The Mathematics of the Relationship between the Default Risk and Yield-to-Maturity of Coupon Bonds

摘要

The paper analyzes the mathematics of the relationship between the defaultrisk and yield-to-maturity of a coupon bond. It is shown that theyield-to-maturity is driven not only by the default probability and recoveryrate of the bond but also by other contractual characteristics of the bond thatare not commonly associated with default risk, such as the maturity and couponrate of the bond. In particular, for given default probability and recoveryrate, both the level and slope of the yield-to-maturity term structure dependon the coupon rate, as the higher the coupon rate the higher theyield-to-maturity term structure. In addition, the yield-to-maturity termstructure is upward or downward sloping depending on whether the coupon rate ishigh or low enough. Similar qualitative results also holds for CDS spreads.Consequently, the yield-to-maturity is an indicator that must be usedcautiously as a proxy for default risk.