Static Portfolio Choice Under Cumulative Prospect Theory
Mathematics and Financial Economics, Vol. 2, No. 4, March, 2010
40 Pages Posted: 30 Apr 2009 Last revised: 19 Jul 2010
Date Written: April 29, 2009
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 that this violation is acceptable.
Keywords: Cumulative Prospect Theory, Portfolio Choice, Behavioral Finance, Omega Measure
JEL Classification: D81, G11, D03
Suggested Citation: Suggested Citation