Shrinking the Term Structure

We propose a new framework to explain the factor structure in the full cross section of Treasury bond returns. Our method unifies non-parametric curve estimation with cross-sectional factor modeling. We identify smoothness as a fundamental principle of the term structure of returns. Our approach implies investable factors, which correspond to the optimal spanning basis functions in decreasing order of smoothness. Our factors explain the slope and curvature shapes frequently encountered in PCA. In a comprehensive empirical study, we show that the first four factors explain the time-series variation and risk premia of the term structure of excess returns. Cash flows are covariances as the exposure of bonds to factors is fully explained by cash flow information. We identify a state-dependent complexity premium. The fourth factor, which captures complex shapes of the term structure premium, substantially reduces pricing errors and pays off during recessions.