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On the Nature of Certainty Equivalent Functionals

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  • Hennessy, David A.
  • Lapan, Harvey E.

Abstract

We explore connections between the certainty equivalent return (CER) functional and the underlying utility function. Curvature properties of the functional depend upon how utility function attributes relate to hyperbolic absolute risk aversion (HARA) type utility functions. If the CER functional is concave, i.e., if risk tolerance is concave in wealth, then preferences are standard. The CER functional is linear in lotteries if utility is HARA and lottery payoffs are on a line in state space. Implications for the optimality of portfolio diversification are given. When utility is concave and non-increasing relative risk averse, then the CER functional is superadditive in lotteries. Depending upon the nature of association among lottery payoffs, CERs for constant absolute risk averse utility functions may be subadditive or superadditive in lotteries. Our approach lends itself to straightforward experiments to elicit higher order attributes on risk preferences.

Suggested Citation

  • Hennessy, David A. & Lapan, Harvey E., 2006. "On the Nature of Certainty Equivalent Functionals," Staff General Research Papers Archive 12552, Iowa State University, Department of Economics.
  • Handle: RePEc:isu:genres:12552
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    Cited by:

    1. Loïc Berger & Johannes Emmerling, 2017. "Welfare as Simple(x) Equity Equivalents," Working Papers 2017.14, Fondazione Eni Enrico Mattei.
    2. Hennessy, David A. & Lapan, Harvey E., 2006. "On the nature of certainty equivalent functionals," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 1-10, December.
    3. Luigi Guiso & Monica Paiella, 2008. "Risk Aversion, Wealth, and Background Risk," Journal of the European Economic Association, MIT Press, vol. 6(6), pages 1109-1150, December.
    4. Colin Lizieri & Gianluca Marcato & Paul Ogden & Andrew Baum, 2012. "Pricing Inefficiencies in Private Real Estate Markets Using Total Return Swaps," The Journal of Real Estate Finance and Economics, Springer, vol. 45(3), pages 774-803, October.

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