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Sample Size Bias and Sharpe's Performance Measure: A Note

Author

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  • Miller, Robert E.
  • Gehr, Adam K.

Abstract

Several years ago Sharpe suggested a measure for the evaluation of portfolio performance. The measure was conceptually simple, easily calculated, and applicable to an entire investment portfolio, in contrast to the measures of Treynor and Jensen which measure only the undiversifiable risk in a portfolio. Sharpe's measure is still a frequently recommended tool for measuring portfolio performance. The measure is, however, biased. It is the purpose of this note to demonstrate the existence of the bias, indicate its size, and provide a means of correcting it.

Suggested Citation

  • Miller, Robert E. & Gehr, Adam K., 1978. "Sample Size Bias and Sharpe's Performance Measure: A Note," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(5), pages 943-946, December.
    • Handle: RePEc:cup:jfinqa:v:13:y:1978:i:05:p:943-946_01
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    Cited by:

    1. Schuster, Martin & Auer, Benjamin R., 2012. "A note on empirical Sharpe ratio dynamics," Economics Letters, Elsevier, vol. 116(1), pages 124-128.
    2. Eric Benhamou, 2018. "Connecting Sharpe ratio and Student t-statistic, and beyond," Papers 1808.04233, arXiv.org, revised May 2019.
    3. Yong Bao & Xiaotian Liu & Aman Ullah, 2020. "On the Exact Statistical Distribution of Econometric Estimators and Test Statistics," Working Papers 202014, University of California at Riverside, Department of Economics, revised Jun 2020.
    4. Shafique, Attayah & Ayub, Usman & Zakaria, Muhammad, 2019. "Don’t let the Greed catch you! Pleonexia rule applied to Pakistan stock exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 157-168.
    5. Steven Pav, 2019. "A post hoc test on the Sharpe ratio," Papers 1911.04090, arXiv.org.
    6. Vitali Alexeev & Katja Ignatieva, 2021. "Biases in variance of decomposed portfolio returns," International Review of Finance, International Review of Finance Ltd., vol. 21(4), pages 1152-1178, December.
    7. John Knight & Stephen Satchell, 2005. "A Re-Examination of Sharpe's Ratio for Log-Normal Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 87-100.
    8. Mahesh K.C & Arnab Kumar Laha, 2021. "A Robust Sharpe Ratio," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 444-465, November.
    9. Raymond Kan & Daniel R. Smith, 2008. "The Distribution of the Sample Minimum-Variance Frontier," Management Science, INFORMS, vol. 54(7), pages 1364-1380, July.
    10. Kourtis, Apostolos, 2016. "The Sharpe ratio of estimated efficient portfolios," Finance Research Letters, Elsevier, vol. 17(C), pages 72-78.
    11. 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.
    12. Attayah Shafique & Usman Ayub & Muhammad Shariq & Muhammad Ashfaq, 2022. "Does Voracious Behavior favor Efficient Market Hypothesis? Role of Performance Measures," Scientific Annals of Economics and Business (continues Analele Stiintifice), Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, vol. 69(4), pages 631-649, December.
    13. Bao, Yong & Ullah, Aman, 2006. "Moments of the estimated Sharpe ratio when the observations are not IID," Finance Research Letters, Elsevier, vol. 3(1), pages 49-56, March.
    14. Eric Benhamou, 2021. "Distribution and statistics of the Sharpe Ratio," Working Papers hal-03207169, HAL.

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