Behavioral Portfolio Choice: An Analytical Treatment∗

This paper formulates a single-period portfolio choice model under Kahneman and Tversky’s cumulative prospect theory, featuring a reference point in wealth, S-shaped utility (value) functions with loss aversion, and distortions in probability. An analytical treatment of the model is carried out. A new measure of loss aversion for large payoffs, called the loss aversion degree (LAD), is introduced. The issue of model well-posedness is brought about, of which the LAD is shown to be a critical determinant. The sensitivity of the prospective value function with respect to the stock allocation is then investigated, which demonstrates as a by-product that this function is neither concave nor convex. Optimal solutions are finally derived explicitly for the cases when the reference point is the risk-free return and when the utility function is piece-wise linear. These results are in turn employed to demonstrate that optimal risky exposures monotonically decrease as the LAD increases.