Comparison of Alternative Utility Functions in Portfolio Selection Problems

This paper examines the effect of alternative utility functions and parameter values on the optimal composition of a risky investment portfolio. Normally distributed assets are the setting for the theoretical and empirical analyses. The results agree well with the available theory and imply utility functions and parameter values that are appropriate for investors with particular risk-bearing attitudes. The results give strong empirical support to the proposition that utility functions having different functional forms and parameter values but “similar” absolute risk aversion indices have “similar” optimal portfolios. These results suggest that over horizons up to one year one can safely substitute “convenient” surrogate utility functions for other utility functions, for reasons of tractability or otherwise. The results also provide guidance regarding the significance of the magnitude and change of particular numerical values of the risk aversion index. Moreover, theoretical (“exact”) results are obtained using Rubinstein's measure of global risk aversion.