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Static Portfolio Choice under Cumulative Prospect Theory

  • Bernard, Carole
  • Ghossoub, Mario

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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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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  1. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.
  2. Enrico Giorgi & Thorsten Hens, 2006. "Making prospect theory fit for finance," Financial Markets and Portfolio Management, Springer, vol. 20(3), pages 339-360, September.
  3. Robert Jarrow & Feng Zhao, 2006. "Downside Loss Aversion and Portfolio Management," Management Science, INFORMS, vol. 52(4), pages 558-566, April.
  4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  5. U Schmidt & H Zank, 2002. "Linear Cumulative Prospect Theory with Applications to Portfolio Selection and Insurance Demand," The School of Economics Discussion Paper Series 0208, Economics, The University of Manchester.
  6. Enrico De Giorgi, . "Reward-Risk Portfolio Selection and Stochastic Dominance," IEW - Working Papers 121, Institute for Empirical Research in Economics - University of Zurich.
  7. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
  8. Shlomo Benartzi & Richard H. Thaler, 1993. "Myopic Loss Aversion and the Equity Premium Puzzle," NBER Working Papers 4369, National Bureau of Economic Research, Inc.
  9. Baucells Alibés Manel & Heukamp Franz H., 2007. "Stochastic Dominance and Cumulative Prospect Theory," Working Papers 201061, Fundacion BBVA / BBVA Foundation.
  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. Francisco J. Gomes, 2005. "Portfolio Choice and Trading Volume with Loss-Averse Investors," The Journal of Business, University of Chicago Press, vol. 78(2), pages 675-706, March.
  12. Enrico De Giorgi & Thorsten Hens & Marc Oliver Rieger, 2007. "Financial Market Equilibria With Cumulative Prospect Therory," Swiss Finance Institute Research Paper Series 07-21, Swiss Finance Institute, revised Aug 2007.
  13. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  14. Berkelaar, A.B. & Kouwenberg, R.R.P., 2000. "Optimal portfolio choice under loss aversion," Econometric Institute Research Papers EI 2000-08/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  15. Neilson, William S, 2002. " Comparative Risk Sensitivity with Reference-Dependent Preferences," Journal of Risk and Uncertainty, Springer, vol. 24(2), pages 131-42, March.
  16. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  17. Wakker, Peter & Tversky, Amos, 1993. " An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-75, October.
  18. U Schmidt & H Zank, 2002. "What is Loss Aversion?," The School of Economics Discussion Paper Series 0209, Economics, The University of Manchester.
  19. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  20. Handa, Jagdish, 1977. "Risk, Probabilities, and a New Theory of Cardinal Utility," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 97-122, February.
  21. 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.
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