The modern theory of finance has produced the capital asset pricing model (CAPM) which is an equilibrium model establishing a relationship among the parameters of the multivariate distribution of returns from assets. Several attempts have been made in the past to empirically validate the CAPM; all of these studies have focused primarily on one parameter, the expected return on the zero-beta portfolio. This paper provides an alternative methodology which utilizes minimum expected loss (MELO) estimation. Estimates of the relevant parameters are provided along with a comparison between one traditional approach and the MELO framework. As a by-product of this research, another example of the usefulness of MELO estimation is provided.