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Inference on the Sharpe ratio via the upsilon distribution

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  • Steven E. Pav

Abstract

The upsilon distribution, the sum of independent chi random variates and a normal, is introduced. As a special case, the upsilon distribution includes Lecoutre's lambda-prime distribution. The upsilon distribution finds application in Frequentist inference on the Sharpe ratio, including hypothesis tests on independent samples, confidence intervals, and prediction intervals, as well as their Bayesian counterparts. These tests are extended to the case of factor models of returns.

Suggested Citation

  • Steven E. Pav, 2015. "Inference on the Sharpe ratio via the upsilon distribution," Papers 1505.00829, arXiv.org, revised Aug 2021.
    • Handle: RePEc:arx:papers:1505.00829
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    References listed on IDEAS

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    3. Min-ge Xie & Kesar Singh, 2013. "Confidence Distribution, the Frequentist Distribution Estimator of a Parameter: A Review," International Statistical Review, International Statistical Institute, vol. 81(1), pages 3-39, April.
    4. 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.
    5. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
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    7. Jaschke, Stefan R., 2001. "The Cornish-Fisher-Expansion in the context of Delta - Gamma - Normal approximations," SFB 373 Discussion Papers 2001,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Poitevineau, Jacques & Lecoutre, Bruno, 2010. "Implementing Bayesian predictive procedures: The K-prime and K-square distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 724-731, March.
    9. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
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