Predictive Regressions: A Present-Value Approach

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Abstract
We show that the price-dividend ratio has strong predictive power for both future stock returns and future dividend growth rates, with R-squared values of 18% and 16%, respectively. To derive this result, we develop a tractable closed-form present-value model that features time-variation in expected returns and expected dividend growth rates. We then combine simple non-linear filtering techniques with the present-value model to recover the time series of expected returns and expected dividend growth rates. This procedure allows us to bypass the standard Vector Auto Regressions, in which the instruments can be misspecified and/or suffer from a selection bias. We show that the expected dividend growth rate is time-varying and has both a transient and a persistent component. We then decompose each historical stock return into shocks to expected returns, unexpected dividend shocks, and shocks to both components of the expected dividend growth rate. Paradoxically, we show that an investor who believes to live in a world with a highly persistent expected dividend growth rate, would have strongly outperformed an investor using a standard predictive-regression framework as well as the market.

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