A minimax regret portfolio model based on the investor’s utility loss

The out-of-sample performance of relative robust portfolio optimization methodologies is still little explored in portfolio literature. In this paper, a new minimax regret portfolio optimization model is presented, where regret is defined as the utility loss for the investor. The real benefits of the proposed methodology were analyzed by comparing in-sample and out-of-sample performances of robust and non-robust portfolios. The results suggest that the proposed relative robust model has more value for risk-taking investors. Furthermore, the proposed relative-robust portfolio outperforms the non-robust portfolios, in many of the time windows under analysis, with the exception of the global minimum variance portfolio. Comparatively to the minimax regret model presented by Xidonas et al. (Eur J Oper Res 262:299–305,2017) and the absolute robust approach developed by Kim et al. (Econ Lett 122:154–158, 2014a), the proposed methodology presents itself as a more consistent approach since it generates portfolios that reveal greater stability concerning in-sample and out-of-sample performances. The developed relative robustness approach stands out as a valuable contribution for the assertion of robust optimization, in particular of relative robust methodologies, within the field of portfolio selection under uncertainty.