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This is to certify that the

thesis entitled

AN EMPIRICAL EVALUATION OF THE STOCK PRICE REACTION
' TO ERRORS IN MANAGEMENT FORECASTS
OF EARNINGS PER SHARE

presented by

Russell Theodore Gingras

has been accepted towards fulfillment
of the requirements for

DBA degree in Business - Accounting

1.4%

Major professor

Date 8/8/74

0-7639

man-In- ‘5‘!
72?
‘

 
    
 

x Bmomc By P“
HMS & SUNS
K BMW" INC

 
  

ABSTRACT

AN EMPIRICAL EVALUATION OF THE STOCK PRICE REACTION
TO ERRORS IN MANAGEMENT FORECASTS
OF EARNINGS PER SHARE

by

Russell Theodore Gingras

The purpose of this research effort was to examine
the stock price reaction to errors in management fore-
casts of earnings per share. It was expected that the
study would provide evidence as to whether such fore-
casts were used by investors. If such forecasts were
not used by investors, then perhaps the other difficult
problems associated with the publication of such fore-
casts could be avoided.

Since questions were directed toward the usefulness
of management forecasts to investors, it was important
to examine the theoretical basis for expecting such
forecasts to be useful to investors. It was found that
many security valuation models depend on expected earnings.
This, coupled with research studies which found that
there was a relationship between reported earnings and

stock prices, strongly indicated that there might be

a relationship between management forecasts of earnings

per share and stock prices.

{1

,t3_ Russell Theodore Gingras

If management earnings forecasts had influenced
investor expectations and reported earnings were dif-
ferent from the earnings which had been forecast, a
reaction in the price of the stock would be expected.
Thus, the stock price reaction to forecast errors was
used as a measure of the usefulness of management fore-
casts to investors. In order to be meaningful, the
study went beyond an analysis of stock price reactions
to management earnings forecasts. It was possible that
similar results could have been obtained using forecasts
generated by naive or mechanical models. Therefore, the
study included an analysis of possible stock price reac-
tion to several naive model forecasts as well as to
management earnings forecasts.

The firms making management forecasts were selected

from The Wall Street Journal. In total, there were 123

 

usable management forecasts.

The computation of forecast errors in an attempt to
relate forecasts to stock price changes made it possi-
ble to examine the accuracy of such forecasts. It was
found using the chi-squareone sample test that there
was no tendency for management to overpredict or under-
predict earnings. The Wilcoxon Signed-Ranks test was
then applied to determine the comparative accuracy of
the forecasts. This test confirmed that management

forecasts were more accurate than those of the naive model.

Russell Theodore Gingras

The first tests of the association between fore-
cast errors and stock prices dealt with the question of
whether the direction of the price response was asso—
ciated with the direction of the forecast error. The
chi-square test was used in determining that there was
no significant association between the sign of the fore-
cast error and the sign of the price response for either
management or naive model forecasts. Cases were then
found where the management forecast and the naive model
forecast were on opposite sides of actual earnings. The
Fisher Exact Probability Test was used to determine, in
these cases, that there was no tendency for the sign of
the price response to follow the sign of the management
forecast error.

In order to include magnitudes of forecast errors
and price responses in the analysis, rank order correla-
tions were obtained between forecast errors and price
responses. It was found that low but positive correla-
tions existed between all forecast errors and price re-
sponses. However, management forecast errors were not
in all cases more highly associated with price responses
than naive model forecast errors.

Since the correlations did not conclusively answer
the question of whether there was a greater association

between management forecast errors and price responses

 

Russell Theodore Gingras

than existed for the naive models, additional tests were
conducted. Cases were found where there were large dif-
ferences between management forecast errors and naive
models forecast errors. Then both the management fore-
cast errors and the naive model forecast errors were cor-
related with the price responses. The results were
again inconclusive. For some methods of computing fore-
cast errors and in comparison with some of the naive
model forecasts, management forecast errors appeared to
be more closely associated with price responses than did
the naive model forecasts.

A nonstatistical matrix analysis was then used to
further examine whether the size of the price response
seemed to be associated with the size of the forecast
error. This analysis confirmed that there did seem to be
an association between the size of the price response
and the size of the forecast error. However, this pattern
was not unique to management forecast errors.

The results of the study taken together indicate no
pattern of consistent superiority in the associations
between management forecasts and stock prices over the
associations between naive model forecast errors and
stock prices. The results of the study do not then
clearly indicate that management forecasts of earnings

per share have informational content.

AN EMPIRICIAL EVALUATION OF THE STOCK PRICE REACTION
TO ERRORS IN MANAGEMENT FORECASTS

OF EARNINGS PER SHARE

BY

Russell Theodore Gingras

A THESIS

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

DOCTOR OF BUSINESS ADMINISTRATION

Department of Accounting and Financial Administration

1974

© Copyright by
Russell Theodore Gingras
1974

ACKNOWLEDGMENTS

I would like to express my appreciation to the
many peOple who contributed to the completion of this
research effort and the doctoral program, the members
of my dissertation committee. Dr. Roland F. Salmonson
(Chairman), Dr. Melvin C. O'Connor, and Dr. Gilbert D.
Harrell provided many useful suggestions as well as con-
tinuous encouragement.

Dr. Daniel W. Collins also made many helpful sug-
gestions. In addition, he was instrumental in arranging
for the use of the CRSP tapes at the University of Iowa.

I also express my sincere thanks to Dr. Gardner M.
Jones, Chairman of the Department of Accounting and
Financial Administration, for his support in completing
the doctoral program.

Finally, I am most indebted to my wife, Carol, for
her support and encouragement in the completion of the
doctoral program. And to my daughter, Rochelle, and my
son, Paul, without whom the effort would have lacked

purpose.

iii

TABLE OF CONTENTS

Page
ACKNOWLEDGMENTS. . . . . . . . . . . . . . . ... . . iii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . Vi
LIST OF FIGURES. . . . . . . . . . . . . . . . . . . ix
Chapter
I. INTRODUCTION. . . . . . . . . . . . . . . . . 1
Purpose . . l
The Relationship Between Earnings and
Stock Prices. . . . . . . . . . . . . . 2
The Research Question . . 5
Arguments for Publication of Management
Forecasts of Earnings . 5
Arguments Against Publication of Manage-
ment Forecasts of Earnings. 7
The Approach of the Research. 3
Organization of the Research. 9
II. REVIEW OF THE LITERATURE CONCERNED WITH
MANAGEMENT FORECASTS OF EARNINGS PER
SHARE....................12
Introduction. . . . . 12

Review of the Literature Concerned With

the Accuracy of Management Forecasts

of Earnings Per Share . . 13
Review of the Literature Relating Analysts'

Forecasts to Stock Price Reactions. . . . 24
Summary . . . . . . . . . . . . . . . . . . 35

III. GENERAL METHODOLOGY . . . . . . . . . . . . . 40

Introduction. . . . . . . . . . . . . . . . 40
Theoretical Basis . . . . . . . . . . . . . 41
Estimation of Parameters. . . . . 45
Management Forecasts and Naive Forecasts. . 49
Naive Forecasts . . . . . . . . . . . . . . 52
Forecast Errors . . . . . . . . . . . . . . 55
Summary . . . . . . . . . . . . . . . . . . 57

iv

Chapter

IV. DESCRIPTION OF THE SAMPLE AND FORECAST
ERRORS . . .

Introduction.

Description of the Sample
Forecast Accuracy

Summary

V. THE PRICE RESPONSE TO MANAGEMENT FORECASTS

OF EARNINGS PER SHARE.

Introduction.
Measurement of Price Response

The Relationship Between Forecast Errors

and Price Responses
Summary .

VI. SUMMARY, CONCLUSIONS, IMPLICATIONS, AND
RECOMMENDATIONS. . . . . . . . .

Summary . . . . . . . . . . . . . . .
Conclusions .
Limitations of the Study.
Implications. . . . . . .
Recommendations . . . . . . .
APPENDIX A .
APPENDIX B

BIBLIOGRAPHY . . . . . . . . .

Page

145
145
148
152
155
157
164

167

LIST OF TABLES

Table Page

1 Distribution of Forecast Errors Per Dollar
of Price (Niederhoffer and Regan). . . . . . 23

2 Number of Usable Management Forecasts. . . . 62
3 Years Beginning With Strong Economic
Performance. . . . . . . . . . . . . . . . . 6S
4 Years Beginning With Weak Economic
Performance. . . . . . . . . . . . . . . . . 65
5 Forecast Errors (Management) . . . . . . . . 68
6 Forecast Errors Naive 1 (Pure Random Walk) . 6g
7 Forecast Errors Naive 2 (Random Walk With
Drift) . . . . . 69
8 Forecast Errors Naive 3 (Moving Average of
A Pure Mean Reverting Process) . . . . . . . 7o
9 Forecast Errors Naive 4 (Pure Mean Rever-
sion--N0 Drift). . . . . . . . . . . . . . . 70
10 Management Forecasts, Tendency to Over-

predict or Underpredict. . . . . . . . . . . 71

ll Naive 1 Forecasts, Pure Random Walk,
Tendency to Overpredict or Underpredict. . . 72

12 Naive 2 Forecasts, Random Walk With Drift,
Tendency to Overpredict or Underpredict. . . 73

13 Naive 3 Forecasts, Moving Average of a
Pure Mean Reverting Process, Tendency to
Overpredict or Underpredict. . . . . . . . . 74

14 Naive 4 Forecasts, Pure Mean Reversion--No

Drift, Tendency to Overpredict or Under—

predict. . . . . . . . . . . . . . . . . . . 75
15 Percentages of Errors Within Error Cate-

gories, 1965-1971, IA-FI/F . . . . . . . . . 84
16 Wilcoxon Signed-Ranks Test, Comparison of

Relative Errors, Management vs. Naive

Models, IA-FI/P. . . . . . . . . . . . . . . 88

vi

Table
17

18

19

20

21

22

23

24

25

26

27

28

29

30

Wilcoxon Signed-Ranks Test, Com arison
Relative Errors, Naive Models, TA-FI/P.
Wilcoxon Signed- Ranks Test, Comparison
Relative Errors, Management vs. Naive
Models, IA- Fl/F .

Wilcoxon Signed-Ranks Test, Com arison
Relative Errors, Naive Models, EA— FI/F
Wilcoxon Signed- Ranks Test, Comparison
Relative Errors, Management vs. Naive
Models, IA- FI/A .

Wilcoxon Signed- Ranks Test, Com arison
Relative Errors, Naive Models, EA- Fl/A.

2

X , Direction of Price Response With

of
of

of

of

Direction of Error, Management Forecasts.

X2, Direction of Price Response With

Direction of Error, Naive 1 Forecasts

X2, Direction of Price Response With
Direction of Error, Naive 2 Forecasts

X2, Direction of Price Response With
Direction of Error, Naive 3 Forecasts

X2, Direction of Price Response With
Direction of Error, Naive 4 Forecasts

Spearman Rank-Order Correlation Coef-
ficients, Forecast Errors With Price
Response. . . . . . . . . . . ,

Fisher Exact Probability Test, Management

vs. Naive 1 (Pure Random Walk).

Fisher Exact Probability Test, Management

vs. Naive 2 (Random Walk With Drift).

Fisher Exact Probability Test, Management

vs. Naive 3 (Moving Average of a Pure
Mean Reverting Process) . . . .

vii

Page

89

90

91

92

93

120

120

121

121

122

125

129

129

130

Table

31 Fisher Exact Probability Test, Management
vs. Naive 4 (Pure Mean Reversion-~No
Drift).

32 Spearman Rank-Order Correlation Coef-

ficients, Forecasts With Price Responses,
41 Largest Differences Between Management

33
34
35
36
37
38
39
4o
41
42
43
44
45
46
47

Forecasts and Naive Forecasts

Confusions
Confusions
Confusions
Confusions
Confusions
Confusions
Confusions
Confusions
Confusions
Confusions
Confusions
Confusions
Confusions
Confusions

Confusions

Matrix,
Matrix,
Matrix,
Matrix,
Matrix,
Matrix,
Matrix,
Matrix,
Matrix,
Matrix,
Matrix,
Matrix,
Matrix,
Matrix,

Matrix,

Management,

Naive 1,
Naive 2,
Naive 3,

Naive 4,

Management (A-F)/F .

Naive 1,
Naive 2,
Naive 3,

Naive 4,

Management,

Naive l,
Naive 2,
Naive 3,

Naive 4,

viii

(A-F)/A .
(A-F)/A .
(A-F)/A .
(A-F)/A .

(A-FJ/F
(A-F)/F

(A-F)/F .
(A-F)/F .

(A-F)/P .
(A-F)/P .

(A-F)/P

(A-F)/P .

(A-F)/A.

(A-F)/P.

Page

130

132
134
134
135
135
136
136
137
137
138
138
139
139
140
140
141

Figure

10

11

12

13

14

15

16

17

18

LIST OF FIGURES

Corporate Profits, Taxes and Dividends
Histogram/Frequencies (A-F)/F Management
Histogram/Frequencies (A-F)/F Naive l.
Histogram/Frequencies (A-F)/F Naive 2.
Histogram/Frequencies (A-F)/F Naive 3.
Histogram/Frequencies (A-F)/F Naive 4.

Scatter Plot Forecast Errors Against Price
Response, Management Forecasts, (A-F)/A.

Scatter Plot Forecast Errors Against Price
Response, Naive l Forecasts, (A-F)/A .

Scatter Plot Forecast Errors Against Price
Response, Naive 2 Forecasts, (A-F)/A .

Scatter Plot Forecast Errors Against Price
Response, Naive 3 Forecasts, (A-F)/A . . .

Scatter Plot Forecast Errors Against Price
Response, Naive 4 Forecasts, (A-F)/A .

Scatter Plot Forecast Errors Against Price
Response, Management Forecasts, (A-F)/F.

Scatter Plot Forecast Errors Against Price
Response, Naive 1 Forecasts, (A-F)/F .

Scatter Plot Forecast Errors Against Price
Response, Naive 2 Forecasts, (A-F)/F

Scatter Plot Forecast Errors Against Price
Response, Naive 3 Forecasts, (A-F)/F .

Scatter Plot Forecast Errors Against Price
Response, Naive 4 Forecasts, (A-F)/F .

Scatter Plot Forecast Errors Against Price
Response, Management Forecasts, (A-F)/P.

Scatter Plot Forecast Errors Against Price
Response, Naive 1 Forecasts, (A-F)/P .

ix

Page

64
79
80
81
82
83

103

104

105

106

107

108

109

110

111

112

113

114

Figure
19

20

21

Scatter Plot Forecast Errors
Response, Naive 2 Forecasts,

Scatter Plot Forecast Errors
Response, Naive 3 Forecasts,

Scatter Plot Forecast Errors
Response, Naive 4 Forecasts,

Against Price
(A-F)/P .

Against Price
(A-F)/P . . .

AgainstPrice
(A-F)/P

Page

115

116

117

CHAPTER I

INTRODUCTION

This chapter includes a statement of the purpose
of the research, an examination of the motivation for
undertaking the research effort, the arguments for and
against the publication of earnings forecasts, and a

presentation of the organization of the dissertation.

Purpose

Accountants are concerned that information presented
in accounting reports be useful to the readers of such
reports. The American Accounting Association has indi-
cated for example. that:

...from the viewpoint of the external user

it is essential that accounting information

be relevant to his needs.1
The American Accounting Association has further indicated
that the:

...accounting discipline could be expanded

either by absorbing additional measurement

methods into the discipline or by broadening

the concept of activities on which it reports.2
One area that has been preposed as an additional area
of reporting, which might be useful to statement users,
is that of forecast earnings.

The possible usefulness of earnings forecasts has

been considered sufficiently important that the Securities

1

and Exchange Commission recently dealt with this issue.
Its decision was to allow, but not require, the inclusion
of management forecasts of earnings in reports filed with
the Commission.4 This process intensified consideration
of the problems and prospects associated with published
forecasts of earnings. Many issues were raised, one of
the most basic being whether or not such reports were
useful to investors. This question must be strongly con-
sidered because a number of problemshave been raised con-
cerning the publication of forecast earnings. Questions
have been raised concerning:
(1) the legal liability of those involved in fore-
casting earnings;
(2) the effect of forecast earnings on stock
prices;
(3) the role of the auditor in the forecasting
process.
Since serious questions of this nature have been raised.
it seemed sensible to this researcher to first examine
whether management forecasts seem to be used by investors.
If such forecasts are not used by investors, it would
seem unnecessary to resolve the other difficult problems

associated with publication of earnings forecasts.

The Relationship Between Earnings and Stock Prices

 

Lorie & Brealey make the point that in almost all

securities valuation models the most important variable

S
is the expected growth in earnings. Many valuation

models assume that investors determine the price of a
security by discounting the future expected stream of

dividends. One form of such a valuation model is stated

below.6
Do
(1) P0 = RTE. (assum1ng k > g)
P0 = the price of the security at time 0.
D0 = dividends per share at time o.
k = the rate of return that investors anti-
cipate.
g = the rate at which the dividend stream
grows.
Do
(131k: p—+g
o

The rate of return on equity investment is then
defined in terms of the current dividend yield and the
growth rate in this yield. But dividends are normally
viewed as being based on earnings. It should be possible,
then, to rewrite these equations in terms of current
earnings. Rewriting equation (1) in terms of current

earnings results in the following equations.

 

(l-b) r A0
(2) P =
o k-rb
Where:
A = firms total assets:

0

retention rate:

l-b = payment rate;
r = rate of return;
g = br

(2a) k = rA 1‘b + rb

The definition of return on equity investment is then
stated in terms of current earnings adjusted for growth
in earnings. The important point here is that many
security valuation models depend on expected earnings.

This theoretical research seems to be supported by
several empirical studies. Two studies, one by Ball and
Brown, and the other by Beaver, strongly indicate that
there is a relationship betWeen earnings and stock prices.7
Since these studies had both theoretical and methodological
implications for this research effort, they are reviewed
in some detail in later chapters.

Baker and Haslem recently conducted a study of
common~stock investors in metropolitan Washington, D.C.
They useda questionnaire to determine which 33 factors
used in investment analysis were considered most important
by the investors questioned. In total they received 851
complete responses. The results showed that:

The factors ranked most highly by the investors

explicitly show that investors are primarily

concerned with expectations about the future.

More specifically, the factor of greatest importance

was the future economic outlook of the company. Expected

future percentage growth in earnings per share was the
sixth ranked factor.9
The importance of expected earnings in the deter-
mination of stock prices, then, has a solid basis in
theory and has been empirically validated to some extent.
Since earnings forecasts provide information to investors

about earnings expectations, they should have an influence

on stock prices.

The Research Question

 

Earnings forecasts are available to investors from
a number of sources. The investor could develop forecasts
himself, he could obtain them from financial analysts, or
he could obtain management forecasts. There have been
previous studies concerned with the apparent usefulness
to investors of both naive model forecasts and analysts'
forecasts. There has not, however, been any empirical
work designed to evaluate the usefulness of management
forecasts to investors. This is the subject of this re-

search project.

Arguments for Publication of Managgment Forecasts of
Earnings

The strongest argument for making management earnings
forecasts public information is that such information is
useful in making investment decisions. Numerous authors

have indicated that such information is considered useful

‘tca investors. The following quotation, taken from the
Iflirrancial Analysts Journal, is illustrative of the argu-

lnerit: made for the publication of management earnings

4
forecasts:

One would expect 11m: impact of forecasts to

be greater than the impact of current earnings,
because the former are more directly relevant to
determinations of investment value; after all, the
primary relevance of current earnings is their
usefulness in forecasting the future. A signifi-
cant change in the earnings forecast of the leading
research firms sometimes has as much impact on
market prices as a comparable change in reported
earnings. The only thing that could give f$6ecasts
more impact would be to make them official.

It is further indicated that management earnings
for‘Eacasts may have some special usefulness. In another

artui.c1e in the Financial Analysts Journal it was indicated

that:

The analyst can bring to his forecasts objectivity
and comparative information. Management has
special knowledge of internal factors and a
greater sensitivity to its own particular environ-

ment, thus, both types, of forecasts are useful
to the investor.1

Another argument for publishing earnings forecasts
is ‘that such forecasts are presently being made but are
mlevenly disseminated; and that publication of corporate
f"DI-‘ecasts of earningswould help to remedy this inequity.
inle: FAF Proposal for Systematic Disclosure of Corporate
EEEI‘ecasts noted in this connection:

Equity in dissemination of corporate information

to all investors will be enhanced. Disclosure

of forecast information is merely another step
foreward in the continuing effort to improve

corporate reporting to investors. The ultimate
benefit to the corporation is a more efficient
capital market in which to raise funds.

Argannents Against Publication of Management Forecasts

of .EEaJnings

The argument is made, that in order for forecast

inf?c>:rmation to be useful to investors, it must be rea-

sorizilaly accurate.13 There have been studies made con-

cerfrl;ing management forecasting, three of which are sum-
mar‘jLzzed later in this paper, which cast doubt on the
abi.]L:ity of professionals to forecast accurately.
Management's lack of ability to accurately predict
e"AI-‘Irlings leads to another argument against the publication
0f eaarnings forecasts. There are some who feel that
inachrate forecasts may have an undesirable influence on
stc><2k price behavior. For example, an article in Busi-

Less Week stated:

Another worry is how the stock market would

behave if a forecast missed its mark badly. Wall
Street's emphasis on short term results and its
obsession with forecasts was vividly illustrated
last week when Digital Equipment Corp., the
Massachusetts mini-compUter manufacturer reported
its results for the July-September, 1972 quarter.
Analysts had predicted per-share earnings of 40¢
for this first quarter of DEC's fiscal year, compared
with 29¢ in 1971. When DEC reported 33¢, its stock
plumented 17 points to 84 in one day.1

Others have amplified this argument. It has been
h1<iicated that publication of near term earnings forecasts
Wowald do the investing public a disservice because it

‘Would benefit only the in-and-out speculator.ls

In addition, it has been charged by some that
p11t>lication of earnings forecasts may lead management
to (either overpredict earnings or underpredict earnings.
Mariaigement might overpredict earnings to impress the
shareholders at the time the forecast was published.

On 1:}1e other hand it could be argued that there might be

a t:e311dency to underpredict earnings in order to be con-

ser"\rzitive. A conservative forecast would make it easier

to lrleeet or exceed the earnings which had been forecast.16
Fut‘t:11er, it has been suggested that publication of earnings
for‘eec:asts may lead management to manipulate income in
OTCIGB r to meet or exceed the income it had forecast.17

Finally, there is the possibility of legal actions

1f Ifforecasts are inaccurate. There is, however, some

ind:i_cation that legal actions may not be a problem bee
caLlSSe the SEC may provide a "safe harbor" rule, stating
Whiift; constitutes a forecast and the steps to be taken

sulDisequent to the forecast.18 In contrast to this posi-

'tiCDII, one author has contended that "Financial performance
SiwEinificantly better or worse than that projected seems

Cl-€>a.rly to be a basis for action for damages."19

IEEEiApproach of the Research
The research question was examined by associating
maflagement forecast errors with stock price reactions.
If ‘management forecasts were being used by investors, it
would seem that there should be a consistent relationship

between the direction and size of the forecast error and

‘tlie direction and size of the price response. Further,
j;f':management forecasts were being used, the same results
ShJDIJld not be obtained using naive forecasts. Several

statistical tests were used in examining these questions.

Qggizariization of the Research

Chapter II contains a review of the literature con-
cerning:

(l) the ability of management to forecast accurately;

(2) the relationship between naive forecasts and

stock price behavior;
(3) the relationship between analysts'forecasts
and stock price behavior.

Chapter III discusses the general methodology of
131$? study, including data selection, measurement of fore-
(”isi‘t errors, and measurement of price response.

Chapter IV presents an analysis of the sample which
”5‘53 obtained in terms of the number of forecasts and the
nattire of the companies making such forecasts. In addition,
tl'lfiere is an analysis of the forecast errors using manage-
mfiilnt and naive forecasts.

Chapter V contains a presentation and analysis of
t}1<e test results concerned with establishing the stock
IIT‘ice reaction to management earnings forecasts.

Chapter VI presents a summary of the study, conclu-

Siuons, implications, and recommendations for further re-

Search.

10

FOOTNOTES
CHAPTER I

American Accounting Association, A Statement of

Bas ic Accounting Theogy (Evanston: Amerchan AccountTng
Association, 1966), p. 27.

 

2Ibid., p. 71.

3E. G. W. W. C00per, N. Dopuch and T. F. Keller,

"Budgeting Disclosure and Other Suggestions for Improving
AC<::c>unting Reports," The AccountinggReview, October, 1968,
XLII III, pp. 640-647, andiRudy Schattke, WExpected Income--

Fieeporting Challenge," The Accounting Review, October,
1962, XXXVII, pp. 670-676.

Les Gapay, ”SEC Plans to Let Concerns Forecast

PI?c>:fit in Filings." The Wall Street Journal, February 2,
19'7'3, LIII(75), p. 3.

5James Lorie and Richard Brealey, Modern Development

irl Investment Management, (New York Praeger PuElishers
1972), p. 597. , ,

 

George C. Philippatos, Financial Mana ement Theogy
3;:Cl Techni ues (San Francisco, Holden-Day, nc., 1973)

7William H. Beaver,'The Information Content of Annual
Earnings Announcements," Empirical Research in Accounting:
:JSEjLected Studies, 1968, A supplement toFVolume 6 of the
..Szllrnal of’AccountinggResearch, pp. 67-101., and Ray Ball
§Tld Phillip Brown, T'An Empifical Evaluation of Accounting

1r1come Numbers." Journal of Accounting Research, Autumn,
S>68, VI, p. 170.

8J. Kent Baker and John A. Haslem, "Information Needs
(’13 Individual Investors,” The Journal of Accountancy,
Ncavember, 1973, 136(15), p. 65.

9Ibid., p. 67.

10"Corporate Earnings Forecasts,” Financial Analysts
Journal, March/April, 1972, 28(2), p. 17.

11

11William 8. Gray, III, ”Proposal for Systematic
Disclosures of Corporate Forecasts," Financial Analysts
Journal, January/February, 1973, 29(1), p. 65.

12Ibid., p. 71.

 

13Charles LeRoy McDonald, An Empirical Examination.
of .P’tiblished Prediction of Future Earnings (Unpublished
Ph.;[).. dissertation.TMiEhigan State University, 1972),
pp. 23—24.

 

 

l4"Business Fears Profit Forecasting," Business Week
November 4, 1972, p. 44.

 

15John A. Prestbo, "...And an Expert Who Says They
WOD.‘ 1: Work," The Wall Street Journal, December 11, 1972,
LIII (42. p. 8.

16For a discussion of arguments why management might

ov1217]predict or underpredict earnings see: McDonald, pp. 22
and 24. '

17Business Fears Profit Forecasting, p. 44.

18"Full Disclosure and the Changing Business Environ-

gerlgg ," Haskins 6 Sells, The Week in Review, April 27, 1973,

19R. Gene Brown, "Ethical and Other Problems in

ishing Financial Forecasts,” Financial Analysts Journal,
a7t-‘<:h/Ap:r11, 1972, 28(2), p. 44.

Put331
'M

CHAPTER I I

REVIEW OF THE LITERATURE CONCERNED WITH

MANAGEMENT FORECASTS OF EARNINGS PER SHARE
Int reduction

The literature in the area of management forecasts

of earnings per share has been primarily oriented toward

analyzing the accuracy of these forecasts. Accuracy of

management forecasts relates strongly to this research

effort which attempts to associate stock price reactions

to management forecast errors. Therefore, the empirical

s‘tl—ldies concerned with the accuracy of management earnings

f0ili‘ecasts will be carefully reviewed.

Since this research effort relates errors in manage-

ment forecasts of earnings per share to stock price

reactions, it would be desirable to review studies dealing
with this specific question. Unfortunately, no such

Studies are available. But there are studies relating

all‘lvalysts' forecasts of earnings per share to stock price

re actions. Since these studies relate forecasts of

eEirnings per share to stock price reactions they will be

I‘eviewed in this chapter.

12

13

[leaview of the Literature Concerned With the Accuracy of
hkariagement Forecasts of Earnings Per Share

Green and Segall in two articles have dealt with

the; question of the accuracy of management forecasts of
euiz'riings.l Answering this question was not, however, the authors'
primary purpose. Their primary purpose was to examine

the: jpredictive power of first quarter earnings reports.
Thj_:s they did by generating forecasts using several naive
motlealls, then comparing the accuracy of forecasts gener-

ateecfl. using first quarter earnings reports with forecasts

rmrt; ‘using first quarter earnings reports.

The naive forecasting models used included three

a“111.1511 models and three interim models.2

Annual 1: Next year's EPS equals this year's.

Annual 2: Next year's EPS equals this year's EPS
plus the difference between this year's
EPS and last year's.

Annual 3: Next year's BPS will differ from this
year's by the same percentage that this
year's EPS differs from last year's.

Interim 1: Next year's EPS equals four times the
first quarter's EPS.

Interim 2: Next year's EPS will differ from this
year's by the same percentage that next
year's first-quarter EPS differs from this

year's first-quarter.

14

Interim 3: Next year's EPS was derived by linearly
regressing annual against first-quarter
EPS for the five years preceeding the year
for which the forecast is desired and
applying the regression estimates to first
quarter earnings of that year.

As a part of this study the authors looked at twelve

management earnings forecasts. This was done to evaluate

the: ‘forecasts made using the naive forecasting models.
Thee :authors point out that interim forecasts used in sim-
plea

‘ways may yield poor forecasts, but when combined with
0t}1<er information, may contribute to forecasting accuracy.3
Pre sumably management has access to a great deal of "other"

infI<Drmation including information available only to those

ins :ide the firm.

The twelve forecasts represented the only firms from

tklei original sample of fifty firms which made management

eéllrliings forecasts. The original fifty firms had been

raIndomly selected from the January, 1964, issue of The

§§£31k and Quotation Record.

The management forecasts were not necessarily point

f0trecasts of earnings per share. In fact, only five of

t}1<e forecasts could be construed as point estimates of

ea-‘rnings per share. The remaining forecasts were con-

Cerrned with the direction of the earnings change. Further,

Sidx of the forecasts were made after 50% of the year had

passed.

15

The authors reported that:

Of the twelve forecasts, five were made before
the first quarter report was available; of these,
four erred in direction, and only two specified
the amount of the earnings forecast for the
year; of the two which gave specific forecasts,
one had an error greater than any of the annual
models. That is, actual forecasts made without
first-quarter earnings reports do not appear to
be more helpful than forecasts of the naive
models. Of the remaining seven forecasts-~made
after first quarter reports were available--one
erred in direction, and only four quantified

the earnings forecast for the year; of the four
which were specific, one was superior to any
naive model, and three were superior to five of
the naive models. That is, where comparison was
possible, most actual forecasts are better than
those of the naive models, bxt, of course, they
were made later in the year.

A replication of the first study was made by Green

5 Fifteen

& Segall using forecasts made during 1965.
management forecasts were obtained and analyzed. The
results obtained were so similar to the initial results
that the replication is not reviewed in detail.

The studies by Green and Segall, in terms of manage-
ment forecast errors, leave much to be desired. The
primary problem was the small number of forecasts which
were obtained. The small number probably resulted from
the selection technique used. First a random sample of
firms was obtained, then they were analyzed to see
whether management forecasts were available for these
firms. Had there first been a search for firms making

management forecasts, perhaps the sample would have been

larger.

16

Another criticism of the study is that comparisons
of the accuracy of management forecasts and naive fore-
casts were not made statistically. The combination of a
small sample and nonstatistical comparisons leaves the
authors' conclusions open to suspicion.

Further, it could be argued that the sample was non-
representative and that the years selected were not
representative. The years 1964 and 1965 were both good
years in terms of corporate profits, with profits rising
sharply throughout both years.6 Perhaps the same results
would not have been obtained had the authors selected
years with poor or variable economic conditions.

The small number of firms again probably contributed
to the lack of representation evidenced by the firms in
the sample. Even where an industry was included in the
sample, it was represented by a small number of firms.

It is, then, questionable whether forecasts by the firms
in the sample are representative of their industry.

Finally, the usefulness of naive and management
forecasts is evaluated solely on the basis of forecast
accuracy. Another measure of usefulness might be the
association between the various types of forecast errors
(naive and management) and stock price movements. The
present study evaluates both forecast accuracy and the

relation between forecast errors and stock prices. It

17

does follow Green and Segall in that comparisons are made
between naive model forecasts and management forecasts.

A second empirical study analyzing the accuracy of
management forecasts of earnings per share was made by

McDonald.7

His study approximates, in part, the methodo-
logy used in the research reported in this dissertation.

McDonald's study specifically focuses on the useful-
ness of published management forecasts of earnings per
share. The point is made that in order for fhese fore-
casts to be useful to investors they must be sufficiently
reliable for investors to include them in their decision
making processes.8 Thus the accuracy of management fore-
casts was examined.

The author selected his sample from management

earnings forecasts published in The Wall Street Journal.

 

The forecasts to be included in the sample must have
been point forecasts of earnings per share made during

the first 120 days of the firm's fiscal year. The Wall

 

Street Journal was examined for the 120 days beginning

 

with January 1 for each year included in the study. It
was felt that forecasts made in the first 120 days of a
firm's year could have been included in the annual report
to stockholders.9
The years 1966 through 1970 were included in the

study. The analysis of forecast accuracy was made on an

overall basis, as well as by year. In addition, an

18

analysis of forecast accuracy was made by industry
groups.

The reliability of the management forecast was
determined by comparing predicted earnings to actual
earnings. The errors were computed relative to pre-
dicted earnings. This procedure allowed the predictions
to be compared. In addition, this method of computing
error might be particularly useful to investors.10

The author found that:

...For the five year period the Relative Prediction

Errors ranged from an overprediction of 395.6 per-

cent to an underprediction of 108.5 percent. The

mean prediction error was a 13.6 percent overpredic-

tion. Of the 201 predictions, 35.3 percent had an

error of 5 percent or less, and 48.5 percent had an
error of 10 percent of less.

It was statistically determined using the chi-square
one sample test, that there was a tendency to overpredict
earnings. When the errors were evaluated by industry
groupings it was found that utilities had the lowest
mean Relative Prediction Error.

As a final step in the research effort, McDonald
examined the association between the Relative Prediction
Errors and several variables. The variables were class-
ified as endogenous and exogenous to the firm. No
attempt was made, however, to associate Relative Predic-
tion Errors with stock price changes.

As a result of the analysis it was determined that
only the endogenous variables were significantly associated

with Relative Prediction Errors at the .05 level.12

19

The associations between Relative Prediction Errors
and the other variables were determined on both a uni-
variate and multivariate basis. The univariate associa-
tions were established using simple correlation analysis,
while the multivariate associations were established using
the multiple regression technique.

The highest association was found to be between
Relative Prediction Errors and Relative Extraordinary
Gains and Loses}3 The second highest association was
between Relative Prediction Errors and Change in Operating

Earnings.14

With regard to the association between
Relative Prediction Errors and Change in Operating Earnings
it was noted that:

This suggested that, in general, the earnings

predictions of firms consist of small adjust- 5

ments to the prev1ous year's actual earnings.

McDonald's study was superior to Green and Segall's
in many respects. The sample of firms obtained using
McDonald's selection technique was far larger than Green
and Segall's. Green and Segall analyzed a total of 27
forecasts which were published during 1964 and 1965.
McDonald analyzed 201 forecasts published during the years
1966 through 1970.

The years included in McDonald's study represented
a wide variety of economic conditions while the years

from which Green and Segall selected forecasts, as pre-

viously indicated, were very good years in terms of

20

corporate profits.16 Further, McDonald Makes a strong
case for his sample being more widely representative of
various industries.17

The major weaknesses of McDonald's study were first,
that it focused on forecast errors as a criterion for
evaluating the usefulness of management earnings fore-
casts; and second, that no comparison was made between
management forecasts and naive forecasts. As the author
pointed out, current management forecasts seem to be
small adjustments to the previous year's actual earnings.
It might have been anticipated, then, that forecasts made
using past years! earnings in a mechanical, or naive,
model might have produced results similar to those ob-
tained using management forecasts.

In another study, Cepeland and Marioni analyzed the
accuracy of management forecasts of earnings per share.18
These authors closely followed the Green and Segall
methodology. Management forecasts were compared with
forecasts generated by the use of six naive models. The
naive models used were the same models used by Green and
Segall, presented earlier in this chapter, with one
exception. The regression model indicated by Green and
Segall as Interim 3 was replaced by the following model:

Model 6: EPS of the current year will equal the

EPS of the last three quarters of the
previous year plus the EPS of the first

quarter of the current year.19

21

The calculation of forecast errors was made using
both relative errors and absolute errors. The absolute
error was calculated by subtracting forecast earnings
per share from actual earnings per share. Relative
errors were calculated by dividing the absolute error by
actual earnings per share.

The authors initially selected 50 management fore-

casts from The Wall StreetJournal. They began with the

 

January 2, 1968 issue, scanning each subsequent issue
until they had obtained fifty management forecasts. The
selection criteria used were:
(1) The forecast consisted of a specific point
or range estimate and (2) quarterly EPS data
of the prediction were available. In cases
where an executives forecast stated that EPS
"approximate," that they "exceed," or that
they will be "at least" a specific figure,
the amount 38clared was used as that firm's
prediction.
The forecasts were not necessarily taken from the
first part of a firm's year. One forecast made after 92
percent of the firm's year had elapsed was included in
the sample. The management forecasts were found to be
accurate in terms of direction. Only 14 percent of the
firms failed to predict the correct direction that the change
in earnings per share would take.21
There were two more overestimates of EPS than there
were underestimates. But the firms overestimating
earnings did so with greater inaccuracy than did firms

22

underestimating earnings. When the naive model forecasts

22

were compared with management forecasts it was found
that management forecasts had the lowest average absolute
error and the lowest average relative error.23
As an additional test the forecasts were ranked
in terms of the absolute amount of the error for each
firm. The most accurate prediction receiving the rank,
7, and the least accurate prediction receiving the
rank, 1. The forecast errors were then compared using
the chi-square and Kolmogrov-Smirnov tests. The authors
note:
Executive forecasts achieved a higher rank
than that expected due to chance (14 percent)
on a significant number of occasions when evaluated
by the x2 test with six degrees of freedom and the
Kolmogrov-Smirnov test with N=50, with significance
set at the .05 level.24
This indicates that the management forecasts are
the most accurate of the forecasts tested. The authors,
however, properly qualify the interpretation of the results
by noting that in regard to the naive models:
...The predictions of the models are available
earlier and our Sgcision may be too dependent on
the year chosen.
In order to see whether the results depended on
the year chosen (1968), the authors replicated the last
test with 25 firms from each of the years 1964 and 1965.
The results, using the Kolmogrov-Smirnov test, again

showed the management forecasts to be significantly more

accurate at the .05 level.

23

The study by Copeland and Marioni had some desirable
features. The authors did compare the accuracy of
management forecasts to the accuracy of forecasts
generated by several naive models. In addition, the
comparisons were made on a statistical basis. Further,
the number of forecasts analyzed was large. In total,

100 management forecasts were analyzed. As a result

of these strengths in the study, the authors' conclusion
that management forecasts are more accurate than fore-
casts of naive models, rests on a reasonably solid founda-
tion. This is not to say, however, that the study had

no weaknesses.

One weak point was that the forecasts were not point
forecasts of earnings per share. Where a range forecast
was made, the authors used the midpoint of the range
as the management forecast of earnings per share. As
McDonald has pointed out, this procedure requires one
to assume that the probability distribution associated
with range predictions is symetrical.26

In addition, the authors include forecasts which
might be termed "open ended." Forecasts in this category
include those stated as "approximate," or "will exceed,"
or be "at least" a specific amount. Forecasts of this
nature made it very difficult to measure the forecast
error. For example, if a forecast stated that "at least"

$1.00 per share would be earned, and earnings of $1.25

24

per share were reported, technically there would be no.
forecast error.

Another problem with Cepeland's and Marioni's
research effort was that the management forecasts were
often made after a considerable portion of the year,
for which the forecasts were being made, had elapsed.
This would give management forecasts a considerable
advantage.

The naive forecasts had the benefit of, at best,
the first quarter earnings during the year for which
the forecast was made. In contrast some of the manage-
ment forecasts were made with the benefit of as many as
three quarterly earnings reports during the year for which
the forecast was made. Thus, typically, the naive
forecasts were available earlier in the year and used
less current information than management forecasts.

Finally, Copeland and Marioni focus exclusively on
forecast accuracy in evaluating the usefulness of
management forecasts of earnings per share. As previously
indicated, another test of the usefulness of management
forecasts of earnings per share might be to associate the

forecast errors with stock price reactions.

Review of the Literature Relating Analysts' Forecasts to

 

Stock Price Reactions

 

The research relating analysts' forecasts to stock

price reactions was pertinent to this research effort in

25

that forecasts made by professional investors were
related to stock prices. It was previously indicated
that the relation between forecast errors and stock price
changes might be a measure of the usefulness of forecasts
to investors. Since both analyst and management fore-
casts are made by professionals, the result might be
similar.

Niederhoffer and Regan, in a study published in
1972, evaluated the relationship between professionally
generated forecasts and stock price reactions.27 In
this study, the authors examined the percentage gains and
losses in price of the 1253 common stocks on the New York
Stock Exchange for the year 1970. They also examined the
percentage gains and losses in price for 650 stocks for
a five year period ending in 1970. The 650 stocks were
those of the nation's 650 largest corporations as pre-
sented in Forbes' "23rd Annual Report on American Indus-
try" in the January 1, 1971, issue.

From these stocks they selected in each year the 50
worst performers, the 50 best performers, and 100 random
stocks. The 50 best performers and the 50 worst perfor-
mers were compared with each other and with the 100 random
stocks on the basis of several variables.

The authors compared:

(1) median change in forecasted earnings per share;

(2) median change in actual earnings per share;

(3) median change in stock price during 1970.

26

The forecasts were taken from the March 31, 1970,

edition of the Standard and Poor's Earnings Forecaster.

 

The Earnings Forecaster is a compilation of analysts'

 

forecasts made by several financial institutions. The
particular forecast used was the forecast made by the
financial institution with the largest number of fore-
casts in the booklet.

The authors concluded, based on a visual analysis,
that:

The median estimated percentage changes in earnings
for the top 50 and the random 100 were comparable

at 7.7% and 5.8% respectively, but neither approached
the predicted 15.3% gain for the bottom 50. Such
results suggest that professional investors would

be wise to cast a suspicious eye on unusually optimis-
tic estimates, since failure on the part of the

firm to realize such expectations will mgst cer-
tainly result in a stock price decline.

It was further demonstrated that the t0p 50 stocks
had a considerably greater median change in actual 1970
earnings per share than did the random 100 stocks. The
bottom 50 stocks had a much lower median change in earnings
per share than did the random 100 stocks.29
The authors then normalized the same data by price.

The following variables were computed for each company:

Estimated earning change

_F_. 1970-E,1969

per dollar of price = ’P,1969

 

Actual earning change

. _ E, 1970-E 1969

 

27

Forecast errors per
E. 1970-F. 1970

 

dollar of price = _P:1969
Where:

E = earnings per share;

F = forecast earnings;

P = the closing price for 1969.

The authors note that:

The major reason for using earnings changes nor-
malized by price rather than percentage earnings
changes was that the latter became statistically
cumbersomgowhenever the base becomes small or
negative.

The top 50 stocks, bottom 50 stocks, and the random

100 stocks were then compared using a non-parametric dis-

criminant analysis.31

The authors conclude, based on this analysis, that:

...We can see that when the forecast was over-
estimated by eight cents or more per dollar of
price, the odds were nearly 17 to 1 that the stock
would finish in the bottom 50 rather than in the
random 100. At the other extreme an underestimate
of one cent or more per dollar of price was almost
a guarantee that the stock would finish in the top
50 rather than in EBe random 100, since the chances
were 24 out of 25.

The discriminant analysis was also conducted with
actual earnings changes per dollar of price. The authors
concluded:

...For all companies with actual earnings gains

of four cents or more per dollar of price, the odds
were 14 to 1 that the company would finish in the
top 50 rather than in the random 100, with virtually
no chance of ending up on the bottom 50. But for
earnings losses of eight cents or more, the odds
were 20 to 1 that the stock would land in the bottom
50 rather than in the random 100. In this case33
there was no chance of finishing in the top 50.

28

TABLE 134

DISTRIBUTION OF FORECAST ERRORS PER DOLLAR OF PRICE

(Niederhoffer and Regan)

 

Forecast Errors TOp 50 Random 100 Bottom 50
6.0 8 over 4.5

5.5 to 6.0

5.0 to 5.5 2.3

4.5 to 5.0

4.0 to 4.5

3.5 to 4.0 2.3

3.0 to 3.5

2.5 to 3.0 4.5

2.0 to 2.5 15.9

1.5 to 2.0 4.5 1

1.0 to 1.5 13.6 1

0.5 to 1.0 13.6 7

0.0 to 0.5 27.2 12

-0.0 to -0.5 18

-0.5 to -l.0 6.8 15

-l.0 to -l.5 2.3 6 12
-1.5 to -2.0 9 3
-2.0 to -2.5 2 3 7 3
-2.5 to -3.0 5 6
-3.0 to -3.5 2 18
-3.5 to -4.0 3 6
-4.0 to -4.5 3

-4.5 to -5.0 5

-5.0 to -5.5 1 3
-5.5 to -6.0 9
-6.0 to -6.5 1

-6.5 to -7.0 6
-7.0 to -7.5 1

-7.5 to -8.0 l 3
-8.0 to -8.5 12
-8.5 to -9.0

-9.0 to -9.5 6
-9.5 to-10.0 6
-10.0 8 over 9

998 W 1752'

 

29

The authors' results would seem to indicate that
stock price changes are closely related to changes in
actual earnings and to forecast errors. Their results
must, however, be viewed with some caution.

The stocks which were analyzed had extremely large
stock price changes. The authors purposely selected
these stocks becaUse it was expected that any relation-
ship would be magnified in this sample.

The results, then, may be dependent on the nature
of the firms selected. This seems to be born out in
part by looking at the random 100 stocks selected from
the Forbes' 650 largest corporations. The random 100
stocks over the five year period had a median earnings
change of +18.3% but the median stock price change
was --4.9%.35 This would not be the expected result
given the authors' conclusion.

Another problem is that the stock price changes are
not adjusted for general market effects. The price of
a stock can be viewed as being made up of three parts.
The first part resulting from factors affecting the
market as a whole. The second part being made up of
factors affecting the entire industry of which the firm
is a part. The final part resulting from factors unique
to the firm. The factors affecting the industry as a
whole have been found to be relatively insignificant.

But factors affecting the entire market have been found

30

to have a relatively large effect on stock prices.36

It would seem, therefore, that the stock prices should
have been adjusted for general market effects. Further,
there is no indication by the authors that prices had
been adjusted for capital changes.

Another problem may have occurred because the
measurement of forecast error and earnings changes, were
normalized by price. The data was normalized by price
in order to avoid the problems associated with calculating
percentage changes in earnings or percentage forecast
errors. This technique, however, also has a problem.
The higher the price of the stock the lower would be
earnings change or forecast error, normalized by price.
Further, the price used to normalize the 1970 variables
was the year-end closing price for 1969. The closing
price at the end of year 1969 may have been unusual for
some reason, thus distorting the error measurement.

A second study relating analysts' forecasts to

stock prices was conducted by Janell.37

This study
overcomes many of the problems present in the study by
Niederhoffer and Reagan.

Janell computed 50 analysts' forecasts for each of
the years 1970 and 1971. The forecasts he computed were

the average of several analysts' forecasts presented in

Standard and Poor's Earnings Forecaster.

 

31

The population from which the sample was selected

met the following selection criteria:

(1)

(2)
(3)

The firms were listed on the New York Stock
Exchange (NYSE), except for firms leaving the
NYSE because of delisting, merging or listing
on other exchanges.

The firms had a fiscal year ending on December 31.
The firms which met the other criteria had to
have a minimum of three analysts' estimates per
month for at least ten months prior to the

announcement of the annual earnings by the cor-
38

 

poration in the Earnings Forecaster.

A random sample of 50 firms was taken from the firms re-

maining after application of the selection criteria for

each of the years 1970 and 1971.

The forecast errors were determined using the fol-

lowing formulas:

(1)
(2)

39

A-F
‘F‘
A-F

Where:

A
F

actual earnings per share for the year;
forecast earnings per share for the year;

the average of the month end closing prices
of the stock for the three months immediately

prior to the forecast of earnings.

32

The author computed forecasts based on analysts'
forecasts and in addition used six naive models to gene-
rate forecasts. The forecasts were then analyzed to see
how accurate they were.

It was found that the forecasts generated using
analysts' predictions were overforecasts in 70% of the
cases.40 When the analysts' forecasts were compared with
forecasts generated by the best naive model, no signi-
ficant difference in forecast accuracy was found.41

Several of the forecasts were then associated with
stock price changes. The methodology utilized was to
associate cumulative stock price residuals with forecast
errors, using the Spearman rank correlation coefficient.

Previously, it was noted that the stock price changes
should be computed by eliminating general market effects.
This was accomplished by Janell through the use of the
market model. This is a technique which through regres-
sion procedures eliminates the market effect from the
stock price by utilizing a general index of market prices.
This technique was essentially the same as that used in
the present study and is thoroughly explained in the
next chapter. The stock prices were then continuously
compounded over the period from the forecast announce-

ment to the date of the announcement of actual earnings.

The result was the cumulative stock return residual.

33

After associations between forecast errors and
cumulative stock return residuals had been determined,
the associations were compared. The associations com-
pared were those of the analysts' forecasts and those
of the three annual naive models. The author stated
that:

At the .05 level of significance it was found

that two of the three annual naive models did not

differ significantly in their association with

stock price returns than did errors in the analysts'

estimates. The conclusion drawn, therefore, was

that analysts' projections do not have greater
utility for investors than do foiscasts generated

by simple naive forecast models.

The author also had available quarterly revisions
of the analysts' forecasts. 'When the revisions were
analyzed, it was found that as the forecast horizon was
reduced, there was a reduction in the mean prediction
errors for both the analysts' forecasts and for forecasts
generated using naive models.43

When the association between the analysts' annual
forecast errors and the cumulative stock price returns
was compared with the association between the analysts'
quarterly revisions and the cumulative stock price
returns, no statistical differences were found.44

Janell's study had a number of desirable features.
The stock prices were adjusted for general market effects.

A relatively large sample (100 firms) was obtained.

Statistical procedures were used to compare analysts'

34

forecasts to those of naive models. These positive fea-
tures are all included in the present study.

There is, however, the question as to whether the
forecast errors were properly measured. The formula

(A-F)/F canlead to different specifications of relative
error among the various forecasts (naive and analysts'),
even if the absolute error is the same for each of the
forecasts. The formula (A—F)/P,might lead to lower rela-
tive errors for higher priced securities.

These error computations, however, also have advan-
tages. The measurement of forecast error relative to
the forecast may be particularly useful to investors.

If the investor has a forecast available for the current
year, he may desire to adjust this forecast for past
experience with forecast errors. The past error measure-
ment most useful to him might, then, be compared rela-
tive to the forecast.

The error normalized by price (A-F)/p would not have
the problems associated with a small or negative base.
This advantage was discussed previously in this chapter
in the review of Niederhoffer and Regan.

The most significant problem with Janell's study
was the specification of the analysts' forecasts. The
author averaged several analysts' forecast for each
firm and used the result as the analysts' forecast. Since

there is really no one analyst forecast for each firm,

35

this was a necessary procedure. But it is questionable
whether the results can be attributed to analysts'
forecasts since the forecasts used were not actual
analysts' forecasts but were rather forecasts derived

from analysts' forecasts.

Summary

This chapter has reviewed previous empirical studies
dealing with the accuracy of management forecasts. In
addition, it contains a review of two studies relating
analysts' forecasts to stock prices. The works relating
analysts' forecasts to stock prices were reviewed be-
cause no studies were available which related management
forecasts to stock prices.

The studies of the accuracy of management forecasts
yielded contradictory evidence. Green and Segall were
not impressed with the accuracy of management forecasts
when such forecasts were compared with forecasts generated
by naive models. But Cepeland and Marioni found manage-
ment forecasts to be more accurate than those of naive
models. McDonald found that management forecasts were
accurate enough to be useful to investors, but no com-
parison was made between management forecasts and fore-
casts of naive models.

Neiderhoffer and Regan and Janell disagree as to the

association between analysts' forecasts and stock prices.

36

Niederhoffer and Regan found a strong association to
exist between stock prices and forecast errors. Janell
found relatively weak associations between stock prices
and forecast errors. In addition, he determined that
there was no greater association between forecast errors
and stock prices for analysts' forecasts than there was
for two of the three annual naive models.

The present study attempted to eliminate some of
the weaknesses present in the studies examining the accuracy
of management forecasts. In addition, there was an ex-
tension of the analysis of the association between fore-
cast errors and stock prices to the area of management
forecasts. Again there was an attempt to overcome any
weaknesses present in the previous studies as well as to

capitalize on their strengths.

 

37

FOOTNOTES
CHAPTER II

1David Green and Joel Segall, ”The Predictive Power
of First-Quarter Earnings Reports," The Journal of Busi-
ness, January, 1967, XXXX, pp. 44-55. And David’Green
and Joel Segall, "The Predictive Power of First-Quarter
Earnings Reports: A Replication," Empirical Research in
Accounting_Selected Studies, 1966, A Supplement to Vol} 4
6fiThe Journal of Accounfing Research, pp. 21-36.

 

 

 

 

zDavid Green and Joel Segall, “The Predictive Power
of First-Quarter Earnings Reports," The Journal of Business,
January, 1967, XXXX, pp. 44-55.

 

3Ibid., p. 52.

41bid., p. 54.

5David Green and Joel Segall, "The Predictive Power
of First-Quarter Earnings Reports: A Replication,"
Empirical Research in Accountigg: Selected Studies, 1966,
A Supplement to—VoIT’ITof The ournaTTof—Accounting Re-
search, pp. 21-36.

 

 

6See Figure 1.

7Charles LeRoy McDonald, An Empirical Examination of
Published Predictions of Future Earnings (Unpfiblished Ph.D.
dissertation. MiChigan State University, 1972.)

 

 

81bid., p. 41.
9 .

Ib1d., p. 44.
10

The computation of forecast errors relative to the
forecast would be useful to the investor in that such an
error rate could be directly used to adjust subsequent
forecasts.

lllklég. page two of the abstract.

12Ibid., p. 111.

38

13Ibid., pp. 112—113.

141616., p. 112.

15Ibid., page three of the abstract.

16See Figure l.

17McDonald, p. 52.

18Ronald M. Cepeland and Robert J. Marioni, "Execu-
tives Forecasts of Earnings Per Share Versus Forecasts
of Naive Models," Journal of Business, October, 1972,

45(4), pp. 497-512.
19

 

Ibid., p. 499.

20Ibid., p. 498.

211bid., p. 499.

22Ibid., p. 502.

 

231bid., p. 505.

 

24Ibid., p. 506.

251bid., p. 506.

 

26McDonald, p. 46.

27Victor Niederhoffer and Patrick J. Regan, "Earnings
Changes, Analysts Forecasts, and Stock Prices," in Modern
DeveloPments in Investment Mana ementJ A Book of Read1ngs.
New Yorkz‘Praeger'PuhliSEErs, 1872, pp. 599-609.

28Ibid., p. 602.

291bid., p. 602.

30

Ibid., p. 605.

 

39

311618., p. 605.

 

321bid., p. 606.

 

331616., p. 605.

 

34Ibid., p. 607.

351616., p. 608.

36Benjamin F. King, "Market and Industry Factors in
Stock Price Behavior," Journal of Business, January, 1966,
34, pp. 139-190.

 

37Paul Andrew Janell, An Empirical Evaluation of the
Relationship Between Errors’in Analysts' Forecasts eff
Earnings Per Share and’Stock Prices, (UnpublishedfiPhTD.
dissertafion. Michigan StateTUniversity, 1974).

 

 

 

381616., p. 146.

 

391618., pp. 67-68.

 

401bid., p. 103.

 

41Ibid., p. 115.

 

42Ibid., page three of the abstract.

 

431616., p. 144.

 

44Ibid., p. 146.

 

CHAPTER III

GENERAL METHODOLOGY

Introduction

 

The research studies reviewed in the second chapter
indicate that management does not always forecast accu-
rately. This lack of forecasting accuracy provided a
means for analyzing the influence of management earnings
forecasts.

If management earnings forecasts had an influence
on investors, it would seem that such forecasts might
have influenced investor expectations about future re-
ported earnings. If management earnings forecasts had
influenced investor expectations and reported earnings
were different from forecasted earnings, a reaction in
the price of the stock would be expected. More specifi-
cally, if reported earnings exceed forecasted earnings,
this should be "good news" to the investor and an in-
crease in the price of the stock should occur. If, how-
ever, reported earnings were less than the forecast
earnings, this would be "bad news" to the investor and
a stock price decline would be expected.

In order to be meaningful, the study could not con-
clude with an analysis of stock price reactions to manage-

ment earnings forecasts. It was possible that similar

40

41

results could have been obtained using forecasts gen-
erated by naive or mechanical models. Therefore the
analysis included the stock price reaction to forecasts
generated by several naive models as well as to manage-
ment forecasts of earnings. In this chapter the theo-
retical basis for the use of this method will be examined
and in the process the general method for determining
stock price reactions will be deve10ped.

The method used required that results obtained using
management forecasts be compared to results obtained
using forecasts generated by naive models. The second
section of this chapter discusses the criteria used in
selecting management forecasts. The naive models used
are then delineated and discussed. The final topic of

the chapter is the measurement of forecast errors.

Theoretical Basis

 

This research effort has benefitted from the pio-
neering works of three accounting scholars, Ball, Brown
and Beaver. The latter was instrumental in establishing
the justification for using stock price movements as a
measure of the usefulness of information to investors.

Beaver indicated that:

Within the context of this study, a firm's

earnings report is said to have informational
content if it leads to a change in investors'

42

assessments of the probability distribution
of future returns (or prices), such that
there is a change in equilibrium value of
the current market price.1

He thus posited a relationship to exist between earnings
and stock prices.
Ball and Brown argue along much the same lines:

An empirical evaluation of accounting income
numbers requires agreement as to what consti-
tutes an apprOpriate test of usefulness. Be-
cause net income is a number of particular
interest to investors, the outcome we use as

a predictive criterion is the investment degi-
sion as it is reflected in security prices.

They support the use of security prices as a measure of
usefulness in the following manner:

Recent developments in capital market theory
provide justification for selecting security
prices as an operational test of usefulness.

An impressive body of theory supports the propo-
sition that capital markets are both efficient
and unbiased in that if information is useful

in forming capital asset prices, then the market
will adjust asset prices to that information
quickly and without leaving any opportunity for
further abnormal gain. If as the evidence indi-
cates, security prices do in fact adjust rapidly
to new information as it becomes available, then
changes in security prices will reflect the flow
of information to the market. An observed revi-
sion of stock prices associated with the release
of the income report would thus provide evidence
that the igformation reflected in income numbers
is useful.

Both Beaver, and Ball and Brown attempt to empiri-
cally validate their suppositions about the relationship
between earnings and stock prices. In doing so, both
make use of the market model. The market model was also

used to measure price response in this research effort.

43

The model can be stated as follows:

Ri = A1 + BiI + Ci

Where R1 was the return on a security, Ai and B1
are parameters, I is the level of some index, and Ci
is a random variable with an expected value of zero.
In a graphical presentation A1 and Bi locate the
line relating the expected value of R1 to 1.4 Ai
represents the intercept of the line and Bi is the
slepe of the line.

The market model has been used in a number of
studies.5 In these studies the index (I) has been a
market price index such as the Standard and Poor's
Price Index. The market model when using a market price
index for (1), allows one to abstract market effects
and thus to concentrate on factors affecting the return

on a security which are unique to the firm.6

This can be shown by manipulating the model. If

R1 = A1 + Bil + C1
then
Ci’ then, is a measure of that part of the return on a

security after removing the influence of the market

(Ai + BiI).

44

The market model using notation apprOpriate to
this study can be stated as:

Rim = 31 * biRsm + Cim

Rim is the rate of return assuming continuous compounding

on security i, for month m. It is computed as follows:

 

Dim * Pim
Rim = loge Pim-l
where:
loge: = the natural logarithm;
Dim = the cash dividend paid on a share of firm
i, in a month m;
im = the closing price for a share of firm i,
at the end of month m;
Pim-l = the closing price for a share of firm i

at the close of month m-l, adjusted for
capital changes.

The price relatives adjusted for dividends and capi-
tal changes (Rim) were taken from the CRSP tapes (Center
for Research in Security Prices). The tapes include
completely adjusted price relatives for virtually all New
York Stock Exchange (NYSE) firms and are prepared by
Standard and Poors.

The market price index used in this study was Fisher's
Arithmetic Investment Performance Index. The index is

the mean of the price relatives (Rim), completely adjusted

45

for dividends and capital changes, for all NYSE securities
on the CRSP tapes.

Rsm is the rate of return assuming continuous com-
pounding of the market price index for month m. It is

computed as follows:

Rsm = log e(FAIPIm)

FAIPIm = Fisher's Arithmetic Investment

Performance Index for month m.

Estimation of Parameters

 

The parameters of the market model, a1 and bi
must be estimated from months other than those being
studied. Least squared regressions of Rim (the rate
of return on an individual security) against R (the

sm

market rate of return) were used to estimate a1 and

bi' The estimates of 3i and bi must be made in the
periods not under study, because it is assumed that for
the periods studied, the expected value of C1 is other
than zero. The use of the study period in estimating the
parameters would then be inconsistent with the market
model which assumes the expected value of C1 to be zero.
Fama, et.al., have found that the distribution of
the return residuals (Ci) is well approximated by the
infinite variance stable Paretian family.7 The authors

indicate that although least squares regressions are not

efficient for these distributions, they provide estimates

46

which are unbiased and consistent.8 They conclude by
saying:

In sum we find that regressions of security

returns on market returns over time are a satis-

factory method for abstracting from the effects

of general market conditions on the month§y

rates of return on 1nd1v1dual secur1t1es.

While the authors agree as to the appropriateness
of measuring price response through use of the market
model, they relate net income to price response in dif-
ferent ways. Beaver examines investor reaction to earnings
announcements by looking at price movements in the weeks
surrounding the announcement date. More specifically,
Beaver measured price response, (Cim)’ over a number of
weeks surrounding the announcement of earnings. The
weeks closest to the announcement date were called the
"report period." Other weeks were designated the "non-
report period."

The procedure was then to: l) compute the average
of the lciml for each firm in the nonreport period,
ICEhI; 2) to compute the ratio for each report (Iciml % ICEhI)
for each week in the report period; and 3) determine the
average of the individual report ratios for each week in
the report period. The average of the lciml % ICEfiI for
the nonreport period would be one.

In performing the procedures above, the comparison

between the residual price responses in the report

period and such responses in the nonreport period was

47

built into the measure. The following hypotheses were
tested.
HO: the mean of the price response ratio for a week in
the report period is less than or equal to one.
H1: the mean of the price response ratio for a week in
the report period is greater than one.
Beaver found that the price responses in the announce-
ment week of the report period were indeed larger than
in the nonreport period, indicating that earnings announce-
ments do have informational content.

The methodology used by Beaver does have one signi-
ficant problem, that problem being that information
about the earnings number becomes available prior to
the announcement of annual earnings. For example, quar-
terly earnings reports would certainly give some indica-
tion of what the annual earnings would be. Beaver does
deal with this problem to some extent by using a 17 week
report period, eight weeks before and eight weeks after
the announcement week. However, this period was not long
enough to include quarterly earnings announcements.

Ball and Brown dealt with this problem by compounding
the price responses over a 12 month period, including the
month in which the announcement of earnings was made.
This procedure allowed the inclusion of information
about the annual earnings coming to the market prior to

the announcement period.

48

The specific methods used by Ball and Brown included
1) the generation of earnings expectations (forecasts)
using two models; 2) comparing actual earnings with the
forecast of earnings to determine forecast errors; and

3) compounding the price responses (C. ) and averaging

1m
them for firms having positive forecast errors and for
firms having negative forecast errors. The authors state:
If the income forecast error is negative (that is
if the actual change in income is less than its
conditional expectation), we define it as bad
news and predict that if there is some association
between accounting income numbers and stock prices,
then the release of the accounting income number
would result in the return on the firm's securities
being less than would otherwise be expected...
the converse should hold for a positive forecast
error. a
The notion of expected versus unexpected returns
relates to the operation of the market model previously
explained in this chapter. The return residuals (Cim)
can be viewed as unexpected or abnormal returns. The
market model asserts that the expected return on a security
conditional on the ex post value of the market price index

is a linear function of the market price index. That is,

)

differs from the expected return given a value of the

the amount by which the return on the security (Rim
market price index (31 + bi Rsm) can be viewed as
unexpected or abnormal return (Cim)°

The authors' results support their hypotheses. The
average price response for firms having negative fore-

cast errors is less than expected while the average price

49

response for firms having positive forecast errors is
greater than expected. It was statistically determined
using the chi-square statistic that there was a signifi-
cant relationship between the sign of the forecast
error and the sign of the rate of return residual.
Further, the authors found that:
...most of the information contained in reported
income is anticipated by the market before the
annual report is released.11
The use of stock prices as a measure of the useful-
ness of information to investors, then, has a solid basis
in previous research efforts. Further the market model
used in the current research effort was successfully used
in these previous research projects. It does appear,
however, that the price response does occur over time.

Therefore the present study uses the basic approach set

forth by Ball and Brown.

Management Forecasts and Naive Forecasts

As was pointed out in the first chapter, the SEC has
now allowed the publication of management earnings fore-
casts in reports filed with it.12 At one time it was
considered possible that the SEC might require the publi-
cation of such forecasts, perhaps in the annual report
(SEC lO-K). The collection of management forecasts to
be used in this research effort was specifically designed

to deal with the question of what would have been the

result of including management forecasts of earnings per

50

share in the published financial statements of the
firm.

Occasionally, such forecasts are included in the
annual report to stockholders, for example, in the presi-
dent's letter. However, it was not felt that there would
have been a sufficient number of such forecasts to enable
a meaningful study to be conducted. Therefore, a surro-
gate for forecasts published in annual reports was used.

The surrogate used was to obtain management fore-
casts published in the Wall Street Journal. The fore-
casts had the advantage of being widely distributed
to investors in much the same manner as would have been
forecasts published in the annual report to stockholders.

In order that the forecasts obtained be as similar
as possible to forecasts published in annual reports,
the timing of the publication of the forecasts was im-
portant. What was of interest in this study were fore-
casts that could have been published as a part of the
annual report or in SEC filings. Therefore, it was con-
sidered desirable to select forecasts published early
enough to be included in the annual report or SEC 10-K
report.

The period from which forecasts were selected was
the period before the required submission of the annual
report (lO-K) for firms listed on the major stock ex-
changes. This period was 120 days after a firm's year

13

end throughout the test period. Forecasts published

51

within a 120 day period following a firm's year end
probably could have been included in the annual report.
However, whether such forecasts are similar to those
which would have been included in the annual report must
ultimately be evaluated by the reader.
There were, in addition, other criteria applied in
the selection of management forecasts of earnings per
share:
1) the forecast must have been made in the first
120 days of the calendar year;

2) the firm's stock must have been traded on the
New York Stock Exchange (NYSE) for the entire
study period;

3) the forecast must have been a point forecast

of earnings per share.
The criteria were applied to ease somewhat the problems
of data collection and analysis.

The requirement that the forecast be published in
the first 120 days of the calendar year eased data col-
lection in that only January-April Wall Street Journals
were analyzed. For the most part, this led to the selec-
tion of firms with years ending on December 31. However,
it was also possible for firms with fiscal years ending
in September, October, or November to be included.

The requirement that the firm's stock be listed on
the NYSE again was partially utilized to ease data col-

lection problems. It was desired that the stock price

52

information be available on the CRSP (Center for Research
in Security Prices) tapes. These computer tapes are avail-
able only for NYSE firms. It was not felt that the use of
NYSE firms overly restricted the research because such firms
represent a major portion of the publicly owned corporations
in the economy.
The criterion that forecasts be point estimates of
earnings per share was included to allow precise determinations
of forecast errors. In the second chapter, the review of
Cepeland and Marioni's article dealt with this problem. It
was noted there that Open ended or range forecasts lead to
difficulties in the determination of forecast errors. The
reader is referred to that discussion.14
The forecasts used were forecasts of net income per share.

This type of forecast was used primarily beCause most of the

published forecasts appeared in this form.

Naive Forecasts

 

In the Opening remarks of this chapter it was indi-
cated that the primary purpose of the dissertation was
to assess the usefulness of management forecasts of earnings
per share to investors. This was to be accomplished by
relating forecast errors to stock price reactions. How-
ever, a finding that management forecasts were related
to stock prices does not in itself establish the useful-
ness of such forecasts. Perhaps similar results would

have been obtained using forecasts from other sources.

53

The investor certainly could generate his own forecasts

(perhaps using some naive model) or could obtain them

from analysts.

In order to deal with this problem, naive

forecasts were generated and the results obtained using

management forecasts were compared with results obtained

using these naive forecasts.

The naive models used in this study were as follows:

Naive l:

Naive 2:

Naive 3:

Pure random walk-~no drift:
The current year's earnings per share is
equal to the prior year's earnings per share.
In mathematical terms this forecast would be
stated as follows:

E(Xit) = xit-1

Random walk with drift:

The current year's earnings is equal to the
prior year's earnings plus the average of
the changes in earnings from year to year
in the past five years. In mathematical
terms this forecast would be stated as follows:
- X

it-l j 1 it-j it-j-l)
Moving average of a pure mean reverting
process:

The earnings process is assumed to follow a
moving average process. A moving average is

used to smooth out fluctuations in time series

Naive 4:

Where:

54

data. In mathematical terms this forecast

would be stated as follows:

SIH
ll M21

E(Xit) = x. -

1t-1 (x. . - x

j 1 1t-j it-j-l)
Pure mean reversion:
Next year's earnings are assumed to revert to
the mean of the earnings for the prior five
years. Mathematically this forecast would be
stated as follows:

1 n

Ecxit) ’ Tjil (Xit-j)

E(Xit) = the expected value of the earnings
variable for firm i in period t;

Xit = the actual value of the earnings
variable for firm i in period t;

n = the number of periods used to esti—

mate the parameters of the model,

five years.

These four models were used by Beaver and Dukes in

a research effort requiring the use of earnings expecta-

tions.15

It was noted by the authors that these models

appear to be consistent with the underlying processes

generating the earnings variables.

16

Ball and Watts have suggested that levels of earnings

are well approximated by a random walk process.r70ne rationale

55

for this result might be that in the absence of further
information no change is expected. Thus, the earnings
expected are last year's earnings. Drift is introduced
in the second random walk model as a measure of unexpected
earnings changes. The mean reverting models assume that
normal or expected earnings are based on the mean of earnings
for some prior period. The moving average of the mean
reverting process assumes that last year's earnings repre-
sent a moving average of earnings. An adjustment is then
made for unexpected earnings to arrive at expected earnings.
The use of the mean reverting models is supported
partially in that they represent processes clearly distin-
guishable from random walk processes. While the evidence
seems to support the idea that random walk processes
best approximate levels of earnings per share, it would
be desirable to include other processes to expand the generality
of the study. Further,Beaver has found that:
Much of the behavior of accounting rates of
return is consistent with these measurements
coming from a moving average model where tflgs
underlying process 15 pure mean revert1ng.
Beaver's conclusions are based on rates of return
and not on levels of earnings. However, it was felt
that these processes might be useful in predicting levels

of earnings as well as rates of return.

Forecast Errors

 

The general approach of the study required that

forecasts be compared with actual earnings in order to

56

compute errors. The forecast errors vary widely in
terms of absolute amount. Therefore, in order to put
such errors on a comparable basis, it was desirable to
compute relative prediction errors. There are a number
of approaches to the computation of relative prediction
errors which have been suggested. Errors have been com-
puted relative to: 1) actual earnings; 2) forecast
earnings; and 3) stock prices.

The computation of error relative to actual earnings
has the advantage of not being biased against over or

under predictions. For example:

Actual Earnings (A) Forecast Earningsjf) jA-Fl/A
Firm 1 $3 $4 .33
Firm 2 3 2 .33

Both overpredictions and underpredictions lead to the
same relative error. However, meaningful errors cannot
be computed when the variables have different signs, and
this method would assign a great weight to small absolute
errors when actual earnings are close to zero.

The use of errors computed relative to forecasts
has the advantage of being useful to investors.19 An
investor might desire to make adjustments for a tendency
of a firm to either underpredict or overpredict earnings.
This would be easier for him to do if errors were

expressed relative to forecast earnings. However,

57

this method of computing relative error is biased

in favor of overpredictions. For example:

Actual Earnings (A) Forecast Earnings (F) |A-F|/F
$3 $4 .25
3 2 .50

 

In this case equal absolute errors result in a lower
relative error being attached to the overforecast.
Again this method could be affected by small or
negative forecasts.

Errors computed relative to price would provide
a more meaningful measure of error when earnings are
small or negative. In addition, there is no bias favor-
ing either underpredictions or overpredictions. However,
there might be a bias depending on the size of price
used to compute the relative error.

Each measure of error has advantages and disadvan-
tages. Therefore, for most of the tests conducted in

the study all three error measures were used.

Summary
The first part of this chapter dealt with the theore-

tical basis for the conduct of the current research
effort. It was indicated that if management earnings
forecasts had an influence on investors, such forecasts

might have influenced investor expectations about future

58

reported earnings. If reported earnings were differ-
ent from forecasted earnings, a reaction in the price
of the stock was expected. However, it was also indi-
cated that if the same result could be obtained using
naive forecasts, the results could not be attributed
solely to management earnings forecasts.

Both Beaver and Ball and Brown supported the use
of stock price changes as a measure of the usefulness
of information to investors. In addition, these authors
both use the market model as the method for measuring
stock price changes. These studies taken together pro-
vide the theoretical basis for measuring the impact of
earnings forecasts on investors. Further they indicated
an operational method of measuring the stock price reac-
tions which are unique to the individual firms.

Both Beaver and Ball and Brown found that income
was a useful concept to investors in that it led to
stock price changes. However, Ball and Brown found that
the stock price changes occured over time. This led to
the conclusion that in this research effort the price
response should be measured over time in a manner simi-
lar to that used by Ball and Brown.

The second major topic of the chapter was to set
forth the selection criteria used in selecting manage-
ment earnings forecasts. Next, the naive models were
set forth and the reasons for their use were explained.

Finally, the measurement of forecast errors was discussed.

59

FOOTNOTES
CHAPTER III

1William H. Beaver, "The Informational Content of
Annual Earnings Announcements," Empirical Research in
Accounting: Selected Studies; 1968, Aisupplement to
Velume 6 of fhe Journal'of Accounting Research, p. 68.

2Ray Ball and Phillip Brown, "An Empirical Evalua-
tion of Accounting Income Numbers," Journal of Accounting
Research, Autumn, 1968, l, p. 160.

 

3Ibid., pp. 160-161.

4William F. Sharpe, ”A Simplified Model for Port-
folio Analysis," in Modern DeveloPments in Investment
Mana ement, A Book of Readings (New Yofk:’Praeger
PuEIishers, 1972), p.—192.

5e.g., Eugene F. Fama, Lawrence Fisher, Michael C.
Jensen, and Richard Roll, "The Adjustment of Stock Prices
to New Information," in Modern DevelOpments in Investment

Mana ement A Book of Readings (New York? _Praeger
Pu511shersi 1972), pP- ’ -

6It has been shown by King that about 10% of the
variability in a stock's monthly rate of return could be
accounted for by industry effects. Thus, the price response
is not entirely unique to the firm but in part may be the
result of industry effects. The industry effect does,
however, appear to be relatively small. Benjamin P. King,
"Market and Industry Factors in Stock Price Behavior,"
Journal of Business, January, 1966, 31, pp. 139-190.

 

7Fama, et.al., p. 192.

Ibid., p. 192.

 

91bid., p. 192.

10Ball and Brown, p. 164.

60

lllbid., p. 170.

12Les Gapay, "SEC Plans to Let Concerns Profit in
Filings," The Wall Street Journal, February 2, 1973,

LIII(75), p. 3.

13New York Stock Exchange Guide,--Related Laws and
Regulations, (Commerce Clearing House, Inc., 1962), III,
p. 6183.

14See Chapter Two, p. 22.

15William H. Beaver and Roland E. Dukes, "Inter-
period Tax Allocation, Earnings Expectations, and the
Behavior of Security Prices," The Accounting Review,
April, 1972, XLVII, pp. 320-332.

 

16Ibid., pp. 323-324.

17Ray Ball and Russ Watts, "Some Time Series Pro-
perties of Accounting Income," Unpublished manuscript,
University of Chicago, 1970.

18Willaim H. Beaver, "The Time Series Behavior of
Earnings,” Empirical Research in Accountin : Selected
Studies, 1972, A supplément to Volume 0 the Journal
ofAccountihg Research, p. 86.

 

 

 

19Charles Leroy McDonald, An Empirical Examination
of Published Predictions of Future Earnin s, Unpublished
PhTD. diSsertation, MiEhigan*State_Univer51ty, 1972,
p. 55.

CHAPTER IV

DESCRIPTION OF THE SAMPLE AND FORECAST ERRORS

Introduction

 

This chapter will first discuss the sample of firms
making management forecasts. The sample was obtained by
applying the selection criteria presented in the previous
chapter. The years from which such forecasts were selec-
ted will be examined in terms of the condition of corpor-
ate profits during those years.

The question of forecast accuracy will then be
addressed. The basic question of the study was not to
examine the accuracy of forecasts. But, the computa-
tion of forecast errors in an attempt to relate forecasts
to stock price changes made it possible to examine the
accuracy of such forecasts. This has the advantage of
allowing the present research effort to be related to others
which had as their primary purpose the analysis of fore-
casting accuracy.1

As a first step in the analysis of forecast accuracy,
management forecasts and naive forecasts were examined
to see whether there appeared to be any tendency to either
underpredict or overpredict earnings per share. Following
this, evidence will be presented and analyzed bearing on

the question of whether management forecasts appear to be

61

62

more accurate than those of the naive models used in this

study.

Description of the Sample

 

The selection of forecasts from the Wall Street
Journal resultedelthe accumulation of 123 usable fore-
casts. The forecasts were made by a total of 90 firms.
The number of forecasts classified by year is presented
in Table 2

TABLE 2
NUMBER OF USABLE MANAGEMENT FORECASTS

 

Yggm_ Number of Usable Forecasts
1965 I 19
1966 22
1967 V 10
1968 22
1969 16
1970 13
1971 _g;_
Total 123

The years 1965-1971 were selected for two reasons.
First, because the selection criteria were reasonably
stringent it was desired to include several years in order
that a sample of reasonable size would be obtained.

Second, it was desired to include these years because

63

they represented a wide variety of situations with regard
to corporate profits. It was thought that selecting
forecasts from such a wide variety of profit conditions
would make the study more general because it could not

be said that the results depended on the existence of a
particular economic situation. Whether the results are
more generalizable as a result of this process is, of
course, the opinion of the reader.

The reader is referred to Figure l which graphically
presents corporate profits for the years included in the
study. It should be noted that two years, 1965 and 1971,
represent climbing corporate profits throughout the year.
The year 1969 was a year in which corporate profits de-
clined throughout the year. The remaining years included
in the study could be characterized as being of a mixed
nature. These years were mixed in the sense that profits
both increased and decreased during each of the years.
The selection of these years, then, in the opinion of the
researcher included a wide variety of economic conditions.
But, again the ultimate opinion must be that of the
reader.

It is interesting to note that those years which had
a strong economic start had more usable forecasts than
did years beginning with weak economic performance. This
could conceivably introduce some bias into the study if
firms failing to forecast in weak years were different from

those which did forecast in these years.

64

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TABLE 3

YEARS BEGINNING WITH

STRONG ECONOMIC PERFORMANCE

1e_a:;.s_
1965
1966
1968
1971
Total

Average number of forecasts =

TABLE 4

YEARS BEGINNING WITH

21.

WEAK ECONOMIC PERFORMANCE

19.21;;
1967
1969
1970
Total

Average number of forecasts =

13.

Number

19
22
22

of

Number of Forecasts

Forecasts

66

McDonald had noted that there tended to be more fore-
casts in good years than there were in bad years.3 His
observations seem to be confirmed by the results of the
current analysis. The forecasts which were included in
the current sample had been published in the first 120
days of the firm's year. In those years where the early
part of the year was good there were more forecasts than
when the reverse was true.

The sample which was selected included, in the
researcher's opinion, firms from a wide variety of indus-
tries. Included are many manufacturing industries such as
machine tools, steel, copper, petroleum and chemicals. In
addition, there were firms from the wholesale trade,
utilities, financial institutions, transportation and com-
munications. The reader is referred to Appendix A which
contains a complete list of the firms in the sample and

their industries.

Forecast Accuracy

 

It is possible to test statistically whether there
was any tendency to either underpredict earnings per share
or overpredict earnings per share. The chi-square one
sample test is an appropriate test to use in this situation.
If there were no differences between the number of firms
underpredicting earnings and the number of firms overpre-
dicting earnings, it would be expected that 50 per cent

of the firms would fall in each category. The chi-square

67

one sample test can be used to test this proposition.
Specifically, the hypotheses are:

'H : the frequency of underpredictions and overpredictions
are equal with 50 per cent of the firms falling in
each category;

A: the frequency of underpredictions and overpredictions
are not equal.

The chi-square one sample test statistic was com-

puted as follows:

 

4
2
2 _ K (Oi ' Bi)
X " E E
i=1 i
where:
01 = observed number of cases in the i-th category;
E1 = expected number of cases in the i-th category
under H ;
0
2K = directs one to sum over all (K) categories.
i=1

Siegel indicates:

"If the agreement between the observed and ex-
pected frequencies are close, the differences
(Oi - Bi) will be small and consequently x2

will be small. If the difference is large, how-
ever, the value of x2... will also be large.
Roughly speaking, the larger x is, the more
likely it is that the observed frequencies did
not come from the population on which the null
hypothesis is based."5

68

“0 will be rejected if the observed value of x2

is such that the probability associated with its occur-
rence under “0 is equal to or less than a = .05.

In conducting the test a decision had to be made
about the nature of the exact forecasts. Were they under-
predictions or overpredictions or should they be omitted
from the analysis? The decision was made to add the
exact forecasts in each case to the smaller number of
either underpredictions or overpredictions. The result
of this process was a conservative test of the tendency
to underpredict or overpredict earnings per share.

The results of the chi-squared one sample test are
displayed in Table 10-14. Tables 5-9 present the actual
number of overpredictions, exact predictions, and under-

predictions for management forecasts and naive model

 

 

forecasts.
TABLE 5
FORECAST ERRORS
(MANAGEMENT)
Overpredictions EEEEE. Underpredictions
1965-1971 59 4 60
1965. 5 0 14
1966 9 l 12
1967 4 1 3
1968 14 0 8
1969 10 l 5
1970 8 0 5

1971 7 1 13

69

TABLE 6
FORECAST ERRORS
NAIVE 1
(PURE RANDOM WALK)

 

 

Overpredictions E5225. Underpredictions
1965-1971 40 7 76
1965 4 0 15
1966 8 1 13
1967 3 0 7
1968 8 0 14
1969 4 5 7
1970 8 0 5
1971 5 l 15
TABLE 7

FORECAST ERRORS
NAIVE 2
(RANDOM WALK WITH DRIFT)

 

 

Overpredictions E5222. Underpredictions
1965-1971 60 3 60
1965 5 0 14
1966 11 0 11
1967 5 0 5
1968 14 0 7
1969 12 0 4
1970 8 0 4

1971 5 0 15

70

TABLE 8
FORECAST ERRORS
NAIVE 3
(MOVING AVERAGE OF A PURE MEAN REVERTING PROCESS)

 

 

Overpredictions E3333 Underpredictions
1965-1971 38 0 85
1965 3 0 16
1966 7 0 15
1967 3 0 7
1968 8 0 14
1969 4 0 12
1970 6 0 7
1971 7 ' 0 14
TABLE 9

FORECAST ERRORS
NAIVE 4
PURE MEAN REVERSION - NO DRIFT

 

 

Overpredictions EEEEE Underpredictions
1965-1971 32 0 91
1965 l 0 18
1966 3 0 19
1967 2 0 8
1968 8 0 14
1969 5 0 11
1970 5 0 8
1971 8 0 l3

71

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76

When the results of this test are analyzed on an
overall basis (for all years in the study) three of the
four naive models tended to produce underpredictions.

This might be expected in an inflationary period.

The only Naive model which did not produce underpredic-
tions was Naive 2, the random walk with drift model.

This would not be entirely inconsistent with expectations.
Ball and Watts had found that random walk processes seemed
to produce the best estimates of levels of earnings.6

The introduction of trend into the random walk process
appears from these results to be important as the pure
random walk model (Naive 1) does lead to underforecasts.

Management forecasts of earnings per share did not
exhibit either a tendency to underpredict earnings per
share or to overpredict earnings per share. This result
is not consistent with McDonald's study where he found
that there was a significant tendency for management to
overpredict earnings per share.7 McDonald indicated that
arguments could be developed to support contentions that
management would either overpredict or underpredict earnings.8
For example, the desire to be conservative might lead to
underpredictions. On the other hand a desire to have an
immediate increase in the price of a firm's stock might
lead to overpredictions. Neither position is supported

by the current reSults when analyzed on an overall basis.

77

The year 1965 when analyzed shows that all naive
models and management tended to underpredict earnings
per share. However, the underpredictions were less
significant for pure random walk with drift forecasts
and for management forecasts. That the naive model fore-
casts should lead to underpredictions is not surprising
since they were computed on the basis of the past five
years'data. The year 1965 was but a continuation of the
strong upward movement in corporate profits that had en-
dured since 1962. The naive model predictions based on
thesepast data would tend to be low. The mean reverting
models did poorer than the random walk models which
utilize more current information.

The results did not hold for 1971 which was again
a year of strong performance in corporate profits. How-
ever, of the five years preceeding 1971, four had mixed
economic performance with one year having declines through-
out. The profits in some of these years were nearly as
high as those in 1971. It would thus be expected that
the random walk models would perform more poorly than
the mean reverting models which made more use of the
previous five years' data.

The only year with continuously poor results in
corporate PTOfitS (1969) led to the only occasion where any
model tended to overforecast earnings. In this year the

random walk with drift model followed this pattern.

78

The years with mixed economic performance (1966, 1967,
1968, and 1970) led to the result that with but one excep-
tion no model tended to either underpredict or overpredict
earnings. This result may have occurred because of the
very unsettled nature of corporate profitability during
those years. The only exception was that the pure mean
reversion--no drift model led to underpredictions in 1966.
That result was not overly surprising since this model
makes more use of past information than any of the other
models.

The distribution of forecast errors for each type
of forecast is graphically presented in Figures 2 - 6.

The analysis of the comparative accuracy of forecasts was
limited to errors computed relative to forecasts. Errors
computed relative to forecasts were used because, as pre-
viously indicated, this sort of error computation seems
particularly useful to investors. In addition, this

process allowed some comparison to be made between the
present research effort and McDonald's work.9 However,

the discussion in Chapter III indicated that errors com~
puted in this manner are biased in favor of overpredictions.
In addition, such errors might be adversely affected by

small or negative forecasts.

79

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84

The graphical presentation strongly indicates that
management forecasts of earnings per share are indeed
quite accurate and seem to be more accurate than fore-
casts generated by the use of the naive models. In
addition, it would appear that the random walk models
are more accurate than the mean reverting models. Table
15 summarizes some of the information presented in the

graphical analysis.

TABLE 15
PERCENTAGBS 0F ERRORS WITHIN
SPECIFIED ERROR CATEGORIES
1965 -_1971
(A-F)/F

Percentages of Errors Within the Error Category

 

 

Eaigzory Management Naive l Naive 2 Naive 3 Naive 4
-.05 to .05 38.3 20.3 26.9 9.8 9.8
-.10 to .10 57.0 33.9 42.4 22.8 13.8
-.15 to .15 66.8 49.7 49.7 38.3 24.4

This summary indicates that for management forecasts
the actual earnings per share were within 10 per cent of
that forecast in 57 per cent of the cases and were within
15 per cent in 66.8 per cent of the cases. This perfor-
mance appears to be much better than any of the naive

models.

85

The analysis of the graphical presentation of
forecast errors does provide some evidence on the
accuracy of the various forecasts. However, it is also
possible to analyze the comparative accuracy of the
various types of forecasts on a statistical basis. In
this research effort the Wilcoxon Signed-Ranks test was
utilized to test whether management forecasts were more
accurate than those of the naive models. In addition,
it was used to determine which of the naive models
seemed to do the best job of predicting levels of earn-
ings per share.

The Wilcoxon Signed-Ranks test is a nonparametric
test. It was used to avoid the distributional assump-
tions of equivalent parametric tests, such as the T
test. This test has the advantage of considering not
only the direction of the differences between fore-
cast errors but their magnitude as well. The test
statistic as computed for large samples (greater than

20) is as follows:

 

 

 

10
N N+1
z = T ' "LT—l
VfiiN+|ikZN+li
2
where:
N = the number of matched pairs minus the number

of pairs where the differences are zero;

86

T = either the sum of the positive ranks or the
negative ranks, whichever sum is smaller.
The specific hypotheses to be tested are:
H10: the accuracy of management forecasts and forecasts
of each of the naive models do not differ;
HlA: management forecasts are more accurate than naive
forecasts;
H20: the accuracy of Naive 1 forecasts and forecasts

of each of the other naive models do not differ;
HZA: Naive 1 forecasts are more accurate than the other

naive forecasts;

H30: the accuracy of Naive 2 forecasts does not differ
from that of Naive 3 and Naive 4 forecasts;
H3A: Naive 2 forecasts are more accurate than either

Naive 3 or Naive 4 forecasts;

H40: the accuracy of Naive 3 forecasts does not differ
from that of Naive 4 forecasts;
H4A: Naive 3 forecasts are more accurate than Naive 4
forecasts.

The region of rejection consists of all Z's which
are so extreme that the probability of their occurrence
under H0 is equal to or less than a = .05. The results
of the tests of these hypotheses are presented in
Tables 16-19.

The results of testing management forecasts against

those of the naive models yield clear and consistent

87

results. Management forecasts are more accurate than
those of any of the naive models at extremely high levels
of significance.

The comparisons of the naive models provide results
which are less clear. When the test was conducted using
errors computed relative to price and actual earnings, the
Naive 1 model (pure random walk) was more accurate than two
of the three remaining naive models. However, it was not
more accurate than the Naive 3 model. The third naive model
was the moving average of a pure mean reverting process.
This then does not entirely confirm Ball and Watt's re-
sults which indicate that random walk processes are the
best predictors of levels of earnings. Further the
second,model, which was a random walk procedure, does not
generate forecasts which are more accurate than either
of the mean reverting models. The moving average mean
reverting model is, however, more accurage than the pure
mean reverting model. This would not be unexpected
since the pure mean reverting model does use older infor-
mation. If one looks at only the number of times one
model was more accurate than the other, the results are
consistent with expectations. The first naive model is
more accurate than any of the other naive models. Naive
2 is more accurate than any of the mean reverting models
and the moving average of the mean reverting process is

the more accurate of the mean reverting models.

88

TABLE 16
WILCOXON SIGNED-RANKS TEST
COMPARISON OF RELATIVE ERRORS
MANAGEMENT vs. NAIVE MODELS

*

IA-Fl/P

*3':
Variable Variable Diff < 0 Diff > 0 Rank Sum Significance

 

Management Naive l 77 32 1549.0 .0000
Management Naive 2 82 40 1747.0 .0000
Management Naive 3 87 34 1825.0 .0000
Management Naive 4 93 28 1607.0 .0000

*The price used to compute relatiVe errors was obtained by
averaging the price of the firm's shares for three months
prior to the month in which the forecast was published.

**A difference of less than zero indicates the management

forecast was more accurate.

89

TABLE 17
WILCOXON SIGNED-RANKS TEST
COMPARISON OF RELATIVE ERRORS
NAIVE MODELS
an
IA-Fl/P

a
Variable Variable Diff < 0 Diff > 0 Rank Sum Significance

 

Naive Naive 2 67 54 2886.0 .0374
Naive Naive 3 73 48 3096.0 .1241
Naive Naive 4 82 41 2739.0 .0067
Naive Naive 3 63 56 3474.0 .7991
Naive Naive 4 71 51 3150.0 .1243
Naive Naive 4 81 42' 2658.0 .0036

*A difference of less than zero means the forecasts generated
by the model in this column are more accurate than those
generated by the model in the second column.

**The price used to compute relative errors was obtained by
averaging the price of the firm's shares for three months

prior to the month in which the forecast was published.

90

TABLE 18
WILCOXON SIGNED-RANKS TEST
COMPARISONS OF RELATIVE ERRORS
MANAGEMENT vs. NAIVE MODELS

IA-FI/F

**
Variable Variable Diff < 0 Diff > 0 Rank Sum Significance

Management Naive l 78 30 1266.5 .0000
Management Naive 2 80 41 1851.0 .0000
Management Naive 3 88 33 1448.0 .0000
Management Naive 4 97 24 1103.0 .0000

*There was one forecast of zero EPS.
**A difference of less than zero indicates the management

forecast was more accurate.

91

TABLE 19
WILCOXON SIGNED-RANKS TEST
COMPARISON OF RELATIVE ERRORS
NAIVE MODELS
lA-FI/F

*
Variable Variable Diff < 0 Diff > 0 Rank Sum Significance

 

Naive l Naive 2 63 59 3647.0 .7895
Naive l Naive 3 77 45 2473.0 .0011
Naive l Naive 4 86 37 2102.0 .0000
Naive 2 Naive 3 72 50 3044.0 .0707
Naive 2 Naive 4 74 49 2453.0 .0006
Naive 3 Naive 4 85 38' 2063.0 .0000

*A difference of less than zero indicates that the fore-
casts generated by the model in this column are more accur-

ate than those generated by the model in the second column.

92

TABLE 20
WILCOXON SIGNED-RANKS TEST
COMPARISON OF RELATIVE ERRORS
MANAGEMENT vs. NAIVE MODELS
IA-FI/A

 

Variable Variable Diff < 0* Diff > 0 Rank Sum Significance
ldanagement Naive 1 77 31 1638.5 .0001
Iflanagement Naive 2 82 40 1825.5 .0000
ldanagement Naive 3 87 34 2006.0 .0000
bdanagement Naive 4 93 28 1826.0 .0000

*A difference of less than zero indicates the management

forecast was more accurate.

Variable* Variable Diff < 0 Diff > 0 Rank Sum Significance

Naive
Naive
Naive
Naive
Naive

Naive

1
1

93

TABLE

21

WILCOXON SIGNED-RANKS TEST

COMPARISON OF RELATIVE ERRORS

Naive
Naive
Naive

Naive

2
3

4

(N

Naive 4

Naive

NAIVE MODELS

lA-FI/A

67
73
82
61
71
81

54
48
41
54
51
42

2720.
3393.
2972.
2038.
3325.
2843.

5
S

.0121
.4424
.0338
.3916
.2758
.0144

* A difference of less than zero means the forecasts

generated by the model in this column are more accurate

than those generated by the model in the second column.

94

The latter analysis also holds for errors computed
relative to the forecasts. However it is again the case
that the statistical results are not entirely consistent.
In this case Naive 1 is more accurate than any model
except Naive 2. Naive 2 is more accurate than Naive 4
but not more accurate than Naive 3. So again it cannot
be definitely said that the random walk models do a bet-
ter job of predicting earnings per share than do the
mean reverting models. However the second test does
confirm that the moving average mean reverting model does
do a better job of predicting earnings per share than

does the pure mean reverting model.

Summary

This chapter was concerned with two major topics.
First, there was a discussion of the sample of manage-
ment forecasts which was selected and the years from
which such forecasts were taken. Second, the sample was
analyzed in terms Of the accuracy of both management
forecasts and forecasts generated by the naive models.

The sample which was selected included 123 fore-
casts made by 90 firms. The firms appear to be widely
representative of industries within the economy. In
addition, the years from which the forecasts were
selected appeared to represent several different condi-

tions with regard to corporate profitability. An

95

analysis of the forecasts taken from each of the years
indicated that there appeared to be more usable fore-
casts in years beginning with strong economic perfor-
mance than there were in years beginning with weak
economic performance.

The first area in the exploration of forecast
accuracy was whether there was a tendency to either
underpredict or overpredict earnings. It was found on
an overall basis that there was no tendency for manage-
ment to either underpredict or overpredict earnings.
This was also the case with the Naive 2 (random walk
with drift) model. The remaining naive models tended
to underpredict earnings.

A graphical analysis gave some preliminary evidence
that management forecasts were more accurate than those
of the naive models. In addition it appeared that the
random walk naive models were more accurate than the mean
reverting naive models.

When statistical tests were made to determine the
comparative accuracy of the forecasts, it was confirmed
that management forecasts were indeed more accurate than
those of the naive models. However, there was not con-
firmation on a statistical basis that the random walk
models were in all cases more accurate than the mean re-
verting models. As a part of the information provided

by the statistical tests it was possible to conclude

96

that the random walk models had a greater number of
accurate forecasts than did the mean reverting models.
As a final note it was possible to conclude that the
moving average of pure mean reverting process model was

more accurate than the pure mean reverting model.

97

FOOTNOTES
CHAPTER IV

lE.g., Charles Leroy McDonald, An Empirical Exam-
ination of Published Predictions of Efiture Earnings.
iUnpuBIiSEEd Ph.D.dissertation. MIEhigan State Univer-
sity, 1972).

 

 

 

2Board of Governors, Federal Reserve System, 1973
Historical Chart Book (Washington D.C. Board of Governors,
Federal’Reserve System, 1973) p. 50.

3McDonald, pp. 49-50.

4Sidney Siegel, Nonparametric Statistics for the
Behavioral Sciences (New York,—McGraw-Hill BOOk Company,
Inc., 1956) p. 43.

 

5Ibid., p. 43.

6Ray Ball and Ross Watts, "Some Time Series Proper-
ties of Accounting Income," unpublished manuscript,
University of Chicago, January, 1970.

7McDonald, p. 68.

81bid.. p- 22-

 

9See McDonald, pp. 59-67.

10Siegel, p. 79.

CHAPTER V

THE PRICE RESPONSE TO MANAGEMENT
FORECASTS OF EARNINGS PER SHARE

Introduction

 

Chapter V is concerned with two major topics. The
first topic is the presentation of the specific method
which was used to compute the price responses to the
forecasts of earnings per share. The second topic is
the presentation of hypotheses and the analysis of test
results concerned with the price response to management

earnings forecasts.

Measurement Of Price Response

 

In the second chapter it was noted that the market
model would be used to obtain stock price changes which
were unique to the firm. In addition it was indicated
that as a result of the findings of Ball and Brown the
price response would be measured over time}' The specific
method used to measure price responses over time was to
compound the price responses (Cim) obtained by applying
the market model over a test period. The test period
which was used began with the month in which the manage-

ment forecast was published in The Wall Street Journal

 

and ended with the month in which the actual earnings were
announced. It was assumed that any price response prior

98

99

to the month of the publication of the forecast would
not be related to the forecast. The price response
during the test period was deemed relevant because

price responses during this period could be the result
of comparisons between the forecast and revised expecta-
tions of actual earnings. Revisions of expectations
could occur for example as quarterly earnings reports
indicate the progress already made in reacning the earnings
which had been forecast. The month in which the actual
earnings were announced should be included in the test
period because the actual earnings figure would allow a
final comparison to be made between forecast earnings
and actual reported earnings.

As was previously indicated the price relatives were
taken from the CRSP (Center for Research in Security
Prices) tapes. These tapes contain monthly closing price
relatives for NYSE firms. This data base necessitated
the compounding of the price response for the entire month
in which the forecast was published and the entire month
in which the actual earnings were announced. This lack
or precision is probably not a serious limitation. Ball
and Brown have found that most of the price response to
earnings occurs over a lengthy period before the announce-
ment of annual earnings. A small addition or deletion
of time, then, probably would not seriouSIy distort the

measurement of price response.

100

The price responses were compounded over this test

period using the method of continuous compounding sug-

2

gested by Beaver and Dukes. The formula for this calcu-

lation or the compound price response (PR) is as follows:

PR = “m eRim - “m eE(Rim Rsm)
t=l t=l
i = the firm;
m = the number of months in the test period;
im = the completely adjusted price relative for firm
i in month m. If log e(y) 8 Rim’ then y = eRim
eECRimlem) = eRim - Cim

This method of compounding is difficult to illustrate.
However, Ball and Brown used and tested a method of dis-
crete compounding which can be illustrated more easily.3
For an example of the calculation of the PR using Ball and

Brown's technique, the reader is referred to Appendix B.

The Relationship Between Forecast Errors and Price Responses
It will be recalled from the discussion in the third

chapter that if actual earnings were in excess of forecast

earnings, this should be “good newS“ to the investor and

an increase in the price of the firm's stock would be ex-

pected. The reverse was also indicated as being an expected

result. In terms of the compound price response after

eliminating market effects an underforecast should lead

101

to a price response greater than zero while an overfore-

cast should lead tO a price response of less than zero.

In order

to present a general picture of the relation-

ship between forecast errors and price responses, scatter

plots were obtained which allow a visual analysis to be

made. The scatter plots are presented in Figures 7 through

21. The following notation was used in the preparation

or the scatter plots.

Figures 7 through 11 (A-F)/A

C2

E-M

E-N1 =

E-Nz =

E-N3 =

E-N4 =

continuouSly compounded price response;
management forecast errors;

Naive l forecast errors;

Naive 2 forecast errors;

Naive 3 forecast errors;

Naive 4 forecast errors.

Figures 12 through 16 (A-F)/F

C2
A-F/FMGT

A-F/F N1

A-F/F N2

A-F/F N3

A-F/F N4

= continuously compounded price responses;
= management forecast errors;

= Naive l forecast errors;

= Naive 2 forecast errors;

= Naive 3 forecast errors;

= Naive 4 forecast errors;

Figures 17 through 21 (A-F)/P

C2 =
EM/P

ENI/P

ENZ/P

continuously compounded price response;
management forecast errors;
Naive 1 forecast errors;

Naive 2 forecast errors;

102

ENS/P = Naive 3 forecast errors;

EN4/P Naive 4 forecast errors.

It had been anticipated at the outset Of the study
that there should be a consistent relationship between the
Sign of the forecast error and the sign of the price
response. In addition, it had been expected that the
size of the forecast error would be related to the size
of the price response. The relationships depicted in the
scatter plots do not seem to confirm either of these
expectations. It would appear that negative forecast
errors are associated With positive price responses
about as Often as with negative price responses. Fur-
ther, the largest price responses do not seem to be con-
sistently associated with the largest errors. However,
any conClusions based on such a visual analysis must be
tentative until they are confirmed by statistical tests.

The first statistical test applied to measure the
association between forecast errors and price responses
was the chi-square test for 2x2 contingency tables.
This test was used to examine the question of wnether
the sign of the price response followed the sign of the

forecast error. The spec1fic hypotheses tested were:

0: There is no difference between positive and nega-
tive forecast errors in the prOportion of price
responses greater or less than zero.

HA: A greater prOportion Of positive forecast errors

have positive price responses than is the case

 

 

 

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103

FIGURE 7

SCATTER PLOT FORECAST ERRORS AGAINST

PRICE RESPONSE

MANAGEMENT FORECASTS (A-F)/A

107 CASES FOR THIS GRAPH

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104

FIGURE 8
SCATTER PLOT FORECAST ERRORS AGAINST
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105

FIGURE 9

SCATTER PLOT FORECAST ERRORS AGAINST

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106

FIGURE 10

SCATTER PLOT FORECAST ERRORS AGAINST

NAIVE 3 FORECASTS (A-F)/A

PRICE RESPONSE

 

 

 

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FIGURE 11

SCATTER PLOT FORECAST ERRORS AGAINST

PRICE RESPONSE

NAIVE 4 FORECASTS (A-F)/A

90 CASES FOR THIS GRAPH

 

 

 

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109 "‘8‘3 FHH THIS GRAPH
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FIGURE 13

SCATTER PLOT FORECAST ERRORS AGAINST

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FIGURE 14
SCATTER PLOT FORECAST ERRORS AGAINST
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FIGURE 15

SCATTER PLOT FORECAST ERRORS AGAINST

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FIGURE 18
SCATTER PLOT FORECAST ERRORS AGAINST
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FIGURE 21

SCATTER PLOT FORECAST ERRORS AGAINST

PRICE RESPONSE
NAIVE 4 FORECASTS (A-F)/P

 

 

 

IIH CASFS F”? THIS GRAPH
I I
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118

With negative forecast errors.

The area of rejection or the null hypothesis was all
values of x2 which were so large that the probability
associated with their occurrence is equal to or less than
a = .05.

The computational formula for the x2 statistic

for a two by two contingency table is as tollows:4

CONTINGENCY TABLE

 

 

 

 

 

 

A* B*
C* D*
N2
X2 = N(|AD-BCI - 7
+ + + +

Where:

2
II

the number of cases in the sample;

8*
II

the frequency of occurrences in cells

A,B,C, and D.

The results or this test are presented in Tables 22
through 26- These statistical results tend to confirm
the visual analysis. With the exception of Naive 1 fore-

casts there was no signiticant association between the

119

direction of the forecast errors and the direction of
the price responses. In the case of Naive 1 forecast
errors there was an association which was significant
at the .05 level, but it was the opposite of that which
had been expected.

If Tables 22 through 26 are analyzed on a nonstatis-
tical basis, the results for all methods of forecasting,
show that more negative price responses are associated
with positive forecast errors than with negative fore-
cast errors. In addition,more positive price responses
are associated Wlth negative forecast errors than with
pOSitive forecast errors. This is not the expected
result. However, many of the forecast errors are small
and small deviations of the price response from the anti-
cipated direction might be expected. This indicated
the need for a test or tests which included the magni-
tudes of the forecast errors and price responses.

A second test of the association between fore-
cast errors and price responses tested whether the
size of the forecast error was associated with the Size
of the price response. Rank order correlations between
the forecast errors and the price responses were com-
puted in order to test this question. Rank order cor-
relations were used because the use of such tests does

not require assumptions about the distributions of either

2

120

TABLE 22

X DIRECTION OF PRICE

RESPONSE WITH THE DIRECTION

MANAGEMENT FORECASTS

OF ERROR

 

 

 

 

 

 

 

 

 

 

 

 

ERROR PR > 0 PR < 0
+ 25 33 58
- 33 28 61
58 61 119
Computed x2 = 1.032
Critical x2 = 2.71
TABLE 23
x2 DIRECTION OF PRICE
RESPONSE WITH THE DIRECTION OF ERROR
NAIVE 1 FORECASTS
ERROR PR > 0 PR < 0
+ 30 44 T4
- 25 17 42
55 61 116
Computed x2 = 3.148529
Critical X2 = 2.71

RESPONSE WITH THE

121

TABLE 24
x2 DIRECTION OF PRICE

NAIVE 2 FORECASTS

DIRECTION OF ERROR

 

 

 

 

 

 

 

 

 

 

 

 

ERROR PR. >0 PR.<
+ 24 34 58
- 34 28 62
58 62 120
Computed x2 = 1.668
Critical x2 = 2.71
TABLE 25
x2 DIRECTION OF PRICE
RESPONSE WITH THE DIRECTION OF ERROR
NAIVE 3 FORECASTS
ERROR PR > 0 PR < 0
+ 36 47 83
_ - 23 17 4O
. 59 64 123
Computed X2 = 1.626
Critical X2 = 2.71

122

TABLE 26

x2 DIRECTION OF PRICE

RESPONSE WITH THE DIRECTION OF ERROR

NAIVE 4 FORECASTS

 

 

 

 

 

ERROR PR > 0 PR < 0
+ ‘ 39 50 89
- 20 14 34
59 64 123

Computed X2
2

1.658

Critical X

II
N

.71

 

123

the forecast errors or the price responses. As was pre-
viously noted, Fama, et.al., have found that the price
responses (Cim) are better approximated by distributions
of the stable Paretian family than by the normal distri-
bution.5
The particular correlation technique used was the
Spearman rank correlation coefficient. In order to com-
pute the Spearman rank correlation between forecast
errors and price responses it was necessary to rank them
in two series. Then the difference is found between the
ranks of the two items for each firm In the sample. The

Spearman rank correlation is then computed. The specific

form for the computation of the correlation coefficient

 

is as follows:6
6 2” di2
r = 1 _ 1:1
N - N
Where:
N = the number of firms in the sample;
d. = the difference for a firm between the rank

of the forecast error and tne rank of tne

price response.

124

If there were perfect correlation between forecast
errors and price responses the rank of the forecast
error for each firm should be the same as the rank of
the price response. The di's would be zero.

The correlation coefficients which were obtained
are presented in Table 27} The correlations which were
Obtained give one overall impression. They appear to
be rather low. If there were perfect correlations, the
coefficients would be one. The coefficients which were
Obtained yield only one case where there was even a .3
level of correlation. These results suggest that there
is a positive but low association between the size of
the forecast error and the size of the price response.
In addition, the results of this procedure show that
for two of the three methods of measuring error, A—F/A
and A-F/F, management forecast errors are not more closely
associated with price responses than are two of the naive
models. Both of the random walk naive models yielded

forecast errors more closely associated with price
responses than management forecast errors. In fact, the
associationswere stronger for the random walk models
than for any of the other forecasts.

When errors are computed relative to price, the
same conclusions cannot be drawn. In this case errors
computed using management forecasts are more closely

associated with price responses than are errors using

125

TABLE 27
SPEARMAN RANK-ORDER CORRELATION COEFFICIENTS

FORECAST ERRORS WITH PRICE RESPONSE

 

Forecast Error (A;§lAA [A;£l/F (A;§l£f
Management .1941 .2905 .2990
Naive 1 .2023 .2982 .2360
Naive 2 .2314 .3146 .2429
Naive 3 .1710 .2662 .2107

Naive 4 .0762 .1706 .1432

126

any of the naive modles. It is the case that errors
computed using the random walk models are the next most
closely associated with price responses.

Whether management forecasts appear to be more useful
to investors is then not clear. The association between
forecast errors and price responses for both management and
the random walk naive models are very similar for all methods
of computing errors. Since this lack of clarity existed,
other tests were utilized to examine the question of whether
management forecast errors seemed to be more related to price
responses than were errors computed with forecasts generated
by the naive models.

In order to specifically examine this question,
comparisons were made between management forecasts and
naive forecasts to determine cases where they were on
Opposite sides of actual results. If there were price
response to management earnings forecasts, the sign of
the price response should follow the sign of the manage-
ment forecast error rather than the sign of the naive
forecast error. Comparisons of this type were made using
management forecasts and each of the naive model forecasts.

It was originally intended to test this question
by using a chi-square test for a 2x2 contingency table.
However, it turned out that the cell frequencies were too
small to justify the use of this test. Siegel indicates
that for a 2x2 contingency table where the total number
is between 20 and 40, the chi-square test should not be

used if the expected frequency of any cell is less than

127

five. He suggests the use Of the Fisher test in cases
where this criterion is not met.7
The Fisher test allows the computation of the exact
probability of Observing the set of frequencies obtained
or results even more extreme, when the marginal totals

are regarded as fixed. The exact probability is given

by the hypergeometric distribution. Where:

p = (Mu! (C+D)!iA+C)! (B+D)!8
NT AT T! D!

The contingency table would be as follows:

 

 

 

 

 

 

A B A + B
C D C+D
A+C B+D N

For example, if the following frequencies had been

observed:

 

 

 

 

 

 

1 6 7
4 1 S
5 7 12

The formula would be applied to that contingency table
and to the more extreme contingency table with the same

marginal totals.

128

 

 

 

0 7 7
5 0 S
S 7 12

 

 

 

 

 

The results would then be summed to find the exact
probability of such an occurrence of frequencies or of
possibilities even more extreme.

The specific hypotheses to be tested are:

HO: Positive management forecast errors and negative
management forecast errors show equal proportions
in the sign of the price response associated with
such errors.

A: A greater prOportion of positive management fore-
cast errors have positive price responses than is
the case with negative forecast errors.

The 2x2 contingency tables for this test are presented

in Tables 28-31. If the exact probability is less than

a, then HO could be rejected and it could be concluded

that there was an association between the direction of

forecast error and the direction of price response. How-

ever, in no case was the exact probability less than a.

The conclusion of this test is that there is no
significant tendency for the sign of the price response to
follow the sign of the management forecast error. However,
neither is there a tendency for the sign of the price
response to follow the sign of the forecast error for any

of the naive models.

129

TABLE 28
MANAGEMENT vs. NAIVE 1

(PURE RANDOM WALK)

 

 

 

 

 

 

 

ERRORS
MGT- MGT+
N1+ N1-
PR > 0 10 4 14
PR < O 11 3 14
21 7 28
Fisher exacted probability = .S
a = .05
TABLE 2 9

MANAGEMENT vs. NAIVE 2
(RANDOM WALK WITH DRIFT)

 

 

 

 

 

 

 

 

 

ERRORS
MGT- MGT+
N2+ N2-
PR > 0 7 7 14
PR < 0 6 7 13
13 14 27
Fisher exacted probability = .5735

.05

a

130

TABLE 30
MANAGEMENT vs. NAIVE 3

(MOVING AVERAGE OF A PURE MEAN REVERTING PROCESS)

 

 

 

 

 

 

 

 

ERRORS
MGT- MGT+
N3+ N3-
PR > 0 14 4 18
PR < 0 . 16 5 21
30 9 39
Fisher exacted probability = .6107
a = .05
TABLE 31

MANAGEMENT vs. NAIVE 4

(PURE MEAN REVERSION - NO DRIFT)

 

 

 

 

 

 

 

 

ERRORS
MGT- MGT+
N4+ N4-
PR > O ‘16 3 19
PR < 0 21 7 28
37 10 47
Fisher exacted probability = .3497

a = .05

131

The above test does give an indication of whether
the price responses are more closely associated with
management forecast errors than with errors of the naive
models. However, in some cases the management forecast
and a naive forecast might be on opposite sides of actual
earnings but the difference between them might be very
small. ‘Therefore the results might be expected to be
similar for the two forecasts. In order to avoid this
problem another test was utilized. Cases were found where
differences between management forecast errors and naive
forecast errors were large. Then, for these cases, both
the management forecast errors and the naive forecast
errors were correlated with the price responses. The
correlation technique used was the Spearman rank correla-
tion coefficient previously described. If there were a
price response to management earnings forecasts, the
association between such forecasts and the price responses
should be greater than for the naive models.

The results of this test are presented in Table 32. The
results are inconsistent. When errors are measured relative
to actual earnings in all cases the management forecast errors
are more closely associated with price responses than forecast
errors of the naive models. However, the differences between
the correlation coefficients for management and the first two
naive models are not large. When errors are measured relative
to the forecasts, management forecast errors are more closely

associated with price responses in only two of the four comparisons.

132

TABLE32
SPEARMAN RANK-ORDER CORRELATION COEFFICIENTS
FORECASTS WITH PRICE RESPONSES
41 LARGEST DIFFERENCES BETWEEN
MANAGEMENT FORECASTS AND

NAIVE FORECASTS

(A-F)/A (A-F)/F (A-F)/P
Management .2490 .3212 .4235
Naive 1 .2402 .3441 .4476
Management .1916 .3769 .3995
Naive 2 .1709 .3251 .5850
Management .0096 .3623 .3791
Naive 3 .0463 .3698 .4549
Management .1307 .3520 .4014
Naive 4 .0904 .3229 .4443

133

If errors are measured relative to price in no case are
management errors more closely related to price responses
than those of the naive models. These results certainly
cannot be construed as strong support for a C856 of
price response specifically related to management earn-
ings forecasts.

Since the results were still inconsistent it was
felt that perhaps some unrecognized bias in the statis-
tics was obscuring the relationships. The solution
adopted was to utilize a nonstatistical approach similar
to that used by Niederhoffer and Regan.9 This involved
the preparation of a matrix which has sometimes been
termed a confusions matrix.‘ This simply involves indi-
cating in how many cases the largest errors are asso-
ciated with the largest price responses, middle price
responses, and low price responses. The same procedure
would then be followed for medium and small forecast errors.

The results of this analysis are presented in Tables
33 through 47. Again there seems to be some small rela-
tionship between the size of the error and the size of
the price response. However, again there seems to be
little difference between management forecast errors and

forecast errors of the naive models.

Error

TOp 1/3
Middle 1/3

Low 1/3

Error

Top 1/3
Middle 1/3

Low 1/3

134

TABLE 33

CONFUSIONS MATRIX

MANAGEMENT

(A-FHA

Price Response

 

 

 

 

 

 

 

 

 

 

 

 

 

Top 1/3 Middle 1/3 Low 1/3
17 10 14
15 18 8
9 13 19
TABLE 34
CONFUSIONS MATRIX
NAIVE 1
(A-FJ/A
Price Response
Top 1/3 Middle 1/3 Low 1/3
19 9 13 14‘
11 20 10_ *d
11 12 18 !
-mJ

 

 

 

 

 

135

TABLE 35
CONFUSIONS MATRIX
NAIVE 2
(A-F)/A

Price Response

 

 

 

 

 

 

 

 

 

 

 

 

Error
Top 1/3 Middle 1/3 Low 1/3
TOp 1/3 18 ll 12
Middle 1/3 14 17 10
Low 1/3 9 13 19
TABLE 36
CONFUSIONS MATRIX
NAIVE 3
(A-F)/A
Price Response
Error
Top 1/3 Middle 1/3 Low 1/3
Top 1/3 17 ‘ ll 13
Middle 1/3 14 16 ll

 

Low 1/3 10 14 17

 

 

 

 

 

136

TABLE 37
CONFUSIONS MATRIX
NAIVE 4
(A-F)/A

Price Response

 

 

 

 

 

 

 

 

 

 

 

 

Error
Top 1/3 Middle 1/3 Low 1/3
Top 1/3 15 12 14
Middle 1/3 15 15 11
Low 1/3 11 l4 16
TABLE 38
CONFUSIONS MATRIX
MANAGEMENT
(A-FJ/F
Price Response
Error
Top 1/3 Middle 1/3 Low 1/3
TOp 1/3 18 10 12
Middle 1/3 16 17 8

 

Low 1/3 '7 13 21

 

 

 

 

 

Error

Top 1/3
Middle 1/3
Low 1/3

Error

Top 1/3
Middle 1/3
Low 1/3

137

TABLE 39

CONFUSIONS MATRIX

NAIVE 1

(A-F1/F

Price Response

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TOp 1/3 Middle 1/3 Low 1/3
19 10 12
12 19 10
10 12 19
1-
TABLE 40
CONFUSIONS MATRIX
NAIVE 2
(A-F)/F
Price Response
Top l/3 Middle 1/3 Low 1/3
19 12 10
12 17 12
10 12 19

 

 

 

138

TABLE 41
CONFUSIONS MATRIX

 

 

 

 

 

 

 

 

 

 

 

 

NAIVE 3
(A-F1/F
Price Response
Error
Top 1/3 Middle 1/3 Low 1/3
Top 1/3 13 ll 12
Middle 1/3 4 16 11
Low 1/3 9 14 18
TABLE 42
CONFUSIONS MATRIX
NAIVE 4
(A-F1/F
Price Response
Error
TOp 1/3 Middle 1/3 Low 1/3
TOp 1/3 * 17 12 12
Middle 1/3 13 16 12

 

Low 1/3 11 13 17

 

 

 

 

 

139

TABLE 43
CONFUSIONS MATRIX

MANAGEMENT
(A-FJ/P

Price Response

 

 

 

 

 

 

 

 

 

 

 

 

Error
Top 1/3 Middle 1/3 Low 1/3
Top 1/3 18 12 11
Middle 1/3 l6 l6 9
Low 1/3 7 13 21
TABLE 44
CONFUSIONS MATRIX
NAIVE 1
(A-FJ/P
Price Response
Error
Top 1/3 Middle 1/3 Low 1/3
TOp 1/3 19 13 9
Middle 1/3 12 16 13

 

 

 

 

Low 1/3 10 12 19

 

 

140

TABLE 45

CONFUSIONS MATRIX

 

 

 

 

 

 

 

 

 

 

 

 

NAIVE 2
(A-F)/P
Price Response
Error
Top 1/3 Middle 1/3 Low 1/3
TOp 1/3 18 13 10
Middle 1/3 l4 16 11
Low 1/3 9 12 20
TABLE 46
CONFUSIONS MATRIX
NAIVE 3
(A'F)/P
Price Response
Error
Top 1/3 Middle 1/3 Low 1/3
Top 1/3 19 12 10
Middle 1/3 13 15 13

 

Low 1/3 9 14 18

 

 

 

 

 

Error

TOp 1/3
Middle 1/3
Low 1/3

141

TABLE ”7
CONFUSIONS MATRIX

NAIVE 4
(A-F)/P

Price Response

 

 

 

 

 

Top 1/3 Middle 1/3 Low 1/3
17 14 10
13 14 14
11 13 17

 

 

 

 

142

Summary

This chapter was concerned with the presentation of
hypotheses and the analysis of test results concerned
with the stock price reaction to management earnings fore-
casts. As was indicated in Chapter III this required
the comparison of price reactions to management earnings
forecasts to the price reactions to forecasts generated
by several naive models.

The first indication of the relationship between
forecasts of earnings per share and price responses was
given by scatter plots of the price responses against the
forecast errors. It appeared from a visual analysis that
there was little if any relationship between the direction
and size of the forecast errors and the direction and size
of the price responses.

These visual analyses were then extended by the use
of statistical hypotheses testing.- It was confirmed
using a chi-square test for 2x2 contingency tables that
there was no tendency for the direction of the price re-
sponse to follow the direction of the forecast error for
any of the forecast errors.

Rank order correlations were then computed relating
the size oftfluaprice response to the size of the forecast
error. Positive but low correlations were found to exist
between forecast errors and price responses. However, only
when errors were computed relative to stock prices were
management forecast errors more closely related to price

responses than errors of the naive model forecasts.

143

Since it was not clear that the price responses were
more closely related to management forecast errors than
to naive forecast errors additional tests were conducted
to examine this question. It was found using the Fisher
test that when management forecasts and naive forecasts
were on opposite sides of actual earnings there was no
tendency for the direction of the price responses to
follow either type of forecast. Further,when there were
large differences between management forecasts and naive
forecasts there was not a consistent tendency for manage-
ment forecasts to be more highly correlated with price
responses than naive model forecasts.

Since the results were not consistent it was thought
that perhaps some unrecognized bias existed in the statis—
tical tests. Therefore a non-statistical matrix analysis
was performed. This analysis indicated that there did
seem to be a weak association between the size of the
forecast error and the size of the price response. How-
ever, there was no clear evidence that price responses
were more closely associated with management forecast

errors than with naive model forecast errors.

 

144

FOOTNOTES
CHAPTER V

1Ray Ball and Ph1111p Brown, "An Empricial Evaluation
of Accounting Income Numbers," Journal pf Accountipg
Research, Autumn, 1968, 1, p. l

 

2William H. Beaver and Roland E. Dukes, "InterperiOd
Tax Allocation, Earnings Expectations, and the Behavior
or Security Prices," The Account1ng_Review, April, 1972, t
XLVII, p. 324.

 

3Ball and Brown, p. 168. Beaver and Dukes, and Ball E
and Brown obtained Similar results using both continuous
compounding and discrete compounding.

 

4Sidney Siegel, Nonparametric Statistics for the
BehaVIoral Sc1ences, (NewTYOrR? IMCGraw:H111 Boox Company,
Inc., 1956) p. 107:

 

— SEugene F. Fama, Lawrence Fisher, Michael D. Jensen
and Richard Roll, "The Adjustment of Stock Prices to New
Information,” in Modern Developments in Investment manage-
ment, A Book of Readingg, (New York: Praeger Publishers,
1972), p. 192.

 

6Siegel, p. 204.

71bid., p. 110.

81bid., p. 97.

9Victor Niederhoffer and Patrick J. Regan, "Earnings
Changes, Analysts Forecasts, and Stock Prices," in Modern
Developments in Investment ManagementL_A Book or Reading;
(Nengork: Praeger PubliShers, l972), p. 607.

CHAPTER VI

SUMMARY, CONCLUSIONS, IMPLICATIONS, AND RECOMMENDATIONS

Summary

The question of the effects of publication of manage—
ment forecasts of earnings per share had recently become
of concern because of the actions of the Securities and
Exchange Commission. This body considered whether such
forecasts might be a useful addition to published finan-
cial statements. Its conclusion was that management
forecasts of earnings would be allowed as a part of
statements filed with the "Commission."

The process of considering the merits of publishing
forecasts of earnings raised a flurry of discussion in
the financial community. Many questions were raised, one
of the most prevalent being whether management forecasts
would, in fact, be useful to investors. Another question
which was brought forth was whether forecasts which were
in error would have an undesirable influence on investors.
Other questions were raised, but these two provided the
incentive for this research effort.

Since questions were directed toward the usefulness
of management forecasts to investors, it was important
to examine the theoretical basis for expecting such fore-

casts to be useful to investors. It was found that many

14S

146

security valuation models depend on expected earnings.
This coupled with research studies which found that
there indeed was a relationship between reported earnings
and stock prices reinforced the researcher's feeling that
there might be a relationship between management earnings
forecasts and stock prices.

The research studies which were reviewed indicated
that management does not always forecast accurately.
The lack of forecasting accuracy provided a means for
analyzing the influence of management earnings forecasts
on stock prices. If management earnings forecasts had
influenced investor expectations and reported earnings
were different from the earnings which had been forecast,
a reaction in the price of the stock would be expected.
Thus, the stock price reaction to forecast errors was used
as a measure of the usefulness of management forecasts
to investors. In order to be meaningful, the study went
beyond an analysis of stock price reactions to management
earnings forecasts. It was possible that similar results
could have been obtained using forecasts generated by
naive or mechanical models. Therefore the study included
an analysis of possible stock price reaction to several
naive models as well as to management earnings forecasts.

The use of stock price changes as a measure of use-
fulness of information to investors is strongly supported

by previous research efforts. These studies also indicated

 

147

_an operational basis for the measurement of price re-
sponses. They suggest the use of the market model as
an appropriate method Of measuring price changes. The
market model allows one to remove the influence of
general stock market conditions.

In the application of the general method the
problem of how best to measure forecast error had to be
confronted. Since forecast errors vary widely in terms
of absolute amount, it was considered desirable to com-
pute relative prediction errors. Several methods of
computing relative errors have been suggested. Errors
have been computed relative to: 1) actual earnings;

2) forecast earnings; and 3) stock prices. Each of
these error computations was found to have advantages
and disadvantages. Therefore for most of the tests con-
ducted in the study all three error measures were used.

The sample of firms used in this research effort was
selected from those publishing forecasts in IES.E§11
Street Journal. In total, 123 forecasts were Obtained
made by 90 firms. The years during which the forecasts
were published included the years 1965 through 1971.

The firms appeared to be widely representative of indus-
tries within the economy. In addition, the years from

which the forecasts were obtained appeared to represent
several different conditions with regard to general cor-

porate profitability. It was felt by the researcher

148

that the heterogeneity of the sample of firms and the
years from which they were obtained benefitted the

study by making it more general.

Conclusions

 

Forecast Errors. The basic question of the study

 

was not to examine forecast errors. However, the com- 3
putation of forecast errors in an attempt to relate fore-
casts to stock price changes made it possible to examine

the accuracy of such forecasts.

 

The chi-square one sample test was applied to
ascertain whether there was a tendency on the part of
management or the naive models to underpredict or over-
predict earnings per share. It was found when all of the
forecasts were used that there was no tendency for manage-
ment to either underpredict or overpredict earnings.

This was also the case with the Naive 2 (random walk with
drift) model. The remaining naive models tended to under-
predict earnings. This was not unexpected because these
models rely heavily on past earnings data.

The Wilcoxon Signed-Ranks Test was then applied to
determine the comparative accuracy of the forecasts.

This test confirmed, using all methods of computing errors,
that management forecasts were more accurate than those
generated by the naive models. However, there was not
confirmation on a statistical basis that the random walk

naive models were in all cases more accurate than the

149

mean reverting models. It was found on a nonstatistical
basis that the random walk naive models had a greater
number of accurate forecasts than did the mean reverting
naive models. When the two mean reverting models were
analyzed statistically it was found that the moving
average of a pure mean reverting process model was more
accurate than the pure mean reverting model. 1.
Forecast Errors Related to Stock Price Changes. The
first tests of the association between forecast errors

and stock prices dealt with the question of whether the

 

direction of the price response was associated with the
direction of the forecast error. The chi-square test

for two by two contingency tables was utilized to examine
this question. As a result of this test it was concluded
that there was no significant association between the
sign of the forecast error and the sign of the price re-
sponse for either management forecasts or forecasts
generated by the naive models.

In order to find whether there was an association
between the direction of management forecast errors and
the direction of the stock price response which was not
present for the naive models the above analysis was ex-
tended. Cases were found where the management forecast
and a naive forecast for the same firm were on Opposite
sides of actual earnings. The test was used to see if

in these situations the sign of the price response tended

150

to follow the sign of management forecast error rather
than the sign of the naive model forecast error. The
technique utilized to examine this question was the
Fisher Exact Probability Test. It was found that in
cases where management forecasts and naive forecasts
were on Opposite sides of actual earnings there was no
tendency for the sign of the price response to follow
the sign of the management forecast error. However,

neither was there a tendency for the sign of price response

 

to follow the sign of the naive model forecast error.

The analysis was then expanded to include not only
the direction of the forecast error and the direction of
the price response but to include their magnitudes as
well. The approach taken was to Obtain rank order cor-
relations between forecast errors and price responses.

It was found that there were low but positive correla-
tions between the size of the forecast errors and the
size of the price responses. This was true for all fore-
cast models and all measures of forecast error. Examina-
tion of the correlations revealed that when errors were
computed relative to stock prices management forecasting
errors were more closely associated with the price re-
sponses than were forecast errors obtained from any of
the naive models, although differences between the models
were small. However, when errors were computed relative
to actual earnings and to forecast earnings, the

management forecast errors were not the errors most

151

closely associated with the price responses.

Since the correlations did not conclusively answer
the question of whether there was a greater association
between management forecast errors and price responses
than existed for the naive models, additional tests
were conducted. Cases were found where there were large
differences between management forecast errors and naive
model forecast errors. Then both the management fore-
cast errors and the naive model forecast errors were
correlated with the price responses. The question was
whether there was a greater correlation between manage-
ment forecast errors and the price responses than there
was between the naive model forecast errors and the price
responses. It was found that when errors were computed
relative to actual earnings management forecast errors
were more closely associated with price responses than
any of the naive model errors. However, the differences
in the associations were small. When errors were computed
relative to forecasts, management forecast errors were more
closely associated with price responses in only two of the
four comparisons with the naive models. When errors were
computed relative to price in no case were management
forecast errors more closely associated with the price
responses than were the naive model forecast errors. The
results were again inconclusive. For some methods of
computing forecast errors and in comparison with some of

the naive model forecasts, management forecasts appeared

 

152

to be more closely associated with price responses than
did the naive model forecasts.

In an attempt to remove tne ambiguity in the interpre-
tation of these test results a final approach was utilized.
This involved a nonstatistical matrix analysis. Matrices
were prepared to examine whether high forecast errors
seemed to be associated with high price responses, medium I
errors with medium price responses, and low errors with
low price responses. The analysis of this matrix data,

although nonstatistical, seemed to confirm that there was i

 

an association between the size of the forecast error and
the size of the price responses. However this pattern

was not unique to management forecast errors.

Limitations of the Study

 

Before examining the implications of the conclusions
obtained from the study the limitations of the study
should be reemphasized. The first limiting factor is
that the management forecasts which were utilized in the
study were not actually a part of published financial
reports. It is possible then that forecasts published
in financial reports could differ from those used in the
present study. However, since the forecasts used were

published in The Wall Street Journal which allowed consider-

 

able exposure to the investing public this may nOt be a

serious limitation.

153

Another limitation of the study is that the subject
firms do not represent a random sample of New York Stock
Exchange firms. Thus, the results of the study cannot
be statistically generalized beyond the firms included
in the study.

It will be recalled that several selection criteria
were applied in the process of gathering the management
forecasts. Not the least significant of these selection
criteria was that the firm must have published a forecast
of earnings per share. This might lead to a bias in the
study because firms not publishing usable forecasts may
be different from those that published usable forecasts.
As an example, a firm might not have published a fore-
cast because it felt unable to generate an accurate fore-
cast.

Another selection criterBNTwas that forecasts were
taken from the January-April editions of The Wall Street
lgnxnal, This meant that most of the firms in the sample
had years ending on December 31. However, it was possible
for a firm having a year ending in September, October,
or November to be included in the sample. The results
of the study could then be peculiar to the period from
which forecasts were selected. However, in view of the
variety of firms selected and of the economic conditions
existing during the selection period this again may not

be a serious limitation.

 

154

Implications

 

The results of the study definitely indicate that
management forecasts are more accurate than forecasts
generated by the naive models used in the study. These
results while significant must be viewed with a certain
amount of caution. Perhaps if alternative naive models
had been used one or more of these models would have
generated forecasts more accurate than those made by

management.

 

Given that management forecasts appeared to be more P;
accurate than forecasts made by the naive models, it is
somewhat surprising that a stronger relation was not
found to exist between management forecasts and stock
prices. It was true that in some cases a stronger rela-
tionship existed between management forecasts and stock
prices than existed between naive model forecasts and
stock prices. However, no pattern of consistent super-
iority was found in the associations between management
forecasts and stock prices. If such superiority had
existed, it could have been concluded that there was a
stock price reaction to management forecasts. However,
in the absence of such clear superiority of management
fdrecasts over naive model forecasts such a conclusion
does not seem warrented.

The results of the study do not then clearly indi-
cate that management forecasts of earnings per share

have informational content.

155

'This finding may have been the result Of manage-
ment forecasts not being sufficiently more accurate than
the naive model forecasts. An alternative explanation
might be that investors make use of other methods in
forming expectations of future earnings per share. This
might explain why low correlations existed between all

of the forecast errors and stock prices.

Recommendations

 

The results of the study seem to point to areas for
future research. As a first step some of the limitations
of the present study could be removed or at least reduced.
Since management forecasts.are now allowed to be a part
of Securities and Exchange Commission reports it may be-
come possible to Obtain a larger sample of management
forecasts. This would allow another limitation to be
eliminated in that forecasts taken from such reports
would have actually been a part of published financial
reports.

It might also be possible to expand the number of
management forecasts available by expanding the portion
of the year from which management forecasts are taken.
This would have the additional advantage of eliminating
any bias which might have existed as a result of the
forecasts being taken from the first four months of the
calendar year. In addition, it might be possible to
use forecasts made by firms listed on other than the New

York Stock Exchange.

156

Another area of research activity could be to
increase the number of naive models used in comparison
to management forecasts. In this same vein perhaps
analysts' forecasts could be included to make further
research more comprehensive.

The first chapter indicated that a number of ques- I
tions had been raised concerning the possible publica- -
tion of management forecasts as a part of a firm's

financial statements. Many of these questions could be

 

developed into researchable areas. For example, does the £~
publication of management earnings forecasts lead to
manipulations of the actual reported earnings to bring
such earnings in line with the forecast?
The area of management forecasting appears to offer
many possibilities for future research efforts. Since
vthis is an area in which the accounting profession might
better serve the investment community, it is hoped that

such research efforts will be pursued.

APPENDIX A

SAMPLE FIRMS

 

 

Indus-
Mfg or try

Company Name Non Mfg, Code Industry,

Airco,Inc. Mfg 281 Industrial Inorgan-
ic and Organic
Chemicals

Allegheny Power System, Inc. Non Mfg 491 Electric Companies
and Systems

Allied Chemical Corp. Mfg 281 Industrial Inorgan-
ic and Organic ;
Chemicals QB

V

Alpha Portland Industries, Inc. Mfg 324 Cement, Hydraulic

Amlac Industries, Inc. Mfg 361 Electrical Equip-
ment and Machinery

American Can Co. Mfg 341 Metal Cans

American Electric Power CO., Inc. Non Mfg 491 Electric Companies
and Systems

American Export Industries, Inc. Non Mfg 441 Deep Sea Transporta-
tion

American Telephone 8 Telegraph Co. Non Mfg 481 Telephone Communica-
tion

Ametek, Inc. Mfg 381 Engineering and
Scientific Instru-
ments

Arizona Public Service Co. Non Mfg 491 Electric Companies
and Systems

Armco Steel Corp. Mfg 331 Blast Furnaces,
Steel Works, and
Rolling and Finishing
Mills

Arvin Industries, Inc. Mfg 371 Motor Vehicles and
Motor Vehicle Equip-
ment

Avco Corp. Mfg 372 Aircraft and Parts

157

158

 

 

Indus-
Mfg or try

Company_Name Non Mfg Code Industry

Bachck 5 Wilcox Co. Mfg 349 Miscellaneous Fabri-
cated Metal Products

Bangor Panter Corp. Mfg 221 Textile Mill Products

Belco Petroleum Corp. Non Mfg 131 Crude Petroleum and
Natural Gas

Bliss G Laughlin, Inc. Mfg 331 Blast Furnaces, Steel
Works, and Rolling
and Finishing Mills

C.I.T. Financial Non Mfg 614 Personal Credit
Institutions

Central Hudson Gas 6 Electric Non Mfg 491 Electrical Companies
and Systems

Central Illinois Light CO. Non Mfg 493 Combination Companies
and Systems-Electric
and Gas

Central 6 Southwest Corp. Non Mfg 491 Electrical Companies
and Systems

Cessna Aircraft CO. Mfg 372 Aircraft and Parts

Chesapeake Corp. (Va.) Mfg 262 Paper and Allied
Products

Chicago Pneumatic Tool CO. Mfg 354 Metalworking Machinery
and Equipment

Commonwealth Edison Co. Non Mfg 491 Electric Companies
and Systems

Continental Can Go. Mfg 341 Metal Cans

Continental Steel Corp. Mfg 331 Blast Furnaces, Steel
Works, and Rolling and
Finishing Mills

Copper Range Co. Mfg 333 Smelting and Refining
of Nonferrous Metals

Crompton & Knowles Corp. Mfg 355 Special Industry

Machinery

 

 

159
Indus-
Mfg or try

Company Name Non Mfg Code Industry

Crown Cork 6 Seal Co., Inc. Mfg 341 Metal Cans

Cummins Engine Co., Inc. Mfg 351 Engine and Turbines

Curtiss Wright Corp. Mfg 372 Aircraft and Parts

Detroit Edison Non Mfg 491 Electric Companies lg
and Systems

Dr. Pepper CO. Mfg 209 Non-alcoholic Bev-
erages and Carbonated
Waters

Dow Chemical CO. Mfg 281 Industrial Inorganic if
and Organic Chemicals

Duke Power Co. Non Mfg 491 Electric Companies
and Systems

Eaton Corporation Mfg 371 Motor Vehicles and
Motor Vehicle Equip-
ment

Evans Products Co. Mfg 241 Lumber and Wood
Products, except
Furniture

Ex-Cell-O Corp. Mfg 354 Metalworking Machinery
and Equipment

Far West Financial Corp. Non Mfg 612 Savings and Loan
Associations

Federal Mogul, Inc. Mfg 356 General Industrial
Machinery and
Equipment

Federal Paper Board Mfg 262 Paper and Allied
Products

Ferro Corp. Mfg 285 Paints, Varnishes,
Lacquers, Enamels
and Allied Products

Flintkote CO. Mfg 326 Miscellaneous Non-

metallic Mineral
Products

 

160
Indus-
Mfg or try
Company Name Non Mfg Code Industry
FMC Corp. Mfg 281 Industrial Inorganic
and Organic Chemicals
Foster Wheeler Corp. Mfg 355 Special Industrial
Machinery
General Public Utilities Non Mfg 591 Electric Companies I;
and Systems F-
General Steel Industries, Inc. Mfg 331 Blast Furnaces, Steel ‘
Works, and Rolling
and Finishing Mills
General Tire 8 Rubber CO. Mfg 301 Tires and Inner Tubes ;;
Gulf Oil Corp. Mfg 291 Petroleum Refining
Gulf States Utilities Co. Non Mfg 491 Electric Companies
and Systems
High Voltage Engineering Corp. Mfg 366 Communication Equip-
ment, Electronic
Components, and
Accessories
Household Finance Non Mfg 614 Personal Credit
Institutions
Iowa Power 8 Light CO. Non Mfg 493 Combination Companies
and Systems-Electric
and Gas
Johns Manville Corp. Mfg 326 Miscellaneous Non-
metallic Mineral
Products
Jonathan Logan, Inc. Mfg 231 Miscellaneous Fabri-
cated Textile Products
Earl M. Jorgensen CO. Non Mfg 509 Miscellaneous
Wholesalers
Joy Manufacturing Co. Mfg 352 Farm Machinery,

 

Construction, Mining
and Materials Handling
Machinery and
Equipment

161

 

 

Indus-
Mfg or try

Company Name Non Mfg, Code Industry

Libby Owens Ford CO. Mfg 321 Blast Furnaces,
Steel Works, and
Rolling and Finishing
Mills

McNeil Corp. Mfg 355 Special Industrial
Machinery

Medusa Portland Cement Mfg 324 Cement, Hydraulic

Montana Dakota Utilities Co. Non Mfg 493 Combination Companies
and Systems-Electric
and Gas

Mountain Fuel Supply Co. Non Mfg 492 Gas Companies and
Systems

NVF Co. Mfg 306 Miscellaneous Rubber
and Plastic Products

National Distillers 6 Chemical Corp.Mfg 208 Alcoholic and Malt
Beverages

National Fuel Gas Co. Non Mfg 492 Gas Companies and
Systems

Occidental Petroleum Corp. Non Mfg 509 Miscellaneous
Wholesalers

Overnight Transportation Co. Non Mfg 421 Trucking, Local and
Long Distance

Pacific Lighting Non Mfg 492 Gas Companies

' and Systems

Pepsico, Inc. Mfg 209 Non-alcoholic
Beverages and
Carbonated Waters

Public Service Co. of Indiana, Inc. Non Mfg 491 Electric Companies
and Systems

Reichhold Chemicals Mfg 281 Industrial Inorganic
and Organic Chemicals

Reliance Electric Co. Mfg 361 Electrical Equipment

and Machinery

162

 

Indus-
Mfg or try

Company Name Non Mfg_ Code Industryp

Royal Crown Cola Mfg 209 Non-alcoholic
Beverages and
Carbonated Waters

Scott Paper Mfg 262 Paper and Allied
Products

Scovill Mfg Co. Mfg 333 Smelting and Refining
of Nonferrous Metals

Simmons Co. Mfg 251 Furniture and Fixtures

Stauffer Chemical Co. Mfg 281 Industrial Inorganic
and Organic Chemicals

Sun Chemical Corp. Mfg 285 Paints, Varnishes,
Lacquers, Enamels and
Allied Products

Sundstrand Corp. Mfg 356 General Industrial
Machinery and
Equipment

Toledo Edison Non Mfg 491 Electric Companies
and Systems

UAL Inc. Non Mfg 451 Air Transportation

United States Gypsum Mfg 326 Miscellaneous Non-
metalic Mineral
Products

U.S. Industries, Inc. Mfg 354 Metalworking Machines
and Equipment

Uniroyal Corp. Mfg 301 Tires and Inner Tubes

Vulcan Materials CO. Mfg 326 Miscellaneous Non-
metalic Mineral
Products

Washington Water Power Co. Non Mfg 491 Electric Companies

and Systems

 

 

163
Indus-
Mfg or try

Company Name Non Mfg Code Industpy
‘Weyerhauser CO. Mfg 241 Lumber and Wood

Products, except

Furniture
White Motor Mfg 371 Motor Vehicles and

Motor Vehicle

Equipment __

*The information included in these columns was taken from Securities
and Exchange Commission, Directory of Companies Filing Annual Reports
With the Securities and Exchange Commission. 1967 (WEShington, D.C.,
UTS. Government Printing Office, 19677}

 

APPENDIX B

AN EXAMPLE OF THE COMPUTATION OF THE PRICE
RESPONSE, ASSUMING DISCRETE COMPOUNDING

The starting point in obtaining the compound price
response was to obtain monthly rates of return for indi-
vidual securities. This was accomplished through the
application of the market model. What was desired, how-
ever, was the price response which occurred over a test
period. To accomplish this end the monthly rates of
return were compounded over the test period for each
security. Assuming discrete compounding, the compounding

formula would be as follows:

M
1

PRM m: (1 + Cim)

Where:

3
n

month 1,2,...T

(3
ll

im the rate of return of firm (i), for month (m).

For purposes of illustration the following monthly

rates of return were assumed for six companies.

164

 

165

Abnormal Rates of Return

Monthly Abnormal Rates of Return
(Cim) for Company

 

 

 

 

Month
_1__ 2 3 _6. __7_
1 -.01 +.01 +.02 -.06 -.O6
2 +.03 +.03 -.01 -.oz -.05
3 +.06 _.O4 +.O3 -.01 -.06
4 +.oo +.01 +.02 -.01 -.05
s +.oz +.02 +.Oz ~.02 -.01
6 +.os +.os +.01 -.03 -.oz
7 - 01 + 02 +.01 - 04 oo
8 +.O3 +.oo +.01 -.03 .01
9 +.02 -.01 ' +.oz +.01 -.02
10 +.OI .+.oo +.03 +.oo +.O3
11 +.01 +.01 +.oo +.02 -.01
12 +.03 .04 +.04 -.O3 -.04

 

Then the monthly rates of return were compounded using
a process of consecutive multiplication. Companies one

and six illustrate the computations.

Calculation of the Compound Price Response of a Company

 

112121 1 6

1 1-.01 = .99 1-.06 = .94

2 .99(1+.03) = 1.0197 .94(1-.02) = .9212
3 1.0197(1+.06) = 1.0808 .9212(1-.01) = .9119

166

The following table presents the results of the discrete

compounding process.

Month

U'chbl

‘OQVO‘

10
11
12

Compound Price Response for Company

 

_1__.

.9900

....-

.0197
.0808
.0808
.1024
.1575
.1459
.1803
.2039

HHHHHHHI—a

.2159
1.2281
1.2649

___?___

.0100
.0403
.0819
.0927
.1146
.1703
.1937

HHHHHHI—IH

.1937
1.1817
1.1817
1.1936
1.2414

__.3___

1.0200
1.0098
1.0401
1.0609
1.0821
1.0929
1.1039
1.1149
1.1372
1.1713
1.1713
1.2182

6
.9400
.9212
.9199
.9107
.8925
.8657
.8311
.8062
.8142
.8142
.8305
.8056

.9400
.8930
.8394
.7975
.7895
.7737
.7737
.7817
.7658
.7428
.7354
.7060

 

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3130