Robustness properties of mean-variance portfolios

In recent years, new ideas for the robustification of the traditional mean-variance frontier have appeared in the literature. One of these approaches is based upon the robust counterpart idea, introduced by Ben-Tal and Nemirovski. To make this idea work in practice, realistic uncertainty sets have to be specified. In this article, we are investigating two popular uncertainty sets together with their impact on the efficient frontier. As a main contribution we will provide two theorems stating that the corresponding robust efficient frontiers are identical to the classical efficient frontier up to some risk level. This especially implies that the classical efficient portfolios are already robust themselves. We will briefly discuss the relevance of this finding for practical applications.