Why does the Cochrane–Piazzesi model predict treasury returns?

Abstract

We explain why the Cochrane–Piazzesi (CP) model, which uses a single tent-shaped linear combination of forward rates, is so effective at predicting bond excess returns. By using a novel statistical test coupled with a popular resampling technique, first we rule out the possibility that the high predictability may be an artefact of in-sample overfitting. Then we find that, contrary to explanations proposed in the original CP paper, neither the specific tent shape of the factor loadings nor the four-to-five-year yield spread are essential for the model’s predictive power. Instead, our analysis suggests that the predictive power of the CP model lies in its ability to identify the cointegration relationship among the quasi-unit-root forward rate regressors needed to produce the stationary process of excess returns. To support this interpretation we show that cointegration relationships among forward rates directly provide strong predictors of excess returns, and we propose that the cointegration modes of attraction generate at least part of the excess returns. Our findings shed new light on the source of bond return predictability captured by the CP factor and highlight the link between cointegration properties and the dynamics of yields.¹