Fast Quadratic Programming for Mean-Variance Portfolio Optimisation

Abstract

In this paper, a vectorised quadratic convex optimisation algorithm based on Matlab's quadprog built-in function is proposed. We target specifically a classic problem confronted by portfolio analysts, that of optimising asset allocation when choosing among several asset classes, in the context of Markowitz's modern portfolio theory. Simulating return trajectories for several asset classes, we formulate the optimisation routine in such a way that is able to handle multiple scenarios at the same time, instead of on a one-by-one basis, reducing computational times significantly, without introducing observable estimation errors. A sensitivity analysis is offered with respect to the optimal batch size.