Recent Advances In Portfolio Optimization

Abstract

This article presents the formulation of the portfolio selection problem, the issue of estimation errors and their impact on mean-variance optimization (MVO), and the use of MVO for portfolio construction. Most economic studies of investor behavior start with a model of investor's preferences typically represented as a utility function of the investor's wealth. After choosing a utility function, we can derive optimal decisions for a rational investor who would try to maximize the expected utility of his or her decisions. Markowitz' theory of mean-variance optimization reduces the problem of portfolio selection into a trade-off between the mean return of the portfolio and its variance. The MVO formulation is consistent with non-quadratic utility maximization only when the returns can be assumed to follow a multi-dimensional elliptical distribution. MVO and its multitude of variations can be viewed as mathematical approximations of the true expected utility maximization problem rather than simplistic trade-offs on two portfolio characteristics that are disconnected from rational investor behavior. The alternative formulations involve the replacement of the variance of the portfolio return with a different measure of risk in the statement of the trade-off function used in optimization. Optimizing portfolios using an objective function that combines expected return with mean absolute deviation are relatively simple as they can be expressed in terms of a linear optimization problem.