On Variance And Lower Partial Moment Betas The Equivalence Of Systematic Risk Measures

The market equilibrium mean‐lower partial moment (LPM) model may serve as an alternative to the traditional mean‐variance (MV) CAPM for security analysis. It appears that the merits of the MV‐CAPM vis‐à‐vis the mean‐LPM model continue to be debated (see Nantell and Price, 1979; Price, Price and Nantell, 1982; and Homaifer and Gaddy, 1990). This paper demonstrates that from a theoretical perspective the two models are equivalent for general riskaverse investors. This modeling consistency is based on the fact that all return distributions which yield the mean‐LPM equilibrium model must permit two‐fund portfolio separation, and the well‐known MV‐CAPM is the direct pricing result of the two‐fund portfolio separation. Hence any debate about the bias of systematic risk measures between the mean‐LPM model and the MV‐CAPM is meaningless. Nevertheless, although the economic equilibrium results of the models are identical, this does not indicate that the LPM portfolio theory is redundant or irrelevant. It may be that some behavioral perspective, sensitivity to downside risk is more appropriate than variance as a risk proxy.