The general restrictions on all economic primitives (i.e., (a) endowments, (b) preferences and (c) asset return distributions) that yield the CAPM under the expected utility paradigm are provided. These results are then used to derive the class of restrictions on preferences and the distribution of asset returns alone that provides the CAPM. We also show that the conditions that provide the CAPM and derived preferences of mean and variance are equivalent. Consequently, this paper also resolves the question of when mean-variance maximization is consistent with expected utility maximization.
There are two related documents referenced in the published paper. Both are available as acrobat pdf files (you need version 3.0 or later):