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Risk Attitudes Toward Small and Large Bets in the Presence of Background Risk

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  • David A. Chapman
  • Valery Polkovnichenko

Abstract

If an individual with expected utility and a reasonable level of wealth rejects a small actuarially favorable gamble, it implies a very high degree of risk aversion. It also predicts (counterfactually) the rejection of more sizable and very attractive bets. If additional background uncertainty affects wealth, this result also applies to non-expected utilities. The authors describe a set of reasonable conditions under which an individual may reject the small bet but accept the large bet, even in the presence of background uncertainty. The two critical assumptions that the authors use are rank-dependent utility and a discrete distribution for background risk. Plausible calibrations can reconcile large/small bet risk attitudes and the empirical evidence on limited stock market participation in the presence of labor income risk. Copyright 2011, Oxford University Press.

Suggested Citation

  • David A. Chapman & Valery Polkovnichenko, 2011. "Risk Attitudes Toward Small and Large Bets in the Presence of Background Risk," Review of Finance, European Finance Association, vol. 15(4), pages 909-927.
    • Handle: RePEc:oup:revfin:v:15:y:2011:i:4:p:909-927
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    File URL: http://hdl.handle.net/10.1093/rof/rfq037
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    Cited by:

    1. Stephen G Dimmock & Roy Kouwenberg & Olivia S Mitchell & Kim Peijnenburg, 2021. "Household Portfolio Underdiversification and Probability Weighting: Evidence from the Field," The Review of Financial Studies, Society for Financial Studies, vol. 34(9), pages 4524-4563.
    2. Han Bleichrodt & Jason N. Doctor & Yu Gao & Chen Li & Daniella Meeker & Peter P. Wakker, 2019. "Resolving Rabin’s paradox," Journal of Risk and Uncertainty, Springer, vol. 59(3), pages 239-260, December.
    3. Haug, Jørgen & Hens, Thorsten & Woehrmann, Peter, 2013. "Risk aversion in the large and in the small," Economics Letters, Elsevier, vol. 118(2), pages 310-313.

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