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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 (CPT). 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 CPT 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 that this violation is acceptable.

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada

    Carole Bernard & Mario Ghossoub

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  1. Carole Bernard
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  2. Mario Ghossoub
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Correspondence to Carole Bernard.

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Bernard, C., Ghossoub, M. Static portfolio choice under Cumulative Prospect Theory. Math Finan Econ 2, 277–306 (2010). https://doi.org/10.1007/s11579-009-0021-2

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  • DOI: https://doi.org/10.1007/s11579-009-0021-2

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