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Fuzzy risk adjusted performance measures: application to Hedge funds

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  • Alfred Mbairadjim Moussa
  • Jules Sadefo Kamdem
  • Michel Terraza

Abstract

In this paper, following the notion of probabilistic risk adjusted performance measures; we introduce that of fuzzy risk adjusted measures (FRAM). 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.

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Paper provided by LAMETA, Universtiy of Montpellier in its series Working Papers with number 12-24.

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Length: 23 pages
Date of creation: Sep 2012
Date of revision: Sep 2012
Handle: RePEc:lam:wpaper:12-24

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  12. Darolles, Serge & Gourieroux, Christian, 2010. "Conditionally fitted Sharpe performance with an application to hedge fund rating," Journal of Banking & Finance, Elsevier, vol. 34(3), pages 578-593, March.
  13. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem & Arnold F. Shapiro & Michel Terraza, 2012. "Capital asset pricing model with fuzzy returns and hypothesis testing," Working Papers 12-33, LAMETA, Universtiy of Montpellier, revised Sep 2012.
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  16. Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
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  19. Edward Leamer, 1906. "Errors in Variables in Linear Systems," UCLA Economics Working Papers 406, UCLA Department of Economics.
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Cited by:
  1. 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.

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