Shrinking the Term Structure

We introduce a conditional factor model for the term structure of treasury bonds, which unifies non-parametric curve estimation with cross-sectional asset pricing. Our robust, flexible and easy-to-implement method learns the discount bond excess return curve directly from observed returns of treasury securities. This curve lies in a reproducing kernel Hilbert space, which is derived from economic first principles, and optimally trades off smoothness against return fitting. We show that a low dimensional factor model arises because a sparse set of basis functions spans the estimated discount bond excess return curves. The estimated factors are investable portfolios of traded assets, which 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 discount bond excess return curve is well explained by four factors, which capture polynomial shapes of increasing order and are necessary to explain the term structure premium. The cash flows of coupon bonds fully explain the factor exposure, and play the same role as firm characteristics in equity modeling. In this sense, “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, and show that changes in market complexity affects the term structure premium.