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Parametric Characterizations of Risk Aversion and Prudence

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  • Lajeri, Fatma
  • Nielsen, Lars Tyge

Abstract

We show that in order to determine whether one decision-maker is more risk averse than another, it is sufficient to consider their attitudes towards a given two-parameter family of risks. When all risks belong to this family, useful comparisons of risk aversion can be made even in situations of ‘background risk’. Since expected utility becomes a function of mean and standard deviation, risk aversion can be measured by the marginal rate of substitution between mean and standard deviation. A utility function exhibits decreasing risk aversion if, and only if, this slope is a decreasing function of the mean. Second, we use the concept of prudence to solve a long-standing problem in mean-variance analysis: what is the economic interpretation of the concavity of a utility function which is a function of mean and variance? We show that in the case of normal distributions, utility is concave as a function of variance and mean if, and only if, it exhibits decreasing prudence.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 1650.

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Date of creation: May 1997
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Handle: RePEc:cpr:ceprdp:1650

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Keywords: Prudence; Risk Aversion;

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Cited by:
  1. Thomas Eichner & Andreas Wagener, 2004. "Relative risk aversion, relative prudence and comparative statics under uncertainty: The case of (μ, σ)-preferences," Bulletin of Economic Research, Wiley Blackwell, vol. 56(2), pages 159-170, 04.
  2. Carstensen, Vivian, 2002. "Reorganization of Firms and Productivity: A Treatment Effects Approach," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Leibniz Universität Hannover dp-257, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  3. Uwe Dulleck & Andreas Loffler, 2012. "μ-σ Games," NCER Working Paper Series 78, National Centre for Econometric Research.
  4. Wenzelburger, Jan, 2008. "A Note on the Two-fund Separation Theorem," MPRA Paper 11014, University Library of Munich, Germany, revised 31 Sep 2008.
  5. Andreas Wagener, 2005. "Linear risk tolerance and mean-variance preferences," Economics Bulletin, AccessEcon, vol. 4(1), pages 1-8.
  6. Thomas Eichner & Andreas Wagener, 2005. "Notes and Comments: Measures of risk attitude: correspondences between mean-variance and expected-utility approaches," Decisions in Economics and Finance, Springer, vol. 28(1), pages 53-65, 06.
  7. repec:ebl:ecbull:v:6:y:2004:i:5:p:1-7 is not listed on IDEAS
  8. Udo Broll & Jack E. Wahl & Wing-Keung Wong, 2005. "Elasticity of risk aversion and international trade," Monash Economics Working Papers 07/05, Monash University, Department of Economics.
  9. Wing-Keung Wong & Chenghu Ma, 2008. "Preferences over location-scale family," Economic Theory, Springer, vol. 37(1), pages 119-146, October.
  10. Lajeri-Chaherli, Fatma, 2003. "Partial derivatives, comparative risk behavior and concavity of utility functions," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 81-99, August.
  11. Andersen, Torben M, 2010. "Incentive and Insurance Effects of Tax Financed Unemployment Insurance," CEPR Discussion Papers 8025, C.E.P.R. Discussion Papers.
  12. Thomas Eichner & Rüdiger Pethig, 2010. "Efficient Management of Insecure Fossil Fuel Imports through Taxing (!) Domestic Green Energy?," CESifo Working Paper Series 3062, CESifo Group Munich.
  13. Wagener, Andreas, 2003. "Comparative statics under uncertainty: The case of mean-variance preferences," European Journal of Operational Research, Elsevier, vol. 151(1), pages 224-232, November.
  14. Ennio Bilancini & Massimo D'Antoni, 2008. "Pensions and Intergenerational Risk-Sharing When Relative Consumption Matters," Department of Economics University of Siena 541, Department of Economics, University of Siena.
  15. Thomas Eichner & Andreas Wagener, 2011. "Portfolio allocation and asset demand with mean-variance preferences," Theory and Decision, Springer, vol. 70(2), pages 179-193, February.
  16. Wagener, Andreas, 2002. "Prudence and risk vulnerability in two-moment decision models," Economics Letters, Elsevier, vol. 74(2), pages 229-235, January.
  17. Jan Wenzelburger, 2010. "The two-fund separation theorem revisited," Annals of Finance, Springer, vol. 6(2), pages 221-239, March.
  18. Udo Broll & Jack E. Wahl, 2004. "Optimal hedge ratio and elasticity of risk aversion," Economics Bulletin, AccessEcon, vol. 6(5), pages 1-7.
  19. Hens, Thorsten & Laitenberger, Jorg & Loffler, Andreas, 2002. "Two remarks on the uniqueness of equilibria in the CAPM," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 123-132, April.
  20. Eichner, Thomas, 2011. "Portfolio selection and duality under mean variance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 146-152, January.

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