A decision-theoretic foundation for reward-to-risk performance measures
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.
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- Enrico De Giorgi, "undated".
"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.
- Serge Darolles & Christian Gourieroux, 2010.
"Conditionally fitted Sharpe performance with an application to hedge fund rating,"
- 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.
- 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.
- 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.
- Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
- 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.
- 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.
- 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.
- 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.
- R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, 01.
- Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
- 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.
- Sergio Ortobelli & Svetlozar T. Rachev & Stoyan Stoyanov & Frank J. Fabozzi & Almira Biglova, 2005. "The Proper Use Of Risk Measures In Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1107-1133.
- 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.
- 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.
- 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.
- 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.
- Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
- 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.
- 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.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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