A New Diagnostic Approach to Evaluating the Stability of Optimal Portfolios

Abstract

We introduce a new quantitative approach that can be used as a diagnostic tool for measuring the stability of optimal portfolio weights for a very general set of mean-variance optimization methods. We present a derivation of the approach within a numerical analysis framework and demonstrate this method’s benefits using a few common examples of shrinkage estimators of the correlation matrix and volatility vector. Our technique has practical importance in evaluating the improvements in stability gained by employing various statistical estimators of covariance matrixes without having to perform complex calculations or use numerical simulations.