THE CAPITAL ASSET PRICING MODEL.
TESTS OF PORTFOLIOS SELECTED FROM
STOCKS WITH POOR PAST PERFORMANCE

AND AN INVESTIGATION OF THE

ABILITY OF DISCRIMINANT ANALYSIS

TO DIFFERENTIATE PERFORMANCE

mmtion to: the Game of Ph. D.
MIOHIGAN STATE UNIVERSITY
WAYNE FAIRBURN
1,975

'4; c“;

 

   

ESTIGATION OF THE ABILITY 0F DISCRIMINANT
ANALYSIS T0 DIFFERENTIATE PERFORMANCE

pfiertte: by

‘-‘_ 7 .‘- §
;- Whilllipiiburn

V J ‘9 .. i...»
has been‘éccepted towards fulfillment
of the requirements for

Ph.D.

   

Business - Finance

degree in

J.» ‘

    
   

kA-AA4 0

.l‘.

‘ Major profmx -‘ ..

 

 

III

2

I

II

III

III

III \I\3

II

3 III

 

 

ABSTRACT

THE CAPITAL ASSET PRICING MODEL, TESTS OF PORTFOLIOS SELECTED FROM
STOCKS WITH POOR PAST PERFORMANCE AND AN INVESTIGATION OF THE
ABILITY 0F DISCRIMINANT ANALYSIS TO DIFFERENTIATE PERFORMANCE

by

Nayne Fairburn

The purpose of this research was twofold.’ The first purpose was
to test the Sharpe-Lintner capital asset pricing model (CAPM), on the
sample of common stocks listed on the New York Stock Exchange which
had the poorest price performance during various calendar years. The
second purpose was to ascertain whether multiple discriminant analysis
could predict future relative performance ranks of a similar sample of
securities based upon a profile of their financial characteristics.

The initial sample for the CAPM tests consisted of those twenty
common stocks which had experienced the greatest percentage price
losses during each of the calendar years 1956 through 1967. Those
firms without calendar year accounting periods as well as utilities,
financial institutions, and transportation companies, were excluded
from the initial sample.

The test of the CAPM entailed the comparison of realized one-year
and three-year holding period returns (exclusive of cash dividends)
subsequent to the year of poor price performance, with returns condi-

tionally expected by the CAPM, given the market return over the holding

wayne Fairburn
periods and given the historically calculated beta coefficients. Twelve
portfolios with one-year holding periods and ten portfolios over three-
year holding periods were tested.

The paired difference t-test of the null hypothesis that the
average differences between realized returns and those conditionally
expected by the CAPM was not significantly different from zero, was not
rejected at the .05 level. The Sharpe-Lintner CAPM gave conditionally
expected return predictions which over the ten year period tested did
not differ on average from.the realized returns. However, it was
found that within individual one-year and three-year holding periods,
large differences between realized and conditionally expected returns
typically occurred.

The tests of the ability of discriminant analysis to differentiate
investment performance involved using the same sample of firms as for
the CAPM'tests, selected in the same manner, but for the calendar years
1962 through 1971. The tests were divided into two parts. The first
series of tests concerned the ability of the discriminant functions to
correctly classify according to performance in nine-month and thirty-
three month holding periods (beginning in April subsequent to each
calendar year of poor price performance), a random holdout sample of
firms from.the same time period as that from.which the discriminant
functions were calculated. This test determined whether the discriminant
functions could detect variable profile relationships which were stable
within the same time period. Each discriminant function was constructed
from a profile of fourteen representative financial characteristics.

The next series of tests evaluated the predictive ability of

wayne Fairburn
discriminant analysis by using the functions developed during the period
1962-1966 to classify firms from the later period 1967-1971 according to
expected relative performance. The estimated performance rankings were
compared with the actual performance rankings for this later period and
correlated using the Spearman Rank Order Correlation Coefficient. The
null hypothesis for both test series was that the correlation between
actual and predictedperformance ranks was less than or equal to zero
and the alternative hypothesis that it was greater than zero. None of
the tests rejected the null hypothesis. The results uniformly indicated
that for the sample and time period tested, discriminant analysis
possessed little ability to differentiate performance among securities
either within the same time period or for future time periods as would

be implied by the use of discriminant analysis for investment purposes.

THE CAPITAL ASSET PRICING MODEL, TESTS OF PORTFOLIOS SELECTED FROM
STOCKS WITH POOR PAST PERFORMANCE AND AN INVESTIGATION OF THE
ACILITY OF DISCRIMINANT ANALYSIS TO DIFFERENTIATE PERFORMANCE

By‘x“

.\ ‘\Lk
Wayne-Fairburn

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Accounting and Financial Administration

1975

To Bea

ii

ACKNOWLEDGMENTS

I wish to express deep and sincere appreciation to my disserta-
tion committee members: Dr. Myles Delano, Dr. Alden Olson, and Dr. Dan

Collins.

iii

TABLE OF CONTENTS

Page

AcmommSo O O O O O O O O O O O O O O O O O O O O O 0 iii

LIST OF TABLES O O O O O O O O O O O O O O O O O O O O O O C v
Chapter

I INTRODUflION O O O O O O O O O O O O O O O O O O O 1

Capital Market Theory . . . . . . . . . . . . . . 1

Multiple Discriminant Analysis. . . . . . . . . . 5

ReseaICh Purpose. 0 O I O O O O O O O O O O O O O 9

outlineOfTeStSoooooooooooooooo. 10

Capital Asset Pricing Model Tests . . . . . . . 10

Discriminant Analysis Tests . . . . . . . . . . 11

II LITRATURE REVIEW 0 O O O O O O O O O O O O I O O O 15

Sharpe-Lintner Model. . . . . . . . . . . . . . . 15

Discriminant Analysis . . . . . . . . . . . . . . 17

FiflflDCial Ratios. O O O O O O O O O O O O O O O O 19

III “momLOGY O O O O O O O O O O O O O O O O O O O O 25

Test of the Capital Asset Pricing Model . . . . . 25

Discriminant Analysis Tests . . . . . . . . . . . 32

Sample and Data Items . . . . . . . . . . . . . 35

Test Procedures . . . . . . . . . . . . . . . . 38

Iv RESULTS 0 O O O O O O O O O O O O O O O O O O O O O 44

Capital Asset Pricing Model Test Results. . . . . 44

Discriminant Analysis Tests Results . . . . . . . 48

v CONCLUSIONS 0 O O O O O O O O O O O O O O O O O O O 55

APPENDIX 0 O O O O O O O O O O O O O O O O O O O O O O O O O 59

BIBLIOGRAPHY O O O O O O O O O O O O O O O O I O O O O O O O 64

iv

Table

4.1

4.2

4.3

4.4

4.5

LIST OF TABLES

One Year Holding Period Return Data . . . .

Three Year Holding Period Return Data . . .

Variables Selected for Each Holding Period-
Discriminant Function Listed in Declining
Order of Importance . . . . . . . . . . .

Variables Common to all Three Data for
Each Holding Period . . . . . . . . . . .

Spearman Rank Correlation Values (R8)
for Each Discriminant Function. . . . . .

Page

46

47

50

51

53

CHAPTER I
INTRODUCTION

Capital Market Theory
Due to the pioneering work of Markowitz1 and to subsequent con-
tributions by Sharpe,2 Lintner,3 Mossin,4 Fama,5 and others, modern
capital market theory has become a widely accepted explanation of the
equilibrium prices of capital assets under conditions of uncertainty.
In recent years the investment community has become increasingly aware
of the implications of capital market theory for investment practice.6

For example, the widely used Value Line investment service includes

beta coefficient data for most stocks listed on the New York Stock

 

1Markowitz, Harry, "Portfolio Selection," Journal of Finance

2Sharpe, William F., "Capital Asset Prices: A Theory of Market
Equilibrium under Conditions of Risk," Journal of Finance (September
1964), pp. 425-442.

3Lintner, John, "The Valuation of Risk Assets and the Selection
of Risky Investments in Stock Portfolios and Capital Budgeting,"
Review of Economics and Statistics (February 1965), pp. 13-17.

4M'ossin, Jan, "Equilibrium in a Capital Asset Market,"
Econometrics (October 1966), pp. 768-783.

5Fama, Eugene F., "Risk, Return and Equilibrium: Some Clarifying
Comments," Journal of Finance (March 1968), pp. 29—40.

6For example, refer to many articles in recent years appearing
in the Financial Analysts Journal, a publication oriented toward the
practicing financial analyst.

Exchange.

The capital asset pricing model (CAPM) in the Sharpe-Lintner
form states three things: (1) that a portfolio or security's covari-
ance of rate of return with that of the market is the appropriate
measure of risk; (2) that the beta coefficient is a useful measure of
this risk; and (3) that expected returns for a portfolio are propor-
tional to the degree of risk as measured by the beta coefficient.7
The CAPM assumes that investment decisions are based upon a trade off
between the two parameters of risk and return. While the model is
obviously a simplification of reality, it nevertheless may provide a
useful means for explaining the process which determines security
prices.

In a test of the CAPM, Sharpe and Cooper have shown that, in
general, average annual returns of lowbrisk portfolios tended to have
lower average returns than high-risk portfolios.9 The annual returns
were generally consistent with the CAPM on average over the entire

holding period (1931-1967), but conformance to the theory declined as

the time period under study was shortened. The degree to which this

 

7For a detailed exposition of the capital asset pricing model and
the beta coefficient, see: Williath. Sharpe, Portfolio Theory and
Capital Market (New York: 'McGrawbHill Book Co., 1970), or see: J. C.
Francis, and S. H. Archer, Portfolio Analysis (Englewood Cliffs, N. J.:
Prentice-Hall, Inc., 1971).

8For a more detailed summary of the explicit and implicit assump-
tions involved in the capital asset pricing model see Jensen, Michael
C., "The Foundations and Current State of Capital Market Theory," in
Studies in the Theory of Capital Markets, M. C. Jensen, ed. (New York
Praeger Publishers Inc., 1972), p. 5.

9Sharpe, William.F., and Guy M. Cooper, "Risk-Return Classes of
New York Stock Exchange Common Stocks, 1931-1967," Financial Analysts
Journal (March 1972).

3
occurred, however, was not specified. The portfolios making up each
tested risk-return decile were also quite large, ranging from.47 to 99
securities each. The fact that firms which did not exist at the end
of the period (but did exist prior to this time) were not included in
the samples constituted a possible source of bias in the return calcu-
lations.

In a similar study of the Sharpe-Lintner form of the CAPM, Black,
Jensen, and Scholes (BJS) found that the model was not completely ade-
quate as a description of security returns since there was a tendency
for high-beta portfolios to offer lower than expected returns and for
lowhbeta portfolios to exhibit higher returns than expected.10 They
then proposed and tested an expanded version of the CAPM which expressed
the return on a security as a linear function of both the market return
and a portfolio whose covariance with the market return was zero.

Over the 35-year holding period of the BJS study extending from
1931 through 1965, the relationship between average excess monthly
returns and the degree of systematic risk, as measured by the beta
coefficient, was approximately linear. The same linear relationship
also was found for the four equal nonoverlapping subperiods of 105
months duration. In the BJS study the portfolios tested were large,

ranging in size from 58 to 109 securities each.

 

10Black, Fisher, Michael C. Jensen, and Myron Scholes, "The
Capital Asset Pricing Model: Some Empirical Tests," in Jensen,
Studies in the Theory of Capital Markets.

4

Studies by both Blume11 and Levy12 have demonstrated that indi—
vidual firms changed risk classes infrequently over time. For diversi-
fied portfolios, risk class levels were very stable since those secu-
rities which moved to higher risk classes tended to be counterbalanced
by those moving to lower risk classes. Investors could it was argued,
select portfolios from any desired utility-maximizing risk level by
simply relying upon the historical beta levels of the component securi-
ties as unbiased estimators of the "true" portfolio beta. The weighted
average beta of the selected portfolio would thus constitute an implicit
forecast of future returns of the portfolio relative to market returns.
For example, if the beta level for the selected portfolio were 1.5,
then the portfolio's future returns should be 1.5 times the market
return.

A study by Evans and Archer showed that the degree of unsystematic
risk could be almost eliminated through diversification using a small
number of issues, thus a large portfolio was deemed to be unnecessary.
In fact, a large portfolio required greater administrative effort as the
number of securities grew beyond the necessary number (usually less than
but seldom more than twenty stocks). After the initial study by Blume
and the later Levy study, the usefulness of historical betas as proxies

for their (unobservable) future values became a matter of great interest.

 

11Blume, Marshall E., "On the Assessment of Risk," Journal of
Finance (March 1971).

12Levy, Robert A., "On the Short-term Stationarity of Beta
Coefficients," Financial Analysts Journal (November 1971).

13Evans, John L., and S. H. Archer, "Diversification and the
Reduction of Dispersion: An Empirical Analysis," Journal of Finance
(December 1968), pp. 761-769.

5

The practical implication of this reasoning was that the investor might
want to select a utility-maximizing level of nondiversifiable or market
risk (represented by the weighted average beta coefficient of the port-
folio). He could diversify away most unsystematic risk (even a few
securities would suffice), and then expect future returns proportional
to the level of systematic risk taken.14

The proportional relationship between risk and return was demon-
strated by the Sharpe and Cooper,15 and the Black, Jensen, and Scholes16
studies. These studies strongly affirmed the existence of a reward for
bearing risk over the long run. While the prOportional relationship
between risk and return is reasonably stable over long time periods,
little is known regarding this relationship over shorter time periods
when small portfolios form the investment vehicle. Knowledge of whether
the CAPM is a valid predictor of the returns to be derived from.small
portfolios over short holding periods is important for two reasons:
First, adequate levels of diversification can be achieved with a small
number of securities, and secondly, many investors do in fact invest

for short holding periods.

Multiple Discriminant Analysis

In investment analysis the price of an equity security is fre-

quently considered to represent the present value of future dividends.17

 

14For example, this basic strategy is advocated by Francis, Jack,
Investments: Analysis and Management (New York: McGraw-Hill Book
Co., 1972), p. 590.

5Sharpe and Cooper, op. cit.
16Black, Jensen, and Scholes, op. cit.

17J. B. Williams, The Theory of Investment Value (Cambridge,
Mass.: Harvard University Press, 1938).‘

6
When this approach is used, fundamental analysis determines a stock's
"intrinsic" value by estimating future dividend streams and then dis-
counting these by a rate dependent upon risk. Intrinsic value would
next be compared with market price and a decision made as to whether
the stock should be bought or sold short. Fundamental analysis assumes
the market at times prices securities inefficiently. In such a case
opportunities exist for the fundamental analyst to acquire underpriced
issues which the market will subsequently reprice.

Numerous common stock investment strategies have been practiced
both individually and in combination with one another.18 The concept
of market inefficiency, however, is perhaps most completely embodied in
the "undervalued issue strategy," popular within the ranks of funda-
mentally oriented investors and analysts. Douglas Hayes provided a
useful description of this strategy:19

"But as a special strategy designed to obtain greater than
average returns available on common stocks generally, it
has come to be identified with a particular type of company
emerging from a behavioral theory of the market. The be-
havioral theory is that the market tends to exaggerate the
importance of unfavorable developments or perhaps the mere
absence of a highly dynamic potential. By the same token
it is held that the market also tends to overemphasize
favorable factors. In short, the theory is the logical
extension of the vogue theory, noted in connection with
growth stocks, to an anti-vogue theory. The view is that
prices of certain stocks may be unreasonably depressed
because of an undue emphasis on the immediate past earnings

performance or on some unfavorable information of a general
sort.

 

8For a discussion of other types of investment strategies such
as trading, cyclical timing, buy—and-hold, etc., see: Hayes, Douglas
A., Investments: Analysis and Management (New York: Macmillan Co.,
1966), Second ed., Ch. 5.

lgIbido’ Pp. 77-78.

7

Substantial returns may well be obtained, it is argued, when
and if it becomes clear that the adverse performance was
indeed temporary or that the potential problems were not as
catastr0phic as was generally believed. Recognition of the
improved situation may take time, but ultimately, it is held,
the market price will reflect the improvement. Note that it
is not growth that is anticipated, but only a reasonable
recovery to former levels of earnings performance. Such a
recovery should, it is argued, ultimately produce investment
returns well in excess of the secular performance of the mar-
ket as a whole. Mbreover, because prices are depressed at
the time of acquisition, dividend yields on cost are usually
quite satisfactory if further reductions in the dividend rate
do not subsequently take place."

Hayes further stated that the undervalued issue strategy would
take a great deal of skill on the part of the investor and often con-
siderable patience while waiting for the market to appropriately value
the stock. The undervalued issue could also be quite risky because of
the difficulty faced in distinguishing temporary from permanent adver-
sity.

Support for the strategy of selecting inappropriately priced
securities can be found in Graham, Dodd, and Cottle's classic work:20

"It is our thesis that the stocks of companies with dis-
appointing showings usually sell lower than they should,
for the same basic reason that stocks as a whole sell too
low during periods of depression. The significance of the
unfavorable conditions is exaggerated. If this view is
correct, the "poorer issues will normally be undervalued
in the market in relation to the better issues, with the
possible exception of low-priced stocks as a whole, which
attract a special sort of speculative interest. Broadly
speaking, this generalization is valid.

Our view is based on the principle that in the majority of
cases companies showing an unfavorable trend of earnings
will reach a bottom at some time and that thereafter their
earnings will fluctuate irregularly around some indicated
average or normal base. The market price will usually

 

20Graham, Benjamin, David L. Dodd, and Signey Cottle, Security

Analysis Principles and Techniques (New York: McGraw-Hill Book Co.,
1962), Fourth Ed., p. 696.

8

have fallen well below the value indicated by the latter

as well as by the asset-value factors. Consequently there
is an undervaluation and a practical opportunity for profit-
able purchase.

Quantitative techniques may play an important role in aiding the
process of security analysis and selection. Multiple discriminant
analysis is one technique which is used in the field of Finance21
which might be useful for security analysis. Edward Altman used
multiple discriminant analysis successfully for the prediction of cor-
porate bankruptcy. He said the following concerning possible applica-
tions of multiple discriminant analysis to investment problems:22

The potentially useful applications of an accurate bank-
ruptcy predictive model are not limited to internal consider-
ations or to credit evaluation purposes. An efficient pre-
dictor of financial difficulties could also be a valuable
technique for screening out undesirable investments. 0n the
more optimistic side it appears that there are some very real
opportunities for benefits. Since the model is basically
predictive the analyst can utilize these predictions to
recommend appropriate investment policy....

While the above results are derived from an admittedly small
sample of very special firms, the potential implications are
of interest. If an individual already owns stock in a firm
whose future appears dismal, according to the model, he should
sell in order to avoid further price declines. The sale would

 

1For example see such studies as J. E. Walter, "A Discriminant
Function for Earnings Price Ratios of Large Industrial Corporations,"
Review of Economics and Statistics, vol. XLI (February 1959), pp. 44-
52; K. V. Smith, Classification of Investment Securities Using MDA,
Institute Paper #101 (Purdue University, Institute of Research in the
Behavioral, Economic, and Management Sciences, 1965); Edward I.
Altman, "Financial Ratios, Discriminant Analysis and the Prediction
of Corporate Bankruptcy," Journal of Finance, vol. XXIII (September
1968), pp. 589-609; W. T. Carlton and E. M. Lerner, "Statistical
Credit Scoring of Municipal Bonds," Journal of Money, Credit, and
Banking I (November, 1969); A. S. McCall and R. A. Eisenbeis, "Some
Effects of Affiliations Among Mutual Savings and Commercial Banks,"
FDIC Working Paper No. 71-1, 1970; R. A. Eisenbeis, "A Study of the
Delineation of Geographic Markets for Business Loans," Unpublished
Ph.D. Dissertation, University of Wisconsin, 1971.

22Altman, p. 608.

 

9
prevent further loss and provide capital for alternative
investments. A different policy could be adopted by those
aggressive investors looking for short-sale opportunities.
An investor utilizing this strategy would have realized a
26 per cent gain on those listed securities eligible for
short-sales in the original sample of bankrupt firms....

Keith Smith, discussing his successful application of multiple
discriminant analysis to the classification of securities into specific
investment grades stated, "In addition, it should be possible to extend
the analysis to other types of investment, i.e., to search for variable

profiles which characterize distinct investment Opportunities and

thereby enhance the portfolio selection process."23

Research Purpose

 

The purpose of this research was twofold. The first purpose was
to test the Sharpe-Lintner capital asset pricing model on the sample of
common stocks listed on the New York Stock Exchange which had the
poorest past price performance during a calendar year° Small portfolios
of less than 20 securities taken over relatively short holding periods
of l and 3 years were tested to ascertain whether their performance
during holding periods subsequent to the year of poor performance
yielded returns consistent with those which would have been expected
according to the Sharpe-Lintner CAPM, given the market performance
during the same holding period. The second purpose of the research was
to ascertain whether multiple discriminant analysis (MDA) could predict
future relative performance ranks of securities based upon a profile of
their financial characteristics. The results provided information rela-

tive to the potential usefulness of MDA as a tool for augmenting the

 

23Smith, pp. 33-34.

10

security analysis process.

Outline of Tests

 

This research was limited to those common stocks which experi-
enced the greatest percentage price declines during each of the calendar
years 1956 through 1968 for the purpose of testing the CAPM, and for
the years 1962 through 1971 for the MDA tests. Various subperiods from
within these yearly groups were selected for the particular tests which

are outlined below.

Capital Asset Pricing Model Tests

The test of the Sharpe-Lintner capital asset pricing model (CAPM)
entailed the comparison of realized one-year and three-year holding
period returns (exclusive of cash dividends) with returns conditionally
expected by the CAPM given the market return over the same holding
periods and the historically calculated beta. The initial sample con-
sisted of the twenty common stocks which had experienced the greatest
percentage price losses during each of the calendar years 1956 through
1967. Firms without calendar year accounting periods as well as
utilities, financial corporations, and transportation companies, were
excluded from the original sample.

The null hypothesis was that no significant different existed
between the expected return (conditional upon the subsequent market
return and the historical portfolio beta) and actual returns. The
conditional expected portfolio return for time t was E<RPtle’RMt)

given the average historical portfolio beta, b and the return of the

P9
market for time t, RMt' The null hypothesis tested was that the aver-

age difference, 3, between expected portfolio return, E(RPt), where

11
= R
Emu) bp Mt
. A

and actual portfolio return, RPt , for time t
D = A-E( /b )

t RPt RPt P’ Rm
was equal to zero. Where

1 Dt

NM :3

B=£
fit

for the n holding periods. Thus the hypotheses were

H :3=0

II!
|._a
0|

#0

The paired difference t-test was made at the .05 level of sig-
nificance for both the twelve one—year holding period returns and the

ten three-year returns.

Discriminant Analysis Tests

 

A set of tests was conducted to evaluate the ability of multiple
discriminant analysis to differentiate the future performance of common
stocks. A set of fourteen representative financial ratios was calcu-
lated for each of the securities from the sample. Utilizing discrimr
inant analysis, the profile of financial measures was selected which
appeared best able to separate those stocks displaying price increases
from those suffering price declines (relative to the market) over the
subsequent nine-month and thirty-three month holding periods. The
financial ratios were taken at the end of the calendar year in which
the stock had experienced the large percentage price decline. The nine

and thirty-three month holding periods began three months after the

12

previous year end when the ratios were calculated. This time lag was

intended to represent the normal lapse of time from.the end of a com-

pany‘s accounting period until the release of that information to the

public.

Several tests were conducted to ascertain the ability of multiple

discriminant analysis to differentiate the performance of common stocks

on the basis of financial characteristics. The two major test cate-

gories are outlined below:

I.

The first category of tests determined whether the selected
profile of financial ratios could differentiate the performs
ance of an independent sample of firms during the same time
period as that in which the profile was selected. The
ratio profile, or discriminant function, was selected

using the stepwise multiple discriminant analysis method
from the group of fourteen representative financial ratios.
The independent samples were randomly withheld from the
qualifying sample before the discriminant functions were
computed. The independent samples were then ranked for
future performance on the basis of their discriminant
scores. The actual and predicted performance ranks were
correlated and tested using the Spearman Rank Order Cor-
relation Coefficient.

Both nine—month and thirty-three-month holding periods
were evaluated for firms having poor price performance during
the calendar years 1962 through 1966. In addition
to the tests discussed above, the firms within this

same 1962 through 1966 sample period were dichotomized

II.

13
according to whether the market increased or
decreased during the year of poor price performance.
From these subgroups were taken random holdout samples
whose performance ranks were predicted according to
their discriminant scores. Again, the discriminant
functions were calculated from the sample of firms
which were not randomly withheld. Using the pro-
cedures discussed above for the non-dichotomized
samples, the predicted and realized return ranks
were correlated and tested with the Spearman Rank
Order Correlation Coefficient. The null hypothesis
was that no correlation existed between predicted
and actual performance ranks in the subsequent nine-
and thirty-three-month holding periods.
The next major category of tests determined whether
discriminant functions, constructed to differentiate
the subsequent nine and thirty-three—month performance
of stocks with poor performance in the 1962 through 1966
period, could predict performance ranks of a similar
sample of stocks taken from a later test period, 1967
through 1971, test. No random holdout samples were taken
from the 1962 through 1966 sample prior to constructing
these discriminant functions since the later test sample
was independent of the sample from the earlier period.
As was done for the previous category, the predicted
and actual performance ranks were correlated and tested

using the Spearman Test. Discriminant functions were

14
also separately constructed and tested for both the
group of years during which the market rose and for

the other group of years in which the market fell.

CHAPTER II

LITERATURE REVIEW

This chapter is composed of three sections. Evidence bearing
upon the validity of the Sharpe-Lintner capital asset pricing model is
taken up first. Next, applications of discriminant analysis in Finance
are surveyed, followed by evidence relating to the ex ante usefulness

of financial ratios.

Sharpe-Lintner Model
The Sharpe-Lintner capital asset pricing model states that
expected "excess" returns (above the riskless rate) on an asset are
equal to the expected excess returns on a "market portfolio" times the
systematic risk of the asset. The market portfolio consists of a market-
value weighted proportional investment in every outstanding asset.
Jensen had this to say about empirical tests of the model:

The Sharpe-Lintner asset pricing model has received wide-
spread attention in the literature in the past five years.
Therefore, it is surprising that there have been so few
attempts at empirical verification of the model. Most of
the early evidence bearing on the model did not represent
direct tests but, rather, emanated primarily from attempts
to use the asset pricing model to derive portfolio per-
formance evaluation models. Treynor, Sharpe, and Jensen
all derived such portfolio evaluation models and applied
them to the historical evidence on mutual funds. The evi-
dence presented by Sharpe and Jensen indicated that the
returns on open-end mutual funds were positively related
to the covariance between the fund returns and the returns
on a market index used as a proxy for the market portfolio.
As such, they provided some indications that the model...
showed potential promise as a description of the process

15

16

generating the returns on assets (if one was willing to
accept the hypothesis that mutual fund managers were un-
able to select undervalued securities and did not generate
excessively large expenses). However, as we shall see, the
direct tests of the model imply that this interpretation of
these results may be incorrect.1

Black, Jensen, and Scholes pointed out the empirical inconsisten-
cies they discovered regarding the Sharpe-Lintner model.

If empirically true, the relation given (by the Sharpe-Lintner
model) has wide-ranging implications for problems in capital
budgeting, cost benefit analysis, portfolio selection, and for
other economic problems requiring knowledge of the relation
between risk and return. Evidence presented by Jensen on the
relationship between the expected return and systematic risk
of a large sample of mutual funds suggests that (the Sharpe-
Lintner model) might provide an adequate description of the
relation between risk and return for securities. On the
other hand, evidence presented by Douglas, Lintner, and most
recently, Miller and Scholes seems to indicate the model does
not provide a complete description of the structure of secu—
rity returns. In particular, the work done by Miller and
Scholes suggest that the o's on individual assets depend in
a systematic way on the 8's: that high-beta assets tend to
have negative a's, and that low-beta stocks tend to have
‘positive a's.

BJS went on to test an expanded two-factor model which would hold
under conditions when riskless borrowing was not available. The present
study did not concern itself with the augmented model, but as previously
Stated, tested the Sharpe-Lintner model on a specific sample of common
stocks have poor past performance.

A study by Sharpe and Cooper (utilizing the CAPM) of annual returns

over the period 1931 through 1967 found that when the entire period was

 

1Jensen,‘Michael C., "The Foundation and Current State of Capital
Market Theory," in Studies in the Theory of Capital Markets, M; C.
Jensen, ed. (New York: Praeger Publishers Inc., 1972), p. 7.

2Black, Fischer, Michael C. Jensen, and Myron Scholes, "The
Capital Asset Pricing Model; Some Empirical Tests," in Jensen,
Studies in The Theory of Capital Markets, p. 80.

17
considered, higher risk portfolios had higher returns on average than
those of lower risk. Market sensitivity which included price changes
but excluded cash dividends, calculated over a previous five-year
period was the risk measure for the study. They found that over
shorter time periods, risk-return expectations were less likely to be

realized than over longer periods.

Discriminant Analysis

 

A 1968 study by Edward Altman was of particular interest to this
research since he successfully used financial ratios in conjunction with
discriminant analysis to predict corporate bankruptcy.3 Sets of bank-
rupt firms and the set of securities with poor price performance com-
prising the present study were expected to have been closely related
groups. More specifically, all bankrupt firms were expected to have had
poor price performance, although, not all firms displaying large losses
in market price would necessarily have been bankrupt. In addition,
Altman's model used financial ratios in combination rather than sepa-
rately as most previous applications of ratio analysis had done.

Altman demonstrated that his bankruptcy prediction model was an
accurate forecaster of failure up to two years prior to bankruptcy. In
a rigorous test of the model, he found that even among a sample of
sixty-six industrial firms showing deficits in the years 1958 and 1961
(sixty-five per cent of them having shown earnings losses two or three

of the previous three years reporting), only fifteen of the firms were

 

3Altman, Edward 1., "Financial Ratios, Discriminant Analysis and
the Prediction of Corporate Bankruptcy," JOurnal of Finance (September
1968), pp. 589-609.

 

18
incorrectly classified. Thus, even in a universe of firms demonstrating
below average performance, the model correctly classified seventy-nine
per cent of the sample firms.

Keith Smith utilized multiple discriminant analysis to classify
common stocks into distinct security groups.4 A discriminant function,
using seven financial variables, was constructed for selecting among
stocks which fell into the three investment categories of investment
type, trading type, and speculative type as defined a priori by the
brokerage house Merrill Lynch, Pierce, Fenner and Smith. This discrimr
inant function was then tested on a random sample of stocks. The stocks
in this second sample were correctly reclassified into the proper groups
in eighty-eight per cent of the cases. These results suggested that the
MDA technique may be of potential value in classifying common stocks for
various investment objectives. Smith went on to say that.... "it should
be possible to extent the analysis to other types of investments, i.e.,
to search for variable profiles which characterize distinct investment
opportunities and thereby enhance the portfolio selection process."5

Williams and Findlay had this to say about discriminant analysis:

...There are other techniques that are gradually coming into
use by the financial community (although they have been em-
ployed by statisticians elsewhere for some time) to measure
prospective asset performance. One of the more interesting
of these techniques is discriminant analysis. This approach

may be used to find those financial characteristics that
best discriminate profitable investments from unprofitable

 

 

4Keith V. Smith, "Classification of Investment Securities Using
Multiple Discriminant Analysis," Institute Paper #101 (Purdue univer-
sity: Institute for Research in the Behavioral, Economic, and Manage-
ment Sciences, 1965).

51bid., pp. 33-34.

l9

ones. The method assumes that observations come from two
distinct universes, the profitable and the unprofitable....

They later sounded a note of caution, however, with the following
statement:
Although discriminant analysis has proved to be very helpful
as a tool for exploratory research, some authorities feel
that it is more appropriately applied to explain past rela-
tionships rather than to predict future ones. The statis-
tical foundation for the procedure is not terribly strong,
and it should be employed only by those who understand the
method very well. Nevertheless, in capable hands the tech-
nique can provide added insight into the problem of classi-
fication.

Both of the above statements, however, were assertions on their

part with no additional explanation or empirical verification cited.

Financial Ratios
Fundamental investment analysis requires the analyst to estimate

future earnings and/or dividend streams in order to arrive at an
"intrinsic value" for the security. The analysis of past and present
financial information has often been employed by financial analysts to
aid in the prediction of future earnings or dividend streams. Financial
ratios based upon publicly available information form an integral part
of much financial analysis. Graham, Dodd, and Cottle stated the need
for studying financial information:

In the selection of common stocks much more emphasis is

placed upon future expectations as the primary basis of

attractiveness and value. In theory these expectations

may be so different from past performance that the latter

could be virtually irrelevant to the analysis. But this
separation of the future from the past rarely occurs in

 

6Williams, Edward E., and M. Chapman Findlay III, Investment

Analysis (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1974), p. 121.

7Ibid., p. 125.

20
practice. A tendency toward an underlying continuity in
business affairs makes the financial record the logical
point of departure for any future projection. Thus, it
is only the trader on market movements or the heedless
speculator following tips or hunches who will ignore
the statistical showing of a common stock. The invest-
ment approach to every kind of security, which is the
analytical approach-requires the proper agplication of
income-account and balance sheet analysis.

In a 1951 study, Latane compared price, earnings, and dividend
history of the twenty-five securities exhibiting the greatest gains and
losses during the four investment periods coinciding with the calendar
years 1948, 1949, 1950, and 1951.9 He found a weak tendency for those
securities which had shown large percentage gains in one year to exhibit
a smaller gain in the following year than that realized by securities
which had shown large losses the first year. Latane also found a slight
tendency for stocks to reverse their direction of price movement over
the years, with stocks selling at a discount from earlier prices having
a slight greater chance for price appreciation. Past price performance
alone, however, was felt to be a poor guide for selecting securities.
Latane found historic dividend yield to be a poor indicator of future
'market performance. Specifically, the dividend yield on the basis of
the previous year's dividend had little or no forecasting value for
future market changes. It was found also that past earnings compared

with current price may have some forecasting value. ~In particular,

stocks which had large current earnings relative to price were more

 

BGraham, Benjamin, David L. Dodd, and Signey Cottle, Security
Analysis: Principles and Techniques (New York: McGraw-Hill Book
Co., 1962), Fourth Edition, pp. 105-106.

9H.A. Latane, "Price Changes in Equity Securities," Journal of
Finance (September 1951), pp. 252-264.

 

I 21
likely to have been in the group having large gains than the group
having large losses.

Murphy, in a 1966 study, found that companies posting relatively
high rates of growth in earnings per share during one time period had
no better than an even chance of recording relatively high earnings
growth in the succeeding period.10 This finding came from conducting
492 tests (covering 12 industries for 36 test periods) which compared
the rate of earnings growth with the rate of price change during the
same time period.11 As might be expected, earnings were shown to have
been of the utmost importance to investors. These findings could ex-
plain the lack of positive correlation of individual share price
movements over time found by Latane. The finding of Latane that stocks
which had large current earnings relative to current price were more
likely to have fallen in the group of firms exhibiting the largest
gains was further supported by a study performed by Nicholson.
Nicholson compared the relative investment performance, in eleven
holding periods from 1939 to 1959, of stocks on the basis of their
price-earnings ratio at the time of investment.12 Investment perfor-
mance in nearly all cases was inversely related to the size of the

price-earnings ratio. In addition, those stocks with large depreciation

 

10J. E. Murphy, Jr., "Relative Growth of Earnings Per Share-Past
and Future," Financial Analysts Journal (November-December 1966),
pp. 73-76.

11J. E. Murphy, Jr., "Earnings Growth and Price Change in the
Same Time Period," Financial Analysts Journal (January—February 1968),
pp. 97-99.

128. F. Nicholson, "Price Ratios in Relation to Investment
Results," Financial Analysts Journal (January-February 1968), pp. 105-
109.

 

22

charges, sales and book value relative to price at the time of invest-
ment nearly always offered superior perfOrmance in future holding
periods compared with securities possessing lower values of these
variables relative to price.

Mblodovsky generally tended to downgrade the significance of the
Nicholson results pointing out that since changes in price-earnings
ratios were the result of thirteen possible combinations of changes in
price and earnings, they had no real existence of their own.13 He also
criticized the study because he felt that cumulative reinvestment into
the low P/E group would "strengthen" that group while the high P/E
group would be steadily "weakened" through this process. Supporters
of Nicholson's study contended that P/E ratios were not meant to be the
sole method of stock selection but were merely a screening device which
possessed considerable merit.14 They further stated that cumulative
reinvestment would not have biased the results but would only have pro—
vided an explanation for why the method apparently worked so well.

A study by Levy and Kripotos found15 that earnings growth (as

measured by the percentage change in latest available twelve-month

 

13M’olodovsky, Nicholas, "Recent Studies of P/E Ratios," Financial
Analysts Journal (May-June 1967). This article was reprinted in C.F.A.
Readings in Financial Analysis (Homewood, Illinois: Richard D. Irwin,
Inc., 1970). Second Edition, pp. 400-413.

14Miller, Paul F., and Thomas E. Beach, "Recent Studies of P/E
Ratios-A Reply," Financial Analysts Journal (May-June 1967). This
article was reprinted in C.F.A. Readings in Financial Analysis (Home-
Zood, Illinois, Richard D. Irwin, Inc., 1970). Second Edition, pp.

14-417.

1
5Levy, Robert A., and Spero L. Kripotos, "Earnings Growth,

P/E's and Relative Price Strength," Financial Analysts Journal
(November-December 1969), pp. 60-67.

 

23

earnings per share over the twelve-month earnings per share for the

year ended with the prior quarter) and relative price strength (as mea-
sured by comparing the current month-end price with the average of the
monthly prices for the preceding six months, inclusive through the cur-
rent month) were valuable as criteria for selecting stocks which would
have offered superior performance over a six-month holding period. The
combination of these two factors was found to be superior to either used
individually. Levy and Kripotos also concluded that P/E ratios were of
comparatively little use either when used individually or in combination
with the two other measures.

Joy and Jones in a follow~up study took issue with the way in which
Levy and Kripotos had calculated the P/E ratio.16 Using data which
closely approximated that used by Levy and Kripotos, Joy and Jones repli-
cated the former study using a definition of P/E which took greater
account of more recent information. Nearly identical results were found
except in the case where P/E ratios were concerned. They found low P/E
ratios to be a very useful method of primary selection for stocks that
would offer subsequent superior performance.

From the studies cited above, it can be seen that many authors
believed that fundamental financial data was useful for objectively
selecting stocks which would subsequently outperform the market. Most
authors did not recommend that the factors examined in the studies should
be the only ones considered for making investment decisions. They

generally recommended that they should be used only as screening devices

 

16Joy, 0. Maurice, and Charles P. Jones, "Another Look at the
Value of PIE Ratios," Financial Analysts Journal (September-October,
1970), pp. 61-64.

 

24

for narrowing down the universe of possible investments to a size more
capable of comprehensive study. Possessing useful screening criteria,
the argument went, the analyst could then best utilize his time studying
and comparing stocks drawn from a set of securities which hoped to offer
price appreciation potential superior to that of the market in general.

The authors of many of the previously cited studies assumed that
objective measures or ratios could be found and applied which would aid
the investment selection process. Those subscribing to this viewpoint
assumed that with the aid of the proper techniques, the investor could
outperform the market even after the appropriate adjustment for risk.
Holding the opposite viewpoint would be those who believe the semi-
strong version of the efficient market hypothesis. This theory states
that the market on average correctly and instantaneously adjusts the
price of any security for all publicly available information.17 The
semi-strong version of the efficient market hypothesis, if true, would
imply that no objective measures, financial ratios, or special quantita-

tive techniques could be used to select securities which would outperform

the market after adjustment for risk.

 

17For example this viewpoint is well expressed in Eugene F. Fama,
"Efficient Capital Markets: A Review of Theory and Empirical work,"
Journal of Finance, vol. 25, no. 2 (May 1970), pp. 383-417.

 

CHAPTER III
METHODOLOGY

Test of the Capital Asset Pricing Model

The initial sample used for testing consisted of the twenty
common stocks listed on the New York Stock Exchange which experienced
the greatest percentage declines in price during the calendar years
1956 through 1971. Various subperiods from these years were selected
for additional tests which were conducted. The firms used were indus-
trial companies (transportation, banking, finance, and utility stocks
were excluded) which had calendar year accounting periods. The sample
of firms is listed in the appendix.

The validity of the Sharpe-Lintner capital asset pricing model
(CAPM) was tested as a guide for small portfolio investment over short
holding periods in common stocks with poor past performance. The
research determined whether securities from the revised sample had
realized returns over the holding periods consistent with returns
conditionally expected by the CAPM, given the holding period return of
the market. Twelve portfolios were tested over the same number of one-
year holding periods. Ten three-year holding period returns were also
tested over the same period of time from 1957 to 1969.

According to the Sharpe-Lintner CAPM each portfolio and holding
period would have an expected return E(Rpt), given the historical
average portfolio beta, bp, and the market return over the same period,

25

26

RMt' This conditional expected return is given as:

(E (Rpt) / bp, 3Mt> (1)

The expected return on a portfolio, E(Rp), is equal to the degree

of nondiversifiable risk, Bp, times the expected return of the market,
E(RM).
R = E 2
E( p) 8p (RM) < >

The CAPM asserts that return should be positively related to Bp’ the

measure of risk. The model was tested using the relationship

E(Rpt) = prMt (2.1)

where E<Rpt) is the conditional expected return of the portfolio over
time t, given RMt’ the realized return of the market over the same time
period and bp, the historical portfolio beta. To use the CAPM as the
basis of an investment strategy it was necessary to have an ex ante
risk level measure, bp, which estimated 8p, the true risk level. The
beta coefficients of individual securities, bi’ are calculated by
regressing historical security returns on historical market returns.
The bp is the weighted average of these individual bi values. Studies
by Levy1 and Blume2 have demonstrated these beta estimates to be quite
stable over time at the portfolio level. While some individual securi-

ties exhibited increasing betas, others showed declining betas, and the

 

1Robert A. Levy, "On the Short—Term Stationarity of Beta Coeffi-
cients," Financial Analysts Journal (November 1971).

2Marshall E. Blume, "On the Assessment of Risk," Journal of
Finance (March 1971).

27
portfolio beta, an average, remained quite stable.

Because of time and resource limitations, beta coefficients for
the firms comprising the study were not calculated. Instead, "market
sensitivity" coefficients supplied by Sharpe and Cooper3 were used.
These coefficients were calculated using the monthly price changes for
the most recent 5 year past.

Market sensitivity coefficients were calculated the same way as
the beta coefficient except that the dividend yield was not a part of
the holding period return. The two measures differ very little, how-
ever, since dividend yields were shown by Sharpe and Cooper to have
been very stable over time, when compared to price changes. Ten risk
return deciles were provided, along with the historical betas which
corresponded to each decile. Thus, given the decile risk class a firm
belonged to, the beta corresponding to that risk class was assigned to
the firm. This beta assignment process was only approximately correct,
however, since the betas for each decile represented the average beta
for that decile over the entire 1931-1967 period. During individual
years the beta for each decile may have varied slightly from its 1931-
1967 average. The degree to which the beta may have varied, however,
was not specified. In light of the previously mentioned Blume and
Levy studies which had demonstrated the stability of portfolio beta
coefficients over time, the long-term average beta for each decile was
felt to constitute a very close approximation to the true yearly decile

beta. Accordingly, the betas in each portfolio of this study were the

 

3William F. Sharpe and Guy M. Cooper, "Risk-Return Classes of
New York Stock Exchange Common Stocks, 1931-1967," Financial Analysts
Journal (March 1972).

28

average of the betas of the risk classes to which each stock of the
portfolio belonged.

The traditional definition of holding period return includes
both price appreciation and cash dividends. Since cash dividends are
difficult to obtain and verify, they were not included in the returns
of the present study. For the purpose of this study the price appreci-
ation figures during the 22 time periods were defined as holding period
returns, realizing that this did constitute a departure from traditional
practice.

Market sensitivity (MS), taking the Sharpe and Cooper definition,
was defined as "the slope of a regression line relating the apprecia-
tion on a portfolio or security to that of the market."4 They found a

very close relationship between MS and beta5

Beta .004 + .997 (MS)

R2 = .996

(3)

The test procedure of the present study involved comparing the
actual holding period return with the conditional expected holding period
return given the return of the market and the measure of systematic risk.
The actual portfolio holding period return (RptA) was the percentage
change in price for the portfolio over each holding period, adjusted
for stock splits and stock dividends. As noted previously, cash
dividends were not included. The conditional expected portfolio holding

period return over time t was

 

Ibid.

Ibid.

29
E(RPt) = MSPRMT (2.2)

where MSP was the measure of systematic risk and was taken from (3) by

solving for market sensitivity

MSP = (bP - .004) /.997

The null hypothesis was that the average difference D, between expected

portfolio return, E(RPt)’ and actual return, Rgt’

A
Dt = RPt - E<RPt)

1
where D = -' D
n

n
t§1 t

was equal to zero while the alternative hypothesis was that they were

not, where

H B=o

0

H1 D # 0

One paired difference t-test was made at the .05 level of signifi-
cance for the 12 one-year holding period return differences, and another
for the 10 three-year holding periods return differences. The t-test
was based upon the three following assumptions.
1. The underlying populations from which the samples were
drawn were normally distributed.

2. The variances of these distributions were the same
(homogeneous).

3. The samples were independently drawn and therefore had inde—

pendent errors.

30
The last assumption was easily satisfied since the samples drawn in
consecutive holding periods were certainly not dependent. This is
supported by abundant evidence available in connection with numerous
tests of the random walk hypothesis which have suggested the lack of
any significant dependence in stock prices over time.6
In regard to the first two assumptions, Fama has suggested that

a stable Paretian distribution (symmetrically shaped like the normal
distribution except for greater thickness in the tails) might more
appropriately describe the distribution of security returns than the
normal distribution.7 There was no a priori reason for believing the
distributions of actual and conditionally expected holding period
returns to be fundamentally different in shape, though the possibility
of unequal variances could not be excluded. In exhaustive empirical
tests assessing violations of assumptions underlying the t-test,
Boneau found that the t-test was remarkably robust under a wide variety
of assumption violations. Quoting in part from the aforementioned study

We may conclude that for a large number of different situa-

tions confronting the researcher, the use of the ordinary t

test and its associated table will result in probability

statements which are accurate to a high degree even though

the assumptions of homogeneity of variance and normality of

the underlying distributions are untenable. This large

number of situations has the following general character-

istics: (a) the two sample sizes are equal or nearly so,

(b) the assumed underlying p0pu1ation distributions are of

the same shape or nearly so. (If the distributions are skewed

they should have nearly the same variance.) If these condi-
tions are met, then no matter what the variance differences

 

6Eugene F. Fama, "Efficient Capital Markets: A Review of Theory
and Empirical WOrk," Journal of Finance 25 (May 1970), pp. 383—417.

7Eugene A. Fama, "Portfolio Analysis in a Stable Paretian Mar-
ket," Management Science, 11: 404-419 (January 1965).

 

 

31

may be, samples of as small as five will produce results
for which the true probability of rejecting the null
hypothesis at the .05 level will more than likely be
within .03 of that level. If the sample size is as large
as 15, the true probabilities are quite likely within .01
of the nominal value. That is to say, the percentage of
times the null hypothesis will be rejected when it is
actually true will tend to be between 4% and 6% when the
nominal value is 52.8

The above quotation demonstrated the robustness of the t-test
under conditions almost identical to those of the present study, there-

fore, the t-test was deemed appropriate. The test statistic was

C”

- O

 

o"?

with n-l degrees of freedom and where SB-= SD//; for a sample of size

n. The same distribution was assumed to apply to each of the individual

pair differences; the sample standard deviation, SD was calculated as

follows:

 

D
“J n-l

 

The l-year tests involved 12 holding periods and therefore 11
degrees of freedom, while the 3-year tests encompassed 10 holding
periods for 9 degrees of freedom. The .05 critical values of t were
for the one and three year tests respectively, i2.201 and $2.262. If
the sample test statistic had possessed an absolute value less than or
equal to the critical value the null hypothesis was not rejected; if

it were greater, the null hypothesis would have been rejected.

 

8C. A. Boneau, "The Effects of Violations of Assumptions Under—
lying the t-Test," Psychological Bulletin, Vol. 57, p. 62.

32

Discriminant Analysis Tests

 

A general problem to which multiple discriminant analysis (MDA)
has been frequently directed is one requiring the ex ante prediction of
which of two or more distinct groups various elements in a population
belong.9 The prediction of group membership is based upon a linear com-
bination of measured characteristics (predictor variables) for each
element. This linear combination, termed the discriminant function,
predicts group membership based upon the numerical value achieved by
each element of a subsequent sample from the same hypothesized popula-
tion. The measured characteristics are multiplied by the constant
coefficients of the discriminant function and assigned to one of the
groups based upon the score achieved. For the two group case, those
with high scores would be assigned to one group while those with low
scores would be assigned to the other.

In general, discriminant analysis would require the following
assumptions when tests of significance are to be made on the functions:1
1. the investigated groups are identifiable and discrete. I

2. measured characteristics can describe each element in

each group.
3. each measured characteristic is assumed to have a multi-

variate normal distribution in each group and an equal

 

9The mathematical development of discriminant analysis is well
treated elsewhere. For example see C. R. Rao, Advanced StatiStical
Methods in Biometric Research (New York: Wiley, 1952), and J. G.
Bryan, "The Generalized Discriminant Function, Mathematical Foundation
and Computational Routine," Harvard Educational Review, vol. XXI, No.
2 (Spring 1951), pp. 90-95.

10Robert A. Eisenbeis, Discriminant Analysis and Classification
Procedures (Lexington, Mass.: D.C. Heath and Co., 1972), pp. 1-2.

 

 

 

33
common variance.

The first assumption would appear to have been satisfied in the
case of this study since there were two distinct mutually exclusive
and collectively exhaustive groups to which a stock could have been
classified into--those who subsequent to the year of large price loss
outperformed the Standard and Poor's 425 Industrial Index, and those
which underperformed the same index during the ensuing holding period.
The financial ratios were measurable for each stock in the study, thus
having satisfied the second condition. It was less clear, however,
whether each measured characteristic was normally distributed in both
groups with a common variance. The small sample sizes of the study
made verification of the third assumption impractical since the central
portion of the sample distribution of measured characteristic values
might appear rather normal while the tails, where there are by defini-
tion few observations, could actually be nonnormal.11

When the third assumption is violated, the F-test for signifi-

cance (the statistic which is used to test the significance of the MDA

function) has been shown to become very nonrobust.12 However, these

 

11For a much fuller discussion of the problem of assumptions
about the underlying population distribution see James V. Bradley,
Distribution-Free Statistical Tests (Englewood Cliffs, N.J.:
Prentice-Hall, Inc., 1968), pp. 6-8.

12While the t-test is reasonably robust against nonnormality,
even infinite sample sizes will not produce perfect robustness against
nonnormality for the F—test, nor can perfect robustness be attained
for heterogeneity of variance in the general case. When both assump-
tions are jointly violated the true significance of the F-test is
nearly impossible to determine. A partial list of the other factors
which bear on robustness includes: location of rejection region,
size of significance level, minimum sample size, absolute sizes of
the other samples, relative sample sizes, total number of samples
upon which the test is based, number of samples of each absolute

34
assumptions may be relaxed when instead of testing for the signifi-
cance of the discriminant function, MDA is used strictly as a classi-
fication technique for predicting group membership.

The evaluation of the usefulness of MDA was based upon how well
it actually succeeded in ex ante classifying securities for investment
purposes.13 Specifically, the actual performance ranks were compared
to the performance ranks predicted by the discriminant function scores.
In all tests the sole criterion for evaluating MDA was its ability to
correctly classify, according to performance ranks, securities which
were not part of the sample from.which the discriminant functions were
calculated.

The tests for determining the ability of discriminant analysis
to select common stocks with superior investment potential, given
objective financial information, were made in two parts. The first
part concerned the ability of the discriminant functions to correctly
classify, during the same time period, securities not included in the
group from.which the discriminant functions were constructed. The
second test determined whether securities from later time periOds
could be correctly classified by the discriminant functions. After
discussing the sample of companies and the data items from each which

were collected, these two tests are specified in detail.

 

(and relative) size, etc. These points are discussed in more detail
in Bradley, Distribution—-Free Statistical Tests, pp. 26-27, and
Bradley, "Studies in Research Methodology VL. The Central Limit
Effect for a Variety of Populations and the Robustness of Z, t, and
F," AMRL Technical Report 64-123, Aerospace Medical Research Labora-
tories, Wright-Patterson Air Force Base, Ohio, December, 1964.

13The significance of the discriminant functions was not calcu-
lated due to the nonrobustness of the F-test, which would make the true
significance level of the functions nearly impossible to determine.

 

35

Sample and Data Items

 

The twenty common stocks listed on the New York Stock Exchange

with the greatest percentage price declines during the calendar years

1962 through 1971 comprised the original sample of companies for the

MDA study.

As in the previous test of the CAPM, those firms which did

not have calendar year accounting periods and which were not indus—

trials (thus excluding transportation companies, utilities, and finan-

cial institutions) were discarded from the sample.

1.

Net Qperatinngargin--defined as net operating income
dividend by sales. This ratio indicated how much of
every sales dollar remained in net operating income.

_Qperating Asset Turnover-defined as sales divided by

 

net operating assets, where net operating assets were
total assets less intangible items such as patents,
copyrights, or goodwill. This ratio measured the
efficiency with which the firm utilized its operating
assets, for the smaller the asset investment necessary
to generate a given level of sales the better off the
firm would be, other things equal.

Net Werking_Capital/Total Assets-—defined as current
assets less current liabilities divided by the book
value of total assets. This was a liquidity ratio
which measured net liquid assets compared to total
capitalization. A firm showing consistent operating
losses would generally exhibit a declining liquidity
position. Altman found this ratio to be more useful

than either the current ratio or the quick ratio in his

36

bankruptcy prediction model.

Net Working_gapital/Market Value of Common Equity--where
market value of common equity was defined simply as the
number of common shares outstanding times the market price
of common stock. Firms having had a high degree of
liquidity relative to market value per share would likely
be stronger financially and more resistant to insolvency
than firms with less liquidity.

Retained Earning/Total Assets-this ratio was found by

 

Altman to be a useful ratio for predicting bankruptcy
because it measured cumulative profitability over time.
Firms which have large cumulative profits have exhibited
a measure of survivability through the crucial early
years of their existence. To the extent that this ratio
can indicate future resistance to bankruptcy, it would
provide a necessary (but not sufficient) precondition for
future earnings and price apprecaition.

Times Interest Charges Earned-—defined as net operating

 

income dividend by fixed interest charges. This ratio was
an indicator of the safety level of long term debt issues.
In general, the more times the interest has been earned,
the safer the company. One minus the reciprocal of this
measure indicates the percentage that operating income
could drop before the most junior debt issue would be
jeopardized.

Earnings ChangeyPer Dollar of Price--defined as the most

recent yearly earnings per share less those of a year

37
previous, divided by the price of the present year.
A similar ratio was utilized by Niederhoffer and Regan
to take account of earnings changes, particularly for
firms showing deficits.14 By normalizing with price,
the large percentage earnings changes which would occur
when earnings change within a very close range of zero
are placed in a format for which interfirm comparisons
could be more easily made.

8. Percentage Change in Sales-firm ‘with growing sales would

 

be expected to be in a relatiavely stronger position,
other things equal, than those with level or declining
sales.

9. Percentage Change in Working Capital--increasing working
capital generally indicated a stronger liquidity position
and more resistance to insolvency, other things equal.

10. Percentege_Change in Net Operating Income-~growing net
operating income usually would indicate greater company
strength arising from the chief lines of business.

11. Current Ratio-defined as current assets divided by

 

current liabilities. This is perhaps the most common
liquidity measure in use.

12. Current Ratio as a Percentage of the Industry Average--
defined as the current ratio of the firm compared to that

of the four digit industry to which the firm belongs.

1['Victor Niederhoffer and Patrick J. Regan, "Earnings Changes,
Analysts' Forecasts and Stock Prices," Financial Analysts Journal
(May 1972), pp. 67-69.

 

38

This and the following two ratios measured the rela-
tive strength of the firm compared to its industry.
It would be expected that for some firms these measures
might be rather high (low) relative to all firms but
quite low (high) compared to other firms in the industry,
thus industry effects would be adjusted for.
13. Net Operating_M§rgin as a Percentage of the Industry_Average
14. Operating Asset Turnover as a Percentage of the Industry
Average
The preceding 14 financial measures were drawn largely from finan-
cial statements found in Moody's Industrial Manuals, since many of the

firms were not included in the Compustat Data Tapes, mainly because of

 

mergers, bankruptcies, and delistings since the years of large losses.
The industry averages for the last three ratios, however, were drawn

from the Qggpustat Tapes. All data items were drawn either during or
before the year of the large price loss with no items taken after the

year of the loss.

Test Procedures

The returns of all companies in the sample were calculated for
holding periods beginning on the first trading day of the April
following the year of the large price loss and extending until periods
one and three years after the year of extreme decline. Thus the holding
periods were nine and thirty-three months in length. April was chosen
as the beginning of the holding periods to ensure that, since public
information for many stocks would not be generally available immediately

following the year of large price loss, an investment strategy of the

39
type tested here could actually have been employed. Cash dividends

were not a part of the holding period returns calculated.

Holding periods of nine and thirty-three months in duration
subsequent to the April following the end of the calendar years of
poor price performance from.l962 through 1966 formed the sample period.
The test period included the calendar years of poor performance from
1967 through 1971. Two dichotomizations of the samples were made. The
first was simply the nine and thirty-three-month holding periods
already mentioned. These holding periods were additionally segmented
according to whether the year of poor performance took place during a
year in which the market either rose or fell, with reference to the
Standard and Poor's 425 Industrial Index. It was determined whether
certain factors became more important for differentiating the future
performance of stocks which had performed poorly during years when the
general market rp§e_than for those stocks which declined markedly in
price during years when the general market fell,

The discriminant analysis tests were of two major categories.

For the first category, the sample from the 1962-1966 period was
utilized to test whether discriminant analysis could on a statistically
significant basis rank stocks according to their performance during the
ggme_holding period in which the discriminant function was calculated.
For the second category, it was determined whether MDA could in a
statistically significant manner, rank according to performance, the
lgger_l967-l97l test period sample. In this latter test, the discrimi-
nant functions calculated from the 1962-1966 period data were tested

on the 1967-1971 data, thus evaluating the predictive ability of MDA.

Computer programs BMD07M, Stepwise Multiple Discriminant Analysis,

40

and BMDO4M, Discriminant Analysis for Two Grqpps were used on the
Control Data 6500 series computer at Michigan State University.
BMDOTM selected the variable combination which best discriminated
between those firms which increased in price relative to the market
and those which decreased during the nine- and thirty-three-month
holding periods relative to the market index. Program BMD04M calcu-
lated the discriminant functions after being given the optimum vari-
able combination determined by BMDO7M.

The first discriminant analysis test category determined whether
MDA, used in conjunction with the financial data items, could select a
linear combination of objective factors (the discriminant function)
which could differentiate performance during the gepe_time period as
that in whidh the discriminant function itself was calculated. The
discriminant process would be biased when the sample utilized to calcu-
late the functions is then classified by these same functions. To
overcome this bias, firms were randomly held out from the sample
before the discriminant functions were calculated. This holdout
sample was later ranked by the functions. The process in which
samples were randomly withheld and then ranked following the procedure
outlined above was repeated twice in order to overcome degree of free-
dom difficulties which would have been encountered if too many firms
were withheld from each run.

To summarize the testing procedure, two holdout runs of tests
were performed to ascertain the performance differentiating ability
of MDA during the gege time period as that from which the discriminant
functions were calculated. One run utilizing the full sample was made

from the 1962-1966 data and tested on the later 1967-1971 test period.

41
Within each data run, six discriminant functions were tested. Of

these six functions, three were concerned with nine-month holding
period returns, and three were for thirty—three-month returns. Of
each set of three, one function was constructed from those calendar
years within the period 1962-1966 during which the S&P 425 Index

rose. Another function included those years in which the market
index fell. Of these three functions, the third included all years
from.the 1962-1966 period without reference to whether the market rose
or fell.

Two holdout sample runs and one full sample run were thus per-
formed. Each run resulted in six discriminant functions. The two
holdout runs were developed using 1962-1966 data and then tested using
the randomly withheld firms from the 1962-1966 period, while the func-
tions calculated from the full sample run (utilizing the entire 1962-
1966 sample) were evaluated for predictive ability in the 1967-1971
test period.

The number of predictor variables utilized in each discriminant
function was in the general case limited to a maximum of six. Fewer
variables were permitted in those cases when the function, in which
these variables were included, was used to reclassify the sample firms
(whose data was used to generate the functions), and perfect reclassi-
fication occurred. More than six variables could have been used in
many cases, however, the marginal improvements in reclassification
ability did not appear striking enough to warrant the inclusion of more
than six variables.

Firms were ranked for predicted performance in the ensuing holding

period according to their discriminant scores. They were also ranked

 

42
by realized return in those holding periods. The null hypothesis was
that no correlation existed between the predicted and actual return
ranks. The alternative hypothesis was that significant correlation
did exist. Realized and predicted return ranks were correlated with
the Spearman Rank Order Correlation Coefficient. The test statistic

was

, i=1 i=1
8 n n n n
2 2 2 2
\/[ “1% "1 ‘ (151 "i’ ] [“151 3'1 " (151 Y1) ]

where n is the number of firms in the holdout sample, x is the actual

 

 

n n

 

integer performance rank in the holdout sample, while y is the integer
rank predicted by the discriminant function. The null and alternative
hypotheses

H0 : p s 0

H1 : p > 0

were tested at the a - .05 level of significance.

The Spearman rank correlation coefficient was selected as the
test statistic since performance ranking abaility was felt to be the
most meaningful criterion of usefulness for investment purposes. The
chief reason for having chosen the nonparametric Spearman rather than
the parametric Pearson correlation coefficient was that the former test
does not depend upon assumptions about the underlying distribution of
the actual and predicted values. It only requires the assumption that
they be continuous, and under the null hypothesis, independent. Both

assumptions were easily satisfied. This test, when compared to the

43

Pearsonian r under conditions where all conditions of the latter test

hold has an asymptotic relative efficiency of .912.15

 

 

15A. Stuart, “Asymptotic Relative Efficiency of Tests and the

Derivatives of their Power Function,"'Skandinavisk Aktaurietidskrift,
parts 3-4, pp. 163-169.

CHAPTER IV

RESULTS

Capital Asset Pricing Model Test Results

 

Table 4.1 below shows the results of the CAPM test for the port—

folios held for one-year periods. Table 4.2 shows the results for the

 

three-year holding periods. Column (1) of each table lists the indi- t:_
vidual periods. These periods ran from.January l to January 1 of the I
years given. Column (2) lists the number of securities which comprised
each individual portfolio. This number differs from the preliminary
sample of twenty due to the exclusion of firms with noncalendar year
accounting periods and those which were not industrials. Column (3)
lists the observed market returns (represented by the S&P 500 Composite
Index), RMt’ for each time period t.
Column (4) lists the historical average beta, bp, for each port-
folio. The portfolio beta is modified by the adjustment factor esti-
mated by Sharpe and Cooper1 and given by equation (3) of the previous
chapter. At two significant digits the beta and market sensitivity
measures for each portfolio were identical in all but one case.
Column (6) lists the conditional expected portfolio return, given the

historical beta and the market return over the same holding period.

 

1William F. Sharpe and Guy M. Cooper, "Risk-Return Classes of
New York Stock Exchange Common Stocks, 1931-1967," Financial Analysts
Journal (March 1972).

44

45
This value was calculated by formula (2.2) of the previous chapter.

Column (7) shows the observed portfolio returns over the holding
periods, while column (8) shows the differences between actual and
expected portfolio returns. As discussed in the previous chapter,
returns were defined for this study so as to exclude cash dividends;
both actual and expected returns were adjusted for this exclusion.
Column 8 of Tables 4.1 and 4.2 show in particular how large the differ—
ences between actual and expected returns frequently were.

The paired difference test of the CAPM involved calculating the
t statistic for the differences between actual and conditional ex-

pected returns:

Where the D values were as given in column (8) of Tables 4.1 and 4.2,

and 'B.-f§' n
:41

differences, while u was the sample size. The hypotheses were

Dt' Sd was the sample standard deviation of return

no :'D'= 0
lenfo
tested at the a level of .05.

For the l-year holding period returns the test statistic was

t . '0415 ' ° = .53225

.2702 / IE5

with a critical value of $2.201 and 11 degrees of freedom. For the

3-year holding period returns

 

46

 

 

coo.l omo. omo. mH.H wH.H Hwo. m momalwomfl
hum. mum. omH. oo.H oo.H cod. m momalhcaa
qu.l omH.l mOH.I mm. mm. mNH.I h nomalooma
omN. mom. CHH. NH.H NH.H «mo. OH comalmomfl
coo. NON. omH. oH.H 9H.H nHH. NH momaleoaa
meN.l HNo.I NNN. NH.H NH.H NON. w eomfllmomfl
«OH.I OMN.I eNH.I mo.H mo.H mHH.I HH mcmHlNomH
NmH.I NMH. «Hm. mm.H mm.H NMN. HH Noafllaomfl
woo.l NOH.I oeo.l mo.H wo.H mmo.l m HomHloomH
moo.l Nno. who. ma. mm. Hwo. m oomdlmmmfi
mme. mam. mow. mN.H mN.H mum. 0H manlmmmH
neN.l 5mm.l omH.l wH.H mH.H BNH.I NH wmmfllnmma
u m u a a. u no u u name 0
Auzm.eo\ummvm3u«muua mm Auzm. o\ mmvm m2. A an Iwuwm weasmwwwm
coupon owaomuuom chauum assume aua>au comm ensued mo ooauom
oouuooxm was oaaomuuom ouuooexm Iwmoom ouaom moxuoz nooaoz mafia
Hmouo< mooauom oo>uomoo Hmoowuwoaoo uoxumz quom
mucouommwa Hmouu<
3v AC A3 A3 A13 A3 ANV A3

 

<H<n ZMDBNM noHMmm 02anom Mdmw mza

H.¢ mam<8

47

 

 

 

NwN.N 0mm.N moa. mm. mm. NNH. N momalooma
Nam. Nmm. med. NH.H NH.H Had. OH womalmoaa
mom. ewe. who. oa.H 0H.H coo. NH Nomanqoma
mmo.| qu. on. NH.H NH.H one. w oomalmeaa
OHN.I moo.l NON. mo.H wo.H Nwa. Ha momHINomH
Nam.t ooa. nae. mn.H mm.H can. HH somalaomn
mHo.I mNo. wee. mo.H co.H coo. m momalooma
CNN.I oao.l ooN. mm. mm. omN. m Nomalmmma
mme. Nnm. «mm. mN.H mN.H NNe. ca HomHImmmH
moo. oNq. Hmm. wa.H mH.H NmN. Ha ooaHINnaH
a
a. ease a. Es}; ..e e. a as has
apnoea ouaowuuom cuouom ensued hua>au moon cuoumm mo powwow
oouuooxu odd oaaomuuom oouoomxm Iwuaom ouaom uoxumz noosuz saga
Honuu< coosuom oo>uomoo Hmaowugoaoo uoxumz quom
oomouowmwn donned
Ame Ame Amy any Rev Amv Auv AHV

 

<H<Q zmmflmm oonmm UZHGAOZ m<mw mummy

N.¢ man<a

48

02634 " 0

' .75141 / 56 " 1'09”

t

with a critical value of $2.262 and 9 degrees of freedom. Both tests
were clearly not able to reject the null hypothesis of no significant
difference between actual and predicted portfolio holding period
returns.

The above t-tests showed that on average the CAPM predictions
were unbiased when the entire test period was taken as a whole, while
for the individual portfolios and holding periods tested, the actual

returns in many cases differed markedly from those predicted by the CAPM;

Discrimingnt Analysis Tests Results
The variables considered by the stepwise multiple discriminant
analysis routine are listed as follows: -

1. Net Operating Margin

2. Operating Asset Turnover

3. Net Working Capital/Total Assets

4. Net Working Capital/Market value of Common Equity

5. Retained Earnings/Total Assets

6. Times Interest Charges Earned

7. Earnings Change Per Dollar of Price

8. Percentage Change in Sales

9. Percentage Change in working Capital
10. Percentage Change in Net Operating Income
11. Current Ratio
12. Current Ratio as a Percentage of the Industry Average

13. Net Operating Margin as a Percentage of the Industry
Average

49

14. Operating Asset Turnover as a Percentage of the
Industry Average

Table 4.3 lists the variables selected by the stepwise discriminant
routine for each of the eighteen discriminant functions. The numbers
correspond to the variable listing shown above. The variables selected
are listed in declining order of importance to their respective dis-
criminant functions. Table 4.4 lists the variables which are common
to all three data runs for each holding period. This gives a rough
indication of the stability of the relationships. That is, the lower
degree of commonality, the greater the likelihood that any relationship
underlying the profile of variables found by the stepwise routine was
spurious rather than real. Table 4.4 indicates that more variables
were common for the calendar years when the market increased than for
those years when the market declined, and that the highest degree of
commonality occurred when all years were combined. More commonality
would be expected to occur if the relationships were stable during the
sample period and to become more pronounced as sample size were increased.
Tests of the classification ability of discriminant analysis were
made utilizing the Spearman Rank Correlation Coefficient as the test
statistic. For each of the eighteen discriminant functions, the pre-
dicted rank order based upon the discriminant score was correlated with
the actual rank order score. For the first twelve discriminant func-
tions, the discriminant scores for each of the firms in the holdout
sample were ordered and compared with their performance ranks based
upon actual returns during the same holding period. For the predictive
power test of discriminant analysis, the last six discriminant functions

were applied to corresponding data for firms in the 1967-1971 period.

50

«:111I11e-

 

 

 

 

 

3|. .

o.ae.~.m.ms.a e.sa.w.~.ma.e e.ea.~.ma.w.e AeesHINemev
mums» Ham on unmovomosm mm cocoa mm

oa.e.ea.~.m.m e.oa.e.ea.~.m e.HH.eH.~.oe.m Aeesaauemav
munch Ham ou uaosvomoom mm cocoa m

a.ae.e.oe.ea.m s.oa.~H.H.eH.m He.ee.m.oa.m.a Ameseumesev seesaw assume
sumo» ou uooauonnom mm cocoa mm

e.~.e.m.a.a ea.ma.e.s.m ~.os.e.ma.m.s flees” .Nemav eueeeoue assume
munch on unmovomoom m: cocoa mm

e.~.e.m.m.a e.s.e.m.w.e e.a.oa.e.m.m Amemsnmemev ewes.» ensues
munch on undocumoam mm ounce m

N.m.a.m.m.n o.m.NH.m o.oa.e.a.m Aoema .Nomav coceauuv oceans
mums» ou unmovoooom mu ounce a
magnum uoooaom unooaom Aoucnauomuoe noon «0 some swoooaoov
Hash vacuum umuam cu unoavoooam Away possum
scam noon wswoaom unasouuuom one no games;

 

moz<Hmom2H no «name UZHZHAUNQ 2H GHHmHA
ZOHHUZDh Hz<ZHZHMUmHQInonmm GZHnAom mo<u Mom amaomgmm mmqdem<>

m.¢ mam<a

51

 

e.HH.~.mH.w.H Aeemenmemav seams Ham on namesameeu mm ences mm
q.¢H.N.oa.m AooaHINoaHv munch Ham on unmouomosm mm :uooa m
He.sfl.oa Amemeumesav emcee» pushes menus on nemesmenne mm ences mm

c.m Aooma .Nomav ooawaooo spasms munch ou ucosvonoom mm ounce mm

o.q.m.m Anomalmoaav possum assume oomph cu unoavomosn mm ounce m

m Asses .Neaev accesses ensues seeps on paupeoeeee as ences a

 

oommeuomuoe Moon MO was» nooooaoov
moaooaum> coaaoo ou unsavooosm Ammv oowuom
mswoaom Hoaoouuunm one no euwooq

 

COHmmm UZHQAOS mumm Mom azam «add mummy AA< OH zczzoo mMAM<HM<>

¢.¢ mum<fi

52
That is, firms in the 1967-1971 test period which were drawn from
years in which the general market declined (1969 and 1970) were used
to test the nine- and thirty-three-month discriminant functions which
had been constructed utilizing only those samples of firms which had
been drawn from those years in the sample period in which the market
had declined (1962 and 1966).

The test statistic was

11 n n
n 151 xiyi ’ (151 *1) (151 yi)

 

r-

S
n n n n
2 2 2 2
‘¢/;1§1 ‘1 ’ (1§1 x1) n1351 Y1 ‘ (1§1 Y1)

 

where n is the number of firms being ranked, x1 is the actual perfor-
mance rank and y1 is the rank predicted by the discriminant function-
for any firm i - 1,2, ..., n. The resulting r8 correlation coefficient
was compared to the .05 significance level for an upper-tail test. If
the r8 value exceeded the critical value, the null hypothesis of "no
association" between actual and predicted ranks would be rejected.
Alternatively, if r8 did not exceed the critical value, the null
hypothesis would not be rejected.

Table 4.5 shows the sample r8 values for each discriminant func-
tion. When these sample statistic values were compared with the
critical values of the test statistic, none were found significant at
the five percent level. That is, correlations of the magnitude found
could be expected to have occurred randomly more often than 5 times
out of 100 if the predicted and actual ranks were uncorrelated. It
also can be seen that 11 of the 18 functions have the correct sign.

If no relationship whatsoever existed, one would have expected roughly

53

 

 

3. S. no. SSTSSV poems in 3 2382:. as 58a mm
8.- .3. S. “SEAS: spams 3. 3 ”.8339. em 5:8 a
Ho.l on. om. Anomalmomav possum uoxuoa munch ou unmovomonm mm ounce mm
No. on.: OH. Aoomfl .momav mooNHooo assume mums» ou uaosvomoam mm :uooa mm
ee.| 00.: oa.| Anomalmoaav woman» uoxuma oomph cu unsavomoom mm ounce m
0N.|. on. 00. Aooma .Nomav oocuaooo uoxuma pump» on unwovomoom mm ounce m
ooauom amok uoooaom usooaom Aoummapomuom soon we use» occupancy ou unoavomoom
Humatnoaa vacuum umuam Ammv oowuom wsfiofiom uoaaofiuumm new no suwcoq

 

m
ZOHHUZDK Hz<zH2HMomHQ mo<m «on A my mMDA<> HZMHUHhmmoo ZOHH¢AMMMOU MZ<M zmzm<mmm

n.< mam<a

54
as many positive as negative correlations; the 11 positive correla-
tions found here were only slightly more than the 9 which would be

expected to occur on average due to random causes.

CHAPTER V

CONCLUSIONS

The results of this study have indicated that the Sharpe-
Lintner capital asset pricing model (CAPM) was not inappropriate when
used as the basis for an investment strategy involving portfolios of
securities with poor past performance. For small portfolios and rela-
tively short holding periods of one and three year duration, the
tests conducted were not able to reject the null hypothesis of no sig—
nificant difference on average between observed portfolio returns and
expected returns conditional upon knowledge of the market return over
the holding period and the historically calculated portfolio beta
coefficient.

While the differences between observed and conditional expected
returns were pp average not significantly different from zero over the
12 one-year periods and 10 three-year periods, they were often quite
large in the individual periods when considered separately. This
phenomenon could be important for the individual small investor since
in the absence of holding shares in a mutual fund or other diversified
portfolio, he may be limited to a small portfolio of securities. If,
as is sometimes the case, his holding period horizon is also relatively
short, the conditional expected return given by the CAPM may not be of
significant value to him. The observation that realized returns may
depart significantly from conditional expected returns during individual

55

56
holding periods was not per se inconsistent with the CAPM, however,
since the model deals with expected returns which are of course observ-
able. The model also was primarily concerned with expected returns pp;
average over many portfolios and time periods, and much less over the
behavior of individual portfolios. The small investor, nevertheless,
should be made aware that his actual portfolio returns during individual
holding periods may frequently be far different from expectations based
upon the CAPM.

The study done by Black, Jensen, and Scholes (BJS) showed evi-
dence that on average over the 35-year period studied, high beta port-
folios consistently returned less than expected according to the Sharpe-
Lintner CAPM and low beta portfolios on average returned more than ex-
pected. This tendency was particularly pronounced in the latest sub-
period (April, 1957 - December, 1965) studied. Since the BJS study
dealt with much larger portfolios, however, the results of the present
study may not present strong evidence to either confirm or deny the
BJS study results.

For all one-year holding periods taken together, the arithmetic
average beta of the present study was approximately 1.1 while the aver-
age difference between actual and conditional expected returns in the
paired-difference t-test was .0415. Thus, average annual observed
returns were on average larger (though not to a statistically signifi-
cant degree) than returns conditionally expected by the CAPM. However,
while a beta of 1.1 is above the market average of 1.0, it is still
definitely in the middle range of possible beta values. The results
appear to have been mildly inconsistent with those of the BJS study

since for their study, the decile (of the April, 1957 - December, 1965)

57

portfolio with a beta closest to the 1.1 of the present study had a
small but negative excess return (thus indicating that observed
returns on average fell short of those predicted by the Sharpe-Lintner
CAPM). For the three-year holding periods of the present study the
average of the separate portfolio betas was again approximately 1.1,
while the average difference between actual and conditional expected
returns was again positive at .2634, and of the wrong sign compared
with the negative excess return given by the BJS study. The results
of the present study were based upon a small sample of firms and con-
cerned average annual and 3-year returns, while the BJS study concerned
average monthly returns. The above interpretation of the results of
this study relative to those of the BJS study must, therefore, be
regarded as tentative and primarily observational.

The results of the tests concerning multiple discriminant
analysis uniformly indicated that it was of little value when used as
a tool for ex ante separating winners from losers on the basis of
known financial variables. It was not suggested anywhere by the tests
that the discriminant functions had any significant ability to rank
securities ex ante according to performance. The classifications of
securities into groups which subsequently either increased or decreased
relative to the market in 9- and 33-month holding periods was generally
quite good when the same securities which were used for deriving the
discriminant functions were reclassified by these same discriminant
functions. That procedure, however, is biased and was, therefore, not
part of the study.

Because of the inability of discriminant analysis to differen-

tiate performance, it may be useful to speculate on reasons why. The

58
first and most persistent explanation would be that the market is semi-
strong efficient, thus any attempt to find superior performing secu-
rities from past publicly available information would be doomed to
failure. Another explanation might be that discriminant analysis is
simply not a powerful enough technique to isolate true relationships
which may exist between past publicly available information and future
price performance. Discriminant analysis would appear to be useful
only for aiding the understanding of past relationships. The inclusion
of subjective informational inputs, however, such as analysts' fore-
casts of such items as earning, sales growth, or market share for par-
ticular company products might be expected to aid the ex ante predic-
tive power of discriminant analysis, although additional research would
be required. As a topic for further study, discriminant analysis per-
haps should be tested on a sample of firms all from the same industry.
It might be that if interindustry differences in ratios are adjusted

away, discriminatory power would improve.

APPENDIX

Listing of Firms in the Sample by Calendar Year of Poor Price
Performance

3.152 leer.
Admiral Corporation 1956
Briggs Manufacturing Company 1956
Granby Consolidated Mining 1956
McCall Corporation 1956
Pfeiffer Brewing Company 1956
Philco Corporation 1956
Rheem Manufacturing Company 1956
Standard Coil Products Company 1956
Telautograph Corporation 1956
United Dye and Chemical Corporation 1956
United Park City Mines Company 1957
Allied-Albany Paper Corporation 1957
Briggs Manufacturing Company 1957
Bullard Company 1957
Butte Capper and Zinc Company . 1957
Comptometer Corporation 1957
Copper Range Company 1957
Detroit Steel Corporation 1957
Howe Sound Company 1957
Industrial Rayon Corporation 1957
Magma Copper Company 1957
Penn-Texas Corporation 1957
Pittsburgh Steel Company 1957
Shahmoon Industries, Inc. 1957
United Dye and Chemical Corporation 1957
U. S. Hoffman Machinery Corporation 1957

59

6O
Firm

West Kentucky Coal Company

Allied Products Corporation
Chrysler Corporation

De Vilbiss Company

Fairbanks, Morse and Company
Fenestra Incorporated

I-T-E Circuit Breaker Company
Lehigh Coal and Navigation Company
Sun Oil Company

United Biscuit Company of America
Foote Mineral Company

Getty Oil Company

Jefferson Lake Sulphur Company
National Can Corporation

Temco Aircraft

Texas Pacific Coal and Oil Company
United Aircraft Corporation
Uhited Fruit Company

Admiral Corporation

Checker Motors Corporation
Colorado Fuel and Iron Corporation
Firth Carpet Company

General Time Corporation

I-T—E Circuit Breaker Company
Lehigh valley Industries, Incorporated
New York Shipbuilding Corporation
Rheem Manufacturing Company
Studebaker-Packard Corporation
United Industrial Corporation
Adams-Millie Corporation

Fenestra Incorporated

General Baking Company

General Dynamics Corporation
General Portland Cement Company

Year

1957
1958
1958
1958
1958
1958
1958
1958
1958
1958
1959
1959
1959
1959
1959
1959
1959
1959
1960
1960
1960
1960
1960
1960
1960
1960
1960
1960
1960
1961
1961
1961
1961
1961

61
Firm

Lionel Corporation

Minnesota and Ontario Paper Company
Natco Corporation

Texas Instruments, Incorporated
Universal Match Corporation
Windsor Industries, Incorporated
Brunswick Corporation

Certain-teed Products Corporation
Chris-Chraft Industries

Foxboro Company

Lionel Corporation

Thompson (John R.) Company
Universal Match Corporation

Ward Industries Corporation

Anken Chemical and Film Corporation
Babbit (B.T.) Incorporated
Brunswick Corporation
Gamble-Skogomo, Incorporated
Hoffman Electronics Corporation
McCrory Corporation

Melville Shoe Corporation

Newberry (J.J.) Company

Standard Kollsman Industries, Incorporated
U. S. Industries, Incorporated
vendo Company

Wheelabrator Corporator

American Photocopy Equipment Company
Anken Chemical and Film Corporation
Electronic Associates, Incorporated
High VOltage Engineering Corporation
Indiana General Corporation

Mattel, Incorporated

Montecatini General Mining and Chemical
Corporation

Year

1961
1961
1961
1961
1961
1961
1962
1962
1962
1962
1962
1962
1962
1962
1963
1963
1963
1963
1963
1963
1963
1963
1963
1963
1963
1963
1964
1964
1964
1964
1964
1964

1964

62
Firm

Mueller Brass Company

Shahnoon Industries, Incorporated

Thor Power Tool Company

Banquet Consolidated

Consolidated Cigar Corporation

General Cigar Company, Incorporated
General Portland Cement

Hazeltine Corporation

Marquette Cement Manufacturing Company
Rayette-Faberge, Incorporated

American PhotocOpy Equipment Company
Arlan's Department Stores, Incorporated
Central Foundry Company

Consolidated Cigar Corporation
International Pipe and Ceramics, Incorporated
Marquette Cement Manufacturing Company
Monsanto Company

Screw and Bolt Corporation of America
Thomasville Furniture

Admiral Corporation

American Broadcasting Companies, Incorporated
NVF Company

Sprague Electric Company

Upjohn Company

Automatic Sprinkler Corporation of America
Bell and Howell Company

Boeing Company

Brown and Sharpe Manufacturing Company
Corning Glassworks

Fansteel, Incorporated

Foxboro Company

Freeport Sulphur Company

General Dynamics Corporation

Itek Corporation

Year

1964
1964
1964
1965
1965
1965
1965
1965
1965
1965
1966
1966
1966
1966
1966
1966
1966
1966
1966
1967
1967
1967
1967
1967
1968
1968
1968
1968
1968
1968
1968
1968
1968
1968

63
Firm

Ling-Temco-Vought, Incorporated

Maremont Corporation

Sunstrand Corporation

Victor Comptometer Corporation

Dynamics Corporation of America

General Host Corporation

Gulf Resources and Chemical Corporation
Hanes Corporation

Ling-Temco-Vought, Incorporated
Londontown Manufacturing Company
National Industries, Incorporated
Northwest Industries, Incorporated
Seilon, Incorporated '
Simmonds Precision Products, Incorporated
Villager Industries

Electronic Memories and Magnetics Corporation
Fairchild Camera and Instrument Corporation
university Computing Company

American Standard Incorporation

Boise Cascade Corporation

General Steel Industries

International Mining

Kaiser Aluminum and Chemical Corporation
MacAndrews and Forbes Company

Memorex

Molybdenum Corporation of America
Northgate Exploration Limited

Technican Corporation

‘Year

1968
1968
1968
1968
1969
1969
1969
1969
1969
1969
1969
1969
1969
1969
1969
1970
1970
1970
1971
1971
1971
1971
1971
1971
1971
1971
1971
1971

BIBLIOGRAPHY

Altman, Edward I. "Financial Ratios, Discriminant Analysis and the
Prediction of Corporate Bankruptcy," Journal of Finance,
vol. XXIII (September 1968).

Ball, Ray, and Philip Brown. "An Empirical Evaluation of Accounting
Income Numbers," Journal of AccountingAResearch, VI (Autumn,
1968).

Bicksler, James L. Methodolggy_in France-Investments. Lexington,
Mass.: D. C. Heath and Co., 1972.

Blume, Marshall E. "On the Assessment of Risk," Journal of Finance,
(erh 1971) o

 

Boneau, C. A. "The Effects of Violations of the Assumption Underlying
the t Test." Psychological Bulletin, Vol. 57, No. l, 1960,
pp. 49-64.

Bradley, James V. Distribution-Free Statistical Tests. Englewood
Cliffs, N.J.: Prentice-Hall, Inc., 1968.

Brealey, Richard A. An Introduction to Risk and Return from Common
Stocks. Cambridge, Mass.: The MIT Press, 1969.

. Security Prices in a Competitive Market. Cambridge, Mass.:
The MIT Press, 1971.

Campanella, Frank B. The Measurement of Portfolio Risk Exposure.
Lexington, Mass.: D. C. Heath and Co., 1972.

Carlton, W. T. and E. MA Lerner. "Statistical Credit Scoring of
Municipal Bonds," Journal of Money, CreditL and Bankin , I
(November 1969).

Cooley, William W., and Paul R. Lohnes. Multivariate Data Analysis.
New York: John Wiley & Sons, Inc., 1971.

Cootner, Paul H., (ed.). The Random Character of Stock Market Prices.
Cambridge: The MIT Press, 1964.

Downes, David, and Thomas R. Dyckman. "A Critical Look at the
Efficient Market Empirical Research Literature as it Relates to
Accounting Information," Accountinijeview (April 1973).

 

64

65

Eisenbeis, Robert A., and Robert B. Avery. Discriminant Analysis
and Classification Procedures. Lexington, Mass.: D. C. Heath
and Co., 1972.

"A Study of the Dolineation of Geographic Markets for
Business Loans." Unpublished Ph.D. dissertation, University
of Wisconsin, 1971.

Evans, John Leslie. "Diversification and the Reduction of Dispersion:
An Empirical Analysis." Doctoral dissertation, University of
Washington, 1968.

Fama, Eugene F. "Risk, Return, and Equilibrium: Some Clarifying
Comments." .Journal of Finance, XXII (March 1968).

. "Efficient Capital Markets: A Review of Theory and
Empirical work," Journal of Finance, XXV (May 1970).

, and others. "The Adjustment of Stock Prices to New Infor-
mation," International Economic Review, X (February 1969).

Francis, Jack C. Investments: Analysis and Management. New'York:
MeGraw-Hill Book Co., 1972.

 

Friedland, Seymour. The Economics of Corporate Finance. Englewood
Cliffs, N. J.: Prentice-Hall, Inc., 1966.

Graham, Benjamin, David L. Dodd, and Signey Cottle. Security
Analysis Principles and Technique. New York: McGraw-Hill
Book Co., 1962.

Granger, Clive W. J., and Oskar Morgenstern. Predictability of Stock
Market Prices. Lexington, Mass.: D. C. Heath and Co., 1970.

Hayes, Douglas A. Investments: Analysis and Management. New York:
Macmillan Co., 1966.

Jensen, Michael E. (ed.). Studies in the Theory of Capital Markets.
New York: Praeger Publishers, 1972.

Jones, Charles P., and Robert H. Litzenberger. "Quarterly Earnings
Reports and Intermediate Stock Price Trends," Journal of Finance
(March 1970).

Joy, Maurice 0., and Charles P. Jones. "Another Look at the Value
of PIE Ratios," Financial Analysts Journal (September-October
1970).

Institute of Chartered Financial Analysts. C.F.A. Readings in
Financial Analysis. Second ed. Homewood, 111.: Richard D.
Irwin, Inc., 1970.

66

King, Leslie J. Statistical Analysis in Geography. Englewood Cliffs,
N. J.: Prentice-Hall, Inc., 1969.

Latane, Henry A., and Donald L. Tuttle. Security Analysis and
Portfolio Management. New York: The Ronald Press Co., 1970.

_________ "Price Changes in Equity Securities," Journal of Finance
(September 1951).

Levy, Robert A., and Spero L. Kripotos. "Earnings Growth, P/E's
and Relative Price Strength," Financial Analysts Journal
(November-December 1969).

 

'. "On the Short-term Stationarity of Beta Coefficients,"
Financial Analysts Journal (November 1971).

Lintner, John. "The Valuation of Risk Assets and the Selection of
Risky Investments in Stock Portfolios and Capital Budgeting,"
Review of Economics and Statistics (February 1965).

Lorie, James E., and Victor Niederhoffer. "Predictive and Statistical
PrOperties of Insider Trading," Journal of Law and Economics
(April 1968).

Markowitz, Harry. "Portfolio Selection," Journal of Finance (March
1952).

Mossin, Jan. "Equilibrium in a Capital Asset Market," Econometrics
(October 1966).

Murphy, J. E., Jr. "Relative Growth of EArnings Per Share-Past and
Future," Financial Analysts Journal (November-December, 1966).

"Earnings Growth and Price Change in the Same Time Period,"
Financial Analysts Journal (January-February 1968).

Nicholson, S. F. "Price Ratios in Relation to Investment Results,"
Financial Analysts Journal (January-February 1968).

Niederhoffer, Victor, and Patrick J. Regan. "Earnings Changes,
Analysts' Forecasts and Stock Prices," Financial Analysts
Journal (May 1972).

Peterson, D. E. A Quantitative Framework for Financial Management.
Homewood, 111.: Richard D. Irwin, Inc., 1969.

Pratt, Shannon P., and Charles W. DeVere. "Relationships Between
Insider Trading and Rates of Return for NYSE Common Stocks,
1960-1966," paper presented at the Seminar on the Analysis
of the Security Prices, University of Chicago (May 1968).

Press, 8. James. Applied Multivariate Analysis. New York: Holt,
Rinehart and Winston, Inc., 1972.

67

Sauvain, Harry C. Investment Management (Fourth Edition). Englewood
Cliffs, N. J.: Prentice-Hall, Inc., 1973.

Scholes, Myron. "A Test of the Competitive Hypothesis: The Market
for New Issues and Secondary Offerings," Unpublished Ph.D.
Thesis, Graduate School of Business, University of Chicago,

1969.

Sharpe, William F. "Capital Asset Prices: A Theory of Market Equilib-
rium under Conditions of Risk," Journal of Finance, XIX (September

1964).

. Portfolio Theory and Capital Markets. New York: McGraw-
Hill Book Co., 1970.

, and Guy M. Cooper. "Risk-Return Classes of New York Stock
Exchange Common Stocks, 1931-1967," Financial Analysts Journal,
(March 1972).

Shelton, J. P. "The Value Line Contest: A Test of the Predictability
of Stock-Price Changes," Journal of Business, XV (July 1967).

Smith, Keith V. "Classification of Investment Securities Using
Multiple Discriminant Analysis," Institute Paper #101, (Purdue
University: Institute for Research in the Behavioral, Economic,
and Management Sciences, 1965).

. Portfolio Management. New York: Holt, Rinehart and
Winston, Inc., 1971.

Stone, Bernell K. Risk, Return and Equilibrium. Cambridge, Mass.:
The MIT press, 1970.

Tatsuoka, Maurice M; Multivariate Analysis. New York: John Wiley
& Sons, Inc., 1971.

walter, J. E. "A Discriminant Function for Earnings Price Ratios of
Large Industrial Corporations," Review of Economics and Statistics

XLI (February 1959).

Williams, Edward E., and Chapman M. Findlay III. Investment Analysis.
Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1974.

Williams, J. B. The Theory of Investment Value. Cambridge, Mass.:
Harvard university Press, 1938.

Ying, C. C. "Stock Market Prices and Volume of Sales," Econometrics
(July 1966).

"‘IIIllllllllllllllI“