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: (i) Both investment and profitability are important contributors to the value spread and stock return news variance. (ii) Asset growth predicts the cross-section of returns primarily because it predicts a long-run decline in future profitability. (iii) The investment spread significantly improves the ability to forecast time-series variation in the value premium and helps justify the poor performance of value in recent years.