Analogous to Stambaugh (1999), this paper derives the small sample bias of estimators in J horizon predictive regressions, providing a plug-in adjustment for these estimators. A number of surprising results emerge, including a higher bias for overlapping than nonoverlapping regressions despite the greater number of observations and particularly higher bias for an alternative long-horizon predictive regression commonly advocated for in the literature. For large J, the bias is linear in 𝐽/𝑇 with a slope that depends on the predictive variable’s persistence. The bias substantially reduces the existing magnitude of long-horizon estimates of predictability.
The information contained herein is only as current as of the date indicated, and may be superseded by subsequent market events or for other reasons. The views and opinions expressed herein are those of the author and do not necessarily reflect the views of AQR Capital Management, LLC, its affiliates or its employees. This information is not intended to, and does not relate specifically to any investment strategy or product that AQR offers. It is being provided merely to provide a framework to assist in the implementation of an investor’s own analysis and an investor’s own view on the topic discussed herein. Past performance is not a guarantee of future results.