A Note on “predicting Returns with Financial Ratios”

This note reinterprets methods that seek to use the aggregate dividend price ratio to predict aggregate stock market returns; specifically, methods which use information about time-varying changes in the dividend-price ratio process to improve the prediction equation. It argues that the empirical evidence is still too weak to suggest practical usefulness of these estimators. ∗We thank John Cochrane and Jonathan Lewellen for their detailed comments and suggestions. †http://www.goizueta.emory.edu/agoyal. E-mail: [email protected]. ‡http://welch.som.yale.edu. E-mail: [email protected]. In Predicting returns with financial ratios, Lewellen (2003) introduces a promising new test to improve on the ability of financial ratios to predict stock returns. This test relies on the fact that dividend yields are close to non-stationary, and have become more so since 1973. The paper has received much attention, even before publication. (For example, Campbell and Yogo (2003) generalize the methodology.) A reader not too familiar with the data would likely conclude that there is no question that dividend yields can help investors predict stock returns, at least prior to 1995. Yet, in Goyal and Welch (2003), we had also documented that dividend yields have becomemore non-stationary over time, even indistinguishable from a randomwalk as of December 2002. We then implemented a test statistic that directly uses Campbell and Shiller’s (1988) identities to instrument not only the time-varying properties of the dividend yield, but also the time-varying changes in the dividend growth process. In contrast to Lewellen, we had concluded that neither the dividend yield, nor our instrumented prediction could help investors predict the equity premium. Predicting the equity premium may well be the most important issue in finance, so it is important to reconcile the two perspectives. Both perspectives have evaluated the same data through similar lenses (time-varying changes in the dividend process) and still have come to opposite conclusions. This note explains why, and gives an alternative perspective on the performance of Lewellen’s improved test. Stambaugh (1999) introduces an underlying process of rt = α+ β·dpt−1 + r ,t (1) dpt = μ + ρ·dpt−1 + dp,t , (2) where r here is the simple1 stock return and dp is the log dividend price ratio. The goal is to estimate the slope coefficient β in the return equation (1). The correlation between r and dp violates the OLS assumption that the independent variable dpt−1 be uncorrelated with the errors r ,t. Therefore, the simple OLS estimate of β is upwardly biased. Denoting the estimator of β by β̂T and the estimator of ρ by ρ̂T , where 1Using log-stock returns instead of simple returns does not matter at monthly frequency for our results. We use the simple stock return to remain directly comparable with Lewellen (2003).