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

See all articles by Carole Bernard

Carole Bernard

Grenoble Ecole de Management; Vrije Universiteit Brussel (VUB)

Mario Ghossoub

University of Waterloo

Date Written: April 29, 2009

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 that this violation is acceptable.

Keywords: Cumulative Prospect Theory, Portfolio Choice, Behavioral Finance, Omega Measure

JEL Classification: D81, G11, D03

Suggested Citation

Bernard, Carole and Ghossoub, Mario, Static Portfolio Choice Under Cumulative Prospect Theory (April 29, 2009). Mathematics and Financial Economics, Vol. 2, No. 4, March, 2010. Available at SSRN: https://ssrn.com/abstract=1396826

Carole Bernard

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003
France

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

Mario Ghossoub (Contact Author)

University of Waterloo ( email )

Dept. of Statistics & Actuarial Science
200 University Ave. W.
Waterloo, Ontario N2L 3G1
Canada

HOME PAGE: http://uwaterloo.ca/scholar/mghossou

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