Fuzzy risk adjusted performance measures: application to Hedge funds
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.
|Date of creation:||Sep 2012|
|Date of revision:||Sep 2012|
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- 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.
- Capocci, Daniel & Hubner, Georges, 2004. "Analysis of hedge fund performance," Journal of Empirical Finance, Elsevier, vol. 11(1), pages 55-89, January.
- Gonzalez-Rodriguez, Gil & Colubi, Ana & Angeles Gil, Maria, 2006. "A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 163-176, November.
- William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, 09.
- John G. Cragg, 1994. "Making Good Inferences from Bad Data," Canadian Journal of Economics, Canadian Economics Association, vol. 27(4), pages 776-800, November.
- 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.
- Serge Darolles & Christian Gourieroux, 2010. "Conditionally fitted Sharpe performance with an application to hedge fund rating," Post-Print halshs-00677727, HAL.
- Leamer, Edward E, 1987.
"Errors in Variables in Linear Systems,"
Econometric Society, vol. 55(4), pages 893-909, July.
- Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
- Amin, Gaurav S. & Kat, Harry M., 2003.
"Hedge Fund Performance 1990–2000: Do the “Money Machines” Really Add Value?,"
Journal of Financial and Quantitative Analysis,
Cambridge University Press, vol. 38(02), pages 251-274, June.
- Gaurav Amin & Harry. M Kat, 2001. "Hedge Fund Performance 1990-2000- Do the "Money Machines" Really Add Value?," ICMA Centre Discussion Papers in Finance icma-dp2001-05, Henley Business School, Reading University, revised Sep 2001.
- Shapiro, Arnold F., 2004. "Fuzzy logic in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 399-424, October.
- Michael C. Jensen, 1968. "The Performance Of Mutual Funds In The Period 1945–1964," Journal of Finance, American Finance Association, vol. 23(2), pages 389-416, 05.
- Tanaka, Hideo & Guo, Peijun, 1999. "Portfolio selection based on upper and lower exponential possibility distributions," European Journal of Operational Research, Elsevier, vol. 114(1), pages 115-126, April.
- Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
- Andersen, Torben G. & Bollerslev, Tim & Meddahi, Nour, 2011. "Realized volatility forecasting and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 220-234, January.
- Mark Mitchell, 2001. "Characteristics of Risk and Return in Risk Arbitrage," Journal of Finance, American Finance Association, vol. 56(6), pages 2135-2175, December.
- Berry-Stölzle, Thomas R. & Koissi, Marie-Claire & Shapiro, Arnold F., 2010. "Detecting fuzzy relationships in regression models: The case of insurer solvency surveillance in Germany," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 554-567, June.
- Luciano Stefanini, 2008. "A generalization of Hukuhara difference for interval and fuzzy arithmetic," Working Papers 0801, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
- Coën, Alain & Hübner, Georges, 2009. "Risk and performance estimation in hedge funds revisited: Evidence from errors in variables," Journal of Empirical Finance, Elsevier, vol. 16(1), pages 112-125, January.
- Treynor, Jack L & Black, Fischer, 1973. "How to Use Security Analysis to Improve Portfolio Selection," The Journal of Business, University of Chicago Press, vol. 46(1), pages 66-86, January.
- Klepper, Steven & Leamer, Edward E, 1984. "Consistent Sets of Estimates for Regressions with Errors in All Variables," Econometrica, Econometric Society, vol. 52(1), pages 163-83, January.
- Dubois, Didier, 2006. "Possibility theory and statistical reasoning," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 47-69, November.
- Daniel Capocci, 2002. "An Analysis of Hedge Fund Performance," Finance 0210001, EconWPA.
- Koissi, Marie-Claire & Shapiro, Arnold F., 2006. "Fuzzy formulation of the Lee-Carter model for mortality forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 287-309, December.
- Smimou, K. & Bector, C.R. & Jacoby, G., 2008. "Portfolio selection subject to experts' judgments," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 1036-1054, December.
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