Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence

Abstract

A new asset pricing model that generalizes earlier results in the downside risk literature is developed and empirically tested using a multivariate approach. By specifying risk as deviations below any arbitrary rate of the generalized Mean-Lower Partial Moment (MLPM) model overcomes the limited appeal of earlier formulations, and, moreover, a large class of extant pricing models using alternative risk measures (variance, semivariance, semideviation, probability of loss, etc.) becomes special cases of the new framework. Empirical tests indicate that the new model cannot be rejected against an unspecified alternative for a large set of rates of return. The traditional CAPM, on the other hand, is rejected as a well-specified alternative. The MLPM rates inferred from market data appear to be related to equity market mean returns rather than to the riskfree rate, the rate that is implicit in the CAPM and explicit in earlier downside risk formulations. The attractiveness of downside risk measures for decision-making purposes has been noted in the financial economic literature for over a quarter of a century.1 Risk, from this perspective, is measured in terms of deviations below some exogenously prespecified target rate of return, and a formal analysis of these risk measures for various utility functions has been presented by Bawa (1975) in terms of the lower partial moment (LPM) of the asset distributions. The appeal of these risk measures has been based, in part, on their consistency with the way individuals actually perceive risk. Notwithstanding its intuitive appeal, this area of research has been virtually neglected in recent years. We believe that this disaffection with downside risk models tends from two sources. First, earlier models of this genre exogenously specify the rate to equal the risk-free interest rate. In the absence of a satisfactory theory for explaining how investors establish their rates, this assumption, as argued herein, has been motivated more by technical reasons than economic considerations. Second, empirical tests