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Utility and the Skewness of Return in Gambling

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  • Michael Cain
  • David Peel

Abstract

This paper demonstrates that the intuitively appealing argument based on the postulated trade-off between expected return, variance and skewness of return of a risk-averse gambler does not provide an explanation of observed betting behaviour. It is shown how the expected utility of a representative gambler faced with a single-prized outcome event can be expressed in terms of the mean and variance of return, the mean and skewness of return or, generally, of the mean and any other single moment of return: and the standard practice of taking a Taylor series expansion/approximation of the expected utility involving moments of return is usually incorrect. Previous analyses have suggested that a punter will accept a lower mean return for higher skewness and this work seems to have involved invalid expansions of the utility function. The upshot is that with certain utility functions which have been used in a number of studies, any analysis based on expansion and estimation of the derivatives of the utility function may be valid only for data based on odds-on favourites and not for longshots.

Suggested Citation

  • Michael Cain & David Peel, 2004. "Utility and the Skewness of Return in Gambling," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 29(2), pages 145-163, December.
    • Handle: RePEc:kap:geneva:v:29:y:2004:i:2:p:145-163
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    Cited by:

    1. D. A. Peel, 2008. "Introduction: economics of betting markets," Applied Economics, Taylor & Francis Journals, vol. 40(1), pages 1-3.
    2. David Peel & David Law, 2009. "A More General Non‐expected Utility Model as an Explanation of Gambling Outcomes for Individuals and Markets," Economica, London School of Economics and Political Science, vol. 76(302), pages 251-263, April.
    3. Christodoulakis, George & Peel, David, 2006. "The relationship between expected utility and higher moments for distributions captured by the Gram-Charlier class," Finance Research Letters, Elsevier, vol. 3(4), pages 273-276, December.
    4. Chiu, Leslie J. Verteramo, 2013. "Risk Rationing and Jump Utility," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150589, Agricultural and Applied Economics Association.
    5. Ebert, Sebastian, 2015. "On skewed risks in economic models and experiments," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 85-97.
    6. D. A. Peel, 2012. "Further examples of the impact of skewness on the expected utility of a risk-averse agent," Applied Economics Letters, Taylor & Francis Journals, vol. 19(12), pages 1117-1121, August.
    7. Chiu, Leslie J. Verteramo & Turvey, Calum G., 2013. "A Risk Rationing Model," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150628, Agricultural and Applied Economics Association.
    8. David A. Peel & Davind Law, 2009. "An Explanation of Optimal Each-Way Bets based on Non-Expected Utility Theory," Journal of Gambling Business and Economics, University of Buckingham Press, vol. 3(2), pages 15-35, September.

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