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Fuzzy risk adjusted performance measures: Application to hedge funds

Author

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  • J. Sadefo Kamdem

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

  • A. Mbairadjim Moussa

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

  • M. Terraza

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

In this paper, following the notion of probabilistic risk adjusted performance measures, we introduce that of fuzzy risk adjusted performance measures (FRAPM). In order to deal efficiently with the closing-based returns bias induced by market microstructure noise, as well as to handle their uncertain variability, we combine fuzzy set theory and probability theory. The returns are first represented as fuzzy random variables and then used in defining fuzzy versions of some adjusted performance measures. Using a recent ordering method for fuzzy numbers, we propose a ranking of funds based on these fuzzy performance measures. Finally, empirical studies carried out on fifty French hedge funds confirm the effectiveness and give the benefits of our approach over the classical performance ratios.

Suggested Citation

  • J. Sadefo Kamdem & A. Mbairadjim Moussa & M. Terraza, 2012. "Fuzzy risk adjusted performance measures: Application to hedge funds," Post-Print hal-02901867, HAL.
    • Handle: RePEc:hal:journl:hal-02901867
    DOI: 10.1016/j.insmatheco.2012.09.005
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    Cited by:

    1. Jules Sadefo Kamdem & Babel Raïssa Guemdjo Kamdem & Carlos Ougouyandjou, 2021. "S-ARMA Model and Wold Decomposition for Covariance Stationary Interval-Valued Time Series Processes," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 191-213, March.
    2. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Shapiro, A.F. & Terraza, M., 2014. "CAPM with fuzzy returns and hypothesis testing," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 40-57.
    3. Babel Raïssa Guemdjo Kamdem & Jules Sadefo-Kamdem & Carlos Ougouyandjou, 2020. "On Random Extended Intervals and their ARMA Processes," Working Papers hal-03169516, HAL.
    4. Christian Biener & Martin Eling, 2013. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 16(2), pages 219-231, September.
    5. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Terraza, M., 2014. "Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns," Economic Modelling, Elsevier, vol. 39(C), pages 247-256.
    6. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.

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