INVESTMENT MANAGEMENT AND THE COMPUTER:
LIMITATIONS AND PROSPECTS
ALFRED LOUIS KAHL, JR.
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
FI Ar rtii ri :
UNIVERSITY OF FLORIDA
I wish to express my sincere appreciation to Dr. John B. McFerrin,
Mr. James G. Richardson, Dr. Ralph H. Blodgett, and Dr. William V. Wilmot,
for their continuing advice, guidance, and constructive comments at
various stages in the preparation of this manuscript. They very gener-
ously devoted valuable time and effort to counsel me in the preparation
and conduct of this study, thus contributing immeasurably to the quality
of the final product.
Appreciation is also due the Standard Statistics Company, which
provided the COMPUSTAT data base used in this study; The International
Business Machines Corporation, which provided the major computer programs
used in this study; and the University of Georgia Office of General
Research, which provided the computer time necessary for the completion
of the study.
The research reported in this dissertation arose out of a desire to
investigate the limitations and capabilities of the electronic computer
as a tool of investment management.
The very nature of this project precludes any hard and fast proofs
and must be to some extent the result of my own reasoned judgment, but
it is hoped that this research sheds some light on the optimal man-machine
relationship in this very important sector of our economy.
The research project which formed the basis of this report actually
began during my graduate studies at the University of Pittsburgh where I
loaned a linear programming program that I had written to a fellow student.
I forgot to warn him of a serious limitation of the program (no degeneracy
stop) and his problem caused the computer to cycle continuously until the
console operator finally stopped it. This incident aroused my curiosity
about the limitations of the computer programs which were written for
investment management purposes but are being used by persons who did not
write the program themselves and may not even know very much about computers.
Preliminary work on this project was continued while I was a faculty
member at Gannon College and while I was a graduate student at the Univer-
sity of Florida. The project was completed after I joined the faculty at
the University of Georgia.
TABLE OF CONTENTS
LIST OF TABLES vii
LIST OF FIGURES xii
1 INTRODUCTION 1
2 INSTITUTIONAL INVESTMENT AND THE COMPUTER 9
The Institutional Investment Process 11
The Institutional Investment Environment 16
Computer Usage by Institutional Investors 19
3 COMPUTER ASSISTED DECISION MAKING 26
The Decision Process 27
Models and Their Structure 30
The Model Building Process 36
Important Limitations of Models 38
Computers and Their Limitations 40
Investment Decisions and Computers 45
4 THE PORTFOLIO SELECTION MODEL 48
The Portfolio Selection Problem 50
Expected Holding Period Return 52
Risk and Diversification 54
Portfolio Selection Theory 58
Limitations of the Model 68
Empirical Tests of the Model 72
Implementation of the Model 74
5 EMPIRICAL EVALUATION OF THE MODEL 79
The Data Base 81
The Samples 83
Risk Classes 84
Security Analysis 86
Selected Portfolios 87
Reference Portfolios 90
Simulation Time Periods 95
Simulation Results 97
Portfolio Efficiency 105
Significance Test of the Simulation Results 108
Additional Tests 111
Portfolio Size 116
The Random Walk Hypothesis 120
Implications for Investment Management 124
6 SUMMARY AND CONCLUSIONS
Institutional Investment and Computers
Investment Decisions and Computers
The Markowitz Model
COMPANIES INCLUDED IN
COMPANIES INCLUDED IN
EQUAL DOLLAR STRATEGY
EQUAL SHARES STRATEGY
EQUAL DOLLAR STRATEGY
EQUAL SHARES STRATEGY
EQUAL DOLLAR STRATEGY
EQUAL SHARES STRATEGY
LIST OF TABLES
1 SPECIFIC COMPUTER APPLICATIONS BY RESPONDING FIRMS,
PRESENT AND FUTURE 21
2 RISK CLASSIFICATION OF SAMPLE STOCKS 85
3 SELECTED AND REFERENCE PORTFOLIOS 94
4 1956-1965 PORTFOLIO HOLDING PERIOD RETURN RESULTS 101
5 1957-1966 PORTFOLIO HOLDING PERIOD RETURN RESULTS 102
6 1958-1967 HOLDING PERIOD RETURN RESULTS 103
7 PORTFOLIO EFFICIENCY, EQUAL DOLLAR STRATEGY 106
8 PORTFOLIO EFFICIENCY, EQUAL SHARES STRATEGY 107
9 SIGNIFICANCE TEST RESULTS FOR COMPUTER AND RANDOMLY
SELECTED PORTFOLIOS, EQUAL DOLLAR STRATEGY AND HOLDING
PERIOD RATES OF RETURN 109
10 SIGNIFICANCE TEST RESULTS FOR COMPUTER AND RANDOMLY
SELECTED PORTFOLIOS, EQUAL SHARES STRATEGY AND HOLDING
PERIOD RATES OF RETURN 110
11 MUTUAL FUND PERFORMANCE 114
12 MUTUAL FUND AND RANDOM PORTFOLIO PERFORMANCE 115
13 PREDICTED AND ACTUAL RETURNS 118
14 EQUAL DOLLAR STRATEGY PORTFOLIO RESULTS, ANNUAL EQUIVALENT
EFFECTIVE RATES OF RETURN 128
15 COMPARATIVE RESULTS, AVERAGE ANNUAL EFFECTIVE RATES OF
16 PORTFOLIO A 1956-1965 RESULTS, EQUAL DOLLAR STRATEGY 190
17 PORTFOLIO B 1956-1965 RESULTS, EQUAL DOLLAR STRATEGY 192
18 PORTFOLIO C 1956-1965 RESULTS, EQUAL DOLLAR STRATEGY 194
19 PORTFOLIO D 1956-1965 RESULTS, EQUAL DOLLAR STRATEGY 196
20 PORTFOLIO E 1956-1965 RESULTS, EQUAL DOLLAR STRATEGY 198
LIST OF TABLES (Continued)
47 PORTFOLIO 0 1956-1965 RESULTS,
LIST OF TABLES (Continued)
LIST OF TABLES (Continued)
101 PORTFOLIO A 1958-1967 RESULTS, EQUAL SHARES STRATEGY
LIST OF TABLES (Continued)
LIST OF FIGURES
1 SECURITY RETURNS AS RANDOM VARIABLES 59
2 PORTFOLIOS DESCRIBED BY VARIANCE AND EXPECTED RETURN 61
3 CRITICAL POINTS FOR THREE AVAILABLE SECURITIES 64
4 CRITICAL LINE FOR FOUR POSSIBLE PORTFOLIOS 64
5 DERIVING INDEX TIE PARAMETERS 66
6 USING INDEX TIE PARAMETERS 66
Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
INVESTMENT MANAGEMENT AND THE COMPUTER:
LIMITATIONS AND PROSPECTS
Alfred Louis Kahl, Jr.
Chairman: Dr. John B. McFerrin
Major Department: Finance and Insurance
The essence of investment management is the selection of efficiently
diversified portfolios of securities, at a given time, the moment of
selection, which are expected to accomplish the investor's goals, usually
to obtain the highest return possible on his investment while not exceed-
ing some specified level of risk exposure. The problem of the investment
decision maker is to allocate a limited amount of investible funds to
those few securities, from among an almost infinite array of alternatives,
which appear most likely to do the job over some period of time in the
A model, suitable for computer implementation, given some input
data concerning present security prices, expected prices, expected divi-
dends, expected variance in the price and dividend estimates, and
expected covariance between and among each and every security, exists
and has been widely acclaimed as a theoretical construct but so far
has not been put into regular use by institutional investors, prima-
rily because of a lack of top management understanding, acceptance, and
This study seeks to fill the present information gap by presenting
the results of a simulation of the model's efficacy over three ten-year
(1956-1965, 1957-1966, and 1958-1967) performance periods, using histor-
ical inputs. Seventeen portfolios are compared in terms of both real-
ized holding period return and risk with both the equal dollar and equal
shares buy and hold strategies. One portfolio, chosen ex post, repre-
sents optimal performance; another represents minimal performance. Two,
ex ante, portfolios representing "market" performance, two representing
mutual fund performance, and five portfolios chosen randomly from the
665 sample stocks are compared with six portfolios chosen by the computer
implemented model. A further comparison with actual results of 100
large mutual funds is also made. In all cases the performance of the
computer selected portfolios is statistically significantly superior to
that of any and all others tested. Neither of the two strategies, equal
dollar or equal shares, is statistically superior to the other.
The results provide sufficient evidence for acceptance of the
primary hypothesis that the model could have been used during the late
1950's to select portfolios for institutional investors which were supe-
rior to those actually selected. The secondary hypothesis that the
Standard and Poor's Stock Ranking is an operationally effective risk
measure is also accepted. Extensive portfolio turnover, such as that
which is often employed by many mutual funds, is shown to be dysfunc-
tional behavior on their part, as is also the observed tendency of
such investors to overdiversify their portfolios by holding an exces-
sive number of issues. Since historical inputs are used and superior
performance results, the random walk hypothesis of stock price behavior
which asserts that past data cannot be used to predict future prices
The only significant limitations of the model uncovered by this
study were: that it is not suitable for frequent use by speculative
traders because it is intended for single point in time decision making
and its cost per use is still rather high, and that it cannot be used
by (those rare) investors who need to impose nonlinear constraints on
The prospects for future use of the model are quite bright if more
institutional investors begin to use the model, as this study indicates
that they should. They can expect higher returns at less risk than they
can achieve without the model. Gradual evolution toward an optimal man-
machine investment management system is foreseen, with man handling the
qualitative aspects of the decision making situation and formulating the
appropriate constraints while the computer performs the quantitative
The essence of investment management is the proper selection of
portfolios of securities. This is a complex decision making problem
which requires the allocation of limited investment funds to only those
few securities, from among an almost limitless array of possible alter-
native securities, which, at a particular time, the moment of decision,
appear to the decision maker to provide the highest probability of
achieving his investment goals over some period of time in the future.
The decision maker must select his portfolio on the basis of his best
estimates of future performance, which are, in turn, based upon incom-
plete information. He must frequently accomplish this difficult task
under time pressure since prices of securities change frequently and a
security which is a good buy at one price may not be at another price.
Most writers on the subject of investment management have distin-
guished two major phases of the investment management process: financial,
or security analysis and portfolio selection. Financial analysis is con-
cerned with the characteristics of individual securities and provides the
necessary input data for portfolio selection. Portfolio selection must
consider the expected performance of several securities as an integrated
entity, the portfolio, which is most likely to achieve the investor's
goals. Since each of the securities included in a portfolio interacts
with and complements the others it is not possible to select an appropriate
portfolio merely by collecting a number of securities which have been clas-
sified as "good" by financial analysis.
Since electronic computers have been used for business data proces-
sing purposes since 1954 and, with the passage of time, have become both
more reliable and much cheaper, thus encouraging users to find even more
work for them to do, it is reasonable to inquire into their usefulness
within the investment management process.
The first modern electronic computer was invented in 1946 as the
result of an effort to build a faster calculating machine for the engineer
developing weapons. This machine was only a super desk calculator,
containing thousands of vaccuum tubes, which could do in seconds, by it-
self, what a man with a desk calculator needed days to complete. Gradual
improvements in operating speeds and memory capacity were made and business
firms began using computers for data processing applications in 1954.
Computers are a new kind of tool, which can be used as an extension
of the brainpower of man, but they can not think and must be supplied with
a very detailed program of instructions which tells the machine just what
to do, exactly how to do it, when to do it, and what to do when it is
finished. The memory capacity and calculational speed of modern computers
far exceed that of humans and they do not become fatigued by working long
hours as mere mortals do.
Computer programs for financial analysis and portfolio selection are
readily available to computer users since some of the computer manufac-
turers provide "canned" programs, free of explicit charges, to their
customers for these functions. Other such programs can be obtained from
independent companies or can be custom made by the programming staff of
the computer user.
Appropriate data for these programs must also, obviously, be avail-
able if practical operations are undertaken. The Standard Statistics
Corporation sells a magnetic tape, computer ready, data base, called
COMPUSTAT, which contains annual financial data for nine hundred large,
well-known industrial firms.
No large financial institution in the United States regularly uses
computers for investment management operations on a day to day basis.
Only a few institutional investors have experimented with such computer
applications and few of these firms are willing to publish the results
of their investigations.
The most important reasons for the observed non use of computers for
portfolio selection problems have been: computational costs, lack of ap-
propriate data, and lack of management understanding, acceptance, and
support for computer assisted decision making. Persons who presently
make portfolio selection decisions are also fearful that computers might
replace them. The continuing decline in computational costs and the avail-
ability of the COMPUSTAT annual and quarterly data bases at reasonable
prices appear to effectively remove these first two major inhibiting factors.
This study seeks to provide the basis for managerial understanding,
acceptance, and support by reporting the results of a simulation study of
the Markowitz portfolio selection model which indicates that the portfolios
chosen by the model were significantly superior to both random portfolio
selection and human portfolio selection, as represented by a sample of one
hundred large, well-known mutual funds, in terms of cumulative holding
period returns (capital gains plus dividend income), at specified levels
of risk exposure.
The Markowitz model is widely acclaimed and accepted as a theoreti-
cal construct which explains the efficient diversification of investment
portfolios by investors who like return but dislike risk. It was first
proposed by H. M. Markowitz in 1952  and later expanded by him in 1959
. The mathematical procedure was, at that time, too complex (for even
the largest computers then available) to apply to practical problems.
The theory has been extended even further by Tobin  and Sharpe ,
among others, so that it has been feasible to apply it to practical
problems since 1964 when both the required programs and data base
became generally available for second generation (solid state) computers
of sufficient size.
The objective of this dissertation is to contribute to our knowl-
edge of the practical efficacity of the Markowitz model by subjecting
it to empirical tests using the same data base and computer programs
generally available to large financial institutions. The specific
hypothesis tested by this research project is that this model could
have been used during the late 1950's to make portfolio decisions for
institutional investors which were superior in terms of realized returns
at specified levels of risk exposure to those actually made.
The realistic emFirical tests of the model, which are reported in
Chapter Five, utilize a relatively new research technique, simulation,
to ascertain the ex post performance of portfolios selected by the model
and by several other methods.
Since the model is intended for single point in time decisions for
selection of portfolios to be bought and held for specified time periods
it is most appropriate for long term investors rather than speculative
The empirical tests, therefore, assume that an investment of
$100,000 is made in seventeen portfolios under both the equal dollar and
equal shares buy and hold strategies at the beginning of a ten-year period
with the portfolio being liquidated at the end of the ten-year period.
The seventeen test portfolios include two mutual fund portfolios, two
market index portfolios, five randomly selected portfolios, six computer
selected portfolios, an ex post optimal portfolio, and an ex post minimal
The minimal portfolio, composed of the twenty sample stocks which
had the lowest returns for the ten-year period, indicates the "worst"
performance which could have occurred over this time period. The opti-
mal portfolio, composed of the twenty sample stocks which had the high-
est returns, indicates the "best" performance which could have been ob-
tained during the ten years. All other portfolios will have performances
between these limits. The two market index portfolios include, in one,
the thirty Dow Jones Industrial Average stocks, and in the other the
twenty-five stocks included in the New York Times Industrial Index. They
indicate "par" performance which the portfolio managers should aspire to
exceed. The five random portfolios were selected from the sample stocks
by a simple random selection process to indicate "chance" performance.
The two mutual fund portfolios are those of the only two funds which have
actually employed a buy and hold strategy during the post World War II
period; one invests new funds in equal dollar amounts while the other
buys an equal number of shares of the stocks on its portfolio list. These
portfolios are used as reference portfolios for the computer selected
portfolios which are chosen to provide higher return at the same level
of risk as the reference portfolios. The performance of the computer
selected portfolios is also compared with that of one hundred mutual funds
which did not follow the buy and hold strategy.
This study uses a much larger sample than any other previous study.
The basic sample includes 665 firms. This sample was reduced to 300 for
the final selection runs because this was the largest number that the
computer used for this study could handle at one time. The 1946-1955
time period was used as the data base for a mechanistic security analysis
procedure which. -xtrapolated the 1946-1955 performance into the future.
Three ten-year performance periods, 1956-1965, 1957-1966, and 1958-1967
are used to evo"uate the performance of the portfolios.
In each of the three performance periods the computer selected port-
folios significantly exceeded the performance of the random, mutual
fund, and market index portfolios. In every case the computer portfolios
provided at least twice as much return at the same or lower level of
risk exposure, as measured by the portfolio risk index. This outstanding
and consistent performance was statistically significant at the .01
level, thus virtually ruling out any possibility that this superior
performance was a chance event. The performance of the one hundred
mutual funds was not significantly different from that of the two mutual
fund reference portfolios.
These empirical tests, utilizing a much larger and more represent-
ative sample than any other published study, with a mechanistic security
analysis procedure, provide, for these performance periods, an affirm-
ative answer to the empirical question: Given some method of security
analysis does the Markowitz model provide portfolios which outperform
those selected by other methods?
The mechanistic security analysis procedure used in this study
minimizes the effects of security analysis on the portfolio selection
results. It is possible that experienced security analysts, such as
those usually employed by institutional investors, could provide more
accurate forecasts for use with the Markovitz model which might lead to
even better results.
Chapters Two and Three provide t .-round information on the insti-
tutional investm nt management process and computer assisted decision
making. A survey and synthesis of the theory of portfolio selection is
provided in Chapter Four. Chapter Five presents the results of the sim-
ulation study and discusses some of their implications. Chapter Six
provides a summary of this research project and a discussion of the im-
portant limitations and prospects of computer assisted investment man-
agement decision making. The appendices provide more detailed informa-
tion about the samples and the individual portfolio results.
1. Markowitz, H. M., "Portfolio Selection," Journal of Finance, March
2. Markowitz, H. M., Portfolio Selection, Wiley, 1959.
3. Sharpe, W. F., "A Simplified Model for Portfolio Analysis," Manage-
ment Science, January 1963, 277-293.
4. Tobin, J., "Liquidity Preference As Behavior Toward Risk," Review of
Economic Studies, February 1958, 65-86.
INSTITUTIONAL INVESTMENT AND THE COMPUTER
This chapter provides background information about the institutional
investment decision making process, the increasing importance of institu-
tional investors in the United States, and computer usage within these
Financial institutions act as middlemen in the economy by bringing
together the suppliers and the users of capital funds, thus contributing
to the economic activity of the nation. They provide a convenient medium
for gathering regular and relatively small amounts of personal savings
from many widely scattered individual savers. These funds are then
combined into relatively large amounts of money which can then be made
available, in economical transactions, to business firms who desire to
make real investments. This process of real investment by business firms
is accomplished by means of the financial investment of the institutional
investors as they purchase newly issued debt (bonds) or equity type
(stocks) securities. Even though financial institutions do not always
and only purchase newly issued securities, they still facilitate the
real investment process by actively participating in the secondary market
for already outstanding securities, thus providing the necessary liquidity
for the original individual investors who may later wish to dispose of
their investment securities.
Included among the financial institutions which perform this important
function are: commercial banks, savings banks, trust companies, savings
and loan associations, credit unions, pension funds, life insurance
companies, casualty insurance companies and investment companies. In
this study it is the common stock investments of the institutional
investors which are of primary interest, and the investment companies
are considered to be the most representative single institution of the
Collectively, all of these financial institutions owned or
controlled (exercised investment decision making responsibility)
approximately 30% of the dollar value of all outstanding common stock
in the United States at the end of 1965 [1, p. 726]. This is a much
larger share of the total than the financial institutions accounted for
twenty years ago, and they are expected to own and/or control an even
larger share of the total outstanding common stock in the future.
These financial institutions operated only 18% of all the computers
in the United States in 1966 (measured by value of installed machines)
but they are expected to also greatly expand their share of the computer
total in the relatively near future. If the fact that manufacturing
firms tend to use scientific computers which are faster and more
expensive than the business computers usually used by non manufacturing
firms is taken into consideration, it is now thought that the financial
institutions probably operate one fourth to one third of the total
number of computers installed in the United States [4, p. 194].
The Institutional Investment Process
The institutional investment process is an unending cycle which is
originally triggered by funds which become available for investment. It
proceeds through the steps of forecasting the future, analysis of invest-
ment requirements, formulation of investment policy, search for relevant
alternatives, security analysis, portfolio selection, and portfolio anal-
ysis. This loop is sometimes shortened in actual practice, going from
portfolio analysis to security analysis to portfolio selection and back
to portfolio analysis again, especially if the investment requirements
and policy remain unchanged.
Most institutional investors have regular daily inflows of new funds
which they seek to invest as soon as possible since no return can be
obtained from cash assets. It is often desirable to forecast the amount
which is expected to flow in and out over a particular planning period so
as to be better able to make transactions of an efficient size. In addi-
tion, most of the institutional investors continually make short term
forecasts of the expected amplitude of changes in market rates of interest,
security prices, and stock market indices to guide them in the timing of
their investments. Knowledge about the magnitude and timing of investible
funds enables the decision maker to decide how much effort to expend on
the other steps in the process.
The next step, analysis of the investment requirements, often can be
performed at rather infrequent intervals. Since an almost infinite variety
of securities with different characteristics is available some method of
narrowing the scope of later analyses is needed. Some securities provide
greater income prospects while others provide greater capital gains pros-
pects. The obligations of the institutional investor to its own suppliers
of capital will have a bearing on its need for liquidity and current income
from its portfolio. This in turn will affect the mix of securities which
it will consider for inclusion in its portfolio.
The requirement for liquidity is primarily affected by the requests
for redemption made by investors. Past experience should be useful to
the decision maker in determining the acceptable amount to be kept in
cash and/or in short term securities which are readily convertible into
cash with minimal probability of loss of principal. The requirement for
current income versus capital gains is affected by the opinion of the
investment managers concerning the tax status of investors and their
other sources of income. The requirement for principal stability is
affected by the investment manager's perception of the personality charac-
teristics of the investors and the likelihood that certain securities
might have to be sold at market prices lower than those in effect when
the securities were purchased since losses can be realized only when secu-
rities are sold [11, p. 343].
The ability of the individual investor to risk loss of principal
depends on the size of his portfolio and the nature and magnitude of his
other sources of income. For most investment companies all of their
assets are invested in portfolio securities and there is no other source
of income. If their portfolio should shrink in value, their stockholders
might sell, forcing them to sell portfolio securities and further reducing
the size of the portfolio, in a possibly continuous cycle resulting in the
demise of the company. Apart from this possibility, the likelihood of the
sale of a depressed security depends on the volatility of that security
itself, and the urgency of the need for funds to meet stockholder demands
when the price of such a security is low.
These factors can be evaluated, along with the quality of the manage-
ment team of the investment company, to determine the degree of risk which
should be assumed by the portfolio. The basic portfolio risk is that of
not meeting the stated objectives because the securities which were
purchased did not perform as expected.
The next step in the process is the formulation of the policy which
will be followed in managing the portfolio. The policy is generally a
written statement concerning actions to be taken from time to time in
selecting securities for purchase or sale and in deciding when such
actions will be taken. The policy frequently specifies that only secu-
rities of certain risk classes (typically the top 4 of 9) may be consid-
ered, and requires or prohibits investments in certain industries or
types of securities. The overall character of the investment policy is
usually specified as either aggressive, defensive, or neutral. A defen-
sive policy is one which is designed to minimize the potential losses
from changes in market prices by selecting stable securities, an aggres-
sive policy attempts to maximize potential gains by selecting volatile
securities, while a neutral policy seeks a balanced approach [11, p. 393].
After the broad policy has been formulated it is possible to proceed
to the next step, that of searching for attractive alternative securities
which generally meet the policy requirements. If the policy, for example,
calls for investment in common stocks rated B+ to B- all other securities
can be ignored and only the stocks of these ratings need be further analyzed.
The next step, security analysis, attempts to grade securities which
meet the broad policy specifications and arrive at a valuation for them.
Financial statements provide the basic raw material at this stage for
quantitative analyses which are supplemented by qualitative data which
are primarily concerned with appraising the quality of the management of
the firm being evaluated. The objective of security analysis is to arrive
at some estimates of the firm's future dividend (or interest) payments,
and the probability distribution of these future payments. This valuation
establishes the expected price of each security at the end of some time
horizon relevant to the investor.
The next step, portfolio selection, is the aspect of the process of
primary interest in this study. It uses as inputs the estimate of the
future return from holding the security for some period and the estimate
for the variance of this return plus an estimate of the covariance among
the returns of various securities, to select a diversified portfolio
appropriate for the investment objectives of the investor. The future
return includes the periodic income during the holding period plus (or
minus) the capital gain (or loss) when the security is disposed of at the
end of the period.
The last step, portfolio analysis, is concerned with ex post port-
folio performance in relation to the objectives specified in the policy
statement. It is usually performed periodically and sometimes reveals
securities which have not performed as well as expected. These then bsconc
candidates for sale if securities with better prospects can be found.
The financial institutions which& i.plen- t this process of investment
-i:,n-. -emnt decision .- tend to be rather "- (in terms of total
assets), to use lar' ffs of investment e 1ists, to lit tieir
interest to stocks of comnani.s w:.ich have 7 wnouts of out-
standing stock for which considerable infor.ation is availa7l-, and to
use cormittees to actually mak the policy decision o 7, p. '-33_.
The corittee process ta-es tim e cu~ ulative c aracter of the
investmn t prev l plus thr amount of new fAuns available for
investment affect the speed with which adjustments can be made in the
portfolio as changing conditions might require. The information which
is perceived by the analytical staff and the committee to be both avail-
able and relevant plus their attitudes toward risk affect the entire
Investment companies (mutual funds) are the major type of institu-
tional investor in common stocks for which considerable information is
readily available. Because of this and the belief that they are typical
of all institutional investors in this area of decision making, they are
used as subjects for the empirical tests reported later in this study.
Among the other institutions, pension funds and trust funds have the most
nearly comparable decision situation but limited data are available on
their activities and performance.
Each investment company sets its own policies within the guidelines
specified in the Investment Company Act of 1940 and it has been said that
no two mutual funds are alike in their investment philosophies [3, p. 31].
However, since almost 300 mutual funds currently exist, it is logical to
expect that there will be some similarities which will make it possible
to classify funds into a few groups so that some comparisons may be made.
The Investment Company Act requires diversified investment companies
to diversify at least 75% of their assets with not more than 5% of their
assets invested in the securities of any one issuer. In addition to these
legal constraints, the directors of most investment companies impose
further limitations on the investment policy of their own firm, such as
requiring or restricting investment in certain industries. In practice
most institutional portfolios include more than twenty companies.
The Institutional Investment Environment
Financial institutions have recently been growing at a far faster
rate than non financial firms. When any firm grows it must acquire the
assets necessary for the conduct of its expanding business, and the growth
of non financial firms can therefore be measured primarily by the increases
in physical assets which occur over time while the growth of financial
firms is primarily measured by the increases in financial assets (secu-
rities) they acquire. Thus it can be said the growth of financial firms
requires them to purchase securities while the growth of non financial
firms requires them to sell securities in order to raise the funds with
which investments in physical assets are made [6, p. 478].
Financial institutions have been growing faster than non financial
firms not only because savings have grown absolutely but also because
their share of these growing amounts has risen sharply since many indi-
viduals who previously invested for themselves now do so through the in-
stitutions. In the post World War II period, for instance, a relatively
new type of financial institution, the corporate pension fund, has become
a strong demander of common stocks. Other institutions, such as life
insurance companies, have devoted increasingly larger portions of their
new funds inflows to common stock investments. The investment company
industry has grown from less than half a billion dollars of assets in 1940
to almost forty-five billion dollars at the end of 1967 and much of this
unprecedented funds inflow has been invested in common stocks [3, p. 10].
Since 1958, the financial institutions have been buying, usually from
individuals, more common stock than the total value of net new stock
issues [6, p. 479]. This institutionalization of common stock invest-
ment is expected to continue, as it has for corporate bonds, over the
foreseeable future (in 1900, institutions held only 35% of all of the
outstanding bonds; now they hold about 95%). The financial institutions,
although they owned only 7.6% of the total outstanding common stock in
1900 and 20.5% in 1952, are expected to own approximately 30% by 1975
[5, p. 489]. Common stock investments controlled by financial institu-
tions, mainly trust accounts for which the trustee (usually a bank) has
discretionary or advisory investment powers, are also increasing, and
may bring the total outstanding common stock subject to institutional
investment decision making power near 75% of the total outstanding
common stock in the nation by 1975.
This increasing institutionalization of investment has also been
accompanied by an increase in the absolute number of individual investors
from just over six million in 1952 to slightly more than twenty million
persons in 1965 [10, p. 35]. These individuals tend to hold fewer shares
of any issue than previously was the case while the institutions hold
more; in addition, both classes of investors tend to make transactions
more frequently than had been the case in earlier years. This tendency
toward ever increasing transactions volume has been especially noticeable
during 1968 when several single day trading volume records were esta-
blished and the markets were forced to curtail trading hours so member
firms could try to keep up with the unprecedented volume of paperwork.
Average daily trading volume on the New York Stock Exchange (the major
stock exchange) has been in a long term upward trend which has accelerated
significantly since 1965 [10, p. 63].
Therefore, in spite of the increasing institutionalization of invest-
ment which might be expected to lead to fewer transactions of larger size
each since the institutions do not need to make so many odd lot trans-
actions, total trading volume is increasing rapidly, largely because
an increasing number of small investors are becoming interested in the
stock market. We are now in the third year of this unprecedented and
largely unexpected (by investment banking firms) development which is
exerting considerable pressure on both the investment banking industry,
which handles most of the transactions, and the investment management
industry, which makes most of the investment decisions, to utilize
computers just to keep up with the ever increasing volume of required
If these financial firms follow the same path already taken by the
more sophisticated computer users they will expand their own usage of
computers by increasing the number of applications for which their
computers are used [2, Ch. 25]. A basic reason for the rapid prolifera-
tion of computer applications which has so far been observed is that
presently available computers are approximately one million times faster
at only one hundredth of one percent of the cost of a human clerk
performing arithmetic operations 3, p. 41
Computer Usage by Institutional Investors
Since no published data were available to indicate the extent to
which these financial institutions used their computers for investment
management rather than routine data processing operations, a sample
survey was conducted by Kahl L4] during 1966.
A total of 150 questionnaires were mailed to a random sample of
financial institutions selected from a list of the largest commercial banks,
savings banks, savings and loan associations, life insurance companies,
property and casualty insurance companies, and finance companies located
within the continental United States.
Replies were received from 112 firms, or 74.7% of those querried,
and indicate that computers are indeed quite pervasive, with 85 (75%) of
the firms using at least one computer and five (4.2%) also making regular
use of a service bureau.
Over half of the responding firms (55.9%) have used computers for
3 to 5 years. In spite of this relatively short time, the importance of
the computer to these firms is apparent from the organizational position
of the top computer executive in the firm. Many of these firms (22%)
have created a Vice President for Data Processing position which directly
supervises the computer function while 78% of the firms have the computer
under either a functional Vice President or the Chief Financial Officer
who, in turn, reports directly to the President. In all of these firms
the computer function provides its services to all parts of the firm.
The responding firms reported that they were able, with the computer,
to provide improved services to their customers with increased efficiency
and that new and better (more up-to-date) information is now available
for management decision making purposes.
The survey revealed that only 30.7% of the responding firms now
use computers for portfolio evaluation (analysis) purposes while an-
other 31.8% intend to do so by 1975. Security analysis is now performed
with the aid of computers in 17.0 of the firms while another 34.1%
plan to do so by 1975. These functions were uppermost in the near
future planning of the responding firms, with credit evaluation close
behind. It appears, therefore, that we are on the threshold of much
more widespread computer usage in the financial industry [4, p. 198].
Table 1 presents a detailed summary of the present and expected future
computer usage by responding firms.
Obvious preconditions to widespread use of computers in the invest-
ment management process are the availability of computers, programs for
the various functions such as security analysis and portfolio selection,
and the necessary computer ready data.
Computers have been, and continue to be, available to firms in the
financial industry, and since the majority of them (72.3% in 1965) are
produced by IBM the programs utilized in this study are also available.
The data problem, although not yet completely solved, is apparently well
under control since COMPUSTAT was announced in 1964. As the services
provided by COMPUSTAT are broadened, availability of the hardware, soft-
ware, and data will cease to be limiting factors, leaving only the short-
age of appropriate personnel and the lack of top management understanding,
acceptance, and support as impeding factors to more widespread intensive
and extensive computer usage.
Computers can be employed to assist investment decision makers in
each step of t'* investment process. If any models are used for fore-
SPECIFIC COMPUTER APPLICATIONS BY RESPONDING FIRMS, PRESENT
(in Percentage of respondents reporting)
Specific Computer Application Present (1966)
Interest Calculation 70.5
Deposit Accounting 62.5
Mortgage Accounting 59.1
Installment Loan Accounting 53.4
Premium Accounting 43.2
Portfolio Evaluation 30.7
Float Analysis 28.4
Trust Account Accounting 27.3
Charge Account Accounting 22.7
Credit Evaluation 20.5
Security Analysis 17.0
Source: Kahl [4, p. 196]
casting purposes they can be programmed so it is only necessary to
provide appropriate input data in order to get forecasts. This will
probably result in decision makers having access to these forecasts
faster than was previously possible.
If the analysis of investment requirements can be reduced to an
algorithm, then computers can be programmed to perform this function.
At least one such algorithm is available in published form [11, Chapter
15] but has not yet been programmed for computer use. Once it is, the
decision maker need only supply input data to get the desired outputs.
Once again computers could perform this function faster than presently.
Likewise, the formulation of policy stage might be reduced to an
algorithm so a computer could be employed. This is conceptually and
technically possible now, but has not yet been done. Policies presently
are established by experienced investment personnel who employ large
amounts of personal judgment in this process.
In the search for attractive investment alternatives computers can
be and are now being used to separate out those securities which obviously
do not fit the policy specifications, or some other specified criteria.
This also would speed up the overall process and get information to the
decision makers faster than other methods.
Since considerable mathematical manipulation is required in the
quantitative area of security analysis, computers can be and are now being
used for these calculations, leaving human security analysts more time for
the difficult qualitative judgments. This teamwork should speed up this
phase of the process and also provide better information to the decision
In the portfolio selection phase of the investment process, the
Markowitz model, which is tested by this study, can be used to make
decisions. It is not yet in operational use by any institutional investor,
however. A theoretical proof that the method does work has been provided
by Markowitz .
The last phase, portfolio analysis, requires calculation of the port-
folio return at a given time. Computers can be and are applied to this
The role of the computer is still in a state of flux; it obviously
can be used to perform the more routine functions, and when so employed
will provide more up to date information to the decision makers. Since
the timing of investment is frequently of critical importance the avail-
ability of information sooner than it is presently obtained might result
in purchases at lower prices and later sales at higher prices with
resultant higher returns. This improved performance is likely to more
than cover the expenses of computer usage within the investment process.
Investment management is a specialized type of decision making
process which endeavors to allocate available investment funds among
those few investment securities which, at a given time, appear to offer
the highest probability of achieving the investor's objectives.
The investment process is an unending cycle which includes the
steps of: forecasting the future, analysis of investment requirements,
formation of investment policy, search for relevant investment alter-
natives, security analysis, portfolio selection, and portfolio analysis.
Computers could be used for each of these steps but so far they have
been applied only to security analysis and portfolio analysis functions.
Financial institutions have been increasing in economic importance
in the last few decades and their increasing workload is likely to
encourage them to make more extensive use of electronic computers, first
for routine data processing applications, and then in the more sophisti-
cated applications such as security analysis and portfolio selection.
A model for use in portfolio selection decision making is presented
in Chapter Four and tested in Chapter Five.
1. Cohen, J. B. and Zinbarg, E. D., Investment Analysis and Portfolio
Management, Irwin, 1967.
2. Gibson, E. D., An Introduction to Automated Data Processing, Business
3. Investment Company Institute, Mutual Fund Fact Book, Investment
Company Institute, 1968.
4. Kahl, A. L., "Computer Use in the Financial Industry," Southern
Journal of Business, April 1968, 193-199.
5. Lindsay, J. R. and Sametz, A. W., Financial Management: An Analytical
Approach, Irwin, 1963.
6. Lindsay, J. R. and Sametz, A. W., Financial Management: An Analytical
Approach, Revised Edition, Irwin, 1967.
7. McDiarmid, F., Investing for a Financial Institution, Life Office
Management Association, 19iI.
8. McLaughlin, J., Information Technology and Survival of the Firm, Dow
9. Markowitz, H., Portfolio Selection, Wiley, 1959.
10. New York Stock Exchange, Fact Book, New York Stock Exchange, 1967.
11. Sauvain, H., Investment Management, Second Edition, Prentice-Hall,
COMPUTER ASSISTED DECISION MAKING
This chapter contains introductory information about the use of
decision models and computers in decision making and about their charac-
teristics and limitations, both in general, and in investment management.
Despite the great apparent diversity of problems faced by business-
men there is rather wide applicability and usefulness for computer imple-
mented mathematical models because of the generality of the decision
making process itself.
The interdisciplinary approach which computers have made practical
was first applied to military problems during World War II. After the
war operations researchers turned to business problems and one technique,
linear programming, proved to be very useful during the decade of the
1950's in many business situations.
Perspective on this systems approach to business problem solving is
provided by this chapter.
The Decision Process
In spite of the great diversity of computer applications the methods
of attacking problems with computers show considerable unity because of
the decision process itself. The decision process consists of: the
analytical stage, the prediction stage, the choice stage, and the control
The analytical stage consists of several steps which are concerned
with identifying the problem and clarifying its boundaries. The decision
maker must first search his environment for problems in need of solution,
identify the most important ones, and arrange them in the order of their
importance so the most important ones can be analyzed first. The bound-
aries of the particular problem situation must be defined and clarified
so further analysis can proceed. The goals pertinent to this problem
must be identified and clarified so a new search procedure can be imple-
mented, if necessary. Once the problem area is identified and goals are
clarified, the decision maker needs to search for feasible alternative
solutions to the problem.
The prediction stage consists of several steps which are concerned
with the consequences of all of the alternatives. In order to evaluate
the alternatives, the decision maker must first choose an appropriate
measure of effectiveness which is relevant to his goals. Then he can
proceed to estimate the probable outcomes of all of the most feasible alter-
native solutions to the problem, taking into consideration the various
strategies available to him and to his competitors, and utilizing the
best information which is available concerning the probability of occur-
rence of each alternative and its related payoff.
In the choice stage, the decision aker must put the particular
problem into its overall broad context in terms of the firm's goals and
means, and select the optimal alternative feasible solution to the problem.
To do this he needs to select first an appropriate decision rule consid-
ering not only ends and means but also the quality and extent of the
information which is available. Then he must analyze the outcoes ard
select the best one which is available.
The control stage consists of several steps concerned with t e. i
mentation and evaluation of the decision to select one of the alternatives.
At the time the chosen alternative is implem nted, the decision mak r sets
up a feedback control system which periodically reports on the status of
the implemented alternative. 'ith this information, the d ecsion m r
can evaluate his decision: to see if the price outcor., di' actual?
occur andany ca asvitai fa .7e er::r a:ny
results. -e can also talke correctiv cion, a. ;n iCr..t.
if that soi be :c-s. ar.
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dure based on the decision maker's judgment is needed and in some cases
computers can be programmed to handle these situations while in others
Computers can be used in the decision process to aid human decision
makers in searching their environment for problems and feasible alter-
natives to these problems. They can be used to generate information to
validate models, to estimate probable outcomes of alternative courses
of action, and to control the implementation of decisions by providing
automatic feedback concerning exception conditions.
Models and Their Structure
Models of problem situations are usually helpful to decision makers
in arriving at proper decisions. Any model is merely a representation
of reality which attempts to explain the behavior of some aspect of it
[18, p. 115]. Models, to be useful, must be simplifications of actual
reality. Some amount of simplification is both necessary and desirable
but oversimplification may destroy the predictive capability of the
model [9, p. 33]. It is frequently unnecessary for the model to be
completely accurate since some amount of error in the decision process
is usually tolerable; therefore, the type of model which should be used
in a particular situation depends on the purpose of the decision, and
the degree of accuracy required of the model depends upon the degree of
accuracy which is needed in the results [8, p. 12].
Models may be used for four different and distinct functions: organ-
izing, heuristic, predictive, or mensurative, depending on the particular
problem situation which is to be attacked with the aid of the model. The
model performs an organizing function if it helps the decision maker to
classify and relate disjointed data so as to convey information and reveal
relationships which were not previously perceived. It performs an heuris-
tic function if it helps to explain and predict the results of these rela-
tionships so as to lead to the identification of pertinent variables
within the situation or to the discovery of new facts or methods of oper-
ation. It performs a predictive function if it helps to predict the
results of these interrelationships and if it is possible to verify also
this predictive capability; and it performs a mensurative function if it
is a model of clearly understood relationships so that data obtained
with its help can be used as measures [21, pp. 79-80].
Models can also be classified, according to their major characte-
ristics, into three basic types: iconic, analog, or symbolic. An iconic
model, such as a scale model of an aircraft design, physically resembles
the real world phenomenon which it represents. Models of this type are
difficult to manipulate and may introduce unwanted variables into the
decision process because of the very process of abstraction necessary to
their creation, hence they usually have a rather low degree of predictive
power and usually must be supported by other techniques. Analog models,
such as the hydraulic model of the circular flow of funds in the economy,
make use of one property to represent some other property which is rele-
vant to the decision process. Such models are frequently very useful
with analog computers.
Symbolic models, such as the Markowitz portfolio selection model
which is the subject of this study, are composed entirely of abstract
mathematical symbols which represent the real world situation of interest
to the decision maker. Since symbolic models use mathematical symbols
they are often called mathematical models. They are the most widely used
and versatile decision models and are most useful to decision makers
when used in conjunction with modern and powerful digital electronic
computers since such computers can be used to solve any problem by compu-
tation after it has first been formulated in the form of a mathematical
model [2, p. 109].
A mathematical model may be either descriptive or predictive depend-
ing upon whether or not it has any demonstrated capacity to predict. Even
if only originally descriptive, a model may become predictive after trans-
formation of some of the variables according to the established laws of
mathematics. This manipulative facility of mathematical models can be
used to transform an organizing model into an heuristic one, and thence
into a predictive one, simply by the use of the computer to perform
mathematical manipulation, and quite apart from any intrinsic heuristic
value which may already exist in the model as a result of the creative
genius of the model builder. Whatever the nature of the phenomenon which
is being studied and however complex it may be, the various components of
the problem situation do bear some relationship to each other, and once
the model builder is successful in formulating these relationships
abstractly and precisely, he can apply the full machinery and power of
mathematical analysis to produce, sometimes wondrous, results which may
be far beyond his wildest expectations [14, p. 8].
Before the advent of computers, business decisions were made by
human decision makers who used their best judgment to arrive at decisions.
As time went by and similar problems recurred, the human decision makers
developed methods (programs) for arriving at decisions based upon their
accumulated experience. These were, in fact, models of the particular
decision making process but they were rarely, if ever, written down or
even made explicit in the minds of the decision makers until after World
War II. The concurrent development of research into the decision making
process and the improvement of computers has now made it possible for
man to transfer some of his more routine decision making to the machine.
Some decision models have been programmed for computers and can be used
now, while more complex models must wait for further research results.
The essential characteristics of a model of a business problem
situation are that at least one input variable must be subject to control,
the relationships among and between the relevant variables must be
specified, and the output variable must be an index or measure of value
of alternative solutions to the decision maker. The essential structural
ingredients of computer models are, therefore, the structural equations,
the variables, and the method of solution.
The structural equations of a mathematical model are of four types:
definitional, technological, behavioral, and institutional. They show
the basic structure of the phenomenon which is being modeled. Defini-
tional equations describe an exact interrelationship between two or more
variables. Technological equations describe the results of interactions
of the variables within an essentially technological or physical process,
such as the production function. Behavioral equations describe the
behavior of human beings within the system being modeled and are also
statements of functional relationships rather than identities. It is
sometimes further possible to differentiate the behavioral equations on
the basis of whether or not the behavior is random, and, if it is, then
it can be referred to as stochastic behavior in contrast to deterministic
behavior which is usually much more easily and accurately predicted.
Stochastic behavior can frequently be predicted with tolerable accuracy
as the'resultant of probabilistic events, if information concerning the
determining events and their probability distributions are known. Insti-
tutional equations describe the environmental constraints within which
the decision maker must operate. These constraints may be either exter-
nally imposed, such as by law, or they may be internally imposed restric-
tions, such as those management policies which require diversification.
For investment decision making problems the behavioral and institutional
equations are likely to be most important.
The variables of the model which are included in these structural
equations may be of two major types: endogenous or exogenous. Endogenous
variables are those which are explained by the model itself, they deter-
mine other variables in the model and arc, in turn, determined by other
variables; their values are obtained by the solution of the simultaneous
equations which comprise the model. The values of the exogenous variables
are not determined by the model but are taken as given in the solution
of the simultaneous equations .which comprise the model, hence they are
outside the scope of the model as far as explanation is concerned but
they are necessary in the determination of at least one of the erdog-
enous variables. These exogenous variables are not under the control of
the decision maker whereas the -enous variables may be.
The method used in the solution of most symbolic models is some
mathematical technique which is chosen on the basis of its efficacy and
practicality -2, p. 117P The method may be analytic and make use of
higher mathematics such as the calculus or it may be simply nu rical
if the structure of the model per .its. If computers are to be us-d,
however, the actual method must be numerical, but ,alytic : c
be performl on the compu by numerical mens evn tn'oug i .;:l
not be "sible for hu. s do likeie. r'at sp of t.L;
computer ik-: this poz ibiq ar: 1 onpirabi, :o th:3 lai )
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executives who may have to implement the decisions which have been
reached with the aid of the model [20, p. 35]. One of the major advan-
tages of computer models is that some of the variables can be slightly
changed in the process of sensitivity analysis so the decision maker can
ascertain the effect of such changes on the final result of the model.
Sensitivity analysis capability enhances the usefulness of models and
may also be helpful in the construction of models.
The Model Building Process
The process of model building is really one of formalizing and
making explicit the implicit and perhaps even unstated traditional
models previously used by decision makers. It follows rather closely
the decision process, and can be thought of as consisting of several
stages: the formulation, construction, solution, testing, control, and
use stages [10, p. 18].
In the formulation stage the model builder first establishes the
need for the model. The area of analysis must be carefully defined so
that the construction stage can begin. The construction stage is perhaps
the most important for it is here that the model builder must identify
the controllable and non-controllable elements which may have an effect
on the desired results, ascertain which of these are actually the crucial
ones, then symbolize and relate these in the form of equations so that a
workable model results. The model builder is aided in this endeavor by
analogies, implicit theories, rules of thumb, the analysis of historical
data, and experimentation. Any or all of these sources may help him
establish the relationships of the model [8, p. 47].
In the solution stage a decision rule which is related to the objec-
tive which the model builder seeks must be chosen and applied with an
appropriate method of solution in order to discover if, in fact, the model
will give some workable output information. The value of the solution
depends on how adequately the model represents reality and the adequacy
of the solution depends on the adequacy of the model. No model can be
more accurate than its underlying assumptions, and the more complex the
model the greater the risk of error because the effect of any single
assumption is less easily discernible in the result [16, p. 70]. The
model must then be tested to determine its reliability and validity, and
to discover if it is biased, and, if so, to what extent. The predictive
power of the model can be tested by comparing its predictions based on
old information with events which have actually occurred. If the model
appears to be valid, useful experiments can be performed upon it in the
control stage, to insure that the values of the parameters have not
changed and to set up a procedure for detecting such changes if they
The usefulness of mathematical models as aids to decision making
depends upon whether or not they are administratively practical. They
will tend to be practical if they include all or most of the important
variables in the problem area under analysis, if they characterize the
problem accurately enough to improve upon the previous method or methods
of analysis, and if they yield a solution which is easily interpreted
and justified in terms of the underlying assumptions used [13, p. 300].
The really telling arguments in favor of using decision models are that
physical experimentation is not possible and the model is faster, less
expensive, and/or more accurate than any other methods for solution of
the particular problem at hand.
The research reported in Chapter Five of this study provides a test
of the power, reliability, validity, and practicality of the Markowitz
portfolio selection model.
Important Limitations of Models
The major limitations of models are of a structural, measurement,
or implementation nature. The structural problems may relate to variables
which have either been omitted, or are improperly included, or are simply
unknown. The structural relationships involved in the equation may be
improper, actually unknown, or too complex for formal mathematical state-
ment. The constraints which were used in the formulation of the model
may have changed or they might have been omitted, or perhaps improper
ones were used in the construction of the model. The model may have been
correctly built but the method of solution may have been improperly used,
or an altogether improper technique may have been specified.
The measurement problems may arise as the result of improper scaling,
or from improper measurement techniques, or from inaccurate measurement.
An improper scale may result in measurements which cannot be used for the
intended purpose because they are not sensitive enough to record signi-
ficant changes in the important variables or because they are oversensi-
tive and produce too many data. Improper measurement techniques, even
if used with proper scales, will not provide the data which the model
builder had expected to be able to use. More frequently the measurement
problems arise from inaccurate measurements which are the result either
of errors of omission or observation [7, pp. 242-243]. Measurements may
be accurate but may not have been taken at the appropriate time, or may
not have been taken on the appropriate variable. The majority of the
measurement difficulties can be expected to be the result of observational
errors which may be due to the use of faulty equipment or which result
from the use of the proper equipment under adverse environmental condi-
tions, or which simply are the result of the inability of human beings
to accurately read and record the required data.
Implementation problems usually result from either the attitudes of
the model builders or those of the model users, or both. The model buil-
ders may have oversimplified the problem in order to construct the model
or they may have oversold management on the usefulness of the model which
they have created so that users expect more than the model can deliver.
The users may feel that the model attacks their secure position within
the organization or they may just be adverse to the use of any mathema-
tical technique. Future implementation problems will probably include
communications difficulties which arise between model builders (program-
mers) and users who are not part of the same organization.
Computers and Their Limitations
The modern electronic digital computer is a machine which can read
many items of data, store them, recall them for later use, manipulate
them, and provide the resulting information in a form which can be read
and utilized by the human brain. It can continually perform a series
of repetitive operations without either getting bored or tired, while
humans performing similar operations are likely to become fatigued, at
least [1, p. 60].
The unique feature of the present-day computers which sets them
apart from earlier machines which had been used to aid human decision
makers who needed to perform some numerical calculations is their capa-
bility of accepting and following an internally stored program which
tells the machine what operations to perform, when and where to perform
them, and what to do when it has finished performing them.
Some of the earlier machines were, in fact, only one piece of
machinery, but most of the present computers are actually composed of
several different units and might more appropriately be referred to as
electronic computer systems. Separate units perform the essential func-
tions of input, working memory, auxiliary memory, arithmetic and logic
operations, and output, although frequently some of these functions,
such as input and output, are combined in one physical unit while others,
such as auxiliary memory, are contained in many units (tape drives).
It has been traditional to consider computer applications as falling
into one or the other of two major categories: data processing or scien-
tific computation; but the trend now is toward so-called general purpose
computers which are capable of doing both types of operations. The
typical data processing operation requires large amounts of input and
output but only small amounts of computation, while the typical scientific
operation is the opposite.
The factors which should determine whether or not a particular appli-
cation will be processed by computer include the following: whether or
not the method of solution is known, the frequency of occurrence of the
problem, the amount of work which is required in order to reach the
solution, and the urgency with which the required processing must be
When the method of solution is known it is called an algorithm.
Algorithms which have been translated into computer machine language are
the programs which this study evaluates. The algorithm may be an iter-
ative one in which the solution process proceeds in step by step fashion
until it reaches a point where it cannot improve upon the solution value
after performing another step.
The computer program must anticipate all questions which might arise
during -the processing of the problem since it must instruct the computer
explicitly, and in great detail, just what to do and how to do it
[17, p. 97]. Programs are usually called software to distinguish them
from the machine (hardware) with which they are associated.
A major barrier to the more widespread use of computers has been
the difficulty of communicating with the machine since computers can only
operate on the basis of instructions which are expressed in the binary
mathematical language of the machine, hence programming is the key to
optimum man-machine cooperation in problem solving. Fortunately special
languages have now been developed to facilitate this process. The program-
mer typically now writes the program in one of these languages and feeds
it to another program (a compiler) which automatically translates it
to machine lan1r --e.
TI.- most coronly used special progr- lan uages in the United
States are -.7 A- (a mathematical 1 _age ) which fist became avail-
ble in 1956 and 7. DL (a co rcial 1: -j..) which was create in 1959
at the request of the U. S. gover:_ nt. 7 L- is the nearest thing
to a universal computer language anr is available for 30' of U. S. and
441 of non U. S. computer models -4, pp. 1-16 and 22-23.
However, many programs now in use were not written in either F(
or COBOL, and while they may be working satisfactorily now, they must b
rewritten if the decision maker changes to another model of computer.
The program will be rewritten, in all likelihood, by a programmer other
than the one Iwo wrote the original program, thereby exposing the dci-
sion rakar to all t'e errors ,:ich a 'E- in ther- pr..... i Ic
unusually ga? 1 s cf c I -rs 0 coA
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TMStyp ey Vh Y0 7- :IDS: 1W
Errors in coding are probably the most frequent and include errors
made by the programmer in writing down the various instructions as well
as errors made by key punch operators when punching these instructions
into the IBM cards which are used, in most installations, for original
Experienced programmers make an average of one error for every
thirty instructions they write [5, p. 30]. Although experienced key
punch operators sometimes make errors when punching these program instruc-
tions, these errors usually are located and corrected by key verifying
the cards against the original source documents but this, of course,
doubles the amount of time required for punching. An even more important
problem arises in the keypunching of large amounts of input data; on one
large project it was discovered that 40% of the input data had been
incorrectly transcribed [ll, pp. 169-71].
Although relatively less frequent, program errors of commission,
such as errors in program flow, scaling, or file design, are much more
serious to the program user since they are usually unseen but significant
factors affecting the quality of the output of the program [19, pp. 143-
145]. Errors in the program flow may result in improper calculations or
operations; scaling errors may result in answers which either lack the
required degree of precision or exceed it; while errors in file design
may result in the recording of data which the decision maker does not
need, or cause truncation of some data which are needed.
These kinds of errors can usually be discovered after many computer
runs and most programmers attempt to find and correct all of them during
the debugging phase of computer program creation, so decision makers need
only concern themselves with input errors most of the time.
Still another type of error, which has now been virtually reduced
to the irreducible minimum, is that of machine malfunction. Although
the present computers are much more reliable than the first generation
machines, parts do sometimes wear out and cause malfunctions, most
commonly with the peripheral equipment or external memory devices attached
to the computer which may cause the dropping of a bit from a character
code, but most machines in use today have built-in automatic detection
routines for finding and correcting such errors.
An error in data transmission from one machine to another, which
was a frequent source of trouble, is now almost non-existent since most
computers have automatic routines to accomplish this function so program-
mers need not be concerned with this task, and transmission over longer
distances can now be handled with equipment (using telephone lines) which
has an error rate in transmission of less than one in every ten million
characters transmitted [12, p. 70]. This equipment also has built-in
automatic error detection and correction routines.
Investment Decisions and Computers
Investment decision making is essentially an allocation problem
[3, P. 38] in which the decision maker must choose from among various
investment alternatives those few alternatives which are most likely
to achieve the desired results. There is general agreement on the set
of investment jobs to be accomplished, insufficient resources are avail-
able to do all of them, and there is not enough time to allow an exhaust-
ive and comprehensive search for the optimal combination. Information
concerning outcomes is uncertain, and some ways of combining securities
into portfolios are likely, in retrospect, to be better than others
[6, p. 219].
The problem is to select that set of securities which, on the basis
of available information, appears to provide the highest probability of
achieving the goal over the time horizon involved. This problem can be
solved with the aid of a digital computer and the Markowitz model if
the human decision maker can provide the appropriate input data. The
model requires the computer to perform the same computations that a
human decision maker would make but it can do so much faster while at
the same time considering many more securities for possible inclusion
in the portfolio.
1. Able, R. L., "The Computer Use of Human Beings," Air University
Review, January-February 1965, 59-62.
2. Ackoff, R. L., Scientific Method, Wiley, 1962.
3. Ackoff, R. L., and Rivett, P., A Manager's Guide to Operations
Research, Wiley, 1963.
4. Adams Associates, Computer Characteristics Quarterly, Adams
Associates, January 1966.
5. Bell, W. D., A Management Guide to Electronic Computers, McGraw-
6. Bierman, H., Fouraker, L. E. and Jaedicke, R. K., Quantitative
Analysis for Business Decisions, Irwin, 1961.
7. Brennan, M. J., Preface to Econometrics, South-Western, 1960.
8. Buzzell, R. D., Mathematical Models and Marketing Management,
Harvard University, 1964.
9. Chorafas, D. N., Operations Research for Industrial Management,
10. Churchman, C. W., Ackoff, R. L. and Arnoff, E. L., Introduction to
Operations Research, Wiley, 1957.
11. Fisher, L., "Use of Computers in the Quality Control of Financial
Data," Proceedings of the Business and Economics Section, American
Statistical Association, 1963.
12. Gentle, E. C., Data Communications in Business, A T and T, 1965.
13. Kaufman, G. M., Statistical Decision and Related Techniques in Oil
and Gas Exploration, Prentice-Hall, 1963.
14. Kemeny, J. G. and Snell, J. L., Mathematical Models in the Social
Sciences, Ginn, 1962.
15. Leeds, H. D. and Weinberg, G. N., Computer Programming Fundamentals,
16. Lindsay, F. A., New Techniques for Management Decision Making, McGraw-
17. Martin, E. W., Electronic Data Processing: An Introduction, Irwin,
18. Miller, D. W. and Starr, M. K., Executive Decisions and Operations
Research, Prentice-Hall, 1960.
19. Oakford, R. V., Introduction to Electronic Data Processing Equipment,
20. Saaty, T. L., Mathematical Methods of Operations Research, McGraw-
21. Shuchman, A., Scientific Decision Making in Business, Holt, Rinehart
and Winston, 1963.
22. Simon, H. A., The Shape of Automation, Harper, 1965.
23. Thompson, J. D., et al. Comparative Studies in Administration, Uni-
versity of Pittsburgh Press, 1959.
THE PORTFOLIO SELECTION MODEL
This chapter describes a model of the ultimate phase of the invest-
ment management process, which has been defined as: "the art of combining
in a portfolio of securities those investments which from time to time
appear most likely to meet a proper balance of the various, changing,
and conflicting requirements of the investor" [1, p. v.].
This definition gives primary emphasis to the ex ante selection of
several securities at a time to make up a portfolio and points out the
dynamic nature of the problem in the real world. The model presented
in this chapter is only a first step in what will be, no doubt, a long
trip toward a dynamic theory of portfolio selection because it is concerned
only with portfolio selection at a given point in time. Before attacking
the complex dynamic problem it is wiser to consider a static case whose
solution might then point out the proper path to be followed in attempting
to solve the dynamic case.
Portfolio selection depends upon security analysis for the proper
input data and this, of course, is another problem area deserving of
study, but, at present, it is outside the scope of this research project.
A mechanical security analysis procedure will be used later to test the
model presented here.
There is general agreement among writers on the subject of security
analysis that its essential function is to forecast the return to be
expected from a security and to estimate the degree of risk associated
with this return [11, p. 717; 33, p. 429].
Many different types of securities exist, such as bonds, preferred
stocks, and common stocks, and they number well up in the thousands.
Given some guidelines based upon the investor's goals and resources,
security analysis can screen out large numbers of securities which
would not be suitable for inclusion within the portfolio and concentrate
on only a few hundred candidates which would be likely to qualify for
inclusion in the portfolio.
The portfolio selection process itself can then begin with only a
few hundred (or even less) securities about which the security analysis
procedure has provided some information and arrive at a portfolio of
appropriate size and composition.
This chapter provides a survey and synthesis of the literature on
the theory of portfolio selection.
The Portfolio Selection Problem
The portfolio selection decision problem is to attempt to maximize
return, both periodic income and capital gains, on assets employed
(which are frequently restricted to securities only) while simulta-
neously minimizing the exposure to risk, or holding it within specified
tolerable limits, over some period of time (the investment horizon).
The decision maker must select, from an almost infinite variety of
available securities, those few which have the highest (to him) joint
probability of achieving the desired objectives over the investment
horizon. Every investor is assumed to prefer more return rather than
less, and less risk rather than more; in other words, he is assumed to
be a risk averting return maximizer. Return is maximized by that port-
folio which provides the highest possible expected return for any given
level of risk (uncertainty of achieving the desired return).
The investor must forecast the future return and degree of risk on
the basis of incomplete presently available information and make the
best possible portfolio selection decision that he can at a particular
time, under time pressure, and within the constraints imposed by law,
tradition, and policy.
Periodically thereafter he must (or should) review the portfolio and
make any necessary adjustments which are warranted in view of changing
conditions in the present and changed expectations about the future. Any
such adjustments need to consider the costs involved in effecting changes
in the portfolio and the expected benefits to be derived therefrom.
The Markowitz model allows man-computer cooperation in the selection
of portfolios in the way in which the rational investor himself would
do it, if he could. The computer merely performs the mechanical calcu-
lation parts of the investment process, allowing consideration of many
more alternatives than an unaided human could consider by himself. The
computer follows a mathematical procedure which chooses a set of efficient
ex ante portfolios from which the investor can select the "optimal"
portfolio for his particular situation. The mathematical procedure is
patterned after a recommended financial decision making procedure of
choosing the most important goal for maximization and formulating all
subsidiary goals as constraints [3, pp. 1-15].
Expected Holding Period Return
The holding period return on common stock investment is composed
of dividend income received periodically (usually quarterly) while the
investor holds the security plus the capital gain (or loss) which occurs
when the investor ceases to hold the security. These two types of
return are analogous to the periodic interest payments (usually semi-
annual) received by bondholders and the principal amount which they
receive at maturity. Portfolio holding period return is the weighted
sum of the returns of the component securities where the weights represent
the proportion of the total investible funds invested in each security.
During the post World War II period the trend of stock prices gener-
ally has been upward so most long term common stock investors can reason-
ably expect a capital gain, which can also be reasonably expected to
exceed the dividend income in magnitude. Since there is considerable
agreement concerning the regularity and predictability of dividends, and
because the U. S. tax system favors capital gains, the long term investor
can logically be expected to obtain most of his return from capital gains.
Mathematically, holding period return on common stocks over some
investment horizon can be written as: HPR = DI + CG
Where HPR = Holding Period Return, expressed as a rate or percentage
of original investment,
DI = Dividend Income received during the holding period,
CG = Capital Gain =.Ending Price Original Cost Basis, and
CB = Cost Basis of original investment [18, p. 12].
This formula can be used for both ex ante and ex post analyses.
The ex ante holding period return analysis would require estimates of
the dividend income to be received during the period and the anticipated
capital gain. Ex post analyses need merely to substitute actual dividend
income and realized capital gain for the estimates. Since portfolio
selection is an ex ante decision problem, it is expected holding period
return which is relevant for decision making.
For the purposes of this research study each security in a given
portfolio will have the same holding period and each portfolio analyzed
will have the same holding period (ten years).
Risk and Diversification
Risk is defined as the uncertainty of achieving the investment
objective and it is usually measured by considering the probability of
loss of principal and/or income [24, p. 7]. Therefore the investor's
capacity for risk taking depends on his ability to risk loss of princi-
pal or income. This is affected by the size of his principal, the
magnitude of his other sources of income, and the time remaining for
achievement of his objectives. A loss of dividend income is more like-
ly to result from actions outside the control of the investor (as, for
example, if the board of directors of one of his companies decides to
omit the dividend or reduce it) but realized capital losses, except for
companies which go bankrupt, can only result from the deliberate action
of the investor to sell his securities.
If the institutional investor has a ten-year investment horizon
(holding period), only the prices of portfolio securities ten years
hence are relevant to the problem of risk measurement. It is, therefore,
improper to consider risk except in terms of some time period. A recent
study of all New York Stock Exchange listed stocks for the period
1926-1965 (820 overlapping one-year time periods) indicates that losses
occurred only 8.8% of the time, and there was no ten-year period within
which the investor earned less than 11 per annum compounded annually
[10, p. 3]. These data would seem to indicate that many investors are
overly concerned about potential losses and are not taking as much risk
as they are capable of safely assuming.
Diversification has been the primary policy for coping with risk.
If the estimate of expected return were correct then diversification
would not be necessary except when required by law, tradition, or policy.
Concentration of investment funds might result in maximum return but, at
least in the present state of human knowledge, it is also likely to
maximize risk during the holding period.
A good summary of the heuristic diversification policies which have
been developed by investors can be found in Hayes' textbook [12, pp. 447-
455] which discusses the principles of risk diversification with respect
to several aspects of risk, among which are: time risk, cyclical risk,
financial risk, interest rate risk, purchasing power risk, market risk,
political risk and foreign exchange risk.
The time risk is the secular risk involved in investments in declin-
ing industries and in investments in other industries at what, in retro-
spect, proves to be an inopportune time; cyclical risk is the result of
the differential effects of business cycles on different industries;
financial risk is probably the most important since it refers to the
ability of the issuer of the securities to make periodic payments and
it is these periodic payments which make most securities desirable invest-
ments; interest rate risk refers to changes in asset values which are
caused by changes in the level and term structure of interest rates and
have their principal impact on bonds and other fixed dollar investment
media; purchasing power risk is the uncertainty surrounding the purchasing
power of the periodic income and future capital gains when received;
market risk refers to the uncertainty arising from the psychological
swings in investor sentiment which cause capricious and sometimes wide
price changes of certain types of stocks (such as international oils, life
insurance companies, or airlines); while political risk and foreign
exchange risk refer to losses which might result from expropriation,
devaluation, or fluctuations in foreign exchange rates.
The recommended policy for U. S. investors wishing to minimize the
political risk and foreign exchange risk is to invest only in domestic
firms. The cyclical, time, and financial risks can be minimized by
diversification among different industries and different companies with-
in industries while the effects of interest rate and purchasing power
risks can be minimized by investment in common stocks [12, pp. 447-455].
Another aspect of risk, valuation risk, is not usually referred to
directly in the literature but is really the major reason for diversifi-
cation. The valuation risk [12, pp. 449-450] refers to errors in the
security analysis phase of the investment management process which is
directed primarily at evaluating financial risk. We must expect errors
in security analysis and these errors will obviously affect the port-
folio selection phase but they cannot be entirely avoided and they will
not necessarily cancel out . The real purpose of diversification,
then, is to reduce the impact of these mistakes but diversification will
also dilute the effects of outstanding performance of individual stocks,
with the result that as diversification increases, the probability
increases that portfolio returns will resemble the average [12, p. 447].
Still another type of risk, liquidity risk, can be identified (and
frequently is cited by professional portfolio managers as an important
type of risk). It refers to the losses which may result when portfolio
securities must be liquidated to make payments from the portfolio corpus
to its beneficiaries. This, of course, is a dynamic problem of consider-
able importance to those institutional investors who are required to
make occasional payments from the portfolio which are larger than new
funds inflows. Many institutional investors protect their portfolios
from this type of risk by always keeping some portion of their assets
invested in cash or in Treasury Bills which can easily and quickly be
converted into cash on short notice at predictable prices.
Portfolio S-ectun Th or
Harry M. IMarkcwitz, in a 1952 Journ. of finnc- article entitled:
"Portfolio S elction" proposed a nor:tive theory which exl: .
efficient diversification by risk avetin inv tors 19, pp. 7-1
This theory was later expa d by rkow in his book _13 ; Tbi
 who used it to formulate a pitive theory, and by Charp 0
devised a more efficient c'omputaioral pro cedre.
The Markow/.itz theory treats olding period return (as WAAfin-d pre-
ously) of any individual security as a ranr. is
expected to vary in a random mu r within limits specific y s.c'rity
analysis. Expected return is thern consider. d to b t- : the ticil
expectation (n -an) of the subjective pr2: dillty iStr 'uti i-: of pVs-~ :'
returns. Riskz is T-: asur ed by the statistical var'i'n" of C:xq-.; t'
returns sincp th nor: <1 fluctuatol- ns wich .r taeo b x-, rct :<
the man rtrn valu. ar likely to b- sy:" tric.
F, graI ic'illy illustr' c s security reun a rr v 1
In th d iras, 2:m....
In the d.-..ras, Ajv V& returns for O1r1- s-curit- r arn. plW v" a!-u.j
the harin -1l ax-- wl t- raltive roar. iilit thr- t- r :. will
actu:1a1 i ri .* oft !
and p!. < :0 i ,lr:l I. 1 3 n A F
by th va n n 2 f, .. .......... .... i
caed b ..
t .. Y r : v: h p of c .a : i.c ny:,- .... A ...is.
A pOr A ':::i 1 td1 i c. .- : SCYCo to c (P u f
Sc l with a Y1. ... in. t f tV t . .. in:......, Q A...S
SECURITY RETURNS AS RANDOM VARIABLES
invested in each selected security. Portfolio return is the sum of the
expected returns from each security weighted by the percentage of the
total invested. Portfolio risk is the variance of the portfolio as a
whole. It depends upon the variance of each component security and the
covariance of each security with each and every other security in the
portfolio, weighted according to the amount invested in each security.
The covariance is a key concept in the theory of portfolio selection.
It is defined as the product of the variance (or standard deviation) of
each of the securities and their correlation coefficient. It measures
that part of the total risk which depends on the degree of price corre-
lation between two securities. Two securities which always move up and
down in price together will have a correlation coefficient of +1 while
two securities which always move in opposite directions at the same rate
will have a correlation coefficient of -1. Whenever there is no statis-
tical association between the prices of two securities the correlation
coefficient will be zero. The lower the correlation (including negative
correlation which is lower than positive correlation of small magnitude)
between two securities the greater the diversification of risk. Lower
correlation is advantageous, of course, only when other factors (return)
Since portfolio variance includes the covariances between each pair
of securities included within the portfolio as well as the variance of
each of the component securities individually, the theory provides a
model which maximizes expected return for a given level of risk or mini-
mizes risk for a given level of return by providing a series of accept-
able and efficient portfolios from which the investment decision maker
can then choose the optimal portfolio for his objectives.
Figure 2 graphically illustrates the domain of all the possible
PORTFOLIOS DESCRIBED BY VARIANCE AND EXPECTED RETURN
portfolios that could be obtained from a given set of securities. Each
point within this domain represents a portfolio defined in terms of its
expected holding period return and variance. Expected return is plotted
along the horizontal axis and variance along the vertical axis of the
graph. The shaded area includes the set of acceptable portfolios.
An acceptable portfolio is defined as one which conforms to all
legal, natural, and policy constraints. In the case of a mutual fund
a legal portfolio would have to include at least 20 securities. Natural
constraints include positive investment (no short sales) in each security
and total investment in all securities not more than 100% of investible
funds (no borrowing). Policy constraints might include a requirement
that not more than a certain percentage (say 10%) could be invested in
any one industry no matter how many firms in the industry might other-
An efficient portfolio is defined as an acceptable portfolio which
provides the greatest possible expected return for a given level of risk
or the lowest possible risk for a given level of return. An efficient
portfolio might be found anywhere between and including the lowest risk
and highest return portfolios. Efficient portfolios lie along the bound-
ary (efficient frontier) of the acceptable portfolio set (between points
A and B in figure 2). They are efficient because portfolios above the
line possess lower return at the same level of risk L18, p. 22]. There
is, actually, a continuous spectrum of efficient portfolios along the
efficiency frontier, no one of which is mathematically any better than
the others. Since this is the case the computer program provides a listing
of all of them because the procedure it follows is to first find the
maximum return portfolios; then proceed down the critical line through
all the other efficient portfolios to the minimum risk portfolio.
The critical line is determined by the critical points which indi-
cate the relationship between return and risk. A critical point occurs
each time a security enters or leaves the portfolio set and each time a
constraint either becomes effective or ceases to be effective in deter-
mining the composition of the portfolio. The critical line actually is
a series of parabolic curves, joined at the critical points, which
express the nonlinear nature of the return-risk relationship.
Figures 3 and 4 illustrate a three-security problem with only natural
constraints. Figure 3 identifies the critical points of the trade-off
relationships which exist among the three securities for four possible
portfolio combinations. Figure 4 provides a close-up of the efficiency
frontier (which in mathematical terminology is the critical line) where
point 1 corresponds to point A of figure 2 and point 4 corresponds to
point B of figure 2, and points 2 and 3 represent intermediate portfolios.
As expected from the financial literature on the subject of risk and
return, a close correlation between risk and return is evident with port-
folio 4 providing the highest expected return and the highest risk while
portfolio 1 has both the lowest expected return and risk.
In the direct form so far described the theory requires, as inputs,
an estimate of expected return for each security plus an estimate of the
variance for each security plus an estimate of the covariance for each
pair of securities. For 100 securities, 100 expected returns, 100
expected variances, and 4,950 covariances are needed, for a total of 5,150
input data items. For 1,000 securities, 501,500 data items would be
required and for an analysis of 2,000 securities over two million data
inputs would be required. Obviously, the data preparation requirements
of this direct format seriously impede its practical operation and add to
TOTAL EXPECTED RTUE'I
FIL Lr 3
1THR AV:. '-. SC .T" S
Fortunately, there is a short-cut method for handling the problem
of providing the covariance data inputs. This short-cut was proposed
by Markowitz [18, pp. 96-101] and first proved by Sharpe [26, pp. 277-
293]. Later supporting evidence has been provided by Cohen and Pogue
[6, pp. 166-193], King [13, pp. 139-190] and Feeney and Hester [9, pp.
The short-cut method is called the index format. Its basic charac-
teristic is the tying of individual security estimates to an index
(such as the Dow Jones Industrial Average) so the needed covariances
can be deduced by the computer program rather than be explicitly stated
by the decision maker. Sharpe proved that this procedure gives the same
results as the direct format while drastically reducing computation
costs. It also conforms with the procedure actually followed by many
investors wherein they first forecast the expected market action as
indicated by some well-known index and then make individual security
forecasts in relation to this market estimate.
The theory of the index tie (and its associated computer program)
requires estimates of the expected return (represented by price) and
variance of each security at some future date, along with estimates of
the value of the index and the variance associated with this index value
for the same future date. A least squares regression line (defined by
its slope and intercept) is then fitted to these points. The slope
represents the relationship between the index value and the expected
return of the security while the intercept represents an imaginary value
for expected return if the index should go to zero. This line can then
be used to calculate the covariances of all securities since they are all
related to the index and also it indicates how much of the expected return
will result from market (movement of the index) factors as well as the
100 200 300
DERIVING INDEX TIE PARAMETERS
-- ESTIMATED PRICE
EXPECTED INDEX GAIN
S- I INDEPENDENT GAIN
I CURRENT PRICE
CURRENT INDEX VALUE
USING INDEX TIE PARAMETERS
amount which is expected to result from the effects of other factors.
Figures 5 and 6 illustrate the derivation and use of the index tie
Considerable theoretical research on the Markowitz model has been
carried out by Tobin , Sharpe [26, 27], Fama , Lintner [15, 16],
Baumol , Samuelson [22, 23] and others. There is general agreement
in the literature that the model is useful as a normative construct and
that Markowitz should be considered the father of scientific portfolio
Limitations of the Model
There is still some dispute among statisticians and decision theo-
rists concerning the applicability of statistical theory to decision
making problems when it is not possible to determine the objective
probabilities which are faced by the decision maker. Decision theory
generally distinguishes between risk and uncertainty, defining risk as
applicable to situations in which it is possible to objectively determine
the probabilities associated with particular outcomes (such as gambling
or insurance) and uncertainty as applicable to situations in which this
is not possible.
Portfolio selection is clearly a problem of uncertainty in the
decision theory sense since no one can know what will happen in the
future. Finance literature, however, has always referred to the port-
folio selection problem as one involving risk and it is so considered
throughout this study.
Classical statisticians reject the use of probabilities for the
portfolio selection problem while Bayesian statisticians feel that some-
thing is better than nothing when a decision must be made, and invest-
ment decisions are being made every day. Game theory and Clarkson's
simulation method  provide possible approaches for those who reject
the statistical nature of the Markowitz model.
For those who accept the basic ideas of the Markowitz model its
point in time approach is felt to be a limitation on its practical use-
fulness. Research aimed at applying the Markowitz model to inter-temporal
situations has been conducted by Mossin , Smith [30j, and Cohen and
Elton  and will doubtlessly be an important area of further research.
It is the viewpoint of this author that the single point in time ap-
proach is a necessary precondition to inter-temporal analysis.
Still others object to the use of the mathematical expectation
(mean) and related variance as parameters to describe the probability
distribution. Classical statistics has used this approach for gambling
problems for at least two centuries. Tobin  and Lintner  as
well as Markowitz  have proved that if the investor is concerned
only with two parameters -- return and risk -- then the mathematical
expectation of return and its variance (or standard deviation) are the
appropriate measures to use. Statistical theory would, furthermore,
lead us to use the coefficient of variation as the appropriate risk
measure since the mean returns from different securities are not likely
to be of the same absolute magnitude. However, since both the standard
deviation and the coefficient of variation which relates the standard
deviation to the mean are derived from the variance, there can be no
worthwhile dispute on this aspect of the Markowitz theory.
The strongest criticisms so far made have been directed at other
aspects of the variance. Fama  and Samuelson , working independ-
ently, both attacked the problem posed by Mandelbrot  who discovered
evidence leading to the conclusion that stock prices do not conform to
a normal distribution but to a stable Pareto-Levy distribution which,
unfortunately, has an infinite variance because it is asymptotic. They
proved, however, that the Markowitz model could still be used even if
stock prices do belong to a stable Pareto type probability distribution.
An apparently very promising area for further empirical research is an
investigation of the properties of a rather new probability distribution
-- the Weibull -- which is enjoying increasing popularity in engineering
applications. This distribution, like the normal, is completely described
by two parameters. It fits most observed data distributions and includes
both the normal and the Pareto-Levy distributions as limiting cases. It
is simple and easy to use, but, so far, in the financial area, it has only
been applied to capital budgeting problems .
Another criticism, frequently voiced by portfolio managers, suggests
that they refuse to use the Markowitz model for the wrong reasons. They
argue that risk cannot be represented by variance since that assumes exis-
tence of a symmetric probability distribution and this clearly conflicts
with reality since it is possible to achieve returns greater than 100p
but impossible to lose more than 100% of the funds invested, and there-
fore it is the semi-variance which should be used rather than the variance
to represent risk because it considers only those downward fluctuations
in return which are thought to be most relevant. Those who make this
criticism ignore the statistical fact that samples from any kind of prob-
ability distribution tend to be normally distributed [32, p. 360] and
individual stock price data are samples. Furthermore, Markowitz proved
in his book [18, pp. 188-201 and 287-297] that the semi-variance produces
the same results as the variance over the most relevant part of the crit-
ical line while its computational costs are much higher for all parts of
the line and its returns are lower on those parts of the critical line
where its portfolios dominate those selected by using the variance along
with the mean.
When all aspects of the situation are considered it appears that
the mean-variance parameters are the most useful and are highly likely
to produce results superior to those resulting from the use of any other
combination of parameters, such as: the mean, median, or mode as a return
measure along with standard deviation, semi-variance, range, expected
value of loss, expected absolute deviation, probable loss equal to or
less than zero, or maximum expected loss as risk measures when the
investor's utility function for wealth is nonlinear and the expected
return data are either normally distributed or are symmetrically non-
normally distributed [18, p. 297].
Another limitation of the Markowitz model, according to some indus-
try critics (based on anonymous responses to a mail survey of financial
institutions conducted by the author for this study), is that the mean-
variance methodology does not capture all of the relevant aspects of risk.
This criticism is largely irrelevant since for practical purposes we do
not need a perfect model but only one which can produce better results
than are obtained without it.
All aspects of risk may not even be relevant to the solution of
the problem. Unless the perceived aspects of risk can affect the price
of the stock and/or its dividend yield the investor cannot suffer an
actual loss. If stock price fluctuations (mostly upward, over long
periods of time) are so large that they overpower dividend fluctuations
it is also highly likely that they will greatly exceed any transactions
Liquidity risks are relevant if and only if the investor has a high
probability of being forced to sell securities at an inopportune time.
This possible loss can be hedged against simply by keeping some portion
of total investible funds in cash or Treasury Bills. The portfolio
selection computer program can be set to keep some set percentage of
funds in cash (which will have zero risk) if the investor is and should
really be concerned about, liquidity risk, or it can be used to specify
the appropriate. percentage.
Empirical Tests of the Model
The Markowritz model has so far been subjected to relatively little
empirical test:;r,. It is likely that some financial institutions have
experimented with it but they have not made their results public.
Farrar, in a Ford Foundation Award winning dissertation 3_, com-
pared Markowitz type efficient portfolios with actual mutual fund port-
folios and found the funds to be very close to the efficient portfolios
predicted by the computer. He also found mutual funds :which cla m d to
be risky holding portfolios near the risky end of the efficient st wile
the less risky mutual -'. held lower risk efficient portfolios. He con-
cluded that the model is a relatively 0ood predictor of actual hr or.
Sharpe provi i corroborative evidence for arrar's fi-lir
and also show d ta te riskier mutual in his spir s
folios with a hLi'-r varianc th-n the ri' fr. i hi-
tati m "25 ar. o. 3.-. 1 .- --I __ -7 ; .., r-. n.2a'n.: -y r c t- t*- -.
the di ii 1 Daich poi "p% s v_. .::. ;
as tle full YVr..J..i -1od but ic c. 011 pr.. 1 -
inl x is z fi& n 't i.' n c -. :, .Y .. w :
of 10* M 1 1L.- nliO r 11--`_
All of these previous research projects used small samples of 100
or less stocks. The research reported in the next chapter of this study
utilizes a much larger (665) basic sample and provides also a test of a
surrogate risk measure which, if operationally useful, would further
reduce computational costs.
Implementation of the Model
The Markowitz model is a single period, point in time portfolio
selection algorithm which is most appropriate for investors who follow
a buy and hold investment strategy. At least three mutual funds, and
many trust funds as well as some pension funds utilize this strategy.
Many other institutional investors pursue a more dynamic strategy which
requires periodic portfolio review and frequent transactions.
Financial institutions which have a high degree of portfolio turn-
over may need to reassess the costs and benefits of such transactions
in view of the results presented in the following chapter. Portfolio
turnover should be engaged in only when results superior to the buy and
hold strategy can reasonably be expected.
If the periodic transactions are infrequent the Markowitz model can
be used for sequential decision making by large institutional investors.
The cost of a single computer run depends upon the number of securities
analyzed, the number of corner portfolios, and the method of providing
In the present state of the art of computing, a typical run of 300
securities for an institutional investor, using the IBM Portfolio Selection
Program, would likely cost at least several hundred dollars for computer
time and data preparation.
The electronic computer has made possible the practical application
of a theoretical portfolio selection model first proposed in 1952 by
Harry M. Markowitz. Computer programs for implementing the model have
been available to IBM computer users since 1963 but so far very few
financial institutions have publicly admitted any attempts to use the
It is likely that many institutional investors are not using the
model for the wrong reasons since the model does provide maximal returns
for specified risk levels or minimal risk for specified return levels
subject to legal, traditional, policy and natural constraints.
Computational costs, data unavailability, and lack of managerial
understanding, acceptance, and support have been the major factors
impeding more widespread usage of the model. Computational costs,
although still not trivial, are declining and computer-ready data are
now available at reasonable cost so managerial acceptance seems to be
the major impeding factor at the present time.
It is unlikely that the computer could ever replace man completely
in portfolio selection decision making since the computer programs require
human input information in order to arrive at efficient portfolios. The
computer, however, can serve as an extension of the investment manager's
brainpower by allowing him more time for consideration of important quali-
tative factors and by helping him to consider many more alternatives than
would be possible otherwise. Future man-machine decisions can, therefore,
be much better decisions in terms of realized returns on investment funds.
1. Bates, G. E., Investment Management: A Casebook, McGraw-Hill, 1959.
2. Baumol, W. J., "An Expected Gain-Confidence Limit Criterion for
Portfolio Selection," Management Science, October 1963, 174-182.
3. Beranek, W. A., Analysis for Financial Decisions, Irwin, 1963.
4. Clarkson, G. P. E., Portfolio Selection: A Simulation of Trust
Investment, Prentice-Hall, 1963.
5. Cohen, K. J. and Elton, J., "Inter-Temporal Portfolio Analysis Based
on Simulation of Joint Returns," Management Science, September 1967,
6. Cohen, K. J. and Pogue, J. A., "An Empirical Evaluation of Alter-
native Portfolio Selection Models," Journal of Business, April
7. Fama, E. F., "Portfolio Analysis in a Stable Paretian Market,"
Management Science, January 1965, 404-419.
8. Farrar, D. E., The Investment Decision Under Uncertainty, Prentice-
9. Feeney, G. J. and Hester, D. D., "Stock Market Indices: A Principal
Components Analysis," Chapter 5 in D. D. Hester and J. Tobin, Risk
Aversion and Portfolio Choice, Wiley, 1967.
10. Fisher, L. and Lorie, J. H., "Rates of Return on Investments in
Common Stock: The Year by Year Record," Journal of Business, July
11. Graham, B. et al., Security Analysis: Principles and Technique,
12. Hayes, D. A., Investments: Analysis and Management, Second Edition,
13. King, B. F., "Market and Industry Factors in Stock Price Behavior,"
Journal of Business, January 1966, Stock Prices Supplement, 139-190.
14. Lamb, W. D., "A Technique for Probability Assignment in Decision
Analysis," G. E. Technical Information Series Publication 67 MAL 02,
15. Lintner, J., "Security Prices, Risk, and Maximal Gains from Diver-
sification," Journal of Finance, December 1965, 587-615.
16. Lintner, J., "The Valuation of Risky Assets and the Selection of
Risky Investments in Stock Portfolios and Capital Budgets," Review
of Economics and Statistics, February 1965, 13-37.
17. Mandelbrot, B., "The Variation of Certain Speculative Prices,"
Journal of Business, October 1963, 394-419.
18. Markowitz, H. M., Portfolio Selection: Efficient Diversification of
Investments, Wiley, 1959.
19. Markowitz, H. M., "Portfolio Selection," Journal of Finance, March
20. Morgenstern, 0., "Qui Numerare Incipit Errare Incipit," Fortune,
October, 1963, 142 ff.
21. Mossin, J., "Optimal Multiperiod Portfolio Policies," Journal of
Business, April 1968, 215-229.
22. Samuelson, P. A., "General Proof that Diversification Pays," Journal
of Financial and Quantitative Analysis, March 1967, 1-13.
23. Samuelson, P. A., "Efficient Portfolio Selection for Pareto-Levy
Investments," Journal of Financial and Quantitative Analysis, June
24. Sauvain, H., Investment Management, Third Edition, Prentice-Hall,
25. Sharpe, W. F., Portfolio Analysis Based Upon A Simplified Model of
the Relationships Among Securities, unpublished doctoral dissertation,
26. Sharpe, W. F., "A Simplified Model for Portfolio Analysis," Management
Science, January 1963, 277-293.
27. Sharpe, W. F., "Capital Asset Prices: A Theory of Market Equilibrium
Under Conditions of Risk," Journal of Finance, September 1964, 425-
28. Sharpe, W. F., "Mathematical Investment Portfolio Selection: Some
Early Results," University of Washington Business Review, April 1963,
29. Sharpe, W. F., "Mutual Fund Performance," Journal of Business, Stock
Prices Supplement, January 1966, 119-138.
30. Smith, K. V., "A Transition Model for Portfolio Revision," Journal
of Finance, September 1967, 425-439.
31. Tobin, J., "Liquidity Preference As Behavior Toward Risk," Review of
Economic Studies, February 1958, 65-86.
32. Wallis, W. A. and Roberts, H. A., Statistics: A New Approach, Free
33. Walter, J. E., The Investment Process, Harvard, 1962.
EMPIRICAL EVALUATION OF THE MODEL
This chapter reports the results of the simulation studies performed
with the Markowitz model which indicate that it was able, for the secu-
rities data base and the time periods used in this study, to select port-
folios which provided statistically significantly (at the .01 level)
greater returns at lower levels of risk than any other comparable selec-
tion method tested.
As mentioned in the previous chapter, very little empirical research
has been published so far concerning the potential practical usefulness
of the Markowitz model despite the fact that many financial and academic
institutions possess the necessary computers and have access to the
required programs and basic data.
This study seeks to fill this information gap by comparing the
performance of computer generated portfolios with random, mutual fund,
and market index portfolios in order to evaluate the efficacity of the
portfolio selection model.
The specific primary hypothesis which is tested by this simulation
study is that an institutional investor whose objective is to maximize
holding period return subject to constraints, at an acceptable level of
risk, over a ten-year investment horizon, with either the equal dollar
or equal share buy and hold strategy, could have selected portfolios
with the Markowitz model in 1956, 1957 or 1958, with information which
was available at that time, which were superior to those actually selected.
The simulation results of portfolios selected in 1956, 1957, and
1958 and held unchanged for ten years are used to evaluate the efficacy
of the portfolio selection process by the only criterion which is rele-
vant to investors: actual performance over the holding period.
The procedure followed in this test is similar to that of Friend
and Vickers  who concluded that the Markowitz portfolio selection
procedure does not provide any clues to future performance of selected
securities and that mutual fund investment managers cannot provide per-
formance better than random selection. The t test at the .01 level of
significance will be used to test the null hypothesis of no difference
between the computer selections and the others.
A subsidiary hypothesis which is also tested herein is that an ex
ante risk index based upon Standard and Poor's stock rankings is an
efficient predictor of ex post variability in portfolio returns. If this
test provides support for this method of handling risk it will provide
the investment community with a significant and relatively inexpensive
extension of the Markowitz model.
The Data Base
The data base used in this study is the annual basic COMPUSTAT
industrials service for the years 1965, 1966, and 1967. This service
consists of one large magnetic tape file for each of the three years,
which contains twenty years of annual financial data on nine hundred
large industrial firms of interest to institutional investors.
The COMPUSTAT service is the only comprehensive computer sensible
data base presently available. It was created in 1962 by Standard
Statistics Company, a subsidiary of Standard and Poor's Corporation,
and is available, for a fee, to any interested investor. Since it was
created in 1962 and does not contain any companies which might have been
bought by investors prior to 1962 which subsequently went bankrupt it
might be somewhat biased. It is not possible, of course, to estimate
exactly how much upward bias there might be in portfolios selected from
this data base but any such bias, if present at all, is not expected to
significantly affect the results of this simulation study since the insti-
tutional investors usually concentrate their investment funds in the
stocks of large well-known firms which rarely go bankrupt.
Many mergers did take place over the 1946-1967 time span covered by
this study and, even though an investment might have been originally made
in a merged company, the simulations reported herein report the name of
the surviving firm only.
All of the sixty individual data items for each firm contained in
the COMPUSTAT data base were not needed for this study, of course, and
only the annual dividends paid, high price for the year, low price for
the year, and closing price for the year were used. These per share
data items on the tape had been adjusted for all stock splits and stock
dividends. Prices on the tape were rounded to the nearest integer and
dividends were carried to two decimal places on the tape. All of these
data items were used as found on the tapes and their accuracy is warranted
by Standard Statistics Company. These data were retrieved from COMPUSTAT
with the IBM Financial Analysis Program which printed out the required
information for each company. It is assumed that no unintentional
biases or errors were introduced at this stage of the study.
Since the portfolio selection program cannot consider more than 300
stocks at one time because of computer memory size limitations the orig-
inal 900 company data file had to be reduced. The first screening was
accomplished by printing out, for all 900 firms, the data for the period
1946-1955 to see if the files on some companies were incomplete. As
expected, some data for some of the companies was not available for this
period of time and a sample of 655 companies was obtained in this manner.
Ten additional firms, from industries such as railroads and public
utilities, which were not included in the COMPUSTAT tape, were added to
this sample because their securities were held by portfolios which were
intended to be used for reference purposes. The necessary data for these
firms were obtained from the standard sources such as Moody's manuals and
the Standard and Poor's Stock Guide. The 665 companies, selected in this
manner, constitute the basic sample used in this study, and these
companies are listed in Appendix A.
The second screening was accomplished by dividing the basic 665
company sample into three groups of approximately equal size. Each of
these groups was then run through the portfolio selection program which
had been set to select the 100 "best" stocks of each group on the basis
of ex post holding period return for the 1946-1955 period. These 300
companies constitute the reduced sample. They are listed in Appendix B.
Since it was desired to test the practical applicability of the
Standard and Poor's Stock Rankings as risk surrogates, each stock in the
basic sample was assigned to one of eight risk classes according to its
Standard and Poor's ranking at the end of 1955.
The ranking is assigned by the investment advisory service to each
company whose record is sufficiently stable to qualify it for ranking.
It is assigned by means of a mathematical and judgmental process which
uses eight years of earnings per share and dividends paid data, adjusted
for non-recurring items, as basic inputs.
It is published monthly in the Standard and Poor's Stock Guide and
represents an easily obtainable and ostensibly objective rating which can
reasonably be expected to be useful to investors generally and users of
the Markowitz model in particular since it is generally assumed in the
financial literature that earnings or dividends (or both) determine stock
prices and the Standard and Poor's ranking is based on precisely this
At the present time, although the COMPUSTAT data base is produced by
the same company, the Standard and Poor's ranking is not included on the
COMPUSTAT tapes. Hence, it was necessary to obtain this information from
the Standard and Poor's Stock Guide. Table 2 indicates the number of
stocks from both the basic and reduced samples which are included in
each risk class.