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On the Nature of Certainty Equivalent Functionals

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Author Info
Hennessy, David A.
Lapan, Harvey E.

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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.

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Publisher Info
Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 12552.

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Date of creation: 23 Mar 2006
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Publication status: Published in Journal of Mathematical Economics, December 2006, Vol. 43, No. 1, pp. 1-10.
Handle: RePEc:isu:genres:12552

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Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
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Related research
Keywords: Association; Convexity; HARA preferences; Standardness; Superadditivity;

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Find related papers by JEL classification:
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming
D8 - Microeconomics - - Information, Knowledge, and Uncertainty
G1 - Financial Economics - - General Financial Markets

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-23, September. [Downloadable!] (restricted)
  2. Monica Paiella & Luigi Guiso, 2004. "Risk Aversion, Wealth and Background Risk," 2004 Meeting Papers 525, Society for Economic Dynamics. [Downloadable!]
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  3. 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. [Downloadable!] (restricted)
    Other versions:
  4. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May. [Downloadable!] (restricted)
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  5. Gollier, Christian, 2002. "Time diversification, liquidity constraints, and decreasing aversion to risk on wealth," Journal of Monetary Economics, Elsevier, vol. 49(7), pages 1439-1459, October. [Downloadable!] (restricted)
  6. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February. [Downloadable!] (restricted)
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  8. Hara, C. & Christoph Kuzmics, 2004. "Representative Consumer's Risk Aversion and Efficient Risk-Sharing Rules," Cambridge Working Papers in Economics 0452, Faculty of Economics, University of Cambridge. [Downloadable!]
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  9. Christian Ghiglino & Marielle Olszak-Duquenne, 2005. "On The Impact Of Heterogeneity On Indeterminacy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(1), pages 171-188, 02. [Downloadable!] (restricted)
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  10. Gollier, C., 1997. "Wealth Inequality and Asset Pricing," Papers 97.486, Toulouse - GREMAQ.
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  11. David A. Hennessy & Harvey E. Lapan, 2003. "A Definition of 'More Systematic Risk' with Some Welfare Implications," Economica, London School of Economics and Political Science, vol. 70(279), pages 493-507, 08. [Downloadable!] (restricted)
  12. Qiang Zhang & Masao Ogaki, 2004. "Decreasing Relative Risk Aversion, Risk Sharing, and the Permanent Income Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 421-430, October. [Downloadable!] (restricted)
  13. Ogaki, Masao & Zhang, Qiang, 2001. "Decreasing Relative Risk Aversion and Tests of Risk Sharing," Econometrica, Econometric Society, vol. 69(2), pages 515-26, March.
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  14. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September. [Downloadable!] (restricted)
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  15. Athey, S., 1996. "Characterizing Properties of Stochastic Objective Functions," Working papers 96-1, Massachusetts Institute of Technology (MIT), Department of Economics.
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  1. Hennessy, David A. & Lapan, Harvey E., 2006. "On the Nature of Certainty Equivalent Functionals," Staff General Research Papers 12552, Iowa State University, Department of Economics.
    Other versions:
  2. Luigi Guiso & Monica Paiella, 2007. "Risk Aversion, Wealth, and Background Risk," Economics Working Papers ECO2007/47, European University Institute. [Downloadable!]
    Other versions:
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