Model risk in mean-variance portfolio selection: an analytic solution to the worst-case approach

Abstract

In this paper we consider the worst-case model risk approach described in Glasserman and Xu (Quant Finance 14(1):29–58, 2014). Portfolio selection with model risk can be a challenging operational research problem. In particular, it presents an additional optimisation compared to the classical one. We find the analytical solution for the optimal mean-variance portfolio selection in the worst-case scenario approach and for the special case with the additional constraint of a constant mean vector considered in Glasserman and Xu (Quant Finance 14(1):29–58, 2014). Moreover, we prove in two relevant cases—the minimum-variance case and the symmetric case, i.e. when all assets have the same mean—that the analytical solutions in the alternative model and in the nominal one are equal; we show that this corresponds to the situation when model risk reduces to estimation risk.