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A decision-theoretic foundation for reward-to-risk performance measures

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  • Schuhmacher, Frank
  • Eling, Martin

Abstract

In this paper we prove that partial-moments-based performance measures (e.g., Omega, Kappa, upside-potential ratio, Sortino–Satchell ratio, Farinelli–Tibiletti ratio), value-at-risk-based performance measures (e.g., VaR ratio, CVaR ratio, Rachev ratio, generalized Rachev ratio), and other admissible performance measures are a strictly increasing function in the Sharpe ratio. The theoretical basis of this result is the location and scale property and two other plausible and mild conditions. Our result provides a decision-theoretic foundation for all these frequently used performance measures. Moreover, it might explain the empirical finding that all these measures typically lead to very similar rankings.

Suggested Citation

  • Schuhmacher, Frank & Eling, Martin, 2012. "A decision-theoretic foundation for reward-to-risk performance measures," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2077-2082.
  • Handle: RePEc:eee:jbfina:v:36:y:2012:i:7:p:2077-2082
    DOI: 10.1016/j.jbankfin.2012.03.013
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    1. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    2. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, 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. Farinelli, Simone & Tibiletti, Luisa, 2008. "Sharpe thinking in asset ranking with one-sided measures," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1542-1547, March.
    5. 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.
    6. Serban, Alina F., 2010. "Combining mean reversion and momentum trading strategies in foreign exchange markets," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2720-2727, November.
    7. 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.
    8. Eling, Martin & Faust, Roger, 2010. "The performance of hedge funds and mutual funds in emerging markets," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1993-2009, August.
    9. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    10. 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.
    11. repec:wsi:ijtafx:v:08:y:2005:i:08:n:s0219024905003402 is not listed on IDEAS
    12. Christian S. Pedersen & Stephen E. Satchell, 1998. "An Extended Family of Financial-Risk Measures," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 23(2), pages 89-117, December.
    13. 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.
    14. Levy, Haim, 1989. "Two-Moment Decision Models and Expected Utility Maximization: Comment," American Economic Review, American Economic Association, vol. 79(3), pages 597-600, June.
    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. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
    17. Alexander, Gordon J. & Baptista, Alexandre M., 2010. "Active portfolio management with benchmarking: A frontier based on alpha," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2185-2197, September.
    18. Szakmary, Andrew C. & Shen, Qian & Sharma, Subhash C., 2010. "Trend-following trading strategies in commodity futures: A re-examination," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 409-426, February.
    19. Farinelli, Simone & Ferreira, Manuel & Rossello, Damiano & Thoeny, Markus & Tibiletti, Luisa, 2009. "Optimal asset allocation aid system: From "one-size" vs "tailor-made" performance ratio," European Journal of Operational Research, Elsevier, vol. 192(1), pages 209-215, January.
    20. 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.
    21. Ding, Bill & Shawky, Hany A. & Tian, Jianbo, 2009. "Liquidity shocks, size and the relative performance of hedge fund strategies," Journal of Banking & Finance, Elsevier, vol. 33(5), pages 883-891, May.
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    Citations

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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. Auer, Benjamin R., 2015. "Does the choice of performance measure influence the evaluation of commodity investments?," International Review of Financial Analysis, Elsevier, vol. 38(C), pages 142-150.
    3. 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.
    4. Auer, Benjamin R., 2014. "Daily seasonality in crude oil returns and volatilities," Energy Economics, Elsevier, vol. 43(C), pages 82-88.
    5. Benjamin R. Auer, 2016. "Do Socially Responsible Investment Policies Add or Destroy European Stock Portfolio Value?," Journal of Business Ethics, Springer, vol. 135(2), pages 381-397, May.
    6. 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.
    7. Volker Stein & Arnd Wiedemann, 2016. "Risk governance: conceptualization, tasks, and research agenda," Journal of Business Economics, Springer, vol. 86(8), pages 813-836, November.
    8. Auer, Benjamin R. & Schuhmacher, Frank, 2016. "Do socially (ir)responsible investments pay? New evidence from international ESG data," The Quarterly Review of Economics and Finance, Elsevier, vol. 59(C), pages 51-62.
    9. Niu, Cuizhen & Wong, Wing-Keung & Xu, Qunfang, 2017. "Higher-Order Risk Measure and (Higher-Order) Stochastic Dominance," MPRA Paper 75948, University Library of Munich, Germany.
    10. Auer, Benjamin R., 2014. "Should hedge funds be cautious reporting high returns?," Research in International Business and Finance, Elsevier, vol. 30(C), pages 195-201.
    11. 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.
    12. León, Angel & Moreno, Manuel, 2017. "One-sided performance measures under Gram-Charlier distributions," Journal of Banking & Finance, Elsevier, vol. 74(C), pages 38-50.
    13. 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.
    14. León, Ángel & Moreno, Manuel, 2015. "Lower Partial Moments under Gram Charlier Distribution: Performance Measures and Efficient Frontiers," QM&ET Working Papers 15-3, University of Alicante, D. Quantitative Methods and Economic Theory.
    15. Benedikt Hoechner & Peter Reichling & Gordon Schulze, 2015. "Pitfalls of downside performance measures with arbitrary targets," FEMM Working Papers 150018, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    16. Benjamin Auer, 2013. "The low return distortion of the Sharpe ratio," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 27(3), pages 299-306, September.

    More about this item

    Keywords

    Asset management; Performance measurement; Sharpe ratio; Location and scale condition; Risk and reward measurement;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • G29 - Financial Economics - - Financial Institutions and Services - - - Other

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