Modern portfolio theory

This chapter reviews Markowitz's work on modern portfolio theory, and covers portfolio optimization techniques that designed to cope with the problems of modern portfolio theory and/or tailor-made for certain investors' demands. The groundbreaking insight of Markowitz was that the risk/return profiles of single assets should not be viewed separately but in their portfolio context. In particular, the risk/return profile of an efficient portfolio can be expressed in terms of a linear combination between the global minimal variance (GMV) portfolio and any other efficient portfolio. The covariance between these two portfolios equals the variance of the minimum variance portfolio. The chapter outlines the theoretical portfolio concepts. The sensitivity of the optimal solutions for mean-variance portfolios with respect to the utilized expected returns is per se not a flaw of the approach proposed by Markowitz, but rather an artifact of the quadratic optimization for deriving the portfolio weights.