The Use of Least Squares in the Optimization of Investment Portfolios

Abstract

An investment manager can solve portfolio optimizations problems in many different ways. However, he needs to be very careful when it comes to selecting optimization algorithms because the performance can be very different especially when the global universe of assets is large. We will in this paper show that the traditional Quadratic Programming (QP) mean-variance portfolio optimization problem can successfully be expressed as a Least Square (LS) problem when the return matrix is either square or column dominant.

Keywords: portfolio theory, optimization, QP, LS

JEL Classification: G00, G1