PORTFOLIO SELECTION
EFFICIENT DIVERSIFICATION OF INVESTMENTS

by
HARRY M. MARKOWITZ
John Wiley & Sons, Inc., New York
Chapman & Hall, Limited, London
1959
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TABLE OF CONTENTS

Chapter  Page 
Preliminary Pages

PART I. INTRODUCTION AND ILLUSTRATIONS

1.  Introduction
2.  Illustrative Portfolio Analyses

PART II. RELATIONSHIPS BETWEEN SECURITIES AND PORTFOLIOS

3.  Averages and Expected Values 37 
4.  Standard Deviations and Variances 72 
5.  Investment in Large Numbers of Securities 102 
6.  Return in the Long Run 116 

PART III. EFFICIENT PORTFOLIOS

7.  Geometric Analysis of Efficient Sets 129 
8.  Derivation of E, V Efficient Portfolios 154 
9.  The Semi-Variance 188 

PART IV. RATIONAL CHOICE UNDER UNCERTAINTY

10.  The Expected Utility Maxim 205 
11.  Utility Analysis over Time 243 
12.  Probability Beliefs 257 
13.  Applications to Portfolio Selection 274 
Bibliography 305 
Appendices
   A. The Computation of Efficient Sets
   B. A Simplex Method for Portfolio Selection
   C. Alternative Axiom Systems for Expected Utility
309 
Index 341