What Drives the Cross‐Section of Credit Spreads?: A Variance Decomposition Approach

• Date: 01 October 2017
• DOI: http://doi.org/10.1111/jofi.12524
• Published date: 01 October 2017

THE JOURNAL OF FINANCE •VOL. LXXII, NO. 5 •OCTOBER 2017

What Drives the Cross-Section of Credit

Spreads?: A Variance Decomposition Approach

YOSHIO NOZAWA∗

ABSTRACT

I decompose the variation of credit spreads for corporate bonds into changing expected

returns and changing expectation of credit losses. Using a log-linearized pricing iden-

tity and a vector autoregression applied to microlevel data from 1973 to 2011, I

find that expected returns contribute to the cross-sectional variance of credit spreads

nearly as much as expected credit loss does. However,most of the time-series variation

in credit spreads for the market portfolio corresponds to risk premiums.

WHAT DRIVES THE CROSS-SECTIONAL variation in credit spreads? Credit spreads

are higher when the corporate bond issuer faces a higher default risk and

when the discount rate for the corporate bond’s cash flows rises. Since ex-

pected default and expected returns are unobservable, past research often

relies on structural models of debt, such as the Merton (1974) model, to de-

compose credit spreads. However, there is little agreement on the best mea-

sures of expected default loss and expected returns. In this article, I take

advantage of a large panel data set of U.S. corporate bond prices and esti-

mate the conditional expectations without relying on a particular model of

default. Based on these estimates, I quantify the contributions of the de-

fault component and the discount rate component to the variation in credit

spreads.

I apply the variance decomposition approach of Campbell and Shiller (1988a,

1988b) to the credit spread. In the decomposition, the credit spread plays

the role of the dividend-price ratio for stocks, while credit loss plays the

role of dividend growth. This decomposition framework relates the current

credit spread to the sum of expected excess returns and credit losses over

the long run. This relationship implies that if the credit spread varies,

∗YoshioNozawa is with the Federal Reserve Board. I am grateful for comments and suggestions

from professors and fellow students at the University of Chicago. I express particular thanks to

John Cochrane, my dissertation committee chair. I also benefited from the comments by Joost

Driessen, Simon Gilchrist, Lars Hansen, Don Kim, Ralph Koijen, Arvind Krishnamurthy,Marcelo

Ochoa, Kenneth Singleton (Editor), Pietro Veronesi, Kenji Wada, Bin Wei, Vladimir Yankov, and

participants in workshops at 10th Annual Risk Management Conference, Aoyama Gakuin, Chicago

Booth, Chicago Fed, Erasmus Credit Conference, Federal Reserve Board, Hitotsubashi, New York

Fed, and the University of Tokyo.The views expressed herein are the author’s and do not necessarily

reflect those of the Board of Governors of the Federal Reserve System. The author does not have

any potential conflicts of interest, as identified in the Journal of Finance disclosure policy.

DOI: 10.1111/jofi.12524

2045

2046 The Journal of Finance R

then either long-run expected excess returns or long-run expected credit loss

must vary.

I estimate a vector autoregression (VAR) involving credit spreads, excess re-

turns, probability of default, and the credit rating of the corporate bond. Since

default occurs infrequently, estimating the expected credit loss and expected

returns by running forecasting regressions requires a large number of obser-

vations. I therefore collect corporate bond prices from the Lehman Brothers

Fixed Income Database, the Mergent FISD/NAIC Database, TRACE, and

DataStream, which together provide an extensive data set on publicly traded

corporate bonds from 1973 to 2011. In addition, I use Moody’s Default Risk

Service to ensure that the price observations upon default are complete, and

thus my credit loss measure does not miss bond defaults that occur during the

sample period.

Based on the estimated VAR, I find that the ratio of the volatility of the

implied long-run expected credit loss to the volatility of credit spreads is 0.67,

while the ratio of the risk premium volatility to the credit spread volatility is

0.52. In a world in which credit spreads are driven solely by expected default,

the volatility ratio for expected credit loss would be one, while the ratio for

the risk premium would be zero. In the data, about half the volatility of credit

spreads comes from changing expected excess returns.

I find a nonlinear relationship among risk premiums, expected credit loss,

and credit spreads, depending on the credit rating of the bond. Much of

the variation in credit spreads among investment grade (IG) bonds corre-

sponds to the risk premium variation, while the expected credit loss ac-

counts for a larger fraction of the credit spread volatility of high-yield (HY)

bonds.

In contrast to the security-level results, the market-wide variation in credit

spreads is driven mostly by risk premiums. The difference arises from the

diversification effects. The default shocks are more idiosyncratic than the

expected return shocks, and thus the expected credit loss component is

more important at the individual bond level than at the aggregate market

level.

I next extend the variance decomposition framework to study the interac-

tion between the expected cash flows and risk premiums of bonds and stocks.

To study this interaction, I jointly decompose the cross section of bond and

stock prices. I find a significant positive correlation in expected cash flows

between bonds and stocks, while the risk premium correlation is insignif-

icant. Interestingly, the correlation between the expected default on bonds

and the risk premium on stocks is negative. Thus, my VAR specification

yields results consistent with the distress anomaly of Campbell, Hilscher, and

Szilagyi (2008), who find that a stock of a firm near default earns lower expected

returns.

In the literature, the papers closest to mine are Bongaerts (2010)andElton

et al. (2001). The idea of applying a variance decomposition approach to cor-

porate bonds is introduced by Bongaerts (2010), who decomposes the variance

of the returns on corporate bond indices. This article complements Bongaerts