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Static Portfolio Choice under Cumulative Prospect Theory

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  • Bernard, Carole
  • Ghossoub, Mario

Abstract

We derive the optimal portfolio choice for an investor who behaves according to Cumulative Prospect Theory. The study is done in a one-period economy with one risk-free asset and one risky asset, and the reference point corresponds to the terminal wealth arising when the entire initial wealth is invested into the risk-free asset. When it exists, the optimal holding is a function of a generalized Omega measure of the distribution of the excess return on the risky asset over the risk-free rate. It conceptually resembles Merton’s optimal holding for a CRRA expected-utility maximizer. We derive some properties of the optimal holding and illustrate our results using a simple example where the excess return has a skew-normal distribution. In particular, we show how a Cumulative Prospect Theory investor is highly sensitive to the skewness of the excess return on the risky asset. In the model we adopt, with a piecewise-power value function with different shape parameters, loss aversion might be violated for reasons that are now well-understood in the literature. Nevertheless, we argue, on purely behavioral grounds, that this violation is acceptable.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 15446.

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Date of creation: 29 Apr 2009
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Handle: RePEc:pra:mprapa:15446

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Keywords: Cumulative Prospect Theory; Portfolio Choice; Behavioral Finance; Omega Measure.;

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References

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  1. Neilson, William S, 2002. " Comparative Risk Sensitivity with Reference-Dependent Preferences," Journal of Risk and Uncertainty, Springer, Springer, vol. 24(2), pages 131-42, March.
  2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 571-87, May.
  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. Handa, Jagdish, 1977. "Risk, Probabilities, and a New Theory of Cardinal Utility," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 85(1), pages 97-122, February.
  5. Ulrich Schmidt & Horst Zank, 2007. "Linear cumulative prospect theory with applications to portfolio selection and insurance demand," Decisions in Economics and Finance, Springer, Springer, vol. 30(1), pages 1-18, 05.
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  7. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 95-115, January.
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  10. 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.
  11. Enrico De Giorgi & Thorsten Hens & Marc Oliver Rieger, 2007. "Financial Market Equilibria With Cumulative Prospect Therory," Swiss Finance Institute Research Paper Series, Swiss Finance Institute 07-21, Swiss Finance Institute, revised Aug 2007.
  12. U Schmidt & H Zank, 2002. "What is Loss Aversion?," The School of Economics Discussion Paper Series, Economics, The University of Manchester 0209, Economics, The University of Manchester.
  13. Shlomo Benartzi & Richard H. Thaler, 1993. "Myopic Loss Aversion and the Equity Premium Puzzle," NBER Working Papers 4369, National Bureau of Economic Research, Inc.
  14. Wakker, Peter & Tversky, Amos, 1993. " An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, Springer, vol. 7(2), pages 147-75, October.
  15. Robert Jarrow & Feng Zhao, 2006. "Downside Loss Aversion and Portfolio Management," Management Science, INFORMS, INFORMS, vol. 52(4), pages 558-566, April.
  16. Francisco J. Gomes, 2005. "Portfolio Choice and Trading Volume with Loss-Averse Investors," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 78(2), pages 675-706, March.
  17. Arjan B. Berkelaar & Roy Kouwenberg & Thierry Post, 2004. "Optimal Portfolio Choice under Loss Aversion," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 973-987, November.
  18. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, Econometric Society, vol. 47(2), pages 263-91, March.
  19. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, Elsevier, vol. 122(1), pages 119-131, May.
  20. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 3(4), pages 323-343, December.
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Citations

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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.
  2. Miklos Rasonyi & Andrea M. Rodrigues, 2012. "Optimal Portfolio Choice for a Behavioural Investor in Continuous-Time Markets," Papers 1202.0628, arXiv.org, revised Apr 2013.
  3. Hlouskova, Jaroslava & Tsigaris, Panagiotis, 2012. "Capital Income Taxation and Risk Taking under Prospect Theory," Economics Series, Institute for Advanced Studies 283, Institute for Advanced Studies.
  4. Miklós Rásonyi & Andrea Rodrigues, 2013. "Optimal portfolio choice for a behavioural investor in continuous-time markets," Annals of Finance, Springer, Springer, vol. 9(2), pages 291-318, May.
  5. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2011. "Prospect theory for continuous distributions: A preference foundation," Journal of Risk and Uncertainty, Springer, Springer, vol. 42(3), pages 195-210, June.
  6. Ghossoub, Mario, 2011. "Towards a Purely Behavioral Definition of Loss Aversion," MPRA Paper 37628, University Library of Munich, Germany, revised 23 Mar 2012.
  7. Matteo Del Vigna, 2011. "Financial market equilibria with heterogeneous agents: CAPM and market segmentation," Working Papers - Mathematical Economics, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa 2011-08, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  8. Matteo Del Vigna, 2012. "Stochastic dominance for law invariant preferences: The happy story of elliptical distributions," Working Papers - Mathematical Economics, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa 2012-08, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  9. Matteo Del Vigna, 2011. "Market equilibrium with heterogeneous behavioural and classical investors' preferences," Working Papers - Mathematical Economics, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa 2011-09, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  10. Laurence Carassus & Miklos Rasonyi, 2013. "Maximization of Non-Concave Utility Functions in Discrete-Time Financial Market Models," Papers 1302.0134, arXiv.org, revised Sep 2014.
  11. Laurence Carassus & Miklos Rasonyi, 2011. "On optimal investment for a behavioural investor in multiperiod incomplete market models," Papers 1107.1617, arXiv.org, revised Oct 2012.
  12. Godfrey Charles-Cadogan, 2012. "Representation Theory for Risk On Markowitz-Tversky-Kahneman Topology," Papers 1206.2665, arXiv.org.

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