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Authors: Patrick L. Brockett (brockett@mail.utexas.edu) and James R. Garven (James_Garven@baylor.edu) Geneva Papers on Risk and Insurance Theory, Vol. 23, No. 2 (December 1998), pp. 127-137.Keywords: Asset preferences, utility functions, moment orderings, Von Neumann-Morgenstern rationality.
ABSTRACT. This paper examines the relationship between risk, return, skewness and utility based preferences. Examples are constructed (and reference given to a general theory) showing that, for any commonly used utility function, it is possible to have two continuous unimodal random variables X and Y with positive and equal means, X having a larger variance and lower positive skewness than Y, and yet X has larger expected utility than Y, contrary to usual folklore concerning U’’’ > 0 implying skewness preference for risk averters. In addition, it is shown that ceteris paribus analysis of preferences and moments as used in the literature is impossible since equality of higher order central moments implies the total equality of the distributions involved. |
