Scale or yield? A present-value identity

We propose a loglinear present-value identity in which investment (“scale”), profitability (“yield”), and discount rates determine a firm’s market-to-book ratio. Our identity reconciles existing influential market-to-book decompositions and facilitates novel insights from three empirical applications: (1) Both investment and profitability are important contributors to the value spread and stock return news variance. (2) Any cross-sectional return predictability has a mirror image in cash-flow fundamentals, providing asset pricing theories with additional moments to match. (3) The investment spread significantly improves the predictability of time-series variation in the value premium and justifies the poor performance of value in recent years.