Asset Pricing and Excess Returns over the Market Return

Some studies have found that the estimated market betas from multi-factor models have much smaller cross-sectional variations than those from the Capital Asset Pricing Model. This paper provides a theoretical explanation for this empirical finding. For the cases in which the market portfolio (of stocks) is a well-diversified but mean-variance inefficient one, we show that the market betas become unitary when the Capital Asset Pricing Model is augmented with the common factors in the space of excess returns. Consequently, the market betas have no power to explain the cross-sectional variation of expected stock returns. Based on this finding, we propose an alternative method that can identify the relevant factors for asset pricing. Specifically, we show that the relevant factors can be extracted by the principal components from a large set of excess stock returns over the market return. Analyzing US data on individual and portfolio stock returns, we develop a benchmark model with five principal component factors. We use the model to study if the five-factor model of Fama and French (2015) captures all the relevant information to span the space of excess returns. We find that the Fama-French model contains a large fraction of the relevant information, but there is still some room for improvement.