The Myth of Long-Horizon Predictability

Motivation(s)

One of the dominant stylized facts in empirical finance is multivariate stock return predictability, regressing on dividend yields, over multiple horizons. The key determinants of long-horizon predictability are the extent of predictability at short horizons and the persistence of the regressor; higher persistence results in a higher fraction of explainable long-horizon returns. This interpretation has been criticized for

• Data Snooping

  • Levels of predictability found at short horizons are not surprising, given the number of variables from which researchers can choose.

• Estimator biases on small sample.

  • The predictive variable’s persistence and the negative correlation between contemporaneous shocks to returns and the predictive variable needs to be taken into account.

• Asymptotic theory where the horizon increases with the sample size.

  • Long-horizon regressions may no longer be consistent and have limiting distributions that are functionals of Brownian motions.

Proposed Solution(s)

The authors assert that researchers should be equally impressed by the short- and long-horizon evidence since the regressions are almost perfectly correlated. Existing measures (e.g. \(R^2\)) emphasize longer horizon due to the sampling error that shows up in regressions with small samples.

To capture the correlations across multiple-horizon estimators, the authors propose analytic expressions that relate the correlations across these estimators to both the degree of overlap across the horizons and the predictive variable’s level of persistence.

While a high level of persistence means that it can be dangerous to interpret regressions over multiple horizons, the proposed joint Wald tests show that this persistence may lead to powerful tests for economies in which predictability exists.

Evaluation(s)

The authors simulate 75 years of annual data under the null hypothesis of no predictability with horizons spanning one to five years. The results exhibited the expected increase in the coefficient estimates as a function of the horizon. Any sampling error in the data appears in the same manner in every multiple-horizon regression when the predictive variable is highly persistent. The high degree of correlation across the multi-period estimators implies the regressions are essentially redundant, and the estimators are asymptotically distributed as multivariate normal with a mean of zero.

Future Direction(s)

• How to utilize the daily activities of a company to predict the direction of its earnings?

Question(s)

• Why choose the Wald test over likelihood-ratio?

Analysis

The paper would have been better if the author had explicitly discussed the result’s trend and significance instead of having the reader interpret the figures. Moreover, it could have been summarized succinctly; nevertheless, the derived equations may be a useful future reference. While the overall work is merely presenting a different analysis, it is worthwhile to note:

• When dealing with multiple estimators, look at the individual results as well as the aggregate.

• Statistical tests should be examined qualitatively and go beyond trendspotting.

References

BRW08

Jacob Boudoukh, Matthew Richardson, and Robert F Whitelaw. The myth of long-horizon predictability. Review of Financial Studies, 21(4):1577–1605, 2008.