A Comprehensive Look at The Empirical Performance of Equity Premium Prediction

Goyal, Amit and Ivo Welch. “A Comprehensive Look at The Empirical Performance of Equity Premium Prediction” The Review of Financial Studies Vol. 21 No. 4 (2008) 1455-1508.

Many variables, in research prior to the present article, had been suggested and tested as predictors of the equity premium. Here, the authors do a study of the in-sample and out-of-sample performance of these variables. The overall results suggest that many of these variables, even prominent ones, now perform very poorly in-sample, out-of-sample, or both. Indeed, in their conclusion, the authors suggest only one variable for which they feel judgement should be reserved and that there are some which should be investigated more in longer term predictions. These results come even as the authors wave their hands at the question of how someone might have known what would have worked in real-time.

One-year predictions:

 

The first panel of Table 1 is analysis of variables which were not significant in-sample. The authors point out that even if these variables were significant out-of-sample, they wouldn’t be that interesting, but they include them because of their place in prior literature. None of the variable are significant out-of-sample for testing period beginning 20 years after the beginning of the data (the first 20 years being used as the initial in-sample period for the out-of-sample predictions), none are significant at with forecasting beginning in 1965, and only two (dividend-yield and earning-price ratio) are significant in in-sample tests using data from 1927-2005.

Among variables in the second panel (those which were significant in-sample), only one (percent equity issuing) has significant out-of-sample performance. This is the one mentioned earlier for which the authors feel judgement should be reserved. It does not have significant out-of-sample performance when forecasts begin in 1965.

In the remainder of the table, one variable has significant out-of-sample performance, though it seems to be a result of construction. The present authors design the test for cayp in similar fashion to the original authors. The representative agent here has knowledge of the full sample cay coefficient, but not the prediction coefficient and thus has to continually update. With this in mind, Goyal and Welch construct caya for true out-of-sample testing where the agent does not have advance knowledge of the cay coefficient. As we see, this entirely nullifies the apparent out-of-sample success of the variable.

Five-year predictions:

The authors disclose that the results of the five-year predictions are preliminary and possibly naïve prompting their suggestion that a few variables deserve further investigation in this realm. Dividend-price ratio and investment-capital ratio are significant in-sample for the full sample and in out-of-sample testing. However, neither is significant in-sample for the 20-year period used to begin the out-of-sample testing.

Similar to the one-year prediction result, cayp is strongly significant. What is different is that caya, the true out-of-sample test variable, is now also significant. Term spread was not significant in-sample for the full sample of available data but was with data beginning in 1927 as well as out-of-sample for forecasts beginning in 1965. Though, it too, failed to be significant for the in-sample portion of the data used to begin the forecast period.

One-month predictions:

The one-month prediction performance looks more promising based on in-sample testing. However, the authors note that only a few of them merit further investigation. In doing so, the variables seem to be inconsistent or heavily rely on only a short period for their overall success.

In summary, many of the variables used in the literature as predictors of the equity premium may be inconsistent and/or spurious. The authors state, “We view OOS performance not as a substitute but as a necessary complement to IS performance.”