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Rationalizing Investors Choice

  • Carole Bernard
  • Jit Seng Chen
  • Steven Vanduffel
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    Assuming that agents' preferences satisfy first-order stochastic dominance, we show how the Expected Utility paradigm can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant (state-independent) setting corresponds to the optimum for an expected utility maximizer with an explicitly derived concave non-decreasing utility function. This result enables us to infer the utility and risk aversion of agents from their investment choice in a non-parametric way. We relate the property of decreasing absolute risk aversion (DARA) to distributional properties of the terminal wealth and of the financial market. Specifically, we show that DARA is equivalent to a demand for a terminal wealth that has more spread than the opposite of the log pricing kernel at the investment horizon.

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    File URL: http://arxiv.org/pdf/1302.4679
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    Paper provided by arXiv.org in its series Papers with number 1302.4679.

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    Date of creation: Feb 2013
    Date of revision: Jan 2014
    Handle: RePEc:arx:papers:1302.4679
    Contact details of provider: Web page: http://arxiv.org/

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    1. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
    2. Dybvig, Philip H & Rogers, L C G, 1997. "Recovery of Preferences from Observed Wealth in a Single Realization," Review of Financial Studies, Society for Financial Studies, vol. 10(1), pages 151-74.
    3. Philip H. Dybvig, 1987. "Distributional Analysis of Portfolio Choice," Cowles Foundation Discussion Papers 827R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1988.
    4. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    5. Dybvig, Philip H. & Wang, Yajun, 2012. "Increases in risk aversion and the distribution of portfolio payoffs," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1222-1246.
    6. Bagnoli, M. & Bergstrom, T., 1989. "Log-Concave Probability And Its Applications," Papers 89-23, Michigan - Center for Research on Economic & Social Theory.
    7. Daniel G. Goldstein & Eric J. Johnson & William F. Sharpe, 2008. "Choosing Outcomes versus Choosing Products: Consumer-Focused Retirement Investment Advice," Journal of Consumer Research, University of Chicago Press, vol. 35(3), pages 440-456, 08.
    8. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    9. Enrico Giorgi & Thorsten Hens, 2006. "Making prospect theory fit for finance," Financial Markets and Portfolio Management, Springer, vol. 20(3), pages 339-360, September.
    10. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    11. Bernard, Carole & Ghossoub, Mario, 2009. "Static Portfolio Choice under Cumulative Prospect Theory," MPRA Paper 15446, University Library of Munich, Germany.
    12. Moshe Levy & Haim Levy, 2002. "Prospect Theory: Much Ado About Nothing?," Management Science, INFORMS, vol. 48(10), pages 1334-1349, October.
    13. Chateauneuf, Alain & Wakker, Peter, 1999. "An Axiomatization of Cumulative Prospect Theory for Decision under Risk," Journal of Risk and Uncertainty, Springer, vol. 18(2), pages 137-45, August.
    14. Chen, An & Pelsser, Antoon & Vellekoop, Michel, 2011. "Modeling non-monotone risk aversion using SAHARA utility functions," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2075-2092, September.
    15. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
    16. Nicholas Barberis & Ming Huang, 2008. "Stocks as Lotteries: The Implications of Probability Weighting for Security Prices," American Economic Review, American Economic Association, vol. 98(5), pages 2066-2100, December.
    17. Birnbaum, Michael H & Navarrete, Juan B, 1998. "Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence," Journal of Risk and Uncertainty, Springer, vol. 17(1), pages 49-78, October.
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