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 target rate of return, 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 target rates of return. The traditional CAPM, on the other hand, is rejected as a well-specified alternative. The MLPM target rates inferred from market data appear to be related to equity market mean returns rather than to the risk-free rate, the target rate that is implicit in the CAPM and explicit in earlier downside risk formulations.