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We study the cross-section of expected corporate bond returns using an inter-temporal CAPM (ICAPM) with three-factors: innovations in future excess bond returns, future real interest rates and future expected inflation. Our test assets are a broad range of corporate bond market index portfolios. We find that two factors – innovations about future inflation and innovations about future real interest rates – explain the cross-section of expected corporate bond returns in our sample. Our model provides an alternative to the ad hoc risk factor models used, for example, in evaluating the performance of bond mutual funds.

We study the factors that explain the cross-section of expected corporate bond returns. Our model adapts the Campbell (1993) inter-temporal CAPM (ICAPM) to the case of an investor who invests only in the bond market. There is, surprisingly, little research on the cross-section of expected bond returns in comparison to that on the cross-section of stock returns.1 This is striking given that, in 2005, according to the International Monetary Fund (2007), the capitalization of the US bond markets was US$24 trillion as compared to US$17 trillion for the US stock markets. The relative sizes of the corporate and government bond markets were US$18.1 trillion and US$5.9 trillion, respectively. More importantly from an investor’s perspective, the most recent data (Investment Company Institute, 2007a) shows that, out of a total of US$18 trillion under management in US mutual funds in 2006, as much as US$2 trillion was invested in bond and money market funds compared to about US$10 trillion in equity funds. In terms of the number of funds, out of a total of about 8100 mutual funds, 2849 (35%) were classified as bond and money market funds, 4770 (58%) as equity market funds and the remaining as hybrid funds (Investment Company Institute, 2007b). Our main results are as follows. Using a return decomposition for a consol bond, we obtain a three-factor ICAPM in the spirit of Campbell (1993). We test this model using returns, over the period 1988–2006, on seven corporate bond index portfolios of different default categories. We find, using a standard Fama–MacBeth approach that our model cannot be rejected. Of the three-factors in our model, innovations in future inflation rates (i.e. news about expected inflation) and future real rates are more important than innovations in expected excess bond returns in determining the cross-section of expected corporate bond returns. Our results are robust to a number of checks including the use of; alternative industry-based portfolios, different sub-samples of the data and an alternative GMM estimation technique. The rest of the paper is organized as follows. Section 2 provides a brief outline of related research on the cross-section of expected corporate bond returns, while in Section 3, we describe the set-up of our model and the test methodology. In Section 4, we provide details of the data that we use and we discuss our empirical results in Section 5. Section 6 presents some robustness checks and Section 7 concludes the paper.

Although the bond market constitutes a separate asset class with a larger market value than that of the entire equity market, there has been little attention paid to the covariance risk of expected excess returns of bonds belonging to different risk classes. Some examples of this research include Chang and Huang, 1990 and Gebhardt et al., 2005. Previous research has used either stock market factor models augmented to include additional factors that affect bonds, or models with ad hoc factors (see for example, Elton et al., 2005) that seem important in the context of bond markets. For example, Huij and Derwall (2008) measure bond fund performance using a model that includes proxies for the overall bond market, low-grade debt, mortgage-backed securities and principal components-based factors extracted from yield changes in certain ranges of the bond maturity spectrum. In contrast, in this paper, we provide a motivation for our news factors based on a simple present value decomposition for consol bonds. Further, we operationalize this using a VAR framework, as in Campbell and Vuolteenaho (2004), to extract factors from variables that forecast bond returns. Clearly, a limitation of this approach are that it assumes that the econometrician knows enough about the investor’s information set using a specific set of state variables and that the parameters of the VAR represent changes in the investor’s environment. Despite this, however, our three-factor model, when taken to the data, is able to give a reasonable account of the cross-sectional variation in expected bond returns. Our main results are as follows: we use a return decomposition for a consol bond, which, combined with Epstein–Zin preferences, leads to a three-factor ICAPM in the spirit of Campbell (1993). An interesting feature of our three-factor ICAPM for bonds is that it does not have the risk aversion coefficient as a free parameter and that the bond betas with the three-factors are entirely data dependent. We test this model and find, using seven index portfolios of different default categories over the 1988–2006 sample period, that our model cannot be rejected. Of the three-factors in our ICAPM, innovations in future inflation rates and future real rates are more important than news about future excess bond returns in determining the cross-section of expected corporate bond returns. Our robustness checks show that these results remain qualitatively similar to the use of an additional state variable, alternative test assets based on industry portfolios, different sub-samples and the use of an alternative estimation methodology. There are a number of ways in which this study could be extended. Firstly, one obvious concern is that our results are sample-specific, especially in relation to the choice of state variables. In ongoing work, we are investigating techniques for estimation that may allow us to be more agnostic about this choice. Secondly, it would be useful to see how the model performs in the analysis of the performance of bond market mutual funds relative to models that use ad hoc factor representations. Finally, extensions to the model that allow for heteroskedasticity (see for example Guo, 2005 and De Goeij and Marquering, 2006) may also be fruitful avenues for future work.