Consistency of robust portfolio estimators

It is a matter of common knowledge that traditional Markowitz optimization based on sample means and covariances performs poorly in practice. For this reason, diverse attempts were made to improve performance of portfolio optimization. In this paper, we investigate three popular portfolio selection models built upon classical meanvariance theory. The first model is an extension of the traditional mean-variance optimization by introducing robust estimators. Second, the recently being en vogue robust counterpart approach is considered. The list of models is concluded by an extended version of Michaud’s resampling approach. We show that for a very broad class of portfolio constraints these models can be seen as a generalization of the classical mean-variance setting: The optimal portfolios converge to the true optimal Markowitz portfolio if only the sample size is large enough.