Can Stochastic Discount Factor Models Explain the Cross Section of Equity Returns?

We propose a multivariate test based on no-arbitrage conditions under the stochastic discount factor approach, which compares cross-sectional variation in equity returns to the cross-sectional variation in their conditional covariance with the discount factors. Using the multivariate generalized heteroskedasticity in mean model to estimate the 25 portfolios formed on size and book-to-market ratio, together each with its own arbitrage condition, we find that the no-arbitrage test rejects the consumption-based capital asset pricing model (C-CAPM). Although the conditional covariances of returns with consumption exhibit negative variation across size, they do not vary across the book-to-market ratio. Thus, the C-CAPM can capture size effect, but not value effect. Allowing the coefficients on the consumption covariances to be different largely improves the fit of the C-CAPM, however. The value effect appears to be associated with book-to-market ratio as well as size. Book-to-market ratio separately does not generate information about average returns that cannot be explained by the C-CAPM. One possible explanation for this extra dimension of risk is the investment growth prospect of firms. Low book-to-market ratio firms may be expected to have higher rates of growth while small firms may also be expected to behave similarly