Much recent work emphasizes the joint nature of the consumption decision and the portfolio allocation decision. In this paper, we compare two formulations of the Capital Asset Pricing Model. The traditional CAPM suggests that the appropriate measure of an asset’s risk is the covariance of the asset’s return with the market return. The consumption CAPM, on the other hand, implies that a better measure of risk is the covariance with aggregate consumption growth. We examine a cross-section of 464 stocks and ﬁnd that the beta measured with respect to a stock market index outperforms the beta measured with respect to consumption growth.
Mankiw, N. Gregory and Shapiro, Matthew D., "Risk and Return: Consumption Beta Versus Market Beta" (1985). Cowles Foundation Discussion Papers. 978.