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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 three-level optimization problem in a two-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.

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