Mean Lower Partial Moment Valuation and Lognormally Distributed Returns

In this paper we develop a capital asset pricing model in a mean lower partial moment framework. Specifically, we show that when partial moments are computed about the expected risky portfolio return, optimal portfolio choice in a mean lower partial framework permits a two-fund portfolio separation between a riskless asset and a "market" portfolio of risky assets. In this new framework, risk is measured as semideviation (for second degree stochastic dominance), and semivariance (for third degree stochastic dominance). Further, when security returns are lognormally distributed and "small risk," this new mean lower partial moment valuation specializes to the mean-logarithmic variance capital asset pricing model.