In this paper, we develop a Capital Asset Pricing Model (CAPM) using a mean-lower partial moment framework. We explicitly derive the valuation formulas for the equilibrium value of risky assets and provide a distribution-free testable hypothesis for empirical validation of the new CAPM. We show the invariance of our results to the problem of estimation risk. We also show that when the probability distribution of security rer turns is the normal distribution, the stable Paretian distribution (with the same characteristic exponent between 1 and 2 and the same skewness parameter (not necessarily zero)), or the multivariate t-distribution, our CAPM reduces to the traditional two-parameter CAPM.