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Global minimum variance portfolios under uncertainty: a robust optimization approach

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Abstract

This paper presents new models which seek to optimize the first and second moments of asset returns without estimating expected returns. Motivated by the stability of optimal solutions computed by optimizing only the second moment and applying the robust optimization methodology which allows to incorporate the uncertainty in the optimization model itself, we extend and combine existing methodologies in order to define a method for computing relative-robust and absolute-robust minimum variance portfolios. For the relative robust strategy, where the maximum regret is minimized, regret is defined as the increase in the investment risk resulting from investing in a given portfolio instead of choosing the optimal portfolio of the realized scenario. The absolute robust strategy which minimizes the maximum risk was applied assuming the worst-case scenario over the whole uncertainty set. Across alternate time windows, results provide new evidence that the proposed robust minimum variance portfolios outperform non-robust portfolios. Whether portfolio measurement is based on return, risk, regret or modified Sharpe ratio, results suggest that the robust methodologies are able to optimize the first and second moments without the need to estimate expected returns.

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Notes

  1. For further readings about the interactive fuzzy method see Duan and Stahlecker [57] and Kato and Sakawa [58].

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

  3. A portfolio is considered a dominant solution when it presents, simultaneously, higher return and lower risk.

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Acknowledgements

This study has been funded by national funds, through FCT, Portuguese Science Foundation, 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 Caçador

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

    Sandra Caçador, Joana Matos Dias & Pedro Godinho

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

    Sandra Caçador, Joana Matos Dias & Pedro Godinho

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

    Joana Matos Dias

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  1. Sandra Caçador
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Correspondence to Sandra Caçador.

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Caçador, S., Dias, J.M. & Godinho, P. Global minimum variance portfolios under uncertainty: a robust optimization approach. J Glob Optim 76, 267–293 (2020). https://doi.org/10.1007/s10898-019-00859-x

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