CDS Spreads Explained with Credit Spread Volatility
and Jump Risk of Individual Firms∗
Arben Kita†
Abstract
This paper attempts to explain the credit default swap (CDS) premium by using a novel
approach to identify the volatility and jump risks of individual firms from a unique dataset of
high-frequency CDS spreads. I find that the volatility risk alone explains 55% of the variation
in CDS spread levels, whilst the jump risk alone explains 45%. After controlling for credit
ratings, macroeconomic conditions and firms’ balance sheet information the model explains
93% of total variation. In the cross-section I find that volatility risk can explain 63% of the
variation in the credit spreads whilst jump risk explains 55%. For the CDX index I find that the
volatility risk alone explains 22% of the variation in the CDX index levels, while the jump risk
alone explains 25%. The results reported in this paper suggest that the time-varying volatility
risk premium and jump risk premium of the credit spreads may play a more important role
than previously attributed to them.
Keywords: Credit Default Swap Spread; Credit Spread Volatility; Credit Spread Jump.
JEL Classification: G12; G13; C14
∗
I thank John Goddard and Qingwei Wang from the Bangor Business School for their very helpful suggestions
and Gordon Gemmill from the Warwick Business School for his valuable comments. Errors and omissions remain the
responsibility of the author.
†
Bangor Business School, Hen Goleg, College Road, Bangor LL57 2DG, United Kingdom. E-mail: arben.kita@bangor.ac.uk
1 Introduction
Previous empirical tests of structural models of credit risk have encountered difficulties in explaining observed default rates. An implicit assumption of these models is that the credit spread is
exclusively driven by the credit risk. The omission of other critical explanatory factors from these
models has resulted in the so-called ’credit spread puzzle’ (Jones, Mason, and Rosenfeld (1984),
Elton, Gruber, Agrawal, and Mann (2001), Collin-Dufresne, Goldstein, and Martin (2001) , Huang
and Huang (2003)).
This paper attempts to explain the variation in credit spreads using a novel empirical approach
based on nonparametric estimation of volatility and jump risk measures directly from credit default
swap (CDS) returns. These measures seek to capture the stochastic volatility and jump effects in
the underlying asset value process, and identify structural variables that may explain the variation
in credit spread, particularly in the cross-section (Huang and Huang (2003), Huang and Zhou
(2008)). The CDS contract is a derivative in which the underlying instrument is a corporate bond.
Finance theory predicts a direct relationship between the CDS and the underlying instrument. The
CDS spread reflects the premium attached to credit risk, which in a frictionless world, would
be exactly equivalent to the credit risk in the underlying corporate bond. However, empirical
studies have shown that credit spreads are subject to random shocks. Random shocks to credit
spreads in non-default states are important, because credit spreads are highly correlated across
different exposures, and therefore non diversifiable in large portfolios. Consequently, accurate
estimation of the underlying asset value dynamics is crucial in modeling credit risk. A relatively
large proportion of the volatility of credit spreads can be attributed to temporary shocks, that are
subsequently reversed by off-setting spread changes. The approach adopted in this study, may be
characterised as filtering out high-frequency components of spread volatility and jumps from the
permanent shocks to spreads, and obtaining volatility risk and pure jump tail risk measures.
The use of firm-level estimates of the upward trend in idiosyncratic equity volatility to explain
credit spreads was proposed originally by Campbell and Taksler (2003). The magnitudes of their
estimated coefficients were however found to be inconsistent with Merton (1974) structural model
of constant volatility. The idea that firm-level credit spreads account for the exposure to market
1
jump risk is eaxmined by Geske and Delianedis (2001) and Zhou (2001). They obtain inconclusive
empirical evidence that jumps explain the level of credit spreads for investment grade bonds at short
maturities. Collin-Dufresne et al. (2001) and Collin-Dufresne, Goldstein, and Helwege (2003) find
market-based jump risk measures have low explanatory power. Cremers, Driessen, and Maenhout
(2008) explain the level of the credit spreads using option-implied jump risk measures. Zhang,
Zhou, and Zhu (2009) use high-frequency equity prices to measure the volatility and jump risk of
individual firms.
The aforementioned studies relying on equity or option-implied volatility to estimate firm-level
volatility and jump risks provide only an approximation to the true dynamics of the underlying
credit spreads. Benefiting from a unique dataset of high-frequency CDS spreads, together with
recent methodological advances in volatility modelling, this paper’s main contribution lies in the
identification of the relationship between stochastic volatility and jumps in the underlying asset
value process, and the level of credit spreads.1 I provide original empirical evidence that the
volatility and jump measures based on high-frequency CDS returns offer substantially greater explanatory power for the time-series and cross-sectional variation in credit spreads. The reported
estimations yield the highest explanatory power, measured in terms of R-square, for the variation
in CDS spreads that has been reported in the literature to date. To the best of my knowledge,
this paper presents the first analysis of the dynamics of CDS spread using high-frequency credit
spreads data.
The methodology used in this paper is based on recent studies which measure volatility and jumps
from high-frequency data. Barndorff-Nielsen and Shephard (2004) show that by taking the difference of the realised variation and the bipower variation of the realised variance it is possible
to separate its continuous and jump components. High-frequency measures of the time variation
in the CDS return, realised volatility and realised jumps, provide more accurate measures of the
short-term volatility and jump risks than low-frequency measures, or measures based on option
prices or high frequency equity prices (Campbell and Taksler (2003), Zhang et al. (2009)).
1
The recent literature on stochastic volatility modeling (Andersen, Bollerslev, Diebold, and Ebens (2001);
Barndorff-Nielsen and Shephard (2002); Meddahi (2002)) suggests that the realised variance measures from highfrequency data provide a more accurate measure of the true variance of the underlying continuous-time process than
those from low-frequency data.
2
CDS spreads are used in this paper as a direct measure of the credit spread. CDS spreads are traded
typically on standardized terms, and provide relatively clean market pricing of the default risk of
the underlying asset. As shown by Blanco, Brennan, and Marsh (2005) and Zhu (2006) the CDS
market leads the bond market in price discovery, it is more liquid that the bond market, and it tends
to respond more rapidly to changes in credit conditions in the short-run. The more timely reaction
of CDS spreads to changes in credit conditions is most likely due to the absence of funding and
short-sale restrictions in derivative markets. Other advantages of the CDS in measuring credit risk
include: i) CDS spreads approximate to a pure credit risk and contain only a very small interest rate
risk component; ii) CDS spreads correspond to a realisable stream of cash flows (as compensation
to investors for the loss of the notional value minus the recovery rate); iii) CDS can be traded
to a number of fixed terms; iv) the CDS market is relatively liquid; consequently CDS spreads
accurately reflect the market price of credit risk.
For the investors in single-named and structured credit portfolios (credit indices) an understanding
of the nature of the risks to which they are exposed and accurate measurement of the extent to
which they are compensated for the risks, is of primary concern. Understanding of the price
dynamics of single-named and structured credit portfolios should be of interest to dealers in these
securities, enabling them to quantify and hedge their inventory risk. The decomposition of credit
spreads presented in this paper enables investors to understand and isolate the exposure to certain
types of risk, (e.g. pure jump-to-default risk), which in the past has commanded a large premium,
leading to the ’credit spread puzzle’.
Empirically, I find that the short-run realised volatility and jump measures have statistically significant and economically meaningful effects on credit spreads. Realised volatility explains 55% of
the variation in credit spreads and realised jump measures explain 45% of the variation in spreads,
which is almost 2.5 times larger than when high-frequency equity prices are employed, as previously reported in Zhang et al. (2009). Historical skewness and kurtosis measures from CDS return
data explain only 3% of the variation in credit spread, in line with previous literature. Taken together the realised volatility and realised jumps measures explain 67% of the variation in credit
spreads. After controlling for the credit rating, macroeconomic variables, balance sheet data and
fixed income markets illiquidity and default risk, I obtain an adjusted R-square of 93%. In the
3
cross-section I find that the realised volatility measure can explain 63% of the variation in spreads,
whilst the jump risk measure explains 55%. Taken together, the realised volatility and realised
jump measures explain 94% of the variation in credit spreads. The volatility and jump risk measures for the CDX index explain 22% and 25% respectively, of the variation in the CDX index
spread. These results are consistent with the Cremers et al. (2008) approach to spreads. They
also lay support to the models of price pressure in the OTC credit markets driving prices away
from fundamentals even in the absence of variation in the firms’ fundamentals, which may trigger
additional volatility in the credit market.2
As a robustness check, I investigate the ability of the volatility and jump risk measures to explain
the variation in the CDS returns. The volatility and jump measures estimated from the highfrequency spreads data, together with macrofinanical and firm specific variables suggested in the
literature are able to explain around 31% of the variation in the CDS returns. Further, I divide
the companies into four rating categories based on S&P ratings reported by Bloomberg (AA, A,
BBB and BB) and perform all the aforementioned analysis for each rating category separately. I
find that the combined explanatory power of the realised volatility and realised jump risk measures
vary between 80% for AA rated companies and 58% for the BB rated companies. The results
are available in the Additional Results Appendix. Panel estimations of the same specification (the
results are available upon request) constitute an additional robustness check; the results remain
materially unchanged. Overall, the results reported in this paper suggest that the time-varying
volatility risk premium and jump risk premium of credit spreads may play an important role in
determining the level of the credit spreads. These risks are heavily dependent on the perceived
tail risk, therefore their understanding and correct measurement becomes crucial in the credit risk
management and asset pricing.
The remainder of the paper is organized as follows. Section 2 introduces the methodology. Section
3 describes and summarizes the data set. Section 4 presents the empirical results. Finally, section
5 concludes.
2
See Duffie (2010) for the theoretical modeling and Feldhütter (2012) for empirical evidence in the bond market.
4
2 Empirical Method
In this section I describe the method used to estimate the CDS excess returns using intraday CDS
spread data, and the calculation of realised volatility and realised jump measures using the CDS
return series.
2.1 CDS Excess Return
A corporate bond can be regarded as a combination of a risk-free bond and a risky asset which
pays out an annual coupon and demands a full notional payment if the credit event occurs. This
risky asset exactly reflects the CDS contract; its payoff can be synthesized by going long on a
corporate bond and shorting the riskless bond. In order to measure the volatility and jump risks
the market observable credit spreads need to be translated into returns. Consider an investor who
sells protection using the CDS contract, j, at time (i − 1)∆, within trading day t at a CDS spread of
CDS j,t,(i−1)∆ paid quarterly. Subsequently, at time (i∆), within trading day t, the investor buys an
offsetting contract at CDS j,t,i∆ spread. The net cash flow generated until the maturity or the default
is therefore 41 (CDS j,t,i∆ − CDS j,t,(i−1)∆ ).3 It follows that the value of this stream on day t, is:
X γ
1
SV γ
= CDS j,t,i∆ − CDS j,t,(i−1)∆
Q
Bt
4
4 t 4
γ=1
4T
R j,t,i
(1)
where Bt ( γ4 ) is the price of the risk-free zero-coupon bond maturing at γ years after day t, QSt V ( γ4 )
is the risk-neutral survival probability from day t until γ years after day t, and T is the maturity of
the CDS contract. The excess return on the CDS is the cash-flow of the contract, discounted by
the risk-free rate and multiplied by the risk-neutral survival probabilities. I ignore the ’accrued’
spreads, as this component is negligible for the intraday data.4
The market microstructure noise, such as price discreteness and bid-ask spread positioning resulting from the dealers’ inventory control, can induce negative autocorrelation in the recorded series.
3
This specification follows Bongaerts, De Jong, and Driessen (2011). Longstaff (2011) discount each cash flow by
the risk-free rate plus the CDS spread only.
4
Appendix A gives more details on the risk-free rate data and the estimation of the risk-neutral default probabilities.
5
To mitigate the impact of these institutional frictions, I apply an MA(1) filter to the returns series.
The next subsection describes the measurement of the realised quadratic variation of returns and its
continuous and discontinuous components, using the filtered high-frequency CDS returns series.
2.2 Realised Volatility and Jumps
The importance of jumps for asset pricing has been recognised since Merton (1976), although
their estimation is not trivial when low frequency data are employed.5 Andersen et al. (2001) and
Barndorff-Nielsen and Shephard (2001) propose a realised variance measure based on intraday
data for measuring and forecasting volatility. Using bipower variation measures, it is possible to
separate realised volatility into continuous and jump components (Barndorff-Nielsen and Shephard
(2004), Barndorff-Nielsen (2006), Andersen, Bollerslev, and Diebold (2007), Huang and Tauchen
(2005)). In this paper I rely on the economic intuition that jumps on financial markets are rare
and of large size, in order to identify realised jumps and to estimate the jump intensity, mean and
volatility parameters.
Let st denote the continuous-time equivalent of the CDS spread recorded as CDS j,t,i∆ at discretetime intervals. st is assumed to evolve in continuous-time as a jump diffusion process,
dst = µts dt + σts dWt + Jts dqt ,
(2)
where µts , σts , and Jts are the drift, diffusion and jump functions respectively. Wt is a standard
Brownian motion, dqt is a Poisson jump process with intensity λ s , and Jts refers to the size of the
corresponding credit spread jump, which is assumed to have a mean µ J and standard deviation σ J .
Barndorff-Nielsen and Shephard (2004) propose two general measures of the quadratic variation
process: realised variance, RVt and realised bipower variation, BVt . RVt and BVt converge uniformly as ∆ → 0 or m = 1/∆ → ∞ to different components of the underlying jump diffusion
process:
5
See Andersen, Benzoni, and Lund (2002) and Ait-Sahalia (2004) among others.
6
RVt ≡
m
X
Z
(R2j,t,i )
t
→
t−1
i=1
σ2s ds
+
m
X
(J sj,t,i )2 ,
(3)
i=1
where the right-hand side is the quadratic variation of the price over the time interval [t, t − 1]. The
R2j,t,i is the squared CDS return estimated in Equation (1). For increasingly fine-sampled increments
(m = 1/∆ → ∞), realised volatility consistently estimates the total ex-post variation of the price
process. By decomposing the summation of the squared increments (of the quadratic variation)
into separate summations of small and large price changes, it is possible to estimate the variation
in the continuous sample price path:
πX
BVt ≡
|R j,t,i∆ | · |R j,t,(i−1)∆ | →
2 i=2
m
Z
t
t−1
σ2s ds.
(4)
The difference between the realised variance and the bipower variation is zero when there is no
jump and strictly positive when there is a jump. The realised jump measure, RJt , is:
RJt ≡
RVt − BVt
.
RVt
(5)
Huang and Tauchen (2005) and Andersen et al. (2007) study alternative jump detection techniques,
and form the ratio test statistic adopted here (Equation (5)). A z-statistic obtained by scaling RJt
by asymptotic standard deviation (see Appendix B for it’s definition) converges to the standard
normal distribution.6 This test identifies whether a jump has occurred on a particular day, and the
contribution of the jump to the total realised variance.
To identify the jumps I adopt Tauchen and Zhou (2010) extension of Andersen et al. (2007) "significant jump" approach, based on the signed square-root of the significant jump:
Jts = sign(R sj,t,i ) ×
p
RVt − BVt × I(z > Φ−1
α ),
(6)
where Φ is the cumulative distribution function of a standard normal, α is the significance level of
6
Appendix B illustrates the implementation details.
7
the z-test and I(z > Φ−1
α ) is the resulting indicator function on whether there is a jump during day t.
The accuracy of the Equation (6) rests upon an assumption that there is only one jump per day, at
best an approximation. The filtered realised jumps enable the estimation of the jump distribution
parameters:
ji =
Number of Realised Jump Days
Number of Total Trading Days
(7)
jm = Mean of Realised Jumps
(8)
jv = Standard Deviation of Realised Jumps
(9)
where, ji, is the jump intensity, jm, is the jump mean and, jv, is the jump volatility.
Tauchen and Zhou (2010) show that under realistic assumptions this method for identifying realised jumps and estimating jump parameters yields reliable results in finite samples as the sample
size increases and the sampling interval shrinks. They also find that a jump volatility measure for
an equity market index has significant explanatory power for credit spread indices.
Section 4 presents evidence that firm-level realised volatility and jump risk measures, estimated
from high-frequency credit spreads data, explain a large portion of the variation in credit spread.
3 Data and Summary Statistics
3.1 Credit Default Swap Spreads
The unique dataset consists of intraday closing values for the 5-year CDX NA IG index (CDX
index for short) and its constituents obtained in Bloomberg. The time period covered is from
22nd September 2010 up to 24th February 2012. However, for the single-name CDS contracts the
average number of intraday prices between 22nd September 2010 and 9th March 2011 is four. I
8
decided to exclude the single-name CDS prices for that time period only. From 9 March 2011, the
average number of intraday observations of single-name CDS spreads varies between a minimum
of nine and maximum of forty-two.
The CDX index itself trades as a single-name contract, with a defined premium based on an
equally-weighted basket of 125 constituents. The CDX index is numbered sequentially. The series
CDX NA IG 1 was the first series of the first basket of 125 firms and was created in 2003. The
data set analyzed in this paper includes series 15, CDX NA IG 15 which starts in September 2010.
The next series, 16, spans the period March 2011 to September 2011 and the last series, 17, covers
the period September 2011 to February 2012. The recorded intraday index price observations are
abundant.
CDS is the most popular asset in the credit derivative market. CDS are traded by commercial
banks, insurance companies, hedge funds, and pension funds. As reported by the International
Swaps and Dealers Association (ISDA), the size of the CDS market had grown to more than $62.2
trillion in notional amount outstanding by the end of the 2007. The equivalent figure for mid2010 had fallen to $26.3 trillion as a result of dealers’ "portfolio compression" efforts (replacing
offsetting redundant contracts), and reached $25.5 trillion in early 2012.7 Under a CDS contract,
the protection seller promises to buy the referenced bond at its par value when a predefined credit
event occurs. Credit events are triggered by bankruptcy, failure to pay, or a debt-restructuring
event. In return, the protection buyer makes periodic payments to the seller until the maturity
date of the contract or until the credit event occurs. These payments are expressed in basis points,
and are known as the CDS spread. The CDS provides a pure measure of the default risk of the
reference entity. I focus on five-year CDS contracts with modified restructuring (MR) clauses, the
most widely in the U.S. market.
As reported in Mayordomo, Peña, and Schwartz (2010), quoted CDS spreads differ considerably
between data providers. I use only the CMN quotes for the entire sample period, for both singlename CDS spreads and the CDX index. Using continuous quotes for the whole sample from the
same data provider mitigates errors in the estimations. The individual firms included in the CDX
basket are updated and revised ("rolled") every 6 months, in March and September, when illiquid
7
See ISDA’s market survey of 2008 at http://www2.isda.org/ and http://www.isdacdsmarketplace.com/market_statistics.
9
names are dropped and replaced. I consider only those single-name CDS contracts that survived
the rolling, yielding a sample of 116 names. The 116 entities are divided into four rating categories
based on S&P rating, as reported in Bloomberg, AA, A, BBB and BB . The credit spreads within
these rating groups vary considerably, indicating that CDS spreads react more promptly to changes
in the soundness of the underlying entities than the ratings. No attempt is made to exclude outliers
from the empirical analysis.
Andersen and Bollerslev (1998) show that the squared returns measure of the realised volatility
produces inaccurate forecasts if daily returns are used. The forecasts improve considerably when
high-frequency data are employed (Barndorff-Nielsen and Shephard (2003)). These results however are based on foreign exchange intraday data known to exhibit little or no autocorrelation.
Ait-Sahalia and Mykland (2005) show that more data does not necessarily lead to better estimates
of the realised volatility owing to the presence of market microstructure noise. To mitigate market microstructure noise I use a 30-minute sampling interval to calculate realised volatility, and
considered only business hour observations.
3.2 Theoretical Determinants of Credit Spread Changes
The literature on structural models of default suggests several determinants of credit spreads.
• The Spot Rate (shtbil). An increase in the spot rate increases the risk neutral drift of the
firm value process, implying a reduced probability of default and lower credit spreads (see
Longstaff and Schwartz (1995)).
• The Slope of the Yield Curve (termspread). An increase in the slope of the term structure
of interest rates is an indicator of an expected improvement in the level of future economic
activity, and should result in a reduction in credit spreads. Alternatively, it might indicate an
increase in expected inflation, which might be followed by a tighter monetary policy.
• Firm Leverage (lev). A leverage ratio approaching unity implies default. Consequently,
credit spreads increase with leverage.
10
• Market Volatility (vix). In a contingent-claim analysis, the debt claim is similar to a short
position in a put option. Since option values increase with volatility, credit spreads should
also increase with market volatility. Intuitively, an increase in volatility increases the default
probability.
• Market Return (spreturn). A higher market return is an indicator of an improved business
climate, implying a reduction in the probability of default or an increase in the recovery
rates. Even if the default probability of the firm is assumed to be constant, a reduction in the
credit spread may follow from an increase in the expected recovery rate.
• Dividend Payout Ratio (div). A higher dividend payout ratio means a decrease in asset value,
and a higher default probability.
• Return on Equity (roe). Credit spreads should be a decreasing function of firm’s return on
equity, cetiris paribus. The default probability is reduced with the increased profitability.
• Credit Spread Skewness (skewcds). Higher skewness implies more positive returns than
negative.
• Credit Spread Kurtosis (kurtcds). Higher kurtosis implies more extreme movements in the
credit spread returns.
• Credit Spread Volatility (hvcds, rv) Higher volatility in credit spreads implies higher asset
volatility, and an increase in the likelihood that the firm’s value hits the default boundary.
• Credit Spread Jumps (ji, jm, jv, jp, jn). Credit spreads increase with increase in jump intensity
and jump variance, both of which indicate more extreme movements in asset returns. (Zhou
(2001)).
• Default Premium Slope (dps). Consistent with the notion that the CDS and corporate bond
markets are closely related, a positive relationship is expected (see Blanco et al. (2005)).
Intuitively, a steeper default premium slope indicates higher probability of default and increased credit spreads.
11
• Changes in the Fixed Income Market Illiquidity (sts). The fixed market illiquidity proxy is
expected to move positively with the CDS spreads. Illiquidity is an indicator of a decline in
expected market activity, and thus increases the default probability.
Daily realised volatility is calculated using the methodology described in Section 2. The realised
volatility is the average of the daily realised volatility within each week. Historical CDS return
volatility (hvcds), skewness (skewcds) and kurtosis (kurtcds) are estimated from weekly CDS returns over the one-year period, prior to the current week. The most recently- available quarterly
balance sheet data on the reference entities are used to calculate: the leverage ratio (lev) the return
on equity (roe) and the dividend payout ratio (div). The S&P index average weekly return over the
past six months, and the VIX index (implied volatility of near-the-money equity index options),
are obtained from Bloomberg.
Weekly series for swap rates and T-bond yields are obtained from the Federal Reserve website. The
latter are used to calculate the slope of the yield curve (termspread), the illiquidity risk (sts) and
the default risk premium (dps) in the corporate bond market (the Moody’s default premium slope).
Appendix C provides details on the data sources and methods of calculation. For the analysis of
the CDX index, all variables are defined in the same way as the single-name CDS contracts.
3.3 Summary Statistics
Table I Panel A reports summary statistics for the weekly CDS returns divided into four rating
groups, and for the whole sample. The sample means suggest the five-year annualised CDS returns
exhibit substantial cross-sectional and time variation. The average annualised CDS return for A to
AA rated entities is 0.214 basis points. For the BBB and BB rated entities the excess returns are
1.316 and 5.485 basis points, respectively. The Anderson and Darling (1952), AD, test statistic is
used to test the deviation of the CDS returns from normality. The higher the AD, the further away
the distribution is from normality. According to the AD test, CDS returns are normally distributed
for the AA and BB rating groups.
I also estimate the historical skewness and historical kurtosis of the weekly CDS returns over a
12
one year horizon. Skewness of multiple periods of returns implies strong extreme correlation or
"tail dependence". Risks associated with skewness would require a very large portfolio in order
to achieve the desired diversification. Skewness is an indicator of asymmetry in asset returns, but
its usefulness as indicator of the presence of jumps is limited when the likelihood of positive and
negative jumps is the same. By contrast, kurtosis provides a direct measure of the existence of
jumps in a continuous-time framework, (Drost, Nijman, and Werker (1998)). However, kurtosis
fails to reflect direction of the jumps, a crucial factor in detecting the pricing effects on credit
spreads. Accordingly, the jump mean, jump intensity and jump volatility measures defined in
Equations (7)-(9) are included in the analysis.
Table I Panel B reports summary statistics for the CDX index. The average excess return of the
index is negative for the period September 2010 to February 2012. The returns of the index for the
whole sample and for the series 16 are all normally distributed.
Panel C of Table I reports the summary statistics of macroeconomic and financial covariates. In
addition to the market returns (spreturn), option-implied market volatility (vix), the level (shtbil)
and the slope of the yield curve (termspread) I further control for the fixed income market illiquidity risk (sts). I also use the Moody’s default premium slope (dps) to control for the default risk
premium in the corporate bond market. Both these variables have been identified as important
sources of risk. I find both measures important in determining the level of the credit spreads.
[Insert Table I about here]
3.4 Volatility Parameter Estimates
Figure 1 plots the square root of the realised variance, the weekly realised volatility series. The
realised volatility exhibits pronounced long memory properties. The resulting realised variation
measures all exhibit the well documented volatility clustering effects, with sharp increases around
the middle of the period, and during the first quarter of 2012. The stochastic volatility process is
13
highly persistent. The positive "realised" volatility (and jumps in Figure 2) significantly influence
the credit spread changes. These results are discussed further in the next section.
Panel A of Table II shows that the average weekly realised volatility is 1.75% for the whole sample
period. The historical volatility of CDS returns and the realised volatility measures have a linear
correlation coefficient of 0.12. However, it appears that the realised volatility measure captures
the changes in asset value process in a more timely manner. The average correlation of realised
volatility and CDS returns is 0.113 higher than the correlation of the historical volatility to the
CDS returns of 0.045.
The correlation of the CDX index return with the short-term realised volatility is -0.0011 and the
correlation of the CDX index return with its historical volatility is -0.042.
The realised volatility of the CDX index reported in Panel C of Table II is 0.46% for the whole
sample period while the correlation of realised volatility with CDX returns is 0.1, lower than the
correlation of historical volatility with the CDX returns of 4%. Figure 1 plots the square root of the
realised variance, the weekly realised volatility series estimates for the average AA and A-rated
entities and the CDX index. These plots show indications of long-memory temporal dependence.
[Insert Figure 1 about here]
3.5 Jump Parameter Estimates
The detection of the jumps is essential for the estimation of the parameters ofjump-diffusion processes. Previously, the literature has relied on methods such as GMM (see Bollerslev and Zhou
(2002)) to estimate the volatility and jump parameters jointly with the conditional moments of
the total return and total realised variance. However, these methods based in "latent" jumps are
subject to limitations. In order to obtain joint moments in closed form, a simple jump distribution
process is assumed. In contrast, the approach adopted in this paper obtains "observable" jumps,
which can be filtered out prior to the estimation of the volatility parameters. Consequently the
14
jump distribution assumptions are more general, and the volatility estimates are more robust.8
As shown in Panel A of Table II the contribution of jumps to the total variance is about 0.52%.
Figure 2 plots the jumps of the A-AA rated companies which are between 0.7% and 4%. The
jumps for the CDS returns are infrequent, but they are highly significant and economically meaningful. Only 11% of the trading days of the sample have significant jumps. I find that 21% of all
trading days for the AA-rated entities have significant jumps. The corresponding figures are 20%
for A-rated entities, 11% for BBB and only 5% of BB-rated entities. The number of positive jumps
is considerably larger than the number of negative jumps. The direction of jumps is important for
risk-averse investors, since negative jumps in credit spreads indicates reduced credit risk. Identifying positive and negative jumps is important for the pricing of CDS. In the empirical analysis, I
include both positive and the negative jumps (jp and jn, respectively).
The contribution of jumps to the CDX index variation is 0.072%. Only 7.5% of all trading days
register significant jumps in the CDX index. The index exhibits positive jumps only during the
sample period.
[Insert Table II about here]
Panel B and D of Table II report the parametric distribution estimates based on the filtered realised
jumps. The jump mean for the whole sample is 8.7 with a standard deviation of 22.7. The jump
intensities vary across ratings, the lowest being the BB rated entities (0.052 and standard deviation
0.022) and the highest being the AA rated entities (0.232 and standard deviation 0.062). The
jump volatility measure has a mean of 9.75 and standard deviation of 45.13. Throughout the entire
sample period, the highest volatility is reported for the BB-rated entities (mean 126.39 and standard
deviation 240.21) and lowest for the A-rated entities (mean 3.7 and standard deviation 3.22).
The CDX index has a jump mean for the entire sample period of 8.2 and a standard deviation of
4.82. The jump intensity for the whole sample is 0.076 and varies across different series ranging
from 0.019 for series 17 to 0.047 for series 16. The jump intensity of 0.076 and the jump volatility
8
See Tauchen and Zhou (2010) for further discussion.
15
of 7.72, are again lower than for the single-name entities. As Figure 2 shows the number of jumps
for the CDX index is smaller than for the single named entities, owing to a diversification effect.
The intensity of the jumps on the other hand is higher compared to the single-named CDS spreads.
[Insert Figure 2 about here]
The time-varying jump intensity and jump volatility are important risk factors in asset pricing,
but until recently most empirical evidence has been drawn from option-implied or latent jump
specifications (Duffie, Pan, and Singleton (2000), Eraker, Johannes, and Polson (2003) among
others). The measures of the credit spread volatility risk and jump risk reported here appear to
capture more effectively the impact of stochastic volatility and jumps on the underlying asset value
process.
4
Empirical Results
The role of the individual-firm credit spread volatility and jumps in explaining the weekly CDS
spread is examined in this section. Within the contingent-claim analysis most of the explanatory
variables employed here are jointly determined with credit spreads. In order to avoid the simultaneity problem, which would artificially increase the explanatory power, only lagged explanatory
variables are employed. The full regression which pools together all valid observations is:
CDS t, j = c + bυ Volatilitiest−1, j + b j Jumpst−1, j + br Ratingst−1, j + b f Firmt−1, j + t, j
(10)
The explanatory variables are described in Section 3.2 and detailed in Appendix C. Firstly I examine the role of the credit spread volatility and jump measures. Other control variables such
as ratings, balance sheet data, macroeconomic variables as predicted by structural models and as
evidenced in the empirical literature are also considered. For robustness I divide the sample into
rating groups and use panel data techniques to conclude that they do not qualitatively alter the
16
results. I find realised volatility and jumps measures play an important role in explaining variation
in the credit spreads.
I use Petersen (2009) adjustment for potential bias in the OLS standard errors. Clustered standard
errors that allow for firm and time effects are used to mitigate the problem of firm effects in the
residual term.
4.1 Effects of Volatility and Jumps on Credit Spreads
Table III reports the findings of the OLS regressions that explain the credit spreads using measures
of the credit spread return volatility and jump risk, or a combination of both. Model (1) uses the
one-year historical credit spread return volatility only. The R2 of 28% is lower than reported in
several previous empirical studies.
[Insert Table III about here]
In Model (2), the short-run realised volatility explains 46% of the variation in the credit spreads.
The adjusted R2 is considerably higher than the 28% reported by Zhang et al. (2009) using realised
volatility measures based on high-frequency equity prices. In Model (3) the combination of the
short and long-run volatility measures produces an adjusted R2 of 55%. The magnitudes of the
coefficients are reasonable. One unit of volatility shock raises the credit spread by 4 to 39 basis
points. The higher R2 reported in this study may reflect the smaller magnitude of the non-default
risk component for CDS, in comparison with bonds (Campbell and Taksler (2003)). The approach
used here is distinct, as it includes both long and short-run volatility measures computed directly
from credit spread returns, rather than equity returns or options as in previous empirical studies.
By using long-run equity volatility measures only, the literature implicitly assumes that the equity
return is constant. This assumption is not justified theoretically (in Merton’s (1974) framework,
asset value is constant, but the volatility of the asset value is time-varying and nonlinear) and
empirically, short-run volatility deviates from long-run volatility in response to changes in market
conditions. The use of both short and long-run volatility measures reflects more adequately the
17
time variation of the credit spread volatility, and captures risks over different time horizons that are
relevant in determining the credit spreads.
Using the historical skewness and kurtosis of the credit spread returns as measures of the presence
and size of jumps produces a very small adjusted R2 of 3% in Model (4). By contrast, the jump
intensity, mean and variance measures yield an adjusted R2 of 45% in Model (7). A unit shock in
the jump mean (jm) increases the CDS spreads by 11.2 basis points according to Model (5). The
jump volatility (jv) reduces the CDS spreads by 6.4 basis points for each unit of shock. When the
jump mean is divided in positive (jp) and negative jumps (jn) the positive jumps increase the spread
by 1.6 basis points whilst the negative jump is statistically insignificant and increases spreads by
15 basis points.
Model (8), in which the covariates include all of the volatility and jump measures used in the other
models, except the historical skewness and kurtosis, yields the highest explanatory power reported
so far in the literature, with an adjusted R2 of 67%. The decomposition of the realised volatility
into continuous and jump components captures the different aspects of the jump risk, and increases
the explanatory power compared to models based on historical volatility measures alone. Using
lagged realised volatility and jump measures over different time horizons Andersen et al. (2007)
also obtain greatly improved goodness of fit measures as confirmed by the results reported here.
Table IV reports the results for the CDX index. In Model (4), the coefficients on the historical
skewness and kurtosis measures for the index returns are statistically significant and economically
meaningful in magnitude. However, the explanatory power is small with an adjusted R2 of 1%. By
contrast Model (2), which uses the proposed realised volatility measure, has an adjusted R2 of 22%.
One unit of volatility shock induces an increase of 3.7 basis points in the index. Taken together,
the traditional volatility measure and the proposed realised volatility measure yield an adjusted R2
of 26%, in Model (3). By contrast with the individual credit spreads, the index return historical
skewness and kurtosis have high explanatory power of 25%, and economically meaningful coefficients implying changes in the index spread of 44 and 2.4 basis points for one unit changes in
these measures, according to Model (4). The jump measures (jump intensity and jump volatility)
are both highly significant, and yield an adjusted R2 of 25% in Model (5). Taken together, the
volatility and the jump risks explain 29% of the variation in the index according to Model (6).
18
[Insert Table IV about here]
4.2 Cross-sectional Analysis
By holding a sufficiently diversified portfolio of CDS, an investor eliminates the impact of firmspecific shocks but is still subject to systematic risk. Table V reports the estimation results for a
cross-sectional analysis of the determinants of CDS spreads. The covariates are the same as in the
previous section. In the cross-section I find that historical volatility explains 36% of the variation
in credit spreads in Model (1), and in Model (2) the realised volatility measure explains 63% of the
variation in credit spreads. Taken together the short and long-run volatility are able to explain 77%
of the variation in the credit spreads in the cross-section, in Model (3). The historical skewness and
historical kurtosis produce an adjusted R2 of only 4% in Model (4). The coefficients on the jump
mean and jump volatility measures are significant and economically meaningful with an adjusted
R2 of 55% as reported in Model (5). A one unit increase in the jump mean measure induces an
increase of 11 basis points in the CDS spread, and one unit increase in the jump volatility measure
induces reduction of almost 5 basis points. By separating the jumps into positive and negative
values in Model (6) it is possible to explain 37% of the variation in credit spreads. The negative
jumps are not statistically significant. Taken together, the jump measures explain 57% of the crosssectional variation in credit spreads (Model (7)). The historical volatility measure, the short-run
realised volatility measure and the jump measures together produce an adjusted R2 of 94%, and all
of these measures have significant and economically meaningful coefficients.
[Insert Table V about here]
4.3 Extended Regression
In this section I repeat estimations which include other explanatory variables, such as macrofinancial conditions, the firms’ balance sheet information, and proxies for the fixed income market
19
illiquidity risk premium and default risk premium. These variables are all theoretically important
in determining credit spreads, and have been used widely in the literature. Table VI reports the
results for the entire sample. The estimations are repeated in pairs; with and without the volatility
and jump risk measures.
[Insert Table VI about here]
By contrast to the results reported previously by Cossin and Hricko (2002) and Zhang et al. (2009)
the rating dummy has relatively low explanatory power with an adjusted R2 of 10%, although
the coefficient is highly significant, in Model (1). It is likely that CDS spreads respond to any
deterioration in credit conditions in a more timely manner then ratings, resulting in companies
with very different credit spreads belonging to the same credit rating category. In Model (2) the
results of volatility and jump risk measures explain 58% of the variation in credit spreads. The
coefficients on the volatility and jump measures, with the exception of the short-run volatility, are
highly significant. All coefficients are of the similar magnitude to those in Table III.
In Model (3) the macrofinancial variables (market return, option-implied market volatility, VIX
index, the level and slope of the yield curve) have relatively high explanatory power, with an
adjusted R2 of 80%. Taken together, the volatility and jump risk measures with macrofinancial and
firm balance sheet variables explain 93% of the variation in the credit spreads in Model (4).
Table VII reports the results for the CDX index. In Model (1) the volatility measures explain 29%
of the variation in the credit spreads, and the coefficients are highly significant. The macrofinancial
variables explain 86% of the variation, in Model (2). Taken together, the volatility risk, jump risk
and macrofinancial variables explain 90% of the variation in the credit spreads in Model (3).
[Insert Table VII about here]
The economic importance of the volatility and jumps is significant. According to Table I the
cross-sectional average standard deviation of the one-year historical volatility measure is 31.39
20
and the standard deviation of the one-week realised volatility measure is 1.51. Shocks in these
two measures leads to a widening of the credit spreads to 73 basis points and 48.5 basis points
respectively (see coefficients in Table III). On the other hand, a shock of one standard deviation in
the jump mean, jm, (22.751) and jump volatility, jv, (45.138) changes the credit spreads by about
256 and -211 basis points respectively.
The one-year historical volatility and one-week realised volatility average standard deviation for
the CDX index are 1.152 and 4.817 leading to a change in the CDX index of 102 and 17 basis
points respectively.
Overall, these results suggest that the volatility and jump effects are different from the effects of
other structural or macrofinancial factors.
4.4 Robustness Check
The results reported in the previous sections showing that the volatility and jump risks have strong
explanatory power on the level of the CDS spreads naturally begs the question if the results are
robust. Both structural models and reduced form models of credit risk constrain the credit spreads
to be stationary, allowing for a pricing relationship between the level of the spreads and underlying
risk levels. As robustness check, I also model the determinants of the returns in the CDS spreads,
calculated as changes in the credit spreads discounted by appropriate risk-free rate and the riskneutral default probability (see Equation (1)).
Further robustness checks are based on estimation of models for the determinants of the levels
of credit spreads for companies divided into credit rating categories; and panel estimations of the
regressions reported previously in Tables III, VI and VIII using random effect estimations.9 The
coefficients of the volatility and jump measures are stable and qualitatively unchanged. Table VIII
reports the results, consistent with Collin-Dufresne et al. (2001), Schaefer and Strebulaev (2008)
and Zhang et al. (2009) who model the changes in the credit spreads rather than returns. The shortterm realised volatility measure remains statistically significant. The Realised jump measures are
all statistically significant in both Models (1) and (3).
9
These results are available upon request from the author.
21
[Insert Table VIII about here]
Table IX reports the results for the CDX index. The coefficients of the volatility and jump measures
are statistically significant. The volatility risk, jump risk measures and the macrofinancial variables
explain 36% of the variation in the index spread changes.
[Insert Table IX about here]
The Appendix reports results obtained by repeating of the estimations in subsections 4.1 to 4.4 for
each rating category individually. The results are generally consistent with those reported above.
5 Conclusion
In this paper I have investigated the determinants of the CDS spreads for single-name contracts and
for the CDX index. To the best of my knowledge this is the first paper to analyse the determinants
of the CDS and CDX index spread changes, using a novel approach to obtain volatility risk and
jump risk measures directly from the credit spreads in a fully ’model-free’ approach.
The results reported here show that the realized volatility risk and jump risk measures have relatively high explanatory power, of 55% and 47% respectively, in the regressions for the level of
credit spreads. The volatility and jump risk measures estimated from the credit spread returns are
the most significant determinants of the credit spread changes, even after controlling for credit
ratings and other structural factors. These effects are economically important. The main results are
substantiated in a cross-sectional analysis, random effects panel regressions and in regressions for
companies in individual rating categories.
The importance for investors of the accurate identification and measurement of the volatility risk
and jump risk is widely accepted. With more reliable estimates of these sources of risk, the volatility risk and jump risk premia can be more precisely quantified. The new measures of volatility
22
and jump risk reported in this paper appear to correlate more closely with the credit risk premia
for CDS and structured credit products than measures used in previous studies, such as interest
rate factors and volatility factors (including option-implied volatility). The results reported in this
paper are consistent with the models of price pressure in the OTC credit markets temporally driving prices away from fundamentals even in the absence changes in firm fundamentals. They also
suggest that the credit spread volatility risk and jump risk are significant risk factors also for asset
classes traditionally considered to be low in volatility, such as credit spreads.
23
6 Tables and Figures
Figure 1
Realized Variance for the average double and single A-rated entities and the CDX index
Average Realized Volatility in Standard Deviation of AA−A rated entities
100
50
0
March 2011
May 2011
July 2011
Sept. 2011
Dec.2011
Feb.2012
Realized Volatility in Standard Deviation of CDX index
100
50
0
Sept.2010 Nov.2010 Jan.2011 March 2011 May 2011 July 2011 Sept 2011 Nov. 2011 Feb. 2012
Note: The top figure shows the average realised volatility (square root) of the double and single A-rated entities. The
bottom figure plots the same variable for the CDX index. Section 1 illustrates the method used in estimation of the
realised volatility. The sample spans from 09 March 2011 to 24 February 2012 for the CDS contracts and from 22
September 2010 until 24 February 2012 for the CDX index.
24
25
S&P 500 return (%)
vix (%)
Spread (10Y-3M, %)
dps
sts
rf
Variable
CDX Return
AD-test
1-year hvcds_i
1-year skewcds_i
1-year kurtcds_i
Variable
CDS Spread
CDS Return
AD-test
1-year hvcsd
1-year skewcds
1-year kurtcds
roe (%)
lev (%)
div (%)
Panel A: Firm Specific Variables
AA
A
BBB
Mean Std dev
Mean Std dev
Mean Std dev
88.720 22.289
88.462 21.735
118.447 25.967
-0.599 23.363
0.1705 22.399
1.316 31.782
0.673
1.057
1.029
1.685
2.136
1.615
1.708
2.292
2.588
0.755
0.200
0.757
0.553
0.659
0.761
1.176
1.108
2.499
3.110
2.321
2.720
32.005 28.242
44.421 60.544
17.230 27.952
55.254 24.612
44.024 20.351
45.497 26.896
0.802
0.215
0.698
0.394
0.548
0.328
Panel B: CDX Index
CDX15
CDX16
CDX17
Mean Std dev
Mean Std dev
Mean Std dev
-0.067
0.602
0.097
1.026
-0.108
1.241
0.597
3.234
0.536
0.250
0.908
0.254
1.254
0.182
1.395
0.277923
0.335546
0.547475
0.745571
0.042714
0.024068
Panel C: Macrofinancial Variables
Mean Std dev
0.144
3.075
24.558
8.269
2.368
0.702
1.029
0.464
0.266
0.066
0.481
0.094
0.337
0.163
1.036
11.967
16.594
0.867
Std dev
91.189
34.896
CDX
Mean Std dev
-0.017
2.489
5.788
0.163
1.152
0.469
0.259623
BB
Mean
301.549
5.485
0.409
2.516
0.106
0.636
-7.826
53.843
1.175
Whole sample
Mean Std dev
113.396 29.286
0.998 28.364
5.017
28.364 31.395
1.765
26.163
This table presents the summary statistics of all regression variables in the four rating groups, the CDX index and its breakdowns in three series. The ratings are from S&P. There are four
AA rated entities, forty A rated, sixty eight BBB and four BB rated entities. The sample covers in total 116 companies and spans from 09 March 2011 to 24 February 2012. The subsequent
tables variables are abbreviated as here. Panel A reports the summary statistics of all firm-specific variables. These variables include (i) CDS return (estimated as from Equation (1)); (ii) the
Anderson-Darling test statistics of normality; (iii) firm-level CDS return for 1 year: historical volatility (hvcds), historical skewness (skewcds) and historical kurtosis (kurtcds) for one-year
horizon.; (iv) firms’ balance sheet information: return on equity (roe), leverage ratio (lev) and dividend payout ratio (div). Panel B reports the summary statistics of the return of the CDX
index and its one-year historical volatility (hvcds_i), skewness (skewcds_i)and kurtosis(kurtcds_i). The sample period spans from 22 September 2010 to 24 February 2012. Panel C reports the
summary statistics of the macrofinancial variables: market return and volatility obtained in Bloomberg. The short risk-free rate (rf, 3-month Treasury rate) the spread (10year-3month Treasury
and swap rates) are obtained by the Federal Reserve’s website. Same data from Fed’s website are used to estimate the default premium (dps) and the illiquidity premium (sts).
Table I
Summary Statistics of All Variables
26
ji_i
jm_i
jv_i
Variable
RV(sqrt)
RV(C)
sum(J 2 )/sum(RV)
sum(J 2 )/sum(sqrtRV)
ji
jm
jv
Variable
RV(sqrt)
RV( C)
sum(J 2 )/sum(RV)
sum(J 2 )/sum(sqrtRV)
Panel A: Firm Specific Volatility Variables
AA
A
BBB
BB
Mean Std dev
Mean Std dev
Mean Std dev
Mean Std dev
1.022
0.471
2.249
0.683
2.622
0.820
1.087
0.549
2.459
0.661
2.249
0.683
2.622
0.820
2.565
0.683
0.502
0.097
0.594
0.567
0.505
0.446
0.185
0.219
0.624
0.075
0.491
0.296
0.435
0.251
0.206
0.219
Panel B: Firm Specific Jump Parameters
0.232
0.062
0.118
0.055
0.111
0.050
0.052
0.022
4.880
6.815
5.398
3.320
7.528
6.683
65.554 118.946
6.668
8.143
3.695
3.227
6.632
7.736 126.392 240.212
Panel C: CDX Index Volatility Variables
CDX15
CDX16
CDX17
CDX
Mean Std dev
Mean Std dev
Mean Std dev
Mean Std dev
0.330
0.109
0.431
0.292
0.622
0.196
0.460
0.244
7.412
2.382
6.014
2.243 14.131
7.126
8.212
4.817
0.012
0.307
0.121
2.501
0.025
1.055
0.072
5.240
2.608
7.508
6.946
9.689
5.758
0.052
Panel D: Jump parameters of the CDX index
0.025
0.047
0.019
0.076
3.860
9.261
10.067
5.009
1.393
15.482
10.665
7.723
0.116
8.703
9.750
1.745
2.573
0.525
0.453
0.056
22.751
45.138
0.631
1.510
0.483
0.268
Whole sample
This table represents the summary statistics for volatility and jump parameter estimation of the four rating groups the CDX index and its breakdown in three series (15, 16 and 17). Panel A
summarizes the cross-sectional averages of weekly annualized realised volatility (rv), the continuous part of the realised volatility (rvc), the average jump contribution to the total variance and the
average jump contribution to the standard deviation. Panel B gives the parameter estimates of the jump intensity (ji); jump mean (jm) and the jump volatility (jv). Panels C and D summarize the
same variables with an _i subscript for the CDX index. The estimation procedure of the jump parameters is discussed in section 4. The sample spans from 09 March 2011 to 24 February 2012. The
CDX index spans from 22 September 2010 to 24 February 2012.
Table II
Summary Statistics of Volatility and Jump Parameters
Figure 2
Realized Jumps for the average double and single A-rated entities and the CDX index
Average Realized Jumps of AA−A rated entities
15
10
5
0
March 2011
May 2011
July 2011
Sept 2011
Dec.2011
Jan.2012
Feb.2012
Nov.2011
Feb.2012
Realized Jumps of CDX index
60
40
20
0
Sept.2010
Dec.2010
Feb.2011
May 2011
Sept. 2011
Note: The top figure shows the average realised jumps of the double and single A-rated entities. The bottom figure
plots the same variable for the CDX index. Section 2 illustrates the method used in the estimation of the realised
jumps. The sample spans from 09 March 2011 to 24 February 2012 for the CDS contracts and from 22 September
2010 until 24 February 2012 for the CDX index.
27
28
R-squared
N
Constant
L.jn
L.jp
L.jv
L.jm
L.kurtcds
L.skewcds
L.rvc
L.hvcds
70.435***
(11.672)
0.28
5452
1
3.910***
(1.202)
14.226
(17.062)
0.46
5452
39.144***
(6.407)
2
5.632
(11.280)
0.55
5452
3
2.335***
(0.860)
32.122***
(4.973)
137.909***
(14.719)
0.03
5452
0.813
(4.678)
-2.189**
(0.911)
4
62.653***
(7.747)
0.44
5452
11.271***
(1.079)
-4.676***
(0.532)
5
1.576***
(0.326)
15.232
(14.170)
98.387***
(5.693)
0.30
5452
6
-6.440***
(0.657)
12.054***
(1.097)
16.568
(12.962)
63.341***
(6.898)
0.45
5452
7
-3.153***
(0.864)
6.101***
(1.506)
12.849
(9.046)
7.906
(14.762)
0.67
5452
8
1.897**
(0.739)
22.376***
(8.288)
The explanatory variables include firm-level CDS return volatility and/or jump measures as reported in table I and II. The prefix L. stands for the first-lag in variables. In parenthesis are the
clustered standard errors adjusted for the firm effects. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
The main regressions employ weekly data to explain the determination of five-year CDS spreads of 116 entities for the March 2011 - February 2012 period. The specification of the OLS
regressions is:
CDS t, j = α + βυ Volatilitest−1, j + βϑ Jumpst−1, j + t, j
Table III
Main Regression of the CDS determinants
Table IV
Main Regression of the CDX index determinants
The main regressions employ weekly data to explain the determination of five-year CDX index spreads for the period 22 September 2010 to
24 February 2012. The specification of the OLS regressions is:
CDXt = α + γa Volatilitest−1 + γb Jumpst−1 + t
The explanatory variables include for each CDX series return volatility and/or jump measures as reported in Table 1 and 2. In parenthesis are
the clustered standard errors. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
L.hvcdx
1
74.897***
(24.680)
L.rv_i
2
3.694***
(0.659)
3
88.697***
(8.852)
3.509***
(0.106)
L.skewcds_i
4
L.jm_i
L.jv_i
Adj. R-squared
N
6
7.585
(12.268)
22.654***
(0.000)
5.649***
(0.462)
-1.484***
(0.177)
66.943***
(1.535)
0.25
68
-16.612***
(0.144)
43.784***
(4.581)
2.429
(1.537)
L.kurtcds_i
Constant
5
106.141***
(8.101)
0.01
68
63.297***
(5.735)
0.22
68
75.594***
(0.816)
0.26
68
29
88.303***
(2.260)
0.25
68
19.139***
(0.770)
0.29
68
30
Adj. R-squared
N
Constant
L.rvc
L.jn
L.jp
L.jv
L.jm
L.kurtcds
L.skewcds
L.rv
L.hvcds
70.435***
(8.084)
0.36
5452
1
3.910***
(0.492)
73.064***
(5.305)
0.63
5452
4.064***
(0.290)
2
50.581***
(5.080)
0.77
5452
3
2.524***
(0.313)
3.448***
(0.244)
137.909***
(12.823)
0.04
5452
0.813
(6.183)
-2.189**
(1.020)
4
62.653***
(7.339)
0.55
5452
11.271***
(1.405)
-4.676***
(0.708)
5
98.387***
(6.108)
0.37
5452
1.576***
(0.225)
15.232
(10.529)
6
63.341***
(7.125)
0.57
5452
-6.440***
(0.913)
12.054***
(1.498)
16.568*
(8.803)
7
-1.600***
(0.405)
2.867***
(0.686)
4.453
(3.471)
60.214***
(3.003)
-58.410***
(6.033)
0.94
5452
8
0.576***
(0.203)
This table presents the cross-sectional baseline regression for all 116 entities. The explanatory variables are explained in Tables 1 and 2. In parenthesis are the robust standard errors. The sample
spans from March 2004 to February 2011. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
Table V
Cross-Sectional Regression of the CDS determinants
Table VI
Extended Regression of the CDS determinants
The extended regressions employ weekly data to explain the determination of five-year CDS spreads of 116 entities for the March 2011 February 2012 period. The specification of the OLS regressions is:
CDS t, j = α + βυ Volatilitest−1, j + βϑ Jumpst−1, j + βr Ratingst−1, j + βm Macrot−1, j + βn Firmt−1, j + t, j
The explanatory variables include lagged firm-specific CDS return volatility and jump measures, rating dummies (d1), macrofinancial variables and firm-specific balance sheet variables as reported in table I and II. In parenthesis are the clustered standard errors adjusted for the
firm effects. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
L.d1
1
45.561***
(14.900)
L.hvcds
2
4
-301.196**
(152.884)
537.105***
(186.394)
80.412
(248.713)
-32.077
(30.636)
27.502
(17.663)
-93.080
(136.541)
-368.054*
(219.082)
583.111***
(195.161)
322.804***
(111.171)
0.80
5452
-29.865
(19.633)
-0.907***
(0.350)
-48.244**
(22.035)
80.455**
(36.590)
-11.374
(10.827)
-197.575**
(79.944)
388.809***
(115.003)
254.691
(316.710)
-39.239
(25.414)
-83.575***
(21.379)
-64.144
(128.313)
-136.422
(132.993)
672.744*
(398.945)
899.568***
(151.093)
0.93
5452
23.694***
(0.959)
0.025
(2.348)
23.057***
(0.801)
-37.742***
(1.314)
22.554***
(0.532)
L.rvc
L.jv
L.jp
L.jn
L.spreturn
L.vix
L.shtbil
L.termspread
L.dps
L.sts
L.roe
L.lev
L.div
Adj.R-squared
N
3
0.10
5452
0.58
5452
31
Table VII
Extended Regression of the CDX index determinants
The extended regressions employ weekly data to explain the determination of five-year CDX index spreads for the period 22 September 2010
to 24 February 2012. The specification of the OLS regressions is:
CDXt = α + γa Volatilitest−1 + γb Jumpst−1 + γc Macrot−1 + t
The explanatory variables include lagged series-specific CDS return volatility and jump measures, macrofinancial variables as default risk
premium, illiquidity premium and Fama and French small-minus-big and high-minus-low factors as reported in tables I and II. In parenthesis
are the clustered standard errors. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
L.hvcds_i
L.rvc_i
L.jv_i
1
-52.045***
(3.421)
11.636***
(0.000)
0.304***
(0.103)
L.spreturn_i
L.mktret_i
L.vix_i
L.shtbil_i
L.termspread_i
L.shtbil_i
L.dps_i
L.sts_i
Constant
Adj. R-squared
N
56.622***
(1.917)
0.29
68
32
2
-102.613***
(38.670)
-0.244
(0.158)
1.244***
(0.206)
37.773
(24.466)
-8.787***
(2.736)
64.352
(39.242)
-14.119
(21.400)
12.201
(44.131)
68.516***
(15.100)
0.86
68
3
-57.400***
(20.553)
-0.317
(0.297)
1.020**
(0.410)
-42.772
(41.827)
-0.105
(0.235)
0.374***
(0.109)
-77.452***
(24.158)
-15.539***
(1.977)
85.679**
(34.624)
4.360
(12.791)
41.624
(42.603)
121.231***
(11.751)
0.90
68
Table VIII
Determinants of CDS returns
The regressions employ weekly data to examine the determination of five-year CDS returns of 116 entities for the March 2011 - February
2012 period. The specification of the OLS regressions is:
CDS rett, j = α + βυ ∆Volatilitest−1, j + βϑ Jumpst−1, j + βm ∆Macrot−1, j + βn ∆Firmt−1, j + t, j
The explanatory variables include weekly changes in volatility measures levels of jump measures, and weekly changes in macrofinancial
variables and firm-specific balance sheet variables as reported in tables I and II. ∆ represents first difference in variables. In parenthesis are
the clustered standard errors adjusted for the firm effects. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
D.rvc
jv
jp
jn
1
2.901***
(0.938)
1.044***
(0.005)
-1.581***
(0.007)
-0.962***
(0.003)
D.spreturn
D.vix
D.shtbil
D.termspread
D.rf
D.dps
D.sts
D.roe
D.lev
D.div
Adj. R-squared
N
0.05
188
2
-364.742**
(142.725)
1389.445***
(366.804)
-17.078
(206.816)
-30.359
(22.670)
373.308***
(136.865)
-342.428***
(126.891)
-496.681
(312.286)
45.420
(70.408)
190.401
(169.002)
15.915
(130.961)
0.27
188
33
3
1.149
(0.739)
1.067***
(0.012)
-1.613***
(0.019)
-1.054***
(0.127)
-351.476***
(124.981)
1370.761***
(361.609)
-72.466
(165.426)
-27.577
(23.992)
376.115***
(130.466)
-343.061**
(136.035)
-498.361
(334.449)
68.680*
(37.116)
-126.804
(192.633)
-84.881
(108.862)
0.31
188
Table IX
Determinants of CDX index returns
The regressions employ weekly data to examine the determination of five-year CDS returns for the period 22 September 2010 - 24 February
2012. The specification of the OLS regressions is:
CDXrett = α + βυ ∆Volatilitest−1 + βϑ Jumpst−1 + βm ∆Macrot−1 + t
The explanatory variables include firm-level CDS return volatility and/or jump measures as reported in table I and II. ∆ represents the first
difference in variables. In parenthesis are the clustered standard errors. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
D.hvcds_i
D.rvc_i
ji_i
jm_i
1
-1.251***
(0.241)
0.133***
(0.023)
9.994***
(2.540)
-0.015
(0.010)
D.spreturn_i
-6.747***
(0.378)
0.003
(0.012)
0.034***
(0.006)
-5.695
(5.940)
0.289
(0.663)
-2.518
(2.261)
1.625*
(0.903)
-2.522
(1.624)
0.31
67
D.mktret_i
D.vix_i
D.shtbil_i
D.termspread_i
D.rf_i
D.dps_i
D.sts_i
Adj. R-squared
N
2
0.08
68
34
3
-0.445
(1.248)
0.012
(0.114)
10.456***
(2.301)
-0.009
(0.013)
-5.923***
(0.668)
0.004
(0.014)
0.024***
(0.006)
-5.409
(6.471)
0.396
(0.899)
-2.818
(2.359)
0.451
(0.977)
-2.833**
(1.405)
0.36
67
Appendix A
Hazard Rate
The risk-free discount rates are needed to construct the excess returns from the CDS spreads. For
this purpose I use the daily data of zero-coupon 3-month LIBOR based swap curve with maturity
of 5 years. These rates have been widely used as markets benchmark of risk-free rates. The swap
rates are obtained from Bloomberg.
The event that firm j has defaulted by time T can be characterized as simple binary or Bernoulli
variate with probability πi = 1 − eξT ; where ξ is a firm-specific constant. Thus the value of the
risky duration or the premium leg is calculated as:
1X
A=
∆te−rt j · (e−ξt j−1 + e−ξt j ),
2 j=1
T −t
(1)
and the protection leg is:
B = (1 − ρ)
T −t
X
e−rt j · (e−ξt j−1 + e−ξt j ),
(2)
j=1
where ρ is the assumed constant recovery rate of 40%. Since we can observe the CDS spread in
the market, we can solve numerically for ξ, that is:
B(ξ) = CDS A(ξ).
(3)
In practice, A and B can be approximated by
A≈
T −t
X
∆te−rt j · (e−ξt j−1 ),
j=1
and B
35
(4)
B = (1 − ρ)
T −t
X
e−rt j · e−ξt j (1 − e−ξ∆t )
j=1
B ≈ ξ(1 − ρ)
T −t
X
∆te−rt j · (e−ξt j−1 )
(5)
j=1
Thus, it follows that the firm-specific constant is:
ξ≈
CDS
(1 − ρ)
(6)
I calculate these probabilities for each observation and for each CDS contract in the empirical
analysis.
Appendix B
Test Statistics of Daily Jumps
Barndorff-Nielsen and Shephard (2004), Huang and Tauchen (2005) and Andersen et al. (2007)
adopt the test statistics of significant jumps on the basis of ratio statistics as defined in Equation
(5) in Section 2,
RJt
−→ N(0, 1)
z= T Pt
((π/2)2 + π − 5) · ∆ · max 1, BV
2
(7)
t
where ∆ is the intraday sampling frequency, BVt is the bipower variation defined by equation (4)
in Section 2 and
m
X
1
T Pt ≡
|R j,t,i |4/3 · |R j,t,(i−1)∆ |4/3 · |R j,t,(i−2)∆ |4/3
·
−1
3
4∆[Γ(7/6) · Γ(1/2) ] i=3
where the ∆ → 0, T Pt →
Rt
t−1
(8)
σ4s ds . Thus, daily jumps can be detected by choosing different levels
36
of significance. To mitigate microstructure noise effects such as the correlation of the adjacent
returns I follow Zhang et al. (2009) approach and use the following bipower measures (j=1):
BVt ≡
m
π X
|R j,t,i∆ | · |R j,t,(i−1)∆ |,
2 i=2+ j
m
X
1
·
|R j,t,i |4/3 · |R j,t,(i−1)∆ |4/3 · |R j,t,(i−2)∆ |4/3
T Pt ≡
4∆[Γ(7/6) · Γ(1/2)−1 ]3 i=1+2(1+ j)
(9)
(10)
Following Andersen et al. (2007) I define the continuous and jump components of realized volatility on each day as:
p
RVt − BVt · I(z > Φ−1
α ),
(11)
p
p
RVt · [1 − I(z > Φ−1
BVt · I(z > Φ−1
)]
+
α
α ,)
(12)
RV(J)t =
RV(C)t =
where RVt is defined by Equations (3) in Section 2, I(·) is the indicator function, and α is the chosen
significance level at 0.99.
Appendix C
Variables Definition and Data Source
The analysis uses the following variables:
• Weekly 5-year CDS spreads are provided by Bloomberg
• Historical volatility (hvcds), historical skewness (skewcds) and historical kurtosis (kurtcds)
are calculated from the weekly 5-year CDS returns. Historical volatility is estimated as
standard deviation of the CDS returns.
• Realized volatility and the realized jumps of the CDS returns are calculated as discussed in
37
section 2. These measures are calculated for each day and then averaged over the week. The
measures are:
realized volatility (rv) : is defined in Equation (3) in section 2.
jump intensity (ji) : is the average frequency of the business days with nonzero jumps.
Jumps are detected on the basis of the ratio statistics in Equation (5) in section 2 and
Appendix B for the implementation details.
jump mean (jm) and jump volatility (jv) : are the mean and the standard deviation of
nonzero jumps.
positive and negative jumps (jp and jn) : the average of the positive and negative jumps
where the later is expressed in its absolute term.
• The last available quarterly observations of the firms balance sheets reported in Bloomberg
constitute the firm specific variables used in the analysis. more specifically, these variables
are:
Leverage ratio (lev) = (Current debt + Long term det)/(Total eqity + Curent debt + Long
term debt)
Return on Equity (roe) = Pre-tax income/Total equity
Dividend Payout ratio (div) = Dividend payout share/Equity price
• The macroeconomic variables: S&P index average weekly return for the past six months;
VIX index (near-the-money equity index option implied volatility).
• Short term bill (shtbill) and the term spread (termspread) where the later is the sloop of the
yield curve calculated as the difference between ten-year and three-month Treasury rates are
obtained in the Federal Reserves website.
• Fixed income market illiquidity risk (sts) is calculated as the difference of five-year swap
rate and the five-year Treasury rate; data obtained in the Federal Reserves website.
38
• The default risk premium (dps) in the corporate bond market is the Moody’s default premium sloop defined as the difference of Baa yield minus Aaa yield spread. This measure is
downloaded from the Federal Reserves website.
The analysis of the CDX index employ same data where the cds is simply replaced by cdx, e.g.
historical volatility of the CDS returns (hvcds) is replaced with the estimates of the historical
volatility of the CDX index (hvcdx) and contain the ’_i’ subscript.
39
REFERENCES
Ait-Sahalia, Yacine, 2004, Disentangling diffusion from jumps, Journal of Financial Economics
74, 487–528.
Ait-Sahalia, Yacine, and Per A. Mykland, 2005, How often to sample a continuous-time process
in the presence of market microstructure noise, Review of Financial Studies 18, 351–416.
Andersen, T.G., T. Bollerslev, F.X. Diebold, and H. Ebens, 2001, The distribution of realized stock
return volatility, Journal of Financial Economics 61, 43–76.
Andersen, Torben G., Luca Benzoni, and Jesper Lund, 2002, An empirical investigation of
continuous-time equity return models, Journal of Finance 57, 1239–1284.
Andersen, Torben G., and Tim Bollerslev, 1998, Answering the critics: Yes, ARCH models do
provide good volatility forecasts, International Economic Review 39, 885–905.
Andersen, Torben G., Tim Bollerslev, and Francis X. Diebold, 2007, Roughing it up: Including
jump components in the measurement, modeling, and forecasting of return volatility, The
Review of Economics and Statistics 89, 701–720.
Anderson, T. W., and D. A. Darling, 1952, Asymptotic theory of certain "goodness of fit" criteria
based on stochastic processes, Annals of Mathematical Statistics 23, 193–212.
Barndorff-Nielsen, O E, 2006, Econometrics of testing for jumps in financial economics using
bipower variation, Journal of Financial Econometrics 4, 1–30.
Barndorff-Nielsen, Ole, and Neil Shephard, 2001, Non-gaussian OU based models and some of
their uses in financial economics, OFRC Working Papers Series 2000mf01, Journal of Royal
Statistical Society, Series B 64.
Barndorff-Nielsen, Ole E., and Neil Shephard, 2002, Estimating quadratic variation using realized
variance, Journal of Applied Econometrics 17, 457–477.
Barndorff-Nielsen, Ole E., and Neil Shephard, 2003, Realized power variation and stochastic
volatility models, Bernoulli 2, 243–265.
40
Barndorff-Nielsen, Ole E., and Neil Shephard, 2004, Power and bipower variation with stochastic
volatility and jumps, Journal of Financial Econometrics 2, 1–37.
Blanco, Roberto, Simon Brennan, and Ian W. Marsh, 2005, An empirical analysis of the dynamic
relation between investment-grade bonds and credit default swaps, Journal of Finance 60,
2255–2281.
Bollerslev, Tim, and Hao Zhou, 2002, Estimating stochastic volatility diffusion using conditional
moments of integrated volatility, Journal of Econometrics 109, 33–65.
Bongaerts, Dion, Frank De Jong, and Joost Driessen, 2011, Derivative pricing with liquidity risk:
Theory and evidence from the credit default swap market, Journal of Finance 66, 203–240.
Campbell, John Y., and Glen B. Taksler, 2003, Equity volatility and corporate bond yields, Journal
of Finance 58, 2321–2350.
Collin-Dufresne, Pierre, Robert S. Goldstein, and Jean Helwege, 2003, Is credit event risk priced?
modeling contagion via the updating of beliefs, Technical Report 15733.
Collin-Dufresne, Pierre, Robert S. Goldstein, and J. Spencer Martin, 2001, The determinants of
credit spread changes, The Journal of Finance 56, 2177–2207.
Cossin, Didier, and Tomas Hricko, 2002, Exploring for the determinants of credit risk in credit
default swap transaction data, FAME Research Paper Series rp65, HEC-Lausanne.
Cremers, K. J. Martijn, Joost Driessen, and Pascal J. Maenhout, 2008, Explaining the level of
credit spreads: Option-implied jump risk premia in a firm value model, Review of Financial
Studies 21, 2209–42.
Drost, Feike C, Theo E Nijman, and Bas J M Werker, 1998, Estimation and testing in models
containing both jump and conditional heteroscedasticity, Journal of Business and Economic
Statistics 16, 237–243.
Duffie, Darrell, 2010, Asset price dynamics with slow-moving capital, Journal of Finance 65,
1237–1267.
41
Duffie, Darrell, Jun Pan, and Kenneth Singleton, 2000, Transform analysis and asset pricing for
affine jump-diffusions, Econometrica 68, 1343–1376.
Elton, Edwin J., Martin J. Gruber, Deepak Agrawal, and Christopher Mann, 2001, Explaining the
rate spread on corporate bonds, Journal of Finance 56, 247–277.
Eraker, Bjørn, Michael Johannes, and Nicholas Polson, 2003, The impact of jumps in volatility
and returns, Journal of Finance 58, 1269–1300.
Feldhütter, Peter, 2012, The same bond at different prices: Identifying search frictions and selling
pressures, Review of Financial Studies 25, 1155–1206.
Geske, Robert L., and Gordon Delianedis, 2001, The components of corporate credit spreads: Default, recovery, taxes, jumps, liquidity, and market factors, Working Paper Series, Anderson
Graduate School of Management, UCLA. .
Huang, Jing-Zhi Jay, and Ming Huang, 2003, How much of corporate-treasury yield spread is due
to credit risk?, Working Paper, Pen State University .
Huang, Jing-Zhi Jay, and Hao Zhou, 2008, Specification analysis of structural credit risk models,
Working Paper, Federal Reserv Board .
Huang, Xin, and George E. Tauchen, 2005, The relative contribution of jumps to total price variance, Journal of Financial Econometrics 3, 456–99.
Jones, E Philip, Scott P Mason, and Eric Rosenfeld, 1984, Contingent claims analysis of corporate
capital structures: An empirical investigation, Journal of Finance 39, 611–25.
Longstaff, Francis A, and Eduardo S Schwartz, 1995, A simple approach to valuing risky fixed and
floating rate debt, Journal of Finance 50, 789–819.
Longstaff, Pan Jun Pedersen Lasse H. Singleton Kenneth J., Francis A., 2011, How sovereign is
sovereign credit risk?, American Economic Journal: Macroeconomics 3, 75–103.
42
Mayordomo, Sergio, Juan Ignacio Peña, and Eduardo S. Schwartz, 2010, Are all credit default
swap databases equal?, NBER Working Papers 16590, National Bureau of Economic Research, Inc.
Meddahi, Nour, 2002, A theoretical comparison between integrated and realized volatility, Journal
of Applied Econometrics 17, 479–508.
Merton, Robert C, 1974, On the pricing of corporate debt: The risk structure of interest rates,
Journal of Finance 29, 449–70.
Merton, Robert C., 1976, Option pricing when underlying stock returns are discontinuous, Journal
of Financial Economics 3, 125–144.
Petersen, Mitchell A., 2009, Estimating standard errors in finance panel data sets: Comparing
approaches, Review of Financial Studies 22, 435–480.
Schaefer, Stephen M., and Ilya A. Strebulaev, 2008, Structural models of credit risk are useful:
Evidence from hedge ratios on corporate bonds, Journal of Financial Economics 90, 1–19.
Tauchen, George, and Hao Zhou, 2010, Realized jumps on financial markets and predicting credit
spreads, Journal of Econometrics 160, 102–118.
Zhang, Benjamin Yi-Bin, Hao Zhou, and Haibin Zhu, 2009, Explaining credit default swap spreads
with the equity volatility and jump risks of individual firms, Review of Financial Studies 22,
5099–5131.
Zhou, Chunsheng, 2001, The term structure of credit spreads with jump risk, Journal of Banking
& Finance 25, 2015–2040.
Zhu, Haibin, 2006, An empirical comparison of credit spreads between the bond market and the
credit default swap market, Journal of Financial Services Research 29, 211–235.
43
Appendix: Additional results for each rating category
44
45
Adj. R-squared
N
Constant
L.rvc
L.jn
L.jp
L.jv
L.jm
L.kurtcds
L.skewcds
L.rv
L.hvcds
38.081**
(7.092)
0.76
188
1
5.396***
(0.241)
42.284**
(11.118)
0.70
188
5.316***
(0.345)
2
34.962***
(5.979)
0.80
188
3
3.515***
(0.272)
2.354***
(0.163)
200.161
(170.969)
0.13
188
116.166
(128.310)
-25.895
(31.545)
4
41.577***
(4.470)
0.76
188
10.236
(5.285)
-0.094
(4.348)
5
31.383
(14.025)
0.76
188
7.357***
(0.332)
2.164
(5.791)
6
41.837***
(0.000)
0.77
188
-26.283***
(0.000)
25.182***
(0.000)
7
16.522**
(3.870)
19.848**
(6.153)
0.80
188
16.224***
(1.732)
1.567***
(0.067)
8
-6.189***
(0.470)
This table presents the baseline regression for S&P AA rated companies. The explanatory variables are explained in Tables 1 and 2. In parenthesis are the clustered standard errors adjusted for
the firm effects. The sample spans from March 2004 to February 2011. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
Table X
Main Regression of the S&P AA rated CDS spreads
46
Adj. R-squared
N
Constant
L.rvc
L.jp
L.jv
L.jm
L.kurtcds
L.skewcds
L.rv
L.hvcds
43.174***
(5.136)
0.54
1880
1
5.173***
(0.573)
38.483***
(3.685)
0.64
1880
7.021***
(0.580)
2
26.431***
(2.797)
0.76
1880
3
2.980***
(0.258)
4.993***
(0.623)
95.013***
(15.386)
0.10
1880
-42.064
(31.440)
3.219
(3.613)
4
17.074*
(9.619)
0.43
1880
10.644***
(3.393)
4.145
(5.749)
5
16.031
(9.858)
0.42
1880
13.674***
(2.302)
6
17.074*
(9.619)
0.43
1880
4.145
(5.749)
10.644***
(3.393)
7
0.695
(1.329)
5.311***
(1.252)
25.889***
(3.824)
-24.491**
(9.188)
0.78
1880
8
2.727***
(0.358)
This table presents the baseline regression for S&P A rated companies. The explanatory variables are explained in Tables 1 and 2. In parenthesis are the clustered standard errors adjusted for
the firm effects. The sample spans from March 2004 to February 2011. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
Table XI
Main Regression of the S&P A rated CDS spreads
47
Adj. R-squared
N
Constant
L.rvc
L.jp
L.jv
L.jm
L.kurtcds
L.skewcds
L.rv
L.hvcds
82.549***
(14.298)
0.27
3196
1
2.957**
(1.358)
78.455***
(8.839)
0.40
3196
4.308***
(1.065)
2
60.253***
(10.938)
0.51
3196
3
2.013**
(0.877)
3.544***
(0.772)
138.571***
(15.505)
0.06
3196
8.054*
(4.521)
-1.971**
(0.970)
4
67.284***
(9.291)
0.41
3196
10.596***
(1.021)
-4.053***
(0.719)
5
69.743***
(12.905)
0.36
3196
6.670***
(1.610)
6
66.609***
(9.548)
0.41
3196
-4.093***
(0.706)
9.198**
(4.363)
7
-2.721***
(0.556)
2.643
(2.843)
31.763***
(3.791)
-3.062
(7.252)
0.69
3196
8
0.851**
(0.331)
This table presents the baseline regression for S&P BBB rated companies. The explanatory variables are explained in Tables 1 and 2. In parenthesis are the clustered standard errors adjusted for
the firm effects. The sample spans from March 2004 to February 2011. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
Table XII
Main Regression of the S&P BBB rated CDS spreads
48
Adj. R-squared
N
Constant
L.rvc
L.jn
L.jp
L.jv
L.jm
L.kurtcds
L.skewcds
L.rv
L.hvcds
-131.487
(295.535)
0.21
188
1
28.533
(21.439)
301.643**
(73.847)
0.01
188
0.101
(0.072)
2
-127.930
(314.537)
0.21
188
3
28.236
(23.152)
0.019
(0.122)
1197.763***
(86.006)
0.49
188
192.330**
(49.556)
-172.371***
(15.761)
4
260.363***
(6.321)
0.58
188
-9.669***
(1.325)
5.384***
(0.658)
5
218.770***
(4.551)
0.55
188
0.991***
(0.072)
3.726
(8.641)
6
260.363***
(6.321)
0.58
188
5.669***
(1.325)
5.384***
(0.658)
7
0.025
(2.348)
244.935***
(10.243)
0.58
188
3.528***
(0.160)
7.380***
(0.072)
8
This table presents the baseline regression for S&P BB rated companies. The explanatory variables are explained in Tables 1 and 2. In parenthesis are the clustered standard errors adjusted for
the firm effects. The sample spans from March 2004 to February 2011. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
Table XIII
Main Regression of the S&P BB rated CDS spreads
49
Adj. R-squared
N
Constant
L.rvc
L.jn
L.jp
L.jv
L.jm
L.kurtcds
L.skewcds
L.rv
L.hvcds
42.701***
(6.626)
0.56
2068
1
5.196***
(0.491)
16.926***
(4.575)
0.64
2068
9.759***
(0.479)
2
18.469***
(4.118)
0.71
2068
3
1.464***
(0.432)
7.773***
(0.726)
94.655***
(17.906)
0.09
2068
-39.299**
(18.303)
2.983
(2.450)
4
22.883**
(11.022)
0.45
2068
10.529***
(2.755)
2.703
(2.606)
5
29.663**
(11.140)
0.41
2068
11.027***
(1.604)
-10.396
(13.569)
6
19.206
(12.081)
0.46
2068
4.072
(3.080)
-9.582
(8.667)
11.182
(16.859)
7
1.181
(1.339)
-11.194***
(3.460)
11.739*
(6.678)
33.374***
(5.818)
-30.772***
(8.504)
0.77
2068
8
2.314***
(0.420)
This table presents the cross-sectional baseline regression for S&P AA and A rated companies. The explanatory variables are explained in Tables 1 and 2. In parenthesis are the robust standard
errors. The sample spans from March 2004 to February 2011. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
Table XIV
Cross-sectional Regression of the S&P AA and A rated CDS spreads
50
Adj. R-squared
N
Constant
L.rvc
L.jn
L.jp
L.jv
L.jm
L.kurtcds
L.skewcds
L.rv
L.hvcds
89.641***
(12.257)
0.19
3384
1
3.179***
(0.682)
87.081***
(6.947)
0.06
3384
3.590***
(0.315)
2
64.570***
(7.480)
0.10
3384
3
2.059***
(0.410)
3.261***
(0.280)
159.811***
(16.479)
0.07
3384
6.745
(7.031)
-2.942**
(1.212)
4
77.356***
(9.221)
0.47
3384
10.003***
(1.592)
-4.091***
(0.798)
5
111.345***
(7.610)
0.37
3384
1.339***
(0.230)
27.864**
(12.337)
6
73.100***
(8.760)
0.53
3384
-4.467***
(1.410)
-0.027
(7.658)
36.586***
(11.563)
7
-2.293***
(0.457)
3.983
(2.406)
6.856*
(3.831)
64.802***
(2.871)
-65.181***
(6.365)
0.48
3384
8
0.088
(0.178)
This table presents the cross-sectional baseline regression for S&P BBB and BB rated companies. The explanatory variables are explained in Tables 1 and 2. In parenthesis are the robust
standard errors. The sample spans from March 2004 to February 2011. Significance levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
Table XV
Cross-sectional Regression of the S&P BBB and BB rated CDS spreads
Table XVI
Extended Regression of the CDS returns for the S&P AA rated companies
This table presents the extended regression for S&P AA rated companies. The explanatory variables are explained in tables I and II. In
parenthesis are the clustered standard errors adjusted for the firm effects. The sample spans from March 2004 to February 2011. Significance
levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
L.hvcds
L.rvc
L.jv
L.jp
1
1.627***
(0.364)
16.522***
(3.870)
-25.063***
(2.675)
24.358***
(2.366)
L.spreturn
-30.703
(64.236)
62.996
(81.073)
-103.495**
(49.739)
-12.863**
(6.455)
7.540
(10.908)
35.276***
(10.618)
-417.681***
(68.879)
274.287***
(14.283)
305.319***
(87.090)
0.90
188
L.vix
L.shtbil
L.termspread
L.dps
L.sts
L.roe
L.lev
L.div
Adj. R-squared
N
2
0.80
188
51
3
-10.883
(19.872)
4.930***
(1.211)
783.597*
(460.176)
-647.471*
(367.233)
-46.114
(56.016)
70.339
(73.831)
-124.395***
(47.909)
-5.530**
(2.389)
2.835
(7.657)
36.316
(24.427)
-799.569
(593.287)
-712.310
(465.920)
412.339
(269.980)
0.92
188
Table XVII
Extended Regression of the S&P A rated CDS spreads
This table presents the extended regression for S&P A rated companies. The explanatory variables are explained in tables I and II. In
parenthesis are the clustered standard errors adjusted for the firm effects. The sample spans from March 2004 to February 2011. Significance
levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
L.hvcds
L.rvc
L.jv
L.jp
1
2.727***
(0.358)
25.889***
(3.824)
0.695
(1.329)
5.311***
(1.252)
L.spreturn
2
-47.737**
(17.787)
79.178***
(24.801)
-72.863***
(18.886)
-3.486
(4.245)
23.469***
(7.670)
42.660***
(15.693)
69.826
(74.562)
-10.968
(35.149)
356.004
(255.695)
L.vix
L.shtbil
L.termspread
L.dps
L.sts
L.roe
L.lev
L.div
L.rf
Adj. R-squared
N
0.78
1880
0.15
1880
52
3
2.625***
(0.433)
24.666***
(3.610)
0.925
(1.602)
5.367***
(1.244)
12.372
(25.243)
-30.610
(30.245)
-118.373***
(25.726)
-3.820
(4.398)
1.276
(6.019)
-32.852*
(17.154)
7.487
(15.668)
3.527
(11.090)
45.966
(38.362)
107.054***
(26.588)
0.81
1880
Table XVIII
Extended Regression of the S&P BBB rated CDS spreads
This table presents the extended regression for S&P BBB rated companies. The explanatory variables are explained in tables I and II. In
parenthesis are the clustered standard errors adjusted for the firm effects. The sample spans from March 2004 to February 2011. Significance
levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
L.hvcds
L.rvc
L.jv
L.jp
1
1.154**
(0.473)
18.773***
(3.170)
-2.887***
(0.651)
7.134***
(1.043)
L.spreturn
-78.666***
(9.609)
123.218***
(13.402)
-97.069***
(15.576)
-1.301
(2.273)
11.326
(7.746)
20.527*
(11.282)
-9.415
(44.574)
30.270
(37.661)
479.549***
(167.308)
0.15
3196
L.vix
L.shtbil
L.termspread
L.dps
L.sts
L.roe
L.lev
L.div
Adj. R-squared
N
2
0.66
3196
53
3
1.428**
(0.607)
10.312***
(2.391)
-3.298***
(0.874)
7.380***
(1.178)
-70.370***
(8.508)
87.937***
(11.136)
-100.827***
(14.017)
2.354
(2.486)
17.881***
(6.381)
43.609***
(12.392)
-3.291
(41.210)
6.415
(14.500)
365.250***
(136.200)
0.65
3196
Table XIX
Extended Regression of the S&P BB rated CDS spreads
This table presents the extended regression for S&P BB rated companies. The explanatory variables are explained in tables I and II. In
parenthesis are the clustered standard errors adjusted for the firm effects. The sample spans from March 2004 to February 2011. Significance
levels : ∗ : 10%
∗∗ : 5%
∗ ∗ ∗ : 1%
L.hvcds
L.rvc
L.jv
L.jp
1
-37.952***
(0.496)
0.025
(2.348)
-13.560***
(0.063)
24.145***
(0.147)
L.spreturn
-301.196**
(152.884)
537.105***
(186.394)
80.412
(248.713)
-32.077
(30.636)
27.502
(17.663)
-93.080
(136.541)
-368.054*
(219.082)
583.111***
(195.161)
322.804***
(111.171)
0.80
188
L.vix
L.shtbil
L.termspread
L.dps
L.sts
L.roe
L.lev
L.div
Adj. R-squared
N
2
0.58
188
54
3
1.223
(10.119)
-0.907***
(0.350)
-29.778***
(4.749)
49.245***
(7.387)
-197.575**
(79.944)
388.809***
(115.003)
254.691
(316.710)
-39.239
(25.414)
-83.575***
(21.379)
-64.144
(128.313)
-136.422
(132.993)
672.744*
(398.945)
899.568***
(151.093)
0.93
188
Table XX
Determinants of CDS returns for the S&P AA rated companies
This table presents extended Regression for the CDS returns for the AA rated companies. The sample spans from January 2004 to September
2011. In parenthesis are the clustered standard errors adjusted for the firm effects. ***, **, and * denote the statistical significance at 1%, 5%
and 10% level respectively.
D.rvc
jm
jv
jp
1
9.785*
(4.110)
-0.466***
(0.033)
-0.544***
(0.021)
1.007***
(0.037)
D.spreturn
-171.180
(146.440)
342.273
(250.857)
-121.891**
(23.340)
8.763
(6.165)
-23.210
(12.722)
19.772
(32.549)
-656.224
(630.703)
-511.276
(511.293)
192.701
(152.189)
0.13
188
D.vix
D.shtbil
D.termspread
D.dps
D.sts
D.roe
D.lev
D.div
Adj. R-squared
N
2
0.04
188
55
3
7.827**
(2.207)
-0.533**
(0.146)
-0.727***
(0.090)
1.183***
(0.150)
-158.428
(131.933)
322.027
(230.870)
-115.033**
(26.241)
10.135
(9.990)
-25.979
(13.699)
20.279
(35.759)
-629.067
(565.912)
-503.353
(449.638)
174.062
(126.852)
0.15
188
Table XXI
Determinants of CDS returns for the S&P A rated companies
This table presents extended Regression for the CDS returns for the A rated companies. The sample spans from January 2004 to September
2011. In parenthesis are the clustered standard errors adjusted for the firm effects. ***, **, and * denote the statistical significance at 1%, 5%
and 10% level respectively.
D.rvc
ji
jv
jp
1
3.542*
(1.791)
9.453
(11.231)
0.482
(0.305)
0.606
(0.451)
D.spreturn
D.vix
D.shtbil
D.termspread
D.dps
D.sts
D.roe
D.lev
D.div
Adj. R-squared
N
0.01
1880
2
-118.348***
(23.444)
304.925***
(57.608)
-100.179***
(19.638)
19.826**
(7.435)
-56.175***
(14.121)
28.554**
(14.093)
-8.288
(10.780)
0.199
(17.528)
104.769
(110.081)
0.10
1880
56
3
2.912*
(1.648)
9.390
(11.295)
0.482
(0.309)
0.603
(0.452)
-116.187***
(23.217)
301.890***
(57.757)
-103.252***
(20.029)
20.693***
(7.177)
-54.338***
(14.025)
28.682**
(13.485)
-9.669
(10.588)
-4.699
(17.525)
106.579
(116.368)
0.11
1880
Table XXII
Determinants of CDS returns for the S&P BBB rated companies
This table presents extended Regression for the CDS returns for the BBB rated companies. The sample spans from January 2004 to
September 2011. In parenthesis are the clustered standard errors adjusted for the firm effects. ***, **, and * denote the statistical significance
at 1%, 5% and 10% level respectively.
D.rvc
ji
jv
jp
1
2.432**
(0.951)
-15.743*
(9.386)
-0.125
(0.089)
0.367***
(0.087)
D.spreturn
D.vix
D.shtbil
D.termspread
D.dps
D.sts
D.roe
D.lev
D.div
Adj. R-squared
N
0.01
3196
2
-145.419***
(17.693)
388.580***
(41.672)
-172.299***
(25.983)
17.660***
(5.166)
-54.019***
(9.917)
-20.519
(15.798)
24.245
(35.730)
-70.429***
(17.759)
4.381
(100.869)
0.16
3196
57
3
1.957**
(0.856)
-15.950*
(9.460)
-0.123
(0.090)
0.367***
(0.088)
-146.173***
(17.727)
386.822***
(41.274)
-175.296***
(26.190)
18.191***
(5.249)
-54.082***
(9.886)
-19.182
(15.483)
23.703
(35.308)
-70.220***
(18.010)
-12.129
(103.667)
0.16
3196
Table XXIII
Determinants of CDS returns for the S&P BB rated companies
This table presents extended Regression for the CDS returns for the BB rated companies. The sample spans from January 2004 to September
2011. In parenthesis are the clustered standard errors adjusted for the firm effects. ***, **, and * denote the statistical significance at 1%, 5%
and 10% level respectively.
D.rvc
jv
jp
jn
1
2.901*
(0.938)
1.044***
(0.005)
-1.581***
(0.007)
-0.962***
(0.003)
D.spreturn
-459.830**
(121.107)
1419.730**
(361.262)
94.820
(181.406)
0.299
(32.107)
-281.577
(135.747)
-284.294
(371.251)
43.761
(78.057)
264.703
(210.347)
50.258
(121.001)
0.25
188
D.vix
D.shtbil
D.termspread
D.dps
D.sts
D.roe
D.lev
D.div
Adj. R-squared
N
2
0.05
188
58
3
1.340
(0.828)
1.064***
(0.010)
-1.610***
(0.018)
-1.008**
(0.183)
-446.793**
(106.576)
1399.383**
(356.625)
39.370
(143.017)
3.625
(32.903)
-280.056
(143.380)
-283.698
(390.480)
64.918
(51.483)
-62.418
(250.752)
-52.503
(102.853)
0.30
188