The Financial Review 46 (2011) 357–383
Credit Spread Changes and Equity
Volatility: Evidence from Daily Data
Ann Marie Hibbert∗
West Virginia University
Ivelina Pavlova
University of Houston—Clear Lake
Joel Barber
Florida International University
Krishnan Dandapani
Florida International University
Abstract
We investigate the determinants of daily changes in credit spreads in the U.S. corporate
bond market. Using a sample of liquid investment grade and high-yield bonds, we show that
both systematic bond and stock market factors as well as idiosyncratic equity market factors
affect changes in the yield spread at the daily frequency. In particular, we find that increase in
stock market volatility has a positive effect on changes in the spread of corporate bonds over
the corresponding Treasuries beyond that captured by standard term structure variables. Our
∗ Corresponding
author: College of Business and Economics, West Virginia University, 1601 University Ave., Morgantown, WV 26506-6025; Phone (304) 293-2447; Fax: (304) 293-5652; E-mail:
[email protected].
We are grateful for the valuable comments of session participants at the 2008 French Finance Association
meeting, the 2010 meeting of the Southwestern Finance Association (SWFA) in Dallas, Texas and the
2010 meeting of the Eastern Finance Association (EFA) in Miami, Florida. We also would like to thank
the editor and an anonymous referee for helpful comments and suggestions. Partial funding for this work
was provided by the Florida International Bankers Association (FIBA).
C 2011, The Eastern Finance Association
357
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A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
results show that there is an almost contemporaneous inverse relationship between changes in
the bond yield spread and the stock return of the issuing firm.
Keywords: corporate bonds, yield spread, volatility
JEL Classification: G12
1. Introduction
This paper investigates the effect of equity market risk factors on daily changes
in corporate yield spreads. Using data on a sample of 2,524 bonds issued by U.S.
corporations from May 2002 to Oct. 2008, we examine whether changes in equity
market volatility and other market risk factors have explanatory power in determining
daily changes in the cross-section of yield spreads beyond that of standard term
structure variables. We also test if the relationship between stock market factors and
corporate bond yield spreads has changed during the recent financial crisis.
When bonds are treated as purely contingent-claims, the difference in yield
on a corporate bond over the corresponding Treasury bond should only reflect the
probability of default and the loss given default. In other words, the credit spread
should provide a measure of the bond’s default risk. However, recent empirical
findings show that other variables such as equity market risk factors help to explain
the credit spread (e.g., see Collin-Dufresne, Goldstein, and Martin, 2001; Campbell
and Taksler, 2003; Chen, Lesmond, and Wei, 2007; and others). In this paper, we
present evidence that both interest rate factors and equity market factors affect changes
in the yield spread at the daily frequency.
The relationship between credit risk and macroeconomic dynamics has been
studied extensively. A related strand of the research concentrates on credit spread
changes. The credit spread can be identified uniquely through the price of the bond,
the expected cash flows and the appropriate risk-free rate. Therefore, theoretically,
changes in the credit spread should be determined by changes in the spot rate,
changes in the slope of the yield curve, changes in leverage, changes in volatility, the
probability of a downward jump in the firm value and changes in the business climate
(Collin-Dufresne, Goldstein, and Martin, 2001).
Recently, researchers have found that the inclusion of additional variables has
explanatory power in the cross-section of yield spread. Examples are the implied
individual stock-option volatility (Cremers, Driessen, Maenhout, and Weinbaum,
2008) and liquidity proxies (Longstaff, Mithal, and Neis, 2005; Chen, Lesmond, and
Wei, 2007). However, these studies have primarily used weekly or monthly data and
in most instances these are averaged quarterly or annually. In addition, most prior
studies have focused only on investment grade bonds (e.g., see Campbell and Taksler,
2003).
Two aspects of this study that differentiate it from prior works are the choice
of daily data and the inclusion of high-yield bonds. In particular, we investigate the
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
359
extent to which changes in equity market volatility and other risk factors help to
explain changes in the yields on corporate bonds over the corresponding Treasuries.
While most of the recent studies on spreads have used weekly or monthly data,
we examine spread models using daily data to accentuate the investment horizon
problem. It is well established in the research that varying the investment horizon
has a profound impact on the variance as well as on the skewness of the probability
distribution of the rates of return and therefore the optimal portfolio allocation (see
Campbell, Huisman, and Koedijk, 2001; Prakash, Chang, and Pactwa, 2003).
Since our data span the recent financial crisis, we also examine the pre- and postSept. 1, 2007 periods to investigate if the linkage between the stock and bond market
has changed. The inclusion of noninvestment grade bonds is crucial for our analysis,
since they exhibit the largest spread fluctuations, especially during the subprime
mortgage crisis.
Our main contributions can be summarized along five dimensions. First, we find
that there are significant changes in the credit spread of corporate bonds at the daily
frequency. This finding is important since, to the best of our knowledge, we are the
first to investigate the factors that affect changes in the corporate yield spread at such
a high frequency. Our second finding is that lagged daily changes in stock market
volatility are positively correlated with subsequent increases in credit spread with
the effect being larger for high-yield bonds. This finding is similar to the observed
phenomenon in the stock market where positive changes in implied volatility are
associated with subsequent decreases in stock market return. Increases in equity
volatility seem to depress corporate bond prices, resulting in an increase in yields.
Third, our results suggest that there is an almost contemporaneous inverse relationship between changes in the bond yield spread and the stock return of the issuing
firm. We also find that all of the three Fama and French (1996) factors (SMB, HML
and MKTRF) have explanatory power beyond equity volatility and idiosyncratic return in explaining changes in the corporate yield spread. Our fourth finding is that all
the equity market factors that we included in our investigation have greater impact on
changes in the yields on noninvestment grade bonds. Further, by including the return
on the Russell 2000 we find that the return on an index of small stocks has as much
explanatory power as the issuing firm’s equity return for daily changes in the crosssection of corporate yield spreads. Finally, we find that the influence of equity market
factors over yield spreads increases as the time to maturity of the bond decreases and
the overall impact has been exacerbated during the recent financial crisis.
The rest of the paper is organized as follows. Section 2 outlines a brief review of
recent studies on the determinants of credit spreads and its changes. Section 3 presents
the data sources and summary descriptive statistics of our sample. In Section 4, we
discuss the models and empirical results, and in Section 5 we perform principal
component analysis on the residuals from our main empirical model. Section 6
tests our results with an independent data set. Our conclusions and implications are
presented in Section 7.
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2. Determinants of corporate yield spread levels
and changes
2.1. Structural models of bond pricing
The question of how well structural models explain the credit spread has been
investigated in a number of recent studies. Explanations in existing studies of why
structural models fail to account for the credit spread variation include illiquidity
effects, systematic risk factors, and idiosyncratic risk factors. One of the most widely
cited empirical studies of the determinants of credit spreads is Collin-Dufresne, Goldstein, and Martin (2001). They extend the treatment of bonds as purely contingentclaims wherein credit spreads should only reflect the probability of default and the
loss given default to include proxies for liquidity changes. Using a number of proxies
that measure both changes in default probability and recovery rates, their regression
analysis explains only 25% of the observed credit spread changes at the monthly
frequency. Huang and Huang (2003) also measure how much of the credit spread
is due to credit risk within the framework of a structural model. They find that for
investment grade bonds, credit risk accounts for a smaller portion of the spread, while
for junk bonds it accounts for a larger fraction.
Eom, Helwege, and Huang (2004) test five structural models (Merton, 1974;
Geske, 1977; Longstaff and Schwartz, 1995; Leland and Toft, 1996; Collin-Dufresne,
Goldstein, and Martin, 2001) and conclude that all the models have “substantial
spread prediction errors” (p. 535), generating extremely low spreads for safe bonds
and extremely high spreads for risky bonds.
2.2. Equity market risk factors
The evidence on the importance of equity market variables in structural models
of the yield spread is mixed. Collin-Dufresne, Goldstein, and Martin’s (2001) model
includes measures of changes in liquidity, variables to allow for nonlinear effects (i.e.,
squared changes in the spot rate), SMB and HML factors, lagged values of economic
state variables, and a proxy for the leading effects of stocks on bonds. They find that
even though some of the additional variables are significant and of the predicted sign,
there is only a marginal increase in the R2 . The authors conclude that credit spread
changes in the corporate bond market are driven by local supply and demand shocks
that are independent of both changes in credit-risk and typical measures of liquidity.
Elton, Gruber, Agrawal, and Mann (2001) find that the credit spread can be
explained by the loss from expected defaults, state and local taxes, as well as a
premium for systematic risk (market, SMB, HML). They find that betas on equity
market factors explain a significant portion of observed yields. Following findings
by Elton, Gruber, Agrawal, and Mann (2001), King and Khang (2005) use a sample
of investment grade corporate bonds over the period 1985 to 1998 to examine the
importance of systematic equity market factors in explaining the cross-sectional
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
361
variation in corporate yield spreads. After controlling for default-related variables,
they find that bond betas (or sensitivities) to aggregate equity market risks have very
limited explanatory power.
King and Khang (2005) suggest that the reason their results differ from Elton,
Gruber, Agrawal, and Mann (2001) is because these authors do not control for the
issue and firm characteristics which are relevant variables from structural models.
They also argue that their methodology is superior since they use individual spreads
on bonds rather than the average spreads across rating or maturity groups. King and
Khang (2005) argue that their result supports the Collin-Dufresne, Goldstein, and
Martin’s (2001) conclusion that most of the time series variation in corporate bond
yield spreads is related to movements in the aggregate corporate bond market even
though bond betas of expected return factors are significant. We expand their study
by investigating how much of the time series variation in spread can be explained by
equity market risk factors.
2.3. Idiosyncratic return/volatility
Studies also have considered company level rather than aggregate market-level
factors. Campbell and Taksler (2003) use several proxies for equity volatility to
investigate the determinants of changes in the credit spreads of investment grade
bonds using monthly data and find that firm-level equity volatility appears to explain
as much of the variation in corporate credit spreads as do credit ratings. Similarly,
Boss and Scheicher (2002) investigate if weekly changes in the spread are explained
by three groups of variables: (1) interest rate sensitive variables, (2) market liquidity
variables and (3) equity-related variables. Their results show that the level and slope
of the risk-free term structure are the most important variables. Nevertheless, they
find that stock returns, equity volatility and liquidity proxies are significant factors.
Motivated by these earlier studies, we also include the daily return on the equity of
the issuing firm in our empirical investigation.
2.4. Credit default swap premia versus bond yield spreads
A number of studies have examined the determinants of credit default swap
(CDS) spreads. Early studies analyze the spreads between zero-coupon swap rates
and the corresponding Treasury zero-coupon yields. Duffie and Singleton (1997)
show that credit and liquidity factors appear to be important sources of variation
in swap spreads, while Grinblatt (2001) examines interest rate swap spreads and
whether liquidity can have significant price effects in fixed income markets. More
recently, Ericsson, Jacobs, and Oviedo (2009) study the explanatory power of firm
leverage, volatility and the risk-free rate on changes and levels of CDS premia at
the daily frequency. They find these three theoretical determinants of credit risk are
significant in explaining CDS premia. The average R2 for the regressions for the
levels of the CDS premia is 60%; for the changes of the CDS premia it is 23%.
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A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
Another study that investigates the relation between CDS premia and firm equity
volatility using monthly data is that by Zhang, Zhou, and Zhu (2009). They show that
long-run and short-run volatility, together with jump risk, account for a substantial
amount of the spread variation even after adjusting for ratings and other firm-specific
and macroeconomic variables in the regressions.
The swap spread research argues that the CDS data are superior to bond credit
spreads because of the higher liquidity and faster price discovery in the credit derivatives market. Furthermore, employing CDS data does not require specifying a model
for the yield curve.1 However, the studies on CDS and bond credit spreads are not
directly comparable because of the different maturity structure of CDSs.2 Further,
the counterparty risk in the CDS market may be reflected in CDS premia. Finally,
although the credit derivatives market has experienced tremendous growth in the
last decade, CDS are issued for only a limited number of bonds (see Dick-Nielsen,
Feldhutter, and Lando, 2009). We therefore use credit spread rather than CDS data
in our empirical models.3
3. Data
Credit spreads and bond characteristics are obtained from Datastream. The
corporate bond yield spread is the difference between the yield on the corporate
bond and the yield on a Treasury security with an identical coupon and maturity.
The initial sample consists of daily spreads for 2,524 U.S. corporate bonds from
May 2002 through Oct. 2008, a total of 1.8 million observations. Based on structural
break tests4 and recent economic developments related to the financial crisis, we also
split the data into two subperiods: before and after Sept. 1, 2007. The first subperiod
contains 1.3 million observations, while the second one consists of approximately
0.5 million observations. The bond characteristics include Moody’s credit ratings,
issue date, maturity date, and coupon payments for each bond. The sample includes
both investment grade and speculative bonds that have between two and 16 years to
maturity. We include only bonds that have fixed rate payments that are nonconvertible,
that do not require a sinking fund, and that are nonputtable and noncallable.
Table 1 presents a summary of the credit spreads by maturity and credit rating
for all bonds in our sample for the full period and for the two subperiods. The
1 For more details on the advantages of CDS data, see Zhu (2006), Zhang, Zhou, and Zhu (2009), Ericsson,
Jacobs, and Oviedo (2009), and Tang and Yan (2010).
2 Most frequently traded maturity of CDS is the five-year contract (Benkert, 2004; Das and Hanouna,
2009).
3 We thank an anonymous referee for pointing out the need to distinguish the difference between using
CDS data and spread data.
4 We conduct structural break tests on credit spread changes for various key dates during the recent financial
crisis. Based on the results of a Chow (1960) test that imposes the Sept. 1, 2007 estimated break, we were
able to reject the null of no break at this date. To conserve space we do not report the results of the tests
here, but they are available from the authors on request.
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
363
results show that the spread widens as the credit quality decreases with the greatest
difference between noninvestment grade and investment grade bonds. For example,
Panel A shows for bonds with five years remaining to maturity that there is more than
a 100 basis points difference in spread between the highest noninvestment grade (Ba)
and the lowest investment grade (Baa). Our average credit spread for Baa bonds with
Table 1
Average credit spreads
This table reports average credit spreads in basis points by rating group and maturity of the bond. Moody’s
ratings are employed and all ratings are aggregated in rating groups (e.g., group Aa includes bonds with
ratings Aa1, Aa2 and Aa3). Panel A provides results for the full sample period from May 2002 to Oct.
2008, Panel B provides results for the subperiod from May 2002 to August 2007 and Panel C provides
results for the subperiod from Sept. 2007 to Oct. 2008.
Maturity
Aa
A
Baa
Ba
B
Caa
43
80
54
77
73
73
95
86
93
87
108
91
122
131
34
109
105
96
98
105
103
115
123
116
115
177
156
126
119
76
157
148
157
161
162
162
170
178
165
169
229
241
143
122
139
263
261
306
307
301
304
296
271
214
300
424
830
233
422
424
473
436
410
396
396
347
357
357
504
388
385
388
954
841
581
746
598
555
509
398
544
829
965
609
574
34
50
64
70
81
85
84
87
90
92
96
117
123
118
119
76
80
100
118
136
133
133
146
142
151
152
215
245
138
122
139
139
178
244
277
257
276
279
229
203
269
455
830
233
260
292
361
373
357
342
355
317
298
337
421
345
385
388
607
552
477
497
506
496
475
395
544
451
740
598
574
Panel A: Full sample
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Panel B: May 2002 to Aug. 2007
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
43
36
42
52
66
65
64
71
67
66
80
74
121
131
(Continued)
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A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
Table 1 (continued)
Average credit spreads
Maturity
Aa
A
Baa
Ba
B
Caa
209
185
167
183
186
176
192
183
171
167
203
187
148
286
254
245
246
258
259
252
245
206
226
250
235
162
479
428
443
387
414
382
361
367
277
375
293
710
616
631
546
532
572
554
463
449
413
636
476
1196
1115
815
1057
872
940
858
506
Panel C: Sept. 2007 to Oct. 2008
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
233
118
135
117
167
220
163
147
128
157
115
128
1332
1156
644
five years to maturity of 157 basis points is in the ballpark of the 127 basis points
reported by Campbell and Taksler (2003).5 For the most part, there is a positive
relationship between the spread as the time to maturity increases, moving from top
to bottom within each of the rating categories. For example, in Panel A of Table 1
the difference in the average spread between 10- and five-year Baa bonds is 21 basis
points. Campbell and Taksler (2003) report a similar differential of 18 basis points in
their BBB bonds spread for short maturities versus medium maturities.
A comparison of the credit spreads in the two subperiods reported in Panels B
and C of Table 1 reveals several interesting things. First, there is a dramatic increase
in credit spreads across all rating groups and all maturities in the second subperiod.
Taking the five-year Baa bonds as an example, the average spread is 118 basis points
before Sept. 1, 2007 and approximately 245 points thereafter. Second, while spreads
generally increase as the time to maturity increases and bond quality decreases in
the first subsample, there is a pronounced rise in spreads in the shorter maturities in
the second subsample. Panel C reports higher spreads for all rating groups for bonds
with three years to maturity than for bonds with five years left to maturity.
To measure the effects of the systematic factors and idiosyncratic volatility,
we gather daily equity returns from CRSP and match the firm data to the respective
R
index used as
bonds. We also obtain Treasury rates, market factors and Russel 2000
independent variables from CRSP. Table 2 shows the means and standard deviations
of the main bond characteristics and variables across the major rating categories for
5 Campbell and Taksler (2003) use S&P 500 ratings and only include investment grade bonds. They define
two to seven years to maturity as short maturities, seven to 15 years to maturity as medium maturities and
15 to 30 years to maturity as long maturities.
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A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
Table 2
Descriptive statistics
This table reports summary statistics for the bonds and the explanatory variables used in the regressions.
We provide means and standard deviation across Moody’s major categories; for example, Aa1, Aa2 and
Aa3 are aggregated as Aa. Coupon is the fixed rate coupon, Maturity is the time to maturity in years, Age
is the average age in years, CS is the mean credit spread and Ret is the daily return on the equity of the
issuer. Slope is the daily change in the slope calculated as the difference between the yield on the 10-year
Treasury note and the two-year Treasury note, Tnote is the change in the 10-year Treasury note rate and
R are the daily
VIX is the daily change in the level of the VIX. MKTRF, SMB, HML and Russell 2000
R
excess return on the market, the return on the Fama-French factors and the return on the Russell 2000
index, respectively.
Mean
Coupon
Maturity
Age
CS
CS
Ret
N
%
Yrs
Yrs
Bp
Bp
%
Aa
A
Baa
Ba
B
Caa
5.789
6.892
3.950
78.535
0.105
0.021
71
6.003
6.844
3.648
105.844
0.258
0.031
595
6.387
7.042
3.098
161.047
0.325
0.036
920
7.151
6.869
2.411
292.281
0.439
0.039
383
7.895
6.712
2.346
416.412
0.773
0.027
427
8.785
6.996
3.875
651.014
1.555
0.017
128
Standard Deviation
Aa
Coupon
Maturity
Age
CS
CS
Ret
Mean
Std. dev.
Skewness
Kurtosis
%
Yrs
Yrs
Bp
Bp
%
1.585
2.931
4.619
61.370
3.561
0.972
A
1.318
2.751
3.987
73.962
4.964
1.077
Baa
Ba
B
Caa
1.238
2.662
3.274
105.938
7.722
1.286
1.136
2.265
2.058
194.483
15.390
1.739
1.239
2.096
1.715
265.868
19.053
1.662
1.429
2.451
4.743
521.137
36.407
2.202
Slope
bp
Tnote
bp
(Tnote)2
bp
VIX
%
Russell
2000 %
MKTRF
SMB
HML
0.092
3.675
0.083
4.694
−0.063
5.957
0.159
1.816
35.486
69.254
4.629
29.054
0.056
1.726
0.528
30.967
0.030
0.845
0.072
3.163
−0.014
1.273
0.106
15.411
0.002
0.576
−0.209
8.264
0.015
0.526
0.775
14.040
the entire sample. As expected, there is an increase in the mean coupon rate and credit
spread with a decrease in rating. Both the average time to maturity and the average
age of the bonds are comparable across all the rating groups with the overall mean
age and years to maturity being approximately three and seven years, respectively.
The distribution of the number of bonds across the rating groups is as expected with
the median being at the middle rating (Baa).
The daily series of 10- and two-year benchmark Treasury rates from CRSP are
used in the determination of the slope of the yield curve. The daily excess return
on the market and the two additional Fama-French risk factors, SMB and HML,
are included to capture the influence of general market conditions. We use the daily
changes in the CBOE volatility index, the VIX, to examine the effect of stock market
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A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
R
volatility. Finally, we use the returns on the Russell 2000
index to examine the
overall effect of small stocks.
4. Empirical results
The key determinants we wish to examine are the forward-looking market
volatility,6 individual stock return, level of interest rates, and the slope of the term
structure. Preliminary analysis was based on bonds pooled by credit quality, as
measured by Moody’s credit ratings. This analysis revealed that the residuals of the
time series regression of credit spread on key variables are unit-root nonstationary
based on the Dickey-Fuller (1979) test. For this reason, we took the first difference
of the credit spread, interest rates, and slope of term structure. Further analysis of the
residuals suggested that an AR(2) model is the best overall specification based on
the decay of the sample partial autocorrelation function and the Akaike information
criterion (Akaike, 1974) as described by Tsay (2005). Consequently, our specification
for bonds pooled by credit rating is given by:
CSjt = αi + β1 CSjt + β2 CSj t−2 + β3 Tnotet + β4 Slopet
+ β5 VIX t−1 + β6 retjt + εit ,
(1)
where CS j t is average of the change in credit spread across rating category j from
day t–1 to day t; CS j t−1 and CS j t−2 are the average changes in the credit spread
across rating category j from day t–2 to day t–1 and t–3 to day t–2; Slopet is
the change in the term structure slope measured as the difference between 10- and
two-year Treasury rates in first difference and is indicative of the overall prospects
of the economy; Tnotet is the change in the 10-year Treasury rate; ret j t is the
average stock return across rating category j; and VIXt– 1 is lagged change in the
VIX, included to measure aggregate market volatility.
The sign of the coefficient on the first lagged dependent variable is positive and
significant at the 5% level. The sign on the second lagged dependent variable tended
to be negative and not significant. The positive and significant coefficient on the
first lagged dependent variable could be the result of nonsynchronous trading (NST)
(Campbell, Lo, and MacKinlay, 1997).
To mitigate the effect of NST, the data in our initial sample were screened for
liquidity based on the number of trading days.7 We included only bonds that had at
least 100 trading days over the first sample period. As a result, the average number of
days for which the daily change in the credit spread is zero is less than 6%. Under the
conservative assumption that most of the zero changes in the credit spread are due to
6 Cai and Jiang (2008) find evidence that bond volatility is a significant factor in predicting bond excess
returns.
7
See Sarig and Warga (1989) and Warga (1992) for a discussion on the issues with bond market data.
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
367
nontrading, bonds in the sample traded an average of 94% of the days.8 The effect of
zero changes in the credit spread is to downward bias the estimates in regressions of
bonds with zero change days.
We also expect that NST in these bonds would create significant, but false,
relationships between changes in the credit spread and lagged independent variables,
which did not show up in the regressions with pooled data. For example, suppose
there is a positive relationship between the change in credit spreads and the contemporaneous value of an independent variable. If on a given day, the change in the credit
spread is zero because the bond did not trade on that day, the next day presumably
(or at least on average) part of the change in the credit spread is due to the value
of the independent variable on the previous day. Roughly speaking, on average we
would expect, due to nontrading, a positive relationship between the credit spread
and the lagged independent variable. This is a false relationship because it is not due
economic factors but due to NST. In short, we dealt with NST by screening the data
for liquidity, developing the model specification using pooled data, where the impact
of NST should be smaller, and including lagged dependent variables.
4.1. Basic model
Based on the specification developed for bonds pooled by credit rating, we
run time series regressions for each bond individually. The results are averaged and
reported by credit rating group to account for credit risk differences. The basic
regression model is
CSit = αi + β1 CSit−1 + β2 CSit−2 + β3 Tnotet + β4 Slopet
+ β5 VIX t−1 + β6 rett + εit ,
(2)
where CSit is the change in credit spread of bond i from day t–1 to day t; CSit– 1
and CSit– 2 are the change in the credit spread of bond i from day t–2 to day t–1
and t–3 to day t–2, respectively; Slopet is the change in the term structure slope
measured as the difference between 10- and two-year Treasury rates in first difference
and is indicative of the overall prospects of the economy; Tnotet is the change in the
10-year Treasury rate; rett is the company stock price return; and VIXt– 1 is lagged
changes in the VIX, included to measure aggregate market volatility.
Panel A of Table 3 summarizes the estimates of Model (2) for each rating group
in the entire sample. The changes in the interest rate level are highly significant for
all rating groups and the sign of the coefficients is as expected. Higher interest rates
are associated with an expanding economy and lower spreads. Changes in the slope
appear to be important in determining credit spreads as well. A steeper slope of the
yield curve, however, is associated with an increase in spreads, which could be due
8
In their analysis of corporate bonds using daily data from TRACE, Hotchkiss and Ronen (2002) note
that their 20 most actively traded bonds transact on 95% of the days in their sample period.
368
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
Table 3
Basic determinants of credit spread changes
This table presents results for the following regression model:
CSit = αi + β1 CSit−1 + β2 CSit−2 + β3 Tnotet + β4 Slopet + β5 VIX t−1 + β6 rett + εit
CSit is the credit spread of bond i on day t, Tnotet is the change in the 10-year Treasury rate, Slopet is
the change in the term structure slope measured as the difference between 10- and two-year Treasury rates
in first difference, VIX t−1 is the one-day lagged changes in the VIX and rett is the company stock price
return. Panel A provides results for the full sample period from May 2002 to Oct. 2008, Panel B provides
results for the subperiod from May 2002 to August 2007 and Panel C provides results for the subperiod
from Sept. 2007 to Oct. 2008. Average estimates and associated t-statistics in brackets are reported for
each rating group.
Aa
A
Baa
Ba
B
Caa
−0.069
[−3.74]
0.003
[0.22]
−0.104
[−3.13]
0.079
[4.58]
0.001
[1.89]
−0.038
[−2.16]
0.000
[0.13]
−0.010
[−0.42]
0.054
[10.34]
−0.050
[−4.75]
0.109
[8.51]
0.002
[13.10]
−0.107
[−7.90]
0.004
[5.94]
0.029
[7.64]
0.043
[11.12]
−0.097
[−6.32]
0.101
[5.71]
0.003
[14.49]
−0.157
[−7.39]
0.005
[13.28]
−0.020
[−3.60]
−0.017
[−4.22]
−0.865
[−47.78]
0.404
[22.19]
0.010
[18.20]
−0.191
[−6.34]
0.004
[9.90]
−0.021
[−4.53]
0.011
[2.51]
−1.020
[−65.73]
0.571
[21.01]
0.012
[14.71]
−0.246
[−7.93]
0.007
[6.99]
0.015
[1.95]
0.030
[3.18]
−0.997
[−24.63]
0.713
[10.63]
0.018
[9.09]
−0.326
[−3.97]
0.014
[7.38]
0.134
0.074
0.097
0.370
0.420
0.270
−0.13
[−2.19]
−0.142
[−1.62]
−0.094
[−2.50]
0.055
[3.03]
0.001
[2.48]
−0.028
[−1.68]
0.000
[0.26]
−0.069
[−2.37]
−0.002
[−0.55]
−0.036
[−6.32]
0.054
[12.15]
0.001
[9.17]
−0.005
[−0.81]
0.000
[6.59]
−0.030
[−1.87]
0.021
[1.32]
−0.138
[−13.74]
0.082
[16.04]
0.002
[12.82]
−0.020
[−4.14]
0.000
[1.32]
−0.035
[−5.54]
−0.019
[−5.14]
−0.799
[−37.48]
0.311
[20.43]
0.008
[15.32]
−0.048
[−3.55]
0.001
[5.34]
−0.036
[−7.35]
−0.012
[−3.60]
−0.992
[−57.94]
0.385
[23.48]
0.009
[19.79]
−0.103
[−5.15]
0.001
[3.39]
0.008
[0.89]
0.003
[0.34]
−0.995
[−22.60]
0.441
[9.00]
0.011
[7.73]
−0.174
[−4.12]
0.001
[1.67]
0.162
0.068
0.097
0.353
0.427
Panel A
CSt−1
CSt−2
Tnote
Slope
VIXt−1
Ret
Intercept
Adj. R2
Panel B
CSt−1
CSt−2
Tnote
Slope
VIXt−1
Ret
Intercept
Adj. R2
0.338
(Continued)
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
369
Table 3 (continued)
Basic determinants of credit spread changes
Aa
A
Baa
Ba
B
Caa
−0.007
[−0.28]
0.042
[2.14]
−0.071
[−1.92]
0.065
[2.68]
0.001
[1.80]
−0.073
[−1.86]
0.002
[0.38]
0.044
[4.97]
0.082
[12.10]
−0.052
[−3.49]
0.149
[8.24]
0.002
[12.12]
−0.202
[9.52]
0.007
[8.71]
0.055
[11.93]
0.059
[10.56]
−0.050
[−2.34]
0.128
[4.92]
0.003
[11.05]
−0.325
[−9.56]
0.011
[22.67]
0.010
[1.48]
−0.014
[−2.31]
−0.953
[−42.27]
0.560
[19.53]
0.010
[14.77]
−0.406
[−7.28]
0.001
[13.30]
−0.005
[−0.92]
0.024
[4.09]
−1.114
[−78.94]
0.755
[19.57]
0.013
[11.05]
−0.556
[−10.05]
0.015
[9.43]
0.011
[1.23]
0.024
[1.99]
−1.172
[−27.81]
1.012
[11.26]
0.023
[7.88]
−0.535
[−4.27]
0.032
[8.35]
0.146
0.098
0.121
0.486
0.535
0.371
Panel C
CSt−1
CSt−2
Tnote
Slope
VIXt−1
Ret
Intercept
Adj. R2
to diminishing expected net present value of future projects available to the company
and consequently lower firm value (Avramov, Jostova, and Philipov, 2007).
Our focus is on the impact of aggregate and idiosyncratic equity variables on
daily changes in the corporate yield spreads. In Panel A of Table 3 we present the
estimates of time series regressions including aggregate and company level variables.
The lagged changes in the VIX are highly significant in explaining daily changes
for the high-yield bonds; spreads widen when equity return volatility increases.9
The firm stock returns are statistically significant for the bonds as well and have
the theoretically expected sign. Our first model has the highest explanatory power
for the high-yield bonds, the adjusted R2 for the Ba, B and Caa ratings groups are
37%, 42%, and 27%, respectively. Our findings are consistent with Huang and Kong
(2003), who document higher explanatory power of the equity variables for the
higher yield bond series.
We present the regression results for Model (2) for the two subsamples in Panels
B and C of Table 3. While in the first subperiod changes in the interest rate levels
influence bond spreads from all rating groups, during the second subperiod higher
yield bond spreads rise with increases in the interest rate, while the coefficients for the
Aa group is not significant. Aggregate equity volatility and firm-level stock returns are
significant over both subperiods but the explanatory power of the regression is notably
9
In a recent study, Jorion and Zhang (2010) investigate the other direction of causation, that is, the effect
of bond risk changes on equity returns.
370
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
higher for the Ba, B and Caa bonds in the second subsample. Again, the stock return
of the issuing firm is more significant explaining changes in the higher yields bonds.
4.2. Fama-French factors
Since implied equity volatility is found to be significant in explaining a portion
of the corporate bond spread changes, we also explore the impact of other systematic
equity return factors. Elton, Gruber, Agrawal, and Mann (2001), Collin-Dufresne,
Goldstein, and Martin (2001), and Huang and Kong (2003) show that SMB and HML
could be considered important determinants of the credit spreads. We extend Model
(2) to include the excess return on the market portfolio (MKTRF) as well as the
additional two factors, SMB (which is the return on a portfolio of small capitalization
stocks minus the return on a portfolio of large capitalization stocks) and HML (which
is the return on a portfolio of stocks with high book-to-market ratio minus the return on
a portfolio of stocks with low book-to-market ratio), from Fama-French three-factor
model as follows:
CSit = αi + β1 CSit−1 + β2 CSit−2 + β3 Tnotet + β4 Slopet
+ β5 smbt + β6 hmlt + β7 Mktrf t + β8 VIX t−1 + β9 rett + εit .
(3)
The estimates for Model (3) are reported in Table 4. Panel A provides average
coefficients and t-statistics for each rating group for our entire sample and Panels B
and C provide the corresponding results for each of the two subsamples.
Our results in Panel A show that the three market risk factors have a statistically
significant impact on daily changes in the corporate yield spread for all rating groups
except the Aa-rated bonds, where the SMB and HML are not significant. A decrease
(increase) in the excess return on the market is associated with an increase (decrease)
in the daily spread changes. Similar to the findings with Model (2), both the implied
stock market volatility and the return on the stock of the issuing firm are more
significant for the high-yield bonds. We also compare the results in Panels B and
C of Table 4 to investigate whether stock market risk factors have had the same
influence on corporate yield spreads over the two subperiods in our study. Whereas
SMB is not significant in the first subperiod, SMB, HML and MKTRF are significantly
related to the spreads for riskier bonds in the post-Sept. 1, 2007 period. Again, the
only exception is the Aa-rated bonds. Consistent with prior studies, the loadings on
SMB, which is usually considered a proxy for risk related to liquidity or maturity, are
positively related to spread changes for low-grade bonds. Further, the significance
of the implied stock market volatility in explaining the credit spread changes for
noninvestment grade bonds is higher in this more recent period.
4.3. Systematic and idiosyncratic factors
Several studies have investigated the relationship between bond yields and the
returns on small stocks. Kao (2000) and Huang and Kong (2003) include the return on
R
as part of their attempt to model credit
an index of small-cap stocks, the Russell 2000
371
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
spreads. They find a strong relationship between the return on small-capitalization
stocks and credit spread changes with the relationship being stronger for high-yield
bonds. Motivated by their findings, we augment Model (2) as follows:
CSit = αi + β1 CSit−1 + β2 CSit−2 + β3 Tnotet + β4 Slopet
+ β5 Russellrett−1 + β6 retresidt + εit .
(4)
R
Russellrett−1 is the one-day lagged return on the Russell 2000
index. Since
R
index and
there is a high correlation between the return on the Russell 2000
Table 4
Additional determinants of credit spread changes
This table presents results for the following regression model:
CSit = αi + β1 CSit−1 + β2 CSit−2 + β3 Tnotet + β4 Slopet + β5 smbt + β6 hmlt
+ β7 Mktrf t + β8 VIX t−1 + β9 rett + εit
CSit is the credit spread of bond i on day t, Tnotet is the change in the 10-year Treasury rate, Slopet
is the change in the term structure slope measured as the difference between 10- and two-year Treasury
rates in first difference, Mktrf, smb and hml are the daily excess return on the market and the return on
the additional two Fama-French factors, VIX t−1 is the one-day lagged changes in the VIX and rett is the
company stock price return. Panel A provides results for the full sample period from May 2002 to Oct.
2008, Panel B provides results for the subperiod from May 2002 to August 2007 and Panel C provides
results for the subperiod from Sept. 2007 to Oct. 2008. Average estimates and associated t-statistics in
brackets are reported for each rating group.
Aa
A
Baa
Ba
B
Caa
−0.068
[−3.60]
0.006
[0.44]
−0.098
[−2.96]
0.070
[3.70]
0.001
[1.38]
0.001
[1.90]
−0.001
[−2.84]
0.001
[2.07]
−0.004
[−0.23]
0.000
[0.09]
0.079
[1.91]
0.067
[5.43]
−0.067
[−1.90]
0.119
[3.00]
0.005
[9.27]
0.002
[3.75]
−0.002
[−5.41]
0.002
[13.91]
−0.029
[−1.97]
0.005
[2.82]
0.037
[9.11]
0.046
[12.46]
−0.102
[−8.64]
0.096
[8.53]
0.004
[5.27]
0.002
[4.55]
−0.003
[−6.56]
0.003
[17.63]
−0.058
[−2.78]
0.005
[10.35]
−0.016
[−3.05]
−0.009
[−2.40]
−0.848
[−46.77]
0.359
[22.85]
0.009
[7.42]
−0.002
[−1.47]
−0.005
[−8.52]
0.010
[18.59]
−0.118
[−3.76]
0.004
[9.65]
−0.016
[−3.43]
0.018
[4.36]
−0.986
[−62.89]
0.485
[22.75]
0.017
[8.18]
0.004
[2.75]
−0.007
[−8.19]
0.012
[15.37]
−0.182
[−5.96]
0.007
[7.56]
0.019
[2.44]
0.035
[3.86]
−0.938
[−23.13]
0.595
[11.18]
0.028
[5.62]
0.015
[2.85]
−0.010
[−3.87]
0.019
[8.91]
−0.334
[−4.93]
0.012
[7.02]
0.143
0.091
0.117
0.388
0.441
0.290
Panel A
CSt−1
CSt−2
Tnote
Slope
Smb
Hml
Mktrf
VIXt−1
Ret
Intercept
Adj. R2
(Continued)
372
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
Table 4 (continued)
Additional determinants of credit spread changes
Aa
A
Baa
Ba
B
Caa
−0.179
[−6.70]
−0.078
[−2.81]
−0.074
[−1.56]
0.339
[22.02]
−0.001
[−0.95]
−0.003
[−2.14]
−0.005
[−8.57]
0.010
[20.14]
−0.081
[4.09]
0.001
[5.51]
−0.003
[−0.08]
0.007
[0.80]
−0.035
[−6.16]
0.045
[10.02]
0.000
[1.42]
−0.000
[−1.07]
−0.001
[−6.36]
0.001
[10.05]
−0.015
[−2.02]
0.001
[7.18]
−0.043
[−2.18]
0.023
[1.41]
−0.136
[−10.21]
0.083
[11.77]
−0.001
[−1.07]
−0.002
[−2.38]
−0.001
[−2.74]
0.002
[11.23]
−0.013
[−2.08]
0.000
[1.56]
−0.036
[−5.87]
−0.020
[−5.18]
−0.792
[−37.60]
0.285
[20.29]
−0.003
[−3.59]
−0.008
[−6.75]
−0.004
[−8.51]
0.008
[37.61]
−0.025
[−1.96]
0.001
[6.44]
−0.036
[−7.32]
−0.011
[−3.56]
−0.979
[−60.57]
0.339
[22.02]
−0.000
[−0.95]
−0.003
[−2.14]
−0.005
[−8.57]
0.010
[20.14]
−0.081
[−4.09]
0.001
[5.51]
−0.007
[−0.81]
0.002
[0.25]
−0.989
[−26.43]
0.405
[9.72]
−0.001
[−0.59]
−0.009
[−3.25]
−0.003
[−1.02]
0.011
[7.25]
−0.146
[−3.73]
0.002
[2.17]
0.163
0.074
0.105
0.362
0.432
0.343
−0.006
[−0.22]
0.048
[2.51]
−0.058
[−1.59]
0.049
[1.71]
0.002
[1.29]
0.003
[3.20]
−0.002
[−3.87]
0.001
[2.07]
0.011
[0.25]
0.001
[0.29]
0.097
[2.50]
0.094
[6.17]
−0.074
[−1.46]
0.165
[2.91]
0.008
[10.29]
0.004
[5.60]
−0.002
[−4.54]
0.003
[12.98]
−0.075
[−2.86]
0.009
[3.66]
0.068
[13.61]
0.066
[12.46]
−0.048
[−3.56]
0.116
[7.13]
0.007
[6.22]
0.005
[9.05]
−0.004
[−7.56]
0.003
[14.77]
−0.116
[−3.28]
0.010
[16.35]
0.012
[2.06]
0.005
[0.92]
−0.928
[−39.44]
0.489
[19.61]
0.022
[10.42]
0.007
[5.18]
−0.005
[−5.00]
0.011
[15.14]
−0.261
[−4.46]
0.009
[11.98]
0.002
[0.35]
0.041
[6.96]
−1.066
[−63.48]
0.642
[20.41]
0.033
[10.19]
0.013
[7.87]
−0.008
[−5.87]
0.015
[11.96]
−0.395
[−7.32]
0.012
[9.51]
0.018
[1.80]
0.035
[3.04]
−1.069
[−20.83]
0.854
[11.40]
0.054
[7.66]
0.036
[5.71]
−0.013
[−3.55]
0.025
[8.04]
−0.625
[−6.30]
0.027
[7.98]
0.164
0.127
0.152
0.514
0.568
0.401
Panel B
CSt−1
CSt−2
Tnote
Slope
Smb
Hml
Mktrf
VIXt−1
Ret
Intercept
Adj. R2
Panel C
CSt−1
CSt−2
Tnote
Slope
Smb
Hml
Mktrf
VIXt−1
Ret
Intercept
Adj. R2
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
373
the return on the stocks of the issuers in our sample, we replace the variable Ret
with retresid, which is the residual from the regression of Ret on Russellret. By
construction, the retresid is uncorrelated with Russellret, and consequently measures
the unique information contained in the return of a given stock. The estimates for
Model (4) are reported in Table 5.
The results for our full sample regression of Model (4) in Panel A of Table 5
show that there is a statistically significant inverse relationship between daily changes
R
index. This effect is beyond
in the yield spread and the return on the Russell 2000
the term structure variables and the market risk factors. The retresid variable is
significant and inversely related to the spread on all bonds in our sample with the
exception of the highest rated bonds (Aa). Similar to our investigation using Models
(2) and (3), we estimate the regression Model (4) for each of the subperiods in our
Table 5
The effect of the return on small-cap stocks
This table presents results for the following regression model:
CSit = αi + β1 CSit−1 + β2 CSit−2 + β3 Tnotet + β4 Slopet
+ β5 Russellrett−1 + β6 retresid t + εit
CSit is the credit spread of bond i on day t, Tnotet is the change in the 10-year Treasury rate, Slopet
is the change in the term structure slope measured as the difference between 10- and two-year Treasury
R index and retresid
rates in first difference, Russellrett−1 is the one-day lagged return on the Russell 2000
is the residual from the regression of the issuing firm stock return, Ret on Russellret. Panel A provides
results for the full sample period from May 2002 to Oct. 2008; Panel B provides results for the subperiod
from May 2002 to August 2007 and Panel C provides results for the subperiod from Sept. 2007 to Oct.
2008. Average estimates are reported for each rating group. Average estimates and associated t-statistics
in brackets are reported for each rating group.
Aa
A
Baa
Ba
B
Caa
−0.071
[−3.98]
0.002
[0.16]
−0.105
[−3.18]
0.081
[4.92]
−0.065
[−2.43]
−0.032
[−1.71]
0.000
[0.14]
−0.009
[−0.34]
0.046
[8.83]
−0.051
[−5.50]
0.081
[4.92]
−0.182
[−12.07]
−0.099
[−6.56]
0.004
[6.28]
0.030
[8.09]
0.040
[8.67]
−0.105
[−5.34]
0.126
[11.31]
−0.203
[−7.46]
−0.174
[−3.06]
0.007
[4.02]
−0.019
[−3.47]
−0.017
[−4.13]
−0.886
[−48.12]
0.419
[22.61]
−0.616
[−10.81]
−0.174
[−4.94]
0.004
[5.26]
−0.023
[−4.83]
0.013
[2.91]
−1.048
[−66.12]
0.596
[21.05]
−1.056
[−10.26]
−0.218
[−7.19]
0.008
[8.95]
0.021
[2.68]
0.029
[3.25]
−1.039
[−25.40]
0.753
[10.23]
−1.820
[−6.24]
−0.275
[−3.89]
0.015
[7.43]
0.127
0.073
0.105
0.379
0.427
0.287
Panel A
CSt−1
CSt−2
Tnote
Slope
Russellrett−1
Retresid
Intercept
Adj. R2
(Continued)
374
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
Table 5 (continued)
The effect of the return on small-cap stocks
Aa
A
Baa
Ba
B
Caa
−0.132
[−2.31]
−0.124
[−1.84]
−0.094
[−2.49]
0.065
[4.31]
−0.052
[−1.60]
−0.026
[−1.68]
0.000
[0.96]
−0.073
[2.30]
−0.004
[−0.86]
−0.036
[−6.36]
0.056
[12.41]
−0.049
[−8.26]
0.009
[1.28]
0.000
[3.40]
−0.031
[−1.91]
0.021
[1.33]
−0.142
[−13.73]
0.090
[16.84]
−0.059
[−13.73]
−0.019
[−2.71]
0.000
[1.11]
−0.032
[−5.19]
−0.019
[−5.30]
−0.806
[−37.87]
0.338
[20.55]
−0.243
[−7.60]
−0.016
[−1.27]
0.001
[3.50]
−0.032
[−6.42]
−0.012
[−3.63]
−0.989
[−63.52]
0.432
[22.86]
−0.467
[−8.77]
−0.078
[−3.83]
0.002
[3.02]
0.014
[1.68]
0.002
[0.25]
−1.010
[−25.41]
0.507
[9.04]
−0.469
[−3.79]
−0.177
[−4.01]
0.002
[2.27]
0.158
0.062
0.098
0.356
0.429
0.348
−0.011
[−0.45]
−0.039
[2.03]
−0.076
[−2.02]
0.071
[0.95]
−0.184
[−3.39]
0.043
[−1.00]
0.002
[0.38]
0.050
[7.03]
0.072
[11.37]
−0.058
[−4.39]
0.155
[9.34]
−0.369
[−15.10]
−0.206
[−7.90]
0.008
[9.36]
0.058
[12.60]
0.056
[8.34]
−0.063
[−2.25]
0.167
[10.02]
−0.415
[−9.91]
−0.319
[−3.67]
0.014
[5.58]
0.001
[0.07]
−0.005
[−0.79]
−0.986
[−44.78]
0.589
[20.19]
−1.504
[−16.37]
−0.402
[−6.13]
0.009
[13.63]
−0.020
[−3.31]
0.036
[6.09]
−1.174
[−78.10]
0.798
[19.65]
−2.248
[−13.85]
−0.485
[−8.88]
0.015
[11.00]
0.012
[1.24]
0.031
[2.81]
−1.221
[−27.25]
1.059
[10.68]
−3.397
[−8.17]
−0.493
[−4.62]
0.032
[8.41]
0.137
0.109
0.129
0.500
0.552
0.382
Panel B
CSt−1
CSt−2
Tnote
Slope
Russellrett−1
Retresid
Intercept
Adj. R2
Panel C
CSt−1
CSt−2
Tnote
Slope
Russellrett−1
Retresid
Intercept
Adj. R2
sample and report the findings in Panels B and C of Table 5. Consistent with our
previous findings for the market volatility in Models (2) and (3), the return on the
R
index is more significant in explaining changes in yield spread in the
Russell 2000
post-Sept. 1, 2007 period. Again, looking at the subsamples, the firm return residual
is not significant for three out of the six rating groups before Sept. 2007 and only for
the Aa group after Sept. 2007.
4.4. Maturity effects
Finally, we investigate whether our results are consistent across bonds with
differing times to maturity. We group the bonds in our sample into three maturity
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
375
bins defined as (i) short maturity, if the bond has less than six years remaining to
maturity, (ii) medium maturity, if the bond has between seven and 10 years remaining
until maturity and (iii) long maturity, if the bond has more than 10 years remaining
until maturity. We estimate Model (3) and report the results by rating groups within
each of the maturity bins in Table 6.
The results show that of the equity market risk factors, the excess return on the
market, the stock market volatility, and the return on the stock of the issuing firm
are most related to the changes in the credit spread, with the effect being greater for
bonds that are riskier and closer to maturity.10
5. Principal components analysis
To further examine the unexplained variation of our regression models, we perform a principal component analysis of the residuals. The objective of the analysis
is to find out whether a considerable systematic variation remains in the regression
residuals. Our analysis is on the average regression residuals of 18 portfolios, determined by three maturity groups (<7 years, seven to 10 years, >10 years), and six
rating groups (Aa, A, Baa, Ba, B, and Caa). To compute the portfolio residuals, we
run time series regressions of Model (2) on each bond and then each day we estimate
the mean of the regression residuals of the bonds assigned to the respective portfolio.
We then compute the covariance matrix of the resulting 18 average residuals and
extract the first five principal components.
The results in Table 7 summarize the proportion of the variance explained by the
first five principal components. When the residuals are grouped in 18 portfolios, the
first component accounts for 73% of the variation, which suggests a large systematic
variation remaining in the residuals. The results are consistent with Collin-Dufresne,
Goldstein, and Martin (2001), who find a common systematic component in the
regression residuals which cannot be explained by the structural framework used in
their study.
To investigate whether the principal component results are driven by the portfolio grouping method, as suggested in Avramov, Jostova, and Philipov (2007), we
average the residuals across 42 portfolios determined by seven maturity groups and
six credit rating groups. The proportion of the variance explained by the first principal component drops to 43%, but still a significant systematic component remains
unexplained. The first two principal components account for 71% of the variance.
These findings are at odds with Avramov, Jostova, and Philipov (2007), who show
that when the number of portfolios is increased to 35 the first principal component
accounts for less than 28% of the variation. The differences in our findings could
possibly be due to the nature of our data set (i.e., daily versus monthly data).
10
We also estimate Model (3) by maturity bin for each of our two subsamples and observe similar results
in each of our subperiods. The results are available from the authors on request.
Caa
B
Ba
Baa
A
Aa
−0.061
[−2.60]
−0.002
[−0.29]
0.022
[3.52]
−0.045
[−4.65]
−0.030
[−4.21]
−0.002
[−0.16]
Short maturity
CSt−1
−0.006
[−0.41]
0.047
[5.21]
0.041
[7.49]
−0.018
[−2.35]
0.015
[3.06]
0.042
[3.88]
CSt –2
−0.077
[−1.85]
−0.029
[−2.56]
−0.085
[−5.49]
−0.857
[−33.73]
−1.038
[−48.21]
−1.060
[−22.25]
Tnote
0.079
[2.91]
0.103
[4.74]
0.128
[11.87]
0.510
[21.5]
0.636
[19.91]
0.770
[12.18]
Slope
0.002
[1.93]
0.004
[8.41]
0.003
[4.14]
0.009
[5.35]
0.017
[7.07]
0.022
[3.72]
smb
0.001
[1.26]
0.001
[3.04]
0.001
[2.17]
−0.002
[−1.43]
0.003
[1.76]
0.025
[4.00]
hml
−0.001
[−2.44]
−0.003
[−7.93]
−0.004
[−10.95]
−0.009
[−8.00]
−0.010
[−9.06]
−0.018
[−4.38]
Mktrf
0.000
[0.81]
0.002
[7.26]
0.002
[8.68]
0.009
[11.60]
0.010
[10.62]
0.018
[6.47]
VIXt−1
−0.067
[−1.31]
−0.045
[−3.38]
−0.061
[−3.29]
−0.128
[−4.40]
−0.324
[−6.41]
−0.513
[−4.88]
Ret
0.003
[1.68]
0.003
[3.41]
0.004
[13.33]
0.004
[4.40]
0.006
[8.73]
0.017
[5.54]
Intercept
(Continued)
0.355
0.460
0.363
0.117
0.088
0.111
Adj. R2
CSit is the credit spread of bond i on day t, Tnotet is the change in the 10-year Treasury rate, Slopet is the change in the term structure slope measured
as the difference between 10- and two-year Treasury rates in first difference, Mktrf, smb and hml are the daily excess return on the market and the return on
the additional two Fama-French factors, VIX t−1 is the one-day lagged changes in the VIX and rett is the company stock price return. Within the table (i)
short maturity includes bonds that have less than seven years remaining to maturity, (ii) medium maturity includes bonds that have between seven and 10 years
remaining until maturity and (iii) long maturity includes bonds with more than 10 years remaining until maturity. Average estimates and associated t-statistics in
brackets are reported for each rating group.
CSit = αi + β1 CSit−1 + β2 CSit−2 + β3 Tnotet + β4 Slopet + β5 smbt + β6 hmlt + β7 Mktrf t + β8 VIX t−1 + β9 rett + εit
This table presents results for the following regression model:
Determinants of credit spread changes by maturity
Table 6
376
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
−0.089
[−3.33]
0.009
[0.45]
−0.002
[−0.33]
−0.043
[−6.61]
−0.045
[−6.12]
−0.022
[−1.60]
Caa
B
Ba
Baa
A
Aa
−0.150
[−2.41]
−0.057
[−2.11]
−0.042
[−2.51]
−0.120
[−1.31]
−0.058
[−3.67]
0.038
[1.44]
Long maturity
Caa
B
Ba
Baa
A
Aa
Medium maturity
CSt−1
−0.054
[−1.76]
0.013
[0.85]
−0.006
[−0.37]
−0.016
[−0.52]
0.062
[2.58]
0.056
[2.03]
0.008
[0.37]
0.026
[3.52]
0.031
[3.16]
−0.010
[−1.92]
0.012
[1.29]
0.017
[1.37]
CSt –2
−0.046
[−0.69]
−0.001
[−0.07]
−0.054
[−2.02]
−0.559
[−7.69]
−0.860
[−11.11]
−0.639
[−5.11]
−0.098
[−2.50]
−0.069
[−2.95]
−0.118
[−5.87]
−0.808
[−31.64]
−0.913
[−42.58]
−0.953
[−16.33]
Tnote
0.011
[0.55]
0.012
[1.19]
0.001
[0.03]
0.303
[1.23]
0.073
[1.79]
−0.060
[−0.66]
0.065
[3.31]
0.111
[3.95]
−0.034
[−0.30]
0.230
[13.88]
0.293
[8.15]
0.459
[5.60]
Slope
Determinants of credit spread changes by maturity
Table 6 (continued)
−0.002
[−1.93]
0.004
[3.20]
0.002
[1.19]
−0.003
[−1.39]
0.010
[2.31]
0.000
[−0.03]
0.000
[−0.27]
0.002
[4.16]
0.002
[2.70]
0.002
[0.98]
0.004
[1.59]
−0.001
[−0.15]
smb
0.001
[0.27]
−0.001
[−0.80]
−0.002
[−1.46]
0.001
[0.10]
0.000
[0.10]
−0.017
[−1.23]
0.001
[0.49]
0.001
[0.85]
0.000
[−0.60]
−0.007
[−2.52]
−0.010
[−1.53]
−0.003
[−0.39]
hml
−0.001
[−0.88]
−0.002
[−3.85]
−0.002
[−3.68]
0.002
[0.27]
−0.011
[−5.28]
−0.014
[−1.38]
−0.001
[−1.29]
−0.001
[−4.24]
−0.003
[−7.46]
−0.010
[−5.45]
−0.011
[−4.88]
−0.016
[−4.12]
Mktrf
0.000
[0.25]
0.000
[1.25]
0.000
[1.20]
0.005
[3.26]
0.007
[3.97]
−0.005
[−0.92]
0.000
[1.06]
0.001
[4.80]
0.002
[8.55]
0.006
[8.90]
0.009
[8.77]
0.011
[4.00]
VIXt−1
0.023
[1.15]
−0.025
[−1.51]
−0.083
[−3.14]
−0.184
[−2.82]
−0.311
[−3.85]
−0.185
[−4.30]
−0.041
[−0.84]
−0.003
[−0.20]
−0.051
[−2.87]
−0.099
[−3.50]
−0.169
[−6.30]
−0.207
[−4.14]
Ret
0.001
[2.05]
0.000
[0.58]
0.002
[2.43]
−0.002
[−1.55]
0.004
[2.35]
0.012
[3.72]
−0.002
[−0.59]
0.004
[3.52]
0.004
[2.81]
0.003
[4.78]
0.006
[3.33]
0.004
[1.88]
Intercept
0.040
0.387
0.360
0.084
0.120
0.180
0.3351
0.439
0.409
0.130
0.097
0.153
Adj. R2
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
377
378
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
Table 7
Principal components
This table reports the Eigenvalues, the proportion of the variance explained and cumulative variance
explained by the first five principal components of the covariance matrix of the residuals from the
following regression model:
CSit = αi + β1 CSit−1 + β2 CSit−2 + β3 Tnotet + β4 Slopet
+ β5 smbt + β6 hmlt + β7 Mktrf t + β8 VIX t−1 + β9 rett + εit
To form 18 portfolios, we average the residuals of time series individual bond regressions based on three
maturity and six rating groups. Similarly, we split the residuals in 42 bins, but instead of three, we use
seven maturity groups. The 21 high-grade bond portfolios are determined by seven maturity groups and
the Aa, A and Baa rating groups, while the 21 low-grade portfolios are based on seven maturity groups
and the Ba, B and Caa rating groups.
Regression residuals
portfolios
Proportion
of the
variance
Cumulative
variance
1052.42
87.91
50.37
19.90
0.73
0.11
0.06
0.03
0.02
0.73
0.85
0.91
0.94
0.96
858.94
551.98
151.71
113.18
78.92
306.96
400.27
38.53
34.26
0.43
0.28
0.08
0.06
0.04
0.43
0.71
0.79
0.84
0.88
First
Second
Third
Fourth
Fifth
29.44
9.60
6.78
4.21
3.50
19.83
2.83
2.56
0.71
0.43
0.14
0.10
0.06
0.05
0.43
0.57
0.67
0.73
0.78
First
Second
Third
Fourth
Fifth
836.69
535.54
146.75
110.60
77.48
301.15
388.79
36.15
33.12
0.44
0.28
0.08
0.06
0.04
0.44
0.73
0.81
0.86
0.91
Principal
component
Eigenvalue
Difference
First
Second
Third
Fourth
Fifth
1244.56
192.13
104.22
53.86
33.95
First
Second
Third
Fourth
Fifth
18 portfolios
42 portfolios
21 portfolios (high-grade bonds)
21 portfolios (low-grade bonds)
The regression results in the previous section show that our models better explain
the variation in credit spread changes of low-grade bonds, particularly during the
second subperiod of our sample. To examine whether we can find differences in
the remaining systematic variation, we perform principal components analysis on
the residuals of high- and low-grade bonds separately. The first 21 portfolios are
formed by the intersection of seven maturity groups and three rating groups (Aa, A
and Baa), while the second 21 portfolios are determined by seven maturity groups
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
379
Table 8
Data robustness
This table presents results for the following regression model:
CSit = αi + β1 CSit−1 + β2 CSit−2 + β3 Tnotet + β4 slopet + β5 VIX t−1 + β6 rett + ε
CSit is the credit spread of bond i on day t; Tnotet is the change in the 10-year Treasury rate; Slopet
is the change in the term structure slope measured as the difference between 10- and two-year Treasury
rates in first difference; VIX t−1 is the one-day lagged changes in the VIX; and rett is the company stock
price return. The table provides results for bonds with 10 years to maturity for the period from May 2002
to Oct. 2008. The data source is TRACE.
CSt−1
CSt –2
Tnote
Slope
VIXt−1
Ret
Intercept
Adj. R2
Aa
A
Baa
Ba
B
Caa
−0.619
[−26.22]
−0.317
[−15.79]
−0.250
[−5.068]
−0.168
[−1.54]
0.001
[0.32]
−0.085
[−1.02]
0.006
[1.79]
−0.620
[−44.98]
−0.292
[−26.55]
−0.431
[−3.33]
−0.382
[−1.13]
0.005
[1.21]
−0.132
[−0.99]
0.001
[0.40]
−0.578
[−29.24]
−0.263
[−17.09]
−0.178
[−2.95]
0.064
[0.72]
0.009
[2.89]
−0.208
[−1.94]
0.011
[4.81]
−0.454
[−10.20]
−0.226
[−7.71]
−0.798
[−7.73]
0.297
[1.46]
0.013
[4.33]
−0.427
[−2.11]
0.018
[2.77]
−0.328
[−6.59]
−0.026
[−0.94]
−0.977
[−8.91]
0.223
[1.07]
0.018
[3.21]
−0.564
[−2.36]
0.009
[2.70]
−0.474
[−12.11]
−0.180
[−5.41]
−0.720
[−3.80]
0.554
[2.18]
0.013
[1.464]
−0.074
[−1.01]
−0.006
[−0.68]
0.316
0.299
0.259
0.230
0.307
0.256
and the lower grade bonds in our sample (Ba, B and Caa). The proportion and
cumulative variance explained by the first five principal components are summarized
in Table 7 as well. The results reported in Table 7 show that there is still a significant
systematic component captured by the first principal component, explaining 43%
and 44% of the variance for high- and low-grade bonds, respectively. The second
principal component, however, captures 28% of the variance in the low-grade bond
portfolios and only 14% for the high-grade bonds. There is a substantial difference
in the cumulative variance explained between the low and high credit risk portfolios,
as well (78% and 91%, respectively), suggesting differences in the set of factors
affecting the two groups.
Overall, the results of the principal components analysis confirm the presence
of a significant systematic factor, which is not explained by the regression models.
Although the regression models better explain the daily credit spread changes in
riskier bonds, they still do not fully capture the common systematic component.
6. Data quality
Several recent studies have examined the limitations of Datastream bond data.
Dick-Nielsen, Feldhutter, and Lando (2009) investigate the liquidity components of
380
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
corporate bond yield spreads using a sample of bonds from TRACE and compare
their results to Chen, Lesmond, and Wei (2007) who use Datastream as a source.11
Dick-Nielsen, Feldhutter, and Lando (2009) argue that Datastream’s bond data can
differ from actual trades and that the zero trading days may not always be identified
correctly.
Since our empirical findings are based on bond data from Datastream, we collect
data for a small sample of bonds from TRACE (Trade Reporting and Compliance
Engine introduced by NASD in July 2002) in order to compare the results from this
independent sample to our results using Datastream. We select all bonds with 10
years to maturity from our sample and run a query in TRACE to obtain the last yield
for the day from May 2002 to Oct. 2008. After we match the collected data back
to our sample and restrict it to bonds with at least 100 daily observations, we get
a sample of 166 bonds. The credit spreads are calculated by subtracting the yield
of the 10-year Treasury from the corresponding bond yield. Using this alternative
data, we re-estimate the basic model of credit spread changes previously reported in
Table 3. The results reported in Table 8 confirm our findings that changes in market
volatility affect credit spreads at the daily level and this effect is more pronounced
for lower rated bonds. The idiosyncratic return has the theoretically expected sign,
that is, negative returns are associated with an increase in spreads. While the T-note
changes are highly statistically significant, the changes in the slope are significant
only for the lowest rated bonds.
7. Conclusions and implications
We investigate the determinants of daily credit spread changes of 2,524 corporate
bonds from May 2002 through Oct. 2008. We split the data into two subperiods
(before and after Sept. 1, 2007) to separately explore the determinants of corporate
bond spreads during the recent financial crisis. The paper documents a significant
link between equity volatility and day-to-day changes in credit spreads, which has
important implications for bond portfolio allocation and credit risk management. Our
findings can be summarized as follows.
First, we examine the importance of variables related to systematic risk and
idiosyncratic risk for explaining daily variations in corporate yield spreads. We show
that even at the daily level, the proxies used for market risk are statistically significant,
particularly for bonds with lower credit ratings. Our findings show that spreads widen
with the increase in the lagged VIX index and that this relation is stronger the shorter
the time to maturity. Aggregate volatility factors seem to explain spreads better than
idiosyncratic returns. Second, the Fama-French factors have significant explanatory
power in our models, especially during the financial crisis period. Since the SMB
11 Recently Michayluk and Zhao (2010) used daily corporate bond price and yield data from Datastream,
Bloomberg, and Bridge to investigate bond yield changes around stock splits.
A. M. Hibbert et al./The Financial Review 46 (2011) 357–383
381
is commonly interpreted as a factor related to liquidity, we expect that our models
can benefit from the inclusion of liquidity proxies as well. Third, we examine the
relation between spread changes and the returns on small stocks. Our results show
R
a significant inverse relation between the returns on the Russell 2000
index and
daily spread changes. The significance of the Russell returns in explaining spreads
changes is more pronounced during the second subperiods.
Finally, we use principal components to analyze the unexplained variation of
our regression models. We find a large systematic component remains that is not
accounted for by the variables used in our models. This result is consistent with
Collin-Dufresne, Goldstein, and Martin (2001), who suggest that an aggregate factor
related to liquidity in bond markets could be affecting their structural model estimates
using monthly data. Including a proxy for daily liquidity changes could potentially
improve the explanatory power of our models.
Our findings have implications for Value-at-Risk (VaR) estimation. In recent
years, increasing algorithmic trading and high-frequency trading have been major
movers in the market. Such trading strategies implicitly assume that there are limited overnight positions and high velocity of trading. Therefore, the compatible and
relevant risk metric for the construction of a daily VaR should be based on daily
bond trades. Campbell, Huisman, and Koedijk (2001) examine the portfolio selection
model that meets the VaR limits set by the risk manager and find that the length of
the investment time horizon (daily as compared to biweekly or monthly) affects the
optimal portfolio selection. Since the bond yield is one of the key inputs in measuring
fixed income portfolio’s VaR, the factors which influence yields and yield spreads are
of great interest to portfolio managers tracking the risk measures related to regulatory
capital requirements. Furthermore, Crouhy, Galai, and Mark (2000) emphasize that
spread risk is interconnected with both market and credit risk, and therefore credit
risk models need to account for this relation.
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