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Financial accounting ( jstor )
Investors ( jstor )
Modeling ( jstor )
Net income ( jstor )
Price levels ( jstor )
Purchasing power ( jstor )
Sampling methods ( jstor )
Security prices ( jstor )
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EMPIRICAL INVESTIGATION OF GENERAL PURCHASING POWER ADJUSTMENTS
ON EARNINGS PER SHARE AND THE MOVEMENT OF SECURITY PRICES
WILLIAM A. HILLISON
A DISSERTATION PRESENTED TO THE GRADUATE
COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
A number of people and organizations contributed toward the suc-
cessful completion of this dissertation. Special appreciation is noted
for the following:
To the members of my supervisory committee--Dr. Gary Holstrum,
Dr. William Collins, and Dr. James Davis--for their input and encourage-
ment during the study.
To the Richard D. Irwin Foundation and the Haskins and Sells
Foundation for their financial support.
To the firm of Fayez Sarofim and Company for the use of its facil-
ities and data base.
To Dr. Marcus Dunn, Dr. James Burton, and Mr. Clifton Brown for
their assistance and encouragement.
To Ms. Laura Andrews for her assistance in typing and editing the
To Sharon, my wife, and Derek, my son, for their love and support
during the total process.
TABLE OF CONTENTS
ACKNOWLEDGMENTS..... ............... ........... .. ............. ii
ABSTRACT........ ....... ............... .......... .............. v
I. PURPOSE AND JUSTIFICATION............................. 1
A Comparison of Income Measurement Models 3
The FASB's Proposal 6
The Cited Research 8
GPPA in the Conceptual Framework 11
Use of Earnings Per Share 13
Use of GPPA Earnings Per Share 14
Hypothesis Stated 19
II. METHODOLOGY........................................... 22
Step One: Sample Selection 23
Step Two: General Purchasing Power Restatement 29
Step Three: Calculation of Unexpected Earnings
Per Share 33
Step Four: Abnormal Market Return Calculation 37
Step Five: Test of the Hypothesis 39
III. RESULTS OF STUDY...................................... 42
Results of the Restatement Procedure 43
Measures of Unexpected Earnings Per Share 46
Regression Results: a and 0 Values 50
Calculation of Abnormal Market Returns 52
Test of the Hypothesis 54
IV. SUMMARY AND CONCLUSIONS ................................ 64
Summary of Results 64
Implications for Further Research 67
A. EXTENSION OF THE TESTS OF ASSOCIATION BETWEEN EPS
AND MARKET PRICES ...................................... 70
TABLE OF CONTENTS--Continued
B. DISTRIBUTION OF ABNORMAL MARKET RETURNS
FOR SAMPLE COMPANIES: 1970-1974........................ 76
C. CONTINGENCY TABLES OF MEASURES OF ABNORMAL
EPS AND MEASURES OF ABNORMAL RETURN BY GROUP
D. FLOWCHART OF GENERAL PURCHASING POWER RE-
STATEMENT COMPUTER PROGRAM .............................. 86
BIOGRAPHICAL SKETCH............................................... 97
Abstract of Dissertation Presented to the Graduate Council of
the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
EMPIRICAL INVESTIGATION OF GENERAL PURCHASING POWER ADJUSTMENTS
ON EARNINGS PER SHARE AND THE MOVEMENT OF SECURITY PRICES
William A. Hillison
Chairman: Gary Holstrum
Major Department: Accounting
The purpose of this study was to supplement the available empir-
ical research concerning the relationship between accounting numbers
and the prices of securities by examining the association between
general purchasing power adjusted (GPPA) earnings per share (eps) and
the movement of security prices. Previous research supported the
supposition that information contained in the traditional eps numbers
was impounded in the prices of firms' securities. Recent studies
have indicated that sufficient financial data may be available to
allow investors to make reasonable estimates of the effects of gen-
eral purchasing power changes on the eps of firms. If investors are
able to derive GPPA data and if they find those data useful in their
investment decision, an association with securities prices would be
This research compared the association between securities' prices
and traditional eps (Traditional Association) with the association
between securities' prices and GPPA eps (GPPA Association). The
following hypothesis was tested:
H : There is no difference between GPPA Association
and Traditional Association.
The following steps were performed to test the hypothesis.
1. A sample of 76 firms was selected for study for the years
1970-1974. Major criteria for inclusion in the sample were: a) the
data be available on both the COMPUSTAT and CRSP tapes and b) there be
an expectation that GPPA eps be significantly different from traditional
eps for the firm-years.
2. Traditional eps for each firm-year were restated via a com-
puter program developed to reflect purchasing power adjustments.
3. Measures of unexpected eps for both GPPA and traditional eps
were calculated for each firm-year by applying random-walk models.
Two expectations models were used: a first-difference and a second-
difference. The first-difference measure was the change in eps from
one firm-year to the next, while the second-difference measure was the
change in the rate of change from one firm-year to the next.
4. A measure of abnormal or unexpected security market returns
was calculated. The Sharpe (or Diagonal) model was used to obtain the
a and a parameters necessary for the calculations.
5. Two-by-two contingency tables were used to determine associa-
tions between unexpected eps and abnormal market returns. For the
test of the hypothesis only those firm-year observations where the
measures of unexpected eps using GPPA data and traditional data were
of opposite sign (thus giving opposite "signals" to the securities
market) were used in the contingency tables. Chi-square tests were
performed to determine whether one measure exhibited stronger market
association than did the other measure.
The results were as follows:
1. Traditional eps and GPPA eps were highly correlated evidenced
by a Spearman Rank Order Correlation Coefficient of .73. This rela-
tionship was significant at the .001 level.
2. There was no statistically significant association between
the market variable and the first-difference unexpected earnings mea-
sures for neither traditional data nor GPPA data.
3. The lack of association between these first-difference mea-
sures of unexpected earnings and the market variable precluded mean-
ingful tests of the hypothesis with respect to first-differences.
4. There was a statistically significant association between the
market variable and the second-difference unexpected earnings measures
for both traditional data and GPPA data.
5. A test of the hypothesis using second-difference measures
where the sign differed between the traditional eps generated measure
and the GPPA eps generated measure supported the contention that tra-
ditional eps were more highly associated with market returns than were
GPPA eps. The nature of the sample selection process allowed only
limited generalization, however.
PURPOSE AND JUSTIFICATION
The Report of the Study Group on the Objectives of Financial
Statements (1973) of the American Institute of Certified Public Accoun-
tants (AICPA) and the Committee to Prepare a Statement of Basic
Accounting Theory of the American Accounting Association (AAA) (1966)
have concluded that usefulness is the primary objective of accounting
data. The Study Group stated, "The basic objective of financial
statements is to provide information useful for making economic deci-
sions" (1973, p. 13). The Committee's opinion was, "Accounting
information must be useful to people acting in various capacities both
inside and outside of the entity concerned" (1966, p. 8).
While usefulness has been accepted as the primary criterion for
accounting data, an operational test for usefulness has not been
developed. Therefore, the determination of accounting standards and
reporting practices is largely a value judgment of policy-making
boards such as the Financial Accounting Standards Board (FASB) and the
Securities Exchange Commission (SEC). Such value judgments are based
on information that these boards perceive as important.
Beaver (1973) and Gonedes and Dopuch (1974) stated that policy-
making boards could find empirical research concerning user behavior
helpful in the task of setting policy. These researchers claimed that
in the past, however, policy boards such as the Accounting Principles
Board (APB) failed to incorporate the available empirical research.
Beaver expressed his opinion strongly when he stated that more research
is needed and said, "If the hopes for success of the FASB are to be
realized, it is imperative that we lead, not lag, in incorporating the
current state of knowledge into the setting of standards" (1973, p.
In early attempts to establish reporting standards, the Account-
ing Principles Board often encountered problems in gaining acceptance
of proposed reporting standards. It appeared at times that standards
were implemented primarily to satisfy powerful interest groups. In
apparent support of this approach to the problem Gerboth stated, "In
the face of conflict between competing interests, rationality as well
as prudence lies not in seeking final answers, but rather in compro-
mise--essentially a political process" (1973, p. 479).
It should be recognized that agreement, even by all members of
the profession, as to what should be reported does not assure one that
the data is useful to the user. The usefulness of any accounting
standard is an empirical question which must be addressed to the user.
Although there is no one optimal test for usefulness, the results of
empirical research into the decision process could be of importance to
the policy-making boards. The task of these boards is to seek out and
incorporate empirical research in conjunction with the other considera-
tions to determine reporting policy. Once policy is determined,it may
take an educational and promotional effort to gain the acceptance of
practitioners; however, that task could be facilitated if empirical
support for standards were available.
1The "pooling" versus "purchase" issue and the controversy sur-
rounding "investment credit" are illustrations of these problems.
The purpose of this paper is to supplement the available empiri-
cal research by examining the relationship between general purchasing
power adjusted (GPPA) earnings per share (eps) and the movements of
security prices. The existence or absence of relationships between
earnings variables and market variables should be of interest to policy
Although there have been a number of income measurement models
discussed in the literature, the usefulness of general purchasing power
adjusted historical cost earnings was selected as the topic of concern
because of the FASB's interest in the area. It is noted that the topic
of general purchasing power adjustments has been incorporated in
several of the recent publications of the Board (FASB, 1974a, 1974b,
1976a, 1976b). Although it is not the purpose of this paper to dis-
cuss the desirability of the various income models, several are
identified in order to place GPPA historical cost reporting in perspec-
A Comparison of Income Measurement Models
Income measurement models can be classified in relationship to
the "reporting errors" inherent in them (Basu and Hanna, 1975). Partic-
ularly, a model may reflect a combination of "measuring unit errors"
and "timing errors." Measuring unit errors arise whenever the unit of
measure fluctuates while timing errors occur basically when a transac-
tion occurs in one period and is recorded in another.
Traditionally, amounts have been stated in financial statements
on the basis of historical cost and measuring unit errors have been
ignored. Although the number of dollars may be properly stated, the
command of goods and services of those particular dollars is generally
disregarded. As the purchasing power of the measuring unit (i.e., the
dollar) changes, measuring unit errors arise. These errors are a
potential problem since empirical observations indicate that the dol-
lar is not a constant measuring unit.
One alternative to this situation is to have amounts stated in
terms of "units of general purchasing power." A unit of general pur-
chasing power is defined as the power of the dollar to purchase goods
and services at a particular point in time. During times of inflation
(deflation) the purchasing power of the dollar declines (increases)
and as such it requires more (fewer) dollars to acquire a given
quantity of goods and services. Without adjustment, financial state-
ments contain a mixture of dollars identified with various dates, each
representing different amounts of purchasing power. Techniques for
preparing financial statements illustrated by the FASB and previously
by the APB attempt to restate mixed dollars in financial statements
into dollars of constant purchasing power. By using a common measure
such as this, measuring unit errors are diminished.2
Timing errors arise whenever a firm's net worth changes (i.e.,
change in asset value + change in liabilities) in one period but is
recorded in another. These timing errors can be classified as either
operating gains (losses) or holding gains (losses). Operating gains
(losses) are identified as the difference between current input and
A further identification of the technical problems of GPPA is
found in the methodology section of this paper. The reader is directed
to APB Statement Number 3, June,1969 and FASB's An Analysis of Issues
Related to Reporting the Effects of General Price-Level Changes in
Financial Statements, February, 1974, for a more complete discussion.
current output prices at a particular point in time. Holding gains
(losses) are those that arise from changes in input prices while goods
are held over time.
Recognition of timing error gains (losses) can be identified
independently from measurement unit errors. Current value models have
been proposed which utilize input prices only or a combination of input
and output prices (Edwards and Bell, 1961; Basu and Hanna, 1975). The
following example illustrates the current value output model:
Assume that a firm held goods during a time of no general price
level change at a cost of $100 and sold them 6 months later at a price
of $200. The current input price at the date of sale was $120.
Current Input Price Initial Input Price = Holding Gain
$120 $100 = $20
Current Output Price Current Input Price = Operating Gain
$200 $120 = $80
If the above items were not sold, but inventoried, the gains would
still have "occurred" but would have been unrealized. The basic dif-
ference between the current value input and the current value output
models is that the unrealized operating gain (loss) would also go
unrecognized in the period using a current value input model.
In times of changing purchasing power of the dollar, "measuring
unit errors" can also be identified along with the "timing errors."
Such identification requires first that an adjustment be made for the
change in the purchasing power of the dollar and then that an
Input prices are defined as those at which a firm acquired goods
and services, while output prices are those prevailing in markets where
a firm disposes of those goods and services.
application of a current value model be used. By using such a tech-
nique both timing errors and measuring unit errors can be recognized.
The following table compares the various models discussed above
and their relationship to historical cost.
MEASURING TIMING ERROR
UNIT ERROR OPERATING HOLDING
Historical Cost Occur Occur Occur
GPPA Historical Cost Eliminated Occur Occur
Current Value-Input Occur Occur Eliminated
Current Value-Output Occur Eliminated Eliminated
GPPA Current Value-Input Eliminated Occur Eliminated
GPPA Current Value-Output Eliminated Eliminated Eliminated
SOURCE: Basu and Hanna, 1975.
The study outlined in Chapter II was concerned with the GPPA Historical
Cost model thus only the measuring unit error problem was considered.
The FASB's view of the expected usefulness of GPPA historical
cost reporting model was represented in their proposal. This proposal
is discussed in the following section.
The FASB's Proposal
On February 15, 1974, the FASB issued a Discussion Memorandum
entitled, An Analysis of Issues Related to Reporting the Effects of
General Price-Level Changes in Financial Statements (1974a). The
FASB's apparent belief that general purchasing power adjusted informa-
tion was necessary was expressed by the release of an Exposure Draft
(1974b) on December 31, 1974. The standard requiring firms to provide
financial information stated in terms of general purchasing power was
to become effective on January 1, 1976. If it had been put into ef-
fect, the FASB Statement would have required yearly comprehensive
restatement4 of financial data in addition to traditional historical
cost data for firms in order to meet "generally accepted accounting
principles." Concerning the proposal, the FASB stated, ". because
of considerable research--both conceptual and empirical--that has been
conducted on the subject (of general purchasing power adjustments),
the Board concluded that further research is not necessary at this
Over a year later, in November 1975, the Board announced that it
would not put the Exposure Draft into effect on the expected date.
Issuance was to be deferred until the results of field tests on
eighty-four companies could be analyzed. Upon completion of the study,
the Board further deferred issuance. Conclusions from the study were
summarized in the June 4, 1976, FASB Status Report:
The Board has only concluded that general purchasing power informa-
tion is not now sufficiently well understood by preparers and users
and the need for it is not now sufficiently well demonstrated to
justify imposing the cost of implementation upon all preparers of
financial statements at this time (p. 1).
The lengthy delay in issuance appears inconsistent with the
statement by the Board concerning the availability of prior research
to support the need for general purchasing power adjustments. A review
Some of the specifics of this restatement procedure are discussed
in a subsequent section dealing with the model used in this research.
The reader is referred to the Exposure Draft for a full discussion of
5This is stated in both the FASB's Discussion Memorandum (p. 3) and
Exposure Draft (p. 20).
of some of the cited research that apparently influenced the Board
originally to promote the concept of general purchasing power is
The Cited Research
Accounting Principles Board Statement Number 3 is referenced as
input into the decision to call for GPPA reporting. Based on the
Statement, the FASB Memorandum stated, "The APB concluded that finan-
cial statements adjusted for changes in the general price level present
useful information not available from basic historical-dollar state-
ments" (1974a, p. 2). If one looks back to the reference made to APB
Statement Number 3, it can be seen that the usefulness issue was
addressed by the assertion, "General price-level financial statements
should prove useful to investors, creditors ." (1969, p. 2). This
normative statement is not supported by referenced empirical evidence.
A study by Rosenfield is cited by both APB Statement Number 3
(1969, p. 7) and by the FASB Memorandum (1974a, p. 18). The Rosenfield
study reported the effects of restatement on the financial statements
of 18 firms. In his summary, Rosenfield stated:
Although statistically valid generalizations are not warranted by
the sample of 18 companies, the results nevertheless seem to sup-
port the view of ARS No. 6 that presentation of supplementary
general price-level financial statements would make available
potentially useful information that otherwise is not disclosed
(1969, p. 49).
Many of the references cited in the Selected Bibliography of the
FASB's Discussion Memorandum relate to the feasibility and technical
aspects of GPPA reporting. Past research does indicate that accounting
for changes in the general price level appears to be technically
feasible. Discussing the cited research, the Board stated in the
These studies indicate that general price-level restatement is
feasible, but consideration still must be given to the question
of whether the benefits outweigh the costs involved (1974a,
Even if the technical problems of detailed restatement can be overcome,
the question, "Is the data useful to decision makers?" still must be
addressed. These questions are empirical in nature and statements such
as "should prove useful" and "potentially useful" must be tested before
the value to the user can be evaluated.
The Memorandum does reference several empirical studies directed
toward the user. This research does not attempt to study the user's
behavior, however, it does ask what the user desires.
In an early study cited by the FASB Memorandum, Horngren inter-
viewed security analysts and asked questions about the problems dealing
with the changing price level. He found a "united stand of security
analysts against 'tampering' with conventional financial statements by
application of price-level adjustments" (1955, p. 577). As late as
1968 Estes stated, ". virtually no empirical evidence has been
offered as to the usefulness of such (price-level adjusted cost) infor-
mation" (1968, p. 201). This statement constituted the justification
for his study. In that study, Estes found that approximately 30% of
the sampled financial statement users would assess presentation of
price-level adjustment information "not useful," another 38% would
find it "somewhat useful," while the other 32% would find it "use-
In another cited empirical study Garner (1972) found that
approximately 60% of the respondents indicated that financial data as
it is now reported did not satisfy their needs, but only 26% indicated
the need for price-level adjusted data. There did not appear to be
substantial support for general purchasing power adjusted statements
from the users.
The cited research appears inconclusive; however, it has been
contended that purchasing power adjustments may not have appeared use-
ful during the 1950's and 1960's when yearly price changes were rela-
tively small. Price changes during that time period were relatively
small when compared to recent price changes. For example, during the
years 1952 to 1967 price changes did not exceed 3.7%, and in ten of
those years did not exceed 2%. Concerning the accountant's attempt
to adjust accounting data to reflect the change in the price-level
for these relatively small differences, Davidson has stated:
I would be surprised to see any substantial growth in price-
level-adjusted statements in the 1970's. The one exception would
be if the rate of inflation were to reach a level of, say, 6 per-
cent or more per year for a period of several years. Barring war
or extreme national emergency, such a rate of price increase seems
unlikely (1969, p. 33).
The 6% expectation referred to by Davidson has become reality in
the 1970's. The Gross National Product Implicit Price Deflator
increase per year has been measured as reported in Figure 1.
It may be contended in light of the recent fluctuations and
increased size of the changes, that results of more recent surveys may
conclusively indicate a desire for GPPA reporting. This supposition
has yet to be supported by empirical research, however. Unlike past
studies, the present research attempts to examine the aggregate
decision-making behavior of users, specifically investors in securities,
in relation to general price level changes.
YEAR % INCREASE
SOURCE: United States Department of Commerce, Bureau of Economic
At the time the Exposure Draft was deferred, it was noted that
the FASB would consider general purchasing power measurement considera-
tions in its forthcoming study concerning the development of a concep-
tual framework for financial accounting. The initial stage of that
study is discussed in the next section.
GPPA in the Conceptual Framework
In December of 1976, the FASB released a discussion memorandum
entitled An Analysis of Issues Related to Conceptual Framework for
Financial Accounting and Reporting: Elements of Financial Statements
and their Measurement. It was stated that the discussion on the
". conceptual framework for financial accounting and reporting is
a major, continuing project that will be carried out in several steps
or phases" (p. 28). Thus, the work was viewed as an initial step to:
(1) identify the problem, (2) outline several possible alternatives,
and (3) call for discussion concerning the desirable attributes of
financial accounting and the associated measurement processes.
The Board identified five possible attributes of assets and
liabilities for possible incorporation into the "framework." These
were: (1) Historical cost/historical proceeds, (2) Current cost/
current proceeds, (3) Current value in orderly liquidation, (4) Ex-
pected exit value in due course of business, and (5) Present value of
expected cash flows.
In order to measure the attributes the Board identified two
units of measure. They were: (1) units of money, and (2) units of
general purchasing power. It was noted that each of the five attri-
butes that might be selected for measurement is equally susceptible
to measurement by either of the two units of measure. Although the
discussion included many exhibits utilizing the concepts of general
purchasing power measurement, it offered little conceptual support
for the method. It stated:
In view of the earlier issuance of the Discussion Memorandum on
"Reporting the Effects of General Price-Level Changes in Financial
Statements" and the amount of information about it already elicited
by the FASB, only limited discussion of the unit of measurement is
included in the Discussion Memorandum (1976b, p. 191).
The research presented in the following chapters deals with
empirical observations concerning the use of general purchasing power
adjusted earnings numbers and, as such, could be of help to the FASB
in assessing the desirability of GPPA reporting.
It is assumed that the investors, in aggregate, set prices, thus
create returns in the market by making investment decisions based upon
the information available. One data item of interest to the investor
may be earnings per share which is selected as the variable of
6The discussion by Basu and Hanna resulting in Table 1 included
attributes one, two and four but did not consider attributes three and
interest in this study. The reasons for its selection are stated in
the following section.
Use of Earnings Per Share
Earnings per share was selected as the variable of interest in
the investor's decision model because:
1. It is one of the most reported and publicized accounting
numbers. Not only is eps incorporated into annual reports, prospec-
tuses, and proxy information, but it is also used in other publications
such as news reports and commercial financial analysts' reports.
2. The accounting profession has indicated its belief in the
importance of the earnings per share number. This is evidenced by the
Accounting Principles Board statement:
The Board believes that the significance attached by investors and
others to earnings per share data, together with the importance of
evaluating the data in conjunction with the financial statements,
requires that such data be presented prominently in the financial
statements (Accounting Principles Board, Opinion Number 15, para.
3. Ball and Brown (1968) and Gonedes (1974) have found evidence
of association between the eps number and security price movement. The
covariate movement of the security prices and the eps number is an
indication of that association. Ball and Brown stated "If, as evidence
indicates, security prices do in fact adjust rapidly to new information
as it becomes available, then changes in security prices will reflect
the flow of information to the market" (1968, p. 160). The importance
of this proposition was revealed in a concluding remark: "Of all
information about an individual firm which becomes available during a
year, one-half or more is captured in that year's income number" (1968,
p. 176). Gonedes (1974) found similar results concerning the earnings
per share number using discriminant analysis on capital asset prices
and seven commonly used financial "ratios." He concluded that the
". results seem to ascribe special importance to the information
reflected in the earnings per share variable, relative to the other
variables examined" (1974, p. 66).
The study outlined in this research utilizes not only the tradi-
tional earnings per share as reported by firms but also employs a
conjunctive estimated general purchasing power adjusted earnings per
share. The use of an estimated GPPA eps relies on several presumptions
which are discussed below.
Use of GPPA Earnings Per Share
A basic premise of the present research is that currently avail-
able, public, financial data currently allows the investor to transform
historical data into GPPA data. That is, for a majority of public
firms, sufficient data concerning financial transactions is now
released through various channels to give the user the capacity to make
his own GPPA adjustments. This premise has some support in the litera-
In a study cited previously, Horngren (1955) interviewed security
analysts and asked questions about the problems dealing with the chang-
ing price level. He found that although analysts did not formally
adjust for the effects of inflation, they may intuitively compensate
for it in their decision process. It was noted that analysts would
mentally "plus or minus" (p. 577) for the price-level changes.
Peterson (1973) determined that a satisfactory estimation of the
effects for most firms could be obtained from published financial data.
He concluded that the information is available, in many cases, to
allow the investor to adjust for changes in the price level. Peterson
stated, ". investors might very well be able to 'adjust' for gen-
eral price level movements when using published financial information
for decision making" (p. 43). He developed, tested, and validated a
computer model to transform available financial data into estimates of
general price level adjusted data.
Davidson and Weil (1975a) developed procedures to adjust earnings
data for the effects of price level changes that ". .. conform gener-
ally with those recommended in Statement No. 3 .. ." (p. 28). They
applied those procedures to published financial information for sixty
larger firms and derived price level adjusted earnings. In an attempt
to validate the procedure, reported GPPA earnings for several companies
were compared to the estimates.
The results from a number of those comparisons are reproduced
below in Table 2. In Table 2, the large deviations in the XYZ Company
for 1968, that of 30.53% difference in net income, are the results of
several factors. First, the income figure for 1968 was 75% less than
in 1967. This number is the denominator in the percentage calculation,
thus even a small absolute deviation results in a large percentage
change. Also, the difference between the estimated gain on monetary
items for 1968 and the reported figure was caused by the XYZ Company
selling a nonmonetary asset on December 1, 1968. The cash realized
from the sale was larger than the total amount of the net monetary
liabilities. The restatement procedure assumes all cash flows occur
evenly throughout the year, thus significant differences resulted in
estimated and reported figures. This situation is viewed as a
somewhat rare case where the assumptions of the model were violated.
The restatement procedure would not be expected to perform well under
these circumstances. The belief of Davidson and Weil that these errors
were not significant is evidenced by their subsequent application of
the procedure to other firms and time periods and the publication of
the results (1975b, 1975c).
PERCENTAGES BY WHICH THE DAVIDSON-WEIL ESTIMATES DEVIATE
FROM THE REPORTED GENERAL PRICE LEVEL ADJUSTED ITEMS
Company and Year
AICPA Rosenfield Study AICPA Demon-
Co. XYZ Company strator
R Co. H Co. J Co. P Company
(1973) (1968) (1968) (1968) (1967) (1968) (1960)
Other Income 0.68% 0.72% 0.05% 0.25% 0.13% 1.38% 0.35%
Cost of Goods
Sold 0.02 0.79 0.11 -1.78 0.07 0.75 0.18
Depreciation 18.74 6.33 2.99 3.45 2.62 -4.29 0.41
and Deductions 0.62 0.94 -0.29 0.31 -0.23 6.30 0.03
GAIN OR LOSS
ITEMS -9.97 10.77 -1.43 24.67 -3.41 60.76 5.01
Gain or Loss
Items 5.80 11.17 -6.08 -53.33 -1.00 -45.12 -4.21
NET INCOME -5.78 -3.03 2.46 7.33 -3.38 30.53 4.62
SOURCE: Davidson and Weil, 1975a, p. 76.
Basu and Hanna (1975) used a procedure similar to Davidson and
Weil's, relying on ". a variety of shortcut procedures that are
applied to publicly available data in performing GPL restatement" (p.
26). While recognizing deficiencies in the data, they restated finan-
cial statements from information drawn from the COMPUSTAT file.
Restatement was made for approximately 425 companies for years 1967
For validity testing purposes, actually reported GPPA data was
obtained for 25 companies covering 61 years of data. Upon statistically
comparing various estimated GPPA financial items with the reported
GPPA items, Basu and Hanna stated:
On the basis of the evidence included in that appendix, (Appendix
A) it seems reasonable to conclude that although our generalized
approach does generate statistically significant differences for
some financial statement items, it is in general, surprisingly
accurate (p. 37).
A portion of Basu and Hanna's Appendix A is reproduced below.
The "Income Statement" data was of particular interest to the current
study because it related directly to the eps number. The table sug-
gests that the restatement procedure performs reasonably well for the
Earnings Available for Common as a whole. For example, using all
information available for comparison, a median difference of 0.1% was
noted. Observation of the two significant factors of restatement
indicated that the restatement procedure for the depreciation factor
did not perform ideally. The median estimated depreciation was 6.9%
greater than that actually reported by the companies.
The restatement model developed for this study attempted to
improve on the problems observed in depreciation expense as experi-
enced by Basu and Hanna. The procedure developed is explained in
THE ACCURACY OF GENERALIZED PROCEDURES IN RESTATING INCOME
STATEMENT ITEMS: SOME SUMMARY STATISTICS
Period Summary Income Statement
Earnings Depre- Purchasing
Available ciation Power
for Common Expense Gain/Loss
Median Difference 0.1% 6.9% 1.2%
Lower 95% Confidence Limit -4.4% 4.8% -4.9%
All Years Hodges Lehmann Estimate -0.7% 6.7% 1.3%
(1970-74) Upper 95% Confidence Limit 3.2% 9.0% 7.5%
Pooled Wilcoxon's Statistic -0.28 4.94b 0.67
Number of Observations (53) (45) (47)
Median Difference 0.7% 4.8% 1.6%
Available Lower 95% Confidence Limit -5.8% 1.6% -6.9%
Data Hodges Lehmann Estimate 0.5% 5.1% 2.1%
Averaged Upper 95% Confidence Limit 7.6% 9.7% 12.2%
by Firms Wilcoxon's Statistic 0.21 2.69b 0.60
Number of Observations (23) (21) (21)
aDifference between estimated parameter and
percentage of the latter.
actual parameter as a
Denotes statistical significance at the 0.01 level.
SOURCE: Basu and Hanna, 1975, p. 60.
Based on the cited studies, evidence appears to support the con-
tention that the investor has the data to make relatively accurate
estimates of GPPA financial information for most publicly held firms.
If GPPA information is obtainable from currently available data and
the investor considers it useful, then it is expected that it would be
incorporated into his investment decision model. This formula can be
E(Return) = F(a, b, c .....)
where one of the relevant independent variables is GPPA earnings per
If this is the case, one might expect to find a greater associa-
tion between GPPA earnings per share and the movement of security
prices than between traditional earnings per share and the movement of
security prices because of the elimination of the measurement unit
error. Testing this conjecture required an operational hypothesis
which is discussed below.
Using the terms "GPPA Association" to represent the association
between GPPA earnings per share and "Traditional Association" to repre-
sent the association between traditionally calculated earnings per
share and the market price movement, the null hypothesis can be stated:
H : There is no difference between GPPA Association
and Traditional Association.
Rejection of the null hypothesis, if due to significantly greater
GPPA Association, would support the supposition that general purchasing
power data was incorporated in the users' decision model. Rejection,
if due to significantly greater Traditional Association, would support
the hypothesis that general purchasing power data was not incorporated
in the users' decision model. Failure to reject the hypothesis if due
to greater Traditional Association could be attributed to any of seve-
ral causes. These are identified below.
a. Visibility--Even though the user may consider GPPA earnings
per share useful, (and assuming it can currently be economically
derived) he may not recognize that the information is available. Re-
search concerning the effects on security market prices has been con-
sistent with the supposition that the market fully reflects all
obviously available, useful information (Fama, 1970). Thus, if the
data is available, visibility is not a major issue. The critical issue
becomes: "Is GPPA earnings per share information obviously available?"
b. Unavailable--It may be suggested that data is not available
to the investor in sufficient detail to allow reasonable estimates of
restatement to be performed. This, however, is not consistent with the
findings of Peterson (1973), Davidson and Weil (1975a, 1975b, 1975c),
and Basu and Hanna (1975). Even though it may be available, the
investor may find the cost prohibitive.
c. Uneconomical--GPPA earnings per share may be relevant but
uneconomical to obtain by the user. The marginal value to the user
would be less than the marginal cost. If this conclusion were
accepted, the primary consideration would be, "Can the accounting
profession provide cost-effective GPPA earnings per share?" Although
this issue is identified, cost-benefit analysis is beyond the scope
of the present study. Given that there are simple estimation proce-
dures, however, the cost of the development of GPPA eps does not
appear to be significant when data are available. Another issue con-
cerns the GPPA model used in the study.
d. Noise Level in Model--The general purchasing power model
used and/or the market model used in this study may not be of suffi-
cient precision to detect significant user responses to GPPA eps. If
the preceding issues can be discounted, the question of relevancy of
GPPA earnings can be addressed.
e. Irrelevancy--The user may consider GPPA earnings per share
of little use. In this case, even if GPPA information became obviously
available to users, it would not be incorporated into a significant
number of decision models. Failure to reject the hypothesis, or rejec-
tion due to significantly greater Traditional Association, would sug-
gest this explanation if the above listed factors can be discounted.
This is discussed further in Chapter IV.
Several steps were necessary to test the hypothesis. The method-
ology for the test is presented in the following chapter.
The methodology presented in this chapter and used in the subse-
quent tests of the hypothesis builds upon past studies relating to the
efficient market hypothesis. Those studies relate to the securities
market apparently efficient impoundment of all publicly available
information (Fama, 1976). Empirical evidence supports the contention
that the market does impound earnings information concerning a firm
(Ball and Brown, 1968). Past research studies, like this one, attempt
to identify "new" or "unexpected" information to the securities market
and test for association with "abnormal" or "unexpected" returns
experienced in that market.
The "unexpected" accounting information in this study was mea-
sures of unexpected eps. These unexpected eps measures were derived
using the traditional accounting model and a GPPA model. The test of
the hypothesis attempted to determine which of the two "unexpected"
eps, traditional or GPPA, was more closely associated with "abnormal"
market returns. The steps necessary to operationalize the test of the
hypothesis were as follows:
1. Sample Selection;
2. General Purchasing Power Restatement of eps;
3. Unexpected eps Calculation;
4. Abnormal Market Return Calculation;
5. Test of the Hypothesis.
Each of the above steps is explained below.
Step One: Sample Selection
Since both market price and financial data were required, only
firms that appeared on both the COMPUSTAT and CRSP2 tapes were consid-
ered. In order that price-level calculations be homogeneous, only
calendar year firms were included in the population.
Sample selection was viewed as a critical step if a substantive
test of the hypothesis was to be expected. Since the major purpose of
this examination was to search for any evidence of greater association
of GPPA earnings with the market price movement, a sample was selected
from those firms whose earnings per share were expected to be signifi-
cantly affected by changes in the purchasing power of the dollar. The
change in the purchasing power of the dollar which caused divergence,
or convergence of the two different eps numbers, was expected to allow
the discrimination necessary to compare the association of each with
the market returns of the security. A simple diagram will help to
illustrate this concept. Assume observations were as follows:
$ Tradit a Traditional
e e ,GPPA eps
1The COMPUSTAT tapes are available through Investors Management
Sciences, Inc., P. 0. Box 239, Denver, Colorado.
2The CRSP tapes are available through the Center for Research in
Security Prices, Graduate School of Business, University of Chicago.
If the slopes of the eps numbers were similar, as in Graph A, the null
hypothesis would not likely be rejected regardless of the absolute
differences in eps. That is, if GPPA derived eps moved parallel to
traditional eps, any association tests based on the eps variables and
a market return variable would exhibit similar results. If, however,
firms were identified where GPPA eps and traditional eps were divergent
given changes in the price-level, differences in association could be
expected. This divergent situation is illustrated in Graph B. The
observed divergence is experienced over "time" which is represented on
the horizontal axis.
The time period selected for the study was 1970 through 1974, as
this period was viewed as one in which significant changes in the gen-
eral purchasing power of the dollar took place. The 11.4% observed
decrease in 1974 was the largest in the past 25 years. Selection of
those firms that were expected to be highly affected by changes in
purchasing power required utilizing conclusions from past studies
(Davidson and Weil, 1975a; Basu and Hanna, 1975). It was observed in
those studies that, in general, most firms are "net debtors"; thus
GPPA eps is augmented during inflation due to monetary gains experi-
enced by the firms. These gains, however, are more than offset, in
general, by the increased depreciation charges generated from the
general purchasing power adjustment procedure. For most firms the
adjustments precipitated by the monetary and depreciation items are of
primary significance in the adjustment process and account for the
majority of the dollar changes in earnings.
As part of the sample selection process for this study, two
indices were constructed from data obtained from firms on the COMPUSTAT
tape file. One index attempted to measure the effect of a firm's
monetary position on its GPPA eps while the other attempted to measure
the effect of the firm's depreciation charges on GPPA eps. The fol-
lowing formulas were calculated for each firm for the years 1970 to
Monetary Index Monetary Liabilities Monetary Assets )
Absolute Value of Earnings Available
For Common Stockholder
Depreciation = Gross Plant Accumulated Depreciation (2
(Age) Index Total Assets Current Depreciation and
In Equation (1), the Monetary Index was calculated as the ratio
of net monetary items4 to the absolute value of net income available
for the common stockholder. As the numerator approached zero, the
firm's "balanced" position precluded changes in GPPA eps due to mone-
tary position. Monetary gains experienced by holding debt would be
offset by monetary losses experienced by holding monetary assets.
Those firms which had a large net monetary position, either positive
or negative, would have eps affected by changes in the purchasing
power of the dollar, ceteris paribus.
3The COMPUSTAT tape available for these calculations contained data
only through 1973. For subsequent steps, the data was augmented to
include 1974 financial data.
Net monetary position was approximated from the COMPUSTAT tapes by
aggregating the following data classifications from the tape:
Monetary Liabilities = Current Liabilities + Long Term
Debt + Preferred Stock at
Monetary Assets = Cash and Equivalent + Receivables
The other consideration couched in the Monetary Index was the
size of the net monetary position in relation to the size of the earn-
ings available to the common shareholder. Other things being equal,
the closer earnings are to zero, the greater would be the percentage
of eps given a change in purchasing power.
Referring to Equation (2), the Depreciation (Age) Index was ex-
pressed as the product of two ratios. The first was an expression of
the "depreciable assets" to "total assets." Those firms with a large
proportion of depreciable assets were expected to have more deprecia-
tion expense "rolled forward," thus reducing GPPA adjusted eps as
compared with traditional eps.
Also, an "age" surrogate of the depreciable assets was consid-
ered. Basically, this age surrogate was calculated by dividing
accumulated depreciation by the current depreciation charge. To
explain this concept, consider two firms, A and B, where straight-line
depreciation expense is $1,000,000 for each. If firm A's depreciable
assets were ten years old while firm B's were new at the beginning of
the year, firm A must first "roll" depreciation expense ahead for the
ten-year period before applying the current year's price level change.
Thus, if the price level had increased by 50 percent in the prior
ten-year period, firm A will apply the current year's change to
$1,500,000 while firm B will apply the change to $1,000,000.
In addition, it should be noted that the ratio of accumulated
depreciation to current depreciation and amortization gives only a
surrogate for the age of the assets. Firms are likely to own assets
with varied lives, thus the calculation aggregates short lived with
long lived assets. Since the measure was used only as an indication
of expected observations for sample selection, the effect of the inex-
actness of this measure was not considered significant.
The Depreciation (Age) Index was expressed as the "percentage
amount of depreciable assets" times the "age" surrogate. Only those
firms that used straight-line depreciation for financial accounting
were considered in the study, since the use of other methods could
have distorted the measure. The expected relationships of the indices
and earnings per share were:
Type of Index Size of Index on GPPA eps
Monetary Large Increase
Depreciation Large Large Decrease
(Age) index Small Small Decrease
Indices were calculated for individual companies for each of the
years, 1970 to 1973. The Monetary Index, across all firms per year,
appeared as a slightly skewed, leptokurtic distribution. The Deprecia-
tion (Age) Index appeared to be a gamma distribution similar to a
chi-square. By matching the opposite tails of each of the indices'
distributions, firms that would report the greatest change in eps due
to changes in the price level were expected to be identified. For
example, those firms with a negative or small Monetary Index and a
large Depreciation (Age) Index would be expected to show a decreased
GPPA eps, with an increase in the general price level ceteris paribus.
The illustration below demonstrates this concept:
in GPPA eps
in GPPA eps
For a firm to have been selected as a member of the sample, its
indices must have been in the opposite tails during a minimum of two
of the four years between 1970 and 1973. Levels of acceptance of the
indices were set to allow approximately 100 firms to enter the sample.
It was recognized that a number of firms would probably be eliminated
due to data limitations and the firm's use of accounting principles
which were inconsistent with the assumptions of the price-level adjust-
ment models used in the study. The object of the sample size specifi-
cation was to minimize the cost of data collection and analysis while
maintaining the desirable attributes of a large sample. Based on these
contingencies, approximately 100 firms were judged to be an adequate
One hundred twelve firms were identified from the indices as
having the desired attributes. Of these, 76 subsequently entered into
the analysis and test of the hypothesis. Fifteen of the original 112
firms were rejected due to an insufficient history of market prices on
the CRSP tapes to generate the regression parameters as outlined in
subsequent analysis explained in Step Four. At least 60 months of
historical price data was needed to make the necessary calculations of
the parameters a and 8. The 15 rejected firms were recent entries on
the New York Stock Exchange and did not have the necessary market
Sixteen additional firms were rejected because they did not use
primarily straight-line depreciation methods for financial reporting
purposes. Since COMPUSTAT does not report depreciation method, these
16 firms could not be identified until additional data was collected
from SEC 10K reports. Five more firms were eliminated due to incom-
plete financial data. COMPUSTAT does report data that are available on
a firm but occasionally this data are unavailable or not timely. The
resulting analysis is based upon the remaining 76 firms. The next
step in testing the hypothesis involved restating the eps number to
reflect changes in the purchasing power of the dollar.
Step Two: General Purchasing Power Restatement
Annual eps for the sample firms over the five-year period were
restated to reflect estimated effects of general purchasing power
changes. A computer program was written to perform the adjustments
using COMPUSTAT and supplemental financial data as input. The proce-
dure was basically that suggested by Davidson and Weil (1975a). Al-
though the Davidson and Weil procedure fundamentally follows APB
Statement Number 3 (1969) and the FASB Exposure Draft concerning pur-
chasing power adjustments (1974b), many assumptions must be made
since the procedure is applied to often incomplete and inconsistent
published financial information. Some of the major assumptions and
considerations of the GPPA model used in this study are outlined
below. The first consideration is the selection of a measure of
general purchasing change.
The measure of general purchasing power change used in this study
was the Gross National Product Implicit Price Deflator. Other possi-
bilities for measurement were the Consumer Price Index or the Wholesale
Price Index, however, these were viewed by the FASB (1974a) as less
comprehensive than the Gross National Product Implicit Price Deflator.
Revenues and Other Income
An assumption was made that revenues for a firm were spread
evenly throughout the year. As such, one-half a year's price change
was applied to the reported revenue to derive GPPA revenue.
Cost of Goods Sold
The procedure handled three cost flow assumptions of inventory--
first-in, first-out (FIFO); last-in, first-out (LIFO); and weighted-
average. COMPUSTAT indicated which method was used by a firm, although
in a number of cases a firm may have used more than one method in a
single period. Using published financial data, it was impossible to
disaggregate the amounts under each assumption of inventory flow that
constituted cost of goods sold. Therefore, the restatement procedure
used the cost flow method listed first by COMPUSTAT for all calcula-
tions. In rare cases where no method was reported, the weighted-
average method was used.
The procedure assumed that purchases occurred fairly evenly
throughout the year. Dates when purchases and inventories entered
cost of goods sold were estimated based upon the cost flow assumptions
and amounts were adjusted accordingly. The technical aspects of the
restatement can be discerned from Davidson and Weil (1975a).
All expenses other than cost of goods sold were assumed to have
been incurred evenly throughout the year. These expenses were adjusted
for one-half year's purchasing power change.
Monetary Gain or Loss
The restatement procedure used the average beginning and average
ending balances of monetary items to derive an average net monetary
gain. The items included as monetary on the COMPUSTAT tape were the
ones identified in Step One above. The average net monetary position
was multiplied by the full year's price change as the assumption was
made that the average monetary position was maintained throughout the
Several modifications were instituted in the depreciation expense
procedure as suggested by Davidson and Weil (1975a) in an attempt to
reduce the noise in the model. First, the method of depreciation was
not stated on the COMPUSTAT tape file. Since the restatement procedure
assumes the use of the straight-line depreciation method, those firms
using other methods for financial accounting purposes were identified
from SEC 10K reports and eliminated from the sample.
In addition, supplemental data on depreciation expense was col-
lected from SEC 10K reports. Depreciable assets were disaggregated
into the reported life classes in order to calculate the estimated
"ages" of the various classes of assets. For each class of asset
reported, the following calculation was used in the restatement proce-
Age of class = Accumulated Depreciation of Class (3)
Depreciation Expense of Class
More than 90% of the firms reported at least two classes of assets,
usually "Buildings & Plant" and "Equipment." Most firms reported
more than two classes including "Transportation Equipment" or Fix-
The procedure to segregate the assets into homogeneous life
groups was designed to overcome the deficiency in the Davidson and Weil
model as noted by Basu and Hanna (1975, p. 34). The Davidson and Weil
The data was taken from SEC Report 10K, Schedule VI, "Accumulated
Depreciation, Depletion and Amortization of Property, Plant and Equip-
ment" as reported under Regulation S-X, Rule 5-04.
Basu and Hanna (1975) recommended a "dollar weighted sum-of-the-
years'-digits" method but failed to demonstrate its superiority.
(1975a) model treated all assets, short and long lived, as one class
to calculate the "average age" of assets. The use of one "average age"
distorts the GPPA depreciation expense estimation according to Basu and
Hanna (1975). The depreciation adjustment was the most difficult one
to estimate. Interpretation of the results of the study should be made
with the awareness that the sample was heavily weighted with firms with
large amounts of depreciation.
Based upon the above assumptions, the adjustment algorithm was
used to generate the data used in the calculation of GPPA eps available
for the common stockholder. The following was calculated for firm-years:
GPPA Earnings GPPA Revenues GPPA Cost of Goods
Available for = Sold GPPA Depreciation GPPA (4)
Common Expenses + Monetary Gain or Loss -
GPPA Earnings Average Shares
GPPA eps = Available for of Common Stock (5)
The GPPA eps was used in the next step.
Step Three: Calculation of Unexpected
Earnings Per Share
The association tests used in this research required an account-
ing measure of "unexpected performance for each firm-year in the
sample. These measures, based upon the GPPA and traditional eps num-
bers, were assumed to be signals to the security market containing
unexpected information concerning the firm.
The two measures selected for use in this study were considered
naive models (Brown and Kennelly, 1972) in the sense that they are
based on random walk premises. One measure is based upon the
"first-difference" of eps while the other is based upon the "second-
difference" of eps. Each of these measures is discussed below.
The first-difference measure of unexpected eps is defined as:
epsut = epst epst1 (6)
eput epspst epst_1 (7)
epsut = the unexpected earnings per share at time period t for
a firm based on the first-difference measure;
epst, epstl1 = the observed, traditionally calculated earnings per share
at time period t and t-1 for a firm;
= similar measure as above except incorporation of GPPA
earning per share numbers generated in Step Two above.
The first-difference measure was used by Ball and Brown (1968) in
conjunction with a more sophisticated measure of unexpected earnings
based on an ordinary least-squares model. The naive model permitted
basically the same implications to be drawn from the Ball and Brown
study as did the more sophisticated model, thus it was selected for use
in this study.
It has been suggested that earnings time series flow may be a
random walk but may incorporate an upward drift (Ball and Watts, 1972).
Interpreted into expectations, this may suggest that investors would
expect some increase in earnings each year. To allow for the possibil-
ity another measure of "unexpected" earnings per share was utilized.
A second-difference measure or the change in the rate of change of
earnings per share was calculated. The following represents that
epsut = (epst eps t) (epst epst2)
epsut = (epst pst-1) (epst_ epst2)
epst, epst_1, epst_
= the unexpected earnings per share at
time period t for a firm based on the
2= the observed, traditionally calculated
earnings per share of time periods t,
t-1, and t-2 for a firm;
* = similar measure as above except incor-
poration of GPPA earnings per share
numbers generated in Step Two above.
An example is given below of the unexpected earnings measures
and their calculation. If the following were observed for a firm, the
calculations would be:
Calculated eps Calculated eps
1970 $1.53 $1.98
1971 1.69 3.19
1972 1.59 4.38
epsut = $1.59 $1.69 = -$.10
epsu = $4.38 $3.19 =+$1.19
epsut = ($1.59 $1.69) ($1.69 $1.53) = -$.26
eps* = ($4.38 $3.19) ($3.19 $1.98) = -$.02
Any combination of results may be experienced depending upon observed
eps numbers for a firm.
To summarize, past studies have indicated that the securities
market is both efficient and unbiased in adjusting prices to reflect
the flow of new or unexpected information. The preceding measures
were an attempt to identify new or unexpected information with respect
to eps. Naive models were selected for use in this study for two
reasons. First, it had not been demonstrated that these models were
inferior to other models and second, the number of data points col-
lected for each firm in this study precluded the use of more sophisti-
There is a question, however, of whether a single model can ade-
quately represent earnings patterns for all firms. Collins (1976)
studied this hypothesis by using the Box-Jenkins approach to identify
time patterns for sample firms. These relatively sophisticated models
were compared with naive models using market association tests. It
was concluded that:
the models individually estimated for each firm (by using
Box-Jenkins) differed from models that have characterized most
previous research that incorporated the time series properties
of earnings (p. 21).
Collins, however, did not find the more sophisticated models superior
in forecasting earnings in relation to the less sophisticated models.
The question concerning the firm's earnings pattern is recognized and
may constitute continued study beyond the scope of the current
Step Four: Abnormal Market Return Calculation
In order to perform the association tests, a market measure of
"abnormal or unexpected return" was required in addition to the mea-
sures of unexpected eps.
The Sharpe (1963) Market (or Diagonal) model was used to generate
the a. and a. parameters necessary to calculate a measure of unexpected
market return. The following regression was performed for the firms in
R. =a. + R + e (10)
it i i mt it
Rit = return on security i in month t;
a., 3. = intercept and slope of linear relationship between R.
and R ;
Rmt = market return in month t;
it = stochastic portion or individualistic component of R.t;
E( it) = 0.
The CRSP market index (Fisher, 1966) was used as the measure for Rt.
The estimates of the coefficients a. and 8i were the parameters of
interest in the model. These parameters, which were calculated from
the immediately prior 60-month period, were used to generate "unex-
pected" market returns for the subsequent 12 months. The following
strategy was used to estimate the a. and 8. estimates:
60 months' data
1/65 to 12/69
1/66 to 12/70
1/67 to 12/71
1/68 to 12/72
1/69 to 12/73
Estimate of a. and 8.
for use in year
In 1970 and following years, the calculation of
upon the a. and 8. for each firm estimated from
the residuals, based
prior data was made as
et = Rt (ai + $iRmt)
Ltit 1 i mt
eit = residual or measure of "unexpected performance;"
ai, 8 =
R. ,R =
estimates of regression coefficients;
It was necessary to estimate the a. and 8i using data outside the
period for which the eit above were observed. The result is due to the
fact that the E(E ) = 0 in the ordinary least squares calculation but
this fact is not assumed in the above calculation (Ball, 1972). The
residual, eit, above, is a measure of the "abnormal or unexpected"
market performance of the firm in month t.
The monthly "unexpected market performance" must be aggregated
into yearly measures. For this the following calculation was made:
1+ UMR = tl (1 + eit)
UMTi t=1 eit)
For each year
T = 1970 to 1974
UMRTi = Unexpected yearly market return;
ei = Monthly measures of unexpected performance.
The values in the calculations of UMRi generated from Equation (10)
are used in the test of the hypothesis. Step Five identifies the role
of UMPi in that test.
Step Five: Test of the Hypothesis
Previous studies (Ball and Brown, 1968; Gonedes, 1974) indicated
an association between unexpected traditional (or "historical cost")
earnings and abnormal market returns. The strength of that association
has been used as an aid in assessing the informational content of
accounting numbers (Gonedes and Dopuch, 1974, p. 83). The test of the
H : There is no difference between GPPA Association
and Traditional Association.
was an attempt to determine if GPPA eps has a greater or lesser asso-
ciation with the securities market variable than does traditional eps.
It must be noted that the methodology, by itself, should not be used
to determine a preference ordering of accounting principles (Gonedes
and Dopuch, 1974). Inefficiencies in the cost and distribution of
accounting data make association tests alone inappropriate for most
normative decisions concerning the desirability of standards and
principles. The expected result of this study was to supplement the
available empirical research concerning earnings variables and their
relationship with market variables.
The test for association was performed using chi-square tests on
two-by-two contingency tables. For each measure of unexpected earn-
ings, first-difference and second-difference contingency tables were
constructed. For each of the measures, the two models of eps were
compared-traditional and GPPA. If either, traditional or GPPA, dis-
played association with the market then the test of the hypothesis to
determine which model had closer association would be meaningful.
Specifically, the firm-years where the models gave different
signals to the market were of prime consideration in the actual test
of the hypothesis.
The following comparisons were made:
First-Difference Measure of EPS
Signal of Signal Observed
Earnings From Market
Those Sign of eps (+)
Where Sign of UMR ()
Signs Sign of epsut (
epsut = unexpected first-difference measure of traditional eps
for a firm-year;
epsut = unexpected first-difference measure of GPPA eps for a
UMR = abnormal market return for a firm-year.
The above comparison was also performed for the second-difference
Of interest was the number of times each of the earnings models,
traditional vs. GPPA, gave the "correct" signal to the market. A
"correct'signal is defined as the same sign on the earnings variable
as observed on the market variable. For example, from Figure 5 in
Step Three, a value of -$.10 for epsut and +$1.29 for epsut was calcu-
lated from assumed data. If UMR- for the same firm-year were observed
to be positive, the epsut was considered the "correct" signal. If
UMRT were observed negative, the epsut was considered the "correct"
signal. If the association between eps and UMRT were the same as for
eps and UMRT, an approximate equal number of "correct" signals should
be observed for each of the models. In this case the hypothesis could
not be rejected as the models would display a similar association with
the market. If one model gave significantly more "correct" signals
than the other, the hypothesis could be rejected. The results of the
tests are presented in the next chapter.
RESULTS OF STUDY
The firms selected for this study were those from the population
which were expected to exhibit changes in eps upon restatement for
purchasing power changes. The sample selection process explained in
Chapter II identified 76 firms on which restatement procedures were
performed. The results of the restatement procedure are to be examined
first. Descriptive statistics are presented and outcomes compared with
Next, the results of the calculations of the measures of unex-
pected earnings are presented and the distributions of the data are
described. After disclosing the unexpected earnings, the results of
the calculations of the measure of unexpected or abnormal market per-
formance are detailed. The data points for the unexpected earnings
and the data points for unexpected market returns are then paired and
a test of the major hypothesis is performed.
Since the testing of the hypothesis relies upon nonparametric
procedures, an exploratory analysis involving parametric procedures
was performed. A discussion of the applicability of these procedures
and the presentation of the general results are detailed in Appendix
A. This presentation deals with an extension into the analysis of the
relationship between eps numbers and the movement of security prices.
Resultsof the Restatement Procedure
The restatement algorithm explained in Chapter II was performed
on the 76 firms for which appropriate data were available. For eight
firms, 1974 financial data were unavailable on the COMPUSTAT tape file
utilized, thus for the year 1974 only 68 firm-year observations were
The sample selection process divided firms into two groups
according to the expected effect on GPPA eps with a change in purchas-
ing power of the dollar. The classification of Group I and Group II
will be carried throughout the discussion in this chapter. Contained
in Group I are those firms identified in the sample selection process
which were expected to experience increased eps upon GPPA restatement
during inflation. In the same context those firms should also experi-
ence decreased restated eps during deflation. The sample selection
process also identified those firms which should experience decreased
eps upon restatement during inflation and vice versa during deflation.
These firms are identified by Group II. During the years of study only
inflation was prevalent, therefore, the subsequent analysis relates to
increases in the price level. As such, Group I firms were expected to
experience increased eps as a result of restatement while Group II
firms were expected to experience decreased eps.
Table 4 summarizes the results from the restatement process. On
an average, Group I eps increased while Group II eps decreased upon
restatement for purchasing power changes as illustrated in the table.
The sample selection process apparently identified firms with the
expected result upon restatement. This is illustrated by the increase
of Group I eps by an average of $.65 and a decrease of Group II eps by
$.55. The end objective, however, was to select those firms in which
eps is significantly affected by purchasing power changes. It follows,
however, that those firms most greatly affected by inflation (defla-
tion) would also be those affected from changes in the inflation
EXPECTED AND OBSERVED EFFECTS UPON RESTATEMENT
OF EPS DURING INFLATION
-yea Mean Reject
Expected Firm-year Mean Mean Mean Reject H 1: i-
Tradl- G"2 = 0 @
Group Effect Observa- Tradi-GPPA Observed 2
on eps tions onal eps Effect Significance
I + 105 $ .87 $1.52 +.65 .0125
II 267 $2.71 $2.16 -.55 .0015
One interesting observation from Table 4 was the absolute differ-
ence in the mean traditional eps numbers between the two groups. It
was observed that the mean for Group I firms was $.87 while the mean
for Group II firms was $2.71. The source of the difference was not
directly apparent. It could be argued, however, that eps itself is not
comparable across firms; thus, the aggregation of the eps for the two
groups identified in Table 4 should not be compared. There may have
been, though, inherent properties in the indices used to select the
sample which warrants consideration of possible biases including the
potential one of differences in eps cited above. The observed proper-
ties are noted below.
One possible area of bias stems from the use of an "earnings"
measure as the denominator in the Monetary Index developed in Chapter
II. Since the attempt was to identify those firms whose eps would be
significantly affected by changes in the inflation (deflation) rate,
the closer to zero the absolute value of the earnings measure, the
more likely the firm would be included in the sample, ceteris paribus.
In the sample, both Group I and Group II include a high proportion of
firms with years of earnings near zero.
It was also observed that the sample selection strategy had a
propensity to place "less stable" firms into Group I and place "more
stable" firms into Group II. That is, firms where eps was expected to
be augmented by applying restatement procedures tended to have more
debt and smaller fixed capital asset balances relative to those firms
where eps was expected to be decreased upon restatement. The amount
of debt and the amount of fixed asset base have been used as measures
of a firm's stability with respect to its ability to cope with economic
fluctuations. The sources of this possible bias can again be attri-
buted to the inherent structure of the indices constructed in the
sample selection process. The question of the stability of the firms
and other risk measures arises in the subsequent presentation and
analysis of the abnormal market returns.
Another possible area of confounding was identified during the
restatement process. Even though measures were taken in the sample
selection step to identify those firms where GPPA adjustments were
most pronounced, a high degree of association was observed between
traditional and GPPA eps. A Spearman Rank Order Correlation of .73
was observed. This observation suggests there was a bias
against finding that there is "no difference" in the degree of
association in the two earnings variables and the market variable.
Measures were taken in the test of the hypothesis, however, to attempt
to reduce noise in the data. These measures are discussed in the
section concerning the test of the hypothesis.
No definitive conclusions can be drawn about the effects of the
areas of possible bias; however, any attempt to generalize findings
must be tempered by these contingencies. The eps numbers, both tradi-
tional and GPPA, were used to derive measures of unexpected earnings
described in Chapter II. Since an analysis of the restatement proce-
dure indicates possible inherent differences of firms in Groups I and
II, the subsequent analysis maintains this dichotomous classification.
Measures of Unexpected Earnings Per Share
Two measures of unexpected or abnormal earnings per share were
utilized in this study. One was the nominal change or first-difference
in earnings per share. As explained in Chapter II, this calculation
was simply the difference between a year's eps and prior year's eps for
each firm year. The other measure of unexpected performance was the
second-difference or change in the rate of change of eps. It is con-
jectured and empirically supported (Beaver, Kettler, and Scholes, 1970;
Eskew, 1975) that these types of measures may be viewed by the secur-
ities market as indicators of unexpected performance of a firm. The
sign of each firm-year's unexpected eps is of particular importance for
this study since prior studies have indicated a positive relationship
between signs of unexpected earnings measures and signs of the measures
of abnormal market performance.
Table 5 presents the results of the calculations based on the
first-difference of the eps variables. This table identifies the
average change in eps from one year to the next. For example, the
average change in the traditionally calculated eps was $.33 for firms
in Group I and $.43 in Group II firms. A test of the difference in
means indicates that we cannot reject the hypothesis that the under-
lying population mean of Group I is equal to Group II.1 Thus, clas-
sification into a group of firms which were expected to have eps
augmented due to inflation and a group of firms which were expected
to have eps decreased because of inflation does not apparently, on the
average, result in significant differences in the first-difference
measure of unexpected eps.
Similar statements can be made for the mean differences for the
GPPA model in Table 5. Those same earnings, adjusted for price-level
changes, exhibit nonsignificant differences in means across the two
groups. It should be noted that the Studentized Range test provides
evidence that the distribution is not normal and any conclusions on
central tendency should be suspect. Observations of the data indicate
that the distributions have distant outlying observations on the
1Test the following hypothesis for traditional first-difference eps
measure: Ho: i 2 = 0 using the sample means and variances.
Z = = .52 cannot reject H at a = .01.
3.5 1.4 o
Test the following hypothesis for GPPA first-difference eps mea-
sure: Ho: 0 i 2 = 0 using the sample means and variances.
Z = = .52 cannot reject H at a = .01.
3.5 2.3 o
positive side. The other measure of unexpected earnings used in this
study was the second-difference of eps. The summary results of that
measure are presented next.
MEASURE OF UNEXPECTED EARNINGS PER SHARE
Mean STD DEV Student-
l Effect of Year Mean STD DEV MIN MAX sizeda
Model 1st Ist id
Restatement Obser- Value Value
DIFF DIFF Range
on EPS nations
tional Group I 105 $.33 $1.87 $-5.64 $12.12 9.5
Model Group II 267 .43 1.18 -3.04 7.85 9.2
GPPA Group I 105 .59 1.88 -4.22 12.74 9.2
Model Group II 267 .48 1.52 -3.20 11.20 9.5
The Studentized Range is a statistic for judging whether the dis-
tribution which generated the sample was normal.
Studentized Range = Max(Xi) Min(Xi)
The number of standard deviations between the maximum and minimum value
should be less than 6.4 and greater than 4.0 99 percent of the time in
a normal distribution of 100 observations. For 200 observations the
upper and lower parameters are 6.9 and 4.6 respectively.
Table 6 presents the results of calculations based on the second-
difference of eps variables. This table indicates the mean change in
the rate of change or second difference of eps from one year to the
next. The same classifications are found in Table 6 as in Table 5.
However, there are a total of 76 fewer firm-year observations in each
of the models, traditional and GPPA. The second-difference calcula-
tion, as explained in Chapter II, requires an additional year of eps
per firm to calculate, thus the period of observation was modified to
1971 through 1974.
MEASURE OF UNEXPECTED EARNINGS PER SHARE
Mean STD DEV Student-
Model Effect of Year MIN MAX student
Restatement Obser- 2nd Value Value
on EPS nations DIFF DIFF Range
adi Group I 83 $.33 $2.58 $-8.49 $13.32 8.5
Model Group II 213 .38 1.30 -3.30 6.06 7.2
GPPA Group I 83 .41 2.44 -7.90 12.45 8.3
Model Group II 213 .52 1.57 -3.91 8.10 7.7
Comparison in Table 6 of the means between groups of the tradi-
tional second-difference eps model indicates there is little support
that the means of the underlying populations are different.3 The same
conclusion can be drawn for the means relating to the GPPA second-
difference groups. Here again, the Studentized Range would indicate
that the underlying distribution was not normal.
H: 1 12 = 0.
Z = =
il 12 = 0.
= 52 .41
for traditional second-difference
.17 cannot reject H
at a = .01
for GPPA second-difference eps
.38 cannot reject H
at a = .01
Regression Results: a and 8 Values
The regression calculations on securities market data as outlined
in Step Four of Chapter II were performed and the estimates of a and 8
were derived for each firm-year. These coefficients were afterwards
utilized to derive the abnormal market returns reported in the subse-
quent section. The 8 values have an independent interpretation from
finance and accounting literature and are of interest in themselves.
The coefficient, 8, is commonly defined as a measure of the systematic
risk of a security in relation with other securities in the population
(Fama, 1976; pp. 73-87). A value of 8 greater than 1.0 indicates that
the security has greater than average systematic risk while a value of
8 less than 1.0 indicates that the security has less than the average
risk. A 8 value of 1.0 indicates an average risk in relation to the
other securities in the population.
An examination of the 8 values derived from the 380 regression
calculations may provide more information about the companies that
comprise the sample. Table 7 presents data concerning the observed
8s for the sample. The same classifications of Group I and Group II
are maintained and the 8s are classified by year.
Interpretation of the data in Table 7 requires caution. Much of
the data used to derive the 8 values for one year within a group was
also used to derive 8 values for the other years. That is, the obser-
vations within each group are not independent. Regardless, there
appears to be evidence that those firms originally selected because of
an expected increase in eps upon restatement for price level have
significantly greater 8s than the average population. Those firms in
Group II, that is, firms in which eps was expected to decrease upon
OBSERVED 8 VALUES FOR FIRM-YEARS
STD STD Reject
Restatement Number of Mean Range DEV Error H
Effect on Year Observa- B of 8 DEV Error Ho-
eps (Infla- tions Value Value of of M = 0
tion)Value Mean @ .05
1970 22 1.64 .80-2.80 .49 .10 *
(Expected 1971 22 1.49 .66-2.43 .41 .08
nree o 1972 22 1.62 .65-2.51 .48 .10
oRestat t 1973 22 1.60 .66-2.58 .57 .12 *
1974 22a 1.55 .59-2.36 .54 .11 *
1970 54 1.03 .13-1.96 .38 .05
(Expected 1971 54 .89 .12-1.66 .36 .05
e of 1972 54 .93 .10-1.74 .36 .05
Restatement 1973 54 .91 .14-1.71 .34 .04 *
1974 54b .87 -.41-1.56 .41 .05 *
Indicates rejection of H .
aSubsequent analysis used
stated previously, the paired
unavailable COMPUSTAT data.
Subsequent analysis used
stated previously, the paired
unavailable COMPUSTAT data.
only 17 of these observations since, as
restated eps was not available due to
only 51 of these observations since, as
restated eps was not available due to
restatement, appear to have S values significantly less than those in
Group I. There is some evidence that those a values are significantly
less than 1.0.
In other terms, those firms in Group I appear to indicate a
measure of systematic risk significantly greater than firms in Group
II. From the previous evaluation of the eps data and the sample
selection technique, this observation was not unexpected. It was
noted that the sample selection procedure had an inherent tendency to
include highly levered firms in Group I while it placed those with a
less levered capital structure in Group II. Debt structure has been
used as an accounting measure of risk (Beaver, Kettler and Scholes,
1970) and empirical evidence supports the hypothesis of the existence
of a relationship between accounting-determined and market-determined
measures of risk (Beaver, Kettler and Scholes, 1970; Eskew, 1975).
Both accounting and market measures support the contention that
firms in Group I are more risky than those in Group II. The possible
consequences of this situation are deferred to the conclusions
presented in Chapter IV. The a and B values from the above proce-
dures were used in the derivation of the measure of unexpected market
performance. These results are presented in the next section.
Calculation of Abnormal Market Returns
The c and a values from the previous step were employed to cal-
culate monthly residuals (e it) for each firm. Unexpected yearly
market returns (UMRTi) were then derived using the monthly residuals
as explained in Step Three of Chapter II. Table 8 presents the
descriptive statistics of these unexpected market returns for the
sample of firms retaining dichotomous classification of Group I and
Group II from the previous analysis.
UNEXPECTED MARKET RETURNS (UMRTi)
Expected of Ob- Mean Value Standard Minimum Maximum
Effect on serva of UMRi Deviation Value Value
Effect on tionsa
Group I 110 .7% 55% -83% 272%
Group II 270 2.2% 35% -92% 208%
As previously stated, eight firm-years were subsequently not used
in the analysis due to unavailable eps data.
Table 8 indicates that although there were wide fluctuations in
the unexpected market returns, the mean values were close to zero for
each group. The hypothesis that the mean of the underlying distribu-
tion of Group I was the same as the mean of the underlying distribu-
tion of Group II could not be rejected. A histogram of the combined
groups is presented in Appendix B. It may be noted that the distribu-
tion is mound-shaped, however, and the test for normality,
Ho: UMRTi N(1.5%, 42%),
The hypothesis H : F1 12 = 0 substituting sample data was
-.7 2.2 -2.9
Z = -.51
4 3025/110 + 1225/270 5.7
not significant at a = .05.
can be rejected by a chi-square test at the .01 level of signifi-
Although minor departures from the normality assumption of the
underlying distribution may be tolerated, problems with assumptions
regarding the normality of the data can be avoided by using nonpara-
metric procedures to test the major hypothesis. These tests are
presented in the next section.
Test of the Hypothesis
Tests of relationships between the abnormal or unexpected market
returns and the abnormal or unexpected eps were performed using
two-by-two contingency tables. The prime consideration was the sign
of the variables. Thus, if a relationship existed, it was conjectured
that a positive sign of the unexpected eps variable would be paired
empirically with a positive sign on the unexpected market return, and
negative signs of the unexpected eps variable would be paired empir-
ically with a negative sign on the unexpected market return.
The test of the hypothesis intended to ascertain whether or not
the unexpected earnings per share, adjusted for the effects of gen-
eral purchasing power changes, have a stronger, weaker, or a similar
relationship to unexpected market returns than does traditional
unexpected earnings per share for firms in the sample. If investors
incorporate the effects of purchasing power changes, as interpreted
by the preceding price-level adjustment model, greater association
between the accounting and market measures of abnormal performance
for the price-level adjusted models would be expected.
6See Appendix B for test.
The contingency tables below are the result of pairing the signs
of the accounting and market measures of abnormal performance. In
this analysis, the previously-used group classifications were dropped,
thus eliminating any prior expectation of how the purchasing power
adjustment affected eps. This elimination was done since previous
analysis of the unexpected eps measures indicated little apparent
difference between Group I and Group II. For example, Table 5 and
Table 6 from Chapter III indicated that the means of the measures,
when compared across groups, were not significantly different from
one another. These data are, however, presented in Appendix C and the
effects of the groupings are identified.
Tests Using First-Difference Measure
Table 9 presents the results of comparing the sign on the first-
difference measure of unexpected earnings based on the traditional
income model and the measure of abnormal market returns. Also
presented in the table is the expected frequency of observations if
assignment to cells were randomly assigned considering the marginal
probabilities. If strong associations exist, it would be expected
that one would find significantly large differences in the expected
frequency and observed frequency within a cell. As can be noted from
Table 9, this apparently is not the case. A chi-square test indi-
cates that the data do not exhibit a strong relationship. Apparently,
for the firms in the sample, the first-difference measure of tradi-
tional eps does not represent unexpected or abnormal earnings perfor-
mance to the securities market.
The data in Table 10 differ in respect to the GPPA earnings
model in generating eps. The first-difference of GPPA eps was used
as the measure of unexpected earnings. The sign of this measure was
matched with the sign of the abnormal market return. The data exhibit
little association as illustrated by a chi-square of .19.7 A similar
conclusion is drawn from the data in Table 10 as from Table 9. That
is, based upon this sample, the investors apparently did not view the
first-difference of GPPA earnings as a measure of abnormal earnings
CONTINGENCY TABLE OF FIRST-DIFFERENCE MEASURE OF
UNEXPECTED EPS USING THE TRADITIONAL MODEL
VS. ABNORMAL MARKET RETURNS
Traditional first-difference of eps
x = 1.42
Not significant at a = .05.
7In the two-by-two contingency tables the number of degrees of
freedom is one. The following are the critical values of chi-square
for each of the probabilities.
8 2 (120-114.8)2 (43-48.2)2 (142-147.2)2 (67-61.8)
x 114.8 + 48.2 + 147.2 61.8
114.8 48.2 + 147.2 + 61.8
Observed 120 Observed 43
Expected 114.8 Expected 48.2
Observed 142 Observed 67
Expected 147.2 Expected 61.8
CONTINGENCY TABLE OF FIRST-DIFFERENCE MEASURE OF
UNEXPECTED EPS USING THE GPPA MODEL VS.
ABNORMAL MARKET RETURNS
GPPA first-difference of eps
x = .19
Not significant at a = .05.
Although the data from Tables 9 and 10 suggest little or no
association and further testing may be inappropriate, the test of the
hypothesis was performed. This is done for illustrative purposes.
Of particular interest were those cases where the measure of unex-
pected earnings under the traditional model gave signals opposite
than from the unexpected earnings measure of the GPPA model. For
example, if the traditional model measure indicated positive unex-
pected earnings performance and the GPPA model indicated negative
unexpected earnings, the observed sign of the abnormal market return
would disclose which model gave the "correct" signal.
In all there were 49 of the 372 first-difference earnings mea-
sures that were of opposite signs. In the other 323 observations the
signs of the measures of unexpected eps were the same for both the
traditional and GPPA model. Those observations where the signs were
9 2 (108-106) (134-136) (55-57) (75-73)
x106 + + + 73
106 136 57 73
Observed 108 Observed 55
Expected 106 Expected 57
Observed 134 Observed 75
Expected 136 Expected 73
the same were eliminated from the test in an attempt to reduce
The illustrations in Table 11, based upon eps measures of oppo-
site signs, are exact opposites of each other. This is observed
because a "correct" signal for one model inherently means an "incor-
rect" signal for the other. The expected frequencies within each
cell reaffirm previous conclusions that the first-difference measure
of neither unexpected earnings model is highly associated with
abnormal market returns. That is, neither model gave significantly
more "correct" signals to the market. This is illustrated by a chi-
square of .19 where significance at the a = .05 would require a chi-
square of 3.84. Thus the hypothesis that there is no difference in
association cannot be rejected. Since there was no apparent associa-
tion observed for either eps variable, the failure to reject the
hypothesis is viewed as inconsequential. The following section
relates to the second-difference measure of unexpected earnings.
Tests Using Second-Difference Measures
The first-difference measure apparently was not viewed by the
securities market as an "unexpected" or "abnormal" measure of earnings
for these sample firms. This section deals with the other measure of
unexpected earnings--that of a second-difference measure.
Table 12 presents the results of comparing the sign of second-
difference measure of unexpected earnings based on the traditional
income model and the sign of abnormal market returns. Again, the
expected frequencies of assignment to cells based upon the marginal
probabilities are included in the table. The results indicate that
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there is an apparent relationship between the sign of the second-
difference of traditional eps and the sign of the abnormal market
return. For example, if observations had been randomly assigned it
would be expected that one would observe approximately 77 firm-years
in the "++" cell. Ninety-six were observed. In the "--" cell approx-
imately 66 should have been observed if there were no relationship.
Actually, 85 were observed in that cell. The chi-square statistic
of 20.46 indicates a high probability that a relationship exists.
Results using the GPPA earnings model are discussed in the next sec-
CONTINGENCY TABLE OF SECOND-DIFFERENCE MEASURE OF
UNEXPECTED EPS USING THE TRADITIONAL MODEL
VS. ABNORMAL MARKET RETURN
Traditional second-difference of eps
x = 20.46
Significant at = .001.1
The data in Table 13 were similarly based upon a second-differ-
ence unexpected earnings measure, however, the underlying eps
calculation was based upon GPPA assumptions. Again, the sign of the
unexpected earnings measure was empirically matched with abnormal
11 2 (96-77.2)2 (31-49.8)2 (84-102.8)2 (85-66.2)
S+ + 102.866.2
77.2 49.8 102.8 66.2
Observed 96 Observed 31
Expected 77.2 Expected 49.8
Observed 84 Observed 85
Expected 102.8 Expected 66.2
market returns. The data support the contention that there is an
association between the sign of the GPPA generated unexpected eps
measure and the sign of the abnormal market return. For example, the
"++" cell contained 93 observations where only 83 would be expected
if observations were assigned according to the marginal probabilities.
CONTINGENCY TABLE OF SECOND-DIFFERENCE MEASURE OF
UNEXPECTED EPS USING THE GPPA MODEL
VS. ABNORMAL MARKET RETURN
GPPA second-difference of eps
x2 = 6.32
Significant at a = .025.12
The chi-square value is smaller for the GPPA generated data than
for the traditionally generated data. From Table 12 the chi-square
value was 20.45, whereas from Table 13, the value was 6.32. Although
there is support that the traditional model had greater association
with the market variable, the significance of the difference cannot
be measured. That is, there is no measure of variability whereby it
can be determined if the association observed under the traditional
model is significantly greater than that observed under the GPPA
12 2 2 2 2
2 2 (93-82.8)2 (34-44.2)2 (100-110.2)2 (69-58.8)
82.2 44.2 110.2 58.8
Observed 93 Observed 34
Expected 82.8 Expected 44.2
Observed 100 Observed 69
Expected 110.2 Expected 58.8
To ascertain if the null hypothesis,
H : There is no difference between Traditional and
GPPA association with abnormal market returns,
could be rejected, only those observations where the sign of tradi-
tional earnings measure was again different from the sign of the GPPA
earnings measure were considered. That is, only firm-year observa-
tions where the traditional eps unexpected return had a positive sign
and the GPPA eps unexpected return had a negative sign, or vica versa,
were used. For those observations, the signs of the unexpected
earnings measures were empirically matched with the signs of the
abnormal market return. A positive-positive or negative-negative
match was an indication of greater association. A positive-negative
or negative-positive match was an indication of a lesser association
and thus an "incorrect" signal to the market.
Table 14 presents the results of the 54 observations. The
traditional model contingency table is necessarily the opposite of
the GPPA model contingency since a "++" match-up in one table forces
a "-+" match-up in the other table, etc. The chi-square of 7.49
indicates that we can be confident that the traditional unexpected
eps measure has significantly greater association with the abnormal
market return than the GPPA unexpected measure. Thus we can reject
the null hypothesis of no difference in association.
The consequence of the rejection of the hypothesis is described
in Chapter IV.
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SUMMARY AND CONCLUSIONS
The purpose of this study has been to explore the relationship
between general purchasing power adjusted earnings per share and the
movement of security prices. A key assumption of the examination was
that investors currently have data available which enables them to
make rudimentary purchasing power adjustments to financial statements.
A summary of the findings of this research is now presented followed
by the basic implications.
Summary of Results
1. The sample selection technique attempted to identify and
apparently did identify those firms which had significant differences
in earnings per share due to purchasing power changes ("Greater" in
Group I and "Less" in Group II);
2. There was an observed close association between traditionally
calculated and GPPA eps indicated by a Spearman Rank Order Correlation
3. The naive models of unexpected earnings displayed little
apparent difference in underlying distribution due to the dichotomous
classification in the sample selection technique. That is, the mea-
sures of unexpected earnings in Group I were not apparently different
from those in Group II;
4. The derivation of the 8 regression coefficients needed for
calculation of the abnormal market return indicated that the sample
selection technique inherently placed "risky" firms in Group I and
"less-risky" firms in Group II;
5. The observed distribution of the unexpected or abnormal
market return for the sample firms, although not normal, was mound-
shaped, with a mean near zero;
6. The first-difference unexpected earnings measures of neither
the traditional nor the GPPA models had significant association with
the measure of the abnormal market return;
7. The lack of association of the first-difference measures of
unexpected earnings precluded a meaningful test of the hypothesis;
8. The second-difference unexpected earnings measure of both the
traditional and the GPPA models exhibited significant association with
the measure of the abnormal market return;
9. A test of the hypothesis using second-difference measures
supports the contention that traditional eps is more highly associated
with market returns than GPPA eps in those cases where the sign of the
second-difference measures differed between historical and GPPA.
The following conclusions are separated into two parts. The first
is concerned with the implications derived from the study preceding the
test of the hypothesis while the second part deals with statements
which can be concluded from the test of the hypothesis.
Implications of Study
1. One area of interest is the inherent nature of general price-
level adjustments and their effect on earnings per share. It has been
observed that most firms are fairly well "balanced" in respect to the
effects of general purchasing power adjustments of eps. That is, the
adjustment process would not significantly alter the traditional eps
signals to the market. This study attempted to examine those less
common occurrences where general purchasing power changes significantly
affected traditional eps. The study disclosed that the market had
judged (or termed) "risky" (i.e., larger value for 0) those firms in
which eps would be augmented due to price-level adjustment during in-
flation. Firms in which eps would be reduced due to price-level adjust-
ments during inflation were determined "less risky" by the market.
It appears there may be some relationships to be explored between
the risk measures accorded in the market and the effects of restate-
ment on earnings. Any evaluation of GPPA reporting policies should
examine these market measures and their significance.
2. Another observation from the study was the apparent failure
of the first-difference earnings model to depict investors' decision
patterns for this data. Apparently, investors expected some improve-
ment in eps and a constant or even a small upward drift was not inter-
preted as "good news" to the market. Most previous empirical studies
have indicated a relationship between first-difference measures of
unexpected earnings and measures of abnormal market performance.
Noise in the model or bias in sample selection could be sources of the
failure of the model to perform as expected, however.
3. Appendix B depicts the observed abnormal or unexpected yearly
market returns for each firm-year. It is of interest that although
the distribution is apparently not normal, it is mound-shaped and may
not severely violate the assumptions of normality. This observation
is encouraging to the applicability of parametric procedures using
abnormal market returns.
Implications of the Test of the Hypothesis
1. General purchasing power adjusted earnings per share for the
firms examined did exhibit a significant association with the movement
of security prices for the second-difference model. This conclusion
was not surprising due to the association of GPPA eps with traditional
eps. Even more significant was the comparison of the two models as
2. Based upon the data for firms with different signs for second-
difference measures of eps, it appears that traditionally calculated
earnings per share have more information consistency with the movement
of security prices than do general purchasing power adjusted earnings
per share. Although the evidence allows only the generalization to
firms that meet the criteria for sample selection and have opposite
second-difference measures, the purpose of the study was accomplished.
Empirical evidence concerning the relationship of earnings variables
and security prices is provided. The evidence does not allow the
assessment of the desirability of alternative accounting techniques,
however, it provides insight into the impoundment of earnings numbers
into security prices, both traditional and GPPA.
Implications for Further Research
There are a multitude of unanswered questions which have emerged
as a result of this research. Several of them are identified below:
1. Is the assumption valid that data is currently available to
the market which allows reasonable estimates of GPPA adjustments?
2. Do the random walk earnings models adequately reflect the
3. Are there visibility problems in the market concerning pur-
chasing power adjustments?
4. Would company reported GPPA earnings alter the findings of
Each of these questions requires research beyond the scope of the cur-
EXTENSION OF THE TESTS OF ASSOCIATION
BETWEEN EPS AND MARKET PRICES
The second-difference measures of unexpected earnings demon-
strated an association with abnormal market returns. The tests of
association utilized nonparametric tests to avoid the presumption of
normality and avoid scaling problems with respect to the data. The
following presentation is an extension of that analysis using regres-
sion analysis and the second-difference measures of unexpected
earnings. It is cautioned that the examination of the data presented
in Chapter III indicated that it is likely the data are not normally
The first set of regression results using nominal measures of
earnings are presented in Table A-i. The use of nominal data may be
questioned since the absolute size of the measure would not be com-
parable across firms and thus a scaling problem exists. That is, an
abnormal earnings measure of +$1.00 for a firm which stock is selling
for $50.00 per share would not necessarily be expected to be reflected
in the market to the same extent as a firm which stock is selling for
$5.00 per share. Since the results may be used to compare with other
models, it is presented below.
REGRESSION ANALYSIS OF SECOND-DIFFERENCE MEASURES OF
UNEXPECTED EPS AND UNEXPECTED MARKET RETURNS
Linear Regression Model
F-Value Significant R-Square
Dependent Independent at Level
UMRTi eputi 9.76 .002 .032
UMR epsuti 2.57 .110 .009
UMRi = Unexpected market return for firm i in year T;
epsuti = Second-difference measure of unexpected earnings per
share for firm i in year t using traditional earnings
epsuti = Second-difference measure of unexpected earnings per
share for firm i in year t using GPPA earnings model.
For the traditional model, the F-value of 9.76 indicates that there is
likely a relationship between the unexpected earnings measure and the
unexpected market return. An R-Square of only .032, however, reveals
that only a small amount of variance in the dependent variable can be
explained by movement of the independent variable. Although the re-
sults indicate relationship, the model has little explanatory power.
A search for a better model is illustrated below.
Table A-2 presents similar tests as Table A-l, except, in an
attempt to make the eps measures comparable across firms, the measures
have been deflated by the bookvalue per share of stock. It was sur-
mised that the investor may view the unexpected earnings signal
relative to some underlying "value" of the share. Bookvalue was used
as a possible measure of that value.
To be consistent, GPPA bookvalue should have been used for the
GPPA earnings model. The additional cost and effort to collect that
data was judged not worth the benefit, thus the surrogate of tradi-
tional bookvalue was used.
REGRESSION ANALYSIS OF SECOND-DIFFERENCE MEASURES OF
UNEXPECTED EPS DEFLATED BY BOOKVALUE AND
UNEXPECTED MARKET RETURNS
Linear Regression Model
F-Value Significant R-Square
Dependent Independent at a Level
UMR esuti ti 27.63 .0001 .086
URi esuti/BVti 11.14 .001 .036
UMRT = Unexpected market return for firm i in year T;
epsuti = Second-difference measure of unexpected earnings per
share for firm i in year t using traditional earnings
epsuti = Second-difference measure of unexpected earnings per
share for firm i in year t using GPPA earnings model;
BVti = Bookvalue per share of firm i at year end t.
Both models represented in Table A-2 demonstrated a significant rela-
tionship with abnormal market returns. The stronger, with an F-value
of 27.63, however, was the traditional model. Again, neither model
performed well in explaining the variance of the dependent variable.
The traditional model had an R-Square of only .086.
One other attempt was made to discover a more useful method to
deflate the eps measures. The measures of unexpected eps were divided
by current market share price to derive an "unexpected price-earnings
ratio." It was conjectured that this measure could be an important
signal to the market. Table A-3 discounts this idea as the models
appear to perform poorly.
The market price Pti is in current dollars thus no price level
adjustment would be necessary to make the models consistent.
REGRESSION ANALYSIS OF SECOND-DIFFERENCE MEASURES OF
UNEXPECTED EPS DEFLATED BY MARKET SHARE PRICE
AND UNEXPECTED MARKET RETURNS
Linear Regression Model
F-Value S cant R-Square
Dependent Independent at a Value
MReputi/Pti 2.47 .11 .008
UMi es ti/Pti .04 .84 .000
UMRTi = Unexpected market return for firm i in year T;
epsti = Second-difference measure of unexpected earnings per
share for firm i in year t using traditional earnings
epsuti = Second-difference measure of unexpected earnings per
share for firm i in year t using GPPA earnings model;
Pti = Market price of common stock of firm i at year end t.
In conclusion, the model using bookvalue as an eps deflator
appears to be the best model tested, although it did not exhibit
strong explanatory properties. These are not the only models that
could have been used, however, they appeared to be ones most reason-
able. In any case, the traditional earnings models consistently
demonstrated greater relationship with the market than did the com-
parable GPPA models.
DISTRIBUTION OF ABNORMAL MARKET RETURNS FOR
SAMPLE COMPANIES: 1970-1974
The bar-graph in this appendix represents the observations of
unexpected market returns (UMR.i) calculated from Step Four of Chapter
II. Three hundred and eighty firm-years are represented on the graph.
The following presents a six interval test of normality for the dis-
Ho: UMRT i 1 N(1.5, 42)
2 (48-63)2 (76-63) (99-63) (66-63)2
x + + +
63 63 63 63
x = 36.9
Reject at a = .01.
Xdf=5,=. 01 5.1.
CONTINGENCY TABLES OF MEASURES OF ABNORMAL EPS
AND MEASURES OF ABNORMAL MARKET RETURNS
BY GROUP CLASSIFICATION
The contingency tables presented below are similar to Tables 9,
10, 12 and 13 in Chapter III except the data is disaggregated into the
two groups identified in the sample selection process. The sample
selection process selected firms that eps was expected to increase
upon restatement for purchasing power changes. These were referred to
as Group I. Group II firms were those that eps was expected to de-
crease upon restatement for purchasing power adjustment. The eight
contingency tables presented are identified in Table C-l.
RELATIONSHIP OF PRESENTED CONTINGENCY TABLES
Measures of Abnormal eps
Traditional Reporting G
GPPA Reporting Model
First- Second- First- Second-
Difference Difference Difference Difference
Models Models Models Models
Group Group Group Group Group Group Group Group
I II I II I II I II
Abnormal Table Table Table Table Table Table Table Table
Market C-2 C-3 C-4 C-5 C-6 C-7 C-8 C-9
The above tables are presented below and the tests of significance are
presented in Table C-10.
GROUP I VS
OF FIRST-DIFFERENCE MEASURE OF
USING THE TRADITIONAL MODEL,
ABNORMAL MARKET RETURNS
Sign of Abnormal eps Measure
Observed 32 Observed 8
Expected 28.2 Expected 11.8
Observed 42 Observed 23
Expected 45.8 Expected 19.2
CONTINGENCY TABLE OF FIRST-DIFFERENCE MEASURE OF
UNEXPECTED EPS USING THE TRADITIONAL MODEL,
GROUP II VS. ABNORMAL MARKET RETURNS
Sign of Abnormal eps Measure
Observed 88 Observed 35
Expected 86.6 Expected 36.4
Observed 100 Observed 44
Expected 101.4 Expected 42.6
CONTINGENCY TABLE OF SECOND-DIFFERENCE MEASURE OF
UNEXPECTED EPS USING THE TRADITIONAL MODEL,
GROUP I VS. ABNORMAL MARKET RETURNS
Sign of Abnormal eps Measure
CONTINGENCY TABLE OF SECOND-DIFFERENCE MEASURE OF
UNEXPECTED EPS USING THE TRADITIONAL MODEL,
GROUP II VS. ABNORMAL MARKET RETURNS
Sign of Abnormal eps Measure
Observed 24 Observed 12
Expected 17.3 Expected 18.7
Observed 16 Observed 31
Expected 22.7 Expected 26.6
Observed 72 Observed 19
Expected 59.8 Expected 31.2
Observed 68 Observed 54
Expected 80.2 Expected 41.8
CONTINGENCY TABLE OF FIRST-DIFFERENCE MEASURE
OF UNEXPECTED EPS USING THE GPPA MODEL,
GROUP I VS. ABNORMAL MARKET RETURNS
Sign of Abnormal eps Measure
CONTINGENCY TABLE OF FIRST-DIFFERENCE MEASURE
OF UNEXPECTED EPS USING THE GPPA MODEL,
GROUP II VS. ABNORMAL MARKET RETURNS
Sign of Abnormal eps Measure
Observed 25 Observed 15
Expected 25.1 Expected 14.9
Observed 41 Observed 24
Expected 40.9 Expected 24.1
Observed 83 Observed 40
Expected 81.1 Expected 41.9
Observed 93 Observed 51
Expected 94.9 Expected 49.1
CONTINGENCY TABLE OF SECOND-DIFFERENCE MEASURE
OF UNEXPECTED EPS USING THE GPPA MODEL,
GROUP I VS. ABNORMAL MARKET RETURNS
Sign of Abnormal eps Measure
GROUP II VS.
OF SECOND-DIFFERENCE MEASURE
EPS USING THE GPPA MODEL,
ABNORMAL MARKET RETURNS
Sign of Abnormal eps Measure
+ ____ -____
Observed 71 Observed 20
Expected 61.9 Expected 29.1
Observed 74 Observed 48
Expected 83.1 Expected 38.9
Observed 22 Observed 14
Expected 20.8 Expected 15.2
Observed 26 Observed 21
Expected 27.2 Expected 19.8
The association between the variables presented in Tables C-2
to C-9 was investigated using chi-square tests and the results are
presented below in Table C-10.
TESTS OF RELATIONSHIPS BETWEEN ABNORMAL
EARNINGS MEASURES AND ABNORMAL
MARKET MEASURE (UMRi)
Contingency Chi-Square Test Significance
Table C-2 2.80 *
Table C-3 .14 *
Table C-4 7.73 <.01
Table C-5 12.68 <.001
Table C-6 .00 *
Table C-7 .24
Table C-8 .29
Table C-9 7.24 <.01
Not significant at level .05 or less.
Not significant at a level .05 or less.
FLOWCHART OF GENERAL PURCHASING POWER
RESTATEMENT COMPUTER PROGRAM
Procedure P procedure
Do KI = Do K3 =
1969 to 1974 1969 to 1974
GPPA RevenueKl ExpenseK3
= RevenueK1 TOT GS
J TOTK3- C K3
tEnd r IGPPA Expense
to Main Prog GPPA ens
~~tPurchas o Main Prog.
Do K2 =
1968 to 1974 1
COGS + INVK2
to Main Progy
Call FIFO -
OGSK4 No Calculate ADJ
INVK4-1 from Average
"Problem i GPPA COGS =
COGS Ex- PRE 1/
ists" / PREK4 1/2
(ADJ) + INVK4
Calculate ADJ R-- -
from Average CO S Proce
GPPA COGS =
PREK4 = COGSK4
GPPA COGS1 +
> INV -
No age Date Approp-
GPPA COGS1 Entered COGS
Amounts of Prior
Calculate Aver- = COGS PLA
age Dates INV
For Each In-
GPPA COGS =
Each INV In-
COGS Each PLA
GPPA COGS1 +
to Main Pro
KEY OF VARIABLES
GPPA = General purchasing power adjusted;
ADJ = General purchasing power adjustment factor for year;
Kl to K7 = Counters;
COGS = Cost of goods sold for a firm;
INV = Inventory for a firm;
TOT = Total expenses reported for a firm;
FIFO = First-in-first-out inventory method;
LIFO = Last-in-first-out inventory method;
WA = Weighted average inventory method;
Classes = The number of fixed asset classes reported by a firm in
DEPR = Depreciation expense;
PLA = Calculated general purchasing power adjustment factor;
MON = Monetary items;
PRE = Purchases of inventory for a firm entering cost of goods
The computer program depicted by the flowchart was validated
using manual adjustment calculations on several firms from the sample.
Accounting Principles Board. APB Opinion No. 15: Earnings Per Share.
American Institute of Certified Public Accountants, December,
Accounting Principles Board. Financial Restatement for General Price-
Level Changes. APB Statement No. 3, American Institute of Certi-
fied Public Accountants, June, 1969.
American Accounting Association Committee to Prepare a Statement of
Basic Accounting Theory. A Statement of Basic Accounting Theory.
American Accounting Association, 1966.
"An Interview with John C. Burton," Management Accounting, January,
1969, pp. 19-23.
Ball, Ray. "Changes in Accounting Techniques and Stock Prices," Empir-
ical Research in Accounting: Selected Studies, 1972, pp. 1-45.
Ball, Ray, and P. Brown. "An Empirical Evaluation of Accounting Income
Numbers," Journal of Accounting Research, Autumn, 1968, pp.
Ball, Ray and Ross Watts. "Some Time Series Properties of Accounting
Income," Journal of Finance, June, 1972, pp. 663-82.
Basu, S. and J. H. Hanna. Inflation Accounting: Alternatives, Imple-
mentation, Issues and Some Empirical Evidence, The Society of
Industrial Accountants of Canada, Circa 1975.
Beaver, William H. "The Behavior of Security Prices and Its Implication
for Accounting Research," Supplement to The Accounting Review,
1972, pp. 407-36.
Beaver, William H. "What Should be the FASB's Objectives?" Journal of
Accountancy, August, 1973, pp. 49-56.
Beaver, William H. and Roland E. Dukes. "Interperiod Tax Allocation,
Earnings Expectations, and the Behavior of Security Prices,"
The Accounting Review, April, 1972, pp. 320-32.
Beaver, William H., P. Kettler, and M. Scholes. "The Association
Between Market Determined and Accounting Determined Risk Mea-
sures," The Accounting Review, October, 1970, pp. 654-82.
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