Set-Portfolio Selection with the Use of Market Stochastic Bounds

This paper proposes an ex-post comparison of portfolio selection strategies. These are applied to certain preselected assets among about ten thousand stocks on the global market. In particular, we preselected a few assets for each portfolio selection problem, taking into account different return characteristics. The preselecting criteria take into account the joint Markovian behavior of the returns; furthermore, they consider the assets who optimize the association with market stochastic bounds, having the highest ex-ante reward-risk performance. The results obtained with different pre-selection criteria are merged in order to identify assets with common characteristics which are appealing for investors. The impact of assets pre-selection on the portfolio choices is also studied. In particular, we compare the performance of different strategies that use or do not use the preselecting criteria. We finally propose the comparison of the ex-post final wealth obtained with the optimization of several reward-risk functionals that use the stochastic bounds of the preselected assets. For every comparison, we assume that the returns follow a non-parametric Markov chain, where the investors recalibrate their portfolios on a weekly basis.