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Greater prudence and greater downside risk aversion

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  • Keenan, Donald C.
  • Snow, Arthur
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    Abstract

    Variation in the degree of downside risk aversion across decision makers has implications for efficient risk sharing. However, except for small differences in risk preferences, there is no index, analogous to the Arrow-Pratt index of risk aversion, that depends only on local properties of the utility function and indicates the degree of aversion to downside risk. A measure that does depend only on local properties of the utility function u, the index of prudence p=-u'''/u'', is related to downside risk aversion, which is indicated by a positive value for u'''. Although we show that the degree of prudence is not an accurate indicator of the degree of downside risk aversion, we nonetheless demonstrate that a uniform increase in prudence accompanied by a uniform increase (decrease) in risk aversion is sufficient to indicate greater downside risk aversion, provided prudence is greater (less) than three times the degree of risk aversion.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 145 (2010)
    Issue (Month): 5 (September)
    Pages: 2018-2026

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    Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:2018-2026

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    Web page: http://www.elsevier.com/locate/inca/622869

    Related research

    Keywords: Downside risk aversion Prudence;

    References

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    1. Modica, Salvatore & Scarsini, Marco, 2005. "A note on comparative downside risk aversion," Journal of Economic Theory, Elsevier, vol. 122(2), pages 267-271, June.
    2. Steve Boucher & Catherine Guirkinger, 2007. "Risk, Wealth, and Sectoral Choice in Rural Credit Markets," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 89(4), pages 991-1004.
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    5. David Crainich & Louis Eeckhoudt, 2008. "On the intensity of downside risk aversion," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 267-276, June.
    6. Miles S. Kimball, 1989. "Precautionary Saving in the Small and in the Large," NBER Working Papers 2848, National Bureau of Economic Research, Inc.
    7. Marie-Cécile Fagart & Bernard Sinclair-Desgagné, 2007. "Ranking Contingent Monitoring Systems," Management Science, INFORMS, vol. 53(9), pages 1501-1509, September.
    8. EECKHOUDT, Louis & SCHLESINGER, Harris, . "Putting risk in its proper place," CORE Discussion Papers RP -1871, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-32, December.
    10. W. Henry Chiu, 2005. "Skewness Preference, Risk Aversion, and the Precedence Relations on Stochastic Changes," Management Science, INFORMS, vol. 51(12), pages 1816-1828, December.
    11. Boucher, Stephen R. & Guirkinger, Catherine, 2007. "AJAE Appendix: Risk, Wealth and Sectoral Choice in Rural Credit Markets," American Journal of Agricultural Economics Appendices, Agricultural and Applied Economics Association, vol. 89(4), November.
    12. Thiele, Henrik & Wambach, Achim, 1999. "Wealth Effects in the Principal Agent Model," Journal of Economic Theory, Elsevier, vol. 89(2), pages 247-260, December.
    13. Sanford J Grossman & Oliver D Hart, 2001. "An Analysis of the Principal-Agent Problem," Levine's Working Paper Archive 391749000000000339, David K. Levine.
    14. Jindapon, Paan & Neilson, William S., 2007. "Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach," Journal of Economic Theory, Elsevier, vol. 136(1), pages 719-728, September.
    15. Keenan, Donald C & Snow, Arthur, 2002. " Greater Downside Risk Aversion," Journal of Risk and Uncertainty, Springer, vol. 24(3), pages 267-77, May.
    16. Keenan, Donald C. & Snow, Arthur, 2009. "Greater downside risk aversion in the large," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1092-1101, May.
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    Citations

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    Cited by:
    1. Gollier, Christian & Hammitt, James & Treich, Nicolas, 2013. "Risk and Choice: A Research Saga," TSE Working Papers 13-444, Toulouse School of Economics (TSE).
    2. Pierre Chaigneau, 2012. "The effect of risk preferences on the valuation and incentives of compensation contracts," FMG Discussion Papers dp697, Financial Markets Group.
    3. Pierre Chaigneau, 2012. "The Effect of Risk Preferences on the Valuation and Incentives of Compensation Contracts," Cahiers de recherche 1209, CIRPEE.
    4. Jindapon, Paan, 2010. "Prudence probability premium," Economics Letters, Elsevier, vol. 109(1), pages 34-37, October.
    5. Donald Keenan & Arthur Snow, 2012. "The Schwarzian derivative as a ranking of downside risk aversion," Journal of Risk and Uncertainty, Springer, vol. 44(2), pages 149-160, April.

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