Two-Piece von Neumann-Morgenstern Utility Functions.

Thirty empirically-assessed utility functions on changes in wealth or return on investment were examined for general features and susceptibility to fits by linear, power and exponential functions. Separate fits were made to below-target data and above-target data. The usual target was the n-change point. The majority of below-target functions were risk-seeking, the majority of above-target functions were risk-averse, and the most common composite shape was convex-concave, or risk-seeking in losses and risk-averse in gains. The least-common composite was concave-concave. Below-target utility was generally steeper than above-target utility with a median below-to-above slope ratio of about 4.8. The power and exponential fits were substantially better than the linear fits. Power functions gave the best fits in the majority of convex below-target and concave above-target cases, and exponential functions gave the best fits in the majority of concave below-target and convex above-target cases. Author