Sensitivity analysis and calibration of the covariance matrix for stable portfolio selection

Abstract

We recommend an implementation of the Markowitz problem to generate stable portfolios with respect to perturbations of the problem parameters. The stability is obtained proposing novel calibrations of the covariance matrix between the returns that can be cast as convex or quasiconvex optimization problems. A statistical study as well as a sensitivity analysis of the Markowitz problem allow us to justify these calibrations. Our approach can be used to do a global and explicit sensitivity analysis of a class of quadratic optimization problems. Numerical simulations finally show the benefits of the proposed calibrations using real data.