Title: Investment management and the computer; limitations and prospects
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Title: Investment management and the computer; limitations and prospects
Physical Description: xv, 415 leaves. : illus. ; 28 cm.
Language: English
Creator: Kahl, Alfred Louis, 1932-
Publication Date: 1969
Copyright Date: 1969
 Subjects
Subject: Investments -- Management   ( lcsh )
Electronic data processing -- Investments   ( lcsh )
Finance, Insurance, and Real Estate thesis Ph. D
Dissertations, Academic -- Finance, Insurance, and Real Estate -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
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Thesis: Thesis -- University of Florida.
Bibliography: Bibliography: leaves 411-415.
Additional Physical Form: Also available on World Wide Web
General Note: Manuscript copy.
General Note: Vita.
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Bibliographic ID: UF00097763
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000574440
oclc - 13867706
notis - ADA1806

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INVESTMENT MANAGEMENT AND THE COMPUTER:
LIMITATIONS AND PROSPECTS











By

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
1969













ACKNOWLEDGMENTS

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.












PREFACE

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


ACKNOWLEDGMENTS ii

PREFACE iii

LIST OF TABLES vii

LIST OF FIGURES xii

ABSTRACT xiii

1 INTRODUCTION 1

2 INSTITUTIONAL INVESTMENT AND THE COMPUTER 9

Introduction 9

The Institutional Investment Process 11

The Institutional Investment Environment 16

Computer Usage by Institutional Investors 19

Summary 24

References 25

3 COMPUTER ASSISTED DECISION MAKING 26

Introduction 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

References 46






4 THE PORTFOLIO SELECTION MODEL 48

Introduction 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

Summary 75

References 76

5 EMPIRICAL EVALUATION OF THE MODEL 79

Introduction 79

Hypotheses 80

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







Summary

References

6 SUMMARY AND CONCLUSIONS

Introduction

Institutional Investment and Computers

Investment Decisions and Computers

The Markowitz Model

Empirical Tests

Implications

Limitations

Prospects

Conclusions


References

COMPANIES INCLUDED IN

COMPANIES INCLUDED IN

EQUAL DOLLAR STRATEGY

EQUAL SHARES STRATEGY

EQUAL DOLLAR STRATEGY

EQUAL SHARES STRATEGY

EQUAL DOLLAR STRATEGY

EQUAL SHARES STRATEGY

BIBLIOGRAPHY


BASIC SAMPLE

REDUCED SAMPLE

PORTFOLIOS, 1956-1965

PORTFOLIOS, 1956-1965

PORTFOLIOS, 1957-1966

PORTFOLIOS, 1957-1966

PORTFOLIOS, 1958-1967

PORTFOLIOS, 1958-1967


131

133

134

134

135

137

138

140

143

145

147

149

151

152

177

189

226

263

300

337

374

411












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
RETURN 130

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

vii







LIST OF TABLES (Continued)


PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO


1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965

1956-1965


RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,


47 PORTFOLIO 0 1956-1965 RESULTS,


EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL


DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR


STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY


DOLLAR STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY


viii


200

203

205

207

209

211

213

216

218

220

222

224

227

229

231

233

235

237

240

242

244

246

248

250

253

255

257






LIST OF TABLES (Continued)


PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO


1956-1965

1956-1965

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966


RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,

RESULTS,


EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL

EQUAL


SHARES STRATEGY

SHARES STRATEGY

DOLLAR STRATEGY

DOLLAR STRATEGY

DOLLAR STRATEGY

DOLLAR STRATEGY

DOLLAR STRATEGY

DOLLAR STRATEGY

DOLLAR STRATEGY

DOLLAR STRATEGY

DOLLAR STRATEGY


DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

SHARES

SHARES

SHARES

SHARES

SHARES

SHARES

SHARES

SHARES


STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY


259

261

264

266

268

270

272

274

277

279

281

283

285

287

290

292

294

296

298

301

303

305

307

309

311

314

316






LIST OF TABLES (Continued)


75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100


PORTFOLIO I

PORTFOLIO J

PORTFOLIO K

PORTFOLIO L

PORTFOLIO M

PORTFOLIO N

PORTFOLIO O

PORTFOLIO P

PORTFOLIO Q

PORTFOLIO A

PORTFOLIO B

PORTFOLIO C

PORTFOLIO D

PORTFOLIO E

PORTFOLIO F

PORTFOLIO G

PORTFOLIO H

PORTFOLIO I

PORTFOLIO J

PORTFOLIO K

PORTFOLIO L

PORTFOLIO M

PORTFOLIO N

PORTFOLIO 0

PORTFOLIO P

PORTFOLIO Q


1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1957-1966

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967


101 PORTFOLIO A 1958-1967 RESULTS, EQUAL SHARES STRATEGY


RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL


SHARES

SHARES

SHARES

SHARES

SHARES

SHARES

SHARES

SHARES

SHARES

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR

DOLLAR


STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY


318

320

322

324

327

329

331

333

335

338

340

342

344

346

348

351

353

355

357

359

361

364

366

368

370

372

375






LIST OF TABLES (Continued)


102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117


PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO

PORTFOLIO


1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967

1958-1967


RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL

RESULTS, EQUAL


SHARES

SHARES

SHARES

SHARES

SHARES

SHARES


STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY

STRATEGY


SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY

SHARES STRATEGY


377

379

381

383

385

388

390

392

394

396

398

401

403

405

407

409












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



By

Alfred Louis Kahl, Jr.



June 1969



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

future.

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


xiii







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

support.

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

xiv






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

is refuted.

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

their decisions.

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

activities.














CHAPTER 1

INTRODUCTION

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.

1





2

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





3

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 [1] and later expanded by him in 1959

[2]. The mathematical procedure was, at that time, too complex (for even




4

the largest computers then available) to apply to practical problems.

The theory has been extended even further by Tobin [4] and Sharpe [3],

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

traders.

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





5

selected portfolios, an ex post optimal portfolio, and an ex post minimal

portfolio.

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




6

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





7

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.




8







References

1. Markowitz, H. M., "Portfolio Selection," Journal of Finance, March
1952, 77-91.

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.













CHAPTER 2

INSTITUTIONAL INVESTMENT AND THE COMPUTER

Introduction

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

institutions.

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

9




10

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

entire group.

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




12

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





13
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





15

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 process.

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





17

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





18

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

bookkeeping.

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





20

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-













TABLE 1

SPECIFIC COMPUTER APPLICATIONS BY RESPONDING FIRMS, PRESENT

(in Percentage of respondents reporting)

Specific Computer Application Present (1966)

Interest Calculation 70.5

Payroll 69.3

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


AND FUTURE



Future (1975)

83.0

89.3

71.6

83.0

62.5

59.1

62.5

46.6

43.2

31.8

31.8

51.1


Source: Kahl [4, p. 196]





22

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

makers.

In the portfolio selection phase of the investment process, the

Markowitz model, which is tested by this study, can be used to make





23

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 [9].

The last phase, portfolio analysis, requires calculation of the port-

folio return at a given time. Computers can be and are applied to this

task.

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.













Summary

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.













References

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
Press, 1966.

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
Jones-Irwin, 1966.

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,
1959.













CHAPTER 3

COMPUTER ASSISTED DECISION MAKING

Introduction

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

stage.

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-





28

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.
.... er-1- :




a1" )"l er' ,r- i .. . .. :' ..'. i"... ............
end res '.s 7f a r 01D

able

the an: .. :

n 1





Lpaf o ;





29

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

they cannot.

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





31

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




32

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





33

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-




34

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 )

problem by .:... .. ei-tr f.n Ta i. ra o- a .i.t t c; th h- . .. 1 M 7 u-.... 7 ,

co. 3 i 0 A.. .'... fo hi 'p c p%" : . a fi










spi'ic *i 2; m '- L ... ". ** .
mlt~- i i-: i , ~ .: \' : -": "



bs,~~-

0~




35

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




37

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

should occur.

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





39
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





41

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

accomplished.

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





42

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


proc t.h f. j- 1 cNo r a ..-. .. if

somet!ir is wit th e Cc Y w w c is ,nloo-A "f.. a .....ain




so .... .. i a itv C 1 .. Oz t. n '


sio- n. n Q pn : ii'',Pr r-

TMStyp ey Vh Y0 7- :IDS: 1W




u 7
q 7sofAY





43

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

computer input.

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





44

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.













References

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-
Hill, 1957.

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,
Reinhold, 1958.

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,
McGraw-Hill, 1958.

16. Lindsay, F. A., New Techniques for Management Decision Making, McGraw-
Hill, 1958.

17. Martin, E. W., Electronic Data Processing: An Introduction, Irwin,
1961.





47

References (Continued)

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,
McGraw-Hill, 1962.

20. Saaty, T. L., Mathematical Methods of Operations Research, McGraw-
Hill, 1959.

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.














CHAPTER 4

THE PORTFOLIO SELECTION MODEL

Introduction

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

48





49

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
CB

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].





53

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.





55

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,





56

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 [20]. 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





57
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

[31] 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 A


RELATIVE RISK


RETURN


SECURITY B


RELATIVE RISK


RELATIVE RISK


SECURITY C

-H
H

0
0


RETURN
FIGURE 1


SECURITY RETURNS AS RANDOM VARIABLES


RETURN





60

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)

are equal.

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




61























B



A









EXPECTED RETURN


FIGURE 2

PORTFOLIOS DESCRIBED BY VARIANCE AND EXPECTED RETURN






62

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-

wise qualify.

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.




63

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

its cost.










10






5C


TOTAL EXPECTED RTUE'I


FIL Lr 3


CRITICAL POIPTTS


1THR AV:. '-. SC .T" S


.05


1
~~----^-----^- --.





65

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.

110-138].

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












LINE OF
BEST FIT


$150




$100




$50


100 200 300


INDEX VALUE


FIGURE 5

DERIVING INDEX TIE PARAMETERS










-- ESTIMATED PRICE
DEVIATION
EXPECTED INDEX GAIN
S-- EXPECTED
S- I INDEPENDENT GAIN


I I
I CURRENT PRICE
I I
I I


100


200


CURRENT INDEX VALUE


300 l
INDEX
CHANGE


INDEX VALUE
INDEX
DEVIATION


FIGURE 6


USING INDEX TIE PARAMETERS


PRICE ESTIMATES
AND DEVIATIONS


$150


$100 4


$50





67

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

parameters.

Considerable theoretical research on the Markowitz model has been

carried out by Tobin [31], Sharpe [26, 27], Fama [7], Lintner [15, 16],

Baumol [2], 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

selection.













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 [4] 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 [21], Smith [30j, and Cohen and





69

Elton [5] 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 [31] and Lintner [16] as

well as Markowitz [18] 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 [7] and Samuelson [23], working independ-

ently, both attacked the problem posed by Mandelbrot [17] 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





70

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 [14].

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





71

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

cost effects.

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--`_


,W





73

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

data inputs.

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.














Summary

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

model.

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.













References

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,
5-18.

6. Cohen, K. J. and Pogue, J. A., "An Empirical Evaluation of Alter-
native Portfolio Selection Models," Journal of Business, April
1967, 166-193.

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-
Hall, 1962.

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
1968, 291-316.

11. Graham, B. et al., Security Analysis: Principles and Technique,
McGraw-Hill, 1962.

12. Hayes, D. A., Investments: Analysis and Management, Second Edition,
Macmillan, 1966.

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,
1967.

15. Lintner, J., "Security Prices, Risk, and Maximal Gains from Diver-
sification," Journal of Finance, December 1965, 587-615.





77

References (Continued)

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
1952, 77-91.

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
1967, 107-122.

24. Sauvain, H., Investment Management, Third Edition, Prentice-Hall,
1967.

25. Sharpe, W. F., Portfolio Analysis Based Upon A Simplified Model of
the Relationships Among Securities, unpublished doctoral dissertation,
UCLA, 1960.

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-
442.

28. Sharpe, W. F., "Mathematical Investment Portfolio Selection: Some
Early Results," University of Washington Business Review, April 1963,
14-27.

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.





78

References (Continued)

32. Wallis, W. A. and Roberts, H. A., Statistics: A New Approach, Free
Press, 1956.

33. Walter, J. E., The Investment Process, Harvard, 1962.













CHAPTER 5

EMPIRICAL EVALUATION OF THE MODEL

Introduction

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.













Hypotheses

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 [5] 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





82

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.













The Samples

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.













Risk Classes

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

information.

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.




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