Addressing estimation errors on expected asset returns through robust portfolio optimization

It is well known that the performance of the classical Markowitz model for portfolio optimization is extremely sensitive to estimation errors on the expected asset returns. Robust optimization mitigates this issue. We focus on ellipsoidal uncertainty sets around a point estimate of the expected asset returns. An important issue is the choice of the parameters that specify this ellipsoid, namely the point estimate and the estimation-error matrix. We show that there exist diagonal estimation-error matrices that achieve an arbitrarily small loss in the expected portfolio return as compared to the optimum. We empirically investigate the sample size needed to compute the point estimate. We also conduct an empirical study of different estimation-error matrices and give a heuristic to choose the size of the uncertainty set. The results of our experiments show that robust portfolio models featuring a family of diagonal estimation-error matrices outperform benchmark portfolio models including the classical Markowitz model.