Bond Durations: Corporates vs. Treasuries

We compare the durations of corporate and Treasury bonds in the reducedform, intensity based credit risk modeling framework. In the case where default risk is independent of default-free interest rates, we provide in each of the three most popular recovery regimes a sufficient condition under which the duration of the corporate bond is smaller than the duration of a similar Treasury bond. In the case where the default intensity and the recovery rate may depend on the default-free interest rate, we also provide a sufficient condition for the duration of a corporate bond to be smaller than the duration of the corresponding Treasury bond, assuming that recovery of market value applies. We illustrate our findings and offer more details in a specific setting in which default-free interest rates follow a Vasicek model and recovery of market value applies with a constant loss rate and a default intensity which is affine in the default-free short rate. While the unanimous conclusion of earlier papers is that the corporate bond has a smaller duration than the corresponding Treasury bond, we demonstrate in this setting that the duration of a corporate coupon bond can very well be greater than that of the similar Treasury bond.