Most research in modern portfolio theory and capital market theory is based on investor selection of portfolios that are efficient in the sense that they are not dominated by other portfolios in terms of their risk-expected return characteristics. The most widely used measure of portfolio risk is the variance about the mean of the exante distribution of portfolio returns. The theoretical framework from which this measure of risk is usually derived was initially suggested by Markowitz [12], and is by now well known. Although variance has the attention of most researchers, another measure, semivariance, had some early support from Markowitz himself, and from Quirk and Saposnik [17], Mao [10], and others. Semivariance as a measure of risk can be derived from the same theoretical framework as is variance; it requires only a slightly different utility function. The semivariance of returns of portfolio p below some point h is defined aswhere fp (R) represents the probability density function of returns for portfolio p. Semivariance portfolio theory is enjoying something of a revival in the works of Porter [15, 16], Hogan and Warren [6] and Klemkosky [8], and semivariance capital market models have been developed by Hogan and Warren [7] and Greene [5].

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.