Portfolio selection under uncertainty: a new methodology for computing relative‐robust solutions

Abstract

In this paper, a new methodology for computing relative-robust portfolios based on minimax regret is proposed. Regret is defined as the utility loss for the investor resulting from choosing a given portfolio instead of choosing the optimal portfolio of the realized scenario. The absolute robust strategy was also considered and, in this case, the minimum investor’s expected utility in the worst-case scenario is maximized. Several subsamples are gathered from the in-sample data and for each subsample a minimax regret and a maximin solution are computed, to avoid the risk of overfitting. Robust portfolios are computed using a genetic algorithm, allowing the transformation of a 3-level optimization problem in a 2-level problem. Results show that the proposed relative-robust portfolio generally outperforms (other) relative-robust and non-robust portfolios, except for the global minimum variance portfolio. Furthermore, the relative-robust portfolio generally outperforms the absolute-robust portfolio, even considering higher risk aversion levels.