Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment

Management Science

36 Pages Posted: 29 Sep 2009 Last revised: 4 Mar 2011

See all articles by Xue Dong He

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: September 13, 2010

Abstract

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 when the reference point is the risk-free return and when it is not (while the utility function is piece-wise 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.

Keywords: Portfolio choice, single period, cumulative prospect theory, reference point, loss aversion, S-shaped utility function, probability weighting, well-posedness

Suggested Citation

He, Xue Dong and Zhou, Xunyu, Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment (September 13, 2010). Management Science, Available at SSRN: https://ssrn.com/abstract=1479580 or http://dx.doi.org/10.2139/ssrn.1479580

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management ( email )

505 William M.W. Mong Engineering Building
The Chinese University of Hong Kong, Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://https://sites.google.com/site/xuedonghepage/home

Xunyu Zhou (Contact Author)

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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