The time-series relations among expected return, risk, and book-to-market

This paper examines the time-series relations among expected return, risk, and book-to-market (B/M) at the portfolio level. I find that B/M predicts economically and statistically significant time-variation in expected stock returns. Further, B/M is strongly associated with changes in risk, as measured by the Fama and French (1993) (Journal of Financial Economics, 33, 3–56) three-factor model. After controlling for risk, B/M provides no incremental information about expected returns. The evidence suggests that the three-factor model explains time-varying expected returns better than a characteristics-based model.