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Generalization of the Sharpe Ratio and the Arbitrage-Free Pricing of Higher Moments

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  • Gaurav Amin

    (ICMA Centre, University of Reading)

  • Harry. M Kat

    (ICMA Centre, University of Reading)

Abstract

We present an extension of the traditional Sharpe ratio to allow for the evaluation of non-normal return distributions. Combining earlier work in this area with stochastic simulation, we develop a procedure that allows for the construction of a benchmark for the evaluation of the performance of funds with a non-normal return distribution, while maintaining the operational ease of the Sharpe ratio. Similar to the latter, our procedure only requires the risk-free rate of interest rate, the distribution of the market index and an assumption about the type of return distributions to be evaluated. Unlike the Sharpe ratio, however, we are not restricted to normality but are able to handle any reasonable type of distribution. Since our benchmarking procedure is based on the no-arbitrage assumption, it also provides insight into the conditional arbitrage-free value of one distributional parameter in terms of another. We show that in case of the Johnson Su distribution the relationship between skewness and mean return is more or less flat. Skewness and median return on the other hand exhibit a strong negative relationship.

Suggested Citation

  • Gaurav Amin & Harry. M Kat, 2002. "Generalization of the Sharpe Ratio and the Arbitrage-Free Pricing of Higher Moments," ICMA Centre Discussion Papers in Finance icma-dp2002-15, Henley Business School, University of Reading.
    • Handle: RePEc:rdg:icmadp:icma-dp2002-15
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    File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2002-15.pdf
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    References listed on IDEAS

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    1. Cox, John C. & Leland, Hayne E., 2000. "On dynamic investment strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1859-1880, October.
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    3. William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 119-119.
    4. Philip H. Dybvig, 1988. "Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 67-88.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Marcos Mailoc López de Prado & Achim Peijan, 2005. "Measuring Loss Potential of Hedge Fund Strategies," Finance 0503010, University Library of Munich, Germany.

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