Robust asset allocation strategies: relaxed versus classical robustness

Many optimization problems involve parameters which are not known in advance, but can only be forecast or estimated. Such problems fit perfectly into the framework of Robust Optimization that, given optimization problems with uncertain parameters, looks for solutions that will achieve good objective function values for the realization of these parameters in given uncertainty sets. Aim of this paper is to investigate and compare alternative forms of robustness in the context of portfolio asset allocation. Starting with a relaxed form of robustness, which allows one to specify not only the values of the uncertainty parameters, but also their degree of feasibility, in the first part of the paper we propose a family of relaxed robust models, called norm-portfolio models, which use general norms to relax the classical notion of robustness. Then, in the second part we test some norm-portfolio models, as well as various robust strategies from the literature, with real market data on different data sets. To the best of our knowledge, this is the first attempt at comparing robust strategies of different kinds in the framework of portfolio asset allocation.