Derivation of Corporate Debt Pricing Model and Its Empirical Implications

• Date: 01 June 2016
• DOI: http://doi.org/10.1111/ajfs.12135
• Published date: 01 June 2016

Derivation of Corporate Debt Pricing Model

and Its Empirical Implications*

Won Kang**

School of Business, Sejong University

Jungsoon Shin

Ewha School of Business, Ewha Womans University,

Received 9 September 2015; Accepted 8 December 2015

Abstract

One of the reasons the empirical capital asset pricing model (CAPM) fails to confirm the the-

ory 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 ver-

sions 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.

Keywords Corporate debt pricing model; Modigliani and Miller; Capital asset pricing model

JEL Classification: G10, G12

1. Introduction

Theoretical perfection of the capital asset pricing model (CAPM) does not seem

to promise empirical confirmation. It is a common finding that individual firm

data do not support a cross-sectional, positive, and linear relationship between

historical betas and observed stock returns. The combination of portfolio betas

and individual stock returns is not enough to enhance the empirical perfor-

mance of the model (Fama and French, 1992). Only when portfolio betas and

*The authors are grateful to the editor and anonymous referees for their insightful comments

and suggestions.

**Corresponding author: Won Kang, School of Business, Sejong University, 209 Neungdong-

ro, Gwangjin-gu, Seoul, Korea, 05006. Tel: +82-2-3408-3140, Fax: +82-2-3408-4310, email:

kangwon@sejong.ac.kr.

Asia-Pacific Journal of Financial Studies (2016) 45, 439–462 doi:10.1111/ajfs.12135

©2016 Korean Securities Association 439

portfolio returns are used do we begin to see some meaningful relationships

(Fama and MacBeth, 1973; Fama and French, 1993). The alternative or

improved models, like the three-factor model (Fama and French, 1992) and the

scaled multi-factor models (Lettau and Ludvigson, 2001; Lustig and Van

Nieuwerburgh, 2005; Piazzesi et al., 2007), use portfolio betas and portfolio

returns when they are tested.

Capturing the time-varying risk premium or investors’ hedging concern is not

the only way to improve the empirical performance of the models. One major

empirical defect lies in the fact that we always use historical returns. If we can con-

struct an empirical version that uses expected returns, as the model mandates, we

may be able to confirm the CAPM even when individual returns and individual

betas are employed. As long as we rely on stock returns it will be extremely difficult

to achieve this goal because the stock returns are always measured over past periods

of time. On the other hand, the corporate bond returns offer us a remedy: the

observed returns on bond at the time of issuance are always expected returns. One

possible solution, thus, may be to alter the model in such a way that its empirical

version is expressed by bond returns.

In this article, we adopt a simple approach where we view the income to

creditors as a contingent claim on the aggregate income to investors (both share-

holders and creditors) within the Modigliani and Miller (MM, 1958, 1963) frame-

works. We further assume that the aggregate income is risky everywhere, that is,

any non-negative value of aggregate income has a positive probability of occur-

rence. By introducing risky corporate debts with no absorption barrier, MM’s

proposition II is undetermined. Since the capitalization rate of risky debt is not

determined, there exist a multitude of solutions to MM’s proposition II. This

loose end again leads us to introduce the CAPM to the system created by MM

propositions with risky corporate debts. If, in equilibrium, the capitalization rate

of equity predicted by MM’s proposition II is equal to the expected rate of return

on equity derived by the CAPM, then we can also determine the capitalization

rates of debt. Combining the two equations we arrive at a corporate debt pricing

model or CDPM. CDPM predicts that the covariance between the returns on cor-

porate debt and the returns on equity market index explain the cross-sectional

variation in the prices of risky corporate debt.

As will be shown later, CAPM and CDPM are theoretically integrated. Empiri-

cally, however, they are not the same. While the CAPM is tested with observed his-

torical returns, CDPM can be tested with observed expected returns. Therefore, if

CDPM is empirically upheld, CAPM is also confirmed, and this empirical improve-

ment can be attributed to the employment of observed expected returns instead of

observed historical returns.

The remainder of this paper is organized as follows. In the next section, the

theory is developed and the sufficient conditions for the model to stand in line

with MM propositions are also investigated. In Section 3, the empirical analyses

are carried out. Here, we run three empirical models to test the corporate debt

W. Kang and J. Shin

440 ©2016 Korean Securities Association