Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment
36 Pages Posted: 29 Sep 2009 Last revised: 4 Mar 2011
Date Written: September 13, 2010
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
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