Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment

We formulate and carry out an analytical treatment of a single-period portfolio choice model featuring a reference point in wealth, S-shaped utility (value) functions with loss aversion, and probability weighting under Kahneman and Tversky's cumulative prospect theory (CPT). We introduce a new...

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Bibliographic Details
Published in:	Management science 2011-02, Vol.57 (2), p.315-331
Main Authors:	He, Xue Dong, Zhou, Xun Yu
Format:	Article
Language:	eng
Subjects:	Applied sciences cumulative prospect theory Decision models Decision theory. Utility theory Exact sciences and technology Financial portfolios Investment analysis Investors Loss Loss aversion Management science Modeling Operational research and scientific management Operational research. Management science Pay-off Portfolio analysis portfolio choice Portfolio management Portfolio selection Portfolio theory Probability probability weighting Prospect theory Rates of return reference point Risk aversion S-shaped utility function single period Studies Term weighting Utility functions Weighting functions well-posedness
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Summary:	We formulate and carry out an analytical treatment of a single-period portfolio choice model featuring a reference point in wealth, S-shaped utility (value) functions with loss aversion, and probability weighting under Kahneman and Tversky's cumulative prospect theory (CPT). We introduce a new measure of loss aversion for large payoffs, called the large-loss aversion degree (LLAD), and show that it is a critical determinant of the well-posedness of the model. The sensitivity of the CPT value function with respect to the stock allocation is then investigated, which, as a by-product, demonstrates that this function is neither concave nor convex. We finally derive optimal solutions explicitly for the cases in which the reference point is the risk-free return and those in which it is not (while the utility function is piecewise linear), and we employ these results to investigate comparative statics of optimal risky exposures with respect to the reference point, the LLAD, and the curvature of the probability weighting. This paper was accepted by Wei Xiong, finance.
ISSN:	0025-1909 1526-5501