A Simple Test of the Affine Class of Term Structure Models

Affine term structure models imply an affine relation between yields and factors, and between yields and yields. Hence, a necessary condition for the affine class to hold is that yield changes are linearly related to changes in as many other yields as the number of underlying risk factors. At the same time, yield changes should be unrelated to changes in nonlinear transformations of other yields. We test this hypothesis using weekly data on U.S. Treasury yields for the June 1961–December 2002 sample period. Bootstrap-adjusted tests lead to only weak rejections of the affine class, and a simulation shows that these tests have correct size and high power. Imposing the cross-equation restrictions deriving from a no-arbitrage affine term structure model leads to stronger rejections, but these stronger rejections have more to do with the no-arbitrage restrictions than with the implication of linearity. In an out-of-sample hedging exercise, the constant hedge ratios implied by the affine class generally outperform time-varying hedge ratios implied by nonlinear models.