Firm size and the information content of prices with respect to earnings

Journal

of Accounting

and Economics

9 (1987) 111-138.

North-Holland

FIRM SIZE AND THE INFORMATION CONTENT OF PRICES WITH

RESPECT

TO EARNINGS*

Daniel W. COLLINS Umsersi
USA

S.P. KOTHARI Universif_v of Rochester. Rochester, NY 1462 7, USA

Judy Dawson University

of Minnesota,

Received October

RAYBURN

Minneapohs,

MN 55455, USA

1985, final version received July 1986

Beaver, Lambert and Morse (1980) suggest that prices may be useful in forecasting future earnings. We explore the information content of prices with respect to earnings by focusing on firm size and its relation to the predictive accuracy of price-based earnings forecasts. Firm size proxies for the amount of information and for the number of traders and professional analysts processing the available information about an enterprise. Our empirical results are consistent with the hypothesis that price-based earnings will outperform univariate time series forecasts by a greater margin for larger firms than for smaller firms.

1. Inhwduction The prediction of earnings and the relation between unexpected accounting earnings and security prices have long been topics of interest to accountants and members of the investment community.’ The focus of the early work on the price-earnings relation was on using earnings measurements to explain differences in return performance. Seminal papers by Ball and Brown (1968) *The authors wish to express their appreciation to participants in the accounting workshops at Cornell, the University of Iowa, the University of Michigan, Northwestern, NYU, and the University of Washington for their helpful comments. Special thanks are due to Vie Bernard, John Elliot, Tom Linsmeier, Bob Lipe and Ross Watts for their detailed comments on earlier versions of this paper. ‘Such interest arises naturally out of the decision usefulness perspective of accounting which asserts that accounting earnings measurements are relevant to assessing the amount, timing and uncertainty of future cash flows of the firm. Popular valuation theories in finance (such as CAPM) model firm values as a function of risk-adjusted expected future cash flows. Changes in price (returns), therefore, reflect changes in the market’s assessment of the future cash flows of the firm. Hence, correspondence between earnings signals and price changes are viewed as a necessary condition for the former to possess information content [Gonedes (1972)].

0165-4101/87/$3.500

1987, Elsevier Science Publishers

B.V. (North-Holland)

112

D. Collins et al., Firm size and information content of prices

and Beaver, Clarke and Wright (1979) demonstrate that cross-sectional differences in annual abnormal security returns can be explained by the sign and magnitude of unexpected changes in annual accounting earnings. It is in this sense that accounting earnings measurements are alleged to be ‘meaningful’ or possess information content. In an extension of this early work, Beaver, Lambert and Morse (1980) (hereafter BLM) invert the traditional price-earnings relation and test for the information content of prices with respect to future earnings. In their analysis, price changes are viewed as a surrogate for additional information available to the market which is not captured in the past time series of earnings. Conditional on their particular valuation and earnings process assumptions, BLM demonstrate how the contemporaneous relation between earnings changes and price changes can be used to infer the earnings process and the expected future earnings as perceived by market participants.2 The results reported by BLM suggest that security prices behave as if earnings are perceived to follow a compound process that is dramatically different from the simple random walk specification which has descriptive validity for the annual accounting earnings series [Ball and Watts (1972)]. In particular, the compound process model identified in the BLM study implies some events that affect a firm’s permanent earnings and security prices will be reflected in accounting earnings with a lag.3 This insight prompted BLM to investigate the usefulness of price changes in predicting future earnings changes. They report that a price-based forecasting model marginally outperforms the random walk plus drift model that Watts and Leftwich (1977) and Albrecht. Lookabill and McKeown (1977) find superior to a broad class of alternative time series forecasting models. BLM caution, however, that their results are preliminary and that further testing is needed to assess the extent to which their findings can be generalized. The objective of this paper is to explore in more detail the information content of prices with respect to future earnings by focusing on firm size and its relation to the predictive accuracy of security prices vis-a-vis univariate time series models. Theoretical and empirical work in accounting and finance suggests that size may be an important conditioning variable when testing the information content of prices with respect to future earnings. Previous research suggests there are greater amounts of information available for large vs. small firms [Atiase (1980, 1985) and Grant (1980)]. Further, 2These

valuation

and earnings

process

assumptions

are discussed

in greater

detail below.

3BLM attribute this to temporal aggregation of earnings for shorter time intervals which causes the annual earnings series to disguise the character of the underlying series. Although the accounting system may be reporting events with significant pricing implications in a timely fashion, the temporal aggregation into annual earnings induces a lagged response relative to price changes. BLM hasten to note, however, that temporal aggregation is by no means a unique interpretation of their results.

113

D. Collins et al., Firm size and information content ofprices

we expect more traders and professional analysts will be processing the available information for large firms as compared to small firms. Ceteris paribus, the more information which is available about an enterprise and the greater the number of traders expending resources on information activities, the more informative prices become [Grossman (1976) Grossman and Stiglitz (1980), and Verrecchia (1979, 1982)]. That is, prices more efficiently aggregate and transmit diverse information held by heterogeneous traders. Accordingly, we hypothesize that price-based earnings forecasts will outperform univariate time series forecasts by a greater margin for larger firms than for smaller firms. Our empirical results are consistent with this hypothesis. Like BLM, the focus of our study is on the prediction of annual earnings over one-year-ahead forecast horizons.4 As such, our results coupled with the findings of BLM have potentially important methodological implications for ‘relation studies’ that examine the degree of association between earnings measurements and stock returns over annual periods. Examples of such studies include Ball and Brown (1968) Beaver, Clarke and Wright (1979) Beaver, Griffin and Landsman (1982) Bublitz, Frecka and McKeown (1985) and Raybum (1986). Essentially, the question addressed in these studies is whether conventional historical cost earnings measurements, or some alternative such as cash flow from operations or replacement cost earnings, capture in a meaningful way the economic events that affect firm values. Stated somewhat differently, the issue is whether alternative earnings measurements are consistent with the underlying information set used by market agents in valuing equity securities. The inferences drawn from these studies are based on the degree of statistical association (correlation) between the unexpected component of earnings (or some other performance measure) and abnormal security returns cumulated over the twelve months leading up to the annual earnings announcement or fiscal year end. Thus, the choice of a proxy for the markets’ expectation of earnings as of the beginning of the cumulation period critically affects the relative strength of association of competing performance measures with stock returns. An inappropriate proxy favors the null hypothesis of no association. Our results together with the evidence presented by BLM suggest that market earnings expectations one year in advance of the fiscal year end reflect a much broader information set than past earnings, at least for larger firms, Thus, measures of unexpected earnings based on univariate time series models contain measurement error. Given that such measures are typically used as predictor variables in testing the information content or ‘meaningfulness’

4The informativeness of prices with respect to earnings subject of on-going research by Kothari (1986).

over shorter

forecast

horizons

is the

114

D. Collins et al., Firm size and information content of prices

of alternative earnings measurements, one encounters the standard errorsin-variable variable problem which biases the coefficients toward zero.5 Our findings on the differential informativeness of prices with respect to future earnings across firm size suggest that the measurement error embedded in proxies for unexpected earnings (formed over one-year-ahead forecast horizons and conditioned on univariate time series models) is greater for larger firms than for smaller firms. Thus, our results help to explain the inverse relation between firm size and the strength of association between unexpected annual earnings and contemporaneous security price changes reported by Burgstahler (1981) and Freeman (1987). An alternative interpretation of our findings is that the cumulation period used in previous studies to measure the security price adjustments to events captured by accounting earnings may be misspecified.6 Specifically, our findings suggest that there is considerable potential for understating the degree of association between price changes and earnings changes if one limits the return cumulation period to the contemporaneous time frame over which the accounting income determination is made. This may be especially true for larger, more widely traded securities. Like BLM, we find evidence consistent with the claim that some events which affect the permanent earnings prospects and stock values of a firm are captured in accounting earnings with a lag (e.g., a new government contract, a new discovery or product breakthrough, or a major strike). BLM attribute this phenomenon to temporal aggregation of earnings for shorter time intervals (e.g., quarters) into annual earnings. Essentially, the aggregation process results in annual earnings numbers changing in a delayed fashion relative to permanent earnings changes. The lead-lag relation between price changes and earnings changes may also be explained by the revenue and expense recognition rules underlying the conventional accrual accounting model. In general, these rules require a completed, arms-length transaction before the economic impact of events is entered into the accounting records. Thus, part of the change in firm value associated with events with earnings implications may well occur in a time frame prior to the accounting period in which the effects of these events are captured by the accounting records. If the objective of earnings association studies is to capture all valuation changes associated with the events reflected in the current period’s reported earnings measure (or some other measure of performance), then our findings suggest it may be necessary to initiate the cumulation of security returns prior to the beginning of the current accounting period. Precisely where to begin the cumulation process is difficult to predict, a priori. It will depend not only on ‘See Maddala (1977) for further discussion of bias in the estimates coefficients when explanatory variables are measured with error. ‘We are grateful

to Ross Watts for suggesting

this alternative

interpretation

of linear to us.

regression

D. Collins ef al., Firm size and information content ojprices

115

the timing of events with lagged earnings implications, but also on the information environment and the availability of alternative sources of information about a firm’s activities. However, given the hypothesized relation between firm size, the amount of information, and number of information intermediaries engaged in information acquisition and dissemination, we expect (and find) stronger evidence of price changes leading earnings changes for larger firms vis-a-vis smaller firms. The remainder of the paper is organized as follows. In section 2 we review relevant literature and develop the hypothesized relation between firm size and the information content of prices. Our data and methodology are described in section 3. The results are presented in section 4, and the implications of our findings for association-type earnings studies are discussed in section 5. Section 6 contains a summary and conclusions. 2. Hypothesis

development

Prior theoretical and empirical work suggests a positive association between capitalized firm value and the amount of information disseminated to market agents. Based on the work of Stiglitz (1971) Hirschleifer (1971) and Wilson (1975) Atiase (1980) analyzes factors that affect returns to private information acquisition. His major conclusions are that (1) the scale of operation (i.e., the amount of potential investment in a particular firm) must be sufficiently large to justify the cost of information acquisition and (2) there must be sufficient demand and supply for a stock such that its price is not easily affected by an individual trader’s activities, thereby revealing his private information at the time of the trade.’ Verrecchia (1980) makes a similar argument. He asserts that as the number of traders in a stock increases, prices will be less sensitive to changes in the level of informedness of a single investor. Hence, the greater the number of investors, the less erosion there is to the size of the potential gain from acting first on the basis of privately obtained information. Atiase reasons that firms with larger capitalized values are much more likely to meet these conditions than smaller sized firms. Accordingly, he hypothesizes that the amount of predisclosure (i.e., non-accounting) information production and dissemination is an increasing function of the capitalized value of the firm. Consistent with this hypothesis, Atiase (1985) finds a much greater price adjustment to the quarterly earnings announcements of small vs. large firms. Grant (1980) corroborates these findings for annual earnings announcements. Both of these studies suggest there is a greater flow of non-accounting ‘Note, however, that privately obtained information will eventually be inpounded in stock prices. This occurs either because the true state of nature is ultimately revealed or because the individual trader, having taken an appropriate long or short position, has an incentive to reveal the true state so that he can capture the gains from the rest of the market reacting to the previously private information.

116

D. Collins et al., Firm size and information content

ofprices

information for large vs. small firms between the releases of accounting reports. Indeed, Grant (1980) finds a significantly greater number of interim news items appearing in the Wall Street Journal for NYSE firms relative to OTC firms. Casual observation also suggests that brokerage houses and investment firms devote a majority of their time and resources to gathering and disseminating information on large, widely traded securities. Grossman (1976, 1978), Grossman and Stiglitz (1980) and Verrecchia (1979, 1982) examine the informativeness of prices in aggregating and transmitting information held by individual investors. Among other things they demonstrate that the informativeness of prices is positively related to: (1) the number of traders who actively participate in the market for a particular security and (2) the proportion of traders who are informed with respect to a given signal. The preceding evidence suggests that both the amount of information about a firm’s activities and the number of informed traders are a positive function of firm size. Moreover, as the number of information signals that have future cash flow implications increases, investors’ prior beliefs about the earnings prospects of a particular firm will become more compact (exhibit less variance), and their consensus judgement as reflected in security prices will approach the ‘true’ or permanent earnings of the firm with greater precision.8 We hypothesize that price changes (i.e., security returns) will provide a more accurate and efficient estimate of permanent earnings changes for larger firms vis-a-vis smaller firms because (1) there is a broader and richer information set available about the activities of larger firms vis-a-vis smaller firms and (2) there are greater numbers of traders and professional analysts expending resources on information activities with respect to large vs. small firms.’ Given the BLM results that accounting earnings tend to reflect permanent earnings changes with a lag, we hypothesize that price-based forecasts (which rely on price changes in the year prior to the year of prediction) will outperform univariate time series forecasts more consistently for larger firms than for smaller firms. 3. Data and methodology 3.1. Sample and security return measures We initially identified a sample of COMPUSTAT-CRSP firms with a December 31 fiscal year end and a minimum of six prior years of earnings data ‘Conceptually, BLM argue that the measured accounting earnings of a firm can be decomposed and a transitory into a permanent component, x,,, which reflects events with pricing implications, We expand on this notion later in the component, E,,, that is void of any pricing implications. paper. ‘Information activities are broadly semination and interpretation.

defined

to include

information

gathering,

processing,

dis-

D. Collins et al., Firm size and information

content of prices

117

for each year from 1968-1980.‘” Total sample sizes during this time frame ranged from 630 firms in 1968 to 1051 firms in 1980. We expect firm-specific events with future cash flow and earnings implications to be revealed in the unexpected return for any given year. The popular market model was used to estimate expected returns. The ai, /? parameter estimates used in computing expected returns for a given year were obtained by regressing weekly returns of individual securities on the equally weighted weekly market return over the previous two years (104 observations). The abnormal or unexpected returns were then computed as a;, = R,, - [g + ,%,,,I.

0)

The cumulative abnormal return over the period January 1 to December 31 of each year was then calculated according to the following expression:” CAR,,=

fi (1 + u,,) - 1, r=l

(2)

where in (1) and (2) = unexpected return for firm i in week t, uir R,,, R,, = realized return for security i and equally weighted market return, respectively, in week t, CAR,, = cumulative risk-adjusted stock return for firm i in year T. The results reported by BLM (1980) suggest that various events which affect the market’s expectations of future cash flows (and, hence, security prices) in the current period are reflected in accounting earnings with a lag. Hence, the CAR,, measure will be used in forming price-based earnings forecasts of individual firms. The price-based forecasting model is described in greater detail below. 3.2. Time series expectations models A popular model used to describe the annual accounting earnings series is the random walk or martingale model [see Beaver (1970) and Ball and Watts (1972)], which may be represented as follows: EPS, = EPS,_, + E,, lOThe sufficient below.

(3)

restriction of at least six prior years of earnings was imposed in order that we have data to estimate a drift term under the random walk plus drift forecast model described

“As in BLM (1980), a January 1 to DecembFr with the firms’ fiscal year and to ensure that information released after year end.

31 cumulation period was chosen to coincide prices were not reflecting any non-earnings

D. Collins et al., Firm size and informabon content of prices

118

where 5, - N(0, I$). According to this specification, the best estimate of EPS, is EPA’_ 1 since E(5,) = 0. Moreover, the annual percentage change in EPS becomes the forecast error (FE) according to the random walk specification, EPS, - EPS, _ 1

FE RW=

EPS,_ 1

A second specification support in the literature Lookabill and McKeown may be formally written

= %AEPS,.

for the annual earnings series which has found wide is the random walk with drift model [see Albrecht, (1977) and Watts and Leftwich (1977)]. This model as follows:

EPS, = EPS,_, + 5, + a,,

(5)

where s, = + $ ( EPS,_, - EP~,_,_,).

(54

J-1

In contrast to the strict random walk model, the average %AEPS is non-zero and is equal to 6,. The percentage forecast error under this specification is given by FE RWD

AEPS, - 6,

EPS, - EPS,_ 1 - 6, =

EPS,_ 1

=

EPS,_,

’

Table 1 presents summary statistics of %AEPS, and CAR, of sample firms for the period of 1968-1980. Since we hypothesize that firm size is related to the amount of information available to assess the amount, timing, and uncertainty of future cash flows, the sample has been ranked according to market value of equity and divided into size quintiles.i2 It is apparent from this table that the average percentage change in earnings of firms in the smallest quintile is approximately zero (0.09%). This suggests that the random walk model is a reasonably good specification of the earnings generating process of smaller firms. It is equally clear from table 1 that the average percentage change in earnings for the larger firms in our sample is approximately 8-9%. This suggests that the random walk with drift model may be a more appropriate specification of the earnings generating process of these firms. “Firms are re-ranked each year according to the market value of equity at the beginning of the year. The summary figures in table 1 are based on pooling observations across years (1968-80) for each size quintile.

1568)

2

5

1877)

1984)

5

2641.6

435.2

157.9

57.1

$14.8

Mean

by size quintile,

1,277.6

420.4

151.6

53.3

$12.4

Median

4.516.0

153.2

61.6

26.6

$10.1

Std. dev.

X.90 (23.14)

7.76 (25.151

7.83 (2X.21)

1.95 (32.X6)

0.09% (42.53)

Mean

9.36 (15.2X)

7.59 (17.34)

7.49 (18.97)

X.16 (21.35)

6.35’% (32.95)

Median

31.06 (22.54)

34.23 (24.47)

38.15 (26.85)

43.83 (30.05)

53.4X% (32.41)

-Std. dev.

0.2X (23.77)

0.04 (23.9X)

0.58 (26.6X)

0.42 (28.75)

-4.11% (30.78)

Mean

CAR value)

~ 3.25 (17.19)

~ 5.56 (17.24)

- 5.63 (19.59)

- 0.483 (22.44)

~ X.X9% (25.01)

Median

Annual (absolute

change in EPS and CA R’s, based on data from 1968-80.”

Percent change in EPS (absolute value)’

market value of equity, percentage

Market value of equity ($ millions)

statistics

aFirm years with negative EPS in the denominator in the calculation of percentage changes were deleted which accounts for the unequal Percentage changes in EPS greater (less) than 100% were set equal to + (-) 100%. ‘Summary statistics in parentheses are for absolute values of percentage change in EPS and annual CAR’s ‘Size is measured by the market value of equity as of the beginning of each year. Size rankings were recalculated each year.

(N=

(A’=

4

(N = 1804)

.

(N = 1722)

(N=

1

Size’ quintile

Summary

Table 1

cell sizes.

33.27 (23.27)

38.69 (30.36)

40.51 (30.4X)

38.72 (25.93)

40.81% (27.09)

Std. dev.

120

D. Collins et al., Firm size and information content of prices

The summary statistics on the absolute value of the %AEPS reported in parentheses reveals an inverse relation between firm size and the magnitude of earnings changes. Together with the standard deviation values reported in table 1, these results indicate that earnings changes of smaller firms are more variable than those of larger firms and, therefore, are likely to be more difficult to predict. Givoly and Lakonishok (1983) Pincus (1983) and Choi (1985) report results consistent with this claim. Table 1 also reveals a negative relation between firm size and the absolute value of the CAR ‘s. Like earnings changes, the price changes of smaller firms tend to be more dramatic than for larger firms. For example, the median absolute value of CAR, for the smallest size quintile is 25.01% compared to a median value of 17.19% for the largest size quintile. In summary, the results reported in table 1 reveal a systematic inverse relation between firm size and the magnitude of earnings changes and abnormal returns. We next turn our attention to the degree of covariability between earnings changes and abnormal returns, first on a contemporaneous basis and then ,on a lagged basis. 3.3. The relation between price changes and earnings changes The forecast error or %AEPS, given in eq. (4) is commonly related to the abnormal security returns in eq. (2) to assess the information content of earnings. The following general model represents the relation between price changes and earnings changes examined by Beaver; Clarke and Wright (1979) and Burgstahler (1981): CAR, = a + b%AEPS,

+ e,.

(7)

Note that in this model earnings changes are used to explain changes in price (returns). As an initial step towards inverting this price-earnings relation, BLM (1980) characterize measured accounting earnings as a mixture of two processes: (1) A permanent process which reflects events which have security pricing implications. This process is characterized as x,. (2) Another process which reflects the impact of events with no pricing implications. This process captures the transitory or temporary fluctuations in accounting earings and is characterized as E,. Thus, the observed or reported EPS series can be viewed as a ‘garbling’ of permanent earnings (x,) because of the existence of transitory fluctuations E,.

121

D. Collins et al., Firm size and information content of prices

More formally, EPS, = x, + E,,

(8)

and AEPS,

= Ax,+

de,.

(9)

BLM assume that both the accounting earnings series and the permanent earnings series can be modeled as a first-order moving average process in first differences. For permanent earnings, this general model may be represented as follows: x,=x,_1

+a,--u,_,,

(10)

Ax, = a, - Ba,_l, where

19 is the moving

01)

average coefficient

and

Ecu,) = 0, u’( a,) = u2, u(u,, a,) = 0.

vt,s,

t#s.

BLM then introduce the valuation assumption that prices at any point in time are equal to the capitalized value of expected future permanent earnings. They further assume that the capitalization rate is constant through time. Given these assumptions and the added assumption that market participants perceive earnings to be a compound process as in eq. (8) they derive the following contemporaneous relation between percentage changes in price and percentage changes in permanent earnings [see pp. 6-10 of BLM (1980)]:

(1 -

AP, -= P r-l

(1 -

B)AEPS,+ EPS,-,

fI)Ba,_,

-8a,_,

- (1-

- E,_~

8)Ae,

(12)

By grouping on the change in price (in our case, CAR,), BLM argue that Qt-1 = E, = Et_, = 0, leaving only the permanent change in earnings. Therefore, eq. (12) yields

gL(l-0)s. f 1

(13) 1

1

Based on their underlying valuation and earnings process assumptions, BLM use the contemporaneous relation in eq. (13) to infer the expected permanent earnings process as perceived by market agents. By grouping on returns, they obtain estimates of (1 - 0) of approximately 2, which implies B = - 1. If permanent earnings follows a random walk process, as suggested by

122

D. Colh

et al., Firm size and information content of prices

various time series studies of annual earnings, then the implied B should be zero. Wheatley (1982) argues that grouping on the dependent variable in eq. (13) may induce an upward bias in the estimated (,1 - 8) coefficients, with a corresponding downward bias in the implied 6 estimates. The potential overstatement stems from the fact that when grouping on the dependent variable one, in part, forms groups by the regression disturbance. This, in turn, induces spurious correlation between the regression disturbance and regressor leading to estimated slope coefficients that are biased away from zero. Beaver, Lambert and Ryan (1987) (hereafter BLR) use reverse regression techniques [see Learner (1978)] to assess the degree of bias in the (1 - S) estimates, and find that grouping on returns does not induce any serious biases. Using valuation and earnings process assumptions that incorporate growth and reverse regression techniques, we were able to replicate the BLM and BLR results. Specifically, for all size quintiles the implied 8 estimates from regressing contemporaneous percentage change in earnings on returns were between -1 and 0.13 The first-order serial correlation for an IMA (1,l) process is given by -8

04

(1 + 62)

Thus, - 1 < 8 < 0 implies positive serial correlation in the first differences of permanent earnings. That is, events which cause permanent earnings (x,) to be a, above E(x,) are expected to induce an additional impact on permanent earnings in period t + 1. From the contemporaneous relation between accounting earnings and permanent earnings given in eq. (8) it follows that accounting earnings will reflect not only random shocks to the permanent earnings series in the current (contemporaneous) period, but also the cumulative effects of random shocks to permanent earnings from previous periods. That is, accounting earnings changes will tend to lag permanent earnings changes. In a rational and efficient market, the effects of random shocks to permanent earnings are reflected in security price changes when these shocks are revealed to market agents. We posit that both the timeliness and extent to which permanent earnings changes are revealed to market agents will be a positive function of firm size. This hypothesis is based on evidence which suggests there is more information available (outside of accounting reports) on the activities of large vs. small firms and there are more individuals (e.g., analysts) processing and disseminating this information to a broader group of market agents. These factors combine to allow the market to achieve greater consensus in forming expectations of permanent earnings of large vs. small I3 These results

are available

from the authors

upon request.

D. Collins et al., Firm size and information content of prices

123

firms, and a more timely and less garbled reflection of such earnings changes in security prices. Thus, we expect security price changes to be more informative with respect to future earnings changes of large vs. small firms. Table 2 provides evidence to support this hypothesis. Here we invert the price-earnings relation and investigate the extent to which CAR’s for period t explain period t + 1 earnings changes. The model we estimate is similar to that reported in table 3 of BLM (1980, p. 21) and is formally represented as follows: %AEPS,,l

= Y,, + Y&AR,

+ y,+tl.

(15)

Recall from our previous arguments that the CAR, variable in eq. (15) reflects changes in the market’s permanent earnings expectations for period t. The dependent variable, %A EPS,, 1, is the one year lagged change in measured accounting earnings which, at the individual security level, includes both a permanent and transitory component. By grouping individual securities into portfolios based on CAR,, we can effectively minimize the measurement error on the left-hand side of the equation by driving the average transitory component of earnings changes to zero at the portfolio level.t4 Accordingly, to estimate eq. (15) we rank observations based on CAR, values from the years 1968-80 and form 25 portfolios, first within each size quintile and then across all firms in the sample irrespective of size. The average values of %AEPS,, 1 and CAR, for each of the 25 portfolios are used in estimating the lead-lag relation between price changes and earnings changes reported in table 2.15 When forming portfolios across all firms in the sample (last line of table 2), there is convincing evidence that current price changes are useful in explaining cross-sectional differences in future earnings changes. Approximately 59% of the cross-sectional variation in %AEPS, f+l is explained by CAR,,. When the data are aggregated within market value‘ranks, we observe that this model has much greater explanatory power for the largest size quintile (adjusted R2 of 0.41) than for the smallest size quintile (adjusted R2 of 0.18). Again, these differences are consistent with greater amounts of information being available on a more timely basis for larger firms vs. smaller firms, and more individuals processing the available information which results in price changes of larger firms representing a more accurate and efficient estimate of changes in expected future permanent earnings. 14Given that the grouping procedure is successful in driving the average transitory component of earnings changes to zero at the portfolio level, differences in the explanatory power of the model across size quintiles cannot be attributed to differential measurement error on the left-hand side of eq. (15). “The number of observations within each portfolio ranges from 62 to 79 securities depending upon the number of observations deleted because of negative EPS in the denominator when calculating %A EPS, + 1.

124

D. Collins et al., Firm size and information content of prices Table 2

Summary

of parameter

estimates

based on pooled data for 1969-80;

25 portfolios

each quintile.a,b

%AEPS,+I =YO+YICAR,+~,+,. Size’ quintile

1

%J

- 0.082 (-2.217)

R

Adj. R2

Prob. > F

0.194 (2.509)

0.18

0.019

2

0.095 (4.237)

0.179 (3.319)

0.29

0.003

3

0.089 (5.306)

0.115 (2.639)

0.20

0.015

4

0.112 (10.103)

0.091 (2.683)

0.21

0.013

5

0.109 (15.302)

0.095 (4.184)

0.41

0.001

0.067 (7.695)

0.135 (5.942)

0.59

0.001

All firms combined

aFor each size quintile, 25 portfolios were formed bt-values in parentheses. ‘Size is measured by the market value of equity.

according

to ranked

values of CAR,.

3.4. Forming price-based earnings forecasts

The previously reported results suggest that current year’s price changes may be useful in predicting future earnings changes, particularly for larger firms. We hasten to note, however, that the predictive power of price changes with respect to future earnings changes at the individual firm level is likely to be considerably less than that which is suggested by the grouped results reported in table 2. As previously noted, this is because the transitory components of earnings changes and the effects of non-earnings-related events on prices have effectively been averaged to zero at the portfolio level. At the individual firm level, earnings changes contain both a permanent and transitory component, and price changes are likely to provide noisier signals of permanent earnings changes. Nevertheless, we maintain that price changes will provide a more efficient and timely signal of future permanent earnings changes of large vs. small firms. As a first step in forming price-based forecasts of earnings, the coefficient estimates from eq. (15) for each size quintile are merged with individual firm CAR,‘s to form a forecasted percentage change in EPS,, 1 as follows:‘6 FQ(%AEPSj,,+,)Price

Model) = $&, + j$&ARj,,

06)

‘6Effectively, this model assumes that the earnings-price relationship is constant across all firms in a given size category. While this may be overly simplistic, we felt it would provide more reliable forecasts than would be obtainable from estimating the relation in eq. (15) for each firm with a limited series of annual data.

D. Collins et al., Firm size and information content of prices

125

where Boo, -&o are the parameter estimates obtained from the cross-sectional regression of %AEPS,,,+, on CAR,, for firms in size quintile Q. To avoid an over-fitting bias, initial estimates are obtained from pooled data for the years 1968-1974 and a forecast is made for 1975. For each subsequent year through 1980, the process is repeated with the previous year’s data added to the estimation period and the poo, fro being re-estimated. The price-based forecast of earnings for firm i in period t + 1 is then formed as -F;,(EPS,+,)

= [l + Fo(%AEPS,,,+,IPrice

Model)] . EPS,,.

07)

By comparison the random walk forecast of EPS is

And the random walk plus drift forecast is given by

4wdEPS;,,+J= Ef’S,,+ 4,>

(19)

where a,, is defined in eq. (5a) and is estimated from all available data through year t. 4. Forecast results Using the three forecast models outlined above, we predicted the earnings of each sample firm from 1975-1980. The absolute percentage forecast error was computed as Actual - Forecasted Actual

.

(20)

Observations with actual earnings less than $0.20/share were deleted to minimize distortions caused by small or negative denominator values. For each firm/year the difference between the univariate time series forecast error and price-based forecast error in eq. (20) was determined, and we calculated the percentage of forecasts for which the time series forecast error exceeded the price-based forecast error. Since percentage forecast errors can become quite large when scaled by relatively small actual EPS, values, we focus on median results rather than averages. Table 3 summarizes our prediction results by size quintile. Consistent with the results reported in table 1, the median absolute percentage forecast error varies inversely with size across all three models. For example, the median absolute error for the smallest quintile of firms is 33.3% for the random walk

Median absolute errorb

0.333 0.269 0.197 0.185 0.162

Size” quintile

1 2 3 4 5

price-based

042.2 054.1’ 054.5’ 057.1’ 060.4’

- 0.0457 0.0015 0.0141 0.0310 0.0366

Median difference RW-priced

walk model

errors,

Percent times higherC

Random

forecast

Table 3

I

- 13.7% 4.3 7.2 16.8 22.6

IRW FE

Median % improvement over

0.352 0.260 0.188 0.165 0.130

Median absolute error

Price-based

model

0.315 0.262 0.185 0.177 0.156

are based

45.5% 48.6 50.4 53.5’ 57.4f

on

-0.0278 - 0.0026 - 0.0007 0.0090 0.0183

Median difference (RW + Drift) Price

walk + drift model

(estimates

Percent times higher

Random

1975-1980,

Median absolute error

Period

median

absolute

percentage

forecast

error yielded by the time

Firm/years with negative actual earnings have been deleted. univariate time series model exceeded the price-based absolute forecasts. forecast error (as defined in footnote 1) minus the price-based

- 8.8% - 1.0 0.4 5.1 11.7

(

Forecast

Median % improvement over IRW + Drift FE

forecasts vs. &variate time series forecasts, parameters estimated at portfolio level).

“Size is measured by market value of equity. bAbsolute percentage forecast errors are determined as ((Actual - Forecasted)/ActualI. ‘Percentage of firm/year forecasts where absolute percentage forecast error based on percentage forecast error. Number of observations varies from 1954 to 1973 firm/year dFor each firm/year the difference in the absolute value of the univariate time series forecast error is determined and the median value of these differences is reported. ‘Median difference in univariate time series forecast error is stated as percentage of series model. ‘Significantly higher than fifty percent at a = 0.01 or less using binomial test.

of earnings

Analysis

P

2 Cs. 2

2 z. S g $

z! il h 5’ f: 4 F

2 2 i: 9 p

D. Collins et al., Firm size and information contenf of prices

127

model, 31.5% for the random walk plus drift model and 35.2% for the price-based model. By comparison, the corresponding forecast errors for the largest size quintile are 16.2%, 15.6% and 13%. Thus, it appears that across all three models earnings are easier to predict for large firms than for small firms. When we compare the price-based forecast results with the univariate results across size quintiles we find differences that are consistent with our main hypothesis. Specifically, the time series models outperform the price-based models for the smallest quintile of firms. Thus, prices would appear to contain little or no information relevant to assessing future earnings beyond that captured by the past time series of earnings for these smaller firms. However, as the size of the firm increases, the price-based forecasts progressively outperform the univariate time series forecasts. For the largest size quintile, the differences are rather dramatic. The median difference between the random walk and price-based model is 3.7%. This difference stated as a percentage of the median absolute forecast error (16.2%) for the random walk model yields a 22.6% improvement for the price-based model over the random walk model. The corresponding percentage improvement for the price-based model over the random walk plus drift model is 11.7%. Another indication of the relative performance of the price-based model vis-a-vis the time series model is the proportion of times the magnitude of the price-based forecast error is smaller than the time series forecast error. Again, we observe a general tendency for the price-based forecasts to outperform the time series forecasts as the size of the firm increases. For example, the price-based model yields a smaller forecast error when compared to the random walk model only 42.2% of the time for the smallest size quintile. For the largest size quintile, the price-based model outperforms the random walk model 60.4% of the time. Using a binomial test, this proportion is significantly greater than 50% with an a-level of 0.01. For the random walk plus drift model, the relevant percentages are 45.5% (not significant) for the smallest quintile and 57.4% (significant at 0.01) for the largest quintile. Overall these results are consistent with our hypothesis concerning the information content of prices with respect to earnings of small vs. large firms. Specifically, we find that prices of smaller firms capture little information with respect to future earnings beyond that conveyed in the past time series of earnings. However, for the largest firms in our sample, there is rather clear evidence that price changes in the current year do provide information about next year’s earnings changes beyond that contained in the time series of earnings. We attribute these differences to the broader information set available for larger firms and to the larger number of traders and professional financial advisors who are actively involved in processing the information available on the activities of larger firms. These factors combine to enhance the informativeness of price changes with respect to future earnings changes for these larger companies.

128

5. Implications

D. Collins et al., Firm size and information content of prices

for earnings-price

association

studies

Our analysis of the relative predictive accuracy of univariate time series vs. price-based forecasting models across firm size has important implications for a variety of studies designed to test the information content or meaningfulness of annual accounting earnings measurements. In the following sections, we briefly discuss these implications and attempt to demonstrate their importance.

5.1. MisspeciJed

model of market earnings expectations

Pate11 (1979) provides a useful analytical framework for characterizing the experimental design of Abnormal Performance Index (API) studies which focuses attention on the central role played by models of investor earnings expectations. Pate11 constructs a set of sufficient conditions under which the API metric (or in our case, the CAR metric) can provide a valid measure of the information content of earnings signals. One of the crucial assumptions he identifies is that of homogeneity of model effectiveness across firms. Specifically. a maintained hypothesis underlying most research analyzing the association between annual earnings measurements and stock returns is that a given model of investor earnings expectations works with equal effectiveness on all firms in the sample. For example, in the context of a Ball and Brown (1968) type study which focuses on the sign of unexpected earnings, the implicit assumption is that a given earnings model works equally well across all firms in identifying positive and negative unexpected earnings. The evidence presented above is clearly inconsistent with this assumption. Our results suggest that as of the beginning of a firm’s fiscal year investors’ earnings expectations for larger firms reflect additional information beyond that contained in the past time series of earnings. Moreover, it appears that these future earnings expectations are revealed in security prices from the previous year. Conversely, for relatively small firms for which there are fewer alternative information sources a price-based earnings expectation model appears to afford little advantage over simple univariate time series models. If we adopt the perspective taken in previous research and use a twelvemonth horizon to measure the association between unexpected annual earnings and security returns, then our predictive ability results suggest that a random walk specification will do a relatively poorer job of distinguishing ‘good’ and ‘bad’ performance for large firms vis-a-vis small firms. That is, a random walk earnings expectations model is likely to result in a greater number of misclassifications of large firms in terms of the sign of unexpected earnings twelve months before the annual earnings announcement. This would result in a lower composite CAR metric over the contemporaneous annual accounting period for large firms as compared to small firms. Moreover, we

D. Collins et al., Firm size and information content of prices

129

would expect these differences in the composite CAR metric to narrow when a price-based expectations model is used to identify firms with positive and negative unexpected earnings over the subsequent twelve-month period. To illustrate this point, we calculated a composite CAR score within each size quintile, first based on the sign of the forecast error using a random walk model and secondly, based on the sign of the forecast error using our price-based model. The composite CAR, score is calculated as

CAR,=

;

g

CAR,, -

i

CAR,,,

r-l

(+)

r=l

(p)

where n + refers to the number of firms with positive unexpected earnings ( + ), refers to the number of firms with negative unexpected earnings (-), and N is the total number of firms in sample. In fig. 1 we plot the composite CAR, for the smallest and largest size quintiles where the random walk model was used to identify positive and negative unexpected earnings. We also present the composite CAR, for these extreme size quintiles using the price-based model to partition firms into positive and negative unexpected earnings groups. It should be noted that in partitioning our samples based only on the sign of unexpected earnings we ignore differences in the magnitude of this variable. The previous results reported in tables 1 and 3 suggest that unexpected earnings of small firms tend to be much greater in percentage terms than those of large firms. Recall that Beaver, Clarke and Wright (1979) report a strong positive association between the magnitude of unexpected earnings and CAR’s. These results suggest that, irrespective of how well the earnings expectations model is specified, one would expect the composite CAR of small firms to be greater than that of large firms because of differences in the magnitude of unexpected earnings. However, in this analysis we are not concerned with the relative positioning of the CAR plots for large vs. small firms. Rather, we focus on within group comparisons to assess how price-based vs. time series expectations models affect the composite CAR,‘s of each size group. The average annual composite CAR, for the small size quintile reported in fig. 1 is 12.9% conditional on the random walk specification and 13.1% conditional on the price-based expectations model. Thus, for small firms the price-based model appears to offer very little improvement over the random walk model in identifying positive and negative unexpected earnings firms. This result is consistent with our prediction that investors’ earnings expectations for small firms reflect little or no additional information beyond that contained in the past time series of earnings. A much greater difference in composite CAR,‘s is apparent for the alremative expectations models for the large firms (quintile 5). The annual composite n:

130

D. Collins et al., Firm size ond information content of prices

\ i \ i i ‘\

D. CoNins et al., Firm sne and information content of prices

131

CAR, conditional on the random walk model is 3.7%, while for the price-based model the composite CAR, is 7.0%. Thus, the composite CAR, is roughly 90% larger when a price-based rather than random walk model is used to identify positive and negative unexpected earnings of large firms. These results are consistent with the hypothesis that price-based forecasts serve as a better proxy (relative to univariate time series models) for the market’s earnings expectations for large firms in annual earnings-return association studies such as those conducted by Ball and Brown (1968) Beaver, Clarke and Wright (1979), Beaver, Griffin and Landsman (1982) and Rayburn (1986). The results in fig. 1 also help to explain the inverse relation between size and the strength of association between unexpected earnings and abnormal returns reported by Burgstabler (1981) and Freeman (1987) who rely on time series models to measure unexpected earnings.

5.2. Misspeci’cation of cumulation period for returns From the standpoint of earnings association studies, the previous discussion treats the implications of our results as an expectations model r&specification issue. This perspective is based on the implicit assumption adopted in the prior literature that the relevant time frame for measuring security price adjustments to events captured by accounting earnings is defined by the firm’s reporting period. That is, events affecting accounting earnings measurements are assumed to affect stock values (returns) in the same time frame for which the accounting earnings number is determined. An alternative interpretation of our results is that the cumulation period which has traditionally been used in measuring the market adjustments associated with events captured by accounting earnings is misspecified. Our findings, together with the evidence presented by BLM, suggest that price changes lead accounting earnings changes, particularly for larger firms. Through alternative (non-accounting) sources of information, the market learns of economic events that have future earnings implications for a firm, and these events are impounded in security prices before they are captured by the accounting process and accounting earnings. Thus, instead of focusing on price changes from the start of the fiscal period, our results suggest that one should consider starting the cumulation of returns at a much earlier point in time. Given our predictive ability results and the hypothesized relation between firm size and the amount and timeliness of information being processed by market participants, we expect price changes will tend to signal future earnings changes at an earlier point in time for large vs. small firms. Alternatively, we expect a greater proportion of the total price change associated with the current year’s earnings change will occur in the prior year for large firms as compared to small firms.

D. Collins et al., Firm size and information content of prices

132

Fig. 2 and table 4 present evidence consistent with these propositions. Here we are interested in making a direct comparison of the time path of returns relative to earnings changes for large vs. small firms. Since we are interested in making between group comparisons, we need to control for systematic differences in the return performance of small vs. large firms (known as the size anomaly) documented by Banz (1981) and Kiem (1983)” This is accomplished using a size-adjusted returns approach proposed by Foster, Olsen and Shevlin (1984). Under this approach, all firms on the CRSP daily return file are ranked according to the market value of equity at the beginning of each year from 1968-1980 and grouped into size quintiles. The average return for all firms in a given size quintile (R,,) is determined for week t and this return is subtracted from the realized return of each security (Ri,) in our sample in that size quintile to yield a size-adjusted return (SAR,,) as follows.: SAR,,

(22)

= R,, - Rpt.

These size-adjusted returns are then cumulated over various specified time periods in the following manner:

CSAR,

= ;

j-j (1 + SAR,,) t 1

- 1.

(23)

In fig. 2 we group firms within the largest and smallest size quintiles according to the sign of the earnings change in year 7 and form a composite CSAR, analogous to the procedures used in eq. (21).18 Rather than starting the cumulation period at the beginning of year 7, however, we start the cumulation process 100 weeks (two years) before the end of year 7.19 By comparing the time path of the composite CSAR, for large vs. small firms we can “Ideally, we would like also to control for differences in the magnitude of unexpected earnings, but this is more problematic. For one thing, we are cumulating portfolio returns over a two-year forecast horizon where the portfolios are formed according to the sign of the change in earnings from r - 1 to r. As of the beginning of r - 1, it is unclear whether earnings changes from 7 - 1 to r are any easier to predict for large vs. small firms. To the extent that they are, we would expect a smaller composite return for our large-firm portfolio vs. small-firm portfolio which works against the findings reported in fig. 2. ‘“Given our portfolio formation rule which is based on the sign of the change in earnings from 7 - 1 to 7, those firms with earnings changes close to zero are more likely to be misclassified relative to what the ‘true’ unexpected earnings are as of the beginning of 7. To minimize this misclassification error, observations with l%A H’S,/ < 10% were deleted. Results are based on pooled data from 1968-1980. ‘9We end up with 100 weeks because the size-adjusted returns were actually computed from the CRSP daily returns file and then summed over successive five-day intervals to form a weekly return. The loss of two weeks each year is due to various holidays on which the exchanges are closed. Thus, there are approximately 250 trading days which translated into 50 trading weeks in our plots.

D. Collins el al., Firm size and information content of prices

I I N

Cl _

I

m

(0

v

N

0

133

134

D. Collins et al., Firm size and information content of prices

determine whether there are systematic differences between firm size and the extent to which price changes anticipate earnings changes. The results in fig. 2 reveal that the two-year composite CSAR, is virtually the same for small and large firms by the end of year 7 (week 100 on the plot). For the small (large) firms, the composite CSAR, is 12.97% (12.21%). Note, however, that there are rather striking differences between large and small firms in terms of the timeliness with which price changes anticipate earnings changes, and in the proportion of the total price change that occurs in the year prior to the year in which the sign of the earnings change is determined. By week 50 (which corresponds to the end of the previous fiscal year), the composite CSAR, of the large firms is 4.2% which is approximately 34% of the total two-year size-adjusted return associated with the sign of the earnings change in year T. By contrast, the composite CSAR, of the small firms in week 50 is 1.6% which is only 12% of the total two-year size-adjusted return. These results are consistent with our earlier price-based forecast results and suggest that price changes anticipate earnings changes, particularly for larger firms. Moreover, these results suggest that for larger firms as much as one-third of the price change associated with events reflected in the current year’s earnings number occurs in the previous year. Thus, for these firms one may significantly understate the degree of association and the amount of price change associated with a given year’s earnings change by ignoring price changes in the previous fiscal year. If annual accounting reports are an important source of information about the economic events that affect earnings, then stock price changes associated with earnings measurements for a given fiscal period may be revealed after the end of the fiscal year through the time of the release of the annual report [see, for example, Ball and Brown (1968)J. Given our previous arguments regarding the availability and timeliness of alternative (non-accounting) sources of information for large vs. small firms one would expect greater evidence of post fiscal year-end price adjustment for small vs. large firms. The CSAR plots in fig. 2 bear this out. The small-firm portfolio exhibits a positive upward drift in cumulative size adjusted returns from week 100 to week 112, while the large-firm portfolio CSAR exhibits a slight downward drift over the same time period. Again, these results are consistent with the claim that market participants are better able to anticipate the contents of earnings reports for large firms vis-a-vis small firms. In table 4 we regress the %AEPS, against size-adjusted returns for year r and 7 - 1 and the first three months of fiscal year r + 1. Data for this pooled regression at the individual security level are for the years 1968-1980. In contrast to the previous results, this analysis focuses on whether price changes (returns) from various time periods are useful in explaining both the sign and magnitude of earnings changes.

135

D. Collins et al., Firm sire and information content of prices Table 4 Cross-sectional

regressions

of percentage change in earnings on leading, lagged size-adjusted returnsa

B

contemporaneous

Adj. R’

and

Prob. > F

N

R

k

R

Punel A Quintile 1 Small firms

964

0.136 (9.53)

0.017 (0.50)

0.654 (15.48)

0.463 (6.84)

0.227

0.0001

Panel B Quintile 5 Large firms

1269

0.063 (7.88)

0.074 (2.54)

0.248 (8.42)

-0.156 (- 2.30)

0.062

0.0001

“t-values in parentheses. ‘%A EPS,, = percentage change in earnings from 7 - 1 to 7 for firm I. ‘CSA R, = cumulative size-adjusted return for firm i. For periods 7 - 1 and r the cumulation ix over a twelve-month period (January-December). For r + 1, the cumulation is over a three-month period (January-March).

For the small firms (panel A), the addition of size-adjusted returns from the previous fiscal period (T - 1) does not significantly increase our ability to explain earnings changes in the current period r [t-value = 0.501. Note, however, that adding size-adjusted returns for the current period (T) and the first three months of the next fiscal period (7 + 1) greatly increases the explanatory power of the model (t-value = 15.48 for period 7 and f-value of 6.84 for period T + 1). This finding is consistent with our earlier results and suggests that prior year price changes of smaller firms convey little or no information with respect to current year earnings changes. For smaller firms, the majority of the price change associated with the earnings changes appears to occur contemporaneous with the earnings measurement and in the three months following fiscal year end. The results for the large firms (panel B) reveal quite a different intertemporal relation between price changes and earnings changes which is consistent with the hypotheses advanced earlier. Specifically, we find that for larger firms size-adjusted returns from both the current year (7) [t-value = 8.421 and the prior year (7 - 1) [t-value = 2.541 exhibit a significant positive association with earnings changes for period 7. Unlike the small firms, subsequent to fiscal year end the relation between period 7 earnings changes and period 7 + 1 returns is negative. ” A gain , these findings are consistent with our previous results and 20A priori, we expected observed negative relation for possible explanations. the results. However, we 1968-80 for our sample

this relation to be insignificantly different from zero. The strength of the was, therefore, surprising and prompted us to probe the data further Plots of the data and removal of outliers had no substantive effect on did note the average percentage change in earnings over the period of large firms was 8.9% (see table 1). while the average cumulative

136

D. Collins et al., Firm size and information content of prices

with the results reported by Freeman (1987). For larger firms, price changes tend to lead earnings changes. We attribute the differences in the price-earnings relation between large and small firms to the broader information set and greater number of individuals processing the information of larger firms. These factors contribute to a more timely reflection of permanent earnings changes in the security prices of large firms as compared to small firms. 6. Summary and conclusions In this paper we have attempted to extend the work of BLM (1980) by partitioning firms according to size to investigate the information content of prices with respect to future earnings. Size is viewed as a proxy for available information in addition to that which is reflected in the past time series of earnings and for the number of market participants gathering and processing information. Consistent with our hypothesis, we find that price-based models outperform both the random walk and random walk plus drift models when forecasting the earnings of larger firms. However, for small firms we found little difference between the price-based model and these two univariate time series models. These findings have important methodological implications for studies that attempt to measure the degree of association between accounting earnings (or other performance measures) and stock returns over annual periods. Specifically, our results suggest that for larger firms, simple univariate time series models are inadequate proxies for the markets’ earnings expectations over one-year forecast horizons. Alternatively, researchers may want to consider starting the cumulation of returns prior to the period for which the earnings number is computed to accommodate the fact that price changes tend to anticipate earnings changes, particularly for larger firms. References

. Albrecht, W., L. Lookabill and J. McKeown, 1977, The time series properties of annual earnings, Journal of Accounting Research, Autumn, 226-244. At&e, R., 1980, Predisclosure information asymmetries, firm capitalization, financial reports. and security price behavior, Unpublished Ph.D. thesis (University of California, Berkeley, CA). Atiase, R., 1985, Predisclosure information, firm capitalization and security price behavior around earnings announcements, Journal of Accounting Research, Spring, 21-35.

size-adjusted return computed over the first three months of each year was slightly negative (- 1.2%). The negative bias in the size-adjusted returns was due largely to the January weeks. Further investigation revealed that because of our sample selection procedures our sample of large firms had a consistently larger average market value than the group of firms that comprised the upper size quintile on the CRSP daily returns tape. This resulted in an over-correction in our adjustment process that imparted a slight negative bias to the size-adjusted returns for our larger firms particularly during the January weeks. This can be seen in the large portfolio CSA R plot in fig. 2 in weeks 51-54 and weeks 101-104. These factors combined to contribute to the negative in table 4 for the large-firm quintile. relation between %AEPS, and CSAR,,,

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Ball, R. and P. Brown, 1968, An empirical evaluation of accounting income numbers, Journal of Accounting Research, Autumn, 159-178. Ball, R. and R. Watts, 1972, Some time series properties of accounting income, Journal of Finance, June, 663-682. Banz, R., 1981, The relationship between return and market value of common stock, Journal of Financial Economics 9, 3-18. Beaver, W., 1970, The time series behavior of earnings, empirical research in accounting: Selected studies, Supplement to Journal of Accounting Research, 62-99. Beaver, W., R. Clarke and W. Wright, 1979, The association between unsystematic security returns and the magnitude of earnings forecast errors, Journal of Accounting Research, Autumn, 316-340. Beaver, W., P. Griffin and W. Landsman, 1982, The incremental information content of replacement cost earnings, Journal of Accounting and Economics 4, 15-40. Beaver, W., R. Lambert and D. Morse, 1980, The information content of security prices, Journal of Accounting and Economics 2,3-28. Beaver, W., R. Lambert and S. Ryan, 1987, The information content of security prices: A second look, Journal of Accounting and Economics, this issue. Bublitz, B.. T. Frecka and J. McKeown, 1985, Market association tests and FASB Statement No. 33 disclosures: A reexamination, Supplement to Journal of Accounting Research, l-23. Burgstahler, D.. 1981, Cross-sectional and cross-temporal differences in the relationship between annual earnings and security returns, Unpublished Ph.D. thesis (University of Iowa, Iowa City, IA). Choi, S., 1985, Differential information content of publicly announced earnings: Theoretical and empirical analysis, Unpublished Ph.D. thesis (University of Iowa, Iowa City, IA). Foster, G., C. Olsen and T. Shevlin, 1984, Earnings releases, anomalies. and the behavior of security returns, Accounting Review, Oct., 574-603. Freeman, R., 1987, The association between accounting earnings and security returns for large and small firms, Journal of Accounting and Economics, this issue. Givoly, D. and J. Lakonishok, 1983, Divergence of earnings expectations: The effect on market response to earnings signals, Unpublished working paper (The Israel Institute of Business Research, Tel Aviv University, Tel Aviv). Gonedes, N., 1972, Efficient capital markets and external accounting, Accounting Review, Jan., 11-21. Grant, E., 1980. Market implications of differential amounts of interim information, Journal of Accounting Research, Spring, 255-268. Grossman, S.J., 1976, On the efficiency of competitive stock markets where traders have diverse information, Journal of Finance 31, 573-585. Grossman, S.J.. 1978, Further results on the informational efficiency of competitive stock markets, Journal of Economic Theory 18, 81-101. Grossman, S.J. and J.E. Stiglitz, 1980, On the impossibility of informationally efficient markets, American Economic Review 70. 393-408. Hirschleifer. J., 1971, The private and social value of information and the reward to inventive activity, American Economic Review 61, 561-573. Kiem, D., 1983, Size related anomalies and stock return seasonahty: Further empirical evidence, Journal of Financial Economics 12,13-32. Kothari, S.P., 1986, A comparison of alternative proxies for the market’s expectation of quarterly earnings, Unpublished Ph.D. thesis (University of Iowa, Iowa City, IA). Learner, E.E., 1978, Specification searches: Ad hoc inference with nonexperimental data (Wiley, New York). Maddala, G., 1977, Econometrics (McGraw-Hill, New York). Patell, J., 1979, The API and the design of experiments, Journal of Accounting Research, Autumn, 528-549. Pincus, M., 1983, Information characteristics of earnings announcements and stock market behavior, Journal of Accounting Research, Spring, 155-183. Raybum, J., 1986, The association of operating cash flow and accruals with security returns, Supplement to Journal of Accounting Research, forthcoming. Ricks, W., 1982, The market’s response to the 1974 Lifo adoptions, Journal of Accounting Research, Autumn, part I, 367-387.

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Stiglitz, J., 1971. Information and capital markets, unpublished paper presented at the New Orleans Meetings of the Econometric Society. Verrecchia, R., 1979, On the theory of market information efficiency, Journal of Accounting and Economics 1,17-90. Verrecchia, R., 1980, The rapidity of price adjustments to information, Journal of Accounting and Economics 2, 63-92. Verrecchia, R., 1982, Information acquisition in a noisy rational expectations economy, Econometrica 50, 1415-1430. Watts, R., 1970, Appendix A to information content of dividends, Unpublished working paper (University of Chicago, Chicago, IL). Watts, R. and R. Leftwich, 1977, The time series of annual accounting earnings, Journal of Accounting Research, 253-271. Wheatley, S., 1982, The information content of security prices: Comment, Unpublished manuscript (University of Rochester, Rochester, NY). Wilson, R., 1975, Informational economies of scale, Bell Journal of Economics, Spring, 184-195.