The adjustment of stock prices to new information

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The adjustment of stock prices to new information a test of market efficiency
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Thesis--University of Florida.
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Bibliography: leaves 104-107.
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by Stewart L. Brown.
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Typescript.
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Vita.

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THE ADJUSTMENT OF STOCK PRICES TO NEW INFORMATION:
A TEST OF MARKET EFFICIENCY














By

STEWART L. BROWN


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY





UNIVERSITY OF FLORIDA


1974















ACKNOWLEDGMENTS

The author would like to thank Dr. C. A. Matthews

for moral and financial support while at the University of

Florida. The author is indebted to Dr. Fred Arditti,

Chairman of the Committee, for many helpful comments and

suggestions and the rest of the Committee: Drs. John

McFerrin, W. A. McCollough, Christopher Barry, and

James McClave for moral support and helpful suggestions.

All deficiencies and mistakes are, of course, the sole

responsibility of the author.

















TABLE OF CONTENTS


ACKNOWLEDGMENTS . .

ABSTRACT . . .

Chapter
I. INTRODUCTION . .

Purpose of the Study ...
Market Efficiency with Respect to
EPS Information7 The Evidence .
Assumptions and Methodology .
The Ball and Brown Study .
The Jones and Litzenberger Study
Reconciling the Two Studies .


II. METHODOLOGY . .

Overview . .
Some General Considerations .
Earnings Models . .
Residual Analysis . .
The Capital Asset Pricing Model, the
Parameter Estimation Problem, and
the Normality Assumption .
The Capital Asset Pricing Model
The Parameter Estimation Problem
The Normality Assumption .
Statistical Tests . .


III. RESULTS . .


Description of the Sample .
An Analysis of Regression Results .
Residual Analysis for Positive
Forecast Error . .
The Abnormal Return . .
The Adjustment Process .
The Speed of Adjustment .. ...
Residual Analysis for Negative Forecast
Error . .
Pre-Announcement Movements in the CAR .


. 17


. 47


. 47
S. 49


. 81
. 89


iii


ii









Chapter
IV. SUMMARY AND CONCLUSIONS .. .. 97

Major Results . .. 97
Limitations of the Study .. 98
Some Implications of the Study .. 100

BIBLIOGRAPHY . . .. 104

BIOGRAPHICAL SKETCH. .. . .... 108














Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in
Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy



THE ADJUSTMENT OF STOCK PRICES TO NEW INFORMATION:
A TEST OF MARKET EFFICIENCY

By

Stewart L. Brown

December, 1974

Chairman: Fred D. Arditti
Department: Finance and Real Estate

The issue of capital market efficiency with respect

to publicly available information has not been resolved.

Studies examining the adjustment of stock prices to new

Earnings Per Share information yield conflicting results.

It seems that stock prices do not adjust instantaneously

although the adjustment process has not been examined in

detail. There is, however, a question as to whether or

not it is possible to earn an abnormal rate of return by

trading on the basis of publicly available information.

The purpose of this dissertation is to examine the adjust-

ment of the stock market to unexpected changes in EPS and

to determine if an abnormal rate of return could have been

earned.












Cumulative average stock price return residuals

from the market model are examined on a daily basis for

twenty market days before and through sixty market days

after publication of annual EPS numbers in The Wall Street

Journal. The market model is used to abstract stock

returns from risk and general market movements. Both

unexpectedly high and unexpectedly low EPS numbers are

examined for a sample of 158 firms listed on the New York

or American Stock Exchanges. All firms in the sample have

at least a 20 percent change in annual EPS and fourth

quarter results different from what could have been

predicted on the basis of the first three quarters of EPS.

A first order autoregressive scheme is fit to the

cumulative average residual and is useful in obtaining an

estimate of the confidence interval around the predicted

cumulative rate of return of the securities in the sample.

Statistically significant returns are observed

around the publication date of the EPS number in The Wall

Street Journal. The lower confidence limit of the

predicted cumulative return is above estimated transactions

costs for both long purchases of securities with unexpectedly

high EPS and short sales of the securities with unexpectedly

low EPS.

The adjustment process takes about forty-five

market days after the EPS publication date. The pattern

vi











of adjustment is similar for both unexpectedly high and

unexpectedly low EPS. There appears to be three distinct

stages in the adjustment process: an initial price trend

directly related to the direction of change in EPS;

a second trend inversely related to the change in EPS;

and a third trend directly related to the change in EPS,

lasting from about day 10 to about day 45 after the

earnings announcement. The price change in the third

stage appears to be permanent. It is speculated that the.

pattern of adjustment is caused by a lag between publica-

tion of the EPS number in The Wall Street Journal and

availability of the more complete information in the Annual

Report.

It is concluded that the stock market was not

efficient with respect to the securities in the sample,

since an abnormal return in excess of transactions costs

could have been earned by purchasing the securities on

the publication date of the EPS number. The implication

is that the stock market may, in general, be less

efficient than has been heretofore believed.


vii














CHAPTER I

INTRODUCTION

Purpose of the Study

The purpose of this paper is to test whether or not

it is possible, in a statistical sense, to earn a rate of

return in excess of the normal rate of return in the stock

market by purchasing securities whose earnings per share

(EPS) are greater than expected as soon as such information

becomes publicly available. A subsidiary purpose is to

examine the pattern and speed with which the stock market

adjusts the prices of securities to reflect new EPS infor-

mation.

This study is concerned with the means by which

information about investments is disseminated to and used

by investors. The concern with the effects if information

on capital asset prices places this study in the realm of

what has come to be called the "Efficient Markets

Hypothesis" (EMH). This hypothesis, which would be better

labeled the "Efficient Capital Markets Hypothesis," has no

generally accepted formal definition other than the rather

vague and basic notion that an efficient market is one that

fully reflects all available information. Sharpe [33]

presents a concise definition:

1











Simply put, the thesis is this: in a well-
functioning market, the prices of capital
assets (securities) will reflect predictions
based on all relevant and available information.

An implication of market efficiency is that it is

difficult to earn a rate of return in excess of the normal

rate of return. If the stock market reflects (has

discounted) all information, then an investment strategy

which is based on some form of information relevant to

share prices, says EPS information, will fail to produce

an abnormal rate of return because such information will

already have been discounted in security prices.

The Efficient Markets Hypothesis is an application

of the theory of perfect capital markets which, in turn, is

derived from the economic theory of price formation under

pure competition. The assumptions concerning the effects

of information on share price is aptly pointed out by a

concise definition of a perfect capital market [27]:

In a "perfect capital market," no buyer or
seller (or issuer) of securities is large
enough for his transaction to have an apprec-
iable impact on the then ruling price. All
traders have equal and costless access to
information about the ruling price and about
all other relevant characteristics of shares.
No brokerage fees, transfer taxes, or other
transactions costs are incurred when
securities are bought, sold, or issued, and
there are no tax differentials ..

Thus, in a perfect capital market, with an absence

of frictions and a perfect information system, the prices

of capital assets are always the "correct" prices in the











sense that they always fully reflect all relevant informa-

tion. Those who believe in the EMH contend that the condi-

tions in actual capital markets are sufficiently similar

to the requirements of a perfect capital market that actual

security prices may be thought of as the "correct" prices;

i.e., they fully reflect all available information.

One difference between a perfect capital market and

an efficient market is that an efficient capital market may

be efficient with respect to some kinds of information and

not efficient with respect to other kinds. Fama [14] has

established a hierarchy of information types to delineate

different degrees of market efficiency.

At its lowest level the stock market is deemed

efficient if it reflects historical information. The stock

market has been found to be quite efficient with respect

to this type of information. Empirical tests at this level,

labeled "weak-form" tests of the EMH by Fama, include tests

of the familiar random walk hypothesis (see Cootner [11]).

At the second level, the market is deemed efficient

if it reflects all publicly available information. Since

publicly available information is also historical informa-

tion, tests at this level of efficiency are typically

concerned with the speed at which the stock market adjusts

to new information. Empirical tests at this level have

been labeled "semi-strong form" tests of the EMH. The











hypothesis has received mixed support at this level, but

the market has generally been found to be quite efficient

(see Fama [14] and Downes and Dyckman [12]).

At its highest level, the stock market is deemed

efficient if it reflects all information, including infor-

mation not publicly available. Empirical tests at this

level are concerned with whether or not some groups of

investors have monopolistic access to sources of informa-

tion which allows them to reap excess returns. Tests at

this level are labeled "strong form" tests of the EMH.

There have been few such tests at this level, but those

which have been conducted have found some market ineffi-

ciencies (see Jaffe [18], Niederhoffer and Osboirne [29],

and Jensen [19]).

Market Efficiency with Respect to EPS
Information; The Evidence

There are two major studies which examine market

efficiency with respect to EPS information. One study, by

Ball and Brown [ 3], purports to show that the market is

efficient with respect to this type of information; i.e., it

is impossible to make money by using EPS information as it

becomes publicly available. The other study, by Jones and

Litzenberger [20], purports to show that the market is

inefficient; i.e., it is possible to earn an abnormal

return by trading on publicly available information.











Thus, the two studies arrived at opposite conclu-

sions about market efficiency with respect to EPS informa-

tion. Each of the two studies will be examined in detail,

and some reasons they arrived at different conclusions

will be explained and discussed. First, however, some

general assumptions and methodological considerations must

be discussed so as to establish an analytical framework

needed to examine the articles.

Assumptions and Methodology

An implicit assumption of studies which examine

market efficiency with respect to EPS information is that

there is a direct relationship between the level of a

firm's EPS and its share price (assuming all other things

are equal, like risk); i.e., the higher the level of EPS,

the higher the firm's share price and vice versa. Empiri-

cal studies have found that this assumption is warranted

(see Malkial [25]).

This relationship between EPS and share price

allows researchers to test market efficiency with respect

to EPS information. The basic method involves identifying

a large sample of securities with changes in EPS and then

looking at the average price change or rate of return from

purchasing those securities after the arrival of the EPS

information. This average price change is typically

computed after abstracting from risk and general market











conditions (the method of abstracting from risk will be

detailed in the next chapter). If it is possible to earn

an excess rate of return from purchasing the securities,

then the market is said to be inefficient. This rate of

return is sometimes compared to transactions costs as a

further test of efficiency.

The method of identifying changes in EPS and, hence,

of determining the securities to be included in the sample

is crucial to the analysis of the subsequent average price

change observed. Different studies use different EPS

models, but all have some implicit underlying assumptions.

Prior to the public availability of the actual EPS number,

there is assumed to exist in the market some expectation

of the EPS number. This expectation of EPS is not observable

but is the consensus of investors' estimates of the forth-

coming EPS. This consensus is reflected in the price of the

security just prior to the arrival of the actual number.

The change in price after the arrival of the actual number

is assumed to be directly related to the difference between

expected and actual EPS numbers. If the actual number is

greater than the expected number, then it is assumed that

the share price will rise, and vice versa. Another assump-

tion is that, ceteis paribus, the greater the difference

between actual and expected EPS, the greater will be the

resultant price change.











Given the above assumptions and discussion, the

Forecast Error (FE) may be defined as the difference

between the actual EPS number (EPSt) in time period t and

the expected EPS in time t, E(EPSt), i.e.

FE = EPSt E(EPSt). (1)

The expected EPS is never known with certainty but

must be estimated. Different studies use different models

to estimate it. This estimate of expected EPS in t will

be labeled E(EPSt), whatever model is used. The estimated

forecast error, FE, may then be defined as

FE = EPSt E(EPSt). (2)

It can be seen that the average price change of the

securities in a sample after the arrival of some new EPS

information will be influenced strongly by the method used

to estimate E(EPSt), since this will directly influence

which securities are included in the sample. The greater

the difference between the actual (but unknown) E(EPSt) and

the E(EPSt) estimated by some model, the smaller will be

the likelihood that the average price change observed will

be representative of the true market reaction. It will be

useful to keep the above discussion in mind as it will bear

directly on the methodology of the studies to be discussed

next.

The Ball and Brown Study

For their main results Ball and Brown used a

regression model to estimate the expected annual EPS of a









sample of securities. This model attempted to take advan-

tage of the facts that the EPS of firms are typically

correlated with one another and that the market may use

this information in forecasting EPS numbers. The procedure

was to regress the change in annual EPS of their sample of

firms on the change in an index of EPS for all firms. This

regression relationship and the change in the index in a

year of interest were used to estimate the change in

annual EPS of the firms in the sample.

The estimated change in EPS for each firm was then

used to estimate the expected EPS which was compared to the

actual EPS number. If the actual number were greater than

the estimated number, then the firm's earnings were classi-

fied as having "increased," and if the actual number were

less than the estimated number, then the firm's earnings

were classified as having "decreased."

Once the securities in the Ball and Brown sample

had been classified by the above procedure, their price

behavior was examined. Ball and Brown constructed what

they call an Abnormal Performance Index (API). It may be

thought of as the average rate of return of the securities

in the sample after abstracting from risk and general

market conditions. They looked at the API for twelve

months before and six months after the arrival of the new

EPS information. The return was examined before the arrival











of the actual number in order to scrutinize the market's

anticipation of EPS.

They found that the API rose throughout the year in

advance of the announcement for the earnings "increased"

category, and fell throughout the year for the earnings

"decreased" category. They found that the drift upward and

downward continued for perhaps as long as two months after

the publication of the actual numbers.

Although the move in the API after the arrival of

the annual report was significantly different from zero in

a statistical sense, it was of a very small magnitude. The

API reached about 8 percent before the arrival of the

actual numbers but increased only about 1 percent after the

arrival. Ball and Brown concluded that it was impossible

to earn an abnormal rate of return by purchasing the

securities in their sample as soon as the annual EPS number

became publicly available:

Even if the relationship tended to persist
beyond the announcement month, it is clear that
unless transactions costs were within about 1
percent, there was no opportunity for abnormal
profit once the income information had become
generally available. Our results are thus
consistent with other evidence that the market
tends to react to data without bias, at least
to within transactions costs.

These results are taken as evidence that the market

accurately anticipated all earnings changes to the point

that there was little or no market adjustment for the actual












information. It will be demonstrated that this conclusion

may be in error.

The regression model used by Ball and Brown to

classify a company's earnings as having "increased" or

"decreased" implies the following decision rule: When the

information becomes publicly available, purchase all those

securities whose actual EPS number is greater than the

estimated expected EPS and sell short all of those

companies whose actual EPS number is less than those pre-

dicted by the regression model. Ball and Brown have demon-

strated that the market is efficient on average to within

transactions costs with respect to this decision rule. It

does not demonstrate that abnormal returns cannot be earned

by using other decision rules.

The methodology of the Ball and Brown study actually

mitigates against finding a significant average increase in

stock prices after the arrival of new EPS information.

Suppose that the regression model predicts that a company

will earn $1, and further suppose that this is an unbiased

estimate of what the market thinks the company will earn.

If the company actually earns $1.01, then according to the

Ball and Brown method, this company will be correctly

classified as having "increased" its earnings. However,

since the market had closely realized its expectation it is

unlikely that there would be much price adjustment as a











result of the confirmation of this expectation. Yet, this

company's return would be included in each calculated

average return and, in a sense, bias it downward after

the receipt of the actual information. Thus, the Ball and

Brown study may have consisted of many firms with little

or no change in their prices and a few firms with a fairly

large change in price. The resulting decision rule appears

to be an unreasonable one.

A second, more serious problem is that the

regression model may not be a good model for estimating the

EPS which the market expects. Indeed, in an earlier study

Ball and Brown [2 ] found that only about 40 percent of the

variance in EPS of the securities in their sample was

explained by an index of all companies' EPS. It may be

that investors are able to utilize other sources of infor-

mation to arrive at an estimate of EPS. Such sources may

include quarterly or interim reports which are ignored in

the Ball and Brown study. Thus, the actual expected EPS by

the market may be quite different from the estimated

expected EPS in the Ball and Brown regression model, which

could have resulted in Ball and Brown classifying some

securities as having "increased" earnings when, in fact, the

market viewed these earnings as decreases. This would mean

that their calculated average return for the two categories

would include some securities whose actual price adjustment










was in an opposite direction to the expected price change.

This could have biased their observed average returns and

thus may have appeared to demonstrate a more efficient

market than actually existed.

Another facet of the Ball and Brown study was that

it used a monthly differencing interval for stock returns.

The procedure was to note only the month in which an annual

EPS number was reported and to ignore the actual date

within the month that the report arrived. This had the

effect of assuming that all reports arrived on the first

day of the month. To the extent that this was not actually

true, the approximate two-month adjustment period was

shortened. While this may not have been serious, the

monthly differencing interval for stock prices precluded a

close examination of the adjustment process, although Ball

and Brown noted that "The actual income number did not

appear to cause any unusual jumps in the abnormal perform-

ance index in the announcement month."

One also has to have some doubts as to the

generality of the Ball and Brown results with respect to

the firms included in their sample, which were all large

firms listed on the New York Stock Exchange. Since such

firms tend to be well established, and their stocks are

widely held, they probably receive close scrutiny from the

market and the investment community. Smaller firms,

perhaps OTC and AMEX firms, would be unlikely to have as










efficient an information system or to be as closely

watched.

The Jones and Litzenberger Study

Jones and Litzenberger estimate expected quarterly

EPS as the projected trend in historical quarterly EPS.

The study hypothesizes "that quarterly earnings reports

significantly greater than anticipated by market profes-

sionals from historical earnings trends would cause gradual

price adjustments over time and generate intermediate stock

price trends." Jones and Litzenberger use quarterly

earnings reports and a selection criteria which implies

the following decision rule: "Purchase those common stocks

whose quarterly earnings exceed their projected quarterly

earnings by at least 1.5 standard errors, and sell short

those securities whose quarterly earnings fall short of

the projected quarterly earnings by at least 1.5 standard

errors." It can be seen that this model not only classi-

fies earnings as increased or decreased, but also limits

the sample to those companies with large increases or

decreases in earnings.

Jones and Litzenberger observed the six-month price

relative of the selected securities and compared this with

the S&P 425 index price relative (rate of return). Six

months was used because of the preferential capital gains

tax treatment involved with this period. No interim prices

were observed. They found that "the average price










relatives of the stocks selected in each period exceed the

price relatives for the Standard and Poor's index in all

ten of the periods examined (a nonparametric test gave

significance at the .01 level)." They conclude that "the

market may not adjust instantaneously and correctly for

every item of information that becomes available."

Surprisingly, Jones and Litzenberger found that this

intermediate stock price trend (17 percent versus 5

percent for the market) happened only for companies with

increased earnings. Those companies with lower earnings

than expected did not decrease significantly.

The study is not a complete test of market effi-

ciency, since the authors did not show that the profits

from the trading rule exceed the cost of information pro-

cessing and transactions. "A computer is necessary to

examine a large quantity of data in a reasonable period of

time," and "although a small investor could use similar

techniques on a more limited scale," the effectiveness of

the latter approach has not been researched.

Another problem is that the study does not look at

intermediate price relatives. Rather, it focuses on the

abnormal rate of return that could have been earned and

ignores the speed of adjustment, other than the obvious

implication that the time period of adjustment is less than

six months. Thus, Jones and Litzenberger tell us little

about their intermediate stock price trend.










Reconciling the Two Studies

The Ball and Brown study and the Jones and

Litzenberger study arrive at completely different conclu-

sions regarding market efficiency. One explanation is

that there are differences in the implied decision rules

of the two studies. A simple model is useful as an

analytical framework to more clearly understand the

differences between the two decision rules.

Using the same notation as before, if we subtract

unity from the quotient of actual EPS divided by expected

EPS, we can define this number as the Relative Forecast

Error (RFE):

EPSt
RFE= -E ) 1 (3)
E (EPSt)

If this number is positive, we expect a price

increase, and if it is negative, we expect a price decrease.

Also, by assumption, the greater the RFE, the greater is

the expected price change. The assumption is reasonable, as

we would expect a greater resultant price change from a RFE

of 50 or 60 percent than we would from a RFE of 1 percent.

Now, assume that in a certain time period we can

examine a large number of securities and that we have a

method by which to discern the expected EPS in the market

of each with certainty. We can, therefore, calculate a

RFE for each security when the actual EPS number is

published. Given these assumptions, we can array all the









RFE's of the securities into a distribution. Over a long

period one would expect a unimodal distribution about zero.

Each study used a model to estimate the expected

EPSt, i.e., 2(EPSt). If this is substituted for the

E(EPSt) in (3) above, it is easy to visualize a distribu-

tion similar to the one described above. This distribution

is useful in analyzing the two studies.

The Ball and Brown study treats any security to the

right of zero in the distribution as an "increased earning"

security. Such a procedure will treat securities with large

and small forecast errors equivalently when looking at

price changes. If we assume that the forecast error dis-

tribution is approximately normal, in random sampling, then

we can expect many more securities with small forecast

errors than with large forecast errors. The net result is

that any price changes resulting from large forecast errors

sampled in this manner are likely to be swamped by small

forecast errors.

Similarly, the Jones and Litzenberger study also

uses a model to estimate conditional EPS, in this case

quarterly EPS, and it also compares this to the actual EPS

numbers. Differences exist because Jones and Litzenberger

include in their sample only those companies with large

relative forecast errors, the equivalent of looking only

at the tails of the forecast error distribution. One

expects these securities to have the largest price changes

if the market is not efficient.














CHAPTER II

METHODOLOGY

Overview

This section presents some design considerations

and an overview of the methodology. Following this section

are other general methodological considerations, including

earnings forecast models, residual analysis, and statisti-

cal tests.

This study has been designed to draw on previous

studies where appropriate, to improve on such studies where

possible, and to introduce new considerations where these

may add to the analysis. For instance, it was decided to

examine price (return) data on a daily basis. This

particular approach has not been previously used, and it

allows for the close examination of the adjustment process

of the stock market to new EPS information. This particu-

lar feature of the design is one of the major differences

between this and other studies of the adjustment process.

The reason that examination of price data on a daily basis

has not been done previously is probably that monthly data

are more widely available and easier to use.

It was decided to examine the market adjustment

process only for annual EPS numbers and not to examine

17











quarterly EPS adjustments, as annual numbers are probably

the most important for price formation. The response of

security prices to the publication of annual EPS numbers

may depend in part on how the annual number compares to

what could have been predicted on the basis of interim

reports, most importantly, the third quarter report. The

potential dependence of price changes on the third quarter

report necessitated the development of an earnings pre-

diction model which took into account the effect of interim

reports on the market expectation of annual EPS.

Companies listed on both the New York and the

American Stock Exchange were included in the sample. The

unavailability of data precluded the inclusion of

securities listed Over-the-Counter. Inclusion of American

Stock Exchange (AMEX) listed securities should increase

the generality of this study's conclusions, as other

studies have examined only New York Stock Exchange (NYSE)

listed securities (see Ball and Brown [3 ], Brown and

Kennelly [ 9], Fama et al. [15], etc.).

Another general consideration is the necessity of

incorporating risk in the analysis and abstracting from

general market movements. The market model, which is

closely related to the capital asset pricing model first

formulated by Sharpe [32], Lintner [23] and Mossin [28],

was utilized.











The general method utilized in this paper is quite

simple. The Wall Street Journal was examined on a daily

basis in selected months to determine the dates on which

EPS numbers first became generally available to the public.

At this point certain preliminary screening criteria (to

be discussed presently) were applied to define and limit

the sample. Once a sample which met the preliminary

requirements was obtained, The Standard & Poor's Stock Guide

was examined to determine the quarterly EPS numbers of the

chosen companies. Comparison of the estimated expected

annual EPS number and the actual annual EPS number of each

firm in an earnings forecast model yielded the direction

and degree of forecast error (equation 3). At this point

certain secondary screening criteria were applied, and the

sample was further limited.

Companies with both negative and positive forecast

errors were included in the sample. In this paper a firm

with a positive forecast error will be defined as a firm

whose actual reported EPS number is greater than its

estimated expected EPS number, estimated on the basis of

the earnings models in this paper. A negative forecast

error will be defined as a firm whose actual EPS is less

than estimated EBS.

Once the companies had been selected, one year of

daily price (return) data was obtained from the Standard &












Poor's ISL Daily Stock Price Tapes, beginning approximately

four months before and ending eight months after the actual

annual EPS number was published in The Wall Street Journal.

Part of this year was utilized for an analysis of the

reaction to the arrival of the EPS information (residual

analysis), and part was utilized to estimate market para-

meters (discussed presently) necessary for the residual

analysis.

Some General Considerations

The Standard and Poor's ISL Daily Stock Price

Tapes were available in the University of Florida Systems

Library from the second quarter of 1962 through the second

quarter of 1972. The tapes contain one calendar quarter

of daily prices, dividends, and stock split and dividend

data for all companies on the New York and American Stock

Exchanges. A program was written to retrieve the daily

price data from the tapes and to calculate the daily holding

period return (HPR) for each security in the sample in any

particular quarter. The holding period return is defined

as

Pjt Pjt-l + D
jft 3,t-i j,t
HPR = (4)
Pj,t-1

where

Pj,t = price of security j in time t

Dj,t = dividend of security j in time t.











The t in this case corresponds to an increment of one day.

The HPR may be thought of as the rate of return accruing to

the holder of security j from holding this security from

time period t-l to time period t, in this case one day.

One of the problems of using daily price data is

the difficulty of keeping track of the individual dates on

which the annual EPS numbers of different securities are

published. This problem was held to within manageable

limits by including in the sample only those securities

whose annual EPS numbers appeared in The Wall Street

Journal between the dates of February 15 and March 20 of

any particular year. These dates were chosen because most

industrial firms have fiscal years ending on December 31,

and a few months elapse before the results of a year's

operations are summarized and made available. Thus, a

majority of annual EPS numbers are made available between

the two above-mentioned dates. The above procedure may

possibly limit the generality of the sample somewhat,

although there is no evidence that companies with

December 31 fiscal years are systematically different from

companies with different fiscal years. Somewhat more than

half of all industrial companies in the United States have

fiscal years ending on December 31.

Some companies furnish preliminary EPS numbers to

The Wall Street Journal and then later report the final

numbers. Other companies have only the final numbers











published. This study did not distinguish between prelim-

inary and final numbers. Each security's publication date

was cross-checked in The Wall Street Journal Index to

insure that no previous annual EPS information had been

reported either as a preliminary number or as news such as

reported at a meeting of security analysts. Thus, all

firms in the study had the first mention of the EPS number

published between February 15 and March 20.

A residual analysis (discussed presently) was

performed beginning twenty days before the publication of

the EPS information and was continued until sixty days

after this date. Since the annual EPS number was always

published in the first quarter of the year after the year

which it summarized, the above period of time always fell

in the first two quarters. These two quarters were the

middle two of the year of HPR's which were collected for

each firm. The two outside quarters of this year were

used to estimate the parameters of the market model. These

two quarters corresponded to the fourth quarter of the year

which the annual number summarized and the third quarter of

the following year. In no case was the residual analysis

performed during a time period which was also used to

estimate the market parameters, preventing a bias in the

estimation of those coefficients.











Earnings Models

Two models were used to estimate the expectation of

annual EPS. The first model, a naive model, estimated that

the market predicts this year's annual EPS number would be

the same as last year's EPS number. This model shall be

called the AF model, which stands for annual forecast.

The second model estimated that the market predicted that

the current year's annual EPS number would equal the sum

of the first three quarters of actual EPS (previously

published) and the fourth quarter results of the previous

year multiplied by the ratio of the first three quarters

of the current year to the first three quarters of the

previous year. This model will be called the QF model,

which stands for quarterly forecast.

The AF model was used as a preliminary screening

device. The Wall Street Journal reports the previous

year's results and compares these to the current year's

results. The preliminary screen consisted of requiring at

least a 20 percent difference between the current year's

annual EPS and the previous year's annual EPS. Those

companies which made it through this initial screen were

then subjected to the QF model.

These models may be stated more precisely and

rigorously in mathematical notation. Assume that a

company's actual annual EPS number was published in The

Wall Street Journal. The year of operations which it












summarizes contains four quarters, the first three quarters

having been previously published and the fourth quarter

results being implied in the annual number. Similarly,

the previous year's annual EPS number summarized four

quarters of results. The subscript k is used to denote the

kth quarter relative to the first quarter of the previous

year; the quarter just prior to the annual report (fourth

quarter) is eight. Similarly, the first three quarters

of the same year would be subscripted five, six, and

seven, respectively; and the four quarters of the previous

year would be subscripted one, two, three, and four,

respectively. Thus, the actual annual results for the

previous year for company j, which is nothing more than the

sum of four quarters of operations for that year, may be

denoted as

4
E EPSj,k
k=l
and the immediate past year's results may be denoted as

8
EPS
SEPS j,k.
k=5

The AF model assumed that the market predicts that

this year's annual EPS will be the same as the previous

year's EPS. Denoting the AF model estimate of this number

as EA, then











4
EA = EPSj,k (5)
k=l

The annual forecast error (AFE) may now be defined

as

8
E EPSjk
k=5
AFEj= 1 (6)
EA

This annual forecast error is always expressed as a

fraction. It can easily be seen that the AFE is nothing

more than the actual current year's EPS number divided by

the estimate of its market expectation (EA) in the AF

model, less one. For instance, if a company had earned

$1.00 the previous year and $1.25 in the current year, then

the AFE would be ($1.25/$1.00 1) = .25 or 25 percent.

Now, the preliminary screen may be denoted mathe-

matically as:

IAFEI 2: 20%.

There are several things to note about the AF

model. First, it is not a very sophisticated model since

it does not adjust for the expected annual growth in EPS.

Since, however, few companies have growth rates in excess

of 20 percent, the possibility of incorrectly classifying

a company is small. Suppose, for example, that in the

previous year a company's annual EPS were $1.00, and that

in the current year the company earned $1.20. The company

would be included in the sample as its earnings increased











by 20 percent. If the market projected that the company's

earnings were going to increase by 15 percent (to $1.15),

then the actual earnings of $1.20 would be viewed as an

unexpected earnings increase by the market, and the price

of the security would be likely to rise. Thus, the model

"correctly" classifies companies as long as the market

expects less than a 20 percent growth in annual EPS.

A second problem with the AF model is that it

ignores interim reports of EPS. Thus, even though all

companies in the sample have at least a 20 percent change

in EPS, no assurance is given that there will be some

price adjustment subsequent to the arrival of the actual

number. Indeed, some people in the market may use only

an AF model or an AF model with growth; i.e., they may

ignore interim reports, but there is no assurance of this.

A second model, which takes into account quarterly reports,

is needed. This quarterly model was the second screen on

EPS. The 20 percent AFE screen was utilized as the pre-

liminary method for identifying those companies which were

most likely to have a price adjustment. The second or QF

(quarterly forecast) model was applied to all companies

which survived this preliminary screen. Mathematically

the estimate of the expected EPS using historical

quarterly EPS information and denoted as EQ is defined as











7
Z EPSjk
7 k=5
EQ = EPSj,k +3 (EPSj,4). (7)
k=5
E EPSj,k
k=l

Verbally, this model predicts that this year's

annual EPS number will be equal to the sum of the actual

first three quarters of EPS plus an estimate of the current

year's fourth quarter, which is estimated to be the

previous year's fourth quarter results multiplied by the

ratio of the current year's three quarter results to the

previous year's three quarter results. Another way of

stating this is that this year's fourth quarter results are

expected to be the same as last year's but adjusted for the

proportion of change in the first three quarters of results

to the previous year's first three quarters of results.

The quarterly forecast error (QFE) for firm j,

always expressed as a fraction, is defined as

8
E EPSj,k
k=5
QFEj = 1. (8)
EQ

The calculated QFE1 may be of either sign; i.e., a

company with an AFE of +20 percent will not necessarily

have a positive QFE. It may have been that the first

three quarters were exceptionally good for the firm and

that the fourth quarter failed to live up to expectations.











Companies which had a conflict in the predicted direction

of forecast error between the AFE and QFE models were

excluded from the sample. This procedure was designed so

that the direction of forecast error could be predicted

with some reliability, constituting the second screen on

earnings.

For instance, suppose that a company had earned

$1.00 per share the previous year and that each of the

four quarters of operations that year had provided $.25.

Suppose also that in the current year the company had

earned $2.25, $.50 a quarter for the first three quarters

and then $.75 for the fourth quarter. These increased

quarterly results for the fourth quarter were better than

would have been predicted on the basis of the first three

quarters of results, and the model showed this; i.e., the

company would have been included in the sample. This

firm's AFE was $2.25/$1.00 1 or 125 percent and its QFE

was ($2.25/[$1.50 + ($1.50/$.75)$.25]) 1 = ([2.25/2.00]-1)

= 12.5 percent. Thus, both the AFE and QFE models predicted

a positive forecast error. The above firm would not have

been included in the sample if it had earned the same $.50

a share in each of the first three quarters but only earned

$.25 in the fourth quarter even though the AFE is a

positive 75 percent ($1.75/$1.00 1). The EQ model would

have made the same estimate, but since the fourth quarter












was less than expected, the QFE would be ($1.75/$2.00 1)

= -8.75 percent.

The above procedure was designed so that the

direction of forecast error could be predicted with some

reliability. Thus, we are relatively confident that any

adjustment in price which occurs as a result of the new

EPS information will be directly related to the direction

of forecast error.

Residual Analysis

The method of residual analysis is fairly standard

and straightforward. It relies on the fact that under

certain conditions the return of a security may be dis-

aggregated into a component which is related to the return

on capital assets in general and a component which is

related only to the specific security. This proposition

may be stated mathematically in what has come to be called

the market model. The model states that the returns of a

security are a linear function of a general market factor

such that

Rjt = j + jRm,t + uj,t (9)

where

E(uj,t) = 0

cov(Rm,t,uj,t) = 0

and

Rj,t = return on security i in time t, including
dividends and capital gains.











Rm,t = return on the general market factor in
time t.

uj,t = the individualistic factor representing
the part of security i's return which is
independent of Rm,t.

aj ,j = intercept and slope, respectively, of the
linear relationship between the securities
return and the return on the general mark-
factor.

The Rj,t and Rm,t correspond to the holding period

return (eq. 4) of the individual securities and the market

index, respectively.

The return generating mechanism of (9), under some

crucial assumptions, is consistent with the capital asset

pricing model. These assumptions and the capital asset

pricing model will be discussed in the next section.

The a and a obtain their economic interpretations

from the capital asset pricing model. The B is a measure

of the systematic or non-diversifiable risk of the

security. The a is the average value, over time, of the

systematic or individualistic portion of a security's

return. It is assumed that the systematic portion of a

security's return is captured by the dj and 8 Rm,t. The

individualistic component represents the classes of events

which have impact only on security j. In an efficient

market this uj,t will fluctuate randomly as random informal

tion about the security is instantaneously reflected in

the market price (and return) of the security. It is this










interpretation of uj,t which has allowed researchers to

use (9) to test market efficiency. The method, outlined

below, estimates the market parameters of (9) for a large

sample of securities and then tests whether, in fact, the

uj,t fluctuates randomly.

The general method is quite simple. First, the

market parameters of (9) are estimated during a time

period when one believes that the assumptions of the model

are met; most importantly E(uj,t) = 0 and cov(uj,t,Rm,t) =

0. (To the extent that this is not true, the estimated

intercept will be biased.) In the present case, (9 ) was

estimated using the two outside quarters of the one year

of holding period-returns (HPR's--eq. 4) which were collect-

ed for each security. Using the same quarterly designa-

tions as used in the earnings forecast models, these four

quarters of HPR's would correspond to quarters 8, 9, 10,

and 11 with 8 and 11 being used to estimate the market

parameters. Notice that quarter 8 occurs during the

fourth fiscal quarter of the companies in the sample. The

middle two quarters of the year (9 and 10) contain the

possible adjustment period of the security price to the new

EPS information. These two quarters were not used in

estimating (9). The S&P 425 Industrial Index was used as a

proxy for the market index, Rm,t.











The next general step in the method is to use the

estimated parameters (9) with the returns to the individual

securities and the market portfolio to estimate u,


uj,t = Rj,t (&j + jRm,t) (10)

The ujt in any particular t represents that

portion of the security's return which reflects events

which are company specific after abstracting from risk and

general market movements. In this study these uj,t were

estimated for each security in the sample for eighty-one

separate days. These eighty-one days began twenty days

prior to the publication of the annual EPS number in The

Wall Street Journal and continued for sixty days after

that date. Since there are typically five trading days in

each week, this period corresponds roughly to one month

before and continues for three months after the publication

date. Only three months of residuals were collected after

publication because any residual after that time cannot be

attributed solely to the arrival of the annual number as

the first quarter results of the new fiscal year were

likely to be reported soon after the end of three months.

The next step in the analysis is to cross-

sectionally average the estimated residuals, u t's. This

averaging is performed relative to the time period in

which the expected disequilibrating information becomes










publicly available; e.g., in this study all t are measured

relative to the publication of the annual EPS number. For

instance, on day 0, the publication date, the firms in the

sample would have all of their estimated residuals (Uj,0's)

averaged together regardless of the chronological dates of

publication. This is called an average residual, ut

n
l ujt
j=1
"t = (11)
n

where there are n securities in the sample. In this study

the sample was split into those firms with positive and

those firms with negative forecast errors. There were

eighty-one separate average residuals (Ut's) calculated for

each of these subsamples.

Note that this u may be thought of as an average

rate of return which would have been earned on a portfolio

of n securities had they been purchased and held for the

time period t (in the present case, one day) after

abstracting risk and general market movements. If the

market is efficient, the u in any t will be very close to

zero as the price movement of the securities from which it

is generated fluctuates randomly. A u which is signifi-

cantly different from zero in a statistical sense is an

indication of market inefficiency with respect to the

information being examined.











If more than one time period is being examined,

then these out's may be accumulated (added) to form a

cumulative average residual (hereafter CAR)

T
CART = t (12)
t=0
where there are T time periods to be examined. The CAR

shows the cumulative effects of the wandering of the

return of the securities of interest around the market

line. A CAR in this study was calculated from day zero to

day sixty after the publication of the earnings announce-

ment and from day -20 to day +10 relative to the publica-

tion. Each was calculated for both negative and positive

forecast errors.

The u's may be accumulated in such a way that the

resulting index, called an Abnormal Performance Index

(API), may be interpreted as the rate of return accruing

to the holder of an equally weighted portfolio of all the

n securities in the sample, had the holder purchased them

at time period t relative to the arrival of the information

of interest and held them until day T.

T+N
APIT+N = T (l+-t) (13)
t=T+l
where the API is compounded from period T+1 to T+N.

It can be seen that the CAR and API correspond to

the well-known arithmetic and geometric rates of return.











The differences between calculated values of arithmetic

and geometric rates of return are trivial at low rates of

return (less than 15 percent). In this study, where the

typical u was less than one-half of one percent, the API

and CAR gave essentially similar results. The cumulative

difference between the two was never greater than .2 per-

cent after sixty days.

An operational definition of market efficiency with

respect to publicly available information has not been

satisfactorily formulated in the literature. In some

cases the market is deemed efficient if it "rapidly"

adjusts to new information. The term "rapidly" has never

been specified in terms of time periods. As Ball [1]

says, "The Efficient Market Hypothesis is limited in

operational content until the speed of adjustment is

specified precisely." In other cases, the market is deemed

efficient if it was not possible to earn an abnormal rate

of return by trading on the information as soon as it

became publicly available. Similarly, some studies have

compared the abnormal rate of return to transactions costs.

Regardless of the criterion of efficiency deemed

appropriate, the u's and CAR may be used to test efficiency.

Since the u's may be expected to fluctuate randomly about

the market line in an efficient market, a test of market

efficiency is whether or not this average residual (u) is










significantly different from zero. That is, if it were

possible to earn an abnormal rate of return by trading on

the basis of some information available in time period t,

then the market had not fully reflected that information.

If the market is inefficient, the average residual

may also be used to test the speed of adjustment by examin-

ing the number of u's (time periods) after the arrival of

the new information it takes for the average residual to

become insignificantly different from zero.

If the disequilibrium lasts more than one time

period, then the CAR may be used to measure the rate of

return from trading on the new information when it became

publicly available and holding the securities for as long

as the disequilibrium persisted. The ending value of the

CAR may be compared to percentage transactions cost as a

further test of efficiency.

The CAR is also an appropriate device with which to

examine the market adjustment process. An increase in the

CAR implies an increase in the prices of the securities

in the sample, and vice versa. A CAR which is wandering

randomly suggests no systematic market adjustment to the

information of interest. Thus, the pattern of market

adjustment may be inferred from examination of the CAR.








37


The Capital Asset Pricing Model, the
Parameter Estimation Problem, and
the Normality Assumption

The Capital Asset Pricing Model

The most important assumptions of the Capital Asset

Pricing Model (CAPM) are that (1) investors are risk

averters, (2) returns are normally distributed, (3) a

riskless rate of interest at which investors can borrow and

lend as much as they want is in existence, and (4) expecta-

tions are homogeneous. If we define Rf as the risk-free

rate and the other variables as before, then the CAPM

suggests that the expected value of the return on any

security j is:

E(Rj) = Rf + (j(E[Rm] Rf) (14)

where 8 = cov Rj,Rm/q2(Rm) (15)

The above model suggests that the return generating

process is the market model (9) if aj = (l-8j)Rf. Written

in terms of excess returns, the model may be tested by add-

ing an intercept to (14) and running the following

regression using ex post rates of return

Rj,t Rf,t = "j + 8j(Rm,t Rf,t) + uj,t (16)

The prime is to distinguish this intercept from aj in (9).

If the CAPM is correct, then the implication is that the

a- in (16) will equal zero. The in (16) is merely the

systematic portion of a security's return expressed in

units of market risk.












If we estimate (9) ex post instead of (16); then,

if we believe that the assumptions of the CAPM are correct,

the estimated a in (9) impounds the risk-free rate and the

systematic risk of the security as well as any systematic

return a' that may accrue to the security due to an

incorrectly specified CAPM or violation of the CAPM

assumptions. The estimated intercept in (9) will be

aj = Rf(l-j) + -a (17)

Note that the risk-free rate in (16) is time

subscripted. This means that variance in a estimated in

(.9.) may in part be due to shifts in the risk-free rate

although this rate, which is thought to be closely

approximated by the treasury bill rate, has historically

been fairly stable relative to stock market stability.

Researchers have found that (14), which is called

the one-factor model, is not well specified empirically

(see Fama and MacBeth [16] and Blume and Friend [7 ]). The

reason for this is that investors may not be able to

borrow and lend as much as they prefer at the risk-free

rate. To overcome this difficulty, researchers have

formulated what is called a two-factor model (see Fama and

MacBeth [16]). The two-factor model relies on the assump-

tion of the existence of a risky portfolio, called the zero

beta portfolio, which is uncorrelated with the market

portfolio and which, when used in lieu of the riskless










rate, yields similar conclusions as to the linear relation-

ship between market risk and return (see Black [ 4]). The

point of this is that if we replace Rf,t with Rzt (the

zero beta return) then we arrive at similar conclusions as

to the estimated intercept in (9). In this case the a

impounds the zero beta rate of return instead of Rf and

some of the variance in & may be due to changes in Rz,t.

The Parameter Estimation Problem

The typical procedure for testing market efficiency

is to estimate (9) by pooling (using) ex post rates of

return from time periods before (pre-period) and after

(post-period) the arrival of the information of interest.

These pre- and post-time periods are typically quite long;

five to ten years of monthly returns are not unusual (see

for example Ball and Brown [ 3] and Fama et al. [15]). It

is assumed that by pooling these pre- and post-time

periods to estimate the parameters in (9), accurate long-

term estimates of these parameters are obtained. Most

studies make the assumption that the parameters do not

change between the pre- and post-time periods. If, in

fact, the parameters do shift, the calculated average

residuals and CAR may not give a true indication of the

adjustment process.

The above problem may not be serious in the present

case as only one year of return data is examined and it is











unlikely that there will be a marked shift in the market

estimate of the risk of the firm during this short time

period. This short time period does, however, give rise

to another problem. Since only about three months of

daily observations are used in each of the pre- and post-

time periods to estimate the parameters in (9), short-term

shifts in the risk-free rate (or the zero beta rate) or

the systematic return to the security, see (17), may bias

the estimate of the market parameters.

The problems of parameter stability and bias in

the estimated parameters between the pre- and post-time

periods are serious in this study. As a means of over-

coming it, the parameters were estimated not only by pool-

ing the two time periods but by estimating them in each

period individually. The average residuals and CAR were

also calculated using these parameters estimated in the

pre-, post-, and pooled-time periods. Comparison of

these three series of CAR's, should they be similar, would

lead to the conclusion that parameter stability and biased

parameters were not a problem. Significant differences in

the CAR's would require the explicit consideration of the

degree of bias present.

The Normality Assumption

One problem with using stock price rates of return

is that observed return distributions have "fat tails" as











compared to normal or Gaussian distributions. It has been

found that monthly rates of return probably conform better

to a non-normal, symmetric, stable distribution than to the

normal (see Mandelbrot [26] and Fama [13]). Since

regression analysis and the planned statistical test of

the average residual require the assumption of normality,

there are some potential problems with using normal statis-

tical techniques on stock returns, as members of the

stable class of distributions do not converge to normality

as the classical central limit theorem suggests.

Researchers have found that regression analysis

and standard errors of means are robust with respect to

violations of the normality assumption for monthly rates

of return as long as the dispersion of the parameted

stable return distribution is defined (see Officer [31]

and Fama and MacBeth [16]). The evidence for daily stock

price rates of return also suggests that the violation of

the normality assumption is not serious. In a recent

study, Blattberg and Gonedes [ 6] find that "for daily

rates of return, the student model has greater descriptive

validity than does the symmetric stable model," and "the

student model has fat tails as does the stable model, but

converges to normality for large sum sizes." Thus, the

observed "fat tails" of stock return distributions is not a

problem for statistical inference in this case because, as











Fama observes, "as long as one is not concerned with

precise estimates of probability levels (always somewhat

of a meaningless activity) interpretation of t statistics

in the usual way does not lead to serious errors [16]."

Statistical Tests

Each of the eighty-one average residuals was tested

to determine if its average value was significantly

different from zero. The specific test performed was to

divide the average residual by its calculated standard

error. The resulting statistic, called a t statistic

(not to be confused with t as in time period) is well

known. A t statistic greater than two (approximately)

indicates that the mean is significantly different from

zero at the .05 level of confidence (approximately). A

statistically significant average residual in the time

period after the receipt of the EPS information implies

that the market was inefficient; i.e., it had not completely

adjusted for or fully reflected the information.

It was discovered that during certain time periods

relative to the announcement date there was no observed

statistical significance in the average residuals but that

the CAR appeared to trend strongly. This trend was due

(apparently) to noise in the average residuals after a

certain length of time which inflated their standard

errors and thus mitigated against statistical significance.











This trend in the CAR resulted from many of the average

residuals being positive (or negative) but not statistically

significant where market efficiency would imply that the

average residuals fluctuate randomly. Thus, it became

necessary to develop a statistical test of this observed

trend in the CAR, as the existence of such a statistically

significant trend implies market inefficiency.

One way to statistically test for the existence

of such a trend in the CAR is to regress it against some

time variable, i.e., fit a linear trend line through it.

CARt = a + b t + e (18)

where the t variable is nothing more than the integer

value of the day t relative to the announcement day. If

the slope coefficient of the time variable is significantly

different from zero, then one can infer that a trend in the

CAR exists, whereas market efficiency would imply that the

CAR should wander randomly.

The above test is not appropriate if the error

term of (18) is autoregressive (serially correlated). The

least squares estimates in such a case are unbiased and

consistent but are not efficient, which means that the

estimated standard error of the estimators (a and b) will

be biased. If the disturbances are autoregressive and we

use (18), the calculated acceptance region for the estima-

tors will be narrower than they should be for the specified

level of significance. This would inflate the calculated











t statistics and bias them toward inferring significance.

In fact, the above regression does have an auto-

correlated error term. The very procedure of accumulating

(adding) the average residuals into the cumulative average

forces the level of the cumulative average at one point in

time to be dependent on its level in previous time periods.

The nature of this autocorrelation would seem to be well

approximated by a first order autoregressive scheme, which

imposes an autocorrelation which dies out exponentially.

Adding the average residuals over time would create an

autocorrelation function which also asymptotically

approaches zero, so that the first order autoregressive

process should provide an adequate approximation.

An accurate estimate of the standard error of the

estimator of the slope coefficient of (18) may be obtained

by estimating the serial correlation coefficient in the

data and using it to fit a first order autoregressive

scheme to the same data.

CARt PCARt-1 = a(l-p) + b(t-pt-l) + (et-Pet-l) (19)

where pis the estimated serial correlation coefficient.

Again, one must believe that a first order autoregressive

scheme best describes the data (and it seems very reason-

able) for (19) to be appropriate (for a discussion of this,

see Cochrane and Orcutt [10]).

The above procedure is a test of whether or not

the adjustment process is instantaneous. It can also be











used to test the abnormal rate of return which could have

been earned. Since the CAR is expressed in terms of the

rate of return which would accrue to the holder of an

equally weighted portfolio of the securities in the

average residual, the slope coefficient of (19) may be

interpreted as an excess rate of return per day. An

estimate of the cumulative rate of return is to compound

this slope coefficient times the number of days over which

the CAR was calculated (T in [121). A confidence interval

around this average cumulative rate of return may be

closely approximately by

2 S
CART (1-2)L (20)

where

CART = a + (T), where a and 8 are the estimated
coefficients in (19).

S = standard error of the regression.


1The confidence interval is only approximate because
the above procedure ignores the fact that a and b in (19)
are estimates and are not known with certainty. The factor
ignored is of order 1/n, so that for large n its contribu-
tion will be small. In general terms, if we estimate
Y = a + bX + e and we want a confidence interval around a
predicted Y, then
E(Y) + E(a + b [X0])

Var (Y) = 2(1 + -+X)
n = )
EX.

The above procedure (20) is equivalent to ignoring the two
terms on the right in the Var (Y). But, since n and Xi are
fairly large in this study (in fact, never less than sixty)
the error in the confidence interval is very small.








46


This confidence interval was used to test the

reliability of the abnormal rate of return indicated by

the average cumulative rate of return.














CHAPTER III

RESULTS

Description of the Sample

The Earnings Digest section of The Wall Street

Journal was examined between the dates of February 15 and

March 20 in the years 1963 to 1971. These nine years

corresponded to the availability of the ISL Daily Stock

Price Tapes in the University of Florida Systems Library.

The initial step in drawing the sample was to examine the

current year's reported annual EPS numbers to determine

those firms which had at least a 20 percent change from

the previous year. The previous year's number is also

reported in the Earnings Digest.

The next step was to examine Standard & Poor's

Stock Guide to determine third quarter results for the

current and previous years. At this point all Over-the-

Counter securities were discarded as the Stock Guide

includes the exchange listing of all firms. Annual and

quarterly earnings were used to calculate the Quarterly

Forecast Error (QFE) (equation 8) for each security.

Those securities whose QFE conflicted in direction with

their Annual Forecast Error (AFE) (equation 6) were

discarded. At this point The Wall Street Journal Index

47











was utilized to cross-check the publication dates of annual

EPS numbers and to insure that no previous publication of

the number had taken place in The Wall Street Journal.

The final sample consisted of 158 firms, 113 with

positive forecast errors and 45 with negative forecast

errors. Table 1 presents a breakdown of these firms

across security exchanges, and it also presents the average

AFE and QFE for both positive and negative forecast errors.

Of the 158 firms, 105 were listed on the New York Stock

Exchange and 53 on the American Exchange. No attempt was

made to manage the proportion of the two different

exchanges in the sample.


TABLE 1

SUMMARY OF THE NUMBER OF FIRMS WITH NEGATIVE AND
POSITIVE FORECAST ERRORS, OF EXCHANGE LISTINGS,
SAND AVERAGE OF PERCENTAGE FORECAST ERRORS

Forecast # NYSE # AMEX Average Average
Error # Firms Firms Firms AFE QFE

Positive 113 74 39 68.6 21.5

Negative 45 31 14 -44 -21.6

All Firms 158 105 53 36 9.3


The range of the positive AFE was 20 percent to 480

percent, and similarly, the range of the positive QFE was

from 0 to 170 percent. The median QFE was 10 percent.

Thus there was a positive skew to the distribution of











Quarterly Forecast Error. The range of the negative AFE

was -20 percent to -93 percent, and the range of the

negative QFE was 0 to -89 percent. Since no firms were

examined with negative earnings, the AFE is bounded in a

negative direction by -100 percent while the positive AFE

is not bounded. This accounts for the difference between

the average positive and negative AFE's. The positive and

negative QFE's were of a similar magnitude.

Table 2 is a summary of the distribution of the

firms whose numbers were examined among the nine years in

the sample. The firms were fairly evenly distributed

among the nine years, but there was a slight tendency for

the negative forecast errors to occur more frequently in

the later years and the positive forecast errors to occur

more frequently in the earlier years.

An Analysis of Regression Results

The daily holding period returns (HPR's--equation 4)

of all 158 securities were regressed against the daily

HPR's of the S&P 425 Industrial Index. These regressions

were run three times for each security in the sample; once

using HPR's from the quarter just prior to the earnings

announcement quarter (pre-period or period 8), once for the

second quarter after the earnings announcement quarter

(post-period or period 11), and once by pooling the HPR's

from both time periods. This procedure yielded three sets




















TABLE 2

SUMMARY OF THE DISTRIBUTION OF FIRMS AMONG
DIFFERENT TIME PERIODS FOR THE TOTAL
SAMPLE AND FOR POSITIVE AND
NEGATIVE FORECAST ERRORS


Positive Negative
Year Total Error Error


1963 29 24 5

1964 20 17 3

1965 13 10 3

1966 31 27 4

1967 9 5 4

1968 9 7 2

1969 14 10 4

1970 16 6 10

1971 17 7 10

158 113 45











of parameters for each security. Table 3 is a summary of

the three sets of regression results for the total sample

and for the sample divided into positive and negative

forecast errors.

The market index, on average, explained about

11.7 percent of the variance of the individual security

returns. This level of explained variance (R2) is roughly

comparable to the results reported by Kaplan and Roll [21]

using a weekly differencing interval. The range of R2's

was from less than 1 percent for several firms to 62

percent for one firm (Boeing).

The most striking feature of the results presented

in Table 3 is the differences between the pre- and post-

periods. There was a systematic tendency for the post-

period to have a higher proportion of the variance of the

individual security returns explained by the market index.

The R2 is almost 70 percent higher in the post- than in

the pre-period for the whole sample. The average estimated

intercept is more than three times as large in the pre- than

in the post-period for those firms with positive forecast

errors (.149 percent versus .04 percent). The average

intercept is negative in the pre-period and positive in

the post-period for negative forecast error firms. There

is also a significant shift (.05 level) in the estimated

market risk of the firms in the sample. The average beta

increased from .897 in the pre-period to 1.076 in the post-

period.
















TABLE 3

AVERAGES OF THE ESTIMATED MARKET PARAMETERS AND EXPLAINED
VARIANCES IN THE PRE, POST, AND POOLED TIME PERIODS
FOR ALL 158 FIRMS AND FOR FIRMS WITH POSITIVE AND
NEGATIVE FORECAST ERRORS


Estimation ^ A 2
Period R

Total Sample (158 Firms)


Pre .001013 .897 .086

Post .000442 1.076 .146

Pooled .000823 .98 .118


Positive Forecast Errors (113 Firms).


Pre .00149 .949 .097

Post .0004 1.08 .152

Pooled .00113 1.04 .130


Negative Forecast Errors (45 Firms)


Pre -.000194 .776 .056

Post .000544 1.063 .131

Pooled .000054 .817 .085











It is apparent from the above results that the

estimates of the market parameters between the pre- and

post-periods are quite different. The problem arises,

therefore, of attempting to determine the cause of this

estimation problem and of attempting to determine which

set of market parameters is the most appropriate to use in

performing the residual analysis to follow. Briefly, it

was determined that the market parameters estimated in the

post-period were more appropriate, as the parameters

estimated in the pre-period were biased due to the way the

sample was drawn. The remaining pages of this section will

be used to present the analysis which led to this deter-

mination.

The estimated residual in each time period for each

security is calculated by (10):

uj,t = Rj,t (j + 8jRm,t), (10)

and the average residual is calculated by

n

j=1
Vt = (11)
n

If the average residual is calculated for a sample of

securities, it will be related to the estimates of their

market parameters, i.e., substituting (10) into (11)

n n n
z Rj,t E &j E RjRm,t
j=l j=l j=l
t = ( + ), (21)
n n n











or t Rt ( + R t) (22)

Thus, the average residual in any time period is

nothing more than the average return of the securities in

the sample for that time period less the average systematic

return of those securities and less the average systematic

risk of the securities times the average return of the

market portfolio in the time period. Note that in (22)

the time period is measured relative to the announcement

date of the new EPS information and thus the Rt and Rm t

represent many different chronological dates.

Equation (22) clearly demonstrates the purpose of

using the market model (9) in a residual analysis to test

market efficiency. If the market is efficient, then

subtracting the average systematic return (T + f ERt) of

a sample of securities from the average return of those

securities in some time period (t-relative to some informa-

tion availability) Rt, should yield approximately a zero

return. This is because the Rt represents many different

chronological dates and thus should be a random number if

the securities in the sample move randomly relative to the

announcement date. If the market is not efficient with

respect to the securities in the sample, then subtracting

the systematic return from the average calculated return in

a time period when the market is systematically adjusting

for some new information will not yield a zero average











return. The above argument assumes that an unbiased

estimate of the systematic portion of each security's

return is obtained, as well as unbiased estimates of the

market risk parameters.

The estimated 8 in the pre-period is slightly

smaller than in the post-period. These differences are

not likely to have a substantial impact upon the estimated

residuals because the average Rm,t is likely to be quite

small on a daily basis.1 In a famous study, Fisher and

Lorie [17] estimated that the average long-term annual rate

of return of all securities listed on the New York Stock

Exchange was about 9 percent. This means that, on average,

the value of Rmt on any particular day is likely to be on

the order of .09/250 = .036 percent if there are 250

trading days in a year. The difference between the two

estimated B's is small (1.076 .897 = .179), and thus the

differences between calculated average residuals as a

result of different estimates of B is likely to be very

small (.179 x .00036 = .0000644).


iTime does not mean that the individual Rmt's in
different time periods cannot be quite large. It is the
8iRm.t term which is used to adjust individual returns for
systematic risk; i.e., if Rm t is 1 percent in some time
period, then a security wiTHEa a of .5 would have '
percent subtracted from its return in the residual
analysis, and a security with a f of 2 would have 2
percent subtracted from its return (eq. 10).











Contrary to the 8j, the differences in the esti-

mates of the acj's in the pre- and post-periods could cause

a significant difference in the estimated average residuals

and one does not know which set of estimated parameters is

appropriate. Thus, the problem arises of determining

whether or not the observed instability in the estimated

average intercepts of (9) between the pre- and post-periods

was caused by some CAPM related instability (perhaps

instability in the zero beta rate of return) or by some

sample specific instability. If the former is the case,

there can be no confidence that the estimated intercept

parameter is appropriate for the period of estimation of

the average residual. If the latter is the case and if

it can be established that either the pre- or post-period

estimated parameters are an accurate estimate of the

extant market relationship, then estimation of the average

residuals is appropriate.

The average &j in the pre-period is .001013 (more

than one-tenth of 1 percent) which is equivalent to an

annual return of 25 percent (.001013 x 250). The equivalent

annual return in the post-period is 11 percent (.000442 x

250). Thus the difference between the average d's

estimated in the pre- and post-periods is on the order of

14 percent on an annual basis and near one-tenth of 1

percent in each period (.081 percent). Thus the observed












differences in the V's can significantly affect the

average residual. The remainder of this section will

identify potential sources of instability and bias in the

s's and will analyze the most probable source of bias in

this study.

Recall from (17) that if one believes that the

assumptions of the capital asset pricing model are met in

the real world, then the estimated aj impounds the riskless

rate Rf, the systematic risk of the security Bj, and the

systematic return of the security aj (if it exists). If

one believes that the assumption of riskless borrowing and

lending is not tenable, then Rf in (17) can be replaced by

the zero beta rate of return Rz.

There is a potential source of bias in the estima-

tion of aj. If the regression model assumption E(ujt) = 0

is not met, then the estimated aj will be biased; i.e., if

E(uj,t) = uj 0 over some period of estimation, then this

specification error will cause the estimated intercept to

be biased by an amount equal to the uj. Adding this -j to

(17) we find

aj = Rf(l-aj) + aj + j. (23)

A market disequilibrium in the estimation period will

cause E(uj,t) ; 0 and by the above argument this trend in

the residual can bias j.











Equation (23) identifies those sources of variance

which are the most likely to affect the estimate of aj.

Note that if all of the assumptions of the CAPM are met,

the !a's (and the aj's) will equal zero. If the two

factor (zero beta model) CAPM is correct, then the Rf will

be replaced by Rz (the zero beta return), a will be

equal to zero, and the aj will equal zero if there is no

trend in the residual. The CAPM in both forms assumes

that the market is efficient; i.e., there is no 3 4 0.

Equation (23) may be used in an analysis of the [ resulting

from estimating (9) in different time periods. The problem

is to identify the most probable cause of the different c

and to determine which set of parameters is appropriate

for the residual analysis.

Note that an average systematic risk of about one

for the securities in the sample means that the riskless

rate (23) is likely to contribute little to the &. The

average treasury bill rate (thought to be a reasonable

surrogate for Rf) was about 4 percent during the period.

The treasury bill rate also had a slight uptrend during the

nine-year period, and since, chronologically, the pre-

period is always before the post-period this uptrend, if it

influenced the 6, should have influenced the post-period

minutely. In fact, the post-period & was systematically

lower than the pre-period.











A similar line of reasoning suggests that the zero

beta rate of return (with the average $ close to one),

Rz, probably did not cause the differences between the

pre- and post-period &'s, although the argument is less

forceful than in the case of Rf since the zero beta rate

has been typically estimated to be of a greater magnitude

and variance than the riskless rate (see Fama and MacBeth

[16]). Fama and MacBeth and Black, Jensen, and Scholes [5 ]

estimate the monthly zero beta rate over many different

time periods, and in no time period do they find a level

of Rz which implies an annual return of greater than about

15 percent. Thus it seems very unlikely that the estimated

annual return of 25 percent in the pre-period could have

been caused by an exceptionally high zero beta return.

However the possibility should be kept in mind if a more

likely explanation cannot be found.

A fairly simple analysis demonstrated that the

most likely explanation of the high T in the pre-period was

a systematic tendency in the error term of (9) to have an

expectation different from zero. This mis-specification

of (9) caused the estimated intercept to be biased; i.e.,

in (23) the u was different from zero. It was found that

(9) was not subject to this same mis-specification when it

was estimated in the post-period.











The pre-period corresponds to the fourth calendar

quarter of a year in which each security in the sample had

at least a 20 percent change in EPS from the previous year.

Table 1 shows that, on average, EPS was about 69 percent

greater than the previous year for the securities with

positive forecast errors and about 44 percent lower for

securities with negative forecast errors. The quarterly

forecast error was about 21 percent (plus and minus) for

both positive and negative forecast errors. This means that

it is very likely that the firms in the sample had third

quarter earnings reports which were different from those

expected by the market. Since AFE was substantially

greater than QFE, on average, the increase in AFE was

likely to be caused by increased third quarter earnings as

well as increased fourth quarter earnings. If the market

is inefficient, then it may be adjusting for the third

quarter EPS report during the fourth quarter: that is,

the quarter used to estimate the pre-period market

parameters. To test whether or not there was any statis-

tical association between the direction and degree of

Annual Forecast Error and the level of a', the following

regression was run for the whole sample:

ai,pre = a + b(AFEj) + e, (24)
where

aj,pre = the estimated intercept of the market
model of security j in the pre-time
period.











AFEj = the percentage difference between this
year's annual EPS number and the previous
year's annual EPS number.

The result of the regression was

-j,pre = .0013 + .00000795 (AFE) 125)
(4.06) (3.415)
The relationship was as significant when the regression

was run for the pooled-time period estimate of &j. There

was no significant relationship found when the regression

was run for the post-period &j's. Thus, the high level of

a in the pre-period and in the instability between periods

appears to have been caused by a mis-specification of the

market model (9) during the pre-period.2

Note that the post-period is not subject to the

same mis-specification. Although the manner in which the

sample was drawn forced a high level of EPS in the pre-

period, there is nothing inherent in the procedure which

leads to a systematic price dis-equilibrium in the post-

period. Researchers have found that high levels of EPS in

one period are typically not followed by high levels of

EPS in subsequent periods; i.e., EPS numbers seem to vary

randomly. Since the post-period corresponds to the quarter

in which stock prices would be adjusting for the second


2Note that the same results could have been obtained
had the market been systematically anticipating fourth
quarter EPS; i.e., it was very efficient. However, the
residual analysis which is to be presented in the next
section suggests that this is unlikely.











quarter EPS number, there is no reason to believe that

this number will be related to the previous year's annual

results. For empirical evidence in this regard, see

Lintner and Glauber [24] and especially Brealey [8].

Comparison of the & in the pre-period between the

sample of positive and negative forecast errors is

revealing. Those securities with positive forecast errors

had an average estimated intercept of .00149, which is an

equivalent annual return of 37 percent (.00149 x 250). If

the market were adjusting for increased third quarter EPS

during the fourth quarter (pre-period), then a u greater

than zero is expected and the estimate of [ would impound

the -. For firms with negative forecast errors the u would

be negative during the fourth quarter, and indeed the

estimated & is negative during that period (Table 3).

This is the most convincing evidence that the different

levels of & were not caused by shifting levels of the zero

beta return. Since there is a significant overlap in the

time period of estimation for negative and positive fore-

cast errors (Table 2), it is highly unlikely that the zero

beta return biased the a downward for negative forecast

error firms and during the same time period biased the i's

upward for positive forecast error firms.

The reason for the differences in the average

level of explained variance (R2) between the pre- and post-

time periods may now be rationalized. During the












pre-period there is reason to believe that some of the

total variance of return was caused by the adjustment

process u and, thus less of the total variance was

explained by the market index.

The above analysis strongly suggests that the

market parameters estimated in the pre-period are systemati-

cally biased away from the normal relationship and thus

should not be used in the residual analysis. Examination

of Table 3 reveals that the parameters estimated by

pooling the pre- and post-time periods may also be severely

biased. It was therefore determined that only the post-

period estimated market parameters were appropriate for

the residual analysis. That analysis will be presented

in the next section.

Residual Analysis for Positive Forecast Error

The market parameters of (9) estimated in the post-

time period were used in (10) to estimate residual for

each firm starting twenty days before and running through

sixty days after the publication of the EPS number. These

estimated residuals were averaged cross-sectionally (11)

relative to the publication date and accumulated (12) to

form a cumulative average residual (CAR). Table 4 shows

the average residual (11) for all firms with positive

forecast errors for the publication date of EPS and ten days

thereafter. The corresponding t statistic for each of these









TABLE 4

THE AVERAGE RESIDUAL, t STATISTIC, AND CUMULATIVE
AVERAGE RESIDUAL FOR POSITIVE FORECAST
ERRORS ON SELECTED DAYS AFTER THE
EARNINGS ANNOUNCEMENT


Day t of u CAR


0 .01097 3.89 .01097

1 .00517 2.22 .01614

2 .00375 1.53 .01989

3 .00204 1.02 .02193

4 .00312 1.22 .02505

5 -.00125 .54 .02381

6 -.00033 .10 .02347

7 -.00218 -1.16 .02128

8 -.00360 -1.58 .01769

9 -.00212 -1.01 .01555

10 -.00244 -1.28 .01312

15 .0153

20 .0172

25 .0260

30 .0307

35 .0327

40 .0463

45 .0514

50 .0491

55 .0495

60 .0577











average residuals is also presented, as is the CAR for

these eleven days. After day 10 the CAR is shown every

five days until day 60.

The t statistic for the average residual is

calculated by dividing the average residual by its standard

error (estimated standard deviation divided by the square

root of the sample size). A t statistic greater than two

implies an average residual which is statistically different

from zero at approximately the .05 level of confidence.

The Cumulative Average Residual for firms with

positive forecast errors is plotted in Figure 1. The

first day plotted (day 0) corresponds to the day the

actual EPS number was published in The Wall Street Journal.

The CAR is plotted for sixty days after publication,

which corresponds to about three calendar months. The

plot of the CAR corresponds exactly to those numbers

presented in Table 4. The remainder of this section will

analyze and interpret Table 4 and Figure 1. This analysis

will include the realized abnormal return, the adjustment

process, and the speed of adjustment.

The Abnormal Return

The average residuals were statistically different

from zero (.05 level) on the date of publication of the

EPS number (day 0) and on the following day (day 1) as

indicated by the t statistic of each individual average






























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residual in Table 4. The cumulative return for these two

days was about 1.6 percent. Current transactions costs

are on the order of 1 percent on both the buy and sell

sides for large round-lot transactions. Since the CAR

did not reach the necessary 2 percent on the two days in

which the average residuals were statistically signifi-

cant, it was not possible to have earned an abnormal

return.

Examination of Figure 1 reveals that, while the

individual average residuals were not statistically signi-

ficant after day 1, the CAR appeared to trend strongly

upward from about day 12 to about day 45. The CAR main-

tained its relatively high level until day 60; its ending

value was 5.77 percent. The cumulative return of 5.77

percent is 3.77 percent greater than the average 2 percent

transactions costs necessary to buy and sell securities in

large round lots. (This assumes that the securities were

purchased at the closing price on the days prior to day 0.)

This abnormal return may be an indication of market

inefficiency, but since the individual average residuals

which comprise the CAR are not generally statistically

significant (.05 level), the 3.77 percent abnormal return

may have been due merely to chance occurrence.

To test for the existence of a statistically

significant trend, the CAR in Figure 1 was regressed against

the integer value of the day relative to the publication











day; i.e., (19) was run. The results of that regression

are summarized in Table 5.3 The t statistic of the slope

coefficient indicates that the slope is statistically

significant at the .01 level. This regression line is

plotted against the CAR in Figure 2.


TABLE 5

SUMMARY OF REGRESSION TESTING THE STATISTICAL
SIGNIFICANCE OF THE CUMULATIVE AVERAGE
RESIDUAL FOR POSITIVE FORECAST ERRORS
AFTER ADJUSTING FOR SERIAL
CORRELATION

Days Rho a b S R2

(t) (t)
0-60 .85 .0129 .00069 .00286 .962

(2.38) (5.08)



SBecause the CAR is scaled in percentage units and

the independent variable in (19) is an integer representing

one day, the slope coefficient in Table 5 may be inter-

preted as an average rate of return per day, and the

cumulative return on any particular day may be predicted

from (19). This predicted cumulative average return is of

interest because the regression results may be used to


3Examination of the R2 term indicates that the first
order autoregressive scheme was appropriate. The regression
coefficient and the serial correlation coefficient together
explain 96 percent of the variance of the CAR.




























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generate a confidence interval around any particular day's

predicted cumulative average return (20).

The upper and lower 95 percent confidence limits

for the regression line plotted in Figure 2 are plotted in

Figure 3. Note that these confidence limits are only

approximate and that the true lines can be expected to bow

slightly at the ends. As indicated in Chapter 2, the error

in the confidence limits is likely to be small.4

The most interesting part of the regression line

and its confidence limits is the predicted cumulative

average rate of return on day 60, the ending day in the

analysis. This predicted cumulative average rate of return

may be interpreted as the average rate of return accruing

to the holder of an equally weighted portfolio of all of

the securities in the sample if held from day 0 to day 60.

Using the numbers in Table 5, the predicted cumulative

average rate of return on day 60 is 5.43 percent. The

95 percent confidence limits around this predicted point

(20) are approximately 4.35 percent to 6.51 percent.

The lower confidence limit of 4.35 percent is an

indication that the purchaser of an equally weighted

portfolio of the securities in the sample would have earned

a minimum of 2.35 percent on average, after transactions


4The error is on the order of 1/n times the absolute
value of the confidence limit. Since n is 60, the error is
on the order of 1.6 percent of the confidence limit.


































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costs, with a 95 percent level of confidence. This return

was in excess of the normal market return. Since this

return accrued over a three calendar month period, if one

assumes such investment opportunities are available year

round, then this 2.35 percent is equivalent to an annual

excess return of 9.4 percent (2.35 x 4). If one assumes

that the average rate of return of 5.43 percent can be

earned each three months, then the equivalent annual

excess return is 13.7 percent ([5.43-2] x 4), after allowing

for transactions costs and normal market returns.

The above results and analysis are an indication

that market inefficiencies existed with respect to the

securities in the sample in the time periods in which they

were examined. The existence of a statistically significant

(.01 level) trend in the CAR indicates that the market

did not instantaneously adjust to the new information, and

the 95 percent confidence interval around the predicted

average CAR indicates that an excess return could have

been earned had one acted upon the publicly available EPS

information as soon as it became available.

The above abnormal return could have been earned

by using a fairly simple investment strategy or decision

rule, although the actual profit from such a strategy may

not have been as large as it would seem. The strategy

would require examining the earnings reports in The Wall













Street Journal on a daily basis and immediately purchasing

those securities which met the necessary criteria implied

in (6) and (8). To the extent that one is not able to

immediately purchase such securities, the minimum 2.35

percent abnormal return may be decreased. For instance,

if the approximately 1 percent average increase on day 0

occurs early in the day, then an investor who was unable

to purchase early on this day would have the average 2.35

percent abnormal return decreased to 1.35 percent. This

might be a problem for some investors who only receive

The Wall Street Journal after a day's delay. If the

individual investor could not afford to buy in large

round lots, then the abnormal return could be further

pared in transactions costs which can be greater than 4

percent for odd-lot purchases and sales.

Another danger is that the individual investor may

be insufficiently wealthy to properly diversify himself,

and thus he may be subjected to the gambler's ruin. The

point of this discussion is that while this study may

have demonstrated a fairly strong degree of market

inefficiency, the individual investor should be very

cautious in trying to implement such an investment strategy

unless he tests such a strategy over a long period of time

without actually investing.













The Adjustment Process

There appear to be three distinct stages in the

adjustment process of stock prices to unexpected increases

in EPS. These three stages are illustrated in Figure 4;

(lines are drawn as illustrations and with no pretense of

accuracy). The first two stages took place during the

first ten to twelve days after publication of the actual

EPS number in The Wall Street Journal. The first stage

consisted of a rather smooth and uninterrupted run-up in

price for about five market days (one week) after publica-

tion. The greatest percentage move (about 1 percent, see

Table 4) occurred on the publication day. This move was

statistically significant at the .05 level as was the move

on the following day. The average cumulative price increase

was 24 percent which was reached after five market trading

days.

After the rather strong spurt of price increases,

there was a five to seven day period of rather smooth and

persistent price decreases. None of these price decreases

during the second stage were statistically significant

(.05 level) although several tended toward significance.

The average cumulative price decrease was about 1i percent.

This reduced the initial price run-up to about 1D percent.

After the initial two stages in the adjustment

process, the market appeared to enter a third stage lasting













































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from about day 15 after publication of EPS to about day 45.

This stage consisted of a persistent drift upward in the

cumulative average residual, while only a few of the

average residuals which comprised the CAR were statistically

significant. Several of the average residuals between days

15 and 30 were negative, causing the increase in the CAR

to be quite jerky. Beginning at about day 30 the CAR

began to trend upward more smoothly than during days 15

to 30. This trend lasted until about day 45 after the

announcement.

After about day 45 the CAR appeared to vary more

randomly than during the first forty-five days. It is

possible that the market had completed its adjustment by

day 45 and was in equilibrium, although it is not clear

that this was so. It is possible that the market began to

anticipate first quarter EPS during this period (days 45

to 60). The preannouncement movement in the CAR will be

examined and discussed in a subsequent section.

From the above discussion it appears as though

there is a three-stage adjustment process involved in the

market reaction to earnings forecast errors. A rationaliza-

tion of this situation may be offered involving the mecha-

nism whereby information is disseminated to and interpreted

by investors. Specifically, the initial two stages of the

adjustment may be a market reaction to incomplete earnings













information in The Wall Street Journal. That is, the price

may initially increase as a result of publication of the

EPS number, but the market may not have sufficient detail

to sustain the initial price run-up. Publication of the

annual EPS number in The Wall Street Journal is accompanied

by only a bare minimum of the fundamental conditions

surrounding the EPS number, usually only total sales, total

costs, earnings and EPS numbers.5

The initial price reaction may cause technical

interest which may cause the market to over-react in the

first stage and as a result to decrease in the second

stage. Thus, it appears as though the initial run-up in

price and subsequent decrease is a possible over-reaction

to incomplete information.

The third stage may result from a lag in the

availability of the annual report to investors and

analysts.6 After about day 15, details of the year's

operations become available in the annual report. This


5A supplementary cause of the initial two stages may
be the actions of a group of investors who trade on the
basis of annual EPS numbers as compared to the previous
annual EPS number and not on the basis of improved fourth
quarter results.

6A small study conducted at the University of
Florida revealed that over a one-month period in March 1974,
there was an average of about a three-week lag between
publication of the annual EPS number in The Wall Street
Journal and the arrival of the annual report of the
company at the University of Florida libraries.













more complete information may cause the cumulative

average residual to begin to drift upward. The detail in

the annual report may cause shareholders to reevaluate

the long-term investment worth of the firm in question and

to, perhaps, re-balance portfolios. At the same time it

is to be expected that analysts will reevaluate the firms

on the basis of the annual report and possibly issue buy

or sell recommendations. The price changes in the third

stage are permanent in nature reflecting the reevaluation

of the long-term investment worth of the firms (price

changes in the first stage were partially eliminated).

The fact that all of the securities in the sample

have at least a 20 percent change in annual EPS may tend

to exaggerate the initial adjustment process. If there

are indeed some traders who buy and sell solely on the

basis of annual EPS numbers and ignore interim earnings,

then this study would tend to overemphasize the action of

such traders when compared to the "normal" adjustment

mechanism. It may very well be that the initial adjust-

ment stage is much less pronounced for securities with

less than a 20 percent change in annual earnings.

The Speed of Adjustmeat

If the above analysis is correct, then the adjust-

ment process of the stock market to published annual EPS

information apparently takes about forty-five days or

about 21 calendar months after the publication of the











annual EPS number. This is entirely in keeping with the

Ball and Brown [3 ] results, as they also found about a

two-month adjustment process. If one concludes that the

market had completed the adjustment process by the end of

the forty-fifth day after the earnings announcement, then

it is apparent that the market was out of equilibrium

for about 75 percent of those sixty days. In this case

we call the market out of equilibrium if it is moving in

other than a random fashion. It appears from the statis-

tical analysis that this is the case.

It would seem as though the two-month adjustment

process would contradict the Jones and Litzenberger

results that the adjustment took place over a six-month

period. This, however, is not true. Since this two-month

adjustment resulted in a permanent price change, it is to

be expected that this price change would have persisted

on average until the end of the six months.

It is interesting to note that the conclusions for

market efficiency would be quite different had the third

stage of the three-stage adjustment not taken place. The

fact that the market took about ten days to adjust for the

earnings announcement and that it eliminated most of the

price change associated with the announcement would have

been strong evidence of a fairly efficient market. The

fact that the third trend existed and, what is more











important, that the price increase appeared to persist is

evidence that the market has reevaluated its fundamental

estimate of the worth of the securities in the sample and

that this reevaluation and adjustment takes a considerable

length of time.

It is not entirely clear that the adjustment process

has been completed by the end of the forty-fifth day. The

findings with respect to the anticipation of the annual

EPS would suggest that a similar process might occur for

quarterly EPS. If the first quarter earnings reports for

most companies in the sample are published about three

months (one quarter) after the annual report, then it may

well be that there is some adjustment occurring during the

last fifteen days also. If this is so, then it may be

that the securities with highly unpredictable components

of their EPS may never reach equilibrium in the sense that

the market has completely adjusted for all available infor-

mation.

Of course, it may very well be that the adjustment

process for securities whose EPS are fairly predictable

is indeed rapid because the arrival of the annual report

could be considered to be no news to the market and thus

little if any adjustment would be expected. The conclusions

seem inescapable, however, that the capital markets were

not very efficient with respect to the securities in this












sample if one uses the speed of adjustment as the criterion

for efficiency.

Residual Analysis for Negative
Forecast Error

Table 6 lists the average residual, t statistic,

and CAR for the forty-five firms in the sample with

negative forecast errors. Each is listed for the eleven

days subsequent to the publication of the actual EPS

number. In addition, the CAR is presented every five days

from day 15 to day 60. Figure 5 is a plot of the CAR on

a daily basis for days 0 to 60.

Examination of Figure 5 reveals that the CAR

generally drifted downward after the announcement date as

would be expected for firms with unexpected decreases in

EPS. As with positive forecast errors, the first two

average residuals are statistically significant at the .05

level. Those two days correspond to the EPS publication

date and the following day. The total price move on the

first two days was a negative 2.8 percent. This is .8

percent greater than average transactions cost. Thus, it

appears profitable to sell short the securities in the

sample, as an excess rate of return of .8 percent could

have been earned. The initial price move was reversed

after only two days, and the CAR appeared to have a slight

upward drift from about days 2 to 10 after publication.












TABLE 6

THE AVERAGE RESIDUAL, t STATISTIC, AND CUMULATIVE
AVERAGE RESIDUAL FOR NEGATIVE FORECAST ERRORS
ON SELECTED DAYS AFTER THE
EARNINGS ANNOUNCEMENT


Day u t of u CAR


-.01740

-.01164

.00108

.00077

.00457

-.00147

.00346

-.00142

.00539

.00288

-.00306


-2.79

-2.15

.23

.20

.92

- .41

.50

- .32

1.46

.96

-1.16


-.01740

-.02857

-.02749

-.02672

-.02215

-.02362

-.02016

-.02157

-.01618

-.01331

-.01637

-.02525

-.03705

-.03492

-.04761

-.04983

-.06539

-.08736

-.08012

-.08254

-.08827
































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Beginning at about day 10 or 11 the CAR started to drift

downward again.

The ending value of the CAR was 8.8 percent after

sixty days, but this level had been essentially attained by

the end of forty-five days. Between days 10 and 60 few of

the individual average residuals were statistically signi-

ficant (.05 level), yet the CAR trended downward fairly

strongly. As a test of the statistical significance of

that trend, the CAR was regressed against the integer

value of the day relative to the announcement day; i.e.,

equation (19) was run. The results of that regression are

presented in Table 7. Table 7 reveals that the slope

coefficient is statistically significant at the .01 level.

This is an indication of a statistically significant trend

in the CAR and this indicates that the market did not

instantaneously adjust to the new EPS information.


TABLE 7

SUMMARY OF REGRESSION TESTING THE STATISTICAL
SIGNIFICANCE OF THE CUMULATIVE AVERAGE
RESIDUAL FOR NEGATIVE FORECAST ERRORS
AFTER ADJUSTING FOR SERIAL
CORRELATION


Days Rho a b S R2

(t) (t)
0-60 .77 -.0064 -.00144 .0039 .976

(-1.28) (-10.95)











Using the estimated coefficients in Table 7, the

estimated cumulative average return after sixty days was a

negative 9.28 percent. The 95 percent confidence interval

around this average return is negative 8.06 percent to

negative 10.5 percent. Assuming average transactions

costs of 2 percent, the minimum expected return for short

sales is 6.06 percent with a 95 percent level of confidence.

This translates to a 24.3 percent excess return on an

annual basis if one assumes that such investments are

available year round.

It appears as though the rate of return from

selling short securities with negative forecast errors is

considerably higher than the rate of return from long

purchases of securities with positive forecast errors, at

least for the securities in this sample. Recall that the

Quarterly Forecast Error for both negative and positive

earnings changes was an almost identical 21 percent

(Table 1). One reason that the ending value of the CAR

was greater for the negative series may be the finding that

there is generally a greater percentage decline in price

relative to a percentage change in earnings for unfulfilled

earnings expectations than there is for earnings greater

than expectations (see Neiderhoffer and Regan [30]).

Another reason may be that the market actually projected

some long-term growth in quarterly earnings, and thus the












actual Quarterly Forecast Error was actually greater than

indicated by the negative QFE.

The similarities in the adjustment process of the

stock market to negative and positive forecast error are

illustrated in Figure 6, which is a plot of the CAR's for

both negative and positive QFE's. The pattern of adjust-

ment for the two series looks remarkably similar, almost

like mirror images of each other; both exhibit statistically

significant price changes on the day of the earnings

announcement and the following day. These price changes

are directly related to the direction of forecast error.

Both series exhibit a second stage just after the first

in which the prices of the securities move inversely to the

direction of forecast error. This situation appears to be

a correction for a possible over-reaction to the earnings

announcement. Both series exhibit a price trend which is

directly related to the direction of forecast error which

begins 10 to 12 days after publication of the EPS number

and lasts until about day 45. From days 45 to 60 both

series appear more or less horizontal and thus appear to

change in a random fashion, although it is not altogether

clear that this is so. The fact that both series begin to

trend in a direct relation to the change in EPS between

days 10 and 15 seems to indicate that some common

occurrence causes this trend, perhaps the arrival of the

















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actual annual report in the hands of investors.

Although the two series exhibit some remarkable

similarities, there are also some distinct differences.

The adjustment process for the first ten days appears to

be slightly different. Both the negative and positive

series peak in absolute value at about 2 percent, yet it

takes the positive series about five days to reach this

level, while the negative series achieves a -2.8 percent

in two large and significant jumps. (Recall from Table 1

that the average QFE for the two series were almost

identical [21.5 percent versus -21.6 percent] and that the

average AFE's were greater for the positive series [68.6

percent versus -44 percent].) One possible explanation

for this is that the two significant moves for the positive

series trigger certain technical indicators such as

relative strength tests and cause investor interest on the

basis of this information. This technical interest could

cause the price to keep increasing for the extra few days.

Such a mechanism is not available for negative price moves,

so that the entire adjustment appears to take place in just

two days.

The second stage of the adjustment process seems

to be more smooth and less random for the positive than

the negative series. Notice that the average residual

tended toward statistical significance between days 5 and












10 for the positive forecast error series, but that the t

statistics are near zero between days 2 and 10 for the

negative series (see Tables 4 and 6). The indication is

that whatever causes the second stage of the adjustment

process, it is not as strong for the negative series as it

is for the positive series.

Pre-Announcement Movements
in the CAR

Examination of the average residuals and CAR prior

to the actual announcement of EPS is of interest because

it gives an indication of how the market anticipates the

earnings announcement. The market may use many different

sources of information in the anticipation process.

Economy-wide movements and earnings of firms in the same

industry may allow investors to form estimates of the

future-EPS of a firm and, perhaps, cause them to purchase

or sell securities on the basis of such information. Move-

ments in the CAR as a result of investors acting on such

information would be an indication of an efficient market.

However, movement in the CAR caused by investors

taking advantage of other sources of information could be

an indication of market inefficiencies. Such sources of

information include news leakages and insiders taking

advantage of monopolistic sources of information.

Unfortunately, it is impossible to tell if movements in

the CAR prior to the EPS announcement are caused by












information of this sort or information about economy-wide

or industry-wide movements. Examination of the CAR prior

to the earnings announcements is, nonetheless, still of

interest.

Figure 7 is a plot of the CAR for both positive and

negative forecast errors beginning twenty days prior to and

ending ten after the earnings announcement. Tables 8 and

9 show the average residual, t statistic of the average

residual, and the cumulative average residual. The CAR's

in both cases started accumulating at day -20 or about one

month before the announcement.

The direction of movement in the CAR's prior to

the announcement date is directly related to the direction

of forecast error. The CAR's begin a rather smooth trend

in anticipation of the announcement approximately fifteen

days (three weeks) before the actual announcement. Both

positive and negative series reach a cumulative absolute

value of 3.9 percent on the day before the announcement.

The average residual is significantly different from zero

(.05 level) on the day before the announcement for the

positive series and on the second day prior to the

announcement for the negative series.

The patterns of adjustment for the positive and

negative series are again remarkably similar. The

indication is that the anticipation and adjustment mechanism

















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TABLE 8

PRE-ANNOUNCEMENT AVERAGE RESIDUAL, t STATISTIC,
AND CUMULATIVE AVERAGE RESIDUALS FOR
POSITIVE FORECAST ERRORS


Day u t of CAR

-20 .00008 .04 .00008
-19 .00091 .03 .00099
-18 .00298 1.29 .00396
-17 .00079 .42 .00495
-16 -.00033 .13 .00442
-15 .00385 1.80 .00827
-14 -.00097 .45 .00730
-13 .00261 1.11 .00991
-12 .00252 1.25 .01243
-11 -.00077 .41 .01165
-10 -.00058 .30 .01108
- 9 .00341 1.62 .01448
- 8 .00374 1.74 .01822
- 7 -.00077 .37 .01745
- 6 .00521 1.64 .02266
- 5 .00137 .52 .02404
- 4 .00488 2.11 .02892
- 3 .00252 1.10 .03143
- 2 .00302 1.15 .03445
- 1 .00504 2.03 .03950
0 .01097 3.89 .05047
1 .00517 2.22 .05564
2 .00375 1.52 .05940
3 .00204 1.02 .06143
4 .00312 1.22 .06455
5 -.00125 .54 .06330
6 .00033 .10 .06300
7 -.00218 -1.16 .0688
8 -.00359 -1.58 .05720
9 -.00212 -1.01 .05510
10 -.00244 -1.28 .05262














TABLE 9

PRE-ANNOUNCEMENT AVERAGE RESIDUAL, t STATISTIC,
AND CUMULATIVE AVERAGE RESIDUALS FOR
NEGATIVE FORECAST ERRORS


Day t of W CAR


-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
- 9
- 8
- 7
- 6
- 5
- 4
- 3
- 2
- 1
0
1
2
3
4
5
6
7
8
9
10


-.00324
.00309
-.00032
-.00171
.00066
-.01255
.00285
-.00356
-.00253
.00317
-.00398
.00203
.00018
-.00602
-.00059
-.00598
.00029
-.00633
-.00776
.00244
-.01740
-.00112
.00108
.00077
.00457
-.00147
.00346
-.00142
.00539
.00288
-.00306


- .90
1.26
- .08
- .45
.18
-3.71
.95
- .89
- .03
- .08
- .96
.62
.05
-1.67
- .17
-1.15
.09
-1.69
-2.45
.53
-2.79
-2.15
.23
.20
.92
- .41
.50
- .32
1.46
.96
-1.16


-.00324
-.00015
-.00047
-.00218
-.00152
-.01407
-.01123
-.01478
-.01731
-.01414
-.01812
-.01609
-.01591
-.02193
-.02252
-.02850
-.02820
-.03454
-.04230
-.03986
-.05727
-.06843
-.06735
-.06658
-.06201
-.06348
-.06002
-.06144
-.05605
-.05317
-.05623