Derivation of Corporate Debt Pricing Model and Its Empirical Implications

Abstract

One of the reasons the empirical capital asset pricing model (CAPM) fails to confirm the theory is because historical returns on stocks are used. On the other hand, the bond returns observed at the time of issuance are expected returns. We combine the empirical CAPM with the Modigliani-Miller propositions adjusted for risky debts, and propose a corporate debt pricing model (CDPM) which is the flipside of the empirical CAPM. The model shows that the systematic risk of defaultable corporate debt can be measured by the covariance between the returns on debt and equity market index. Using individual firm data, we test three versions of CDPM. All validate the positive relationship between individual deltas and returns with full or partial samples. Since CDPM is directly derived from CAPM, the results prove that CAPM can be validated even with individual firm data if proper expected returns are used in the test.