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

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Abstract

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.

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Notes

  1. In the in-sample analysis, the overall in-sample period was used in order to compute estimators for the models.

  2. A portfolio is a dominated solution when it shows, simultaneously, lower return and higher risk than another portfolio.

  3. Notice that the out-of-sample periods of the windows 1993–2008 and 1996–2011 overlapped the subprime mortgage crisis and the European debt crisis, respectively.

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Acknowledgements

This study has been funded by national funds, through the Portuguese Science Foundation (FCT), under project UID/Multi/00308/2019.

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Authors and Affiliations

  1. Higher Institute for Accountancy and Administration, University of Aveiro, R. Associação Humanitária dos Bombeiros Voluntários de Aveiro, 3810-500, Aveiro, Portugal

    Sandra Cruz Caçador

  2. Centre for Business and Economics Research (CeBER), University of Coimbra, Av. Dias da Silva, 165, 3004-512, Coimbra, Portugal

    Sandra Cruz Caçador, Pedro Manuel Cortesão Godinho & Joana Maria Pina Cabral Matos Dias

  3. Faculty of Economics, University of Coimbra, Av. Dias da Silva, 165, 3004-512, Coimbra, Portugal

    Sandra Cruz Caçador, Pedro Manuel Cortesão Godinho & Joana Maria Pina Cabral Matos Dias

  4. Institute for Systems Engineering and Computers at Coimbra, Rua Antero de Quental, Nº199, 3000-033, Coimbra, Portugal

    Joana Maria Pina Cabral Matos Dias

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  1. Sandra Cruz Caçador
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  2. Pedro Manuel Cortesão Godinho
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Correspondence to Sandra Cruz Caçador.

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Caçador, S.C., Godinho, P.M.C. & Dias, J.M.P.C.M. A minimax regret portfolio model based on the investor’s utility loss. Oper Res Int J 22, 449–484 (2022). https://doi.org/10.1007/s12351-020-00550-0

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