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Robust performance hypothesis testing with the Sharpe ratio

  • Ledoit, Oliver
  • Wolf, Michael

Applied researchers often test for the difference of the Sharpe ratios of two investment strategies. A very popular tool to this end is the test of Jobson and Korkie [Jobson, J.D. and Korkie, B.M. (1981). Performance hypothesis testing with the Sharpe and Treynor measures. Journal of Finance, 36:889-908], which has been corrected by Memmel [Memmel, C. (2003). Performance hypothesis testing with the Sharpe ratio. Finance Letters, 1:21-23]. Unfortunately, this test is not valid when returns have tails heavier than the normal distribution or are of time series nature. Instead, we propose the use of robust inference methods. In particular, we suggest to construct a studentized time series bootstrap confidence interval for the difference of the Sharpe ratios and to declare the two ratios different if zero is not contained in the obtained interval. This approach has the advantage that one can simply resample from the observed data as opposed to some null-restricted data. A simulation study demonstrates the improved finite sample performance compared to existing methods. In addition, two applications to real data are provided.

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Article provided by Elsevier in its journal Journal of Empirical Finance.

Volume (Year): 15 (2008)
Issue (Month): 5 (December)
Pages: 850-859

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Handle: RePEc:eee:empfin:v:15:y:2008:i:5:p:850-859
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  1. Olivier Ledoit & Pedro Santa Clara & Michael Wolf, 2001. "Flexible multivariate GARCH modeling with an application to international stock markets," Economics Working Papers 578, Department of Economics and Business, Universitat Pompeu Fabra.
  2. 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.
  3. Joseph P. Romano & Michael Wolf, 2002. "Improved nonparametric confidence intervals in time series regressions," Economics Working Papers 635, Department of Economics and Business, Universitat Pompeu Fabra.
  4. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
  5. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 631-653.
  6. Romano, Joseph P. & Shaikh, Azeem M. & Wolf, Michael, 2008. "Formalized Data Snooping Based On Generalized Error Rates," Econometric Theory, Cambridge University Press, vol. 24(02), pages 404-447, April.
  7. Dominic Gasbarro & Wing-Keung Wong & J. Kenton Zumwalt, 2007. "Stochastic Dominance Analysis of iShares," Finance Working Papers 21919, East Asian Bureau of Economic Research.
  8. Jobson, J D & Korkie, Bob M, 1981. "Performance Hypothesis Testing with the Sharpe and Treynor Measures," Journal of Finance, American Finance Association, vol. 36(4), pages 889-908, September.
  9. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 53-89.
  10. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
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