Yields versus Expected Returns of Corporate Bonds: Some Unexpected Results

Abstract

We derive expected bond return equations for various structural credit valuation models with alternative stochastic processes and boundary conditions for default given in Merton [1974], Merton [1976], Black and Cox [1976], Heston [1993], Longstaff and Schwartz [1995], and Collin-Dufresne and Goldstein [2001]. We investigate the relationship between bond yields and expected returns under each of these models. We show that for the case of low leverage, bond yields are inversely related to expected returns for a range of maturities that lie beyond the hump of the term structure of bond yields. We also show that for the bonds of same maturity, the option characteristics of the bonds often lead to an inverse relation between bond yields and expected returns. For example, callable bonds have higher yields, but lower expected returns, than the corresponding yields and expected returns of the underlying straight bonds. Convertible bonds have higher yields but lower expected returns for the case of high leverage, and lower yields but higher expected returns for the case of low leverage, than the corresponding yields and expected returns of the underlying straight bonds.