IDEAS home Printed from https://ideas.repec.org/a/eee/empfin/v15y2008i5p850-859.html
   My bibliography  Save this article

Robust performance hypothesis testing with the Sharpe ratio

Author

Listed:
  • Ledoit, Oliver
  • Wolf, Michael

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 [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.

Suggested Citation

  • Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 850-859, December.
    • Handle: RePEc:eee:empfin:v:15:y:2008:i:5:p:850-859
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0927-5398(08)00018-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Romano, Joseph P. & Wolf, Michael, 2001. "Improved nonparametric confidence intervals in time series regressions," DES - Working Papers. Statistics and Econometrics. WS ws010201, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Dominic Gasbarro & Wing-Keung Wong & J. Kenton Zumwalt, 2007. "Stochastic Dominance Analysis of iShares," The European Journal of Finance, Taylor & Francis Journals, vol. 13(1), pages 89-101.
    4. Romano, Joseph P. & Shaikh, Azeem M. & Wolf, Michael, 2008. "Formalized Data Snooping Based On Generalized Error Rates," Econometric Theory, Cambridge University Press, vol. 24(2), pages 404-447, April.
    5. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    6. Dominic Gasbarro & Wing-Keung Wong & J. Kenton Zumwalt, 2007. "Stochastic Dominance Analysis of iShares," The European Journal of Finance, Taylor & Francis Journals, vol. 13(1), pages 89-101.
    7. 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.
    8. 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.
    9. John Douglas (J.D.) Opdyke, 2007. "Comparing Sharpe ratios: So where are the p-values?," Journal of Asset Management, Palgrave Macmillan, vol. 8(5), pages 308-336, December.
    10. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 53-89.
    11. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    12. Craig Israelsen, 2005. "A refinement to the Sharpe ratio and information ratio," Journal of Asset Management, Palgrave Macmillan, vol. 5(6), pages 423-427, April.
    13. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    14. Luis Ferruz & Luis Vicente, 2005. "Style portfolio performance: Empirical evidence from the Spanish equity funds," Journal of Asset Management, Palgrave Macmillan, vol. 5(6), pages 397-409, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Olivier Ledoit & Michael Wolf, 2018. "Robust performance hypothesis testing with smooth functions of population moments," ECON - Working Papers 305, Department of Economics - University of Zurich.
    2. 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.
    3. Jose Dias Curto & Jose Castro Pinto, 2009. "The coefficient of variation asymptotic distribution in the case of non-iid random variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(1), pages 21-32.
    4. Guillermo Badía & Vicente Pina & Lourdes Torres, 2019. "Financial Performance of Government Bond Portfolios Based on Environmental, Social and Governance Criteria," Sustainability, MDPI, vol. 11(9), pages 1-13, April.
    5. Ardia, David & Boudt, Kris, 2015. "Testing equality of modified Sharpe ratios," Finance Research Letters, Elsevier, vol. 13(C), pages 97-104.
    6. Gabriel Frahm & Tobias Wickern & Christof Wiechers, 2012. "Multiple tests for the performance of different investment strategies," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 343-383, July.
    7. 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.
    8. Massimo Guidolin & Erwin Hansen & Martín Lozano-Banda, 2018. "Portfolio performance of linear SDF models: an out-of-sample assessment," Quantitative Finance, Taylor & Francis Journals, vol. 18(8), pages 1425-1436, August.
    9. Bai, Zhidong & Phoon, Kok Fai & Wang, Keyan & Wong, Wing-Keung, 2013. "The performance of commodity trading advisors: A mean-variance-ratio test approach," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 188-201.
    10. Michael Wolf & Dan Wunderli, 2009. "Fund-of-funds construction by statistical multiple testing methods," IEW - Working Papers 445, Institute for Empirical Research in Economics - University of Zurich.
    11. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
    12. Ekaterini Panopoulou, 2005. "A Resolution of the Fisher Effect Puzzle: A Comparison of Estimators," Money Macro and Finance (MMF) Research Group Conference 2005 18, Money Macro and Finance Research Group.
    13. Wouter J. Den Haan & Andrew T. Levin, 1995. "Inferences from parametric and non-parametric covariance matrix estimation procedures," International Finance Discussion Papers 504, Board of Governors of the Federal Reserve System (U.S.).
    14. Nikolay Gospodinov & Ian Irvine, 2005. "A ‘long march’ perspective on tobacco use in Canada," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(2), pages 366-393, May.
    15. Marian Vavra, 2015. "On a Bootstrap Test for Forecast Evaluations," Working and Discussion Papers WP 5/2015, Research Department, National Bank of Slovakia.
    16. Héctor F. Salazar-Núñez & Francisco Venegas-Martínez & José Antonio Lozano-Díez, 2022. "Assessing the interdependence among renewable and non-renewable energies, economic growth, and CO2 emissions in Mexico," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 24(11), pages 12850-12866, November.
    17. David R. Bell & Olivier Ledoit & Michael Wolf, 2012. "A new portfolio formation approach to mispricing of marketing performance indicators with an application to customer satisfaction," ECON - Working Papers 079, Department of Economics - University of Zurich, revised Dec 2013.
    18. Gabriel Frahm, 2018. "An Intersection–Union Test for the Sharpe Ratio," Risks, MDPI, vol. 6(2), pages 1-13, April.
    19. Mertens, Elmar, 2012. "Are spectral estimators useful for long-run restrictions in SVARs?," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1831-1844.
    20. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.

    More about this item

    Keywords

    Bootstrap HAC inference Sharpe ratio;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:empfin:v:15:y:2008:i:5:p:850-859. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jempfin .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.