Can Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models

We investigate whether bonds can hedge volatility risk in the U.S. Treasury market, as predicted by most ‘affine’ term structure models. To this end, we construct powerful and model-free empirical measures of the quadratic yield variation for a cross-section of fixed-maturity zero-coupon bonds (‘realized yield volatility’) through the use of high-frequency data. We find that the yield curve fails to span yield volatility, as the systematic volatility factors appear largely unrelated to the cross-section of yields. We conclude that a broad class of affine diffusive, quadratic diffusive and affine jump-diffusive models is incapable of accommodating the observed yield volatility dynamics. Hence, yield volatility risk per se cannot be hedged by taking positions in the Treasury bond market. We also advocate using these empirical yield volatility measures more broadly as a basis for specification testing and (parametric) model selection within the term structure literature.