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ALTERNATIVE ECONOMETRIC MODELS
FOR DETECTING THE EFFECTS OF
ACCOUNTING POLICY DECISIONS

By
Joel Edward Thompson

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Accounting

1982

ABSTRACT

ALTERNATIVE ECONOMETRIC MODELS
FOR DETECTING THE EFFECTS OF
ACCOUNTING POLICY DECISIONS

By
Joel Edward Thompson

The primary purpose of this study is to compare
the power of three models in detecting the effects of
accounting policy decisions on individual firm common
stock returns. The three models are the market model,
the valuation model, and the zero model.

The problem inherent in models which contain a stock
market index is that the stock market index may be affected
by an accounting policy decision. Hence, the market
model is examined when the market index is affected by
an accounting policy decision as well as when the market
index is not affected by an accounting policy decision.

The power comparisons in this study are based on a
simulation procedure similar to that used by Brown and
Warner (1980). The simulation procedure is performed by
adding an artificial accounting policy decision effect to
actual firm stock returns for a randomly selected set of

months. Abnormal firm returns are examined statistically

to determine which model can best detect the presence of
the artificial effect.

For market index effects (the relative size of the
accounting policy decision effect on the market index
compared to the accounting policy decision effect on a
firm) as large as 50%, the valuation model and zero model
are more powerful than the market model in right-hand
tail tests. Further, they are more powerful than the
market model with a 50% index effect for larger accounting
policy decision effects in left-hand tail tests and in
two tail tests.

For hypothetical average firms with estimated betas
greater than or equal to one and after adjusting for
levels of significance, the valuation model becomes more
powerful than the market model when the index effect reaches
a level of about 4% in right-hand tail tests and 12% in
left-hand tail tests. For the zero model the comparable
percentages are 7% in a right-hand tail test and 5% in
a left-hand tail test.

One method of adjusting levels of significance is
described and the problem of using the market model for

a representative sample of firms is discussed.

To Barbara

ii

ACKNOWLEDGMENTS

Special thanks to Ken Janson, Ron Marshall, and
Peter Schmidt for their numerous useful suggestions.
Also thanks to Deloitte, Haskins, and Sells for financial

support.

iii

TABLE OF CONTENTS

LIST OF TABLES
INTRODUCTION
LITERATURE REVIEW
THE MODELS
A. The Market Model
B. The Zero Model
0. The Valuation Model
PROCEDURES
A. Individual Firm Tests
B. Adjusting Levels of Significance

0. Market Index Effects
D. Sample of Firms Tests

A. Power Comparisons

B. Levels of Significance

0. Market Index Effects

D. Testing Samples of Firms
SUMMARY AND CONCLUSIONS
APPENDIX A-PROOFS
APPENDIX B-OTHER ECONOMETRIC MODELS

A. Sets of Variables
B. Procedures and Results

BIBLIOGRAPHY

iv

Page

_L...\._s
\OCXJQ

24
28
30
32

35
97
102
106
113

119

128
138

148

Table

4.

10.

11.

LIST OF TABLES

Number of rejections of null hypothesis March,
1976, in right-hand tail tests for 457 firms
with a=.025.

Number of rejections of null hypothesis March,
1976, in left-hand tail tests for 457 firms
with a=.025.

Number of rejections of null hypothesis March,
1976, in two tail tests, positive effects,
for 457 firms with a=.05.

Number of rejections of null hypothesis March,
1976, in two tail tests, negative effects,
for 457 firms with a=.05.

Number of rejections of null hypothesis April,
1976, in right-hand tail tests for 457 firms
with a=.025.

Number of rejections of null hypothesis April,
1976, in left-hand tail tests for 457 firms
with a=.025.

Number of rejections of null hypothesis April,
1976, in two tail tests, positive effects,
for 457 firms with a=.05.

Number of rejections of null hypothesis April,
1976, in two tail tests, negative effects,
for 457 firms with a=.05.

Number of rejections of null hypothesis May,
1976, in right-hand tail tests for 457 firms
with a=.025.

Number of rejections of null hypothesis May,
1976, in left-hand tail tests for 457 firms
with d=.025.

Number of rejections of null hypothesis May,
1976, in two tail tests, positive effects,
for 457 firms with d=.05.

V

Page

36

37

38

39

4O

41

42

43

44

45

46

Table Page

12. Number of rejections of null hypothesis May,
1976, in two tail tests, negative effects,
for 457 firms with a=.05. 47

13. Number of rejections of null hypothesis June,
1976, in right-hand tail tests for 457 firms
with a=.025. 48

14. Number of rejections of null hypothesis June,
1976, in left-hand tail tests for 457 firms
with a=.025. 49

15. Number of rejections of null hypothesis June,
1976, in two tail tests, positive effects,
for 457 firms with a=.05. , 50

16. Number of rejections of null hypothesis June,
1976, in two tail tests, negative effects,
for 457 firms with a=.05. 51

17. Number of rejections of null hypothesis July,
1976, in right-hand tail tests for 457 firms
with a=.025. ' 52

18. Number of rejections of null hypothesis July,
1976, in left-hand tail tests for 457 firms
With OL=.O25. 53

19. Number of rejections of null hypothesis July,
1976, in two tail tests, positive effects,
for 457 firms with a=.05. 54

20. Number of rejections of null hypothesis July,
1976, in two tail tests, negative effects,
for 457 firms with a=.05. 55

21. Number of rejections of null hypothesis August,
1976, in right-hand tail tests for 457 firms
with d=.025. 56

22. Number of rejections of null hypothesis August,
1976, in left-hand tail tests for 457 firms
with a=.025. 57

23. Number of rejections of null hypothesis August,
1976, in two tail tests, positive effects,
for 457 firms with a=.05. 58

24. Number of rejections of null hypothesis August,
1976, in two tail tests, negative effects,
for 457 firms with d=.05. 59

vi

Table Page

25. Difference in means statistics March, 1976,
for right-hand tail tests.. 60

26. Difference in means statistics March, 1976,
for left-hand tail tests. 61

27. Difference in means statistics March, 1976,
for two tail tests with positive effects. 62

28. Difference in means statistics March, 1976,
for two tail tests with negative effects. 63

29. Difference in means statistics April, 1976,
for right-hand tail tests. 64

30. Difference in means statistics April, 1976,
for left-hand tail tests. 65

31. Difference in means statistics April, 1976,
for two tail tests with positive effects. 66

32. Difference in means statistics April, 1976,
for two tail tests with negative effects. 67

33. Difference in means statistics May, 1976,
for right-hand tail tests. 68

34. Difference in means statistics May, 1976,
for left-hand tail tests. 69

35. Difference in means statistics May, 1976,
for two tail tests with positive effects. 70

36. Difference in means statistics May, 1976,
for two tail tests with negative effects. 71

37. Difference in means statistics June, 1976,
for right-hand tail tests. . 72

38. Difference in means statistics June, 1976,
for left-hand tail tests. 73

39. Difference in means statistics June, 1976,
for two tail tests with positive effects. 74

40. Difference in means statistics June, 1976,
for two tail tests with negative effects. 75

41. Difference in means statistics July, 1976,
for right-hand tail tests. 76

vii

Table Page

42. Difference in means statistics July, 1976,

for left-hand tail tests. 77
43. Difference in means statistics July, 1976,

for two tail tests with positive effects. 78
44. Difference in means statistics July, 1976,

for two tail tests with negative effects. 79
45. Difference in means statistics August, 1976,

for right-hand tail tests. 80
46. Difference in means statistics August, 1976,

for left-hand tail tests. 81
47. Difference in means statistics August, 1976,

for two tail tests with positive effects. 82
48. Difference in means statistics August, 1976,

for two tail tests with negative effects. 83
49. Right-hand tail power comparisons. 86
50. Left-hand tail power comparisons. 88
51. Two tail power comparisons--positive effects. 90
52. Two tail power comparisons--negative effects. 92
53. Observed vs. specified a levels. 99
54. Adjusted vs. specified a levels. 99
55. Average number of rejections--a levels not

adjusted. 101
56. Average number of rejections-~a levels adjusted. 101

57. Average standard errors and corresponding

critical values. 103

58. Market index effects--d levels not adjusted. 103

59. Average a adjustment factors over 6 months. 105

60. Average critical values-~a levels adjusted. 105

61. Market index effects--d levels adjusted. 105

62. Predictive ability, average of 20 firms. 108
viii

 

Table Page

63. Average and standard error of prediction errors. 108
64. (T-1) values. 110
65. (T-2) values. 110
66. F variables. 130
67. S variables. 130
68. T variables. 132
69. INT variables. 134
70. NBER variables. 135
71. TNBER variables. . 137

72. Predictive ability, average of 20 firms,
October, 1972 through March, 1973. 139

73. Predictive ability, average of 20 firms,
October, 1969 through March, 1970. 147

ix

INTRODUCTION

Accounting policy decisions are pronouncements by
organizations such as the Financial Accounting Standards
Board and the Securities and Exchange Commission concern-
ing the content of the financial statements of firms. Being
able to detect the effects of accounting policy decisions-
on common stock returns of firms provides objective evi-
dence on some of the consequences of accounting policy
decisions. Common stock returns are examined in this study
as in most accounting policy decision research (Foster,
1980. p. 30).

Evidence on the consequences of accounting policy
decisions on stock returns can help answer the following
questions: (1) did the accounting policy decision produce
any results which affected the investment behavior of common
stock investors; (2) how many firms' common stock prices
were affected by the accounting policy decision; (3) which
firms' common stock prices were affected by the accounting
policy decision; and (4) by how much were firms' common
stock prices changed because of the accounting policy
decision. Answers to these questions are the first steps
in determining why common stock prices were affected by
an accounting policy decision and whether or not the

1

2
accounting policy decision was beneficial to society.
Answers to all of these questions should provide useful
feedback to members of policy making organizations.

This dissertation is concerned with the first three
questions listed above. Thus, the primary purpose of this
study is to compare the power of three models in detecting
the effects of accounting policy decisions on individual
firm common stock returns. The three models are the market
model, a valuation model which is based upon the present
value of the expected cash dividends per share of common
stock, and the zero model which treats stock returns as
random error terms.

The power comparisons in this study are based on a
simulation procedure similar to that used by Brown and
Warner (1980). The simulation procedure is performed by
adding an artificial.accounting policy decision effect, DR,
to actual firm stock returns for a randomly selected
set of months. Thus, the simulated firm return equals DR
plus the actual firm return.

Next, individual firm returns are predicted by each
of the models. Abnormal firm returns, which are defined
as the simulated firm return minus the predicted firm
return, are examined to statistically determine which model
can best detect the presence of the artificial accounting
policy decision effect. In studies of actual accounting
policy decisions, abnormal firm returns are the actual

firm return minus the predicted firm return. Examples of

3
studies which analyze individual firm abnormal returns
are Hong, Kaplan, and Mandelker (1978), Lev (1979), and
Gheyara and Boatsman (1980).

The problem inherent in models which contain a stock
market index such as the market model is that the stock mar-
ket index may be affected by an accounting policy decision.
Thus, in examining abnormal.returns, part of the effect of
the accounting policy decision may be hidden by the effect on
the stock market index. In evaluating the research methodol-
ogy of Gheyara and Boatsman (1980), Watts and Zimmerman
(1980, p. 101) claim: "Since ASR 190 affected about 55% of
the firms listed on the NYSE, the market index contains a
portion of the average effect of ASR 190 and the measured
residual contains less than the total effect on each firm."
Moreover (p. 102): "At present, no one has overcome the
problem of using market model residuals...to effect a
completely satisfactory control."

A major objective of this study is to retain the entire
effect of an accounting policy decision in a firm's abnormal
return. Further, to determine the consequences of the impact
of an accounting policy decision on the stock market index,
the market model is examined when the market index is affect-
ed by DR as well as when the market index is not affected by
DR. The equally weighted market index is used in both forms
of the market model.

In the case of the market index being affected by an

accounting policy decision the entire accounting policy

4

decision effect may be removed from the abnormal return. As
an example, suppose that the accounting policy decision
effect on the return of firm i, DRi’ is equal to the average
accounting policy decision effect on the returns of those
firms comprising the market index, %.§1DR1. Also, suppose
that the estimate of the coefficientlof the market index in
the market model for firm i is one. DRi is in the return of
the firm while 1.%ig1DRi is in the predicted return of the
firm. Thus, in computing the firm return minus the predicted
firm return the entire accounting policy decision effect is
removed from the abnormal return. In this case, the account-
ing policy decision effect on firm i cannot be detected by
examining the abnormal return based on the market model for
firm i. Lemma 1 gives a more general statement concerning
the removal of the accounting policy decision effect from
the abnormal return. All proofs are contained in Appendix A.
Lemma 1. Let pi be the ratio of the average accounting
policy decision effect on the returns of those firms
comprising the market index to the non-zero accounting
policy decision effect on the return of firm i. Let bi
be the estimate of Bi, the coefficient of the market index
in the market model for firm i. Then bipi= 1 implies
that the abnormal return based on the market model for
firm i contains zero accounting policy decision effect.

In the simulations in this study, pi = .5 for all

i. This will sometimes be called a 50% index effect.

This level of pi was chosen since about 55% of the firms

5
listed on the New York Stock Exchange (NYSE) were affected

by Accounting Series Release (ASR) 190 (Watts and Zimmerman,
1980, p. 101). If each of the 55% of the firms was affected
by k% because of the accounting policy decision, then pi
would be .55 for all i.

The general findings of the simulations are the
following.

(1) The market model without an index effect tends
to be more powerful than the market model with a 50% index
effect in all tests while the market model without an
index effect tends to be more powerful than the valuation
model and the zero model in left-hand tail tests.

(2) The market model without an index effect is
statistically more powerful than the market model with a
50% index effect when the accounting policy decision effect
is as small as 1% for positive effects and as small as l-4%[
for negative effects.

(3) The valuation model is statistically more
powerful than the market model with a 50% index effect when
the accounting policy decision effect is as small as 0.5%
for positive effects and as small as l-5%I for negative
effects. However, there do exist instances in which the
market model with a 50% index effect is statistically more
powerful than the valuation model.

(4) The zero model is statistically more powerful
than the market model with a 50% index effect when the

accounting policy decision is as small as 4% for positive

6
effects and as small as [-10%] for negative effects.
However, there do exist instances in which the market model
with a 50% index effect is statistically more powerful
than the zero model.

(5) The valuation model tends to be statistically more
powerful than the zero model when detecting negative
effects. The two models tend to have about the same
power when detecting positive effects.

(6) The market model without an index effect, the
valuation model, and the zero model, are statistically more
powerful than the market model with a 50% effect for
sufficiently large effects in absolute value. This state-
ment is true for each of the six cases examined in this
study even though the levels of significance of the tests
which used the valuation and zero models tended to be
smaller than the levels of significance for the tests
which used the market.model with.a 50% index effect.

The results of this study also showed that for a
hypothetical average firm with bi = 1, the valuation model
becomes more powerful than the market model when the
market index effect reaches a level of about 19%. For
this same hypothetical firm, the zero model becomes more
powerful than the market.model when.the index effect reaches
a level of about 21%.‘ After adjustingfor levels of.
significance, the valuation model becomes more powerful
than the market model when the market index effect reaches

a level of about 4% in right-hand tail tests

7
and 12% in left—hand tail tests. For the zero model the

comparable percentages are 7% in a right-hand tail test
and 5% in a left-hand tail test.

The detection ability of the market model, the
valuation model, and the zero model were also considered
in tests of samples of firms in addition to the tests of
individual firms. Numerous other models were considered
in tests of samples of firms. While conclusions cannot be
drawn from these tests since the approximate true levels
of significance were not determined, these investigations
led to two statements which may not be fully appreciated in
the accounting literature. The first statement is the
following theorem.

Theorem 1. On average in a representative sample of firms

 

of the population, the market model, with an equally
weighted index based on the population, is unable to detect
the effects of an accounting policy decision.when the sta-
tistic of interest is the average abnormal return of the

sample.

The second statement is a corollary of Theorem 1 and con-.
cerns individual firm tests.

Corollary 1.1. In a representative sample of firms,
examination of abnormal returns in individual firm tests
based on the market model, with an equally weighted index
based on the population, is equivalent to trying to detect

a quanity which on average is zero in the sample of firms.

8

Thus, Theorem 1 and Corollary 1.1 describe circumstances
where the market model will not generally aid in the
detection of the effects of those accounting policy deci-
sions which affect firm stock returns in one direction.

This study explores the usefulness of the valuation
model and the zero model as alternatives to the market
model for detecting the effects of accounting policy
decisions on stock returns. The use of these models in
accounting research may help provide additional objective

evidence on the consequences of accounting policy decisions.

LITERATURE REVIEW

Studies which examine the possible effects of account-
ing policy decisions on common stock returns are given an
important place in the accounting literature. An entire
1980 issue of the Journal 9§_Accounting and Economics was
devoted to studies trying to detect.the effects of Account-
ing Series Release 190 on stock returns. Foster (1980, p.
29) states that there has been substantial research activity
of the effects of accounting policy decisions on stock
returns and claims that there were at least five such
studies concerning Statement gijinancial Accounting §£§E‘
dgrdgjflg. 8 and at least four such studies concerning
Statement 2; Financial Accounting Standards N2, 12.

Other techniques besides analyzing abnormal returns
are used in market-based research in accounting, but these
techniques may be deficient in determining the effects of
accounting policy decisions. Watts and Zimmerman (1980, pp.
100-102) in their review of three studies examining the
effects of ASR 190 cite criticisms of partitioned portfolios
used by Beaver, Christie, and Griffin (1980) and a matched-
pair design used by R0 (1980) and Gheyara and Boatsman
(1980). The partitioned portfolios technique involves the

examination of differences in returns between two portfolios

9

10
based upon the expected different effects of the account-
ing policy decision, but it cannot detect the effect which
is common to both portfolios. A matched-pair design in-
volves finding a control firm for each firm subject to an
accounting policy decision and analyzing the differences in
returns. However, it is difficult to find a suitable con-
trol group in accounting studies since ideally the only dif-
ference between the firm subject to an accounting policy
decision and the control firm should be the possible effect
of the accounting policy decision (see Foster, 1980, pp.
42-47, for a discussion).

As an example of the difficulty involved in finding a
control group, consider the study by Vigeland (1981).
Vigeland used three criteria in trying to match each of 122
firms affected be Statement 23 Financial Accounting Stan-
ggggg N3. g (pp. 319-320): (1) same three or four digit
S.I.C. code: (2) a beta within plus-or-minus 0.4 of the
affected firm: and (3) total sales or total assets within
plus-or-minus 50 percent of the comparable figures for the
affected firm. If no potential control firm met all three
criteria, criterion (3) was drOpped. Following these cri-
teria which are not very restrictive, Vigeland was unable
to find a suitable match for 27 of the 122 firms.

Thus, to avoid the problems with a partitioned port-
folio or a matched-pair design, this study examined individ-
ual firm abnormal returns without the use of control groups.

Examples of studies which examine individual firm abnormal

11
returns are Hong, Kaplan, and Mandelker (1978), Lev (1979),
and Gheyara and Boatsman (1980). However, there are prob-
lems with the existing methodology of examining individual
firm abnormal returns.

The problem of a market index effect for models
employing a market index is a major issue of this disserta-
tion. Watts and Zimmerman (1980, p. 101) and Noreen and
Sepe (1981, p. 259) have pointed out the problem.

Thus, one of the major objectives of this study is
to try to retain the entire effect of an accounting policy
decision in a firm's abnormal return. The approach in this
study is to use independent or right-hand side variables
in a regression model which should be affected very little
or not at all by accounting policy decisions. The use of
this type of variable should allow most of the total effect
of an accounting policy decision to be retained in the
abnormal return.

Researchers have used right-hand side variables other
than stock market indexes in regressions with stock prices
or stock returns as the dependent variable. However,
researchers generally have stock market indexes as right-
hand variables in these regressions.

The purpose here is to review the literature to
determine what right-hand side variables have been used by
other researchers in regression equations which use stock
prices or returns as dependent variables. Except for non-

monthly data such as financial statement items, most of

12
the variables used in the studies cited here have also been
used in this study.

Homa and Jaffe (1971) estimated the following regres-
sion equation using quarterly data for the period, fourth
quarter, 1954, to the fourth quarter, 1969:

SP = -26.77 + .61M + 3.140 + 1.46C}_1 + .87U_1
R2 = .968 Se = 3.70 D.W. = 2.14
where: SP = S&P 500 index:

M = money supply narrowly defined:

0 = (M - M_1)/M_1:

C:
II

_1 previous period's residual error.

Thus, Home and Jaffe are able to explain.much of the vari-
ation of the S&P 500 index based on their description of
the relationship between the money supply and stock prices.

Malkiel and Quandt (1972) replicated Homa and Jaffe's
results and also examined the relationships of fiscal vari-
ables to stock prices. Malkiel and Quandt were able to
explain almost as much of the variation (.947) using the
following variables: triple A corporate bond rate: new
defense obligations incurred: new orders for durable goods:
unemployment rate; consumer price index: and index of
consumer sentiment. These variables were lagged one period
compared to the S&P 500 index. When the lagged money
supply and growth of money supply variables were included
in the regression, R2 remained the same and the coeffi-
cients of the monetary variables were not significant.

Keran (1971) was able to explain 98%.of the variation

13
for the S&P 500 index using quarterly data with the following
variables: changes in the real money supply for the current
and prior two quarters; changes in real growth of GNP for
the current and prior seven quarters: changes in implicit
price deflator divided by unemployment rate for the current
and prior 16 periods: and changes in earnings adjusted for
inflation for the current period and prior 20 periods.
Keran used Almon distributed lags in his estimation proce-
dure. Keran also linked the.behavior of the S&P 500 index
with the St. Louis monetarist model of the U.S. economy.

The leading composite index may be useful in explaining
returns. Umstead (1977) was able to obtain an R2 of .623
fOr the S&P 500 index by using a transfer function and the
leading composite index. However, this series is not suit-
able for this study since the S&P 500 index is part of the
leading composite index.

Researchers have used P/E ratios (Malkiel and Cragg,
1970: Whitbeck and Kisor, 1963) and rates of return
(Nerlove, 1968: McKibben, 1972) as the dependent variables
in cross-sectional regressions. Variables employed in these
studies include: financial statement variables such as
earnings, sales, and growth rate of earnings: dividends:
market price of stock; and systematic risk.

Researchers have used time series regressions for
individual stocks with returns as the dependent variable.
Variables in addition to stock market returns include:

profitability variables, leaverage, and dividends (Lee

14
and Zumwalt, 1981; Lee and Vinso, 1980); short and long-

term bond return indexes (Lynge and Zumwalt,.1980):
industry variables (King, 1966): and 30-day Treasury
bill rate, 20-year Aaa corporate bond rate, FRB index of
industrial production, and consumer price index (Aber,
1976).

Equilibrium pricing models of individual stock
returns provide some guidance as to which non-stock return
variables should be associated with firm returns. The
Sharpe-Lintner model (Sharpe, 1964: Lintner, 1965) uses
a risk-free interest rate. The arbitrage pricing theory
assumes that returns are a function of expected returns
and several common factors which each have a zero mean (Roll
and Ross, 1980, p. 1076). Based on factor analysis, Roll
and Ross conclude (1980, p. 1092) "...that at least three
factors are important for pricing, but that it is unlikely
that more than four are present." Further, they suggest
that if only a few factors are important, then (p. 1077)
"...one would expect these to.be related to fundamental
economic aggregates, such a GNP, or to interest rates or
weather (although no causality is implied by such rela-
tions)."

Merton (1973) constructs an intertemporal capital
asset pricing model which contains terms representing
unfavorable shifts in the investment opportunity set or
other economic conditions. Although not derived from the

model, Merton (p. 879) suggests that interest rates may

15
describe shifts in the investment opportunity set.

Breedon (1979) deveIOps a single-beta intertemporal
asset pricing model in which equilibruim returns are related
to changes in consumption. Schipper and Thompson (1980), ex-
amining models based largely on Merton's and Breedon's work,
show that individual firm returns are related to unantici-
pated changes in consumption and GNP, and almost statisti-
cally related to changes in the price level.

In cross-sectional regressions with firm returns as
the dependent variable, Banz (1981) and Reinganum (1981)
find evidence that firm market value, in addition to
systematic risk, is associated with firm returns, Litzen-
berger and Ramaswamy (1979) find that dividend yield and
systematic risk are related to firm returns.

There have been other criticisms of the market model
such as nonstationarity of systematic risk or the coeffi-
cient of the market index (Blume, 1971: Levy, 1971).
However, similar criticisms may apply to models which do
not use market indexes as right-hand side variables.

However, the most important question is the ability
of models to detect the effects of accounting policy
decisions on firm returns. To help answer that question,
the procedure introduced by Brown and Warner (1980) is
used in this study. The simulation procedure is performed
by adding an artificial effect.to actual firm stock returns.
Abnormal returns are examined to statistically determine

which model can best detect the presence of the artificial

 

16
effect.

Brown and Warner examined tests of sample of firms
rather than tests of individual firms. Further, Brown and
Warner were concerned with comparing existing methodologies
and they did not consider market index effects. They found
that the market model did as well as other models in
detecting the artificial effects which occur in the same

month for all firms in a sample (Brown and Warner, 1980,

p. 234).

THE MODELS

A. The Market Model

The purpose of this chapter is to introduce the models
in this study.
The market model is (Sharpe, 1963):

~

Rit = "i + BiRmt + 8it

where: git = return of firm i in month t:

Rmt = market index:

git = error term of firm i in month t which is
assumed to be normally distributed with a
zero mean and variance oi2 for all t, i.e.,
git ~ N(0,oiz) for all t;

“i = E<fiit) ' BiE(Emt);

Bi = cov(RiE,Rmt).

02(Rmt)

Brown and Warner (1980) used both an equally weighted
index and a value weighted index in some of their simula-
tions. The equally weighted index was slightly better than
the value weighted index in detecting the presence of
artificial effects (Brown and Warner, 1980, p. 243).

Hence, the equally weighted index from the CRSP tapes was

17

18

used in this study. Thus,

~ 1N...
R = - Z R.
mt Nj=1 jt
where N = the number of firms in the market index. The

market model can be derived from the assumption that
returns are multivariate normal (Fame, 1976, pp. 63-69).
The predicted return using the market model for the

month t is:

Pit = ai + biRmt
where: ai = the ordinary least squares estimate of di:
bi = the ordinary least squares estimate of Bi.

Thus, the abnormal return for firm i in month t, Ait' is:

~

A. = R

1t it ‘ a1 ' biRmt°

B. The Zero Model

The zero model is:

~ Rit = 8it
where git ~ N(O,oiz) for all t. The predicted return

using the zero model is:

Thus, the name, the zero model. The abnormal return for

firm i in month 0 is

A10 10'

Although naive, the zero model serves as a useful bench-

: R

mark for models of firm returns.. Predictions of the zero
model are made without any information regarding the

behavior of other variables. Lev (1979) used this model.

19
C. The Valuation Model

The valuation model is:

 

Bit = 810 + 811 ~' + 812TBt-1 + 8it
TBt

~

where: TBt = the effective interest rate on new issues
of three-month U.S. Treasury bills for month
t:
BiO’ 811. Bi2 = coefficients:
Eit - N(O,oi2) for all t.
The predicted return using the valuation model is:

~ TB

PiO = c. + di ,:1
1 TB

 

+ eiTB_1

0
where ci, di, and ei are the respective ordinary least

squares estimates of BiO’ B , and 812. The abnormal

i1
return for firm i in month 0 is :

~ ~ TB 1
A. = R. - c. + d. .5 + e.TB
l l l -

lO 0 1
TBO

 

1 O

The valuation model is derived in the following manner.

A popular valuation model for the common stock of a firm
is (Sharpe, 1981, p. 366: Haley and Schall, 1979, p. 191):
m d

t
PR = Z --—-
O t=O (Hr-O)t+1
where: PRt = price per share of stock at beginning of
period t;
dt = expected cash dividend per share occuring

at the end of period t;

20
rt = firm specific effective interest rate at
beginning of period t, rt > 0 for all t.

Then, letting d = the actual cash dividend during

A0

period 0,
m dt
PR1 + dA0 = [tE1 (T:;:)E} + dA0
which is a convergent series since, based upon empirical
observation, PR0 + dA0 is finite. It can be shown that
there exists a real number D1 such that:
m D

1
PR + d = z ———————
1 A0 t=0 (1+r1)t

where Dt = a firm's expected "normal" cash dividend per
share per period determined at the beginning of period t.
00 D,1

Now, 2 -—-———E is a convergent geometric series
t=0 (1+r1)

since r1 > 0. Thus (Olmsted,.1961, p. 383):

 

 

 

 

 

w D1 _ D1
Z—'——,E" 9
t=0(1+r1) 1_ 1
1+r1
which can be written as,
__Ii1___-__31_-31£1£11-fl.+1,
- _ _ 1,
[1+r1-1] [ r1] I.1 r1
1+r1 1+r1
Similarly,
PRo = E dtt+1 = ; Dot+1
t=0 (1+ro) t=0 (1+rO)

21

 

t=0 (1+r

00 DO
2 ""“E ‘ Do
t=O (1+r0)

00 D0
D0 + z t+1 ' Do
0)

Do _ D0
= -—»+ D - D _ -—.
r0 0 0 r

Since the common stock return for period 0, R0, is:

R = PR1 + dA0 - PRO

0 PRO
then by substituting from above,
D D

1
r + D1 '
D

_8

D1r0 + Elr
DOr1 DO 0

Now, suppose rt = RKtRFt

-1.

where: RFt = the risk-free interest rate at the beginning
of period t;
RKt = the firm specific risk adjustment factor at

the beginning of period t, RKt z 1.
Further, suppose RFt = TBt-1' That is, stock market par-
ticipants use the effective interest rate on new issues
of three-month U.S. Treasury bills during month t-1 as the
risk-free rate at the beginning of month t.

Substituting for rO and r1 in the previous expression

for R0 gives:

 

22

 

D RK TB D RK
R = 1 0 '1 + 1 0TB - 1
o DdRK1T86 DO -1

or, more generally for firm i and period t:

D RK. TB D

't+1 1t t-1 it+1
R. = —$———————————— + ———-—RK. TB - 1.
1t DitRKit+1TBt Dit it t-1
This can be estimated as:
~ TBt-1 ~
Rit = Bio+Bi1"1'5'-§" + Bi2TBt.1 + 8it'
t

An assumption of ordinary least squares is that the

coefficients are constant parameters (Neter and Wasserman,
1974, p. 30). This leads to Lemma 3.
Lemma 3. When applying ordinary least squares to the valua-
tion model, it is implictly assumed that RKit and Dit+1/Dit
are constant for t = 2,...,T+1. T is the number of consecu-
tive time series observations used to estimate the model.

Hence, if the valuation model does not fit the data
well during the estimation period, it may be because the
risk adjustment factor or the normal dividend ratio,

D is not constant during the estimation period.

it+1/Dit’
Alternative reasons for possible lack of fit include: an
inappropriate model of the price per share of common stock:
an invalid assumption of the relationship between the firm
specific effective interest rate and the risk-free rate:

an invalid assumption that the risk-free rate is equal to
the effective interest.rate on new issues of three-month

U.S. Treasury bills; or that common stocks are mispriced.

An important feature of the valuation model is that

23
the predicted return should not be significantly affected
by an accounting policy decision. In particular, the
Treasury bill rate should not be significantly affected
by a contemporaneous accounting policy decision. Thus,
most of the accounting policy decision effect on firm i
will be retained in the abnormal return of firm i. It
is assumed throughout this study that the Treasury bill
rate is not affected by an accounting policy decision.
Obviously, the zero model's prediction will not be affected
by an accounting policy decision. AHence,.all of the
accounting policy decision effect will be retained in the
abnormal return of each firm.

Thus, the potential usefulness of both the zero and
valuation model lies in the fact that the predicted firm
return is not affected by an accounting policy decision.
Hence, although these models may not fit the firm return
data as well as the market model, if they fit the data
sufficiently well they may be used as a more powerful
procedure than the market model with an index effect for

detecting the effects of accounting policy decisions.

 

PROCEDURES

A. Individual Firm Tests

The models in this study were compared by conducting
simulations similar to those conducted by Brown and Warner
(1980). The purpose of the simulations was to compare
the power of the models for detecting the effects of
accounting policy decisions on individual firms. Power
is the probability of rejecting a false null hypothesis:

t
probability:

Pr(reject DRi = OIDRit # 0)

where: Pr

~

DRit

return of firm i in month t due to an
accounting policy decision.

The simulations were conducted.in the following
manner. For the event month, i.e., the month in which
a hypothetical accounting policy decision took place,
artificial accounting policy decision effects were added
to the actual returns of each firm in the sample. Thus,
simulated firm return equals artificial accounting policy
decision effect (DRit) plus actual firm return. The sizes
of the artificial accounting policy decision effects
examined were the following monthly return percentages:
0, 30.5, 11.0, 11.5, t2.0, i3.0, :4.0, i5.0, i7.5, :10,
:15. :20, :30, :40. :50, :75, and i100. Hence, a wide

24

25
range of monthly return percentages were examined.

Next, predictions of the firm return were made by
each model. For each model an abnormal return was computed
and then statistically analyzed to determine if the null
hypothesis of no accounting policy decision effect could
be rejected. This null hypothesis is: H6:DRit = 0.

Six event months were examined. The six months were
March, 1976, through August, 1976. All firms had the same
event months since accounting policy decisions generally
affect firms in the same month. Consecutive event months
were examined so that a single estimated model could be
used for each event month. Models estimated on 60 monthly
observations should be valid for the subsequent six months.
Six months were examined so that the findings were not
unduly influenced by an unusual month.

The six month period was.selected at random from the
period July, 1968, to June, 1979. This eleven year
period covers several pronouncements by regulatory bodies
including the effective date of Accounting Principles
Egggd Opinion N3, 12 through the issuance of Statement 32
Financial Accounting Standard N3. 22 (AICPA, 1980). Hence,
the eleven year period contains several accounting policy
decisions which researchers may wish to analyze with the
models examined in this study.

The 60 month period from March, 1971, through Feb-
ruary, 1976, was used to estimate each of the models.

A 60 month estimation.period has been used in accounting

26

research. For example, Beaver, Christie, and Griffin
(1980, p. 141) used 60 months to estimate beta in the
market model.

Four hundred fifty-seven firms were selected at
random without replacement.from the CRSP monthly tape
available at Michigan StateUniversity. Each firm that
was selected had to have complete data for the 66 month
period from March, 1971, to August, 1976. A sample size
0f 457 and an observed level of significance of .05 in
a two-tail test ensures that the true level of significance
is within $.02 of .05 at a 95%.confidence level. A range
of $.01 requires a sample size of 1,825 firms which
exceeds the number of firms which satisfy the data require-
ments. These calculations are based on the normal
approximation to the binomial distribution (Mood, Graybill,
and Boes, 1974. pp. 395-396). The observed level of signif-
icance of a model for a given month t is defined as:

~

# of rejections of H5 whenDRit = 0 for all i
457__—__L— '

 

 

The true level of significance of a model for a given
month t is defined as:

o 1 ~ _
Pr(rejectHOIDRi - 0).

t
Dummy variables were employed to compute the abnormal

returns. Six dummy variables, one for eabh event month,

were added to the right-hand side of each model. Each

dummy variable had the value 1 for its corresponding

event month and had the value zero for the other 65

27
observations. The coefficient of the dummy variables is
equal to the abnormal return for the corresponding month
as stated in the following theorem.
Theorem 2. In an ordinary least squares regression of
n + k observations, the coefficient of a dummy variable
that is 1 for period n + j and 0 for all other periods,
j = 1,...,k, is the abnormal return for period n + j where
the equation is estimated over n observations without the

k dummy variables.

This theorem allows the fitting of the model and computa-
tion of the abnormal returns to be accomplished in the
calculation of a single regression equation.

The usual t-statistic for testing if a coefficient,
i.e., abnormal return, is significantly different from
zero was employed to test H6 (for example, see Neter and
Wasserman, 1974, p. 230). The degrees of freedom depended
on the model: market, 58; valuation, 57: and zero, 60.
The specified levels of significance depended on the test:
two tail, .05: right-hand tail, .025: and left-hand
tail, .025.

A difference in means for paired observations test
was employed to compare the power and levels of signifi-
cance of the models in tests of H6. The null hypothesis
of this test is:

H6:Pr(model X rejects HalDRit*)
= Pr(model Y rejects HalDRit*)

where DRi * has a specified value. The statistic is

t

28

 

 

'5
n< )2
2 D. - D
i=1 1
n(n-1)*5
where: D1 = Xi - Yi;
n
5:31;: Di:
1::

X1 = a binomial random variable, taking the value
1 if H0 is rejected and zero.otherwise, for
model X:

Y1 = same as Xi except for model Y.

The statistic is derived by applying the Central
Limit Theorem (Conover, 1971, pp. 53-54) to the Di's
which are assumed to be independent.and identically distrib-
uted. Thus, the standard normal distribution is the approx-
imate distribution of this statistic. The correlation of
X1 and Yi is taken into account by the statistic.

For this study two tail tests were performed using
the difference in means for paired observations statistic.

The sample size was 457 and the level of significance

was .05.

B. Adjusting Levels of Significance

Examination of the results of the next chapter
reveals that many of the observed levels of significance
are significantly different from the specified levels of
significance in tests of Hg. A method for adjusting the

observed levels of significance is the following.

29
Compute the critical point for each firm during a set
of time periods during which no unusual event such as an
accounting policy decision has~taken place“ The critical
point is the distance between the observed abnormal return
and the standard error times the appropriate percentile
of the t-distribution. For the market model, with 58
degrees of freedom, the critical point for firm i in

month t, CRPit’ is:

for a right-hand tail test, and
CRPit = -2.0028.E. - (Rit - Pit)

for a left-hand tail test. Here, S.E. represents the
standard error which is the denominator of the individual
firm t-ratio. The critical point is the amount which
would need to be added to the abnormal return to just
reject H6.

In a sample size of 457 firms and a specified level
of significance of .025, one would expect to observe
457 x .025 = 11.425 or about 11 rejections of H6 when
there is no unusual event such as an accounting policy
decision. Thus, one can now compute the.c adjustment
factor which is the amount that would need to be added to
each firm abnormal return for a given time period in order
to reject H; 11 times in the sample of 457 firms.

For a specified event month, the d adjustment factor

was computed for the other five event months. 'The average

a adjustment factor for these other.five months was added

30
to the abnormal returns of the firms in the specified

event month. On average the number of rejections of H5

in the specified event month when DRit = 0 for all i should
be about 11. The assumption of this procedure is that
the distribution of the t-statistics.used to test H5 is

the same for all the event months.

C. Market Index Effects

The purpose of Part C of the next chapter is to
determine the magnitudes of market.index effects which
make the valuation and zero models as powerful as the
market model. The procedure is to examine a hypothetical
average firm. Recall that the numerator of the t-ratios
is the abnormal return, Eit’ which can be written as:
A. = DRit + WRit - Pit
where: DRit = return of firm i in month t due to an

accounting policy decision;

WR. = return of firm i in month t due to all

causes except the accounting policy

decision;
Pit = the predicted return of firm i in month t.
If Pit is an unbiased estimate of WRit, then on average
Kit = DRit. Thus, in this case the power of the t~tests

depends on the denominator of the t-ratios, i.e., the
standard error, and the degrees of freedom.
The models are compared by examining their average

standard errors.in the sample of 457 firms and their

31
appropriate degrees of freedom. For the market model,
with 58 degrees of freedom, the critical value for a
hypothetical average firm, CRM, is:
CRM = 2.002S.E.M.

where S.E.M. is the average standard error for the market
model. The critical value is.the size in absolute value
of the accounting policy decision effect which would be
required to just reject H6 for a hypothetical average
firm.

The numerator of the t-ratio for the market model,

assuming Pit = WRit’ when there is an index effect is:

DRit(1 - pibi)

where: pi market index effect;

b.
1

the estimated coefficient of the market
index in the market model for firm i.
Thus, for the market model.when there is an index effect,

the critical value for a hypothetical average firm, CRI,

 

 

 

is:
2.002S.E.M. CRM
CRI = = . .
1 ’ pibi 1 ' pibi
Solving:
_ CRM
CRV — 1 - p.b.*
1 1

for pi shows how large the market index effect would

have to be in order for the valuation model to be just as
effective in detecting DRit as the market model. Here, CRV
is the critical value for a hypothetical average firm for
the valuation model and bi* is a specified value for bi'

A similar computation is made for the zero model.

32

D. Sample of Firms Tests

Now, Ait = DRit + WRit - Pit; ~
Clearly, the ideal prediction is Pit = WRit since then
Ait = DRit which makes the accounting policy decision

directly observable. Failing the achievement of the
ideal, intuitively one would expect that the smaller the
prediction errors, the easier it would be to detect the
accounting policy decision effect.

For example, consider the following two statistics.
The event month t-statistic for a sample of n firms is

(Mood, Graybill, and Boes, 1974, p. 250):

 

 

KO
n % .. t(n_1). (T-1)
1 _
‘ETTiE1(Aio ' "0)2
n5

The statistic (T-1) is derived under the assumptions that
the Aio's are independent and identically distributed
as N(0,oz) and that there is no accounting policy decision

effect. In (T-1) and the statistic (T-2) below, Xi =

1 n
HZA..

i=1 1
However, suppose that the Aio's are not independent.

Then (T-1) is not distributed as t(n-1)' A more appro-

priate statistic may be:

“ t<5) (T'Z)

33
where, 0 represents the month in which the accounting
policy decision takes place and -1,...,-5 represent months
in which the accounting policy decision does not take
place and in which predictions are made by the prediction
models. The statistic (T-2) is derived under the assumption
that the At's are independent and identically distributed
as N(O,oz) and that there is no accounting policy decision
effect. Cross-sectional dependence of firm abnormal
returns is taken into account by (T-2) since the variance
of Kt includes the effects of any cross-sectional dependence.
The statistic (T-2) is similar to the t-statistic with
crude dependence adjustment suggested by Brown and Warner
(1980, p. 251).

Inspection of (T-2) shows that as prediction errors
become uniformly smaller across firms, the denominator
is smaller since the denominator is.a function of only
prediction errors under the null hypothesis of no accounting
policy decision effect. Hence, as the prediction
errors tend to become smaller, the more likely it is to
reject the null hypothesis when it is false and the more
powerful the testing procedure.

It is more difficult to see the importance of small
prediction errors for (T-1) since the denominator is
affected by an accounting policy decision effect. However,
if the effect of the accounting policy decision on the

denominator is small, then smaller prediction errors will

tend to result in a smaller denominator and a more powerful

34
tests.

Thus, one way to compare the power of models in sample
of firm tests is to examine how well the models predict.
The mean absolute prediction error (MAPE) and the mean
square prediction error (MSPE) were used in a preliminary
study to compare power. These results are reported in the
next chapter. Also reported are (T-1) and (T-2) for the
market model, the valuation model, and the zero model
when there is no simulated accounting policy decision
effect for the sample of 457 firms used in the individual

firm tests.

RESULTS

A. Power Comparisons

The null hypothesis of the individual firm t-tests,
H5, is that the accounting policy decision effect for a
firm is zero. Table 1 through Table 24 show the number of
rejections of H6 in a random sample of 457 firms when the
same simulated effect has been added.to each firm's
actual return. Thirty-three levels of accounting policy
decision effects were simulated. The simulated effects
range from -100% to 100%. Right-hand tail tests (a = .025),
left-hand tail tests (a = .025), and two-tail tests (a =
.05) are presented for each of the six event months.

Table 25 through Table 48 show the difference in
means for paired observations statistic. The null hypo-
thesis of these tests, H8,
rejection of H6 by two models are equal. Difference in

is that the probabilities of

means statistics are presented for all pairs of models for
all levels of accounting policy decision effects reported
in Tables 1 through 24. The names of the models are
abbreviated in these tables as follows: .market model
without an index effect, M; market model with a 50% index
effect, I: valuation model, V: and zero model, Z. H8

is rejected if the difference in means statistic in absolute

35

36

Table 1. Number of rejections of null hypothesis March,
1976, in right-hand tail tests for 457 firms
with a=.025.

 

 

Model

Ef%60t Market MIidzi Effgcioz Valuation Zero
0 15 15 7 8
0.5 17 16 10 8
1.0 20 16 10 9
1.5 21 18 13 10
2.0 23 20 13 13
3.0. 30 23 16 16
4.0 38 25 19 20
5.0 45 29 25 25
7.5 78 38 44 36
10.0 108 59 74 68
15.0 213 97 164 153
20.0 309 154 260 248
30.0 417 254 384 382
40.0 447 323 439 438
50.0 457 355 452 452
75.0 457 400 457 457

100.0 457 420 457 457

 

37

Table 2. Number of rejections of null hypothesis March,
1976, in left-hand tail tests for 457 firms
with a=.025.

 

 

Model

Efgect Market MIEESE Effgcioz Valuatign Zero
0 2 _ 2 0 O
-0.5 3 2 0 0
-1.0 4 4 O 0
-1.5 4 4 O 0
-2.0 6 4 2 1
-3.0 7 7 3 1
-4.0 15 8 3 3
-5.0 22 10 4' 3
-7.5 51 18 14 11
.10.0 94 36 31 25
-15.0 194 82 101 89
-20.0 284 138 192 188
-30.0 396 221 345 344
-40.0 433 293 412 415
-50.0 452 349 437 436
-75.0 456 400 455 455

-100.0 457 417 456 456

 

 

38

Table 3. Number of rejections of null hypothesis March,
1976, in two tail tests, positive effects,
for 457 firms with d=.05.

 

 

Model
EfgeCt Market MIiggi Eff2c30% Valuation Zero
0 17 17 7 8
0.5 19 18 10 8
1.0 22 18 10 9
1.5 22 18 13 10
2.0 23 20 13 13
3.0 30 23 16 16
4.0 38 25 19 20
5.0 45 29 25 25
7.5 78 38 44 36
10.0 108 59 74 68
15.0 213 97 164 153
20.0 309 154 260 248
30.0 417 254 384 382
40.0 447 323 439 438
50.0 457 355 452 452
75.0 457 400 457 457

100.0 457 420 457 457

 

39

Table 4. Number of rejections of null hypothesis March,
1976, in two tail tests, negative effects,
for 457 firms with a=.05.

 

 

 

Model

Effect Market with 50%
% Market Index Effect Valuation Zero
0 17 17 7 8
-0.5 17 16 7 6
-1.0 17 18 6 6
-1.5 16 18 6 6
~2.0 18 17 8 7
--3.0 17 19 9 6
-4.0 22 19 7 8
-5.0 28 21 8 7
-7.5 55 28 17 14
-10.0 97 43 33 26
-15.0 195 87 102 90
-20.0 285 143 193 189
-30.0 396 222 345 344
-40.0 433 294 412 415
-50.0 452 350 437 436
-75.0 456 400 455 455

-100.0 457 417 456 456

 

 

40

 

 

Table 5. Number of rejections of null hypothesis April,
1976, in right-hand tail tests for 457 firms
with d=.025.

- Model

Ef%GCt Market MIigzi EEEZCEO% Valuation Zero
0 10 10 4 4
0.5 12 11 4 4
1.0 13 13 4 4
1.5 15 13 4 5
2.0 18 15 5 6
3.0 22 16 5 8
4.0 30 17 9 10
5.0 37 23 9 13
7.5 64 36 15 18
10.0 107 52 29 45
15.0 196 95 86 106
20.0 280 140 166 197
30.0 413 239 311 341
40.0 445 299 407 423
50.0 455 344 441 445
75.0 457 400 456 457
100.0 457 422 457 457

 

 

41

Table 6. Number of rejections of null hypothesis April,
1976, in left-hand tail tests for 457 firms
with a=.025.

 

 

Model
Effect Market with 50%
% Market Index Effect Valuation Zero
0 O O 1 O
-O.5 O 0 1 O
-1.0 2 1 3 0
-1.5 2 2 3 0
-2.0 3 2 3 1
-3.0 7 4 6 2
-4.0 10 6 8 2
-5.0 12 7 11 3
-7,5 29 1O 28 10
-10.0 74 16 6O 26
-15.0 200 62 195 122
-20.0 314 124 307 249
-30.0 422 247 415 386
-40.0 450 301 451 440
-50.0 454 345 454 453
-75.0 455 406 455 455

-100.0 457 427 456 457

 

 

42

Table 7. Number of rejections of null hypothesis April,
1976, in two tail tests, positive effects,
for 457 firms with a=.05.

 

 

Model

Ef580t Market MIigzi g%;:c€0% Valuation Zero
0 10 10 5 4
0.5 12 11 5 5 4
1.0 13 13 4 4
1.5 15 13 4 5
2.0 18 15 5 6
3.0 22 16 5 8
4.0 30 17 9 10
5.0 37 23 9 13
7.5 64 36 15 18
10.0 107 52 29 45
15.0 196 95 86 106
20.0 280 140 166 197
30.0 413 239 311 341
40.0 445 299 407 423
50.0 455 344 441 445
75.0 457 400 456 457

100.0 457 422 457 457

 

43

Table 8. Number of rejections of null hypothesis April,
1976, in two tail tests, negative effects,
for 457 firms with d=.05.

 

 

Model
Ef%GCt Market “5:52: E§520€0% Valuation Zero
0 10 10 5 4
-0.5 8 9 4 4
-1.0 9 9 4 4
-1.5 8 10 4 4
-2.0 9 9 4 5
-3.0 11 10 7 6
-4.0 14 12 9 6
-5.0 16 12 12 7
-7.5 33 14 29 13
-10.0 78 20 61 29
-15.0 203 66 196 123
-20.0 315 128 307 249
.30,0 422 249 415 386
-40.0 450 303 451 440
-50.0 454 347 454 453
-75.0 455 408 455 455

-100.0 457 428 456 457

 

44

Table 9. Number of rejections of null hypothesis May,
1976, in right-hand tail tests for 457 firms
with a=.025.

 

 

 

Effect Market withMgggl
% Market Index Effect. Valuation Zero
0 4 4 0 0
0.5 4 4 1 0
1.0 4 4 2 0
1.5 4 4 3 1
2.0 6 6 3 3
3.0 12 7 5 3
4.0 16 9 8 6
5.0 24 13 9 6
7.5 47 23 19 14
10.0 77 34 36 30
15.0 189 70 102 86
20.0 303 135 205 182
30.0 412 222 356 342
40.0 448 306 434 423
50.0 454 _ 346 451 450
75.0 457 395 457 457

100.0 457 423 457 457

 

45

Table 10. Number of rejections of null hypothesis May,
1976, in left-hand tail tests for 457 firms
with a=.025.

 

 

Model
Effect Market with 50%

Market Index Effect Valuation Zero

0 1 1 0 1
-0.5 3 3 0 1
-1.0 4 3 1 1
-1.5 4 4 1 1
-2.0 5 4 2 2
-3.0 8 5 2 2
-4.0 11 8 3 4
-5.0 20 10 8 6
-7.5 45 18 19 19
-10.0 98 35 .43 46
-15.0 213 80 146 149
-20.0 295 145 247 249
-30.0 414 232 380 383
-40.0 450 302 436 443
-50.0 455 352 455 455
-75.0 457 409 457 457

-100.0 457 427 457 457

 

 

46

Table 11. Number of rejections of null hypothesis May,
1976, in two tail tests, positive effects,
for 457 firms with a=.05.

 

 

Model
Effect Market with 50%

% Market Index Effect Valuation Zero
0 5 5 0 1
0.5 5 1 1
1.0 5 5 2 0
1.5 5 5 3 1
2.0 7 7 3 3
3.0 12 B 4 5 3
4.0 16 1O 8 6
5.0 24 13 9 6
7.5 47 23 19 14
10.0 77 34 36 30
15.0 189 70 102 86
20.0 303 135 205 182
30.0 412 222 356 342
40.0 448 306 434 423
50.0 454 346 451 450
75.0 457 395 457 457

100.0 457 423 457 457

 

47

Table 12. Number of rejections of null hypothesis May,
- 1976, in two tail tests, negative effects,
for 457 firms with a=.05.

 

 

Model
Effect Market with 50%
% Market Index Effect Valuation Zero
0 5 5 O 1
-O.5 7 7 O 1
-1.0 8 7 1 1
-1.5 7 7 1 1
-2.0 8 7 2 2
-3.0 10 8 2 2
-4.0 11 11 3 4
-5.0 20 12 8 6
-7.5 45 19 19 19
-10.0 98 35 43 46
-15.0 213 80 146 149
-20.0 295 145 247 249
-30.0 414 232 380 383
-40.0 450 302 436 443
-50.0 455 352 455 455
-75.0 457 409 457 457

-100.0 457 427 457 457

 

 

48

Table 13. Number of rejections of null hypothesis June,
1976, in right-hand tail tests for 457 firms
with a=.025.

 

 

Model
Effect ’Market with 50%
% Market Index Effect Valuation Zero
0 1O 1O 15 10
0.5 11 1O 17 10
1.0 13 11 17 13
1.5 17 13 17 16
2.0 18 16 2O 20
3.0 20 18 26 21
4.0 28 19 33 28
5.0 38 23 45 34
7.5 65 33 78 63
10.0 105 49 127 109
15.0 213 97 242 219
20.0 315 146 334 311
30.0 411 251 417 413
40.0 445 314 448 447
50.0 452 353 453 453
75.0 457 405 457 457

100.0 457 422 457 457

 

49

Table 14. Number of rejections of null hypothesis June,
1976, in left-hand tail tests for 457 firms
with a=.025.

 

 

Model
Ef580t Market MIEESE ETEECEO% Valuation Zero
0 2 2 0 0
-0.5 4 3 0 0
-1.0 5 4 0 O
-1.5 6 z. 0 o
-2.0 8 5 0 1
-3.0 11 8 1 1
-4.0 12 9 1 1
-5.0 18 10 1 1
-7.5 39 14 2 2
-10.0 79 30 8 6
-15.0 189 71 47 47
-20.0 293 118 118 115
-30.0 407 216 291 300
-40.0 443 305 403 403
-50.0 453 350 436 435
-75.0 356 395 455 455

-100.0 357 422 457 457

 

50

Table 15. Number of rejections of null hypothesis June,
1976, in two tail tests, positive effects,
for 457 firms with a=.05.

 

 

Model
Effect Market with 50%
z Market Index Effect Valuation Zero
0 _ 12 12 15 10
0.5 13 12 17 10
1.0 15 13 17 13
1.5 18 15 17 16
2.0 19 18 2o 20
3.0 21 19 26 21
4.0 28 20 33 28
5.0 38 24 45 34
7.5 65 34 78 63
10.0 105 50 127 109
15.0 213 97 242 219
20.0 315 146 334 311
30.0 411 251 417 413
40.0 445 314 448 447
50.0 452 353 453 453
75.0 457 405 457 457

100.0 457 422 457 457

 

51

Table 16. Number of rejections of null.hypothesis June,
1976, in two tail tests, negative effects,
for 457 firms with a=.05.

 

 

Model
EfgeCt Market MI:§:: Efggcioz Valuation Zero
0 12 12 15 10
-0.5 14 13 14 10
-1.0 14 13 11 8
-1,5 14 13 9 6
-2.0 14 14 7 6
-3.0 15 16 7 6
-4.0 15 15 6 5
-5.0 21 16 4 4
-7.5 41 17 5 4
-10.0 81 33 10 8
-15.0 191 74 49 49
-20.0 293 121 120 117
-30.0 407 219 291 300
-40.0 443 307 403 403
-50.0 453 351 436 435
-75.0 456 396 455 455

-100.0 457 423 457 457

 

52

Table 17. Number of rejections of null hypothesis July,
1976, in right-hand tail tests for 457 firms
With a=00250

 

 

Model

Ef560t Market M5852: E352c50% Valuation Zero
0 10 10 4 4
0.5 11 11 4 4
1.0 12 11 4 4
1.5 13 12 4 4
2.0 18 14 5 5
3.0 20 19 5 5
4.0 24 20 6 11
5.0 29 21 9 15
7.5 53 30 20 27
10.0 94 42 33 42
15.0 198 74 82 108
20.0 292 128 177 205
30.0 414 229 348 368
40.0 446 306 425 433
50.0 456 351 447 449
75.0 457 400 457 457

100.0 457 427 457 457

 

53

Table 18. Number of rejections of null hypothesis July,
1976, in left-hand tail tests for 457 firms
with a=.025.

 

 

Model
Effect Market with 50%
% Market Index Effect Valuation Zero
0. 1 1 1 1
-O.5 1 1 1 1
-1.0 2 2 1 1
-1.5 2 2 2 1
-2.0 2 2 2 2
-3.0 6 3 4 2
-4.0 7 5 5 2
-5.0 7 6 6 2
-7,5 28 7 16 5
-10.0 71 16 47 16
-15.0 207 64 163 89
-20.0 . 322 126 272 216
-30.0 420 244 407 382
-40.0 445 307 440 435
-50.0 455 346 453 450
-75.0 457 412 457 457

-100.0 457 423 457 457

 

 

54

Table 19. Number of rejections of null hypothesis July,
1976, in two tail tests, positive effects,
for 457 firms with d=.05.

 

 

Model

Effect Market with 50%
% Market Index Effect- Valuation Zero
0 11 11 5 5
0.5 12 12 5 5
1.0 13 12 5 5
1.5 14 13 5 4
2.0 19 15 6 5
3.0 21 20 5 5
4.0 24 21 6 11
5.0 29 22 9 15
7.5 53 30 20 27
10.0 94 42 33 42
15.0 198 74 82 108
20.0 292 128 177 205
30.0 414 229 348 368
40.0 446 306 425 433
50.0 456 351 447 449
75.0 457 400 457 457

100.0 457 427 457 457

 

55

Table 20. Number of rejections of null hypothesis July,
1976, in two tail tests, negative effects,
for 457 firms with a=.05.

 

 

Model
Ef%QCt Market Mggggi E%E2c20% Valuation Zero
0 11 11 5 5
.0,5 10 1O 5 5
-1.0 11 11 5 4
-1,5 8 11 6 4
-2.0 8 11 6 5
-3.0 11 10 8 5
.4.0 11 11 9 5
-5.0 11 12 10 5
-7,5 32 12 19 8
-10.0 74 20 48 18
-15.0 209 67 164 90
.20.0 322 129 272 216
-30.0 420 245 407 382
-40.0 445 308 440 435
-50.0 455 346 453 450
.75,0 457 412 457 457

-100.0 457 423 457 457

 

 

56

 

 

Table 21. Number of rejections of null hypothesis August,
1976, in right-hand tail tests for 457 firms
with a=.025.

Model

Efgect Market MIEEEE Efficipg 'Valuation Zero
0 9 9 2 2
0.5 11 10 2 2
1.0 13 11 2 2
1.5 14 14 2 3
2.0 16 15 3 5
3.0 23 15 5 6
4.0 31 20 6 9
5.0 35 25 9 13
7.5 73 35 20 23
10.0 102 53 37 46
15.0 193 91 88 103
20.0 297 131 162 187
30.0 410 234 325 347
40.0 444 309 412 426
50.0 454 354 443 446
75.0 457 401 457 457
100.0 457 421 457 457

 

 

57

Table 22. Number of rejections of null hypothesis August,
1976, in left-hand tail tests for 457 firms
with d=.025.

 

 

Model
Efgect Market MTEEE: Effgc50% Valuation Zero
0 3 3 2 1
-0.5 3 3 2 1
-1.0 3 3 2 2
-1.5 3 3 3 2
-2.0 5 3 3 3
-3.0 7 6 6 3
-4.0 10 6 7 5
-5.0 11 6 10 6
-7.5 33 10 19 10
-10.0 63 18 50 19
-15.0 187 52 159 109
-20.0 297 124 282 222
-30.0 425 233 411 395
-40.0 451 303 450 440
-50.0 455 358 455 455
-75.0 457 405 457 457

-100.0 457 422 457 457

 

58

Table 23. Number of rejections of null hypothesis August,
1976, in two tail tests, positive effects,
for 457 firms with a=.05.

 

 

Model

Effect Market with 50%
% Market Index Effect Valuation Zero
0 12 12 4 3
0.5 13 3 12 4 3
1.0 15 13 4 2
1.5 15 15 4 3
2.0 17 16 5 5
3.0 23 16 6 6
4.0 31 20 6 9
5.0 35 25 9 13
7.5 73 35 20 23
10.0 102 53 37 46
15.0 193 91 88 103
20.0 297 131 162 187
30.0 410 234 325 347
40.0 444 309 412 426
50.0 454 354 443 446
75.0 457 401 457 457

100.0 457 421 457 457

 

59

Table 24. Number of rejections of null hypothesis August,
1976, in two tail tests, negative effects,
for 457 firms with a=.05.

 

 

Model
§E%GCt Market M5352: Eff2c50% Valuation Zero
0 12 12 4 3
.0,5 11 11 3
-1.0 9 11 4 4
-1.5 7 9 5 4
-2.0 9 8 4 5
-3.0 9 10 7 4
-4.0 12 9 8 6
-5.0 13 9 11 7
-7.5 35 12 20 11
-10.0 64 20 51 20
-15.0 188 53 159 110
-20.0 298 125 282 222
.30.0 425 234 411 395
-40.0 451 304 450 440
-50.0 455 359 455 455
-75.0 457 405 457 457

-1oo.o 457 422 457 457

 

60

 

 

Table 25. Difference in means statistics March, 1976,
for right-hand tail tests.
Model Comparison1
Effect
% Mlgg MV MZ IV IZ VZ

0 0 2.851 2.663 2.851 2.663 -1.000
0.5 1.000 2.663 3.027 2.463 2.851 1.416
1.0 2.007 3.194 3.354 2.463 2.663 0.577
1.5 1.736 2.545 3.079 1.895 2.545 1.736

2.0 1.736 2.910 2.910 2.345 2.345 0

3.0 2.663 3.796 3.544 2.663 2.119 0
4.0 3.654 4.447 4.094 2.130 1.670 -0.577

5.0 4.067 4.568 4.568 1.416 1.266 0
7.5 6.164 5.703 6.622 -1.903 0.577 2.851
10.0 7.400 5.703 6.440 -3.483 -2.335 2.463
15.0 12.455 7.237 8.147 -8.851 -7.980 2.862
20.0 . 15.299 6.940 8.227 -11.735 -10.866 3.027
30.0 15.900- 5.957 6.150 -13.464 -13.320 0.577
40.0 13.031 2.851 3.027 -12.455 -12.383 0.378

50.0 11.446 2.246 2.246 -11.084 -11.084 0

75.0 8.061 0 O -8.061 -8.061 0

100.0 6.338 0 0 -6.338 -6.338 0

 

zero model.

market model: I = market model with 50% index effect:
valuation model: Z =

61

 

 

 

Table 26. Difference in means statistics March, 1976,
for left-hand tail tests.
Model Comparison1
Effect
4% MI MV MZ IV IZ VZ
0 0 1.416 1.416 1.416 1.416 0
-0.5 1.000 1.736 1.736 1.416 1.416 0
-1.0 0 2.007 2.007 2.007 2.007 0
-1.5 0 2.007 2.007 2.007 2.007 0
-2.0 1.416 2.007 1.895 1.416 1.343 0.577
-3,0 0 2.007 2.463 2.007 2.463 1.416
-4.0 2.663 3.507 3.507 2.246 2.246 0
-5.0 3.507 4.324 4.447 2.463 2.663 1.000
-7.5 5.957 6.338 6.614 1.636 2.663 1.736
-10.0 8.142 8.539 9.005 1.670 3.354 2.130
-15.0 12.167 10.794 11.663 -4.222 -2.119 3.027
-20.0 14.631 10.721 11.012 -7.817 -7.485 1.069
-30.0 16.822 7.568 7.652 -13.031 -12.958 0.333
—40.0 14.191 4.687 4.324 -12.671 -12.887 -1.134
-50.0 11.879 3.934 4.067 -10.794 -10.721 1.000
-75.0 7.980 1.000 1.000 -7.899 -7.899 0
-100.0 6.614 1.000 1.000 -6.523 -6.523 0
1M market model: I = market model with 50% index effect:

V

valuation model: Z =

zero model.

62

 

 

 

Table 27. Difference in means statistics March, 1976,
for two tail tests with positive effects.
Model Comparison1
Effect
% MI MV MZ' IV ' IZ V2

0 0 3.194 3.027 3.194 3.027 -1.000
0.5 1.000 3.027 3.354 2.851 3.194 1.416
1.0 2.007 3.507 3.654 2.851 3.027 0.577
1.5 1.000 2.733 3.240 2.345 2.910 1.736

2.0 0.447 2.910 2.910 2.733 2.733 0

3.0 2.130 3.796 3.544 2.851 2.320 0
4.0 3.240 4.447 4.094 2.345 1.903 -0.577

5.0 4.067 4.568 4.568 1.416 1.266 0
7.5 6.614 5.703 6.622 -1.903 0.577 2.851
10.0 7.400 5.703 6.440 -3.483 -2.335 2.463
15.0 12.455 7.237 8.147 -8.851 -7.980 2.862
20.0 15.299 6.940 8.227 -11.735 -10.866 3.027
30.0 15.900 5.957 6.150 -13.469 -13.320 0.577
40.0 13.031 2.851 3.027 -12.455 -12.383 0.378

50.0 11.446 2.246 2.246 -11.084 -11.084 0

75.0 8.061 0 0 -8.061 -8.061 0

100.0 6.338 0 0 -6.338 -6.338 0

 

market model: I
valuation model; Z =

= market model with 50% index effect;

zero model.

 

63

 

 

Table 28. Difference in means statistics March, 1976,
for two tail tests with negative effects.
Model Comparison
Effect
% M17 MV MZ IV IZ VZ
O 0 3.194 Q3.027 3.194 3.027 -1.000
-0.5 1.000 3.194 3.354 3.027 3.194 1.000
-1.0 -1.000 3.354 3.354 3.507 3.507 0
-1.5 -1.416 3.194 3.194 3.507 3.507 0
-2.0 0.577 3.194 3.079 3.027 2.910 0.577
-3.0 -1.416 2.851 3.354 3.194 3.654 1.736
-4.0 0.904 3.934 3.796 3.507 3.354 -1.000
-5.0 1.701 4.568 4.687 3.654 3.796 1.000
-7.5 4.410 6.431 6.704 3.079 3.796 1.736
-10.0 7.233 8.618 9.158 2.691 4.198 2.345
-15.0 11.342 10.794 11.663 -3.027 -0.774 3.027
-20.0 13.785 10.721 11.012 -6.891 -6.540 1.069
-30.0 16.591 7.568 7.652 -12.817 -12.745 0.333
-40.0 13.902 4.687 4.324 -12.248 ~12.464 -1.134
-50.0 11.593 3.934 4.067 -10.367 -10.294 1.000
-75.0 7.980 1.000 1.000 -7.899 -7.899 0
-100.0 6.614 1.000 1.000 -6.523 -6.523 0

 

market model: I =
valuation model; Z = zero model.

market model with 50% index effect;

64

Difference in means statistics April, 1976,
for right-hand.tail tests.

Table 29.

Model Comparison

 

 

 

 

Effect '
EAA MI MV MZ IV IZ VZ
O 0 2.463 2.463 2.463 2.463 0
0.5 1.000 2.851 -2.851 2.663 2.663 0
1.0 0 3.027 3.027 3.027 3.027 0
1.5 1.416 3.354 3.194 3.027 2.545 -1.000
2.0 1.736 3.654 3.507 3.194 3.027 -1.000
3.0 2.463 4.198 3.796 3.353 2.851 -1.736
4.0 3.654 4.687 4.568 2.851 2.663 -1.000
5.0 3.796 5.455 5.027 3.796 3.194 -2.007
7.5 5.455 7.400 7.144 4.687 4.324 -1.343
10.0 7.899 9.688 8.460 4.916 1.461 -4.067
15.0 11.374 12.023 10.575 2.511 -3.079 -4.568
20.0 14.191 12.311 9.776 -5.245 -8.061 -5.760
30.0 16.744 11.446 9.234 '9.086 -11.446 -5.469
40.0 14.631 6.431 4.802 -11.879 -13.031 -4.067
50.0 12.095 3.796 3.194 -11.084 -11.374 ~2.007
75.0 8.061 1.000 0 -7.980 -8.061 -1.000
100.0 6.150 0 0 -6.150 -6.150 0
market model: I = market model with 50% index effect:

valuation model; Z = zero model.

65

 

 

 

Table 30. Difference in means statistic April, 1976,
for left-hand tail tests.
Model Comparisog
Effect
% MI MV MZ IV IZ VZ
0 0 -1.000 0 -1.000 0 1.000
-0.5 0 -1.000 03 -1.000 0 1.000
-1.0 1.000 -1.000 1.416 -1.416 1.000 1.736
-1.5 0 -1.000 1.416 -1.000 1.416 1.736
-2.0 1.000 0 1.000 -1.000 0.577 1.000
-3.0 1.736 1.000 2.246 -1.416 1.416 2.007
-4.0 2.007 1.416 2.851 -I.416 2.007 2.463
-5.0 2.246 0.447 3.027 -2.007 2.007 2.851
-7.5 4.447 0.242 4.447 -4.324 0 4.324
-10.0 8.142 3.161 7.315 -6.977 -2.910 6.054
-15.0 13.902 0.762 9.688 -13.681 -8.147 9.162
-20.0 18.014 1.402 8.695 -17.451 -13.103 7.986
-30.0 16.822 1.947 6.245 -16.281 -13.975 5.559
-40.0 14.852 -0.577 3.194 -14.926 -14.118 3.350
-50.0 11.951 0 1.000 -11.951 -11.879 1.000
-75.0 7.400 0 0 -7.400 -7.400 0
-100.0 5.660 1.000 O -5.559 -5.660 -1.000
1M = market model: I = market model with 50% index effect:
V = valuation model; Z = zero model.

66

 

 

 

Table 31. Difference in means statistics April, 1976,
for two tail tests with positive effects.
Model Comparison1
Effect
% MI MV MZ IV IZ VZ
0 0 1.895 42.463 1.895 2.463 1.000
0.5 1.000 2.345 2.851 2.130 2.663 1.000
1.0 0 3.027 3.027 3.027 3.027 0
1.5 1.416 3.354 3.194 3.027 2.548 -1.000
2.0 1.736 3.654 3.507 3.194 3.027 -1.000
3.0 2.463 4.198 3.796 3.353 2.851 -1.736
4.0 3.654 4.687 4.568 2.851 2.663 -1.000
5.0 3.796 5.455 5.027 3.796 3.194 -2.007
7.5 5.455 7.400 7.144 4.687 4.324 -1.343
10.0 7.899 9.688 8.460 4.916 1.461 -4.067
15.0 11.374 12.023 10.575 2.511 -3.079 -4.568
20.0 14.191 12.311 9.776 -5.245 -8.061 -5.760
30.0 16.744 11.446 9.234 -9.086 -11.446 -5.469
40.0 14.631 6.431 4.802 -11.876 -13.031 -4.067
50.0 12.095 3.796 3.194 -11.084 -11.374 ~-2.007
75.0 8.061 1.000 0 -7.980 -8.061 -1.000
100.0 6.150 0 0 -6.150 -6.150 0
M = market model: I = market model with 50% index effect:
V = valuation model; Z = zero model.

67

 

 

 

Table 32. Difference in means statistics April, 1976,
for two tail tests with negative effects.
Model Comparison
Effect
z MI MV MZ IV IZ vz
0 0 1.895 2.463 1.895 2.463 1.000
-0.5 -1.000 1.636 2:007 1.895 2.246 0
-1.0 0 1.343 2.246 1.134 I 2.246 1.000
-1.5 -1.416 1.000 2.007 1.636 2.463 1.000
-2.0 0 1.343 1.636 1.343 1.636 0.447
-3.0 0.447 1.416 2.246 0.447 2.007 1.343
-4.0 0.816 1.736 2.851 0.447 2.463 1.895
-5.0 1.636 0.816 3.027 -0.816 2.246 2.345
-7.5 4.447 0.471 4.568 -3.962 1.000 4.324
-10.0 8.142 3.591 7.400 -6.222 -2.511 5.501
-15.0 13.690 1.044 9.837 -13.050 -7.483 9.162
-20.0 ’17.308 1.571 8.773 -16.539 -12.274 7.986
-30.0 16.365 1.947 6.245 -15.832 -13.555 5.559
-40.0 14.419 -0.557 3.194 -14.492 -13.690 3.354
-50.0 11.529 0 1.000 -11.529 -11.457 1.000
-75.0 6.910 0 0 -6.910 -6.910 0
-100.0 5.351 1.000 0 -5.043 -5.351 -1.000
1M market model: I = market model with 50% index effect:

V

valuation model:

Z = zero model.

68

 

 

 

Table 33. Difference in means statistics May, 1976,
for right-hand tail tests.
Model Comparison1
Effect
2 M; MV MZ IV IZ vz

O O 2.007 2.007 2.007 2.007 O
0.5 0 1.736 2.007 1.736 2.007 1.000
1.0 O 1.000 2.007 1.000 2.007 1.416
1.5 0 0.447 1.736 0.447 1.736 1.416

2.0 0 1.736 1.343 1.343 1.736 0
3.0 2.246 2.663 3.027 1.416 2.007 1.416
4.0 2.663 2.545 3.194 0.577 1.736 1.416
5.0 3.354 3.934 4.324 1.636 2.663 1.736
7.5 5.027 5.259 5.957 1.155 2.733 2.246
10.0 6.882 6.531 7.230 -O.707 1.636 2.463
15.0 12.671 10.073 11.240 -5.860 -3.827 3.625
20.0 16.281 11.157 12.814 -9.082 -7.230 4.519
30.0 18.014 7.980 8.932 -13.754 -12.742 3.544
40.0 14.705 3.796 5.137 -13.681 -12.887 2.862
50.0 11.879 1.736 2.007 -11.663 -11.591 1.000

75.0 8.460 O O -8.460 -8.460 0

100.0 6.054 O 0 -6.054 -6.054 O
1M market model: I = market model with 50% index effect:

V valuation model: Z = zero model.

69

 

 

 

Table 34. Difference in means statistics May, 1976,
for left-hand tail tests.
Model Comparison1
Effect
% MI MV MZ IV IZ V2
0 0 1.000 0 1.000 0 -1.000
-0.5 0 1.736 1.416 1.736 1.416 -1.000
-1.0 1.000 1.736 1.736 1.416 1.416 0
-1.5 0 1.736 1.736 1.736 1.736 0
-2.0 1.000 1.343 1.343 1.000 1.000 0
-3.0 1.736 2.463 2.463 1.736 1.736 0
-4.0 1.736 2.851 2.663 2.246 1.636 -1.000
-5.0 3.194 3.507 3.796 1.000 2.007 1.416
-7.5 5.351 5.043 5.245 -0.378 -0.378 0
-10.0 8.460 7.817 7.568 -2.851 -3.354 -1.736
-15.0 13.539 8.557 8.465 -8.773 -8.855 -0.688
-20.0 14.926 7.400 7.144 -11.374 -11.449 -0.625
-30.0 17.372 6.054 5.760 -14.779 -15.000 -1.134
,-40.0 14.779 3.796 2.663 -13.754 -14.264 -2.345
-50.0 11.519 0 0 -11.519 -11.519 0
-75.0 7.315 0 0 -7.315 -7.315 0
-100.0 6.150 0 0 -6.150 -6.150 0
1M market model: I = market model with 50% index effect:

V

valuation model: Z = zero model.

70

 

 

 

Table 35. Difference in means statistics May, 1976,
for two tail tests with positive effects.
Model Comparison1
Effect
Z «MIV MV MZ IV IZ V2
0 0 2.246 , 2.007 2.246 2.007 -1.000
0.5 0 2.007 2.007 2.007 2.007 0
1.0 0 1.343 2.246 1.343 2.246 1.416
1.5 0 0.816 2.007 0.816 2.007 1.416
2.0 0 2.007 1.636 1.636 2.007 0
3.0 1.636 2.663 3.027 1.736 2.246 1.416
4.0 2.130 2.545 3.194 1.000 2.007 1.416
5.0 3.354 3.934 4.324 1.636 2.663 1.716
7.5 5.027 5.259 5.927 1.155 2.733 2.246
10.0 6.882 6.531 7.230 -0.707 1.636 2.463
15.0 12.671 10.073 11.240 -5.860 -3.827 3.625
20.0 16.281 11.157 12.814 -9.082 -7.230 4.519
30.0 18.014 7.980 8.932 -13.754 -12.742 3.544
40.0 14.705 3.796 5.137 -13.681 -12.887 2.862
50.0 11.879 1.736 2.007 -11.663 -11.591 1.000
75.0 8.460 0 0 -8.460 -8.460 0
100.0 6.054 0 0 -6.054 -6.054 0
1M = market model: I = market model with 50% index effect;
V = valuation model: Z = zero model.

71

 

 

 

3
II II

valuation model: Z = zero model.

Table 36. Difference in means statistics May, 1976,
for two tail tests with negative effects.
M0del Comparison1
Effect
% MI MV MZ IV IZ VZ
0 0 2.246 2.007 2.246 2.007 -1.000
-0.5 0 2.663 2.463 2.663 2.463 -1.000
-1.0 1.000 2.663 2.663 2.463 2.463 0
-1.5 -1.000 2.463 2.463 2.663 2.663 0
-2.0 1.000 2.130 2.130 1.895 1.895 0
-3.0 1.000 2.851 2.851 2.463 2.463 0
-4.0 0 2.851 2.663 2.851 2.345 -1.000
-5.0 2.320 3.507 3.796 1.636 2.463 1.416
-7.5 5.043 5.043 5.245 0 O 0
-10.0 8.460 7.817 7.568 -2.851 -3.354 -1.736
-15.0 13.539 8.557 8.465 -8.773 -8.855 -0.688
-20.0 14.926 7.400 7.144 -11.374 -11.449 -0.625
-30.0 17.372 6.054 5.760 -14.779 -15.000 -1.134
-40.0 14.779 3.796 2.663 -13.754 -14.264 -2.345
-50.0 11.519 0 0 -11.519 -11.519 0
-75.0 7.315 0 0 -7.315 -7.315 0
-100.0 6.150 O 0 -6.150 -6.150 0
market model: I = market model with 50% index effect:

72

 

 

Table 37. Difference in means statistics June, 1976,
for right-hand tail tests.
Model Comparison1
Effect
gz MI MV MZ IV .lZ VZ

0 0 -1.895 0 -1.895 0 2.246
0.5 1.000 -2.130 0.447 -2.345 . 0 2.663
1.0 1.416 -1.636 0 -2.130 -1.000 2.007
1.5 2.007 0 0.577 -1.636 -1.343 0.577

2.0 1.416 -0.816 -1.000 -1.416 -1.636 0
3.0 1.416 -2.130 -0.447 -2.545 -1.343 1.895
4.0 3.027 -1.388 0 -3.544 -2.733 1.667
5.0 3.934 -2.119 1.155 -4.588 -3.079 3.079
7.5 5.860 -3.184 0.632 -7.058 -5.660 3.934
10.0 7.980 -4.400 -0.816 -9.688 -8.302 4.324
15.0 12.455 -5.031 -1.134 ~14.558 -12.887 4.206
20.0 16.358 -3.574 -0.816 -17.852 -16.052 4.916
30.0 15.673 -1.736 -0.500 -16.128 -15.824 1.416
40.0 13.537 -1.736 -1.000 -13.754 ~13.681 1.000

50.0 11.230 -1.000 -1.000 -11.302 -11.302 0

75.0 7.652 0 0 -7.652 -7.652 0

100.0 6.150 0 0 -6.150 -6.150 0

 

zero model.

market model: I = market model with 50% index effect:
valuation model: Z =

 

73

 

 

Table 38. Difference in means statistics June, 1976,
for left-hand tail tests.
Model Comparison
Effect
% MI MV MZ IV IZ VZ
O 0 1.416 1.416 1.416 1.416 0
-0.5 1.000 2.007 2.007 1.736 1.736 0
-1.0 1.000 2.246 2.246 2.007 2.007 0
-1.5 1.416 2.463 2.463 2.007 2.007 0
-2.0 1.736 2.851 2.345 2.246 1.636 -1.000
-3.0 1.736 3.194 3.194 2.663 2.663 0
-4.0 1.736 3.354 3.354 2.851 2.851 0
-5.0_ 2.851 4.198 4.198 3.027 3.027 0
-7.5 5.137 6.338 6.338 3.507 3.507 0
-10.0 7.400 9.158 9.311 4.802 5.027 1.000
-15.0 12.598 14.337 14.337 5.027 5.027 0
-20.0 16.822 16.822 17.056 0 0.727 0.904
-30.0 17.934 12.313 11.807 -9.462' -9.989 -2.511
-40.0 14.045 6.614 6.614 -11.157 -11.157 0
-50.0 11.519 4.198 4.324 -10.281 -10.208 1.000
-75.0 7.125 1.000 1.000 -8.302 -8.302 0
-100.0 6.150 0 0 -6.150 -6.149 0

 

market model: I
valuation model;

= market model with 50% index effect:

Z = zero model.

74

 

 

 

Table 39. Difference in means statistics June, 1976,
for two tail tests with positive effects.
Model Comparison
Effect
Ml, MV MZ IV IZ VZ

O O -1.000 0.816 -1.000 -1.000 2.246
0.5 1.000 -1.266 1.134 -1.510 0.816 2.663
1.0 1.416 --0.707 0.707 -1.266 O 2.007
1.5 1.343 0.577 1.000 -0.707 0.378 0.577

2.0 0.577 -0.378 -0.447 -O.632 -O.707 0
3.0 1.416 -1.667 O -2.119 -O.816 1.896
4.0 2.545 -1.388 O -3.184 -2.320 1.670
5.0 3.544 -2.119 1.155 -4.279 -2.691 3.079
7.5 5.571 -3.184 0.632 -6.801 -5.365 3.934
10.0 7.740 -4.400 -0.816 -9.466 -8.066 4.324
15.0 12.455 -5.031 -1.134 -14.558 -12.887 4.206
20.0 16.358 ~3.574 -0.816 -17.852 -16.052 4.916
30.0 15.673 -1.736 -0.500 -16.128 -15.824 1.416
40.0 13.537 -1.736 -1.000 -13.754 -13.681 1.000

50.0 11.230 -1.000 -1.000 -11.302 -11.302 0

75.0 7.652 0 0 -7.652 -7.652 0

100.0 6.150 O O -6.150 -6.150 O
1M market model: I = market model with 50% index effect:

valuation model:

Z = zero model.

75

 

 

 

Table 40. Difference in means statistics June, 1976,
for two tail tests with negative effects.
Model Comparison1
Effect
% MI MV MZ IV IZ VZ
O O -1.000 0.816 -1.000 0.816 2.246
-O.5 1.000 0 1.416 -0.333 1.134 2.007
-1.0 1.000 0.904 1.903 0.632 1.670 1.736
-1.5 0.577 1.670 2.545 1.416 2-345 1.736
-2.0 0 2.119 2.545 2.345 2.545 0.577
-3.0 -0.378 2.320 2.733 2.511 2.910 1.000
-4.0 O 2.511 2.910 2.511 2.910 1.000
-5.0 1.510 4.198 4.198 3.507 3.507 0
-7.5 4.820 6.064 6.338 3.240 3.654 0.577
-10.0 7.151 9.158 9.311 4.916 5.137 1.000
-15.0 12.385 14.278 14.337 5.137 5.137 0
-20.0 16.144 16.365 16.596 0.301 0.943 0.904
-30.0 17.240 12.313 11.807 -8.809 -9.365 -2.511
-40.0 13.756 6.614 6.614 -10.732 -10.732 0
-50.0 11.446 4.198 4.324 -10.063 -9.989 1.000
-75.0 8.302 1.000 1.000 -8.222 -8.222 0
-100.0 6.054 0 0 -6.054 -6.054 0
1 market model: I = market model with 50% index effect:

3
II II

valuation model; Z = zero model.

76

 

 

 

 

valuation model: Z = zero model.

Table 41. Difference in means statistics July, 1976,
for right-hand tail tests.
Model Comparison
Effect
MI MV MZ IV IZ VZ

0 0 2.463 2.463 2.463 2.463 0

0.5 0 2.663 2.663 2.663 2.663 0

1.0 1.000 2.851 2.851 2.663 2.663 O

1.5 1.000 3.027 3.027 2.851 2.851 0

2.0 2.007 3.654 3.654 3.027 3.027 0

3.0 1.000 3.934 3.934 3.796 3.796 0
4.0 2.007 4.324 3.654 3.796 3.027 -2.246
5.0 2.851 4.568 3.796 3.507 2.463 -2.463
7.5 4.916 5.957 5.245 3.194 1.343 -2.663
10.0 7.652 8.381 7.652 3.027 0 -3.027
15.0 13.031 12.455 10.575 -2.545 -6.054 -5.245
20.0 15.976 12.383 10.211 -7.400 -9.613 -5.455
30.0 17.611 8.773 6.977 -12.671 ~14.118 -4.568
40.0 14.191 4.687 3.395 -12.671 -13.247 -2.545
50.0 11.663 3.027 2.663*-11.012 -11.157 -1.416

75.0 8.061 O O -8.061 -8.061 0

100.0 6.150 O O -6.150 -6.150 0
market model: I = market model with 50% index effect:

 

77

Table 42. Difference in means statistics July, 1976,
for left-hand tail tests.

Model Comparison1

 

 

Effect
% MI MV MZ IV IZ VZ
0 0 0 0 0 0 0
-0.5 0 0 0 0 0 0
-1.0 0 1.000 1.000 1.000 ’1.000 0
-1.5 0 0 1.000 0 1.000 1.000
-2.0 0 0 0 0 0 0
-3.0 1.736 1.416 1.736 -1.000 0 1.000
-4.0 1.736 1.416 2.007 -0.577 1.000 1.416
-5.0 1.000 0.577 2.007 0 1.736 1.736
-7.5 4.687 3.026 4.916 -3.027 1.416 3.354
-10.0 7.899 4.472 7.899 -5.760 0 5.760

-15.0 14.411 6.231 12.598 -11.230 -4.932 9.386
-20.0 18.505 7.170 11.735 -14.631 -10.432 7.980
-30.0 16.900 3.654 6.431 -15.900 -14.045 4.932
-40.0 14.045 2.246 3.194 -13.681 -13.320 2.246
-50.0 11.951 1.416 2.246 -11.807 -11.591 1.736

 

‘7500 7.057 O 0 ’70057 “7.057 0
‘10000 6.054 O 0 -60054 '60054 O
1M = market model: I = market model with 50% index effect:
V = valuation model; Z = zero model.

78

 

 

 

valuation model:

Z = zero model.

Table 43. Difference in means statistics July, 1976,
for two tail tests with positive effects.
Model Comparison1
Effect
% MI MV MZ IV IZ VZ

0 0 2.463 2.463 2.463 2.463 0

0.5 O 2.663 2.663 -28663 2.663 0

1.0 1.000 2.851 2.851 2.663 2.663 0
1.5 1.000 3.027 3.194 2.851 3.027 1.000
2.0 2.007 3.654 3.796 3.027 3.194 1.000

3.0 1.000 4.067 4.067 3.934 3.934 0
4.0 1.343 4.324 3.654 3.934 3.194 -2.246
5.0 2.345 4.568 3.796 3.654 2.663 -2.463
7.5 4.916 5.957 5.245 3.194 1.343 -2.663
10.0 7.652 8.381 7.652 3.027 0 -3.027
15.0 13.031 12.455 10.575 -2.545 -6.054 -5.245
20.0 15.976 12.383 10.211 -7.400 -9.613 -5.455
30.0 17.611 8.773 6.977 -12.671 -14.118 -4.568
40.0 14.191 4.687 3.395 -12.671 -13.247 -2.545
50.0 11.663 3.027 2.663 -11.012 -11.157 -1.416

75.0 8.061 O 0 -8.061 -8.061 0

100.0 6.150 0 O -6.150 -6.150 0
market model: I = market model with 50% index effect:

 

79

 

 

 

Table 44. Difference in means statistics July, 1976,
for two tail tests with negative effects.
Model Comparison1
Effect
% MIgfi MV MZ IV IZ VZ

0 0 2.463 2.463 2.463 2.463 0

-0.5 0 2.246 2.246 2.246 2.246 0

-1.0 0 2.463 2.463 2.463 2.463 0
-1.5 -1.736 1.416 1.736 2.246 2.463 1.000

-2.0 -1.736 1.416 1.000 2.246 1.895 0
-3.0 0.447 1.736 2.007 1.000 1.736 1.000
-4.0 0.447 1.416 2.007 0.447 1.736 1.416
-5.0 -O.577 0.577 2.007 0.816 2.246 1.736
-7.5 4.347 3.184 5.027 -2.119 2.007 3.354
-10.0 7.657 4.701 7.980 -4.922 0.707 5.469
-15.0 14.193 6.321 12.671 -10.806 -4.354 9.386
-20.0 17.786 7.170 11.735 -13.990 -9.812 7.980
-30.0 16.668 3.654 6.431 -15.676 -13.829 4.932
~40.0 13.829 2.246 3.194 -13.990 -13.105 2.246
-50.0 11.951 1.416 2.246 -11.807 -11.591 1.736

-75.0 7.057 0 0 -7.057 -7.057 0

-100.0 6.054 0 0 -6.054 -6.054 0

 

7
.a.
II II

market model: I
valuation model: Z = zero model.

= market model with 50% index effect:

 

80

 

 

 

valuation model: Z = zero model.

Table 45. Difference in means statistics August, 1976,
for right-hand tail tests.
Model Comparison1
Effect
z MI MV MZ IV :2 vz
0 O 2.663 2.663 2.663 2.663 0
0.5 1.000 3.027 3.027 2.851 2.851 0
1.0 1.416 3.354 3.354 3.027 3.027 0
1.5 0 3.507 3.354 3.507 3.354 -1.000
2.0 1.000 3.654 3.354 3.507 3.194 -1.416
3.0 2.851 4.324 4.198 3.194 3.027 -1.000
4.0 3.354 5.137 4.802 3.796 3.354 -1.736
5.0 3.194 5.245 4.802 4.067 3.507 -2.007
7.5 6.431 7.725 7.485 3.934 3.240 -1.736
10.0 7.400 8.695 ”7.980 4.067 2.119 -3.027
15.0 11.446 11.663 10.575 1.000 -3.240 -3.934
20.0 16.128 13.827 128023 -5.760 -7.980 -5.137
30.0 16.900 10.208 8.539 ~10.648 -12.239 -4.802
40.0 13.827 5.860 4.094 -11.519 -12.527 -3.796
50.0 11.302 3.354 2.545 -10.501 -10.721 -1.736
75.0 7.980 0 0 -7.980 -7.980 0
100.0 6.245 0 0 -6.245 -6.245 0
market model: I = market model with 50% index effect:

 

81

 

 

Table 46. Difference in means statistics August, 1976,
for left-hand tail tests.
Model Comparison1
Effect
% MI MV MZ IV IZ VZ
O 0 1.000 1.416 1.000 1.416 1.000
-0.5 0 1.000 1.416 1.000 1.416 1.000
-1.0 0 1.000 1.000 1.000 1.000 0
-1,5 0 0 1.000 0 1.000 1.000
-2.0 1.416 1.416 1.000 O 0 0
-3.0 1.000 1.000 2.007 O 1.736 1.736
-4,0 2.007 1.736 2.246 -1.000 1.000 1.416
-5.0 2.246 0.447 2.246 -2.007 0 2.007
-7.5 4.916 3.544 4.907 -2.733 0 3.027
-10.0 7.057 2.427 6.970 -5.860 -0.378 5.760
-15.0 13.754 4.111 9.688 -11.735 -7.980 7.322
-20.0 16.667 2.713 9.462 -15.523 -11.157 8.302
-30.0 18.176 3.544 5.660 -17.056 -15.825 4.067
-40.0 14.779 1.000 3.354 -14.705 -13.973 3.194
-50,0 11.084 0 0 -11.084 -11.084 0
-75.0 7.652 0 0 -7.652 -7.652 0
~100.0 6.150 O 0 -6.150 -6.150 0

 

3’
II II

market model: I
valuation model:

= market model with 50% index effect:

Z = zero model.

82

 

 

 

valuation model: Z = zero model.

Table 47. Difference in means statistics August, 1976,
for two tail tests with positive effects.
Model Comparison1
Effect
2 MI MV MZ IV IZ VZ
0 0 3.027 2.851 3.027 2.851 1.000
0.5 1.000 3.026 3.194 2.851 3.027 1.000
1.0 1.416 3.354 3.654 3.027 3.354 1.416
1.5 0 3.079 3.507 3.079 3.507 0.577
2.0 1.000 3.240 3.507 3.079 3.354 0
'3.0 2.345 3.962 4.198 3.194 3.194 0
4.0 3.345 5.137 4.802 3.796 3.354 £1.736
5:0 3.194 5.245 4.802 4.096 3.507 -2.007
7.5 6.431 7.735 7.485 3.934 3.240 -1.736
10.0 7.400 8.695 7.980 4.067 2.119 -3.027
15.0 11.446 11.663 10.575 1.000 -3.240 -3.934
20.0 16.128 13.827 12.023 -5.760 -7.980 -5.137
30.0 16.900 10.208 8.539 -10.648 -12.239 -4.802
40.0 13.827 5.860 4.094 -11.519 -12.527 -3.796
50.0 11.302 3.354 2.545 -10.501 -10.721 -1.736
75.0 7.980 0 0 -7.980 -7.980 0
100.0 6.245 0 0 -6.245 -6.245 0
market model: I = market model with 50% index effect:

 

83

 

 

Table 48. Difference in means statistics August, 1976,
for two tail tests with negative effects.
Model Comparison1
Ef%eCt MI MV MZ IV IZ VZ
0 0 2.851 3.027 2.851 3.027 1.000
-0.5 0 2.663 2.851 2.663 2.851 1.000
-1.0 -1.416 2.246 2.246 2.663 2.663 0
-1,5 -1.416 1.416 1.736 2.007 2.246 1.000
-2.0 0.577 2.246 1.636 2.007 1.343 -0.577
-3.0 -0.577 1.416 2.246 1.736 2.463 1.736
-4.0 1.343 2.007 2.463 0.577 1.736 11.416"
-5.0 1.636 0.816 2.463 -0.816 .1.416 2.007
-7.5 4.916 3.688 5.027 -2.320 0.447 3.027
-10.0 6.801 2.427 6.970 -5.571 0 5.760
-15.0 13.754 4.218 9.688 -11.521 -7.980 7.083
-20.0 16.667 2.850 9.537 -15.300 -10.942 8.302
-30.0 17.934 3.544 5.660 -16.823 -15.600 4.067
-40.0 14.559 1.000 3.354 -14.486 -13.756 3.194
-50.0 10.868 0 0 -10.870 -10.870 0
-75.0 7.652 0 0 -7.652 -7.652 0
-100.0 6.150 0 0 -6.150 -6.150 0

1

 

I

.-

<7

market model: I
valuation model: Z = zero model.

= market model with 50% index effect:

84

value is greater than or equal to 1.96 (a = .05).

The order of the models listed in the column headings
show how the comparisons were made. For example, IV
means that I was the Xi variable and V was the Yi variable
in computing Di = Xi - Yi (see Procedures, Part A). Thus,
in Table 25, the difference in means statistic of 2.851
in the column IV and in the row of 0% effect implies that
the probability of rejecting H6 by I is significantly
greater than the probability of rejecting H5 by V. However,
the difference in means statistic of -3-483 in the column
IV and in the row of 10% effect.implies that the probability

of rejecting H5 by V is significantly greater than the

probability of rejecting H5 by I.

In making power comparisons between two tests it is
important that the true level of significance in the two
tests be the same or at least nearly the same. Increasing
the true a level increases the power of the test (Chou,
1969, Chapter 10). Thus, one test may appear more powerful
than another test simply because the first test has a higher
true a level than the second test.

The observed a levels for each of the models in this
study was determined by examining the proportion of rejec-
tions of H6 in the sample of.457 firms when the simulated
effect was 0% (as defined in Procedures, Part A). These
observed 0 levels were compared using the difference in

means statistic to determine whether the true a levels

of two models were significantly different from one another.

85

That is, H8 was tested with DRit* = 0 as described in
Procedures, Part A. The results of these comparisons are
reported in Table 25 through Table 48 in the rows for 0%
accounting policy decision effects.

All power and a level comparisons are summarized
in Table 49 through Table 52. For models whose true 0
levels were not significantly different from each other,
power comparisons were made at each level of simulated
accounting policy decision effects. These power comparisons
,are classified into three categories based on the difference
in means statistic: greater, less, and equal. The order
of listing of the models in the comparison column of Table
49 through Table 52 tells how the power comparisons were
made. For example, in comparison MI, the comparisons are
reported as M has "greater" power than L: M has "less"

power than I: and M and I have "equal" power.

For models whose true 0 levels were significantly

different from each other (H6 was rejected when DRit* 0),
power comparisons could be made at only certain levels of
simulated accounting policy decision effects. Suppose

model A had a significantly greater 0 level than model B.
Then for simulated effects where model A had a significantly
greater probability of rejecting H6 than model B, the
simulated effects are reported as not comparable in Table

49 through Table 52. However, if model B had a signifi-
cantly greater probability of rejecting H6 than model A,

model B was considered more powerful. Similarly, if model

 

 

 

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94
B did not have a significantly different probability of
rejecting H5 than model A, the power of model B was consid-
ered equivalent to that of model A. For example, examine
the IV comparison for March, 1976, in Table 49. I had a
significantly greater 0 level than V. However, V was con-
sidered more powerful than I for the simulated effect
levels of 10 to 100%.

Also reported in Table 49 through Table 52 is the
length of the 95% confidence interval for the difference
in the true a levels. The largest confidence interval
for <1 levels which were not significantly different has
length 2.574% (MV and IV comparisons in two tail tests for
June). Most of the confidence intervals for a levels which
were not significantly different have length less than 1%
Thus, for a levels which were not significantly different,
the true a levels appear sufficiently close to make valid
power comparisons at all levels of simulated accounting
policy decision effects.

Examination of Table 49 reveals that in right-hand
tail tests, M has significantly more power than I when the
accounting policy decision effect.is as small as 1% per firm
(see March) and M has significantly greater power than I
in every event month at accounting policy decision effect
levels of 2 4%. Thus, a 50% market index effect can have
a significant impact on the detection of even small account-
ing policy decision effects.

V has significantly more power than M for certain

95

simulated effect levels for June, 1976. But, for the most
part, power comparisons could not be made between V and M.

V has significantly more power than I when the account-
ing policy decision effect is as small as .5% per firm
(see June) and V has significantly greater power than I in
every event month at accounting policy decision effect
levels of 2 20%. This is true even though I has a signifi-
cantly greater true a level than V in every event month
except June.

While Z and M have equal power in the one event month
in which all simulated effect levels could be compared
(see June), Z has significantly greater power than I
when the accounting policy decision effect is as small as
4%. Z has significantly greater power than I in every
event month at accounting policy decision effect levels
2 15%. As with V, this is true even though I has a signifi-
cantly greater true a level in five of the six event months.

Finally, comparisons of V and.Z reveal that one model
is not clearly more powerful than the other model.

Examination of Table 51 for positive effects in two
tail tests leads to observations similar to those made for
right-hand tail tests. The one major difference being
in comparisons between M and V. Now, M has significantly
more power V for certain simulated effect levels for April,
1976, while V still has significantly more power than M
for certain simulated effect levels for June, 1976. Thus,

the dominance of one model over the other is not established

 

96
in a two tail test.

Examination of Table 50 reveals that in left-hand
tail tests, M has significantly more power than I when the
accounting policy decision effect is as small as l-4%l per
firm and M has significantly greater power than I in every

event month at accounting policy decision effect levels of

[-7.5%

 

. M is more powerful than V or Z for certain
simulated levels of accounting policy decisions in every
event month examined.

As with the right-hand tail tests, both V and Z exhibit
more power than I for sufficiently large effects in absolute
value in every event month. However, there do exist
occurences<mf Iexhibiting more power than V and Z at some
of the smaller simulated effect levels in absolute value
for some of the event months. Finally, V tends to be more
powerful than Z in left-hand tail tests.

Examination of Table 52 for negative effects in two
tail tests leads to observations similar to those for left-
hand tail tests although fewer comparisons can be made.

That is, M tends to be more powerful than I, V, or Z.

V and Z are more powerful than I for sufficiently large
effects in absolute value in every event month. V tends to
be more powerful than Z.

The implications for an accounting researcher of the
results of this study at this point are the following.
In right-hand tail tests both V and Z are more powerful

than I based on the one month (June) in which the true a

97

levels of the models were not significantly different from
one another. This conclusion is supported by the other
five event months in which V and Z had smaller true a
levels than I. In these months V and Z were still more
powerful than I for a wide range of accounting policy
decision effects. There are too few power comparisons to
choose between M and V or M and Z. An accounting researcher
could use V or Z since they seem to have about the same
power in right-hand tail tests.

In left-hand tail tests I is more powerful than both
V and Z when the accounting policy decision effect is less
than about [-5%l. V seems more powerful than I for account-
ing policy decision effects greater than about I-5%I.
Z seems more powerful than I for accounting policy decision
effects greater than about [410%]. V is more powerful than
Z while M is more powerful than both V and Z.

In two tail tests both V and Z are more powerful than
I for accounting policy decision effects larger than about
[15%l. This is true even though I has a significantly
larger true a level than V in four of the six months (except
April and June) and I has a significantly larger true a
level than Z in five of the six months (except June). There

are not clear conclusions regarding other power comparisons.

B. Levels of Significance
Examination of Tables 1 through 24 reveals that

many of the observed levels of significance are

98
significantly different from the specified levels of
significance. For one tail tests if the number of rejec-
tions of H5 when shit = o for all 1 falls between 4.88
and 17.97, the observed level of significance is not
significantly different from .025. For two tail tests,
if the number of rejections of H6 when shit = O for all
i fall between 13.72 and 31.98, the observed level of
significance is not significantly different from .05.
These calculations are based on the normal approximation
to the binomial distribution (a = .05).

Table 53 summarizes the number of event months in
which the observed a level is not significantly different
from the specified a level. Only the observed a levels
for the market model in a right-hand tail test tend to
correspond to the specified a levels. Further, in every
case in which the observed 0 levels are significantly
different from the specified a levels, the observed a levels
are significantly smaller than the specified a levels.
Hence, the individual firm t-tests tend to be conservative
in terms of the true levels of significance. However,
conservative levels of significance make it more difficult
to reject the null hypothesis since there is a direct
relationship between the level of significance and the
power of the test. Hence, it is desirable to obtain the
specified a levels in actual tests.

The d adjustment procedure (described in Procedures,

Part B) was applied to each event month in this study

99

Table 53. Observed vs. specified a levels.

Number of cases out of 6 in which the
observed a level is not significantly
different from the specified a level

 

 

 

1 Right-hand Left—hand Two
Model ' Tail Tail Tail
M or I 5 O 1
V 2 O 1
Z 2 O O
1M = market model; I = market model with 50% index effect;
V = valuation model; Z = zero model.

Table 54. Adjusted vs. specified a levels.

Number of cases out of 6 in which the
adjusted a level is not significantly
different from the specified a level

 

 

 

1 IHight-hand Left-hand Two
Model Tail Tail Tail
M or I 5 6 ‘ 5
V 4 4 4
Z 4 A 4
1M = market model; I = market model with 50% index effect;
V = valuation model; Z = zero model.

100
using the other five eVent months to compute the average a
adjustment factor. Table 54 summarizes the number of
event months in which the adjustedcxlevel is not signifi-
cantly different from the specified a levels. While the
adjustment procedure is not 100% effective, it does
considerably better in obtaining the specified 0 levels than
when the levels are not adjusted.

Tables 55 and 56 report respectively the average
number of rejections of H5 when fifiit = 0 for all i over
the six event months when the 0 levels are not adjusted and
when a levels are adjusted. Recall that for the right and
left-hand tail tests the number of rejections of the null
hypothesis at a specified a level of .025 should be about
11. For a two tail test the number of rejections of the
null hypothesis at a specified a level should be about 23.
In every case reported in Tables 55 and 56 the average
of the number of rejections is closer to the proper number
when the a levels are adjusted than when the 0 levels are
not adjusted.

Hence, on average the a level adjustment procedure
does better in obtaining the specified a levels than not
adjusting the a levels. However, there are periods in
which the observed a level after adjustment was signifi-
cantly different from the specifed a level. .Further,
unlike the unadjusted a levels, the true a level after
adjustment may be unconservative. There are six occur-

rences of unconservative d levels in right and left-hand

101

Table 55. Average number of rejections-u-a levels not

 

adjusted.

1 Bight-hand Left-hand Two
Model Tail Tail Tail
M or I 9.67 1.50 11.17

V 5.33 0.67 ’ 6.00
Z 4.67 0.50 5.17

 

1 market model: I = market model with 50% index effect;
valuation model; Z = zero model.

3
II II

Table 56. Average number of rejections-u-a levels adjusted.

 

 

1 Right-hand Left-hand Two
Model Tail Tail Tail
M or I 10.50 12.00 22.50
V 13.50 12.50 26.00
Z 13.00 13.50 26.50
1M = market model; I = market model with 50% index effect;
V = valuation model; Z = zero model.

102
tail tests. The observed rejections of the null hypothesis

in these cases were: 38, 32, 29, 23, 20, and 20.
There are two implications for an accounting research-
er. First, for all the models examined in this study,
the true a levels tend to be smaller than the specified
0 levels. Conservative 0 levels make it more difficult
to reject H6. Second, on average the a adjustment procedure
described in this study will approximate the specified
a level although there may be occurrences of unconservative

true 0 levels.

0. Market Index Effects

The purpose of this section is to determine the
magnitude of market index effects which make the valuation
and zero models as powerful as the market model. The
method of analysis is explained in Part C of Procedures.

Table 57 reports the average standard errors of the
457 firms. Also reported in Table 57 are the corresponding
critical values, i.e., the size in absolute value (the t
distribution is symmetric) of the accounting policy decision
effect which would be required to just reject H5. Table
58 reports, using the average critical values for the
six event months, how large the market index effect would
have to be in order for the valuation or zero model to
be equally effective in detecting DRit'

For hypothetical firms with bi 2 1.00, the valuation

model is more effective than the market model when the

Table 57.

103

Average standard errors and corresponding
critical values.

 

 

 

 

 

Month Average Standard Errors1 Critical Values1
(1976) M v z M v z
March 0.0879 0.1088 0.1110 0.1759 0.2179 0.2221
April 0.0879 0.1088 0.1110 0.1760 0.2179 0.2221
May 0.0879 0.1090 0.1110 0.1761 0.2182 0.2221
June 0.0881 0.1087 0.1110 0.1764 0.2177 0.2221
July 0.0879 0.1086 0.1110 0.1759 0.2177 0.2221
August 0.0879 0.1086 0.1110 0.1760 0.2175 0.2221

‘6:month -
Average 0.0879 0.1087 0.1110 0.1760 0.2178 0.2221
1M = market model; V = valuation model; Z = zero model.

 

 

Table 58. Market index effects--d levels not adjusted.
The size of p. which makes the‘
valuation or zero model as power-
ful as the market model for hypo-
thetical firms
bi Valuation Zero
0.25 0.7673 0.8294
0.50 0.3836 0.4147
0.75 0.2558 0.2765
1.00 0.1918 0.2074
1.25 0.1534 0.1659
1.50 0.1279 0.1382
1.75 0.1096 0.1185
2.00 0.0959 0.1037

 

104

index effect is greater than or equal to about 19.2%.
Similarly, the zero model is more effective than the market
model when the index effect is greater than or equal to
about 20.7%. Implicit in the comparisons in Table 57
and Table 58 is that each model has the same a level. Based
on the empirical results of Part A of Results, the market
model tends to have a higher a level than both the valuation
and the zero model. Hence, the results are slightly
biased in favor of the market model.

It is interesting to look at these comparisons
when the 0 levels are nearly the same. This is accomplished
by adjusting the critical values listed in Table 57 for
the average a adjustment factor over the six event months.
The average a adjustment factors are listed in Table 59.
Recall that the a adjustment factor is that amount which
would need to be added to each firm's abnormal return
to observe 11 rejections out of 457 firms when the simulated
accounting policy decision effect is zero.

Table 60 reports the average critical values with the
a levels adjusted. While the market model is still the
most powerful, its advantage over the other two models
has been significantly reduced- Also, the valuation model
is more powerful than the zero model in right-hand tail
tests and less powerful in left-hand tail tests.

The left-hand tail results for the valuation and
zero model are the opposite of the findings of Part A

of Results. Recall that the results here are based only

105

 

 

 

 

 

 

 

 

Table 59. Average 0 adjustment factors over 6 months.
Right-hand Left-hand
Model Tail Tail
market 0.0025 -0.0422
valuation 0.0367 -0.0663
zero 0.0353 20.0809
Table 60. Average critical values--d levels adjusted.

, Right-hand Left-hand
Model Tail Tail
market 0.1736 -O.1337
valuation . 0.1812 -0.1515
zero 0.1868 -0.1412

Table 61. Market index effects--d levels adjusted.

The size of p. which makes the valuation or

zero model aslpowerful as the market model for

hypothetical firms if

Right-hand Tail Left-hand Tail

bi Valuation Zero Valuation Zero
0.25 0.1674 0.2835 0.4696 0.2112
0.50 0.0837 0.1418 0.2348 0.1056
0.75 0.0558 0.0945 0.1565 0.0704
1.00 0.0419 0.0709 0.1174 0.0528
1.25 0.0335 0.0567 0.0939 0.0422
1.50 0.0279 0.0472 0.0783 0.0352
1.75 0.0239 0.0405 0.0671 0.0302
2.00 0.0209 0.0354 0.0587 0.0264

 

106
on a hypothetical average firm. Further, the shape of
distribution of the abnormal returns has been removed
from this analysis. These comments also apply to compari-
sons between the market model and the other models.

In any case, the size of the index effect which would
make the valuation models and zero models equally effective
has been reduced after taking into account the a levels
as reported in Table 61. Thus, for hypothetical firms with
b1 2 1.00, the valuation model is more effective than
the market model when the index effect is greater than or
equal to about 4.2% in right-hand tail tests and 11.7%
in left-hand tail tests. Similarly, the zero model becomes
more effective than the market model when the index effect
is greater than or equal to about 7.1% in right-hand tail
tests and about 5.3% in left-hand tail tests. The
implication for an accounting researcher is that for firms
with b1 2 1.00 both the valuation model and zero model
can be more powerful than the market model for relatively

small index effects.

D. Testing Samples of Firms

There are several questions which tests on individual
firms can answer but tests on sample of firms cannot
answer. Individual firm tests can reveal which firms were
affected by an accounting policy decision. Examining the
affected firms can lead to a greater understanding of the

information preferences of investors. Individual firm tests

107

can reveal how many firms were affected by an accounting
policy decision as noted by Lev (1979, p. 498). Individual
firm tests can detect accounting policy decisions effects
whose average effect in a sample of firms is zero.
Individual firm tests can detect effects of accounting
policy decisions on a small number of firms which would
escape detection in examining the average accounting policy
decision effect in a large number of firms. However,
testing samples of firms is common in accounting literature
and was examined in part in this study.

Table 62 shows the average mean absolute prediction
error and the average mean square prediction error for
the three models during two different time periods. The
average MAPE and average MSPE are based upon two different
random samples of 20 firms each. Each model was used to
predict the monthly returns of the firms for the specified
time periods. The market model and valuation model were
estimated over the 60 month period immediately preceding
the six month prediction period. The market model is the
best predictor although the valuation model and zero model
do not predict a great deal worse. Appendix B discusses
numerous other models which were used to predict firm
returns. None of the models in Appendix B do significantly
better than the valuation model.

Table 63 shows the average prediction errors and their
standard errors for the sample of 457 firms used in the

individual firm t-tests. The average prediction errors

108

 

 

 

 

Table 62. Predictive ability, average of 20 firms.
MAPE MSPE
Model 7077533773 10/69-3/70 10 72-3 73 10 7-3 70
market 0.0662 0.0578 0.0085 0.0059
zero 0.0738 0.0669 0.0095 0.0076
valuation 0.0713 0.0697 0.0089 0.0079
Table 63. Average and standard error of prediction errors.
Market Model Valuation Model Zero Model
Month Standard Standard Standard
(1976) Average Error Average Error Average Error
March 0.0109 0.0042 0.0222 0.0042 0.0222 0.0041
April 0.0014 0.0037 -0.0367 0.0039 -0.0107 0.0038
May -0.0017 0.0032 -0.0092 0.0033 -0.0170 0.0033
June 0.0080 0.0038 0.0598 0.0039 0.0541 0.0038
July -0.0006 0.0034 -0.0207 0.0035 0.0012 0.0033
August 0.0014 0.0033 -0.0298 0.0033 -0.0093 0.0033

 

109
of the market models tended to be considerably smaller
than the average prediction errors of the valuation and
the zero models. However, the standard errors of all the
models are about the same which is consistent with the
models having about the same predictive power.

Table 64 reports the (T-1) statistics for each of
the models. At a level of significance of .05 in a two
tail test, a t-ratio of greater than or equal to 1.96
causes the null hypothesis to be rejected. All the models
tended to reject the null hypothesis too often since the
probability of observing two or more rejections at a level
of significance of .05 in a sample of six is .0328 based
on the binomial distribution and assuming that the six
samples are independent (Conover, 1971, p. 368).

Table 65 reports the (T-2) statistics for each of the
models. The statistic was computed for each event month
by using the average prediction errors of the other five
event months to compute the denominator. In this case, the
number of rejections is not too many since the probability
of observing one rejection is .2321 and for no rejections
it is .7351 (Conover, 1971, p. 368). The critical t-value
is 2.571 at a level of significance of .05 with five
degrees of freedom (Neter and Wasserman, 1974, p. 805).
Although the power of the models cannot be assessed since
the level of significance cannot be determined in such a
small number of trials, the market model would appear to

have the greatest power since the denominators of its

110

 

 

 

 

 

Table 64. (T-1) values.

¥$972) Market Model . Valuation Model Zero Model
March 2.6005 5.2905 5.3922
April 0.3877 -9.5130 -2.8435
May -O.5155 -2.8055 -5.1511
June 2.0864 15.4393 14.0597
July -0.1599 -5.9226 0.3664
August 0.4202 -8.9222 -2.8476
Table 65. (T-2) values.

Month Market Model Valuation Model Zero Model
(1976) Denominator (T-2) DenominatorfiKT:2) Benominator (T:2T
March 0.0038 2.8910 0.0356 0.6250 0.0262 0;8510
April 0.0061 0.2373 0.0331 -1.1107 0.0276 -0.3886
May 0.0061 -0.2721 0.0367 —0.2516 0.0269 -0.6329
June 0.0050 1.5940 0.0255 2.3459 0.0141 3.8472
July 0.0061 0.0896 0.0357 -0.5783 0.0280 0.0436
August 0.0061 0.2242 0.0344 -0.8658 0.0277 -0.3373

 

111

(T-2) statistic are by far the smallest.

Examination of Table 63 reveals that the reason that
the denominators of the market model's (T-2) statistics
are relatively small compared with the other models' (T-2)
statistics is that the average prediction errors of the
market model are relatively small compared with the other
models' average prediction errors. These observations led
to Theorem 1 (see Introduction). The essence of the proof
of Theorem 1 is that in a representative sample of firms,
the average accounting policy decision effect in the sample
is the same on average as the average accounting policy
decision effect in the market index times the average Bi in
the sample of firms which is 1. These terms cancel each
other out removing the entire accounting policy decision
effect from the average abnormal return.

This theorem is important, as stated in Corollary
1.1, to individual firm tests which employ the market model.
The importance of Corollary 1.1 is that it holds when
firm returns are affected by an accounting policy decision
in one direction.

The proof of the theorem also explains why one would
expect the average prediction errors of the market model
to be small. In a representative sample of n firms from

n 1 N 1-n 1
Z WRi = N 2 WR. - X b. .
i=1 j=1 i=1 1)

III-4

a population of N firms,

The tendency of the average prediction errors to be

greater than zero in Table 56 can be explained in part by

112
4 7

5
1 _ . .
the fact 457iE1bi - .917. HaVlng an average bi < 1 18

not surprising given the data requirements. One would
expect that those firms which do not survive on the New
York Stock Exchange very long also would tend to be the
riskier firms whose Bi's would tend to be greater than one.
Note that with an average bi of about .9, only about 10%

of the accounting policy decision effect would appear

in the abnormal return (subject to how representative the
sampled firms are of the population as a whole).

Theorem 1 and Corollary 1.1 are important to those
accounting researchers who may examine a representative
sample of firms from the New York Stock Exchange (NYSE).
Accounting researchers may wish to examine a representative
sample of firms when an accounting policy decision affects

all firms on the NYSE such as Accounting Principles Board

 

Opinion N3. 15 Earnings Per Shara (AICPA, 1980). Theorem
1 and Corollary 1.1 state conditions where the market
model will not generally aid in the detection of the
effects of those accounting policy decisions which affect

firm stock returns in one direction.

SUMMARY AND CONCLUSIONS

The primary purpose of this study is to compare the
power of three models in detecting the effects of account-
ing policy decisions on individual firm common stock returns.
The three models are the market model, the valuation model,
and the zero model.

The problem inherent in models which contain a stock
market index such as the market model is that the stock
market index may be affected by an accounting policy
decision. A major objective of this study is to try to
retain the entire effect of an accounting policy decision
in a firm's abnormal return. Hence, the market model
is examined when the market index is affected by DR as
well as when the market index is not affected by DR. In
the simulations in this study, the market index effect
is 50%. The equally weighted index is used in both forms
of the market model.

The power comparisons in this study are based on a
simulation procedure similar to that used by Brown and
Warner (1980). The simulation procedure is performed by
adding an artifical accounting policy decision effect,

DR, to actual firm stock returns for a randomly selected

set of months. Abnormal firm returns are examined

113

114
statistically to determine which model can best detect the
presence of the artificial accounting policy decision
effect.

The implications for an accounting researcher of
the simulation results are the following. In right-hand
tail tests both the valuation and zero models are more
powerful than the market model with a 50% index effect.

In left-hand tail tests the market model with a 50% index
effect is more powerful than both the valuation and

zero models when the accounting policy decision effect is
less than about l-5%l. The valuation model seems more
powerful than the market model with a 50% index effect

for accounting policy decision effects greater than about
l-5%I in left-hand tail tests. The zero model seems more
powerful than the market model with a 50% index effect for
accounting policy decision effects greater than about
l-10%I. In two tail tests both the valuation and zerO'
models are more powerful than the market model for account-
ing policy decision effects larger than about [15%].

The valuation model is more powerful than the zero
model in left-hand tail tests. The market model without
an index effect is more powerful than both the valuation
and zero models in left-hand tail tests. There are no
clear conclusions regarding other power comparisons.

The results of this study show that for all the
models the true levels of significance tend to be conserva-

tive in tests of H5. Hence, accounting researchers may

115

wish to adjust the levels of significance. One method of
adjusting levels of significance is described which does
better than not adjusting levels of significance in
achieving the specified levels of significance.

For hypothetical average firms with bi 2 1, the
valuation model becomes more powerful than the market
model when the index effect reaches a level of about
19%. For this same hypothetical firm, the zero model
becomes more powerful than the market model when the index
effect reaches a level of about 21%. After adjusting for
levels of significance, the valuation model becomes more
powerful than the market model when the market index effect
reaches a level of about 4%.in right-hand tail tests and
12% in left-hand tail tests. For the zero model the
comparable percentages are 7% in a right-hand tail test
and 5% in a left-hand tail test. The implication for an
accounting researcher is that for firms with bi 2 1.00
both the valuation model and zero model can be more powerful
than the market model for relatively small index effects.

Theorem 1 shows that on average the effects of an
accounting policy decision cannot be detected in a repre-
sentative sample of firms by examining the average abnormal
return of the sample when employing the market model with
an equally weighted index.

Corollary 1.1 shows that in a representaive sample
of firms, examination of abnormal returns in individual

firm tests based on the market model, with an equally

116

weighted index based on the population, is equivalent to
trying to detect a quantity which on average is zero
in the sample of firms. The importance of Corollary 1.1
is that it holds when firm returns are affected by account-
ing policy decision effects in one direction.

The overall results of this study lead to the following
comments for an accounting researcher who is interested
in detecting the effects of accounting policy decisions
on stock returns. There is little chance of detecting
accounting policy decision effects which occur in one
direction in representative samples of firms when using
the market model.

The market model seems to be the best choice of the
models examined in this study when market index effects
are expected to be very small. There is no conclusive
evidence in this study which shows that the zero or valuation
models are more powerful than the market model without
an index effect. Perhaps the best single comparison
of the market model with the other models is based on
Table 60. The market model has the smallest critical
values for both right and left-hand tail tests with the
0 levels adjusted. Yet, the advantage of the market
model with respect to the critical values over the zero and
valuation models is small as can be seen in Table 60.
Thus, the zero and valuation models become more powerful
than the market model for relatively small index effects

as can be concluded from examining Table 61.

117

Market index effects are more important with respect
to power for firms with larger bi's. Examination of
Table 61 suggests that an accounting researcher might
consider using the market model for firms with smaller
bi's and the valuation or zero model for firms with larger
bi's. An even more sophisticated approach would be to
compute both a market model and (say) a valuation model
for a given firm and then use that model which would be
more powerful on average after taking into account the
denominators of the t-ratios, the degrees of freedom,
the c adjustment factors, bi' and the likely size of the
market index effect.

There is need to improve models used to detect account-
ing policy decision effect on individual firms. For the
market model without an index effect and with the 0 levels
adjusted to about .025, an accounting policy decision effect
would have to be about 17.4% or larger to be detected in
a right-hand tail test and |-13.4%| or larger to be
detected in a left-hand tail test for the average firm
(see Table 60). Until improvement in models is accom-
plished, many accounting policy decision effects may not
be detected in individual firm tests applied on a monthly
basis.

If models cannot be easily improved with respect to
power, perhaps an accounting researcher should try to
suggest accounting policies to policy makers whose effects

on stock returns could be detected. That is, perhaps an

118
accounting researcher's time would be better spent by
taking a more direct role in developing accounting policies
which would have significant meaning to investors.

In any event, for market index effects as large as
50%, the valuation model and zero model are more powerful
than the market model in right-hand tail tests. Further,
they are more powerful than the market model with a 50%
index effect for larger accounting policy decision effects
in left-hand tail tests and in two tail tests.

Thus, both the valuation and zero models should aid
in the detection of accounting policy decision effects.
Improvement in detecting the effects of accounting policy
decisions should provide additional feedback to members

of policy making organizations.

APPENDICES

APPENDIX A-PROOFS

Lemma 1. Let pi be the ratio of the average accounting
policy decision effect on the returns of those firms
comprising the market index to the non-zero accounting
policy decision effect on the return of firm i. Let bi

be the estimate of Bi, the coefficient of the market index
in the market model for firm i. Then, bipi = 1 implies that
the abnormal return for firm i contains zero accounting
policy decision effect. This lemma applies as well to a

value weighted index.

Prggf. Let git = DRit + WRit
where: git = return of firm i in month t;
DRit = return of firm i in month t due to an
accounting policy decision;
WRit = return of firm i in month t due to all

causes except the accounting policy decision.

The market model is:

~ ~ ~

where: R
m

2
II

the number of firms in the market index;

the error term of firm i in month t;

0)
ll

Q
ll

intercept coefficient;

119

120
Bi = s10pe coefficient.
The predicted return of firm i in month t using the

market model is:

~ ~

Pit = a1 + biRmO

where: ai = the estimate of dis

b. = the estimate of 8..
l 1

Let the accounting policy decision effect take place

in month 0. Then the abnormal return for firm i in month

0, AiO’ is:

A10 = Rio ' PiO'

Substituting for Rio and Pio using the expressions from

~

above gives:

 

~ AiO = DRiO + WRi0 - ai - biRmO°
R can be written as:
m0
~ 1 N ~ 1 N (.. ~ )
R = r I R. - Z R. + WR.
m0 Nj=1 jO = Nj=1 jO jO
1 N ~ 1 N 4»
= - 2 DR. + - Z R. o
Nj=1 JO Nj=1 JO ~
Substituting for Rm0 in the previous equation for AiO
gives:
Ai0 - DRi0 + WRi0 - a - bifiji1 RJO - bifij§1 RjO'
By hypothesis,
N ~
1
M.§ R30
_ .1-1
pi - 08
i0
~ 1 N ..

121

~

Substituting for % Rjo in the previous equation for

3

"NZ

~ 1
Ai0 gives:

~ ~ ~

- ~ .1
A10 — DRiO + WR. - a. - bipiDRiO - b.N

By hypothesis bipi= 1. So,

~

AiO = WRiO - ai - b.- X RjO'

~

N
Lemma 2.‘ In a population of N firms, % 2 Bi = 1 and
i=1
1 N
fi 2 d. = 0 when the market index in the market model is
i=1 '

the equally weighted average of the returns of the N
firms. (For convenience, the "~" denoting random variables

will be omitted.)

 

 

 

 

l ._
Proof: Now, Bi = 1-1 by Fama (1976, p. 67).
N
var % Z R.]
i=1 3
Hence, - Z 8. — Z J
N. l N._
1:1 1‘1 [1 N ]
var - Z R.
Nj=1 j
1 N 1 N
= Z COV Rl'N Z R.
1 N i=1 3:1 3‘
Nvar N X R.
H 3

122

 

Mir? oov[R l
- 9

Ni=1 l Nj-

Also, by Fama (1976, p. 67),

N ]i
2 R.
-1 J

< > [‘N J
a. = E R - 8 E — R .
l Nj=1 j
N 1 N ( ) [1 N 1
Hence, 2 a. = - 2 E R. - B E - Z R.
i=1 1 Ni=1 1 1 Nj=1 J
1 N 1 ) [1 N 11 N
= - z E R. - E - 2 R.‘- z B.
Ni=1 1 Nj=1 3 Ni=1 1
1 N ‘ 1 N
=t.E We - nE E<Rj> = 0-
1-1 j—1

Theorem 1. On average in a representative sample of firms,
the market model, with an equally weighted index based

on the pOpulation, is unable to detect the effects of an
accounting policy decision when the statistic of interest
is the average abnormal return of the sample. (For
convenience, the "~" denoting random variables will be
omitted.)

2322;: Let n be the number of firms in the sample from

a population of N firms. The average abnormal return

using the market model is:

1 n 1 n 1 N
H 2 Ai = H z Ri + DR - u - Blfi 2 (WR + DR.)
i=1 i=1 j=1 J
n n n n N N
= % 2 WR. + i Z DRi - % Z oi - i 2 Bi % 2 WR. + % 2 DR.].
i=1 1 i=1 i=1 i=1 j=1 3 3:1 3
On average in a representative sample of firms:
1 n 1 N
— 2 WR. = fi 2 WR.;
ni=1 1 j=1 3
n N
% 2 DR. = 4 2 DR.:
i=1 1 j=1 J
n N
% Z ai = % Z 0.:
i=1 j=1 J
N
1 n 1
-2: B. =-2 Bo.
ni=1 1 Nj=1 J
1 N 1 N
By Lemma 2, fi 2 a. = O and fi 2 B. = 1.
11:13 j:1']
Thus,
1 n 1 N 1 N 1 N 1 N
- Z A. = fi 2 WR. + fi 2 DR - 0 - 1 fi 2 WR. + N 2 DR. = O.
ni=1 1 *j21 J 3:1 3:1 J 3:1 J

Corollary 1.1. In a representative sample of firms,
examination of abnormal returns in individual firm tests
based on the market model, with an equally weighted index
based on the population, is equivalent to trying to detect
a quanity which on average is zero in the sample of firms.
nggf. The accounting policy decision effect in the

abnormal return of firm i based on the market model is:

1
0- DRO.
1N3. 1 j

DRi - B

IIMZ

124

In a representative sample of n firms

1 n 1 N
H 2 DR. - BiN.E DR.

i 1 1 3 1 J
n N n
= 1 2 DR - § 2 DR.% 2 8.
ni=1 1 3:1 3 i=1 1
1 N 1 N
= - 2 DR. - — 2 DR. = 0.
Nj=1 J N3:1 3

Lemma 3. When applying ordinary least squares to the
valuation model, it is implicitly assumed that RKit and
Dit+1/Dit are constant for t = 2,...,T+1. T is the number
of consecutive time series observations used to estimate
the model.

33233. Since an assumption of ordinary least squares is

that the coefficients of the valuation model are constant:

 

 

[Dit+1RKit]

B. D.

12 _ lt _ _

E.—- —RKit+1 fort-1900091..

11 Dit+1RKit

D. RK.

it it+1
Thus, RKit is constant for t = 2,...,T+1.
Further,
D. RK. D.
Bi1:W=%w_fort=2,..o,T+1,
it‘ it+1 it

since RKi = RK for t = 2,...,T+1.

t it+1
Thus, Dit+1/Dit is constant for t = 2,...,T+1.

Theorem 2. In an ordinary least squares regression of

 

n + k observations, the coefficient of a dummy variable

125
that is 1 for period n + j and 0 for all other periods,
j = 1,...,k, is the abnormal return for period n + j
where the equation is estimated over n observations without
the k dummy variables.
23223. The ordinary least squares solution is that set

of coefficients, b0....,b , which minimizes:
p+k

n+k ~
Q = 1:1(Yi - BO - B1X1i - 82X2i -000- Bpoi
2
' Bp+1d1i ’ Bp+2d2i.‘:°*’ Bp+kdki)

where: Y = dependent variable:

X1,...,X = right-hand side variables excluding

P
dummy variables and the constant term:

p+1 S n;

d

ji 0 for i # n+j, j = 1,...,k;

d 1 for i

ii n+3. j =1.....k.

After substituting in Q the values of the dummy variables,

the first order conditions are:

-...- b X .)

n
22. - _ - - -
' 2 1 (Yi b0 b1X11 b2X2i p pl

880 i=1
n+k.

-2 Z Y. - b - b X o ‘ b X . '0..- b X o
'i=n+1( l 0 1 11 2 2i p pl

- bp+1-n) = O;

F

n

.2ii1x1iwi - b0 - b1X1i - b2X2i -...- prpi)
n+k

-2 z X1i(Y. - b - b
i=n+1 1

-bp+i-n) : O;

Q)
'm
.4

1X11 - b2X2i -000“ bpxpi

126

n
22...- - - - - -
33p 21§1Xpi(ri b0 h1X1i 62X2i ... prpi)
n+k
-2i=§+1xpi(Yi - b0 - b1X1i - bZiX2i -...- bpxpi
-bp+i-n) = O;
.22.. = - - - - -
38p+1 2(1n+1 b0 b1X1n+1 b2X2n+1 "‘
-prpn+1 - bp+1) = O;
a = -2(Y - b - b X — b X -
a8p+k n+k 0 1 1n+k 2 2n+k "'
- prpn+k - bp+k) = 0'
For p+i-n, i = n11,...,n+k, §§§9-— = 0 implies
p+i-n
= _ - _ _ _ 13(-
bp+i_n Y1 b0 b1X1i 62X2i ... prpi ( ).

The first order conditions (*) imply:

n
22. _ _ - _ _ _
380 ‘ 2.1 (Yi b0 b1X11 b2X2i °°°
1-1
"bX.)=O’
p pl
8. n
88p e '2iE1XPi(Yi - bO : b1X1i - 62X21 -...

- prpi) = 0,
which are the first order.conditions for n observations
when no dummy variables are present. Thus, the ordinary

least squares solution for b0....,bp is the same regardless

of the inclusion of k dummy variables. Further, the

127

coefficient of the n + jth dummy variable given by (*)
is the abnormal return for the n + jth observation,
j = 1,...,k.

The theorem holds regardless of the ordering of the
observations. The event periods, each represented by a
dummy variable, and the estimation periods can be inter-

mixed. The theorem also holds when 80 = O.

APPENDIX B-OTHER ECONOMETRIC MODELS

A. Sets of Variables

As stated in Part B of Procedures for tests on

~ ~

samples of firms, the ideal prediction is Pit = WRit
since then Kit = DRit which makes the accounting policy
decision directly observable. It was also argued that the
smaller the prediction errors, the easier it is to detect
the accounting policy decision effects.

Also, the objective is to predict WRit whether or

not it represents an equilibrium return or some other

concept such as the return expected by investors. Suppose

A. ~

WRit = ORit + ERit

where: ERit = equilibrium return;
ORit = other disequilibrium effects besides DRit'
And suppose that ERit could be predicted with certainty

by Pi *. Then,

t ~ ~ ~
Ait=1it‘PrJ ~ ~
= 9Fit + Qfiit 1 ERit ‘ it
= DRit + 0811.

~

The examination of Ait for DRit is confounded by ORit'

Hence, WRit is the relevent return to predict. Moreover,

~

an equilibrium model may not be able to detect DRit as

well as a model designed to predict WRi Thus, the

t.
128

129
predictive ability of regression models based on six sets
of variables was examined. It is assumed that DRit = O
for all i and t in these tests.

The first set of variables is listed in Table 66.
These variables were selected in the following manner.

A popular valuation model gives the market price of common
stock as a function of expected.dividends and discount rates
(Sharpe, 1981, p. 366). Hence, returns, which are primarily
a function of prices, are a function of expected dividends
and discount rates. Based on empirical work and interviews
with corporate executives, Sharpe claims that most firms
have a desired ratio of dividends to long-run earnings
(Sharpe, 1981, p. 371). Thus, expected dividends may be
viewed as a function of expected earnings. Alternatively,
Miller and Modigliani (1961) show that under perfect
markets, rational behavior, and perfect certainty, a firm
may be valued based directly on earnings and investments.
Thus, returns may be a function of earnings. The first
three variables listed in Table 66 may be associated with
expected earnings although the series should be more
appropriate for manufacturers than, for example, banks.

It is assumed that investors determine the appr0priate
discount rates by adjusting the future risszree interest
rates for risk (Haley and Schall, 1979, p. 191). Types
of risk include (Latané, Tuttle, and Jones, 1975, pp. 240-
243; Stevenson and Jennings, 1976, pp. 106-109): interest

rate risk, purchasing power risk, market risk, industry

130

Table 66. F variables.

 

 

Series Source1
Index of industrial materials ~ HCI
prices
Index of labor cost per unit HCI
of output, total manufacturing
Manufacturing and trade sales HCI
in 1972 dollars
3-month U.S. Treasury bill rate BS
Consumer price index BS
Prime commercial paper rate, FRB
4-6 months
1

HCI = The Handbook of Cyclical Indicators: BS = Business

Statistics: FRB = ngeral Reserve Bulletin.

Table 67. S variables.

 

Series Source1
Triple A corporate bond rate ‘BS
(used Aaa corporate bond rate)
New defense obligations incurred HCI
(used defense department
obligations total, excluding
military assitance)
New orders for durable goods ‘BS
Unemployment rate HCI
Consumer price index BS

 

1

HCI The Handbook BB Cyclical Indicators; BS_= Business

Stat'stics.

|._l

131
risk, and political risk. The 3-month U.S. Treasury bill
rate was used as the risk—free rate. Market risk, industry
risk, and political risk may be taken into account to some
extent by the prime commercial paper rate. Although the
consumer price index may not be a godd indicator of pur-
chasing power risk, the consumer price index may still
be associated with discount rates since it seems plausable
that the higher the consumer price index, the higher the
discount rate which would.be desired by investors.

The second set of variables is listed in Table 67.
Malkiel and Quandt (1972) were able to explain almost 95%
of the variance in the quarterly level of the S&P 500
index by using this set of variables and the index of
consumer sentiment. Since individual security returns
are generally related to the market return which is a
function of security price levels, then individual security
returns may be associated with these variables.

The third set of variables is listed in Table 68.
These variables were chosen by examining three finance
textbooks (Latané, Tuttle, and Jones, 1975; Stevenson and
Jennings, 1976: Fischer and.Jordon, 1979) for economy-
wide variables which are claimed to be associated with
stock prices or returns. Those variables which were men-
tioned in at least two of the three books are listed in
Table 68. Also shown are the monthly series selected for
each variables. Variables were considered available if they

are included on a monthly basis in Business Statistics,

132

Table 68. T variables.

 

Variable Series (Source1)
GNP --2
Corporate profits --
Interest rates Aaa corporate bond rate (BS)
Taxes --
Employment Unemployment rate (BS1)
Consumer sentiment --
Industrial production Index of industrial produc-

tion total (HCI)

Federal government expenditures --

State and local government --
expenditures

Investment in plant and Contracts and orders for
equipment plant and equipment in

current dollars (HCI)

Inventory investment Ratio of inventory to sales
(E)

Money supply M1 (BBB)

Inflation Consumer price index (BS)

Personal income Personal income (BS)

 

HCI = The Handbook 2B Cyclical Indicators; BS = Business

tat’stics.

2series not available on a monthly basis.

133
Federal Reserve Bulletin, or The Handbook 2i Cyclical
Indicators.

Each textbook also included at least a partial list
of the "Short List of Indicators" compiled by the National
Bureau of Economic Reaearch (Moore and Shiskin, 1967).
There are twenty-five indicators in the short list some
of which are included in Table 68. The remaining variables
were omitted from Table 68 to keep the number of variables
manageable. However, the.fifth and sixth set of variables
are based on variables provided by the National Bureau
of Economic Research.

The fourth set of variables, which is listed in Table
69, is a collection of twenty-one interest rates, discount
rates, and yields on investments. Based on earlier
prediction attempts, it was found that regression models
based on the Aaa corporate bond rate had an average MSPE
of .0089 compared to the market model's average MSPE of
.0085 for a random sample of twenty firms. All the models
were estimated over a 60 month period and the predictions
were made for the subsequent six month period. Since it
seemed unlikely that this interest rate was the Optimal
interest rate from a predictive ability point of view, a
more comprehensive set of interest rates, discount rates,
and yields was considered.

The fifth set of variables is listed in Table 70.
These variables were selected based on the information

compiled by the National Bureau of Economic Research and

134
Table 69. INT variables.
Series Source1

Finance co. paper placed directly, 3-6 month rate FRB

Prime bankers' acceptances, 90 days rate BBB
3-month U.S. Treasury bills, market yield BBB
3-month U.S. Treasury bill rate BBB
6-month U.S. Treasury bills, market yield BBB
6-month U.S. Treasury bill rate BBB
9-12 month U.S. Treasury bills, market yield BBB
9-12 month issues of other U.S. government BBB

securities rate

3-5 year issues of U.S. government securities rate FRB

Prime commercial paper rate, 4-6 months BBB
U.S. government long-term bond yield BBB
Aaa state and local government bond yield BBB
Baa state and local government bond yield BBB
Aaa corporate bond yield BBB.
Baa corporate bond yield BBB
Federal funds rate BS;
Home mortgage rates - new home purchase {BS
Home mortgage rates - existing home purchase BS
New York Federal Reserve Bank discount rate BS
Federal intermediate credit bank loan rate BS
Prime rate HC

 

1HCI = The Handbook of Cyclical Indicators: B = Business

Statistics; FRB = ngeral Reserve Bulletin.

 

135

 

Table 70. NBER variables.

Series Source1
Inventory investment and purchasing BBB
Vendor performance, slower deliveries BS;
New orders capital goods industries, BS;
non-defense, current dollars
Net change in inventories on hand and BS;
on order in 1972 dollars, smoothed data -
Change in sensitive prices HCI

 

1 CI = The Handbook 2f Cyclical Indicators

136
reported in Table 2 of BBB Handbook BB Cyclical Indicators
(1977, pp. 6-8). In particular, Table 2 reports the mean
and standard deviation in months of the timing of numerous
variables at peaks and troughs of their respective cycles
compared to the business cycle. For example, the peak of
the index of stock prices, 500 stocks,has historically
had an average lead of nine months with a standard deviation
of 3.2 months with respect to the peak of the business
cycle. The trough of the index of stock prices, 500 stocks,
has historically had an average lead of five months with
a standard deviation of 1.6 months with.respect to the trough
of the business cycle.

Those variables whose peaks and troughs have a timing
similar to that of the index of stock prices, 500 stocks,
with respect to the business cycle, may be associated with
the movement in prices of stocks. Such variables may pro-
duce reasonable prediction models of individual firm
returns. Thus, Table 70 reports those variables whose
average timing at peaks and troughs with respect to the
business cycle are within one standard deviation of the
average timing of the index of stock prices at peaks and
troughs with respect to the business cycle.

The sixth set of variables is reported in Table 71.
These variables were also selected based upon their
timing with respect to the business cycle. Table 71 lists
those variables whose difference between the average

timing at peaks and the average timing at troughs is within

137

 

Table 71. TNBER variables.

Series Source1
Four roughly coincident indicators BS;
Inventory investment and purchasing BS;
Employee hours in non-agricultural establishments BBB
Employees in goods-producing industries BS;
Wages and salaries in mining, manufacturing, BS;
and construction, 1972 dollars
Industrial production, durable manufacturers BS;
Vendor performance, slower deliveries BS;
Manufacturing and trade sales, current dollars BS;
New orders, capital goods industries, non-defense, BBB
current dollars
Net change in inventories on hand and on order, BS;
1972 dollars, smoothed data
Manufacturers' inventories of finished goods BS;
Labor cost per unit of output, manufacturing BS;
Money supply (M1), 1972 dollars BS;
Ratio, personal income to money supply (M2) BS;
Treasury bond yields BBB
Ratio, consumer installment debt to personal HCI

income

 

101::

The Handbook BB Cyclical Indicators

138
-3 to -5 months. For the index of stock prices this
difference is -9 -(-5) = -4 months. Thus, by suitable
lagging or leading of variables, the cycle of the variables
in Table 71 can be made to approximately agree with the
cycle of the index of stock prices. Hence, the variables
upon lagging and leading in Table 71 may exhibit an associ-

ation with stock prices and returns.

B. Procedures and Results

Table 72 shows the average MAPE and average MSPE for
models based on the six sets of variables described above.
Also shown are the results for the market, zero, and
valuation models. All of the models were used to predict
the same returns for the same set of 20 firms which were
randomly selected from the CRSP tapes. For each firm the
prediction period was the six month period of October, 1972,
through March, 1973, which was randomly selected from the
period July, 1968, to June, 1979. The estimation period
for the models was the period immediately preceding the
prediction period.

The first entry in each model description shows the
number of months used to estimate.the model. The second
entry in each model description identifies the set of
variables used to estimate the model: F = Table 66;

S = Table 67: T = Table 68: INT = Table 69; NBER = Table
70; and TNBER = Table 71. The models ALLTRY and INALLTRY

are described below.

139

 

Table 72. Predictive ability, average of 20 firms,
October, 1972 through March, 1973.
Model

Description MAPE MSPE
60 market 0.0662 0.0085
0 zero 0.0738 0.0095
60 valuation 0.0713 0.0089
48 valuation 0.0705 0.0087
36 valuation 0.0709 0.0089
60 F L 0.0750 0.0096
60 F C 0.0775 0.0099
60 F F 0.0721 0.0092
60 F LC 0.0777 0.0106
60 F CF 0.0775 0.0098
60 F LCF 0.0804 0.0103
60 S L 0.0742 0.0093
60 S 0 0.0717 0.0088
60 S F 0.0732 0.0093
60 S LC 0.0706 0.0085
60 S CF 0.0717 0.0088
60 S LCF 0.0717 0.0086
60 T L 0.0756 0.0102
60 T C 0.0727 0.0089
60 T F 0.0731 0.0092
60 T LC 0.0769 0.0099
60 T CF 0.0731 0.0090
60 T LCF 0.0717 0.0097
48 F L 0.0743 0.0097

Table 72 (cont'd.)

140

 

Model.

Description MAPE MSPE
48 F 0 0.0776 0.0098
48 F F 0.0723 0.0095
48 F LC 0.0753 0.0104
48 F CF 0.0763 0.0094 '
48 F LCF 0.0782 0.0102
48 s L 0.0748 0.0094
48 s 0 ‘0.0716 0.0086
48 s F 0.0741 0.0094
48 8 LC 0:0720 0.0087
48 8 CF 0.0680 0.0090
48 s LCF 0.0681 0.0089
48 T L 0.0757 0.0104
48 T 0 0.0743 0.0090
48 T F 0.0748 0.0099
48 T LC 0.0772 0.0096
48 T CF 0.0726 0.0085
48 T LCF 0.0761 0.0095
36 F L 0.0738 0.0096
36 F 0 0.0793 0.0107
36 F F 0.0719 0.0092
36 F LC 0.0793 0.0104
36 F CF 0.0771 0.0102
36 F LCF 0.0764 0.0100
36 s L 0.0741 0.0094
36 S 0 0.0714 0.0085

Table 72 (cont'd.)

141

 

Model

Description MAPE MSPE
36 S F 0.0738 0.0092
36 S LC 0.0723 0.0087
36 S CF 0.0739 0.0090
36 S LCF 0.0738 0.0092
36 T L 0.0753 0.0103
36 T 0 0.0727 0.0089
36 T F 0.0712 0.0091
36 T LC 0.0733 0.0091
36 T CF 0.0725 0.0084
36 T LCF 0.0748 0.0094
60 NBER 0 0.0769 0.0103
60 NBER LCF 0.0840 0.0122
60 TNBER 0 0.0822 0.0119
60 TNBER LCF 0.1105 0.0211
60 ALLTRY 0 0.0721 0.0083
60 INT 0 0.0702 0.0081
60 INTALLTRY 0 0.0689 0.0077

 

142

The third entry in each model description, if appli-
cable, shows the timing of the right-hand side variables,
which were eligible for incluSion in the models, with respect
to the firm returns: L, the right-hand side variables
were lagged one month; 0, the right-hand side variables
were contemporaneous with firm returns: F, the right-
hand side variables were led one month and also included
as a contemporaneous variable: CF, each right-hand side
variable was led one month and also included as a contempo-
raneous variable: LCF, each right-hand side variable was
lagged one month, led one month and also included as a
contemporaneous variable.

However, for 60 TNBER C, the right-hand side variables
were suitably led or lagged so that the peak of a right-
hand side variable agreed with the peak of the index of
stock prices. This leading and lagging of variables is
defined as a 0 model. The 60 TNBER LCF variables have the
same timing as those in the 0 model but each right-hand
side variable was additionally included after lagging
one additional month and leading one additional month.

The variables for the models F, S, T, and INT were
transformed as follows. All variables whose units were
dollars were put into constant dollars by dividing each
observation by the corresponding level of the consumer
price index: the first difference of these constant 1
dollar variables was used as the right-hand side variables

in the regression models. All variables which were

143
indexes or ratios were converted to percentage changes.
The first difference was taken for all other variables.

The purposes of these transformations were twofold.
First, since Malkiel and Quandt (1972) found that the
level of stock prices was associated with the level of
economic variables, then it seemed reasonable, as a first
approximation, that returns which are percentage changes
would be associated with changes or the first differences
of the economic variables. Second, the purpose of the
constant dollar and percentage changes transformations was
to put the variables into constant units. The same trans-
formations were applied to the NBER and TNBER variables
except that dollar variables were not converted into con-
stant dollars since this could alter the timing of the
variables at peaks and troughs. Also, the seasonally
adjusted version for all variables was used whenever it
was available.

The F, S, and T models were constructed in the
following manner. The zero model was considered as the
base model. A stepwise regression program to construct
the models (see Neter and.Wasserman, 1974, pp. 382-386 for
a discussion) was used. A variable had to have at least
a F ratio of 1.0 to enter the model at a given step, and
had to have at least a F ratio of 0.999 to be retained in
the model at a given step. This procedure will give a
solution which approximates the minimum mean square error

criterion for selection-of variables (see Neter and

144

Wasserman, 1974, p. 379 for a discussion of the minimum
mean square error criterion model). If the final model
contained no variables, then the zero model was used to
make predictions.

Also for the F, S, and T models the variables which
were eligible for inclusion in the models were modified
in the following way. If the range of the right-hand
side variable during the prediction period was not within
the range of that same variable during the estimation
period than that variable was omitted from the set of.
variables eligible for inclusion in the model. Neter
and Wasserman (1974, pp. 248-249) caution against making
predictions outside of the region used to estimate the
model. In a prior study based on four firms, this modifi-
cation of the variables eligible for inclusion in the models
improved the predictive ability of the models.

Examination of Table 72 reveals that none of the F,
S, and T models had a lower average MAPE than the market
model and only one of the models, 36 T CF, had a lower
average MSPE than the market model. Thus, attempts were
made to find a better set of variables than F, S, and T.

The first attempt consisted of treating F, S, and T
as a single set of variables and trying to find how good
a model could be constructed. The following-procedure
was performed in the search for a better set of variables.
The zero model with an average MSPE of .0095 for the 20

firms was considered as the base model. The variable

145

which decreased the average MSPE the most, using the
stepwise procedure described above to construct the firm
models, was added to the set of variables eligible for
inclusion in the firm models. The procedure terminated
when the average MAPE of the 20 firms could not be reduced
by the addition of a single variable to the set of variables
eligible for inclusion in the firm models. The procedure
was applied to only contemporaneous variables using 60
observations to estimate the model. The resulting model
is reported as 60 ALLTRY C in Table 72. The average MSPE
of 60 ALLTRY C was .0083 which was not a large improvement
over the average MSPE of .0085 for the market model.

Hence, the procedure which was used to construct 60
ALLTRY C was applied to the set of 21 variables named INT.
The resulting model is reported as 60 INT C in Table 72.
The average MSPE of 60 INT 0 was .0081 and, again, this
was not a large improvement over the average MSPE for the
market model.

So, the set of variables used for 60 INT 0 was supple-
mented by the variables in F, S, and T. That is, the set
of variables used for 60 INT 0 was considered as the base
set of variables. Then, the procedure used to construct
6O ALLTRY C was applied to see if any further reduction in
the average MSPE could be obtained by including variables
from F, S, and T. The resulting model is reported as 60
INTALLTRY C. The improvement of 60 INTALLTRY C over the

market model is nearly as good as the improvement of the

146
market model over the zero model.

To determine if the procedure which was used to con-
struct 60 ALLTRY 0 would lead to sets of variables which
would predict well in different time periods and for
different firms, another randomly selected six month period
for a different set of 20 randomly selected firms was
selected. Models were constructed using the stepwise
regression program. Table 73 shows the average MAPE and
average MSPE for 60 INT C and 60 INTALLTRY 0. Since these
models do considerably worse than the market model, it does
not appear that the procedure used to construct 60 ALLTRY
C will lead to sets of variables which predict stock returns
well in general.

Thus, the NBER and TNBER sets of variables were tried
using the stepwise regression program with the zero model
as the base model. Table 72 reveals that all of these
models did considerably worse than the market model.

Although the models examined.do not predict better
than the market model, their potential usefulness lies in
the fact that the variables employed in these models may
not be affected by accounting policy decisions. Thus,
these models may be able to detect accounting policy
decisions better than the market model. On the other hand,
the valuation model does better than most of the models
reported in Table 72. Thus, the potential benefits of the
F, s, T, NBER, and TNBER models over the valuation model

seem small.

147

Table 73. Predictive ability, average of 20 firms,

October, 1969 through March, 1970.

 

Model

Description MAPE MSPE

60 market 0.0578 0.0059
0 zero 0.0669 0.0076
60 valuation 0.0697 0.0079
48 valuation 0.0683 0.0076
36 valuation 0.0692 0.0077
60 INT 0 0.0740 0.0104
60 INTALLTRY 0 0.0765 0.0117

 

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