The derivation of observable implications of the conditional CAPM theory often includes the joint (internally inconsistent) hypothesis that the stock portfolio used in the tests is the theoretical, mean-variance efficient, market portfolio. The present paper generalizes this derivation by avoiding this joint hypothesis. The generalization reveals that the conditional CAPM plausibly explains asset pricing anomalies, such as the unconditional alphas and betas of momentum, value, and size portfolios, while the unconditional CAPM theory is still rejected by portfolios with negative unconditional betas and positive unconditional alphas. Hence, relaxing this joint assumption does not render the CAPM theory untestable.