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An Analytical Confidence Interval for the Treynor Index: Formula, Conditions and Properties

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  • Matthew R. Morey
  • Richard C. Morey

Abstract

The Treynor index, a well‐known, widely‐used measure of portfolio performance, is the ratio of the mean excess rate of return of the portfolio to the portfolio's beta. We derive an analytical formula that is designed to yield rigorous confidence intervals on the index. Necessary and sufficient conditions for the Treynor index to be statistically different from zero, are provided. We illustrate our approach with detailed examples and include simulations to help analysts choose the number of periods to study. Finally, some interesting properties of the interval and some sensitivity results are provided.

Suggested Citation

  • Matthew R. Morey & Richard C. Morey, 2000. "An Analytical Confidence Interval for the Treynor Index: Formula, Conditions and Properties," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 27(1‐2), pages 127-154, January.
    • Handle: RePEc:bla:jbfnac:v:27:y:2000:i:1-2:p:127-154
    DOI: 10.1111/1468-5957.00308
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    Cited by:

    1. Lean, Hooi Hooi & McAleer, Michael & Wong, Wing-Keung, 2010. "Market efficiency of oil spot and futures: A mean-variance and stochastic dominance approach," Energy Economics, Elsevier, vol. 32(5), pages 979-986, September.
    2. Lean, H.H. & McAleer, M.J. & Wong, W.-K., 2010. "Investor preferences for oil spot and futures based on mean-variance and stochastic dominance," Econometric Institute Research Papers EI 2010-37, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Hooi Hooi Lean & Michael McAleer & Wing-Keung Wong, 2013. "Risk-averse and Risk-seeking Investor Preferences for Oil Spot and Futures," Documentos de Trabajo del ICAE 2013-31, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Aug 2013.
    4. Lean, Hooi Hooi & McAleer, Michael & Wong, Wing-Keung, 2015. "Preferences of risk-averse and risk-seeking investors for oil spot and futures before, during and after the Global Financial Crisis," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 204-216.

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