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Value Functions for Prospect Theory Investors: An Empirical Evaluation for US Style Portfolios

We employ two reward and risk measures, the Upper Partial Moment and the Lower Partial Moment, in order to maximize different value functions under the budget and the short-selling constraints. We find that agents seem to prefer small capitalization and high value stock portfolios (which are positively skewed) and reject large capitalization and growth stock portfolios (which are negatively skewed) for all types of preferences (S-shaped, reverse S-shaped, kinked convex and kinked concave value function). This behavior is consistent with the value and the size effects. Probability distortion plays a significant role in the determination of the optimal perspective value; however, it is not significant for the determination of the optimal asset allocation.