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Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement

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  • Homm, Ulrich
  • Pigorsch, Christian

Abstract

We 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.

Suggested Citation

  • Homm, Ulrich & Pigorsch, Christian, 2012. "Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2274-2284.
  • Handle: RePEc:eee:jbfina:v:36:y:2012:i:8:p:2274-2284
    DOI: 10.1016/j.jbankfin.2012.04.005
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    References listed on IDEAS

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    1. 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.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. De Giorgi, Enrico, 2005. "Reward-risk portfolio selection and stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 895-926, April.
    4. Patrick L. Brockett & Yehuda Kahane, 1992. "Risk, Return, Skewness and Preference," Management Science, INFORMS, vol. 38(6), pages 851-866, June.
    5. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785-814.
    6. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    7. 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.
    8. Vikas Agarwal, 2004. "Risks and Portfolio Decisions Involving Hedge Funds," Review of Financial Studies, Society for Financial Studies, vol. 17(1), pages 63-98.
    9. Dowd, Kevin, 2000. "Adjusting for risk:: An improved Sharpe ratio," International Review of Economics & Finance, Elsevier, vol. 9(3), pages 209-222, July.
    10. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    11. 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.
    12. 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.
    13. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    14. 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.
    15. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    16. 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.
    17. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
    18. 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 904-910, December.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    25. 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;Society for the Advancement of Economic Theory (SAET), vol. 35(2), pages 343-366, May.
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    Cited by:

    1. Guo, Biao & Xiao, Yugu, 2016. "A note on why doesn't the choice of performance measure matter?," Finance Research Letters, Elsevier, vol. 16(C), pages 248-254.
    2. Caporin, Massimiliano & Costola, Michele & Jannin, Gregory & Maillet, Bertrand, 2018. "“On the (Ab)use of Omega?”," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 11-33.
    3. Shakouri, Mahmoud & Lee, Hyun Woo & Choi, Kunhee, 2015. "PACPIM: New decision-support model of optimized portfolio analysis for community-based photovoltaic investment," Applied Energy, Elsevier, vol. 156(C), pages 607-617.
    4. Ehsani, Sina & Lien, Donald, 2015. "A note on minimum riskiness hedge ratio," Finance Research Letters, Elsevier, vol. 15(C), pages 11-17.
    5. Schuhmacher, Frank & Auer, Benjamin R., 2014. "Sufficient conditions under which SSD- and MR-efficient sets are identical," European Journal of Operational Research, Elsevier, vol. 239(3), pages 756-763.
    6. Chang, C-L. & McAleer, M.J. & Wong, W.-K., 2018. "Management Information, Decision Sciences, and Financial Economics : a connection," Econometric Institute Research Papers 2018-004/III, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Tinbergen Institute Discussion Papers 18-024/III, Tinbergen Institute.
    8. Auer, Benjamin R. & Schuhmacher, Frank, 2013. "Robust evidence on the similarity of Sharpe ratio and drawdown-based hedge fund performance rankings," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 24(C), pages 153-165.
    9. Cuizhen Niu & Xu Guo & Wing-Keung Wong & Michael McAleer, 2017. "Theory and Application of an Economic Performance Measure of Risk," Documentos de Trabajo del ICAE 2017-18, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    10. Klaas Schulze, 2015. "General dual measures of riskiness," Theory and Decision, Springer, vol. 78(2), pages 289-304, February.
    11. Schulze, Klaas, 2014. "Existence and computation of the Aumann–Serrano index of riskiness and its extension," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 219-224.
    12. repec:eee:jimfin:v:80:y:2018:i:c:p:59-74 is not listed on IDEAS
    13. repec:gam:jecomi:v:5:y:2017:i:4:p:38-:d:115667 is not listed on IDEAS
    14. Auer, Benjamin R. & Schuhmacher, Frank, 2013. "Performance hypothesis testing with the Sharpe ratio: The case of hedge funds," Finance Research Letters, Elsevier, vol. 10(4), pages 196-208.
    15. Chang, C-L. & McAleer, M.J. & Wong, W.-K., 2015. "Informatics, Data Mining, Econometrics and Financial Economics: A Connection," Econometric Institute Research Papers EI2015-34, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    16. repec:gam:jjrfmx:v:11:y:2018:i:1:p:15-:d:137130 is not listed on IDEAS
    17. Galagedera, Don U.A. & Watson, John & Premachandra, I.M. & Chen, Yao, 2016. "Modeling leakage in two-stage DEA models: An application to US mutual fund families," Omega, Elsevier, vol. 61(C), pages 62-77.
    18. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(1), pages 1-29, March.
    19. Chen, Yi-Ting & Ho, Keng-Yu & Tzeng, Larry Y., 2014. "Riskiness-minimizing spot-futures hedge ratio," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 154-164.
    20. Bosch-Badia, Maria Teresa & Montllor-Serrats, Joan & Tarrazon-Rodon, Maria-Antonia, 2014. "Unveiling the embedded coherence in divergent performance rankings," Journal of Banking & Finance, Elsevier, vol. 42(C), pages 154-165.

    More about this item

    Keywords

    Performance measurement; Sharpe ratio; Aumann–Serrano index of riskiness; Skewness; Kurtosis; Non-normality;

    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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