The Cochrane-Piazzesi Return Forecasting Factor

The Cochrane and Piazzesi (2005, CP) return-forecasting factor is a single, tent-shaped linear combination of forward rates that predicts excess returns on Treasury bonds across all maturities. In my view, the CP factor is truly a pioneering breakthrough in the history of macro-finance term structure models (MTSMs). It also laid the empirical foundation for the Unspanned Macro Risk (UMR) framework pioneered by Duffee (2011) and Joslin, Priebsch, and Singleton (2014), which was a needle in a haystack discovery and serves as a crucial stepping stone toward the eventual complete MTSM.

From CP(2008)

While standard Level, Slope, and Curvature factors explain cross-sectional yields, they fail to capture the time-varying bond risk premia reflected in the CP factor. Connecting term structure dynamics to the macroeconomy, this factor demonstrates that expected excess returns are countercyclical, rising in recessions and falling in expansions. Furthermore, this empirical finding sparked the spanning versus unspanning debate, demonstrating that key risk premia are unspanned by the yield curve.


Robert Hodrick's Lecture on His Paper regarding CP Factor

Robert Hodrick: Predicting Returns on Bonds and Currencies