Using Div Yield to Predict Returns: A lesson in Predictive Regressions

Filip Lacerda and Pedro Santa-Clara have an interesting paper that investigates the use of dividend growth to predict future returns.
Here is the abstract:

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 R² of 16.27% and an out-of-sample R² 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 subsamples.

One of my students–Heng Qiao–took on a difficult project and replicated the results from the paper.

Here is Heng’s summary of his work:

Out-of-sample R², which is the ratio between the sum squared error of a “smart” model with that of a simple model (historical average forecasting), helps researchers identify if a model actually improves prediction.  This paper develops two new variables dp_t and x_t , which are the unadjusted dividend-price ratio and the adjusted dividend price ratio, respectively. In the paper, dp_t and x_t were created through a simple auto-regression, a first-order Taylor Expansion, and a simplification of infinite series. My work was aimed at replicating the paper’s results, and it turns out that there are slight differences between my result and that in the paper. Dealing with the monthly data, my work generated a R² of 0.53% and R²_OOS of 0.8% for dp_t,  and a R² of 0.49% and R²_OOS of 0.78% for x_t. When moved to the annual data, the results are more statistically significant, with R² of 2.27% and R²_OOS of 9.1% for dp_t, and R² of 20.31% and R²_OOS of 20.31% for x_t.

Below is a copy of the spreadsheet for your learning pleasure.
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predregression.xlsx
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Here is a picture showing the forecast error using the simple dp_t model in the paper (9.1% R²_OOS):

Here is a picture showing the forecast error using the more complex x_t model in the paper (20.31% R²_OOS):

Based on the numbers, the fancy dividend prediction model does enhance the forecasting ability. Visually, as represented in the 2 charts above, there really isn’t much improvement in forecast errors over a simple average return prediction model…

Predicting the stock market is probably the biggest sucker bet out there…