Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement
AbstractWe propose a performance measure that generalizes the Sharpe ratio. The new performance measure is monotone with respect to stochastic dominance and consistently accounts for mean, variance and higher moments of the return distribution. It is equivalent to the Sharpe ratio if returns are normally distributed. Moreover, the two performance measures are asymptotically equivalent as the underlying distributions converge to the normal distribution. We suggest a parametric and a non-parametric estimator for the new performance measure and provide an empirical illustration using mutual funds and hedge funds data.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Banking & Finance.
Volume (Year): 36 (2012)
Issue (Month): 8 ()
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Web page: http://www.elsevier.com/locate/jbf
Performance measurement; Sharpe ratio; Aumann–Serrano index of riskiness; Skewness; Kurtosis; Non-normality;
Find related papers by JEL classification:
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
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- Dean P. Foster & Sergiu Hart, 2007.
"An Operational Measure of Riskiness,"
Discussion Paper Series
dp454, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Robert J. Aumann & Roberto Serrano, 2006.
"An Economic Index of Riskiness,"
321307000000000585, UCLA Department of Economics.
- Robert J. Aumann & Roberto Serrano, 2007. "An Economic Index of Riskiness," Discussion Paper Series dp446, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Robert J. Aumann & Roberto Serrano, 2007. "An economic index of riskiness," Working Papers 2007-08, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
- Roberto Serrano & Robert J. Aumann, 2007. "An Economic Index Of Riskiness," Working Papers wp2007_0706, CEMFI.
- Robert J. Aumann & Roberto Serrano, 2007. "An Economic Index of Riskiness," Levine's Bibliography 321307000000000836, UCLA Department of Economics.
- Robert J. Aumann & Roberto Serrano, 2006. "An Economic Index of Riskiness," Working Papers 2006-20, Brown University, Department of Economics.
- Enrico De Giorgi, .
"Reward-Risk Portfolio Selection and Stochastic Dominance,"
IEW - Working Papers
121, Institute for Empirical Research in Economics - University of Zurich.
- De Giorgi, Enrico, 2005. "Reward-risk portfolio selection and stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 895-926, April.
- Farinelli, Simone & Ferreira, Manuel & Rossello, Damiano & Thoeny, Markus & Tibiletti, Luisa, 2008. "Beyond Sharpe ratio: Optimal asset allocation using different performance ratios," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2057-2063, October.
- R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor and Francis Journals, vol. 1(2), pages 223-236.
- Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-30, June.
- Patrick L. Brockett & Yehuda Kahane, 1992. "Risk, Return, Skewness and Preference," Management Science, INFORMS, vol. 38(6), pages 851-866, June.
- Tim Bollerslev & Uta Kretschmer & Christian Pigorsch & George Tauchen, 2010.
"A Discrete-Time Model for Daily S&P500 Returns and Realized Variations: Jumps and Leverage Effects,"
10-06, Duke University, Department of Economics.
- Bollerslev, Tim & Kretschmer, Uta & Pigorsch, Christian & Tauchen, George, 2009. "A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects," Journal of Econometrics, Elsevier, vol. 150(2), pages 151-166, June.
- Tim Bollerslev & Uta Kretschmer & Christian Pigorsch & George Tauchen, 2007. "A Discrete-Time Model for Daily S&P500 Returns and Realized Variations: Jumps and Leverage Effects," CREATES Research Papers 2007-22, School of Economics and Management, University of Aarhus.
- Homm, Ulrich & Pigorsch, Christian, 2012. "An operational interpretation and existence of the Aumann–Serrano index of riskiness," Economics Letters, Elsevier, vol. 114(3), pages 265-267.
- Jushan Bai & Serena Ng, 2005.
"Tests for Skewness, Kurtosis, and Normality for Time Series Data,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 23, pages 49-60, January.
- Jushan Bai & Serena Ng, 2001. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Boston College Working Papers in Economics 501, Boston College Department of Economics.
- Gerry Boyle & Denis Conniffe, 2008. "Compatibility of expected utility and μ/σ approaches to risk for a class of non location–scale distributions," Economic Theory, Springer, vol. 35(2), pages 343-366, May.
- Zakamouline, Valeri & Koekebakker, Steen, 2009. "Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1242-1254, July.
- Dowd, Kevin, 2000. "Adjusting for risk:: An improved Sharpe ratio," International Review of Economics & Finance, Elsevier, vol. 9(3), pages 209-222, July.
- Andersson, Jonas, 2001. "On the Normal Inverse Gaussian Stochastic Volatility Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 44-54, January.
- Meyer, Jack & Rasche, Robert H, 1992. "Sufficient Conditions for Expected Utility to Imply Mean-Standard Deviation Rankings: Empirical Evidence Concerning the Location and Scale Condition," Economic Journal, Royal Economic Society, vol. 102(410), pages 91-106, January.
- Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
- Vikas Agarwal, 2004. "Risks and Portfolio Decisions Involving Hedge Funds," Review of Financial Studies, Society for Financial Studies, vol. 17(1), pages 63-98.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Loistl, Otto, 1976. "The Erroneous Approximation of Expected Utility by Means of a Taylor's Series Expansion: Analytic and Computational Results," American Economic Review, American Economic Association, vol. 66(5), pages 904-10, December.
- Schuhmacher, Frank & Eling, Martin, 2011. "Sufficient conditions for expected utility to imply drawdown-based performance rankings," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2311-2318, September.
- Yong Bao, 2009. "Estimation Risk-Adjusted Sharpe Ratio and Fund Performance Ranking under a General Return Distribution," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(2), pages 152-173, Spring.
- Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
- Eling, Martin & Schuhmacher, Frank, 2007. "Does the choice of performance measure influence the evaluation of hedge funds?," Journal of Banking & Finance, Elsevier, vol. 31(9), pages 2632-2647, September.
- Joseph Golec & Maurry Tamarkin, 1998. "Bettors Love Skewness, Not Risk, at the Horse Track," Journal of Political Economy, University of Chicago Press, vol. 106(1), pages 205-225, February.
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