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Performance Hypothesis Testing with the Sharpe and Treynor Measures

J. D. Jobson and Bob M. Korkie
The Journal of Finance
Vol. 36, No. 4 (Sep., 1981), pp. 889-908
Published by: Wiley for the American Finance Association
DOI: 10.2307/2327554
Stable URL: http://www.jstor.org/stable/2327554
Page Count: 20
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Performance Hypothesis Testing with the Sharpe and Treynor Measures
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Abstract

Asymptotic distributions of the estimators of the Sharpe and Treynor performance measures are derived. Multivariate performance comparison measures, based on the traditional Sharpe and Treynor measures, are developed with their corresponding asymptotic distributions. The behavior of these new performance measures are evaluated in small samples. For single comparisons, a Sharpe z statistic is well behaved and for multiple comparisons a Sharpe chi-square statistic is reasonably well behaved. The powers of the tests are quite sensitive to the population coefficients of variation. Multivariate test statistics based upon the Treynor measure were not very satisfactory.

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