Parametric Support approach for solving Mean-Variance problem under general constraints

Abstract

The intuitive and natural formulation of the Mean-Variance (MV) model has attracted the attention of researchers over the years. This model is typically presented as a constrained Quadratic Problem (QP), although the practical aspects of investment often require risk tolerance to be considered. In such cases, Parametric Quadratic Programming (PQP) is employed to explore all optimal solutions on the efficient frontier. In this paper, we propose a novel approach for solving the portfolio optimization problem of the mean-variance model. This problem is considered in its parametric formulation under general linear equality constraints with bounded assets. The proposed algorithm iteratively derives the exact efficient frontier by calculating all corner portfolios as a function of the risk aversion parameter. Finally, we test the computational performance of our algorithm in comparison with two state-of-the-art approaches using a set of real benchmarks. The results demonstrate the effectiveness of our approach in solving such problems and in identifying the efficient frontier. Additionally, considering large-scale randomly generated problems with dense covariance matrices, we show that our algorithm can efficiently solve this class of problems in a reasonable computation time.