A Linear Programming Approximation for the General Portfolio Analysis Problem

Abstract

Almost twenty years ago, Markowitz [4] first suggested that portfolio selection be regarded as a parametric quadratic programming problem. Risk is stated in terms of the predicted variance of portfolio return — a function that is quadratic in the decision variables (the proportions of the portfolio invested in various securities). All other functions (e.g., expected return) and constraints are assumed to be linear. The objective is to find the set of efficient feasible portfolios. A portfolio is feasible if it satisfies a set of relevant linear constraints; it is efficient if it provides (1) less variance than any other feasible portfolio with the same expected return and (2) more expected return than any other feasible portfolio with the same variance.