Mean-Variance Analysis in Portfolio Choice and Capital Markets

In 1952, Harry Markowitz published "Portfolio Selection," a paper which revolutionized modern investment theory and practice. The paper proposed that, in selecting investments, the investor should consider both expected return and variability of return on the portfolio as a whole. Portfolios that minimized variance for a given expected return were demonstrated to be the most efficient. Markowitz formulated the full solution of the general mean-variance efficient set problem in 1956 and presented it in the appendix to his 1959 book, Portfolio Selection. Though certain special cases of the general model have become widely known, both in academia and among managers of large institutional portfolios, the characteristics of the general solution were not presented in finance books for students at any level. And although the results of the general solution are used in a few advanced portfolio optimization programs, the solution to the general problem should not be seen merely as a computing procedure. It is a body of propositions and formulas concerning the shapes and properties of mean-variance efficient sets with implications for financial theory and practice beyond those of widely known cases. The purpose of the present book, originally published in 1987, is to present a comprehensive and accessible account of the general mean-variance portfolio analysis, and to illustrate its usefulness in the practice of portfolio management and the theory of capital markets. The portfolio selection program in Part IV of the 1987 edition has been updated and contains exercises and solutions.

Foreword. Preface to Revised Reissue. Preface. PART I: THE GENERAL PORTFOLIO SELECTION MODEL. 1. Portfolio Selection Models. 2. The General Mean-Variance Portfolio Selection Model. 3. Capabilities and Assumptions of the General Model. PART II: PRELIMINARY RESULTS. 4. Properties of Feasible Portfolio Sets. 5. Sets Involving Mean, Variance, and Standard Deviation. 6. Portfolio Selection Models with Affine Constraint Sets. PART III: SOLUTION TO THE GENERAL PORTFOLIO SELECTION MODEL. 7. Efficient Sets for Nondegenerate Models. 8. Getting Started. 9. Denegerate Cases. 10. All Feasible Mean-Variance Combinations. PART IV: SPECIAL CASES. 11. Canonical Form on the Two-Dimensional Analysis. 12. Conical Constraint Sets and Efficiency of the Market Portfolio. PART V: A PORFOLIO SELECTION PROGRAM. 13. Program Description (By G. Peter Todd). Appendix: Elements of Matrix Algebra and Vector Spaces. References. Index.