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Rationalizing Investors Choice

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  • Carole Bernard
  • Jit Seng Chen
  • Steven Vanduffel
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    Abstract

    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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    Bibliographic Info

    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

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    1. Birnbaum, Michael H & Navarrete, Juan B, 1998. "Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence," Journal of Risk and Uncertainty, Springer, Springer, vol. 17(1), pages 49-78, October.
    2. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
    3. Enrico Giorgi & Thorsten Hens, 2006. "Making prospect theory fit for finance," Financial Markets and Portfolio Management, Springer, Springer, vol. 20(3), pages 339-360, September.
    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, American Economic Association, vol. 38(2), pages 332-382, June.
    5. Bagnoli, M. & Bergstrom, T., 1989. "Log-Concave Probability And Its Applications," Papers, Michigan - Center for Research on Economic & Social Theory 89-23, Michigan - Center for Research on Economic & Social Theory.
    6. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 61(3), pages 369-93, July.
    7. Chen, An & Pelsser, Antoon & Vellekoop, Michel, 2011. "Modeling non-monotone risk aversion using SAHARA utility functions," Journal of Economic Theory, Elsevier, Elsevier, vol. 146(5), pages 2075-2092, September.
    8. Dybvig, Philip H. & Wang, Yajun, 2012. "Increases in risk aversion and the distribution of portfolio payoffs," Journal of Economic Theory, Elsevier, Elsevier, vol. 147(3), pages 1222-1246.
    9. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, American Finance Association, vol. 7(1), pages 77-91, 03.
    10. Bernard, Carole & Ghossoub, Mario, 2009. "Static Portfolio Choice under Cumulative Prospect Theory," MPRA Paper 15446, University Library of Munich, Germany.
    11. Nicholas Barberis & Ming Huang, 2008. "Stocks as Lotteries: The Implications of Probability Weighting for Security Prices," American Economic Review, American Economic Association, American Economic Association, vol. 98(5), pages 2066-2100, December.
    12. Chateauneuf, A. & Wakker, P., 1998. "An Axiomatization of Cumulative Prospect Theory for Decision Under Risk," Papiers d'Economie Mathématique et Applications, Université Panthéon-Sorbonne (Paris 1) 98.51, Université Panthéon-Sorbonne (Paris 1).
    13. 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, Society for Financial Studies, vol. 10(1), pages 151-74.
    14. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 95-115, January.
    15. 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, University of Chicago Press, vol. 35(3), pages 440-456, 08.
    16. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, Springer, vol. 5(4), pages 297-323, October.
    17. Moshe Levy & Haim Levy, 2002. "Prospect Theory: Much Ado About Nothing?," Management Science, INFORMS, INFORMS, vol. 48(10), pages 1334-1349, October.
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