Forecasting Dividend Growth to Better Predict Returns

The dividend-price ratio changes over time due to variation in expected returns and in forecasts of dividend growth. We adjust the dividend-price ratio to isolate the fluctuations that are due to variation in expected returns from those that are due to changing forecasts of dividend growth. This adjusted dividend-price ratio is statistically significant in predictive regressions and yields an in-sample R^{2} of 16.27% and an out-of-sample R^{2} of 12.35%, which compare with 7.88% and -2.94% for the unadjusted multiple. Structural estimation of our model obtains even higher measures of fit. Our results are robust across sub samples.

**Introduction**

Variation in the dividend-price ratio is the result of two things: fluctuations in expected returns and changes in investors' forecasts of cash-flows. If investors expect to receive higher cash-flows, then stocks will be worth more today. If investors require a higher rate of return, future cash-flows will be more heavily discounted, and stocks will be worth less today.

This relation between the dividend-price ratio and expected returns justifies using the dividend-price ratio to forecast returns. This has been done by Dow (1920), Campbell (1987), Fama and French (1988), Hodrick (1992), and more recently by Campbell and Yogo (2006), Ang and Bekaert (2007), Cochrane (2008), and Binsbergen and Koijen (2009). However, the evidence of return predictability has been questioned by Goyal and Welch (2008), among others, who show that the dividend-price ratio, along with several other variables, has no ability to forecast stock returns out of sample.4 Whether returns are predictable is still an open debate.

We provide strong evidence that returns are indeed predictable. Our point is that changes in forecasts of dividends need to be taken into account when forecasting returns with the dividend-price ratio. We use a simple present-value model to propose an adjustment to the dividend-price ratio that isolates the component due to expected returns from that caused by changing forecasts of dividend growth. The adjusted and unadjusted versions of the dividend-price ratio are positively correlated but the former is far more volatile than the latter.

We compare the adjusted and unadjusted versions of the dividend-price ratio to forecast returns with predictive regressions and find a significant difference in performance. In sample, the adjusted multiple has an R^{2} of 16.27% whereas the unadjusted ratio has an R^{2} of 7.88%. Out of sample, the difference is even more impressive since the adjusted ratio has an R^{2} of 12.35% whereas the unadjusted ratio as a negative R^{2} of -2.95%. The coefficient of the adjusted ratio in predictive regressions is statistically significant at the 1% level.

We attribute the success of our approach to the fact that we are able to pin down part of the variation in investors' forecasts of future dividend growth in a robust way. We provide evidence of the importance of past lags of dividend growth in capturing variation in future growth rates. By taking a linear combination of past growth rates we are able to identify part of the variation in forecasts of future dividend growth, and therefore better forecast stock returns.

Finally, when we estimate our structural model, we obtain an even more impressive out-of-sample R^{2} of 18.62%. The parameter estimates we obtain imply that expected returns are extremely persistent, and can, for practical purposes, be approximated by a random walk.

**A simple model**

Our economy has a simple setup. We assume that investors' expectations of future stock market returns follow the simplest persistent time-series process, an AR(1), and that the parameters governing this process are known to them. It appears sensible to assume that agents fully know the dynamics of conditional expected returns since these result from the solution of the investors' own problem of inter temporal utility maximization. For simplicity, similarly to Pastor and Stambaugh (2009) and to Binsbergen and Koijen (2009), instead of specifying a utility function and deriving the dynamics for expected returns, we assume that preferences are such that conditional expected returns follow this auto-regressive process.