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In your own words, explain the efficient market hypothesis. Do you agree that the market is efficient? Why or why not?
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Schroeder, R.G., M.W. Clark, and J.M. Cathey. 2020. Financial Accounting Theory and Analysis. Text and Cases.
13th ed. Hoboken, NJ: Wiley.
An Empirical Evaluation of Accounting Income Numbers
Author(s): Ray Ball and Philip Brown
Source: Journal of Accounting Research , Autumn, 1968, Vol. 6, No. 2 (Autumn, 1968),
pp. 159-178
Published by: Wiley on behalf of Accounting Research Center, Booth School of
Business, University of Chicago
Stable URL: http://www.jstor.com/stable/2490232
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An Empirical Evaluation of Accounting
Income Numbers
RAY BALL* and PHILIP BROWNt
Accounting theorists have generally evaluated the usefulness of accounting practices by the extent of their agreement with a particular analytic
model. The model may consist of only a few assertions or it may be a
rigorously developed argument. In each case, the method of evaluation has
been to compare existing practices with the more preferable practices implied by the model or with some standard which the model implies all
practices should possess. The shortcoming of this method is that it ignores
a significant source of knowledge of the world, namely, the extent to which
the predictions of the model conform to observed behavior.
It is not enough to defend an analytical inquiry on the basis that its
assumptions are empirically supportable, for how is one to know that a
theory embraces all of the relevant supportable assumptions? And how does
one explain the predictive powers of propositions which are based on unverifiable assumptions such as the maximization of utility functions?
Further, how is one to resolve differences between propositions which arise
from considering different aspects of the world?
The limitations of a completely analytical approach to usefulness are illustrated by the argument that income numbers cannot be defined sub-
stantively, that they lack “meaning” and are therefore of doubtful utility.’
The argument stems in part from the patchwork development of account* University of Chicago. t University of Western Australia. The authors are
indebted to the participants in the Workshop in Accounting Research at the University of Chicago, Professor Myron Scholes, and Messrs. Owen Hewett and Ian Watts.
1 Versions of this particular argument appear in Canning (1929); Gilman (1939);
Paton and Littleton (1940); Vatter (1947), Ch. 2; Edwards and Bell (1961), Ch. 1;
Chambers (1964), pp. 267-68; Chambers (1966), pp. 4 and 102; Lim (1966), esp. pp. 645
and 649; Chambers (1967), pp. 745-55; Ijiri (1967), Ch. 6, esp. pp. 120-31; and Sterling
(1967), p. 65.
159
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160 JOURNAL OF ACCOUNTING RESEARCH, AUTUMN, 1968
ing practices to meet new situations as they arise. Accountants have had to
deal with consolidations, leases, mergers, research and development, pricelevel changes, and taxation charges, to name just a few problem areas.
Because accounting lacks an all-embracing theoretical framework, dissimilarities in practices have evolved. As a consequence, net income is an aggregate of components which are not homogeneous. It is thus alleged to be
a “meaningless” figure, not unlike the difference between twenty-seven
tables and eight chairs. Under this view, net income can be defined only as
the result of the application of a set of procedures { X1, X2, … } to a set of
events { Y1, Y2, -.. } with no other definitive substantive meaning at all.
Canning observes:
What is set out as a measure of net income can never be supposed to be a fact in
any sense at all except that it is the figure that results when the accountant has
finished applying the procedures which he adopts.2
The value of analytical attempts to develop measurements capable of
definitive interpretation is not at issue. What is at issue is the fact that an
analytical model does not itself assess the significance of departures from its
implied measurements. Hence it is dangerous to conclude, in the absence
of further empirical testing, tha~t a lack of substantive meaning implies a
lack of utility.
An empirical evaluation of accounting income numbers requires agreement as to what real-world outcome constitutes an appropriate test of usefulness. Because net income is a number of particular interest to investors,
the outcome we use as a predictive criterion is the investment decision as it
is reflected in security prices.3 Both the content and the timing of existing
annual net income numbers will be evaluated since usefulness could be impaired by deficiencies in either.
An Empirical Test
Recent developments in capital theory provide justification for selec
the behavior of security prices as an operational test of usefulness. An impressive body of theory supports the proposition that capital markets are
both efficient and unbiased in that if information is useful in forming capital
asset prices, then the market will adjust asset prices to that information
quickly and without leaving any opportunity for further abnormal gain.4
If, as the evidence indicates, security prices do in fact adjust rapidly to new
information as it becomes available, then changes in security prices will re2 Canning (1929), p. 98.
8 Another approach pursued by Beaver (1968) is to use the investment decision,
as it is reflected in transactions volume, for a predictive criterion.
4 For example, Samuelson (1965) demonstrated that a market without bias in its
evaluation of information will give rise to randomly fluctuating time series of prices.
See also Cootner (ed.) (1964); Fama (1965); Fama and Blume (1966); Fama, et al.
(1967); and Jensen (1968).
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EMPIRICAL EVALUATION OF ACCOUNTING INCOME NUMBERS 161
fleet the flow of information to the market.’ An observed revision of stock
prices associated with the release of the income report would thus provide
evidence that the information reflected in income numbers is useful.
Our method of relating accounting income to stock prices builds on this
theory and evidence by focusing on the information which is unique to a
particular firm.6 Specifically, we construct two alternative models of what
the market expects income to be and then investigate the market’s reactions when its expectations prove false.
EXPECTED AND UNEXPECTED INCOME CHANGES
Historically, the incomes of firms have tended to move together. One
study found that about half of the variability in the level of an average
firm’s earnings per share (EPS) could be associated with economy-wide
effects.7 In light of this evidence, at least part of the change in a firm’s in-
come from one year to the next is to be expected. If, in prior years, the income of a firm has been related to the incomes of other firms in a particular
way, then knowledge of that past relation, together with a knowledge of the
incomes of those other firms for the present year, yields a conditional ex-
pectation for the present income of the firm. Thus, apart from confirmation
effects, the amount of new information conveyed by the present income
number can be approximated by the difference between the actual change
in income and its conditional expectation.
But not all of this difference is necessarily new information. Some changes
in income result from financing and other policy decisions made by the firm.
We assume that, to a first approximation, such changes are reflected in the
average change in income through time.
Since the impacts of these two components of change-economy-wide
and policy effects-are felt simultaneously, the relationship must be estimated jointly. The statistical specification we adopt is first to estimate, by
Ordinary Least Squares (OLS), the coefficients (aijt, a2pt) from the linear
regression of the change in firm j’s income (AIlj,t) on the change in the
average income of all firms (other than firm j) in the market (AMj,tT)8
using data up to the end of the previous year (r = 1, 2, … , t – 1):
ljt- = dljt + 42itAMj,t-r + U3,t-T r = 1, 2, … , t – 1, (1)
5 One well documented characteristic of the security market is that useful sources
of information are acted upon and useless sources are ignored. This is hardly surprising since the market consists of a large number of competing actors who can gain from
acting upon better interpretations of the future than those of their rivals. See, for
example, Scholes (1967); and footnote 4 above. This evaluation of the security market
differs sharply from that of Chambers (1966, pp. 272-73).
6 More precisely, we focus on information not common to all firms, since some industry effects are not considered in this paper.
7Alternatively, 35 to 40 per cent could be associated with effects common to all
firms when income was defined as tax-adjusted Return on Capital Employed. [Source:
Ball and Brown (1967), Table 4.]
8 We call M a “market index” of income because it is constructed only from firms
traded on the New York Stock Exchange.
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162 RAY BALL AND PHILIP BROWN
where the hats denote estimates. The expected income change for firm j in
year t is then given by the regression prediction using the change in the,
average income for the market in year t:
AIit = dlit + 42jtAMjt
The unexpected income change, or forecast error (pjt), is the actual income
change minus expected:
Uit =Ijt – At . (2)
It is this forecast error which we assume to be the new information conveyed by the present income number.
THE MARKET’S REACTION
It has also been demonstrated that stock prices, and therefore rates of
return from holding stocks, tend to move together. In one study,’ it was
estimated that about 30 to 40 per cent of the variability in a stock’s monthly
rate of return over the period March, 1944 through December, 1960 could
be associated with market-wide effects. Market-wide variations in stock
returns are triggered by the release of information which concerns all firms.
Since we are evaluating the income report as it relates to the individual
firm, its contents and timing should be assessed relative to changes in the
rate of return on the firm’s stocks net of market-wide effects.
The impact of market-wide information on the monthly rate of return
from investing one dollar in the stock of firm j may be estimated by its
predicted value from the linear regression of the monthly price relatives of
firm i’s common stock’0 on a market index of returns:”1
9 King (1966).
10 The monthly price relative of security j for month m is defined as dividends
(dim) + closing price (pjmpi), divided by opening price (pjm):
PRim = (pi,m+i + djm)/pim.
A monthly price relative is thus equal to the discrete monthly rate of return plus
unity; its natural logarithm is the monthly rate of return compounded continuously.
In this paper, we assume discrete compounding since the results are easier to interpret in that form.
11 Fama, et al. (1967) conclude that “regressions of security on market returns over
time are a satisfactory method for abstracting from the effects of general market
conditions on the monthly rates of return on individual securities.” In arriving at
their conclusion, they found that “scatter diagrams for the [returns on] individual
securities [vis-A-vis the market return] support very well the regression assumptions
of linearity, homoscedasticity, and serial independence.” Fama, et al. studied the
natural logarithmic transforms of the price relatives, as did King (1966). However,
Blume (1968) worked with equation (3). We also performed tests on the alternative
specification:
In. (PRim) = b1i + b2In6 (L.) + vim (3a)
where Ine denotes the natural logarithmic function. The results correspond closely
with those reported below.
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EMPIRICAL EVALUATION OF ACCOUNTING INCOME NUMBERS 163
[PRim – 11 = bij + b2j[Lm – I] + VjmX (3)
where PRjm is the monthly price relative for firm j and month m, L is the
link relative of Fisher’s “Combination Investment Performance Index”
[Fisher (1966)], and vjm is the stock return residual for firm j in month m
The value of [Lm – 1] is an estimate of the market’s monthly rate of return.
The m-subscript in our sample assumes values for all months since January,
1946 for which data are available.
The residual from the OLS regression represented in equation (3) meas-
ures the extent to which the realized return differs from the expected return
conditional upon the estimated regression parameters (bj, b2J) and the
market index [Lm – 1]. Thus, since the market has been found to adjust
quickly and efficiently to new information, the residual must represent the
impact of new information, about firm j alone, on the return from holding
common stock in firm j.
SOME ECONOMETRIC ISSUES
One assumption of the OLS income regression model
are uncorrelated. Correlation between them can take at least two forms,
namely the inclusion of firm j in the market index of income (Mj), and the
presence of industry effects. The first has been eliminated by construction
(denoted by the j-subscript on M), but no adjustment has been made for
the presence of industry effects. It has been estimated that industry effects
probably account for only about 10 per cent of the variability in the level
of a firm’s income.’3 For this reason equation (1) has been adopted as the
appropriate specification in the belief that any bias in the estimates aljt and
a2jt will not be significant. However, as a check on the statistical efficiency
of the model, we also present results for an alternative, naive model which
predicts that income will be the same for this year as for last. Its forecast
error is simply the change in income since the previous year.
As is the case with the income regression model, the stock return model, as
presented, contains several obvious violations of the assumptions of the OLS
regression model. First, the market index of returns is correlated with the
residual because the market index contains the return on firm j, and because of industry effects. Neither violation is serious, because Fisher’s index
is calculated over all stocks listed on the New York Stock Exchange (hence
the return on security j is only a small part of the index), and because industry effects account for at most 10 per cent of the variability in the rate
12 That is, an assumption necessary for OLS to be the minimum-variance, linear,
unbiased estimator.
13 The magnitude assigned to industry effects depends upon how broadly an industry is defined, which in turn depends upon the particular empirical application being
considered. The estimate of 10 per cent is based on a two-digit classification scheme.
There is some evidence that industry eff ects might account for more than 10 per cent
when the association is estimated in first differences [Brealey (1968)].
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164 RAY BALL AND PHILIP BROWN
of return on the average stock.’4 A second violation results from our predic-
tion that, for certain months around the report dates, the expected values
of the v/s are nonzero. Again, a~ny bias should have little effect on the results, inasmuch as there is a low, observed autocorrelation in the Vj’s,’5 and
in no case was the stock return regression fitted over less than 100 observations.16
SUMMARY
We assume that in the unlikely absence of useful information about a
particular firm over a period, its rate of return over that period would re-
flect only the presence of market-wide information which pertains to all
firms. By abstracting from market effects [equation (3)] we identify the
effect of information pertaining to individual firms. Then, to determine if
part of this effect can be associated with information contained in the firm’s.
accounting income number, we segregate the expected and unexpected
elements of income change. If the income forecast error is negative (that is,
if the actual change in income is less than its conditional expectation), we
define it as bad news and predict that if there is some association between
accounting income numbers and stock prices, then release of the income
number would result in the return on that firm’s securities being less than
14 The estimate of 10 per cent is due to King (1966). Blume (1968) has recently
questioned the magnitude of industry effects, suggesting that they could be somewhat
less than 10 per cent. His contention is based on the observation that the significance
attached to industry effects depends on the assumptions made about the parameters
of the distributions underlying stock rates of return.
15 See Table 4, below.
16 Fama, et al. (1967) faced a similar situation. The expected values of the stock
return residuals were nonzero for some of the months in their study. Stock return
regressions were calculated separately for both exclusion and inclusion of the months
for which the stock return residuals were thought to be nonzero. They report that
both sets of results support the same conclusions.
An alternative to constraining the mean v; to be zero is to employ the Sharpe Capi-
tal Asset Pricing Model [Sharpe (1964)] to estimate (3b):
PRjm-RFm- 1 = b’i + b;j [Lm-RFm- 1] + vm (3b)
where RF is the risk-free ex ante rate of return for holding period m. Results from
estimating (3b) (using U.S. Government Bills to measure RF and defining the abnor-
mal return for firm j in month m now as b’1 + v’m) are essentially the same as
results from (3).
Equation (3b) is still not entirely satisfactory, however, since the mean impact
of new information is estimated over the whole history of the stock, which covers at
least 100 months. If (3b) were fitted using monthly data, a vector of dummy variables
could be introduced to identify the fiscal year covered by the annual report, thus
permitting the mean residual to vary between fiscal years. The impact of unusual
information received in month m of year t would then be estimated by the sum of the
constant, the dummy for year t, and the calculated residual for month m and year t.
Unfortunately, the efficiency of estimating the stock return equation in this particular form has not been investigated satisfactorily, hence our report will be confined
to the results from estimating (3).
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EMPIRICAL EVALUATION OF ACCOUNTING INCOME NUMBERS 165
TABLE 1
Deciles of the Distributions of Squared Coefficients of Correlation, Changes in Firm
and Market Income*
Decile
Variable
.1
.2
.3
.4
.5
.6
.7
.8
.9
(1) Net income .03 .07 .10 .1-5 .23 .30 .35 .43 .52
(2) EP S .02 .05 .11 .16 .23 .28 .35 .42 .52
* Estimated over the 21 years, 1946-1966.
would otherwise have been expected.17 Such a result (a2 < 0) would be evidenced by negative behavioi in the stock return residuals (P < 0) around
the annual report announcement date. The converse should hold for a
positive forecast error.
Two basic income expectations models have been defined, a regression
model and a naive model. We report in detail on two measures of income
[net income and EPS, variables (1) and (2)] for the regression model, and
one measure [EPS, variable (3)] for the naive model.
Data
Three classes of data are of interest: the contents of income reports; th
dates of the report announcements; and the movements of security prices
around the announcement dates.
INCOME NUMBERS
Income numbers for 1946 through 1966 were obtained from St
and Poor's Compustat tapes.18 The distributions of the squared c
of correlation' between the changes in the incomes of the indivi
and the changes in the market's income index20 are summarized
For the present sample, about one-fourth of the variability in t
17 We later divide the total return into two parts: a "normal return," d
the return which would have been expected given the normal relationship b
stock and the market index; and an "abnormal return," the difference
actual return and the normal return. Formally, the two parts are given by: b i +
b2s [Lm - 1]; and vim.
18 Tapes used are dated 9/28/1965 and 7/07/1967.
19 All correlation coefficients in this paper are product-moment correlation coefficients.
20 The market net income index was computed as the sample mean for each year.
The market EPS index was computed as a weighted average over the sample members,
the number of stocks outstanding (adjusted for stock splits and stock dividends)
providing the weights. Note that when estimating the association between the income
of a particular firm and the market, the income of that firm was excluded from the
market index.
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166 RAY BALL AND PHILIP BROWN
TABLE 2
Deciles of the Distributions of the Coefficients of First-Order Autocorrelation in the
Income Regression Residuals*
Decile
Variable
.1
.2
.3
.4
.5
.6
.7
.8
.9
(1) Net income... -.35 -.28 -.20 -.12 -.05 .02 .12 .20 .33
(2)EPS.......... -.39 -.29 -.21 -.15 -.08 -.03 .07 .17 .35
* Estimated over the 21 years, 1946-1966.
in the median firm's income can be associated with changes in the market
index.
The association between the levels of the earnings of firms was examined
in the forerunner article [Ball and Brown (1967)]. At that time, we referred
to the existence of autocorrelation in the disturbances when the levels of
net income and EPS were regressed on the appropriate indexes. In this
paper, the specification has been changed from levels to first differences
because our method of analyzing the stock market's reaction to income
numbers presupposes the income forecast errors to be unpredictable at a
minimum of 12 months prior to the announcement dates. This supposition
is inappropriate when the errors are autocorrelated.
We tested the extent of autocorrelation in the residuals from the income
regression model after the variables had been changed from levels to first
differences. The results are presented in Table 2. They indicate that the
supposition is not now unwarranted.
ANNUAL REPORT ANNOUNCEMENT DATES
The Wall Street Journal publishes three kinds of annual report a
ments: forecasts of the year's income, as made, for example, by co
executives shortly after the year end; preliminary reports; and the com-
plete annual report. While forecasts are often imprecise, the preliminary
report is typically a condensed preview of the annual report. Because the
preliminary report usually contains the same numbers for net income and
EPS as are given later with the final report, the announcement date (or,
effectively, the date on which the annual income number became generally
available) was assumed to be the date on which the preliminary report
appeared in the Wall Street Journal. Table 3 reveals that the time lag
between the end of the fiscal year and the release of the annual report has
been declining steadily throughout the sample period.
STOCK PRICES
Stock price relatives were obtained from the tapes const
Center for Research in Security Prices (CRSP) at the Univer
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EMPIRICAL EVALUATION OF ACCOUNTING INCOME NUMBERS 167
TABLE 3
Time Distribution of Announcement Dates
Fiscal year
Per cent of
firm s- _ _ _ - _ _ _ _ _ _ - _ _ _ _ _ _ - _ _ _
1957 1958 1959 1960 1961 1962 1963 1964 1965
25 2/07a 2/04 2/04 2/03 2/02 2/05 2/03 2/01 1/31
50 2/25 2/20 2/18 2/17 2/15 2/15 2/13 2/09 2/08
75 3/10 3/06 3/04 3/03 3/05 3/04 2/28 2/25 2/21
a Indicates that 25 per cent of the income reports for the fiscal year ended 12/31/
1957 had been announced by 2/07/1958.
TABLE 4
Deciles of the Distributions of the Squared Coefficient of
Return Regression, and of the Coefficient of First-Order
Autocorrelation in the Stock Return Residuals*
Decile
Coefficient
name
.1
.2
.3
.4
.5
.6
.7
.8
.9
Return re-
gression r2... .18 .22 .25 .28 .31 .34 .37 .40 .46
Residual autocorrelation.. -.17 -.14 -.11 -.10 -.08 -.05 -.03 -.01 .03
* Estimated over the 246 months, January, 1946 thr
cago.2' The data used are monthly closing prices on the New York Stock
Exchange, adjusted for dividends and capital changes, for the period January, 1946 through June, 1966. Table 4 presents the deciles of the distributions of the squared coefficient of correlation for the stock return regression
[equation (3)], and of the coefficient of first-order autocorrelation in the
stock residuals.
INCLUSION CRITERIA
Firms included in the study met the following criteria:
1. earnings data available on the Compustat tapes for each of the years
1946-1966;
2. fiscal year ending December 31;
3. price data available on the CRSP tapes for at least 100 months; and
4. Wall Street Journal announcement dates available.22
Our analysis was limited to the nine fiscal years 1957-1965. By beginning
the analysis with 1957, we were assured of at least 10 observations when
21 The Center for Research in Security Prices at the University of Chicago is sponsored by Merrill Lynch, Pierce, Fenner and Smith Incorporated.
22 Announcement dates were taken initially from the Wall Street Journal Index,
then verified against the Wall Street Journal.
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168 RAY BALL AND PHILIP BROWN
estimating the income regression equations. The upper limit (the fiscal
year 1965, the results of which are announced in 1966) is imposed because
the CRSP file terminated in June, 1966.
Our selection criteria may reduce the generality of the results. The sub-
population does not include young firms, those which have failed, those
which do not report on December 31, and those which are not represented
on Compustat, the CRSP tapes, and the Wall Street Journal. As a result,
it may not be representative of all firms. However, note that (1) the 261
remaining firms23 are significant in their own right, and (2) a replication of
our study on a different sample produced results which conform closely
to those reported below.24
Results
Define month 0 as the month of the annual report announcement, and
APIM , the Abnormal Performance Index at month M, as:
1N M
APIM = -Z II (1 + Vnm).
Nn m=-11
Then API traces out the value of one dollar invested (in equal amounts) in
all securities n (n = 1, 2, * *, N) at the end of month -12 (that is, 12
months prior to the month of the annual report) and held to the end of
some arbitrary holding period (M = -11, -10, * * * , T) after abstracting
from market affects. An equivalent interpretation is as follows. Suppose
two individuals A and B agree on the following proposition. B is to construct a portfolio consisting of one dollar invested in equal amounts in N
securities. The securities are to be purchased at the end of month -12
and held until the end of month T. For some price, B contracts with A to
take (or make up), at the end of each month M, only the normal gains (or
losses) and to return to A, at the end of month T, one dollar plus or minus
any abnormal gains or losses. Then APIM is the value of A's equity in the
mutual portfolio at the end of each month M.25
Numerical results are presented in two forms. Figure 1 plots APIm
first for three portfolios constructed from all firms and years in which the
income forecast errors, according to each of the three variables, were positive
(the top half); second, for three portfolios of firms and years in which the
income forecast errors were negative (the bottom half); and third, for a
single portfolio consisting of all firms and years in the sample (the line
which wanders just below the line dividing the two halves). Table 5 includes the numbers on which Figure 1 is based.
23 Due to known errors in the data, not all firms could be included in all years. The
fiscal year most affected was 1964, when three firms were excluded.
24 The replication investigated 75 firms with fiscal years ending on dates other
than December 31, using the naive income-forecasting model, over the longer period
1947-65.
25 That is, the value expected at the end of month T in the absence of further abnormal gains and losses.
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EMPIRICAL EVALUATION OF ACCOUNTING INCOME NUMBERS 169
1.12
1.10
Variable 2
1.08
1.08 'tVariable I
1.06
1.04
-S1.02
E 1.00
0
i
?j< _ To~ai sampie r . . .". . . . . . . . . . .". . . . .Total a
a 0.98
0.9
s Variable 1
0.92
0.90 Variable
Variable. 2
0.88
-12
-10
-8
-6
-4
-2
0
2
4
6
Month Relative to Annual Report Announcement Date
FIG. 1 Abnormal Performance Indexes for Various Portfolios
Since the first set of results may be sensitive to the distributions of th
stock return disturbances,26 a second set of results is presented. The third
column under each variable heading in Table 5 gives the chi-square statistic
for a two-by-two classification of firms by the sign of the income forecast
error, and the sign of the stock return residual for that month.
OVERVIEW
As one would expect from a large sample, both sets of results convey
essentially the same picture. They demonstrate that the information contained in the annual income number is useful in that if actual income differs
26 The empirical distributions of the stock return residuals appear to be described
well by symmetric, stable distributions that are characterized by tails longer than
those of the normal distribution [Fama (1965); Fama, et al. (1967)].
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170 RAY BALL AND PHILIP BROWN
TABLE 5
Summary Statistics by Month Relative to Annual Report Announcement Date
Month rela- Regression model Naive model
tive
to
annuali
Total
report an- Net income EPS EPS sample
nouncement
date
d()a (2) (3) (1) (2) (3) (1) (2) (3)
-11 1.006 .992 16.5 1.007 .992 20.4 1.006 .989 24.1 1.000
-10 1.014 .983 17.3 1.015 .982 20.2 1.015 .972 73.4 .999
-9 1.017 .977 7.9 1.017 .977 3.7 1.018 .965 20.4 .998
-8 1.021 .971 9.5 1.022 .971 12.0 1.022 .956 9.1 .998
-7 1.026 .960 21.8 1.027 .960 27.1 1.024 .946 9.0 .995
-6 1.033 .949 42.9 1.034 .948 37.6 1.027 .937 19.4 .993
-5 1.038 .941 17.9 1.039 .941 21.3 1.032 .925 21.0 .992
-4 1.050 .930 40.0 1.050 .930 39.5 1.041 .912 41.5 .993
-3 1.059 .924 35.3 1.060 .922 33.9 1.049 .903 37.2 .995
-2 1.057 .921 1.4 1.058 .919 1.8 1.045 .903 0.1 .992
-1 1.060 .914 8.2 1.062 .912 8.2 1.046 .896 5.7 .991
0 1.071 .907 28.0 1.073 .905 28.9 1.056 .887 35.8 .993
1 1.075 .901 6.4 1.076 .899 5.5 1.057 .882 9.4 .992
2 1.076 .899 2.7 1.078 .897 1.9 1.059 .878 8.1 .992
3 1.078 .896 0.6 1.079 .895 1.2 1.059 .876 0.1 .991
4 1.078 .893 0.1 1.079 .892 0.1 1.057 .876 1.2 .990
5 1.075 .893 0.7 1.077 .891 0.1 1.055 .876 0.6 .989
6 1.072 .892 0.0 1.074 .889 0.2 1.051 .877 0.1 .987
a Column headings:
(1) Abnormal Performance Index-firms and years in which the income forecast
error was positive.
(2) Abnormal Performance Index-firms and years in which the income forecast
error was negative.
(3) Chi-square statistic for two-by-two classification by sign of income forecast
error (for the fiscal year) and sign of stock return residual (for the indicated month).
Note: Probability (chi-square > 3.84 2= 0) = .05, for 1 degree of freedom.
Probability (chi-square > 6.64 x2 = 0) = .01, for 1 degree of freedom.
from expected income, the market typically has reacted in the same direction. This contention is supported both by Figure 1 which reveals a marked,
positive association between the sign of the error in forecasting income and
the Abnormal Performance
