Forecasting Stock Returns: A Predictor-Constrained Approach

We develop a novel method to impose constraints on univariate predictive regressions of stock returns. Unlike the previous approaches in the literature, we implement our constraints directly on the predictor, setting it to zero whenever its value falls below the variable's past 12-month high. Empirically, we find that relative to standard unconstrained predictive regressions, our approach leads to significantly larger forecasting gains, both in statistical and economic terms. We also show how a simple equal-weighted combination of the constrained forecasts leads to further improvements in forecast accuracy, with predictions that are more precise than those obtained either using the Campbell and Thompson (2008) or Pettenuzzo, Timmermann, and Valkanov (2014) methods. Subsample analysis and a large battery of robustness checks confirm that these findings are robust to the presence of model instabilities and structural breaks.