Duration, Default Risk, and the Term Structure of Interest Rates

Abstract

We examine the interactive effect of default and interest rate risk on duration of defaultable bonds. We show that duration for defaultable bonds can be longer or shorter than default-free bonds depending on the relation between default intensity and interest rates. Empirical evidence indicates that in most cases duration for defaultable bonds is much shorter than for their default-free counterparts because of the negative relation between default risk and interest rates. Results suggest that the duration measure must be adjusted for the effects of default risk and stochastic interest rates to achieve an effective bond portfolio immunization. 2005 The Southern Finance Association and the Southwestern Finance Association.

The effects of default and call risk on bond duration

“…He indicates that at the aggregate level, lower interest rates are typically associated with economic recession and higher default probability, which implies that a negative relation exists between default intensity changes and interest rate changes. 6 On the other hand, Xie et al (2005) find that changes in default probability can be positively or negatively related to changes in interest rate. They argue that, at the firm level, as the interest rate goes up, a firm's financing costs rise and its available cash flow decreases.…”

“…His study shows that the default risk-adjusted durations of defaultable zero-coupon bonds can be shorter than, equal to, or longer than the Macaulay durations. Xie et al (2005) apply a reducedform model to examine the interactive effect of default and interest-rate risk on the durations of defaultable zero-coupon bonds. They find that the duration for a defaultable straight bond can be longer or shorter than that of its default-free counterpart, depending upon the relation between default intensity and interest rates.…”

An accurate formula for bond‐portfolio stress testing

“…For duration analysis: on defaultable bonds see, e.g. Fooladi et al (1997), Jacobi (2003, and Xie et al (2005); on callable defaultable bonds see, e.g. Jacobi and Roberts (2003); and on convertible bonds see, e.g.…”

A comprehensive structural model for defaultable fixed-income bonds

“…The result is that a default-prone zero-coupon bond has a duration lower than its maturity and, thus, is less sensitive to interest rates than its default-free counterpart. On the other hand, Xie et al (2005) shows that the duration of a defaultable bond can be longer or shorter than that of a similar Treasury bond, depending on the relation between default intensity and interest rates, which is supported by empirical evidence. Thus, as Kraft and Munk (2007) point out, 'the statements on the duration of a corporate bond seem to be conflicting'.…”