Static Portfolio Choice under Cumulative Prospect Theory

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 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. Key-words: Cumulative Prospect Theory, Portfolio Choice, Behavioral Finance, Omega Measure. JEL codes: D81, G11, D03. [email protected], tel: +1 519 888 4567 ext:35505 [email protected], tel: +1 519 888 4567 ext:33835 We would like to thank Phelim Boyle, Virginia Young and Harry Panjer for helpful discussions. Both authors acknowledge support from the Natural Sciences and Engineering Research Council of Canada.