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

TL;DR

This paper explores how default risk, recovery rate, and bond characteristics like maturity and coupon rate influence the yield-to-maturity of coupon bonds, revealing complex dependencies and cautioning against using yield-to-maturity as a sole default risk indicator.

Contribution

It provides a mathematical analysis showing that bond features beyond default risk significantly affect yield-to-maturity and its term structure, a novel insight in bond risk modeling.

Findings

Yield-to-maturity depends on coupon rate and maturity.

Higher coupon rates lead to higher yield-to-maturity levels.

Yield-to-maturity slope varies with coupon rate, affecting risk assessment.

Abstract

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