Ye Ye (MS&E): Shrinking the Term Structure
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Shrinking the Term Structure
Damir Filipovic, Markus Pelger, Ye Ye
We develop a conditional factor model for the term structure of treasury bonds, that unifies non-parametric term structure estimation with cross-sectional factor modeling. We show that a low dimensional factor model for the cross-section of discount bond returns arises because a sparse set of basis functions spans the term structure return curve. Our robust, flexible and easy-to-implement method learns a sparse set of optimal basis functions in reproducing kernel Hilbert spaces to span the term structure curve. Our shrinkage solution optimally trades off the smoothness of the term structure with returns errors. The estimated basis functions directly map into cross-sectional factors. Our estimated factors are investable portfolios of traded assets, that replicate the full term structure and are sufficient to hedge against interest rate changes. In an extensive empirical study on U.S. treasuries, we show that the term structure of excess returns is well explained by four factors, which capture polynomial shapes in the term structure curve. These four factors are necessary to explain the term structure premium and systematic dependency in forward returns. The cash flows of coupon bonds fully explain the factor exposure, and play the same role as firm characteristics in equity modeling. As a result we show that "cash flows are covariances". We introduce a new measure for the time-varying complexity of bond markets based on the exposure to higher-order factors.