Abstract
The hedge funds performance evaluation requires an adequate characterization of returns distributions shape. This characterization is made by thorough probabilistic moments. Different types of moments were used in the literature, namely, the conventional (central or raw) moments (Sharpe, 1966, Treynor and Black, 1973), the partial moments (Sortino and van der Meer, 1991, Sortino, van der Meer and Platinga, 1999, Bernardo and Ledoit, 2000, Sortino and Satchel, 2001, Farinelli and Tibiletti, 2008) and more recently the Trimmed L-moments (Darrolles et al., 2009). These authors generally define the performance ratio by dividing a location measure by a dispersion measure. The seminal approach deriving from the Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965), Mossin (1966) and Treynor (1962) uses the sample mean and the standard deviation of excess returns as location and dispersion measures respectively. These two statistics do not always adequately describe the returns distributions, especially in the presence of heavy tails and/or of skewness.
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References
Agarwal V. and N. Naik (2000), “On taking the alternative route: Risks, rewards, style and performance persistence of hedge funds”, Journal of Alternative Investments, 2, 6–23.
Amin G. A. and H. M. Kat (2003), “Hedge fund performance 1990–2000: Do the “money machines” really add value?”, Journal of Financial and Quantitative Analysis, 38, 251–274.
Bernardo A. E. and O. Ledoit (2000), “Gain, loss and asset pricing”, The Journal of Political Economy, 108 (1), 144–172.
Black F. and J. L. Treynor (1973), “How to Use Security Analysis to Improve Portfolio Selection”, The Journal of Business, 46, 1, 66–86.
Carlsson C. and R. Fullèr (2001), “On possibilistic mean value and variance of fuzzy numbers”, Fuzzy Sets and Systems, 122, 315–326.
Chanas S. and M. Nowakowski (1988), “Single value simulation of fuzzy variable”, Fuzzy Sets and Systems, 25, 43–57.
Darolles S., Gourieroux C. and J. Joann Jasiak (2009). “L-performance with an application to hedgefunds”, Journal of Empirical Finance. 16 (4), 671–685.
Delgado M., Vila M.A. and W. Woxman (1998), “On a canonical representation of fuzzy numbers”, Fuzzy Sets and Systems, 93, 125–135.
Dubois D. (2006), “Possibility theory and statistical reasoning”, Computational Statistics & Data Analysis. 51 (1), 47–69.
Dubois D. and H. Prade (1987), “The mean value of a fuzzy number”, Fuzzy Sets and Systems, 24, 279–300.
Dubois D., Foulloy L., Mauris G. and H. Prade (2004), “Probability-Possibility transformations, triangular fuzzy sets, and probabilitistic inequalities”, Reliable Computing, 10, 273–297.
Dubois D., Prade H., and S. Sandri (1993), “On Possibility/Probability Transformations”, in: Lowen, R. and Roubens, M. (eds), Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 103–112.
Dubois D. and H. Prade (1980), Theory and application, fuzzy sets and systems, New York: Academic Publishers.
Eling M. (2006), “Autocorrelation, bias, and fat tails — are hedge funds really attractive investments?”, Journal of Derivatives Use, Trading & Regulation, 12, 28–47.
Farinelli S. and L. Tibiletti (2008), “Sharpe Thinking in Asset Ranking with One-Sided Measures”, European Journal of Operational Research, 185, 1542–1547.
Fullèr R. and P. Majlender (2003), “On weighted possibilistic mean and variance of fuzzy numbers”, Fuzzy Sets and Systems, 136, 363–374.
Heilpern S. (1992), “The expected value of a fuzzy number”, Fuzzy Sets and Systems, 47, 81–86.
Mbairadjim Moussa A., Sadefo Kamdem J. and M. Terraza (2012), “Moments partiels crédibilistes et application à l’évaluation de la performance des fonds spéculatifs”, 44ème Journées des Statistiques de la Société Franccaise de Statistique, Bruxelles.
Mitchell M. and T. Pulvino (2001), “Characteristics of risk and return in risk arbitrage”, Journal of Finance, 56, 2135–2175.
Oussalah M. (2000), “On the probability/possibility transformations: a comparative analysis”. Int. Journal of General Systems, 29, 671–718.
Sharpe W. F. (1964), “Capital asset prices: a theory of market equilibrium under conditions of risk”, Journal of Finance, 19 (3), 425–442.
Sortino F. A. and S. Satchell (2001), Managing Downside Risk in Financial Markets, Butterworth Heinemann: Oxford.
Sortino F. A. and R. van der Meer R. (1991), “Downside risk”, The Journal of Portfolio Management, 17(4), 27–31.
Sortino F. A., Van der Meer R. and A. Plantinga (1999), “The dutch triangle: a framework to measure upside potential relative to downside risk”, The Journal of Portfolio Management, 26(1), 50–57.
Zadeh L. A. (1975), “The concept of a linguistic variable and its application to approximate reasoning”, Information and Science. 8, 199–249.
Zadeh L. A. (1965), “Fuzzy sets”, Information and Control, 8, 338–353. 73
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© 2013 Alfred M. Mbairadjim, Jules Sadefo Kamdem, and Michel Terraza
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Mbairadjim, A.M., Kamdem, J.S., Terraza, M. (2013). Hedge Funds Risk-adjusted Performance Evaluation: A Fuzzy Set Theory-Based Approach. In: Terraza, V., Razafitombo, H. (eds) Understanding Investment Funds. Palgrave Macmillan, London. https://doi.org/10.1057/9781137273611_4
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DOI: https://doi.org/10.1057/9781137273611_4
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