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Increases in risk aversion and the distribution of portfolio payoffs

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  • Dybvig, Philip H.
  • Wang, Yajun

Abstract

Oliver Hart proved the impossibility of deriving general comparative static properties in portfolio weights. Instead, we derive new comparative statics for the distribution of payoffs: A is less risk averse than B iff Aʼs payoff is always distributed as Bʼs payoff plus a non-negative random variable plus conditional-mean-zero noise. If either agent has nonincreasing absolute risk aversion, the non-negative part can be chosen to be constant. The main result also holds in some incomplete markets with two assets or two-fund separation, and in multiple periods for a mixture of payoff distributions over time (but not at every point in time).

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Bibliographic Info

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

Volume (Year): 147 (2012)
Issue (Month): 3 ()
Pages: 1222-1246

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:3:p:1222-1246

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

Related research

Keywords: Risk aversion; Portfolio theory; Stochastic dominance; Complete markets; Two-fund separation;

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References

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  1. Mark J Machina, 1982. ""Expected Utility" Analysis without the Independence Axiom," Levine's Working Paper Archive 7650, David K. Levine.
  2. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  3. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-38, May.
  4. Rothschild, Michael & Stiglitz, Joseph E., 1972. "Addendum to "increasing risk: I. A definition"," Journal of Economic Theory, Elsevier, vol. 5(2), pages 306-306, October.
  5. Machina, Mark J., 1989. "Comparative statics and non-expected utility preferences," Journal of Economic Theory, Elsevier, vol. 47(2), pages 393-405, April.
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  7. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-20, June.
  8. Dybvig, Philip H. & Liu, Hong, 2010. "Lifetime consumption and investment: Retirement and constrained borrowing," Journal of Economic Theory, Elsevier, vol. 145(3), pages 885-907, May.
  9. Ross, Stephen A., 1978. "Mutual fund separation in financial theory--The separating distributions," Journal of Economic Theory, Elsevier, vol. 17(2), pages 254-286, April.
  10. Dybvig, Philip H & Ingersoll, Jonathan E, Jr, 1982. "Mean-Variance Theory in Complete Markets," The Journal of Business, University of Chicago Press, vol. 55(2), pages 233-51, April.
  11. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
  12. Hart, Oliver D, 1975. "Some Negative Results on the Existence of Comparative Statics Results in Portfolio Theory," Review of Economic Studies, Wiley Blackwell, vol. 42(4), pages 615-21, October.
  13. Cox, John C. & Huang, Chi-fu, 1991. "A variational problem arising in financial economics," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 465-487.
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Cited by:
  1. Carole Bernard & Jit Seng Chen & Steven Vanduffel, 2013. "Rationalizing Investors Choice," Papers 1302.4679, arXiv.org, revised Jan 2014.

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