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Deviation from normality and Sharpe ratio behavior: a brief simulation study

Author

Listed:
  • Hayette Gatfaoui

    (Pôle Finance Responsable - Rouen Business School - Rouen Business School)

Abstract

Sharpe ratio has been widely used in the portfolio management industry as well as fund industry (Robertson, 2001; Scholz and Wilkens, 2005). Users often forget the main core assumption describing the appropriateness of such a riskadjusted performance measure, namely asset return normality. This concern is of huge significance insofar as performanceindicators drive the asset allocation policy, performance forecasts and cost of capital assessment among others (Farinelli et al., 2008; Lien, 2002; Christensen and Platen, 2007). We employ a brief simulation study to assess the impact of deviations from normality on the performance measures and rankings inferred from Sharpe ratio's estimates. Our analysis allows for assessing the possible bias in both performance measurement and ranking, which results from the existence and the magnitude of skewness and kurtosis patterns in asset returns. This study proposes a method to extract an unbiased performance measure (i.e. unbiased Sharpe ratios) from observed classic Sharpe ratios after accounting for the returns' skewness bias. The resulting unbiased Sharpe ratio outperforms its classic counterpart at the stock picking level.

Suggested Citation

  • Hayette Gatfaoui, 2010. "Deviation from normality and Sharpe ratio behavior: a brief simulation study," Post-Print hal-00568613, HAL.
    • Handle: RePEc:hal:journl:hal-00568613
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    References listed on IDEAS

    as
    1. Morten Mosegaard Christensen & Eckhard Platen, 2007. "Sharpe Ratio Maximization And Expected Utility When Asset Prices Have Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(08), pages 1339-1364.
    2. Klemkosky, Robert C., 1973. "The Bias in Composite Performance Measures," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(3), pages 505-514, June.
    3. Ferson, Wayne E & Harvey, Campbell R, 1991. "The Variation of Economic Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 385-415, April.
    4. Hendrik Scholz, 2007. "Refinements to the Sharpe ratio: Comparing alternatives for bear markets," Journal of Asset Management, Palgrave Macmillan, vol. 7(5), pages 347-357, January.
    5. Carol Alexander, 2005. "The Present and Future of Financial Risk Management," Journal of Financial Econometrics, Oxford University Press, vol. 3(1), pages 3-25.
    6. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    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. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    9. 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, September.
    10. Hayette Gatfaoui, 2012. "A correction for classic performance measures," Post-Print hal-00809485, HAL.
    11. 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.
    12. 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.
    13. Donald Lien, 2002. "A note on the relationships between some risk‐adjusted performance measures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 22(5), pages 483-495, May.
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    Cited by:

    1. Michele Costola & Massimiliano Caporin, 2016. "Rational Learning For Risk-Averse Investors By Conditioning On Behavioral Choices," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-26, March.

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