ON VARIANCE AND LOWER PARTIAL MOMENT BETAS THE EQUIVALENCE OF SYSTEMATIC RISK MEASURES
从理论上证明均值-下半矩模型与均值-方差CAPM对一般风险厌恶投资者是等价的，因此关于两种模型系统风险度量偏差的争论没有意义。
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.