The Dynamics of Corporate Credit Spreads
Fred Joutza, Sattar A. Mansib and William F. Maxwellb

Corresponding author:
William Maxwell
Texas Tech University
College of Business Administration
Box 42101
Lubbock, TX 79409
e-mail: maxwell@ba.ttu.edu
Voice: (806) 742-3365
Fax: (806) 742-2099
abGeorge Washington University
Texas Tech University***

The authors would like to thank Scott Hein, Richard Sweeney, seminar participants at the 2000
FMA Conference, Georgetown University and Texas Tech University, and the anonymous referee forvaluable comments and suggestions.

1

The Dynamics of Corporate Credit Spreads

Abstract
We examine how default and systematic risk measures influence corporate credit
spreads for investment and non-investment grade corporate bonds over the 1987 to
1997 time period. We find a long-run relation between credit spreads and default risk
as measured by the level and the slope of the Treasury term structure. However, therelation between credit spreads and the term-structure variables can vary based on thetime to maturity and credit quality of corporate bonds. In the short-run, credit spreads
are influenced by default risk and the Fama and French systematic risk factors. The
results have implications for parameterizing bond and credit derivative pricing models.

Keywords: credit spreads, bond pricing, treasury term structure

JEL Classification: C4, E4

1. Introduction
Recently, a great deal of attention has been devoted to understanding the stochastic nature anddeterminants of credit spreads. This issue plays a central role in the fixed income literature, primarily
because of its importance in the pricing of risky debt and credit derivatives (e.g., Duffee (1999), Duffieand Singleton (1997), Longstaff and Schwartz (1995b), and Jarrow and Turnbull (1995)). In theliterature, there are two theoretical approaches to the pricing of risky debt. First, reduced form, or
hazard rate, models, which take as a premise that bonds when grouped by ratings are homogeneouswith respect to risk (e.g., Duffie and Singleton (1999), and Madan and Unal (1998), and Das andTufano (1996)). Second, diffusion-based, or option pricing models, which approximate the asset valueof the firm as a stochastic process and price the debt as an option on the value of the firm (e.g.,Longstaff and Schwartz (1995a), and Merton (1974)). Both approaches take into account credit
spreads as a central component in their pricing models.1
We extend this literature by empirically examining the determinants of credit spreads and theireffects on the valuation of risky debt. We do this in four ways. First, previous research focuses on thedeterminants of either default risk (e.g., Duffee (1998)) or systematic risk (e.g., Elton, Gruber, Agrawal,
and Mann (2001)). In this paper, we jointly model default and systematic risk measures. Second, weuse cointegration analysis to examine the relation between credit spreads, and the Treasury term
structure categorized by the level and slope. Third, we confirm the findings of Elton et al. (2001) that
the Fama and French (1993) systematic risk factors play a role in the pricing of risky debt. Fourth, we

1Credit spreads, or the spread between corporate bond yields and Treasury yields with a corresponding duration, arethe risk premium associated with holding risky debt; they represent the payment to a risk averse investor for
accepting default risk. Since default risk premium changes over time due to a change in the perception of theprobability or severity of default, average credit spreads measure the general perception of the risk of investing in
general risk categories.

1

include an analysis of investment and noninvestment grade bonds to better understand how these risk
factors change across risk classes.
Elton et al. (2001) examine corporate bond spreads based on reduced form models andmeasure credit spreads as a function of local and state taxes, default risk, and systematic risk factors. In
contrast, Duffee (1998) and Morris, Neal, and Rolph (1998) apply macroeconomic changes captured
in the Treasury curve as a proxy for changes in default risk. While these studies provide useful insight
into the empirical determinants of credit spreads, they leave several questions unanswered. For
example, by analyzing how systematic risk and default risk influence credit spreads separately, previous
research fails to account for the potential correlation between these variables. Hence, the Treasury
curve variables found in Duffee (1998) and Morris et al. (1998) may proxy for the systematic risk
measures in Elton et al. (2001) or visa versa. In addition, with the exception of Morris et al., thesestudies focus on the short run dynamics and have not examined the long-run relation among thedeterminants of credit spreads. In the case of Morris et al., the focus is solely on the long run relation.
These studies also examine investment grade bonds only, leaving out the most volatile segment of themarket, the non-investment grade bond market.

In this paper, we examine the short- and long run

relation between the default and systematic risk factors and jointly estimate these determinants toseparate out the interaction among the variables
Bond pricing models, either implicitly or explicitly, include a correlation between credit spreads
and the level of interest rates. However, theoretical models reach different conclusions with respect tothe sign of this relation. For example, most of the recent research documents a negative correlation
between changes in credit spreads and changes in the level of interest rates (e.g., Duffee (1998), andDas and Tufano (1996)). A negative relation between credit spreads and the Treasury yield is consistent2with Merton’s (1974) contingent claims approach where the firm is valued in an option framework. An
increase in the level of the Treasury rate should increase the value of firm moving it farther away fromthe exercise price and hence lowering the probability of default. This implies that an increase in the levelof the Treasury rate should have a negative relation with yield spreads. In contrast, Leland and Toft
(1996) discuss the possible direct influence and positive relation between the Treasury yield and credit
spreads. The Treasury yield influences not only the discount rate but also directly influence the value ofthe underlying asset. Thus, the value of the firm would decrease and the probability of default would
correspondingly increase, implying a positive relation between credit spreads and the level of Treasury
yields. Therefore, we examine the sign of the relation between Treasury yields and credit spreads andwhether this relation is consistent in the short versus long run and whether the relation changes forintermediate and long-term bonds, or by the riskiness of the bonds.
Additionally, we examine the effect of the slope of the Treasury yield curve on credit spreads.
The slope provides information about the default-free term structure (e.g., Litterman and Iben (1991),
and Chen and Scott (1993)) and credit spreads (e.g., Duffee (1998)). We examine the relation of theslope of the Treasury yield curve in both the long and short run to credit spreads.
Elton et al. (2001) and Guitteriez (2001) find that similar to stock returns there are systematic
risk factors in the returns of bonds. They both find that the systematic risk factors identified by Fama
and French (1993) are priced in bond returns. These factors include: market risk premium (excess of
the return on the market minus the risk-free rate), SML (size variable--small minus large portfolio
returns), and HML (book-to-market variable--high minus low book-to-market portfolio returns).
While controlling for changes in default risk, measured by the Treasury yield curve, we examine if thesystematic risk variables have a significant influence on credit spreads.
3

We also test for the significance of other variables, which have been found to influence
corporate yield spreads.2 We examine whether the leading or coincidental economic indicators are
better default indicators than the Treasury term variables. To examine this, we test the economic
indicators in the cointegrating vectors and the error correction models (ECM) and find they do notprovide statistically significant explanatory power to the models.3 In addition, most interest rate models(e.g., Hull and White (1990), Heath, Jarrow, and Morton (1992), Vasicek (1977)) include volatility asa factor. We test for the significance of interest rate volatility in the ECMs and find it to be statisticallyinsignificant. Finally, Barnhill, Joutz, and Maxwell (1999) document the influence of mutual fund flow on
noninvestment grade bond yields. When including systematic risk factors, we find mutual fund flow to
be statistically insignificant in the models.
The results of this study have a number of implications. First, future researchers who study theeffect of Treasury rates and other macroeconomic variables on credit spreads should focus on both thelong- and short-run dynamics of the model. Information about the long-run equilibrium provides
information about short-run changes in credit spreads. Second, in terms of the pricing models of risky
debt that incorporate a correlation to interest rates, we find a complex relation between interest rates
and credit spreads. The relation between credit spreads and interest rates differ based on the maturity,
credit ratings, and the sign of the relation changes based upon the time frame. The slope of the Treasury
curve provides explanatory power in understanding changes in credit spreads, but this relation changes
based upon maturity and the riskiness of the debt. Finally, accounting for changes in the Treasury yield2

In order to be succinct, we do not report all the results. However, the results are available upon request from theauthors.
3
The first systematic risk factor, the return on the market minus the risk-free rate, or a close variation is actually
included in the leading economic indicator. Hence, an argument could be made that the stock market return insteadof measuring systematic risk could in fact be measuring default risk.

4

curve, which serves as a proxy for default risk, we find that the Fama and French systematic risk factors
are also priced in the bond market.
The remainder of the paper is organized as follows. Section II describes the data. Section III
examines the long-run relation between credit spreads and the level and slope of the Treasury curveusing cointegration analyses.

Section IV estimates error-correction models to investigate thedeterminants of credit spreads, and section V concludes the paper.

2.

The Data and the Statistical Properties of Credit Spreads

2.1.

Constructing Indexes of Credit Spreads
We utilize the Lehman Brothers Bond database (LBBD) to construct yields on corporate bondindexes. The LBBD contains institutional month-end transaction data for Treasury and corporate bonds
for the 1973-1997 time period and is commonly used in the fixed income literature. The database
contains debt security information such as bid price, accrued interest, coupon, duration, convexity, yield,
credit ratings, call and put provisions, and sinking fund characteristics. Although the database does notcontain the universe of traded debt, we have no reason to suspect any systematic bias within thesample.4
We use a sub-sample of bonds in the LBBD to construct bond indexes. We eliminate all bondsthat are matrix priced rather than trader priced.5 A trader price is a dealer quote from which the yieldon the securities is determined. We also eliminate all bonds that are not included in the Lehman
Brothers Indexes as more care is taken in assigning the dealer quote (see Elton et al. (2001)). Given

4

Elton, Gruber, Agrawal, and Mann (2001) compare the accuracy of trader quoted bond price information in the LBBD
and CRSP and conclude the LBBD is comparable in accuracy to the CRSP data.

5

this restriction, all bonds with less than a year to maturity are eliminated. We further eliminate all bonds
with embedded options (either puts or calls 6) or have a sinking fund provisions. From this sample, we
segment the bonds by Standard and Poor’s rating category (AAA, AA, A, BBB, BB, and B) and bytime to maturity (intermediate from 3 to 7.5 years and long-term greater than 7.5 years) to create
indexes.7
Given our selection criteria, our sample is limited, with the elimination of callable bonds as themost significant restriction.

As a result, we cannot create a reliable index for the AAA, BB, and B

category. For example, in the early 1990s we only find nine AAA noncallable intermediate bonds in our
sample. In addition, we find a consistent crossing of yields between AAA and AA rated indexes forboth the long and intermediate ranges (the AA rated bonds have a lower yield than AAA securities).
Therefore, we eliminate the AAA index from our analysis.8 For the noninvestment grade bonds (BBand B), very few bonds are noncallable and for a series of months, there are no noncallable B rated
bonds. However, instead of eliminating the BB and B categories from our sample, we use the Lehman
Brothers Bond Indexes for these categories, which include both callable and noncallable bonds.9 This
clearly limits our ability to directly compare the results of the investment and noninvestment grade
indexes. Even with this restriction, we believe it is informative to examine the noninvestment grade
categories.

5

Elton, Gruber, Agrawal, and Mann (2001) and Schultz (2001) discuss the problems inherent in using matrix prices.
Duffee (1998) finds a difference in the sensitivity of callable and noncallable bonds to changes in the Treasury yieldand slope of the Treasury curve.
7
Our selection criteria is similar to those of Elton et al. (2001).
8Duffee (1998) is able to create indexes for AAA securities from the LBBD using a less restrictive selection criteria.
9
We do not create index for these categories because there is some concern about the accuracy of the bond rating
before 1992 for noninvestment grade bonds. Instead we rely on the Lehman Brothers Indexes.
66

To create credit spreads, we subtract the spreads on corporate bond indexes from the Treasuryindex with a similar maturity (A intermediate spread = A intermediate index yield – Treasury
intermediate index yield). This provides us with a complete data set for all indexes and maturities forthe period January 1987 through March 1998.
Table 1 provides descriptive statistics for the intermediate and long-term indexes. Included are
the means for maturity, duration, and yield to maturity, and standard deviation of yield to maturity forintermediate and long-term indexes for all bond rating categories. The intermediates indexes have with amean maturity of 5.5 to 7.4 years and a mean duration in the range of 4.3 to 4.6. Long-term indexes
have maturity in the range of about 13.3 to 17.7 years, with a mean duration in the range of about 6.5 to
8.4 years.
In comparing the mean YTM for the indexes, the term structure for investment grade bonds is
on average upward sloping while the term structure for noninvestment grade bonds is on average
downward sloping. These results are consistent with the theoretical models of Merton (1974), Longstaff
and Schwartz (1995a), and Leland and Toft (1996), and the empirical results of Sarig and Warga(1989). The latter suggest an upward sloping or humped yield curve for low risk debt and a downward
the sloping term structure of credit spreads for high risky debt.
Table 1 also provides descriptive statistics for intermediate and long term credit spreads. The
mean and standard deviation of credit spreads for intermediate- and long-term indexes increases as
ratings decline. This increase becomes larger as ratings change from investment to noninvestment grade
categories. Figure 1 provides various graphs of credit spreads for long and intermediate indexes of A

7and B rated bonds.10 The results show a gradual drift downward in the10

We only show graphs of two representative categories. However, the A rated bonds are representative of theinvestment grade category and the B rated bonds are representative for the noninvestment category.

8

spread for A rated bonds and a less noticeable drift in the B rated bonds. The yield on the long-term
Treasury also has a downward drift.

2.2.

Explanatory Variables
To measure the level of the Treasury yield curve, we use a long-term index (Treasuries withmaturities greater than 15 years). This is in contrast to Duffee (1998) who uses a 3 month T-Bill rate.
We find that long-term indexes provide more explanatory power. We also find that long-term Treasuryindexes with maturities greater than 10 years have correlations greater than 0.98, and therefore, thechoice of the long-term index is insignificant to the final results. To measure the slope of the yield curve,
we subtract the 30-year Treasury bond yield from the 30-day Treasury bill yield. We use the Fama andFrench factors to measure systematic risk, which includes the excess return on the market, the return ona portfolio of small stocks minus the return on a portfolio of large stocks, and the return on the portfolioof high minus low book-to-market stocks.

2.3.

Stationarity of Credit Spreads
The stationarity of credit spreads is a significant issue in the pricing models of risky debt andcredit derivatives as well as in the choice of the appropriate econometric method.11 We examine thestationarity of credit spreads and of the explanatory variables using the augmented Dickey-Fuller test
statistic. As shown by Shiller and Peron (1985), the power of unit-root tests is a function of the span ofthe data and not the number of observations. Hence, our conclusions

11

For example, Das and Tufano (1996) and Jarrow, Lando, and Turnbull (1997) assume a stationary process of credit
spreads in their valuation models.

9

are appropriate when describing monthly data over 12 years. Since a non-stationary process implies
an explosive volatility structure over time, it seems implausible that the Treasury yield, the slope of theTreasury curve, or credit spreads are non-stationary over long periods of time. However, since mostpricing models have a relatively short time horizon, it seems plausible over an investment horizon thatcredit spreads could be non-stationary.

That is, the investment horizon drives the data frequency

chosen and the form of the model considered.
We test the stationarity of credit spreads for all bond ratings categories, AA through B, for bothintermediate and long-term indexes and for other explanatory variables in Panel A of Table 2. The beta
estimates in the augmented Dickey-Fuller (lag = 2) ranged from .97 to .95 for the spread on theintermediate indexes and from .85 to .96 for the spread on long-term indexes. We find similar results
for the level and the slope of the Treasury yield curve. The beta is .97 for the level and .98 for the slopeof the yield curve. We fail to reject the null hypothesis of non-stationarity for any of the credit spreads
or for the Treasury yield curve variables. For the Fama and French systematic risk factors measures,
we can conclude that the processes do not have a unit root. Figure 1 also shows the time-series plotsof the variables of interest. The graphical analysis seems to be consistent with the test statistics. Given
the lack of power in the augmented Dickey-Fuller, we cannot conclusively conclude that credit spreads
or the Treasury curve variables are nonstationary. 12 However, the evidence suggests that credit spreads
and the Treasury curve variables are a unit-root or near unit-root process, again subject to using
monthly data. 13

12

The nonstationarity of the risk-free interest rate has been well documented by Fama (1976, 1977) and Rose (1988).

13

Pedrosa and Roll (1998) examine the daily time-series properties of credit spreads from October 1995 to March 1997,
and cannot reject the null hypothesis that credit spreads are non-stationary. However, they conclude that it is
implausible for credit spreads to have a unit root.

10

Panel B of Table 2, provides the results of the stationarity test on the first differences of credit
spreads and Treasury curve variables. The evidence suggests that first differences are stationary.
Based on the analysis, our results are consistent with the level of the Treasury curve, the slope of theTreasury curve, and credit spreads as being non-stationary at least when examining the variables over amonthly time frame. The systematic risk factors, changes in credit spreads, and the Treasury curve
variables, are stationary. We also find, interestingly, that credit spreads seem to follow the patternfound in the risk-free term structure in which long term bonds have less volatility than intermediate term
bonds. This same pattern is generally found in credit spreads.

3.

Cointegration Analysis
Our analysis of monthly credit spreads suggests that credit spreads follow a process that is non-stationary.14 This has implications with respect to the appropriate statistical methodology. Longstaff
and Schwartz (1995a and 1995b) and Duffee (1998) avoid the problem of a spurious regression by
examining factors that influence changes in credit spreads. While focusing on changes in credit spreads
eliminates the problem of spurious regressions, it also results in a potential loss of information on thelong-run interaction of variables (e.g., Engle-Granger (1987)). Therefore, instead of directly moving toa model utilizing differences, we first test for a cointegrating vector. The implication of a cointegrating
vector is that while the variables may be individually non-stationary, a linear combination of variables isstationary. Hence, a cointegrating vector indicates a long-run relationship between the variables.
To perform the cointegration analysis, we must identify the variables to test in the cointegrating
vector. The implication of a cointegrating vector is that the individual variables are nonstationary but a11

linear combination of the variables produces a stationary error structure. We test for the presence of acointegrating vector between credit spreads and the level and slope of the yield curve using theJohansen maximum likelihood procedure for a finite-order vector autoregression (e.g., Johansen (1988
and 1991)).
We estimate a system of equations with credit spreads (AA, A, BBB, BB, B), the level of theTreasury curve, and the slope of the Treasury curve, using two lags (similar to the ADF tests). We also
include the three Fama and French systematic risk factors as unrestricted variables.15 The Johansen
procedure is used to test for a cointegrating vector. The null hypothesis is that there is no cointegrating
vector (rank=0), and the alternative hypothesis is that there is a single cointegrating vector (rank=1).
We further test for the significance of a second cointegrating vector (rank ≤ 1).
Tables 3 and 4 provide the cointegration results for credit spreads on the intermediate- and thelong-term indexes, respectively. We report the Johansen maximal eigenvalue and trace statistics. For
both the intermediate and long-term credit spread indexes, we reject the null hypothesis at the 1% levelthat there is no cointegrating vector for all the different credit spread models implying a cointegrating
vector exists for each of the indexes.

We interpret the cointegrating relation as an equilibrium

expression for the determinants of credit spreads.
Before examining the long-run relation between the variables, we test the significance of the level
and the slope of term structure as well as joint test of both variables in the cointegrating

14

Elliott (1998) points out the pitfalls in using cointegration methods when the data are stationary. However, this is alimitation of any paper using this methodology. We thank the referee for this comment.
15

We also ran the models with a trend term but did not include it in our final analysis as it did not add additional
explanatory power to the models.

12vector. To test the significance of the different variables in the vector autoregressions, we place general
restrictions on the cointegrating vector. To do this, we normalize the system by restricting the betacoefficient of the variable being tested to zero to examine if the beta coefficient is significantly different
from zero. The Chi-Square (χ2(d.f.)) p-values for the significance of the level and slope of the term
structure in the cointegrating vector are at the bottom of Tables 3 and 4.
The standardized eigenvectors are the estimated cointegrating vectors for the different spreads.
For example, the cointegrating vector for the credit spread on long-term and intermediate AA bonds
can be written as (p-values):

Credit Spread AALT = 0.097 Level of Treasury – 0.114 Slope of Treasury(0.001)(0.000)(1)

Credit Spread AAINT = 0.163 Level of Treasury + 0.203 Slope of Treasury (2)(0.000)(0.000)The long-term AA credit spread relation suggests that a 100 basis point change in the level ofTreasuries leads to a 10 basis point increase in the spread. There is a roughly offsetting effect for a 100
basis point increase in the slope of the yield curve. The intermediate AA credit spread is more sensitive
to changes in the level of Treasuries, but in contrast to the long-term credit spread, the slope is positively
related to the intermediate credit spread.
When examining all the results, the level of the Treasury curve is statistically significant at aminimum 5% level for all the credit spreads.

The beta (standardized eigenvalue) of the level of theTreasury curve suggests a positive relation to credit spreads. The positive relation between the level ofthe yield curve and credit spreads suggests that over the long run the Leland and Toft (1996) model iscorrect. The Treasury coefficient is increasing in magnitude as rating declines and is higher for similar
13

rated intermediate indexes as compared to the long-term indexes. We find this to be consistent with theadditional risk inherent in long-term bonds relative to short-term ones.
The effect of slope on credit spreads is more complex. For the intermediate credit spreads inTable 3, the slope of the yield curve has a positive relation and is statistically significant at a minimum
5% level for the intermediate indexes rated AA through BB. For the long-term indexes, the slope has anegative relation and is statistically significant for the AA (1% level) and A (10% level) credit spreads.
This suggests a complex relation between credit spreads and the slope of the Treasury curve.

Forintermediate indexes rated BB and higher there is a statistically significant positive relation. In contrast,
for the long-term indexes there is a statistically significant negative relation at least for the AA and A
rated categories. These results seem consistent with the idea that the highest risk bonds (low rated andlongest maturity) are more sensitive to long-term changes in the slope of the yield curve, which is related
to economic activity.

For example, if the yield curve inverts, which is typical during economic

downturns, the spreads on the lowest rated bonds and bonds with long maturities increase.
The alpha coefficients represent the speed of adjustment back towards the long-run equilibrium.
The alphas for the intermediate indexes are relatively small suggesting that a pull back towards anequilibrium is relatively quick. In comparison, the alphas for the long-term indexes are a higher
magnitude suggesting a slower pull back towards a long-term equilibrium.
Overall, when examining the cointegration results, we find a long-run relation between credit
spreads and the level and slope of the Treasury term structure. The level is statistically significant in all
the models while the slope is statistically significant in 6 out of the 10 categories. This suggests that
there is a long-run pull towards equilibrium over time. Thus by differencing the variable to induce
stationarity, a researcher would lose the information contained in the long run interaction of the variables.
14

4.

Determinants of Credit Spreads
To fully understand the dynamics of credit spreads, we must understand the determinants ofcredit spreads and examine if these factors differ in strength based upon the risk or maturity of thebonds. General risk categories are measured by bond ratings, and bond ratings are relative measures.
This leads to credit spreads changing over time due to changes in macroeconomic conditions as theperceived risk of owning a bond fluctuates over time (Fridson, Garman, and Wu, 1997). In this section,
we examine the factors that can cause the premium for owning risky debt to fluctuate over time.
Consistent with Elton et al. (2001), we include measures of default risk and systematic risk in theanalysis.

4.1.

Error-Correction Models
After determining the long-run relation between the Treasury curve and credit spreads, we next

estimate error correction models (ECMs) to determine the factors which influence credit spreads overthe short and long run. ECMs combine the information from the short-run dynamics of the credit
spreads while directly incorporating the long-run relation found in the cointegration analysis. In addition,
we include Fama and French’s three factors to measure systematic risk. Table 5 provides the results of
the analysis.
We find that all models are statistically significant at the 1% level. With the exception of the AA
category, we find that the models explain more of the changes in the intermediate than long-term indexes
as measured by the coefficient of determination, R-square. Even though credit spreads volatility

15increases as bond ratings decline (see Table 1), we find that we can generally explain more of thisvolatility.

4.2.

Determinants of Credit Spreads

Consistent with the time period plots, we find that the constant is negative in 9 out of the 10
categories and is statistically significant at the 5% level in 5 out of 10 of the categories. In particular, theconstant is significant in both the BB and B models for the intermediate and long-term indexes. The
declining spread is consistent with the growing optimism regarding the U.S. economy from the late1980s to the late 1990s.
The error correction coefficient is negative for all the categories and is statistically significant for
all the long-term indexes. However, for the intermediate indexes it is only statistically significant for the
BB and B categories. The results from the cointegration analysis and from the error correction models
suggest there is long-run relation for long-term bonds and for the noninvestment grade intermediate
bonds, but the results for the intermediate investment grade bonds suggest only a weak relation.
However, for the BB and B intermediate models the error correction term suggests a speed ofadjustment 2-3 times slower than for the long-term indexes.
There is a statistically significant negative relation between changes in the credit spreads andchanges in the Treasury yield in 9 out of the 10 categories (significant at a minimum 5% level). Thus, thesign of the relation between the level of the risk-free rate and credit spreads differs based the length oftime analyzed. In the long-run there is a positive relation (see Table 3 and 4), and in the short-run(Table 5) there is a negative relation.

16

A negative relation between credit spreads and the Treasury yield is consistent with Merton's(1974) contingent claims approach where the firm is valued in an option framework. In the short run,the theoretical pricing models are correct in that there is a negative relation between changes in credit
spreads and changes in the Treasury yield.
The change in the slope is statistically significant and positive at a minimum 5% level for all theintermediate indexes. For the long-term indexes, the slope is only significant for the B category.
Overall, we find the slope is a significant variable in understanding intermediate credit spreads. For theintermediate indexes, we find the slope to be highly significant and positive related to credit spreads inboth the long run (from the cointegration analysis) and the short run. The effect of the slope of the yield
curve and long-term credit spreads is less significant and more complex. In the long run we find anegative relation between the slope and long-term credit spreads, at least for the AA and A category.
In the short run the slope is only significant for the credit spread on B rated long-term bonds but
positive.

This suggests the information contained in the slope of yield curve has very different

implications for long-term versus intermediate maturity credit spreads.
We find results that are consistent with Elton et al. (2001) and Gutierrez (2001). The Fama andFrench three factors are generally negative and significant, which support a systematic component tocredit spreads similar to stock returns. The market risk premium is statistically significant in for all ten
categories, and in 8 out of the ten categories it has the highest explanatory power. The second
systematic factor, small minus large returns, is statistically significant in 6 of the categories. Generally,
the SMB factor has more explanatory power for the intermediate credit spreads. The high minus low
book-to-market factor is significant in 8 categories and similar to the SMB factor seems to explain moreof the variation in the intermediate versus long-term credit spreads.
17

When comparing the overall models for the intermediate versus long-term credit spreads, wefind the long-run relation between the level and the slope of the yield curve to have a more significant
effect on long-term credit spreads. On the other hand, the systematic risk factors seem to have agreater effect on the intermediate credit spreads. This is consistent with the conclusion that long-termbonds are more sensitive to changes in default risk and intermediate bonds are driven more by thesystematic component of credit spreads.
Finally, we examine the stability of the ECMs using recursive analysis. We estimate the ECMs
using the first three years of observations and then examine the stability of these estimates as anadditional observation is added. The easiest way to examine the output is in graphical form. Figures 2
through 5 show the beta estimates for the explanatory variables in the ECMs. In the figures, the beta
estimates are bounded by lines representing two standard deviations from the coefficient estimates. We
show results for the A rated and BB rated credit spreads for both the intermediate and long term.
While we find some volatility over the first half of the model, the beta estimates appear to be relatively
stable and constant over time 16.

5.

Conclusion
We examine the dynamics of changes in corporate credit spread risk for investment andnoninvestment grade bonds. Our evidence, based on monthly data, suggests that over a twelve year
period credit spreads are a non-stationary or at least close to a unit-root process, but the changes incredit spreads are stationary. To induce stationarity, researchers difference the16

We also ran N-down Chow tests to test for structural breaks in the model and find no evidence of any structural
breaks in the model. (available upon request).

18

variables, but this can lead to a loss of information. Therefore, we examine the presence of stationary
cointegrating vectors between credit spreads and the Treasury term structure. Using the Johansen
maximum likelihood procedure for finite-order vector autoregressions, we find a stationary long-run
relation between credit spreads and the level and slope of the Treasury term structure. We then use
error correction models to determine the factors that influence credit spreads over the short and longrun. The rationale is that estimating the short- and long-run dynamics of credit spreads simultaneously
allows us to investigate the speed of adjustment to disequilibrium in the long-run relation, while
examining the short-run dynamics of credit spreads.
In aggregate, the results suggest that Treasury yields are positively related to credit spreads inthe long run, but negatively related in the short run. This has implications in the contingent claims and the
reduced form approaches for valuing risky debt. In the contingent claims approach framework, anincrease in Treasury yields is a negative signal to the market over the long run about the firm's future
cash flows. In the short run, however, an increase in the Treasury yield indicates an increase in the valueof the call option. As for the slope of the term structure, the relation between credit spreads and theslope is complex. For intermediate investment grade bonds, there is a positive relation in both the shortand long run, but for long-term bonds the predominant relation in the long run is negative and there is no
statistically significant relation in the short run. We also find that Fama-French systematic risk factors
influences changes in credit spreads over time. Hence, corporate credit spreads are driven by bothdefault and systematic risk.
Finally, our study has two main implications. The first is methodological. Future researchers
who study the effect of Treasury rates and other macroeconomic variables on credit spreads should
consider using cointegration analysis when conducting their empirical tests. Our results demonstrate a19complex relation between credit spreads, the level, and the slope of the Treasury yield curve. In thelong run there is a positive relation but in the short run this relation turns negative. The second implication
relates to pricing risky debt. The determinants of credit spreads differ based upon time to maturity andcredit risk, but also the sign of these relations change based upon the maturity and the credit rating of thebond. This has implications for the development of accurate models to price risky debt and credit
derivatives.

20

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Fama, E., 1977, Interest rates and inflation: The message it entrails, American Economic Review 65,
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Fama, E. F. and K. R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of
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Flannery, M. and S. Sorescu, 1996, Evidence of bank market discipline in subordinated debenture
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Heath, D., R. Jarrow, and A. Morton, 1992, Bond pricing and the term structure of interest rates: A
new methodology for contingent claims valuation, Econometrica, 60, 1992, 77-105.
Hull, J. and A. White, 1990a, Pricing interest-rate derivative securities, The Review of Financial
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University of Houston.
Jarrow, R., D. Lando, and S. Turnbull, 1997, A markov model of the term structure of credit risk
spreads, Review of Financial Studies 10, 481-523.
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Financial Economics 5, 177-188.

23

TABLE 1
Descriptive Statistics for Yield on Corporate Bond Indexes and Credit Spreads Calculated as the Difference between Yield on
Corporate Bond Indexes and Treasury Yield with a Corresponding Maturity
This table shows intermediate and long term corporate bond indexes and credit spreads. The data comes from the Lehman Brothers Bond
database available on a monthly basis from January 1987 through October 1998. For corporate bond indexes, included are the mean maturity, mean
duration, mean yield to maturity, and standard deviation of yield to maturity for intermediate and long term indexes for all rating categories. For
credit spreads, included are the mean, standard deviation, skewness and kurtosis for intermediate and long term indexes for all rating categories.
Maturity and duration are in years, and yields are in basis points based on a par bond value of $100.
Bond Indexes

Credit Spreads

Maturity

Duration

YTM

Std. Dev.
Of YTM

Intermediate Indexes
AA
A
BBB
BB
B

5.548
5.592
5.661
6.790
7.415

4.459
4.475
4.497
4.348
4.576

7.706
7.919
8.262
10.50512.335

1.335
1.365
1.393
2.318
2.509

0.927
1.141
1.483
3.813
5.643

0.308
0.375
0.510
1.439
1.674

0.419
0.382
0.708
0.984
1.481

-1.093-1.013-0.255
1.498
2.875

Long-Term Indexes
AA
A
BBB
BB
B

16.421
15.18315.35317.67213.305

8.395
8.134
8.012
7.428
6.543

8.127
8.350
8.735
10.12312.137

1.151
1.172
1.233
1.584
2.327

0.408
0.632
1.017
2.521
4.535

0.219
0.256
0.368
0.722
1.564

0.654
1.253
1.574
1.467
1.579

-0.396
1.344
2.321
3.756
2.174

Mean

Std. Dev.

Skewness

KurtosisTable 2
Augmented Dickey-Fuller Test Statistics Examining the Stationarity of Credit Spreads and Changes in
Credit Spreads
The augmented Dickey-Fuller test statistics is used to test the stationarity of credit spreads and changes in credit
spreads. The null hypothesis is that βt-1=1 (a nonstationary process) and the alternative is that βt-1=0 (a stationary
process). Critical t-values are: 5%=-2.88, 1%=-3.48 with a constant included. Panel A represents a test for
stationarity on the spread between corporate bonds and Treasury yields. Panel B represents a test for stationarity on
the change in the spread between corporate bonds and Treasury yields. Statistical significance is denoted by a, b, and c
for the 99%, 95%, and 90% confidence levels respectively.
Panel A – Test of Stationarity Levels
Std. Dev. t-statistic
βt-1

Panel B – Test of Stationarity First DifferenceStd. Dev. t-statistic
βt-1Intermediate Index Credit Spreads
AA
A
BBB
BB
B

0.965
0.966
0.962
0.947
0.947

0.080
0.095
0.119
0.438
0.470

-1.50
-1.51
-1.79
-1.87
-2.04

-0.614
0.129
0.198
0.106
0.177

0.149
0.096
0.119
0.444
0.475

-6.48a-5.42a-5.53a-5.48a-5.48aLong-Term Index Credit Spreads
AA
A
BBB
BB
B

0.949
0.936
0.936
0.853
0.959

0.068
0.082
0.119
0.381
0.555

-1.77
-2.17
-2.14
-2.81
-1.31

-0.281-0.399-0.080-0.182-0.137

0.066
0.109
0.119
0.393
0.551

-8.09a-7.27a-6.94a-5.85a-5.46aTreasury Curve Variables
Level
Slope

0.971
0.977

0.263
0.198

-1.21
-1.62

-0.007
0.472

0.264
0.200

-6.05a-4.36aMeasures of Systematic Risk
Market excess return
Small minus large firmHigh minus low book/market

0.017
0.082
0.097

4.056
2.640
2.313

-8.10 a7.82 a-7.80 a

Table 3
Cointegration Analysis of Credit Spreads, the Level of the Treasury Curve, and the Slope of theTreasury Curve Using the Johansen Methodology with the Fama and French Risk Factors as
Unrestricted Variables for Intermediate Indexes
λmax and λαmax are Johansen’s maximal eigenvalue statistics, and λtrace and λαtrace are Johansen’s trace
eigenvalue statistics. An α signifies the statistic is adjusted for degrees of freedom. The null hypothesis isthat there is no cointegrating vector (rank=0) against the alternative hypothesis that there is one cointegrating
vector (r=1). Rank<=1 tests the null hypothesis that there is more than one cointegrating vector. The Fama
and French three systematic risk factors (market risk premium, small minus large firm, and high to low bookto-market) are included as unrestricted variables.

AA

Credit Spreads Intermediate Indexes
A
BBB
BB

Cointegration Statistics
Null Hypothesis rank = 0
λmax
λαmax
95% critical value

36.20a34.55a21

41.58a39.69a21

38.14a36.41a21

36.71a35.04a21

34.22a32.67a21

λtraceλαtrace
95% critical value

42.67a40.73a29.7

46.98a44.85a29.7

43.31a41.34a29.7

43.11a41.15a29.7

41.44a39.56a29.7

Null Hypothesis rank <= 1
λmax
λαmax
95% critical value

4.71
4.49
14.1

4.50
4.30
14.1

4.82
4.60
14.1

6.36
6.07
14.1

7.20
6.87
14.1

λtraceλαtrace
95% critical value

6.47
6.18
15.4

5.40
5.15
15.4

5.17
4.93
15.4

6.40
6.11
15.4

7.22
6.89
15.4

-0.1626-0.2029-0.2097-0.2477-0.2517-0.2905-1.0146-0.3598-0.1234-0.1200-0.0039-0.0049-0.0822-0.0787

B

Standardized Eigenvalues, beta
Level
Slope

Standardized Adjustment Coefficientalpha-0.0134

Test statistic for the significance of the variable in the cointegrating variable
P-value from Chi-square 1 df.
Level
Slope
Joint

0.000a0.000a0.000a0.000a0.000a0.000a0.000a0.000a0.000a0.000a0.010b0.000a0.020b0.490
0.050b

Table 4
Cointegration Analysis of Credit Spreads, the Level of the Treasury Curve, and the Slope of theTreasury Curve Using the Johansen Methodology with the Fama and French Risk Factors as
Unrestricted Variables for Long-Term Indexes
λmax and λαmax are Johansen’s maximal eigenvalue statistics, and λtrace and λαtrace are Johansen’s trace
eigenvalue statistics. An α signifies the statistic is adjusted for degrees of freedom. The null hypothesis isthat there is no cointegrating vector (rank=0) against the alternative hypothesis that there is one cointegrating
vector (r=1). Rank<=1 tests the null hypothesis that there is more than one cointegrating vector. The Fama
and French three systematic risk factors (market risk premium, small minus large firm, and high to low bookto-market) are included as unrestricted variables.

AA

Credit Spreads Long-Term Indexes
A
BBB
BB

Cointegration Statistics
Null Hypothesis rank = 0
λmax
λαmax
95% critical value

31.15a29.73a21

27.59a26.33a21

26.96a25.74a21

33.83a32.29a21

42.91a40.96a21

λtraceλαtrace
95% critical value

39.33a37.54a29.7

36.57a34.91a29.7

36.66a34.99a29.7

38.37a36.63a29.7

48.85a46.63a29.7

Null Hypothesis rank <= 1
λmax
λαmax
95% critical value

7.70
7.35
14.1

8.41
8.03
14.1

9.67
9.23
14.1

4.52
4.31
14.1

5.92
5.65
14.1

λtraceλαtrace
95% critical value

8.18
7.81
15.4

8.99
8.58
15.4

9.69
9.25
15.4

4.54
4.33
15.4

5.95
5.68
15.4

-0.0973
0.1143-0.1603
0.0613-0.1636
0.0567-0.4675-0.0577-0.80140.0855-0.1146-0.1059-0.2665-0.1757

B

Standardized Eigenvalues, beta
Level
Slope

Standardized Adjustment Coefficient
alpha-0.2587

Test statistic for the significance of the variable in the cointegrating variable
P-value from Chi-square 1 df.
Level
Slope
Joint

0.001a0.000a0.000a0.001a0.070c0.001a0.030b0.250
0.050b0.000a0.460
0.001a0.000a0.550
0.001aTable 6Error Correction Models Examining the Relation between Changes in Credit Spreads and the Error Correction Coefficient, Changes
in the Level and Slope of the Treasury Curve, and the Fama and French Systematic Risk Factors
Below the estimated coefficients in parentheses are the absolute value of the t-statistic, and statistical significance is represented by: *** at the 0.01
level, ** at the 0.05 level, and * at the 0.10 level.

∆ Spread to Treasury

Constant

Panel A: Intermediate IndexesAA-0.016(0.32)
A-0.017(0.56)
BBB
0.002(0.06)
BB-0.357b(2.27)
B-0.166b(2.33)
Panel B: Long-Term IndexesAA-0.040a(3.69)
A-0.035(1.41)
BBB-0.032(1.56)
BB-0.333a(4.07)
B-0.467a(4.01)∆ LevelError
LT Treasury
Correctiont-1
Yield∆ Slope
Treasury
Curve

MarketSMB

HML

Chi-Square

R2

3.86a

0.16

12.85a0.39

10.83a0.35

12.85a0.39

19.14a0.48

11.15a

0.35

4.10a

0.17

6.89a

0.25

6.36a

0.24

10.24a0.34-0.031(0.43)-0.025(0.80)-0.006(0.25)-0.068b(2.39)-0.069a(2.99)-0.122b(2.00)-0.113a(3.57)-0.142a(3.34)-0.641a4.43-0.712a(4.77)

0.163b
(2.14)
0.128a(3.22)
0.110a(2.06)
0.429b
(2.47)
0.407b
(2.29) b-0.010b(2.59)-0.011a(5.46)-0.015a(5.27)-0.038a(4.05)-0.050a(5.18)-0.005(0.96)-0.008a(2.70)-0.011a(2.76)-0.046a(3.38)-0.065a(4.70)

0.002(0.28)-0.011a(3.40)-0.017a(3.81)-0.043a(2.78)-0.057a(3.59)-0.234a(4.87)-0.093c(1.82)-0.080b(2.35)-0.236a(4.42)-0.149a(4.54)-0.054b(2.29)-0.050(1.18)-0.093b(2.09)-0.431a(2.89)-0.710a(3.67)-0.052(0.98)-0.042(-0.85)-0.041(0.76)
0.115(0.68)
0.407c(1.81)-0.007a(4.83)-0.008a(2.76)-0.013a(4.44)-0.017c(1.74)-0.044a(3.57)-0.002(0.89)-0.007c(1.86)-0.0006(1.51)-0.007(0.51)-0.041b(2.29)-0.007a(2.99)-0.010b(2.22)-0.013a(2.75)-0.008(0.56)-0.073a(3.55)

Figure 1
Time Series Plot of Variables of Interest

6

Spread on Long-Term A Bonds

Spread on Long-Term B Rated Bonds

10

Spread on Intermediate A Bonds

Spread on Intermediate B Bonds

4
5
2
1990

1995

1990

Yield on Long-Term Treasury

10

1995
Slope of the Treasury Curve

4
8

2

6

0
1990

20

1995
Market Excess Return

1990

1995
Size Factor (Small minus Large)

10
5

0

0
-5

-20
1990

1995

1990

Book-to-Market Factor (High minus Low)

Change in Treasury Slope

5

.5

0

0

-5

-.5
1990

1995

1990

1995
Change in Yield of LT Treasury

1995

Figure 2
Stability of Beta Estimates for the Change in the Spread of the Long-Term A Index(The Beta Estimate is Bounded +/- Two Standard Errors)
Error Correction Coefficient (t-1)

Change in the Level of the LT Treasury

0

0

-.1
-.2

-.2

1990
.2

1995

1990

1995
FF1 - Market Risk Premium

Change in Slope of Yield Curve

0

0

-.01

-.2
1990

1995
FF2 - Small to Large

1990

1995
FF3 - High minus Low Book-to-Market

.025

0
0
-.02
-.025
-.04
1990

1995

1990

1995

Figure 3
Stability of Beta Estimates for the Change in the Spread of the Intermediate A Index(The Beta Estimate is Bounded +/- Two Standard Errors)
Error Correction Coefficient (t-1)

0Change in the Level of the LT Treasury

.1
-.1
0

-.2

-.1

-.3
1990

1995

1990

Change in Slope of Yield Curve

1995
FF1 - Market Risk Premium

0
.3
-.005

.2
.1

-.01

0

-.015
1990

1995
FF2 - Small to Large

1990

1995
FF3 - High minus Low Book-to-Market

.02

.01
0
0
-.01
-.02
-.02
1990

1995

1990

1995

Figure 4
Stability of Beta Estimates for the Change in the Spread of the Long-Term BB Index(The Beta Estimate is Bounded +/- Two Standard Errors)

Error Correction Coefficient (t-1)

Change in the Level of the LT Treasury

0

0
-.5
-.2
-1
-.4
.2

Error Correction Coefficient (t-1)

1990
.1

0

1995
Change in Slope of Yield Curve

10

Change in the Level of the LT Treasury

1990
-.5

1995
FF1 - Market Risk Premium

-1

0

-.1

-1.5

0

1990

1995

1990

FF1 - Market Risk Premium

Change in Slope of Yield Curve

1.5 1990

1995
FF2 - Small to Large

1

0
.5

0 19901995
FF3 - High minus Low Book-to-Market

.1
-.05

0

-.050
-.1

1995

1990

1995
FF2 - Small to Large

1990

1990

-.1

1995

0 Figure 5

1995
FF3 - High minus Low Book-to-Market

1990

1995

0

Stability of Beta Estimates for the Change in the Spread of the Intermediate BB Index(The Beta Estimate is Bounded +/- Two Standard Errors)
-.1

-.1
1990

1995

1990

1995