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Robust Performance Hypothesis Testing with the Sharpe Ratio

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  • Oliver Ledoit
  • Michael Wolf

Abstract

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 (1981), which has been corrected by Memmel (2003). 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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Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 320.

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Date of creation: Jan 2008
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Handle: RePEc:zur:iewwpx:320

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Keywords: Bootstrap; HAC inference; Sharpe ratio;

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  1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 817-58, May.
  2. Olivier Ledoit & Pedro Santa-Clara & Michael Wolf, 2003. "Flexible Multivariate GARCH Modeling with an Application to International Stock Markets," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 735-747, August.
  3. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 942, Cowles Foundation for Research in Economics, Yale University.
  4. Joseph P. Romano & Michael Wolf, 2001. "Improved Nonparametric Confidence Intervals In Time Series Regressions," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws010201, Universidad Carlos III, Departamento de Estadística y Econometría.
  5. Eling, Martin & Schuhmacher, Frank, 2007. "Does the choice of performance measure influence the evaluation of hedge funds?," Journal of Banking & Finance, Elsevier, Elsevier, vol. 31(9), pages 2632-2647, September.
  6. Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers 0144, National Bureau of Economic Research, Inc.
  7. Dominic Gasbarro & Wing-Keung Wong & J. Kenton Zumwalt, 2007. "Stochastic Dominance Analysis of iShares," The European Journal of Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 13(1), pages 89-101.
  8. Romano, Joseph P. & Shaikh, Azeem M. & Wolf, Michael, 2008. "Formalized Data Snooping Based On Generalized Error Rates," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(02), pages 404-447, April.
  9. Jobson, J D & Korkie, Bob M, 1981. "Performance Hypothesis Testing with the Sharpe and Treynor Measures," Journal of Finance, American Finance Association, American Finance Association, vol. 36(4), pages 889-908, September.
  10. 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.
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