Kelly Price, Discussion: An Analysis of the Effects of a Multi-Tiered Stock Market, The Journal of Financial and Quantitative Analysis, Vol. 16, No. 4, Proceedings of 16th Annual Conference of the Western Finance Association, June 18-20, 1981, Jackson Hole, Wyoming (Nov., 1981), pp. 577-579

Bawa [3] has argued that mean-lower partial moment portfolio selection rules are more general than mean-variance rules in that they rely on fewer restrictive assumptions regarding investor utility functions and/or distributions of security returns. As with the mean-variance model, it is possible to formulate equilibrium security prices under the assumption that expected utility-maximizing investors utilize mean-lower partial moment portfolio selection rules. This paper has investigated the empirical relationship between the resultant mean-lower partial moment pricing model and the long established mean-variance pricing model.

ABSTRACT As a measure of systematic risk, the lower partial moment measure requires fewer restrictive assumptions than does the variance measure. However, the latter enjoys far wider usage than the former, perhaps because of its familiarity and the fact that two measures of systematic risk are equivalent when return distributions are normal. This paper shows analytically that there are systematic differences in the two risk measures when return distributions are lognormal. Results of empirical tests show that there are indeed systematic differences in measured values of the two risk measures for securities with above average and with below average systematic risk.