In 1952, Markowitz published an article, Portfolio Selection , in The Journal of Finance, which became the foundation for modern portfolio analysis. His model of portfolio selection is known today as Mean-variance Criterion (hereafter referred to as MVC or sometimes MV). Since then, many results about how to construct the MV-efficient portfolios have been published. As a portfolio selection model, the Mean-Variance is a quantitative treatment of the trade-off between profit and risk. Some of the results we present in this thesis follow closely the articles “ Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis ”, written by M. C. Steinbach, in Siam Review, Volume 43(2001), No. 1, pp. 31–85, and On the Utility Theoretic Foundations of Mean-Variance Analysis by David P. Brown which appeared in The Journal of Finance, Volume 32, No. 5, pp. 1683–1697. Although this thesis is primarily based on those two articles, many of the proofs are redone by the author with details. The preliminaries needed are introduced in chapter one. In chapter two, we present the most frequently used measures of risk, and we give some of the reasons why some are preferred to others. In section three of this chapter we explore the use of efficiency criterion for a preliminary screening of investments. This allows us to introduce the Mean-variance model as an efficiency criterion. The chapter three is devoted to the Mean-Variance model, while the chapter four is devoted to the Expected Utility model.
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