpreting publicly observable signals, and (2)
private information is more easily inferred by investors if it is not combined with other
signals whose information content is open to individual interpretation.4

Table 4.1 provides summary statistics on each of these variables. An overview of
the correlation matrix of these variables, which is presented in Table 4.2, reveals that the
magnitude of current year’s earnings is positively correlated with the magnitude of
forecasts and is negatively correlated with the magnitude of the previous year’s forecast
overoptimism. An interesting finding is that the previous year’s overoptimism is also
strongly negatively correlated with the magnitude of the previous year’s earnings per
share. This may be another indication that forecast bias is driven by negative earnings.
There is a small positive correlation between the magnitude of the current year’s earnings
and the market value of the firm. Current year’s earnings are also positively correlated
with the magnitude of the previous year’s earnings, as they should be in this cross-
sectional sample.

The results of a Multiple Discriminant Analysis using the forced entry method are

presented in Table 4.3, including the coefficient values and p-values for univariate F-ratio

 

4 Klein (1990) provides evidence that is not supportive of the cognitive bias theory where
the market should form overly pessimistic (optimistic) forecasts of future earnings for
stocks that have experienced sharp price declines (increases). Klein finds that analysts do
not underpredict earnings following large price declines. Rather, they remain overly
optimistic about future earnings.

63

statistics.5 Under the forced entry method, all independent variables that satisfy tolerance
criteria are entered simultaneously. For each one-year estimation period from 1985 to
1991, SUM3QEPSt has a significantly strong explanatory power at a .05 confidence level.
With the exception of 1989 and 1990, FEPSt is also significant in predicting the sign of
earnings per share. The coefficient estimates of these two variables are stable and
consistent from year to year except for 1986, where they have the opposite signs
compared to other years.

An intuitive explanation of the sign of these coefficients requires an explanation
of the MDA’s classification principle. The probability that a case with a discriminant
score D belongs to a group SIGNEPS, (sign of earnings per share) is estimated in MDA
using the following principle:

P(D|SIGNEPSa).P(SIGNEPSa)
Z P(D| SIGNEPSi). P(SIGNEPSi)

 

P(SIGNEPSi| D) =

P(SIGNEPS,), which is called the prior probability, is an estimate of the likelihood that
an observation belongs to a particular sign group when no information is available.
P(D|SIGNEPS,) is the conditional probability of D given the group. It is calculated by
assuming that an observation belongs to a particular group, and the probability of the
observed score given that particular group membership is estimated. P(D|SIGNEPSi),

which is called the posterior probability, is a representation of how likely membership in

 

5 Another measure of significance for the discriminatory power of a variable is Wilks’
lambda. Wilks’ lambda is a multivariate measure of group differences over the
discriminating variables. Values of lambda that are near zero denote high discrimination.
As lambda increases toward its maximum value of 1.0, it is reporting progressively less
discrimination (Klecka (1980)).

64

a certain group is, given the available information. An observation is classified into a sign
group for which the posterior probability with the given discriminant score is the largest.

Discriminant scores at negative and positive earnings group centroids (presented
on the bottom of Table 4.3) show that the negative earnings group consists of smaller
(and on average negative) discriminant scores with the exception of the 1986 sample. In
this case, a negative coefficient for FEPSt implies that inclusion of this variable is helping
to classify those observations with positive forecasts and negative earnings into the
negative earnings group. The opposite effect of classifying observations with positive
forecasts and positive earnings into the negative earnings group is counter-balanced by
the inclusion of SUM3QEPSt where a negative value for this variable would imply a
large negative D score and hence a negative earnings classification.‘5 Also, PRICECHGt
has strong predictive power in four of the seven sample periods. OVERESTH and EPSH
have statistically significant coefficients only in the 1986 and 1990 samples. F OLLCHGt
and MVt have statistically significant predictive power only in one yearly sample.

Table 4.4 shows that the MDA function does a better job than the analysts in
predicting negative earnings outcomes. In the positive forecast sample, analysts have a
0.00% success rate in predicting negative earnings by construction. In the pooled sample
positive forecasts of negative earnings are correctly reclassified 57.01% of the time. This
improvement is achieved at the expense of classifying some positive actual earnings into

the negative earnings group. The overall correct classification rate is not significantly

 

6 Note the strong positive correlation of SUM3 QEPS with EPS. One should be careful
when interpreting the coefficient of a single variable in isolation from the others. Since
the variables are correlated, the coefficient value for a certain variable depends on the
other variables in the analysis.

65

improved through a Multiple Discriminant Analysis. However, because the largest
forecast errors are in the sample of positive forecasts of negative earnings, this
reclassification may provide improved forecast accuracy. That is, even MDA
misclassifies the sign of earnings, it correctly identifies the overestimated earnings.7

In order to ensure the viability of variable selection in the analysis, the MDA
function is also estimated using a stepwise selection method that involves forward
selection and backward elimination.8 The variable selection criterion is based on the p-
value of the F statistic, where the entry value is set to .05 and the removal value is set to
.10. Table 4.5 shows the coefficient values and p-values of their F statistics for the
variables that remain in the analysis. Summary statistics in Table 4.6 for the stepwise
selection method are qualitatively similar to those in Table 4.4 for the forced entry
selection method.

Improvements on these results might be achieved by (1) including other variables
that proxy predisclosure information, or (2) extending the estimation period and

estimating the discriminant function by pooling data into two (or more) years.

 

7 The next chapter shows that positive earnings outcomes that are misclassified as
negative in Table 4.4 are in fact much more likely to be overestimated by security
analysts.

8 Different variable selection criteria such as minimization of Wilks' Lambda, Rao's V or
the Lawley-Hotelling trace, and the sum of unexplained variance can be employed to
determine the most important variables in discriminant analysis.

66

Predicting the Sign of Earnings Using Logistic Regression (LR)

Focusing mainly on bankruptcy prediction, several authors (Press and Wilson
(1978), Zavgren (1983, 1985), Ohlson (1980)) have debated the choice between multiple
discriminant analysis and logistic regression for predictive model building in accounting
and finance. The consensus of these studies is that logistic regression is less restrictive in
terms of its statistical assumptions and provides better results than multiple discriminant
analysis in cases where MDA's assumptions are violated. Moreover, the rationale for the
choice of a cut-off point is an ongoing issue in multiple discriminant analysis (Altman
(1968), Edmister (1972), Zavgren (1983)).

Logistic regression involves obtaining the probability of an event occurring
conditional on a linear combination of independent variables. The functional form the
logistic regression is of a logistic cumulative density function. The parameters of the
logistic regression are estimated from the data using the maximum likelihood method.
Thus, the estimated parameters are such that they make the observed outcomes most
likely.

In the case of predicting the sign of earnings per share, the logistic regression
model can be written as:

1

1+ e'z
P{EPS 2 0| X} = 1 — Prob{EPS < 0| X}

P{EPS<O|X} = and

 

where

X = a vector of explanatory variables, X = [x], ........ xn]
z = the linear combination, 2 = b0 + b'X
b = the vector of coefficients, b = [b], ........ ,bn]

67

Using the same variables as in MDA, the coefficients of the function 2 have been

estimated for each year of the sample data from 1985 to 1991:

2 = be + b, .EPS H + b2 .FEPSt + b3.OVEREST,,1 + b., .FOLLCHGt + b5 .SUM3QEPSt
+ b6 .MVt + 7 .PRICECHGt V FEPSt > 0 t =1985,....,1991

Values of the coefficients and the p-value of their Wald statistic as well as model chi-
square and its significance value are presented in Table 4.7.9 With the exception of the
1987 sample, the coefficient of SUM3QEPSt is statistically significant at a 5% level.
FEPSt has no explanatory power in any of the sample periods. PRICECHGt, which is a
good discriminatory variable in MDA, has a statistically significant coefficient value
except for the 1987 and 1988 samples. FOLLCHGt and EPS ,4 have discriminatory power
in two of the eight sample periods, OVEREST,_1 is significant only in the 1988 sample.
The coefficient of MVt is insignificant in each sample. The variables are entered into the
regression equations using the forced entry method.

Classification results are presented in Table 4.8. Logistic regression has a better
overall success rate in correct classification compared to both the analysts and MDA. The
percentage of correct classification by LR is better than the correct classification rate of

the analysts in each estimation period from 1985 to 1991. In the pooled sample, LR

 

9 The Wald statistic, which has a chi-square distribution, is used in order to test the
hypothesis that a coefficient is zero. The Wald statistic is calculated by squaring the ratio
of the coefficient to its standard error (when a variable has a single degree of freedom).
Large Wald statistic values result in rejecting the null hypothesis that a coefficient has a
value of zero.

68

achieves a success rate of 96.12% in correctly predicting negative earnings given a
positive forecast. Although this is not as good as MDA’s success rate, MDA makes more
reclassification errors than LR. Correct classification of positive earnings is very close to
100% in each of the sample periods. For example, in the pooled sample, LR correctly
classifies 39.25% of the negative earnings while misclassifying only 14 of 1930 positive
earnings outcomes. 1986 and 1991 samples give similar results; about a 50% success rate
in correctly predicting negative earnings with a very small reclassification error for

positive earnings.

Summary

In this chapter, firm specific variables that can help predict the sign of an earnings
outcome are tested in estimation samples of positive forecasts between 1985 and 1991.
Using MDA and LR, observations are classified into negative and positive earnings
groups. Classification rates of both methods are evaluated against a benchmark of correct
classification by security analysts. Both MDA and LR outperform security analysts in the
prediction of negative earnings outcomes. In terms of the overall correct classification LR
tops the list while analysts and MDA come second and third, respectively. However,
MDA performs better than both LR and the analysts in correctly predicting the negative
earnings outcomes.

The best variables for predicting negative earnings in MDA are SUM3QEPS,,

FEPS ,, and PRICECHGt, respectively. Although LR gives results that agree with MDA

69

for the inclusion of SUM3QEPSt and PRICECHGt, the same cannot be said for FEPSt
which is insignificant in each sample period.

Previous research studies conclude that analysts outperform time-series models
because they are able to utilize a broader set of information in forming their earnings
forecasts. The results in this chapter show that analysts’ predictions of the sign of
earnings can be improved by them with the sum of the first three quarters’ earnings per
share and the percentage change in stock price from the previous year. This is an
indication that analysts exclude or fail to include some relevant information when
forming their forecasts. The findings are more in line with studies that show analysts
forecasts can be improved when they are combined with other information such as time-
series characteristics of earnings (Guerard (1987), Lobo (1992)).

The next chapter involves (1) obtaining MDA parameters in an estimation period,
(2) using these parameter estimates in a hold-out test period to predict the sign of
earnings, and (3) adjusting those forecasts that correspond to the negative earnings group
using an adjustment factor obtained in the estimation period. MDA is chosen as the
methodology for the next chapter because of its better success rate in predicting negative
earnings. Also, the LR results have been only recently added to this chapter. A
comparison of the MDA and LR methods in the context of Chapter 5 has not been

possible in the time frame of this study.

70

 

 

 

 

 

 

 

 

 

 

 

 

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Chapter 5

IMPROVING THE ACCURACY OF POSITIVE EARNINGS FORECASTS

In this chapter, the parameters of the MDA discriminant function are estimated
using an estimation period sample. Discriminant scores from the analysis are saved and
regressed against the forecast errors. Then, estimated discriminant function parameters
are applied to a test period sample to predict the sign of actual earnings. Positive earnings
forecasts that are predicted to be associated with negative earnings according to MDA are
adjusted in the test period using the regression parameters of the forecast errors against
the discriminant scores. In line with the findings of Chapter 4, the sum of the first three
quarterly earnings announcements and the November consensus forecast are used as

discriminatory variables in the MDA to predict the sign of actual earnings outcomes.

Estimation Period

When analysts produce their November forecasts of annual earnings per share,
they have the advantage of knowing the earnings numbers for the first three quarters.
However, the large proportion of over-optimistic forecasts of negative earnings
announcements suggests that they disregard this information when forming their forecasts

of earnings outcomes that turn out to be negative. If the overoptimism is intentional,

78

79

analysts will continue reporting optimistic forecasts regardless of the bad news revealed
in the first three quarters. This results in overoptimistic positive forecasts of negative
earnings. Because analysts are quite accurate when reporting positive forecasts of
earnings that turn out to be positive, an attempt to correct positive forecasts must first
predict the sign of actual earnings outcomes. As the results in Chapter 4 suggest,
combining this predisclosure information with the analyst forecasts may yield an

improved forecast of the sign of earnings, especially for negative earnings outcomes.

SIGNEPSit = f (SUM3QEPSit, FEPS“)
where

SIGNEPS,t = sign of the annual earnings per share for firm i in period t

FEPS“ = median forecast of earnings per share for firm i in period t
SUM3QEPS" = sum of the first three quarters' earnings per share for firm i in
period t

The following unstandardized canonical discriminant function is used to compute

discriminant scores (D_SCORE),

D_scom=.it = a, + b, . SUM3QEPS“ + ct . FEPS" v FEPS“ > o t =1984,....,1990

Coefficients have been estimated for each year of the sample data from 1984 to 1990. The
coefficient values and the p-values of the univariate F -statistic for each variable are
shown in Table 5.1. As is apparent in the table, both variables have statistically

significant discriminating power. The coefficient of SUM3QEPS has positive values and

80

the coefficient of FEPS has negative values in each estimation period, and both
coefficients are significant at a 5% level in each period.

The percentage of correct classifications for each estimation period is
presented in Table 5.2. The percentage of negative earnings correctly classified is above
50% in four of the eight estimation samples, reaching a maximum of 75% in the 1984
sample. This improvement comes at the expense of classifying some positive earnings
outcomes as negative. With the exception of 1984 and 1990, the overall proportion of
correct classifications stays very close to that of the analysts.

The second step in the estimation period involves determining the size of the
forecast errors corresponding to the earnings that are predicted as negative. Positive
forecasts of positive earnings are quite accurate whereas positive forecasts of negative
earnings are grossly over-optimistic. Therefore, forecasts that correspond to a negative
earnings number should have the largest forecast error. In order to obtain information on
the size of the forecast adjustment, discriminant scores from the analysis are saved and
regressed against the forecast errors for the positive forecasts that are relassified as

negative by MDA:

PCBit = a, + b, . D_SC0REit + eit v SIGNEPSit' and v FEPS“ > o t =1984,....,1990

where
FCE" = forecast error (= EPS - F EPS) for firm i in period t
D_SCOREit = discriminant score firm i in period t
SIGNEPSi{ = sign of earnings per share predicted as negative for firm i in

period t

81

Results presented in Table 5.3 show that discriminant scores have statistically significant
explanatory power in predicting the size of the forecast error in each year except 1987. R2
values range between 4.73% and 91.97%, and the coefficient of D_SCORE is significant
at 5% level in each of the sample periods except 1987. The mean value of the forecast
error is large and negative in each period indicating that forecasts of earnings that are
predicted as negative have an optimistic bias. A positive coefficient for D_SCORE means
that the smaller the D_SCORE the more optimistic a forecast is likely to be.

This result gains more significance when the following OLS regression is run for

the positive forecasts that are not reclassified:

F CE“ = a1 + bt . D_SCORE" + en \7’ SIGNEPS"+ and V FEPS“ > O t =1984,....,l990
where

SIGNEPSit+= sign of earnings per share predicted as negative for firm i in period t

As is apparent in Table 4.4, the regressions result in small R2 values and significantly
non-zero intercept terms. Also, F CE has a negative and smaller mean compared to the
mean in the negative prediction group, whereas the mean of D_SCORE is positive. This
suggests that, in contrast to the group of negative earnings prediction, D_SCORE does
not explain the variation in FCE as successfully in the sample of positive earnings

forecasts that are not reclassified as negative by MDA.

82

Test Period
In this section, parameters of the discriminant function estimated in one year (the
estimation period) are used to predict the sign of earnings in the following year (the test
period). Earnings that are predicted as negative are then adjusted using the regression
parameters of the forecast error versus the discriminant scores from the estimation period.
The following equation is used to predict the sign of the earnings in the test

period:

D_SCORE" = aH + bH . SUM3QEPS" + c H . FEPS“ v FEPS" > o t= 1985,....,1991

The D_SCORE that is computed for each observation is compared with the cut-off
discriminant score from the estimation period.1 If the calculated D_SCORE for the test
period is greater than the cut-off point, the observation is assigned into the positive
earnings group. Otherwise, the observation is classified into the negative earnings group.
The classification results for the test period are presented in Table 5.5. For each test
period from 1985 to 1991, the percentage of negative earnings correctly classified by
MDA is an improvement over analysts' predictions. Correct classification of negative

earnings by MDA ranges from 38.89% to 85.29% in the seven test period samples

 

1 The cut-off discriminant value is obtained from the estimation period sample using a
procedure suggested by Altman [1968]. This procedure uses the estimation period
discriminant scores to select a cut-off point that minimizes the misclassification error in
the “area of ignorance” where distributions of discriminant scores overlap. Hsieh (1993)
suggests an alternative method that minimizes the cost of misclassification when the costs
of misclassification are not symmetric.

83

between 1985 and 1991. Although it falls below 90.00% in 1985 and 1991, the overall
correct classification is still comparable to that of the analysts. With the exception of
these two years, probability of incorrectly predicting negative earnings when actual
earnings are positive is between 2 and 5 percent of the positive earnings outcomes.

To identify and adjust the forecasts of negative earnings, those observations in the
negative earnings group are used with the following equation to predict the size of the

forecast error and hence the magnitude of the forecast adjustment (ADJ).

ADJit = aH + b,l . D_SCORE" v SIGNEPSR' and v FEPS“ > 0 t = 1985,....,1991

Finally, positive forecasts that are predicted by MDA to correspond to negative earnings

are adjusted using the following equation:2

AFEPSi, = FEPS“ + ADJ“ v SIGNEPSR' and v FEPS“ > 0 t= 1985,....,1991

The improvement in forecast accuracy as a result of these adjustments is presented
in Table 5.6. Adjusted forecasts outperform analysts' consensus forecasts in relative
forecast accuracy in each period except 1987. Relative forecast accuracy (the ratio of the

MSE after adjustment to the MSE before adjustment) ranges between 9.11% and 62.36%

 

2Using the conventional measure of forecast error (actual earnings - forecasts) the sign of
an over-optimistic forecast error and hence the sign of the adjustment factor will be
negative. Adding a negative adjustment factor to the forecast will therefore have the
effect of a downward adjustment.

84

in six test periods, and it is 53.01% in the pooled sample. MSE is reduced by downward
adjusting the forecasts of earnings reclassified as negative by MDA. Another important
implication of these results pertains to the positive forecasts of positive earnings that are
adjusted as a result of the misclassification by MDA. Despite a classification error, the
majority of the positive forecasts of positive earnings that are misclassified as negative
earnings forecasts are still overoptimistic. As is apparent in the bottom panel of Table 5.6,
the proportion of positive earnings that are overestimated by analysts is around 50%
(ranges from 40.72% to 56.33%) in the test period samples. Positive earnings that are
classified as negative by MDA are overoptimistic up to 88.24% of the time. This suggests
that when SUM3QEPS and FEPS are used as discriminatory variables, MDA can
discriminate not only the positive forecasts of negative earnings outcomes but also the
optimistic positive forecasts of positive earnings. When the predicted forecast errors are
added to the optimistic positive forecasts of positive earnings, this results in a downward
adjustment in the correct direction.3 The proportion of downward adjustments that are in
the correct direction ranges between 61.90% and 93.33% in the overall positive forecast
sample. Forecasts of positive earnings are correctly downward adjusted at a success rate
of above 70% in four of the seven test period samples and 70.69% in the pooled sample.
Improvements on these results might be achieved by extending the estimation period by

pooling data into two (or more) years.

 

3 Kwok and Lubecke (1990) use the “correctness” criterion in assessing improvements in
foreign exchange forecasts.

85

Summary

Although security analysts do a relatively good job when they report forecasts for
positive earnings that turn out to be positive, they suffer from an optimistic bias when
forecasting earnings that turn out to be negative. That is, positive consensus forecasts are
fairly symmetrically distributed around actual earnings when they correspond to a
positive earnings outcome. Overoptimistic bias in positive forecasts is driven by earnings
that turn out to be negative. In this chapter, a methodology is tested to identify and adjust
positive forecasts that are predicted to correspond to negative earnings outcomes.

The methodology involves using consensus forecasts of annual earnings with the
sum of the first three quarters’ earnings to predict the sign of an earnings announcement.
First, the coefficients of SUM3QEPS and F EPS and the cut-off discriminant values from
Multiple Discriminant Analysis for each annual sample period are estimated between
1984 and 1990. OLS regression parameters of the forecast errors against the discriminant
scores are obtained for those earnings predicted as negative by MDA in the estimation
period. Coefficient values of the MDA function and cut-off discriminant scores are then
used in an out-of-sample test period to predict the sign of actual earnings outcomes. An
adjustment factor is obtained by using the previously estimated regression parameters of
the forecasts errors versus the discriminant scores. Earnings that are predicted as negative
in the test period are then adjusted using the adjustment factor. Test period results
indicate that this methodology provides forecasts that outperform security analysts’
consensus forecasts. Mean square error before adjustment is greatly reduced in all but one

test period.

86

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Chapter 6
A COMPARATIVE ANALYSIS OF ANALYSTS’ EARNINGS FORECASTS IN
INTERNATIONAL EQUITY MARKETS

Investors who seek to diversify their portfolios through international equity
investments face the difficult task of evaluating the market values of stocks in different
institutional environments. Valuation of a stock requires estimation of its future cash flow
performance. Expectations of market participants on company fundamentals, which serve
as measures of future performance, play an important role in driving the market values of
stocks.

Research studies of US. and other equity markets have shown that analysts
forecasts’ of earnings proxy for investors’ expectations of firms' future performance. For
example, Jacques and Rie (1994) examine which company fundamentals are important in
determining stock prices in the US, the UK. and Japan. They find that current earnings
are important to investors in all three countries and that earnings estimates dominate both
current earnings and dividends.

Several studies have documented the association of earnings forecasts with stock
prices and returns in international equity markets. Bercel (1994) shows that changes in
analysts’ earnings per share forecasts and the number of analysts changing their forecasts
are related to abnormal stock returns in several international markets. Erickson and

Cunniff (1995) find that the appeal of working with consensus forecasts of earnings is

92

93

even greater for international markets, where differences in accounting standards are
significant. In a study that covers quarterly periods between 1988 and 1993, they find that
consensus earnings estimates are important, but in varying degrees across different world
markets, and that they can effectively contribute to stock selection models. Sultan (1994)
examines the relationship between unexpected earnings announcements and stock prices
in Japan and shows that firms announcing better than expected earnings outperform those
announcing worse than expected earnings. Conroy, Harris and Park (1994) investigate the
link between share prices in Japan and earnings forecasts by both analysts and
management. Their evidence shows that earnings fundamentals are priced in the Japanese
market, and that both analyst and management forecasts convey significant information to
the market participants. In spite of important institutional differences between Japanese
and US. equity markets, this study finds significant value effects of earnings in both
markets. Conroy et al. conclude that stock prices react to announcements of recent
earnings when actual earnings differ from analysts’ forecasts. Elton and Gruber (1989)
explore the impact of a change in analysts’ forecasts of earnings and sales on the
subsequent price performance of a sample of Japanese stocks. Their study finds that
changes in earnings and sales estimates affect price and that the impact is incorporated
slowly over time.

In light of studies demonstrating the importance of analysts’ earnings forecasts in
international equity markets, research has increasingly focused on issues of rationality
and accuracy in these forecasts. For example, Capstaff, Paudyal and Rees (1995) examine

whether forecasts of corporate earnings in the UK. are formed in a rational manner based

94

on a sample of individual forecasts of annual earnings for the years ending in 1987 and
1991. Their results show that analysts generally provide more accurate forecasts than
naive time series models, but that forecast errors are larger when earnings decrease than
when earnings increase. These authors also suggest that analysts overreact to recent
information when making forecasts. Capstaff, et al. conclude that these results cast
considerable doubt on the rationality of earnings forecasting in the United Kingdom.
Conroy and Harris (1995) analyze two distinct sources of analysts’ earnings forecasts for
Japanese stocks, one from sell-side analysts and another from an information provider
that does not make stock recommendations. Their results indicate that forecasts from sell-
side analysts are more optimistic and less accurate than the second set of forecasts,
possibly reflecting analyst incentive structures and traditional role of Japanese securities
houses.

Harris, Lang and Moller (1994) compare the value relevance of accounting
measures of earnings for US. and German firms matched on industry and firm size.
Contrary to the notion that accounting data are essentially meaningless for German
corporations, the study finds that these data are significantly associated with stock price
levels and returns. Harris, et al. also find that the explanatory power of earnings for
returns in Germany is comparable to that in the US, which suggests that German
earnings are not as imprecise as often perceived.

In this chapter, analysts' earnings forecasts in Japan, the United Kingdom, and
Germany are investigated to find out whether (1) there exists a bias in analysts’ consensus

forecasts of earnings per share in these markets, (2) bias (if present) has any systematic

95

component and/or is symmetric across the magnitude of forecasts, (3) negative earnings
forecasts differ from positive forecasts in terms of bias, and (4) the US. phenomenon of
overoptimistic forecasts of negative earnings also appears in these international equity

markets.

Data

Data for analysis is gathered using the Institutional Brokers Estimate System
(I/B/E/ S) International history date tapes. This data base provides information on security
analysts’ consensus earnings forecasts for over forty countries. The sample is reduced to
include Japan, U.K., and Germany to focus on relatively better established international
capital markets. Using similar filters as in the US. case, a sample of median consensus
forecasts of those companies with three or more forecasts of primary earnings per share
reported to I/B/E/ S during November for a December fiscal year-end is constructed.
Earnings per share figures are taken from the Background Data File of the I/B/E/S history
tape. Both earnings per share forecasts and actual earnings per share for each firm are
divided by beginning-of-year share price in order to scale for cross-sectional differences
in the level of earnings and share price. Hereafter, “earnings” and “EPS” refer to the
earnings/price ratio and “forecasts” and “FEPS” refer to the ratio of consensus forecasts
to price. The final sample covers the period 1987-94 and includes 1,056 observations for
Japan, 2,049 for the UK. and 1,035 for Germany. Tables 6.1-6.3 present descriptive
statistics on actual earnings (EPS) and earnings forecasts (FEPS) for Japan, the UK. and

Germany, respectively.

96

Forecast Bias

Figures 6.1-6.3 plot actual (EPS) against expected (FEPS) earnings over the
pooled sample period 1987-94 for Japan, the U.K., and Germany, respectively (Figures
6.4-6.6 provide a more detailed view using a larger scale). As is evident in the figures,
analysts in these countries rarely report a negative forecast for earnings that turn out to be
positive (about 1% of all observations across all three countries). In fact, forecasts of
positive earnings are clustered around a 45-degree line through the origin. (Some U.K.
forecasts in the northeast quadrant show a larger deviation from the 45-degree line than
those in Japan and Germany). On the other hand, forecasts associated with negative
earnings outcomes are located mostly to the right of the 45-degree line, indicating
overoptimism by security analysts. The ray of observations scattered along the y-axes in
the southeast quadrants of Figures 6.1-6.3 reflect a tendency of analysts to report positive
forecasts even when actual earnings are negative. These preliminary observations are
similar to those for US. forecasts in Table 1.

Tables 6.4-6.6 show the percentage of cases where forecasts overestimate actual
earnings on a year-by-year basis and categorized according to the sign EPS and the sign
of the FEPS for the three countries.

The pooled sample results in Japan shows that analyst forecasts are overoptimistic
63.87% of the time with a statistically significant forecast bias of (0008233). The
proportion of optimistic forecasts is 67.50% when forecasts have a negative sign and

63.57% when they have a positive sign. The magnitude of the average forecast error in

97

the pooled sample of negative forecasts (-O. 1 35330) is greater than the magnitude of the
average forecast error in the pooled sample of positive forecasts (-0.005493). When
analysts report a positive forecast for earnings that turn out to be positive, they are
optimistic 62.02% of the time with an average forecast error of (-0.002138). On the other
hand, when they issue negative forecasts for earnings that turn out to be negative, this
overoptimism is magnified. In this case 85.71% of the earnings are overestimated with a
large average bias of (0075761). Analysts forecast 39 of the 102 (38.24%) negative
earnings outcomes as positive. Analysts report negative forecasts for only 17 of 936
(1.82%) positive earning announcements.

Analysts in the UK. are also overoptimistic as reported in Table 6.5. Forecasts
turn out to be larger than actual earnings 70.52% of the time with an average forecast
error of (-0.01 1660) in the pooled sample. Negative earnings forecasts show an optimistic
bias of (0.002231) and the percentage of overestimated earnings is 35.71%. Analysts’
negative forecasts of negative earnings have an average forecast bias of (-0.115973). In
the case of positive earnings forecasts, the proportion of over-optimistic forecasts is
71.51% and the average forecast bias is (-0.012053). U.K. analysts report positive
forecasts for 64 of 96 (66.67%) negative earnings outcomes. On the other hand, they
report a negative forecast for 24 of 1943 positive earnings outcomes.

In Germany, analysts overestimate actual earnings 67.64% of the time with an
average forecast bias of (-0.010450) in the pooled sample period of 1987-1994. About
two-thirds of both negative (66.67%) and positive (67.79%) forecasts are overoptimistic.

However, the magnitude of the average bias in negative forecasts (-0.106934) is higher

98

than that of positive forecasts (-0.00491 3) indicating that negative earnings forecasts
contribute proportionally more to bias in the pooled sample. With the exception of 1992
and 1993 analysts in Germany do not report negative forecasts for earnings that turn out
to be positive. Nevertheless, 28 out of 71 negative earnings announcements are predicted

as positive in the pooled sample of 1987-94.

Are Forecast Errors Symmetric?

To test whether forecast errors are symmetric, the pooled sample is divided into
deciles based on the size of the earnings forecasts. Forecast errors and the percentage of
forecasts that overestimate actual earnings are calculated for each decile. Then, forecast
error and mean square forecast error for equal-sized top and bottom samples based on one
or more deciles are compared using a paired sample t-test and analysis of variance.

Results of the analysis are presented in Tables 6.7-6.9 for Japan, the U.K., and
Germany, respectively. The top decile of forecasts are compared to the bottom decile of
forecasts in the firs row of the table labeled “10%”. The top half is compared to the
bottom half in the “50%” row of the table.

Results presented in Table 6.7 show that forecasts errors are significantly different
from zero in both the bottom and top deciles. Negative signs on the forecast errors
indicatethat forecasts are optimistic across each sample. In fact, a paired samples t-test
cannot reject the hypothesis that forecast errors in corresponding bottom and top deciles
are equal. For example, the average forecast error in the bottom half of the sample is (-

0.008196). The forecast error for the top half is (-0.009110). The hypothesis that they are

99

equal cannot be rejected at a 5% significance level. Similarly, the hypothesis that mean
square forecast errors in the bottom and top halves of the sample are equal cannot be
rejected by an analysis of variance at a 5% level of significance. The percentage of
forecasts overestimating actual earnings are significantly different from 50% in both
bottom and top decile groups where the overestimation rate is higher in the top decile
groups. In contrast to the United States (see Table 2.6), large forecast errors do not seem
to be driven by the lowest forecasts in Japan. A statistical comparison of the top and
bottom deciles fails to reveal any asymmetry in forecast errors in Japan. These results
suggest that analysts forecasts of earnings per share in Japan are consistently
overoptimistic regardless of the magnitude of the forecasts.

In the United Kingdom (Table 6.8), the percentage of forecasts that overestimate
actual earnings is significantly higher than 50% in each sample. Mean forecast errors
have a negative sign in each group, indicating consistent overoptimism. However,
forecast errors are statistically significant only for the bottom 50 percentile and the top
40—50 percentiles of forecasts. As in Japan, neither average forecast errors nor mean
square errors are statistically different for the matching pairs of bottom and top decile
groups. These results can be interpreted as an indication that overoptimism is symmetric
and consistent across analyst forecasts in the United Kingdom.

Table 6.9 shows the results for Germany. The percentage of forecasts
overestimating actual earnings is again significantly different from 50% in both the
bottom and top decile groups. A comparison of matched pairs of decile groups reveals

that analysts overestimate earnings at a higher proportion in the lower decile groups. As

100

the magnitude of forecasts increases, the number of forecasts overestimating earnings
decreases. For example, analysts overestimate earnings 66.67% of the time in the bottom
decile, and overestimate earnings 57.14% of the time in the top decile. Average forecast
errors are significantly different from zero in each group. The negative signs indicate
overoptimism. A comparison of forecast errors in the bottom and top groups with a
paired-sample t-test suggests that forecast errors in the bottom groups are significantly
greater than the forecast errors in the top groups. A comparison of mean square forecast
errors also shows the same result. These findings show that the magnitude of the
optimistic bias increases as the forecasts become smaller in this sample of German

companies between 1987 and 1994.

Forecast Bias and the Sign of Forecasts

In this section samples of earnings forecasts by analysts in Japan, the UK. and
Germany are investigated to understand whether or not predictions of negative earnings
are different from predictions of positive earnings in these countries. The null hypothesis
is that analysts’ earnings forecasts are accurate and rational, and therefore should lie on a
45-degree line drawn through the origin. In order to test this hypothesis the following
OLS regressions are run using samples of Japan, the UK. and Germany for the period

between 1987 and 1994:

EPS, = a, + b, . FEPS“ + eit v FEPS
EPSit = a, + b, . FEPS" + eit v FEPS < o
EPSit = a, + bt . FEPS“ + eit v FEPS 2 0

where

101

EPS,t = actual earnings per share for firm i and fiscal year t
FEPS,t = earnings forecast per share for firm i and fiscal year t

The first regression uses all observations. The second and third regressions use negative
FEPS and positive FEPS samples separately to examine whether predictions of negative
earnings are different than those of positive earnings. The results are summarized in
Tables 6.10-6.12 for each of the three countries.

For the Japanese sample, the first regression yields a significantly negative
intercept term (-0.0072l6) and a slope term (0.913400) that is statistically different from
1. This suggests that forecasts of Japanese earnings have a significant optimistic bias
component. A slope term that deviates from the slope of the theoretical relationship
indicates a slight inefficiency in the analysts’ forecasts of Japanese earnings. An
examination of annual samples shows that the intercept term is negative in five of the
eight sample periods. With the exception of two annual samples, the intercept term
largely deviates from that of a 45-degree line.

In the case of the second regression with the pooled sample of negative F EPS, an
intercept term which is negative but not significantly different from zero and a slope term
which is significantly larger than one at 10% level indicate that negative forecasts are
inefficient in the pooled sample of 1987-1994.

The third regression uses the 1987-1994 pooled sample of positive forecasts. The
intercept term in the third regression is significantly different from zero (0.018849) and
the slope (.057077) is significantly different fi'om one. A review of Figure 6.1 suggests

that this result may be driven by negative forecasts of earnings that turn out to be

102

positive. In fact, the negative slope term for the 1994 sample of positive forecasts is a
consequence of overoptimistic positive forecasts of negative earnings.

Table 6.11 presents the regression results for the sample of forecasts in the United
Kingdom. In the pooled sample, the intercept term is significantly different from zero and
negative (-0.011730) while the slope term is greater than one (1.056217). This suggests
both bias and inefficiency in the UK. analysts’ earnings forecasts.

In the case of negative forecasts, the pooled sample of 1987-1994 results in a
negative SIOpe term (-0.032981) which is not statistically significant and a slope term of
(0.718784). These results imply inefficiency in negative forecasts of the UK. analysts. A
review of Figure 2 suggests that this result is likely to reflect the problem of negative
forecasts of earnings that turn out to be positive. Negative forecasts of positive earnings
almost equal the number of negative forecasts of negative earnings in the pooled sample.
An implication of this result is that, unlike the US, Japan and Germany, a negative
forecast in the UK. cannot be presumed as Optimistic.

The pooled sample of positive earnings forecasts (the third regression) indicates
both bias and inefficiency with a significantly negative intercept term (—0.040993) and a
slope term (1.386220) that differs significantly from one. Similar results are observed in
six of the eight annual samples with a negative intercept and a slope that is larger than
one. The negative intercept is likely to be capturing the impact of negative forecasts of
earnings that turn out to be positive, which extend close to the y-axis on the southeast

quadrant of Figure 6.2.

103

In the case of Germany, the first regression provides a negative intercept term of
(-0.019978) which is significantly different from zero and a slope term of (1.13761 5)
which is significantly different from one. These results can be interpreted as indication of
inefficiency and optimistic bias in the analysts’ forecasts of earnings per share in
Germany. Regressions that use all observations result in significantly negative intercept
terms in five annual samples. The slope is significantly different from one in all annual
samples. In this case, too, the negative bias term may reflect the reluctance of analysts to
report negative forecasts for some earnings that turn out to be positive.

Regression results in the negative forecast sample exhibit a statistically significant
negative intercept term (-0. 129640) and a slope term (0.745287) which is less than one at
10% level. These are evidence of optimistic bias as well as inefficiency in the pooled
sample of negative earnings forecasts in Germany.

The pooled sample of positive forecasts gives similar regression results where the
intercept term (-0.008151) significantly differs from zero. The slope term is close to one
(statistically not different from one at 5% level) in the pooled sample and in three of the
eight annual samples. This suggests that, in spite of some bias and inefficiency, positive
earnings forecasts in the pooled sample of Germany more closely relate to the theoretical
relationship of earnings to forecasts designated by a 45-degree line passing through the

origin.

104

Summary

In this chapter, the accuracy of security analysts' median consensus forecasts in
Japan, the U.K., and Germany is investigated using a sample that covers the period of
1987-94. Results indicate that analysts’ forecasts contain an optimistic bias in all three
countries. A majority of negative forecasts are overoptimistic in Japan and Germany
where analysts rarely report a negative forecasts for earnings that turn out to be positive,
and their negative forecasts of negative earnings are clearly overoptimistic. On the other
hand, negative earnings forecasts in the UK. are on average pessimistic. This is because
about half of the negative forecasts in the UK. pertain to earnings that turn out to be
positive (the northwest quadrant of Figure 6.2). This pessimism dominates the other half
where the negative forecasts that relate to negative earnings are over-optimistic 62.50%
of the time (the southwest quadrant of Figure 6.2). Positive forecasts are on average over-
optimistic in all three countries. Large magnitude of forecast errors posed by positive
forecasts of negative earnings accounts for a significant portion of this optimistic bias in
positive forecasts.

The tests of symmetry suggests that the average forecast error is negative and its
magnitude is symmetric regardless of the size of forecasts in Japan and the United
Kingdom. On the other hand, the forecast errors become larger and more negative as the
forecasts become smaller in Germany.

Regression results show that both negative and positive forecast samples as well
as the sample of all forecasts in Japan, the UK. and Germany deviate from the theoretical

relationship between forecasts and actual earnings represented by a 45-degree line

105

passing through the origin. This outcome is magnified in the case of the negative forecast
sample where regressions result in intercept and slope terms varying widely from year to
year and reflecting bias and/or inefficiency in forecasts. Regressions using the positive
forecasts sample also indicate bias and/or inefficiency in all three countries. This result
can be attributed to the positive forecasts corresponding to negative earnings outcomes.
Especially in the German sample, a majority of positive forecasts tightly cluster around
the 45-degree line passing through the origin in Figure 6.3. However, the regression of
actual earnings against the forecasts in the positive forecast sample yields a significantly
negative intercept term which indicates optimistic bias.

In light of these observations, further research may focus on (1) determining
whether this over-optimistic bias observed in forecasts of analysts in Japan, the UK. and
Germany is intentional and (2) developing methods to improve the accuracy of earnings

forecasts in these countries.

106

Figure 6.1. EPS Versus FEPS in Japan

Annual earnings per share (EPS) are plotted against analysts’ forecasts of annual earnings per
share (FEPS) for the Japanese companies in a pooled sample between 1987 and 1994.

 

 

 

 

 

 

 

 

 

 

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Figure 6.2. EPS Versus FEPS in the United Kingdom

Annual earnings per share (EPS) are plotted against analysts’ forecasts of annual earnings per
share (FEPS) for the UK. companies in a pooled sample between 1987 and 1994.

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Figure 6.3. EPS Versus FEPS in Germany

Annual earnings per share (EPS) are plotted against analysts’ forecasts of annual earnings per
share (FEPS) for the German companies in a pooled sample between 1987 and 1994.

 

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Figure 6.4. EPS Versus FEPS in Japan (Larger Scale Graph)

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Annual earnings per share (EPS) are plotted against analysts’ forecasts of annual earnings per
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FEPS

110

Figure 6.5. EPS Versus FEPS in the United Kingdom (Larger Scale Graph)

Annual earnings per share (EPS) are plotted against analysts’ forecasts of annual earnings per
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Figure 6.6. EPS Versus FEPS in Germany (Larger Scale Graph)

Annual earnings per share (EPS) are plotted against analysts’ forecasts of annual earnings per
share (F EPS) for the German companies in a pooled sample between 1987 and 1994.

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Chapter 7

CONCLUSION AND DIRECTIONS FOR FUTURE RESEARCH

This study investigates bias in security analysts’ forecasts of annual earnings per
share. Forecasts reported to the Institutional Brokers Estimate System (I/B/E/ S) of Lynch,
Jones and Ryan are examined for US. firms with December fiscal year-ends. Methods to
identify bias and to improve the accuracy of analyst forecasts are suggested and tested.
Earnings forecasts of firms in Japan, the U.K., and Germany are also examined for bias.

In Chapter 2, analysts median consensus forecasts of earnings per share are
evaluated for forecast bias in a sample of November forecasts from 1984 through 1991.
Negative earnings forecasts are found to be overoptimistic. Analysts overestimate
earnings 71.71% of the time when they report negative forecasts, and out of the 258
negative forecasts only 14 correspond to a positive earnings outcome. Positive forecasts
of earnings per share, however, overestimate actual earnings only 54.19% of the time.
Positive forecasts of positive earnings are overoptimistic only 50.50% of the time.
However, 5.16% of these positive forecasts grossly over-estimate earnings that actually
turn out negative.

In terms of the magnitude of bias, negative earnings forecasts are more optimistic
than positive earnings forecasts. Negative earnings forecasts have an average bias of

(-0.074176) and positive earnings forecasts have an average bias of (-0.0l 0772) in the

124

125

pooled 1984-91 sample. For both negative and positive forecast samples, bias is
optimistic every year from 1984 to 1991.

An examination of empirical regression lines in Chapter 2 reveals that the
relationship of forecasts and actual earnings deviates from the 45-degree line through the
origin. This deviation is most apparent for the negative forecast sample in the form of
large optimistic biases. Regressions using the positive forecast sample result in parameter
estimates that reflect bias and inefficiency.

The findings in the chapter suggest that the observed overoptimism is mostly
driven by the forecasts of companies with negative earnings. The percentage of earnings
overestimated is 50.32% and average bias is (-0.002439) in the positive earnings sample.
On the other hand, analysts are overoptimistic 86.69% of the time with an average bias of
(-O.l 17492) in the negative earnings sample.

The main conclusions of Chapter 2 are that (1) forecasts are on average optimistic,
(2) biases in negative forecasts and in negative earnings are more obvious than those in
positive forecasts and earnings, (3) positive forecasts that overestimate negative earnings
are the biggest source of forecast error, (4) optimistic bias in forecasts seems to be driven
by firms with negative earnings.

In light of these observations, Chapter 3 investigates methods to improve the
accuracy of negative earnings forecasts. Chapters 4 develops a methodology to predict the
sign of actual earnings. Chapter 5 corrects positive earnings forecasts that are likely to be

associated with negative earnings.

126

The first part of Chapter 3 provides information on the increase in relative
forecast accuracy (measured by mean square error) one might expect from adjusting
negative forecasts downward by various amounts. Since security analysts are likely to be
measured by more than just forecast accuracy, this chapter also investigates how
downward adjustments of varying amounts affect (1) the probability of being closer to
actual earnings than the consensus, and the (2) probability of underestimating actual
earnings. These additional two measures will be of interest to those analysts (1) rewarded
for “beating the consensus”, and (2) exposed to criticism by corporate management for
underestimating earnings.

Results in Chapter 3 show that adjustments of up to 1% of share price result in
improved forecast accuracy, an increased probability of beating the consensus forecast,
and little increase in the probability of underestimating actual earnings. Forecast
adjustments of between 1% and 2% of share price consistently beat consensus forecasts
and continue to improve forecast accuracy, although there is an increasing risk of
underestimating earnings. Relative forecast accuracy continues to improve for
adjustments of up to 5% of share price. While the probability of beating the consensus is
still on average greater than one-half for adjustments of up to 5% of share price, the
extent to which forecasts can be adjusted and still beat the consensus more than half the
time exhibits a good deal of year-to-year variation. The maximum adjustment before the
probability of beating the consensus falls below one-half in the yearly samples ranged
from 2% to 11% of share price. Beyond an adjustment of 2% of share price there is

substantial risk of underestimating earnings. Forecast adjustments of up to 11% of share

127

price are still likely to be superior to unadjusted forecasts on forecast accuracy, although
by this point one has probably overshot the mark. The probability of beating the
consensus and the probability of underestimating earnings are both unacceptably high.

Each analyst must make an individual decision on how much to adjust negative
earnings forecasts according to the incentives and penalties they face in their individual
circumstance. Small downward adjustments can improve forecast accuracy as well as the
probability of beating the consensus forecast. Larger adjustments continue to improve
forecast accuracy at the expense of an increasing probability of under-estimating earnings
and a lower probability of beating the consensus forecast.

In Chapter 4, firm-specific variables that can help predict the sign of an annual
earnings outcome are tested in samples of positive forecasts between 1985 and 1991.
Using Multiple Discriminant Analysis (MDA) and Logistic Regressions (LR),
observations are classified into negative and positive earnings groups and the correct
classification rates of each method is evaluated against a benchmark of correct
classification by security analysts. Both MDA and LR outperform security analysts in the
prediction of negative earnings outcomes. MDA performs better than both LR and
analysts in correctly predicting negative earnings outcomes. In terms of the overall
correct classification, LR tops the list while analysts and MDA come second and third,
respectively.

The best variables in terms of explanatory power in MDA are the sum of the first
three quarterly earnings (SUM3QEPS), the magnitude of the consensus forecast (FEPS),

and the percentage change in share price during the year (PRICECHG). Although LR

128

gives results that agree with MDA for the inclusion of SUM3QEPS and PRICECHG,
F EPS is not a significant explanatory variable.

MDA is chosen to be the methodology for adjusting positive forecasts in Chapter
5 because of its better performance in explaining negative earnings outcomes.

Chapter 5 involves (1) obtaining MDA parameters in an estimation period, (2)
using these parameter estimates in a hold-out test period to predict the sign of earnings,
and (3) adjusting those forecasts that correspond to the negative earnings group using an
adjustment factor obtained in the estimation period. Out-of-sample tests are performed to
assess the power of the model in predicting negative earnings outcomes. Also, forecast
improvement is evaluated using the same out-of-sample tests. Although security analysts
do a relatively good job when they report positive consensus forecasts, these forecasts
suffer from an optimistic bias stemming from overoptimistic positive forecasts of
negative earnings. Positive consensus forecasts are fairly symmetrically distributed
around actual earnings when they correspond to a positive earnings outcome. On the
other hand, overoptimistic bias in positive forecasts is heavily driven by earnings that
turn out to be negative.

The methodology developed in Chapter 5 uses consensus forecasts of annual
earnings (F EPS) with the sum of the first three quarters’ earnings (SUM3QEPS) in MDA
to predict the sign of an earnings announcement. First, the coefficients of SUM3QEPS
and FEPS and cut-off discriminant values for each annual sample period are estimated
between 1984 and 1990. OLS regression parameters of forecast errors against

discriminant scores are also obtained for the earnings predicted as negative in the

129

estimation period. Then, coefficient values of the MDA function and cut-off discriminant
scores are used in an out-of-sample test period to predict the sign of actual earnings. An
adjustment factor is obtained by using the previously estimated regression parameters of
forecasts errors versus discriminant scores. Earnings that are predicted as negative in the
test period are then adjusted using the adjustment factor. Test period results indicate that
this methodology outperforms security analysts’ consensus forecasts in predicting
negative earnings outcomes. Mean square forecast error is greatly reduced in all but one
test period. The methodology also predicts the optimistic positive forecasts of positive
earnings at a success rate of up to 88.24% while the observed probability of an optimistic
positive forecast is about 50.00% across the test period.

In Chapter 6, the accuracy of security analysts' median consensus forecasts in
Japan, the U.K., and Germany is investigated using a sample that covers the period 1987-
94. Results indicate that analysts’ forecasts contain an optimistic bias in all three
countries. A majority of negative forecasts are overoptimistic in Japan and Germany,
where analysts rarely report negative forecasts for earnings that turn out to be positive.
Negative forecasts of negative earnings are clearly overoptimistic in Japan and Germany.

In contrast, negative earnings forecasts in the UK. are on average pessimistic.
This is because about half of the negative forecasts in the UK. pertain to earnings that
turn out to be positive. Positive forecasts are also on average over-optimistic in all three
countries. The large magnitude of forecast errors posed by positive forecasts of negative

earnings accounts for a significant portion of this optimistic bias in positive forecasts.

130

Tests of symmetry suggest that the average forecast error is negative and its
magnitude is symmetric regardless of the size of forecasts in Japan and the United
Kingdom. On the other hand, the forecast errors become larger and more negative as the
forecasts become smaller in Germany.

Regression results show that both negative and positive forecast samples as well
as the sample of all forecasts in Japan, the UK. and Germany deviate from the theoretical
relationship between forecasts and actual earnings represented by a 45-degree line
passing through the origin. This outcome is magnified in the case of the negative forecast
sample where regressions result in intercept and slope terms varying widely from year to
year and reflecting bias and/or inefficiency in forecasts. Regressions using the positive
forecasts sample also indicate bias and/or inefficiency in all three countries. This result
can be attributed to the positive forecasts corresponding to negative earnings outcomes.
Especially in the German sample, a majority of positive forecasts tightly cluster around
the 45-degree line passing through the origin. However, the regression of actual earnings
against the forecasts in the positive forecast sample yields a significantly negative
intercept term which indicates optimistic bias.

In light of the findings of this study, further research should focus on (1)
investigating the association of adjusted forecast errors to the post announcement stock
price changes in the US, (2) determining the underlying institutional implications of
over-optimistic bias observed in forecasts of analysts in Japan, the UK. and Germany,
and (2) developing methods to improve the accuracy of earnings forecasts in these

countries.

APPENDIX

APPENDIX

DECOMPOSITION OF THE FORECAST ERROR

At this point, it is useful to reconsider the multiple regression model employed in
Chapter 2:

EPS=a+b.FEPS+e
where

EPS = actual earnings per share
FEPS earnings forecast per share

Using this model, the sources of forecast error in the composition of mean square error
(MSE) can be reviewed. The forecast error (FCE) can be computed as:

FCE = EPS - FEPS

The variance of the forecast error is 02(FCE) and r2 is the coefficient of determination of
the regression model. Applying the method suggested by Theil (1966) (see also Mincer

(1969)), the mean square error of the forecast can be decomposed as follows:

MSE = E(EPS - FEPS) 2 = E(FCE) 2 = [130703)] 2 + 02(FCE)
= [E(FCE)1 2 + [o2(FCE) - 0%)] + ole)
= [E(FCE)] 2 + (1 - b) 2 . 02(FEPS) + (1 - r2) . 02(EPS)

= bias + inefficiency + error

131

132

Bias in the prediction of EPS relates to the difference between the actual mean

EPS and the mean FEPS. In line with a rational expectations framework, an unbiased

estimate involves an average FEPS (FEPS) which is equal to average EPS (ES). In this

case, the regression equation passes through the point:

(x.y>=(FEP—s,f~f17§)

on the 45-degree line of perfect fit.

The inefficiency of the forecast is represented by the magnitude of 62(FCE)
relative to the residual variance 02(e) in the regression equation. When the forecast error
(FCE) is uncorrelated with the FEPS, the slope coefficient (b) must be equal to unity.
This implies that 62(FCE) = 0'2 (e) and the EPS prediction is efficient. If, however, the
FCE is related to the F EPS, then the forecast is inefficient. In this case, b is not equal to
unity and 02(FCE) is different from 02(e).

Figure A.1 demonstrates four different cases where (a) the forecast is unbiased
and efficient although a random estimation error exists, (b) forecast exhibits only bias, (c)

forecast is inefficient, and (d) forecast is both biased and inefficient.

133

Figure A.1. Decomposition of Mean Square Forecast Error of EPS Forecasts

 

 

 

 

 

 

 

EPS / EPS/\
/
//
mm_ _._ IAS ///
EPS 4* V7 EPS --——‘L—-
1 // 5
l / i
450 , \ 450 .// \
A / FEPS / __ ._;. 7 FEPS
FEPS FEPS
/ (b)
(a)
EPSA EPS /\
__ //,.// '/' _hm BLA J ,2,
EPS ; :;.—, ’ EPS - "*-'- -"—:::-»/w"
0 o I
45 45
.. -_ , Ax FEPS _; > FEPS
FEPS FEPS

 

(C) (d)

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