Mathematical Programming of Portfolio Selections

The purpose of this paper is to analyze and explain, by reference to empirical data, some of the recent work done in this area by Dr. Harry Markowitz under the sponsorship of the Cowles Commission (Cowles Commission Discussion Papers in Economics Nos. 294, 2005, and 2019. Also, “Portfolio Selection,” Journal of Finance, March 1952.). This article is divided into four parts. Part I contains a heuristic introduction to the basic problem together with a mathematical statement of Markowitz's theory of portfolio selection and its basic assumptions. Part II contains a discussion of some of the problems involved in formulating probability beliefs for available investment opportunities. In Part III, the selection technique is demonstrated by application to a very simplified case, and many of the problems involved in more complex cases are brought out. The final section contains a summarization and critique of the theory, its limitations, and its possibilities as a guide to practical decision-making.