Bernard, Carole and Ghossoub, Mario (2009): Static Portfolio Choice under Cumulative Prospect Theory.
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Abstract
We derive the optimal portfolio choice for an investor who behaves according to Cumulative Prospect Theory. The study is done in a oneperiod economy with one riskfree asset and one risky asset, and the reference point corresponds to the terminal wealth arising when the entire initial wealth is invested into the riskfree 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 riskfree rate. It conceptually resembles Merton’s optimal holding for a CRRA expectedutility maximizer. We derive some properties of the optimal holding and illustrate our results using a simple example where the excess return has a skewnormal 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 piecewisepower value function with diﬀerent shape parameters, loss aversion might be violated for reasons that are now wellunderstood in the literature. Nevertheless, we argue that this violation is acceptable.
Item Type:  MPRA Paper 

Original Title:  Static Portfolio Choice under Cumulative Prospect Theory 
Language:  English 
Keywords:  Cumulative Prospect Theory, Portfolio Choice, Behavioral Finance, Omega Measure. 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty G  Financial Economics > G1  General Financial Markets > G11  Portfolio Choice; Investment Decisions 
Item ID:  16474 
Depositing User:  Mario Ghossoub 
Date Deposited:  29. Jul 2009 14:38 
Last Modified:  12. Feb 2013 03:39 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/16474 
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Static Portfolio Choice under Cumulative Prospect Theory. (deposited 01. Jun 2009 07:02)

Static Portfolio Choice under Cumulative Prospect Theory. (deposited 13. Jul 2009 23:43)
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Static Portfolio Choice under Cumulative Prospect Theory. (deposited 13. Jul 2009 23:43)