Static Portfolio Choice under Cumulative Prospect Theory
AbstractWe 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 15446.
Date of creation: 29 Apr 2009
Date of revision:
Cumulative Prospect Theory; Portfolio Choice; Behavioral Finance; Omega Measure.;
Find related papers by JEL classification:
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
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