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Static Portfolio Choice under Cumulative Prospect Theory

By Carole Bernard and Mario Ghossoub

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.

Topics: D81 - Criteria for Decision-Making under Risk and Uncertainty, G11 - Portfolio Choice; Investment Decisions
Year: 2009
DOI identifier: 10.1007/s11579-009-0021-2
OAI identifier: oai:mpra.ub.uni-muenchen.de:15446

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