A macro–financial analysis of the corporate bond market

Abstract

We assess the contribution of economic and financial factors in the determination of euro area corporate bond spreads over the period 2001–2015. The proposed multi-market, no-arbitrage affine term structure model is based on the methodology proposed by Dewachter et al. (J Bank Finance 50:308–325, 2015). We model jointly the ‘risk-free curve’, measured by overnight index swap (OIS) rates, and the corporate yield curves for two rating classes (A and BBB). The model includes four spanned and six unspanned factors. We find that, in general, both economic (real activity and inflation) and financial factors (proxying risk aversion, flight to liquidity and general financial market stress) play a significant role in the determination of the spanned factors and hence in the dynamics of the risk-free yield curve and corporate bond spreads. Across the risk-free OIS curve, macroeconomic and financial factors are each responsible on average for explaining 30 and 65% of yield variation, respectively. For A- and BBB-rated corporate debt, the selected financial variables explain on average 50% of the variation in corporate spreads during the last decade.

Appendix A: Risk premium computation

This appendix shows the computations for the risk premium (rp) considering a 1-year (12 months) holding period.

1. Bond risk premium (expected excess holding period return)

Yields are affine in factors, and factors follow a VAR(1):

$$\begin{aligned} y_{m,t}= & {} A_{m}+B_{m}X_{t} \\ X_{t}= & {} \mu +\Phi X_{t}+\Sigma \varepsilon _{t}. \end{aligned}$$

Log bond prices are likewise affine in factors:

$$\begin{aligned} p_{m,t}= & {} -\frac{y_{m,t}}{m}=-\frac{A_{m}}{m}-\frac{B_{m}}{m}X_{t}. \end{aligned}$$

The risk premium is the expected return from holding an m-month bond for 12 months in excess of the risk-free 1-year rate:

$$\begin{aligned} rp_{t+12,t}= & {} E(p_{m-12,t+12})-p_{m,t}-y_{12,t} \\ E(p_{m-12,t+12})= & {} -\frac{y_{m,t}}{m}=-\frac{A_{m-12}}{m-12}-\frac{B_{m-12}}{m-12}E(X_{t+12}), \end{aligned}$$

where

$$\begin{aligned} E(X_{t+12})= & {} \mu +\Phi X_{t+11}=\mu +\Phi \mu +\Phi ^{2}X_{t+10} \\= & {} \mu \sum _{j=0}^{11}\Phi ^{j}+\Phi ^{12}X_{t}. \end{aligned}$$

Expressing the risk premium in terms of factors:

$$\begin{aligned} rp_{t+12,t}= & {} E(p_{m-12,t+12})-p_{m,t}-y_{12,t} \\= & {} -\frac{A_{m-12}}{m-12}-\frac{B_{m-12}}{m-12}E(X_{t+12})+\frac{A_{m}}{m}+\frac{B_{m}}{m}X_{t}\\&-\,\frac{A_{12}}{12}-\frac{B_{12}}{12}X_{t} \\= & {} -\frac{A_{m-12}}{m-12}-\frac{B_{m-12}}{m-12}\left[ \mu \sum _{j=0}^{11}\Phi ^{j}+\Phi ^{12}X_{t}\right] +\frac{A_{m}}{m}\\&+\,\frac{B_{m}}{m}X_{t}-\frac{A_{12}}{12}-\frac{B_{12}}{12}X_{t} \\= & {} -\frac{A_{m-12}}{m-12}-\frac{B_{m-12}}{m-12}\mu \sum _{j=0}^{11}\Phi ^{j}+\frac{A_{m}}{m}-\frac{A_{12}}{12}-\frac{B_{m-12}}{m-12}\Phi ^{12}X_{t}\\&+\,\frac{B_{m}}{m}X_{t}-\frac{B_{12}}{12}X_{t} \\= & {} -\frac{A_{m-12}}{m-12}-\frac{B_{m-12}}{m-12}\mu \sum _{j=0}^{11}\Phi ^{j}+\frac{A_{m}}{m}-\frac{A_{12}}{12}+\left[ -\frac{B_{m-12}}{m-12}\Phi ^{12}\right. \\&+\,\left. \frac{B_{m}}{m}-\frac{B_{12}}{12}\right] X_{t}. \end{aligned}$$

2. Risk premium per rating

$$\begin{aligned} rp_{t+12,t}^{OIS}= & {} -\frac{A_{m-12}^{OIS}}{m-12}-\frac{B_{m-12}^{OIS}}{m-12}\mu \sum _{j=0}^{11}\Phi ^{j}+\frac{A_{m}^{OIS}}{m}-\frac{A_{12}^{OIS}}{12}\\&+\,\left[ -\frac{B_{m-12}^{OIS}}{m-12}\Phi ^{12}+\frac{B_{m}^{OIS}}{m}-\frac{B_{12}^{OIS}}{12}\right] X_{t} \\ rp_{t+12,t}^{j}= & {} -\frac{A_{m-12}^{j}}{m-12}-\frac{B_{m-12}^{j}}{m-12}\mu \sum _{j=0}^{11}\Phi ^{j}+\frac{A_{m}^{j}}{m}-\frac{A_{12}^{j}}{12}\\&+\,\left[ -\frac{B_{m-12}^{j}}{m-12}\Phi ^{12}+\frac{B_{m}^{j}}{m}-\frac{B_{12}^{j}}{12}\right] X_{t} \\ j= & {} A,~BBB. \end{aligned}$$

3. Risk premium differential

The risk premium differential is computed as the difference between the risk premium on a specific corporate bond (A and BBB) and the risk premium on the benchmark risk-free rate (OIS rate).

$$\begin{aligned} rp^{j-OIS}=rp_{t+12,t}^{j}-rp_{t+12,t}^{OIS} ~~~\text {where}~~~j=A,~BBB. \end{aligned}$$

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