Contagion and Excess Correlation in Credit Default Swaps
Mike Anderson1
May 2011
Abstract
This paper documents an increase in the correlations between credit default swap (CDS) spread
changes during the credit crisis and investigates the sources of that increase. One possible
explanation is that correlations increased because fundamental values became more correlated
during the crisis. However, I find that changes in the fundamental determinants of credit risk
account for only 20% of the increase in correlations on average. Further, I show that changes
in counterparty risk did not affect correlations during the turmoil. In contrast, I find that
changes in liquidity risk contributed to the increase in correlations; however, liquidity alone
cannot explain the full increase. Finally, I show that a systematic re-pricing of credit risk, as
evidenced by increased volatility in the default risk premium, was the main factor that amplified
correlations.
1
Contact information: Department of Finance, Fisher College of Business, Ohio State University, Columbus OH
43210; E-mail: anderson 1345@cob.ohio-state.edu. I am grateful for helpful discussion and suggestions from Jack
Bao, Phil Davies, Kewei Hou, Andrew Karolyi, Rose Liao, Bernadette Minton, Taylor Nadauld, Tim Scholl, René
Stulz, Jennifer Sustersic, Jérôme Taillard, and Scott Yonker. I thank seminar participants at the Ohio State
University, The Securities and Exchange Commission, Dimensional Fund Advisors, The University of New South
Wales, The Federal Reserve Board and George Mason University. I also thank the Dice Center for research support.
1
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1
Introduction
A well-documented phenomenon is that asset returns become more correlated in times of crisis.
However, there is much debate surrounding the interpretation of this result [see Forbes and Rigobon
(2002)]. One possible explanation is that comovement increases because fundamental values become
more correlated.2 Alternatively, correlations can increase for reasons beyond what can be explained
by fundamentals, a condition that Bekaert, Harvey and Ng (2005) refer to as contagion. In this
study, I find a significant increase in the comovement between CDS spreads during the credit crisis,
which was also observed by market participants. A recent Fitch survey of CDS dealers identified
contagion, along with liquidity and counterparty risk, as major factors that facilitated the spread
of the subprime turmoil. Specifically, they noted the speed at which CDS spreads widened along
with amplified correlations as indicators of contagion. The purpose of this paper is to investigate
why CDS correlations increased during the credit crisis. In particular, I investigate whether the
increase in correlations was a function of fundamental values or non-fundamental factors.
[INSERT Figure 1]
Figure 1 shows that the average pairwise CDS correlation spiked in July of 2007 and remained
high through the first quarter of 2009. I find that only a small fraction of this increase in correlation
can be explained by changes in the fundamental factors that determine credit risk. Therefore, I turn
to non-credit risk explanations. Specifically, I examine whether liquidity risk, counterparty risk,
or risk premiums increased correlations. The empirical results show no evidence that correlations
increased because of counterparty risk. In contrast, I find convincing evidence that the default risk
premium was the main factor that amplified correlations. Finally, I find that liquidity risk played
a significant, but smaller, role in increasing correlations.
In this study, I focus on a sample of 150 corporate investment grade CDS contracts, which are
included in one or more rolls of the CDX North American Investment Grade (CDX.NA.IG) index
8-12. Collectively, these contracts make up the most liquid sector of the CDS market during the
crisis. For each contract, I obtain daily, dealer-averaged, mid-quotes from July 2005 to March 2009.
From these data, I calculate daily CDS spread changes for each firm in the sample; the correlations
between these series are the subject of this paper.
As a first step, I document an increase in the comovement between CDS spread changes during
the crisis. To do this, I test the intraclass correlation coefficient, the average Spearman’s correlation
coefficient, and the average fraction of firms that move together each week [see Morck, Yeung and
Yu (2000)].3 I find that intraclass correlation increased from 20% prior to the crisis (July 31, 2007)
2
I define fundamentals as those factors implied by Merton (1974). A similar definition is used by Colin-Dufresne
Goldstein and Martin (2001) and Ericsson Jacobs and Oviedo (2009). I consider liquidity risk, counterparty risk,
and risk premiums to be non-fundamental influences.
3
Intraclass correlation is a measure of the average correlation among CDS spread changes and is closely related to
Pearson’s correlation. The main difference is that Intraclass correlation measures the comovement between CDS
2
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to 44% during the crisis (from July 31, 2007 to March 3, 2009). A similar result holds for the
average Spearman’s correlation, which more than doubled over this period. Finally, the average
fraction of firms with CDS spreads that move in the same direction each week increased from 73%
to 83% during the crisis. These changes are significant at the 1% level.
To better understand why CDS correlations increased, I investigate excess correlation, which
is the correlation between CDS spread changes that cannot be explained by changes in the fundamental determinants of credit risk. Estimating excess correlation requires a strong stance on
fundamental factors, as well as the form by which these factors determine CDS spreads. As noted
by Bekaert et al. (2005), this will always be a point of controversy.4 Therefore, I rely on the extensive credit risk literature to specify the model. Following Collin-Dufresne, Goldstein and Martin
(2001) and Ericsson, Jacobs and Oviedo (2009), I define a linear factor structure to control for
changes in the fundamental values of CDS contracts. Under this framework, excess correlation is
the correlation between factor model residuals [see Kallberg and Pasquariello (2008)].
Tests for a change in excess correlation show that it increased within the full sample, within
industry groups, and across industry portfolios. This confirms that contagion, which I define as an
increase in excess correlation, occurred during the crisis. My investigation begins with a firm-level
analysis, which shows that the intraclass correlation among OLS residuals, over the full sample and
within industry categories, increased significantly. Next, I aggregate to the industry level to examine
the excess correlation across six equally weighted industry portfolios of CDS contracts. This allows
for a more powerful test of the fundamental credit risk hypothesis. In the reduced dimension of
the industry analysis, I am able to estimate the fundamental model and the excess correlation in
a system of seemingly unrelated regressions (SUR). I find that controlling for the common factors
that drive credit risk reduces the increase in inter-industry correlation from 0.25 to 0.19 on average.5
This confirms that changes in credit risk cannot fully explain the increase in correlations. Moreover,
excess correlations increased significantly across all industry pairs, providing additional support for
the argument that common, non-credit factors amplified correlations.
After documenting contagion, I investigate why it occurred. Specifically, I examine whether
liquidity risk, counterparty risk, or risk premiums were significant channels of contagion during
the crisis. Currently, the evidence on liquidity risk in credit default swaps is mixed. Bongaerts,
de Jong and Driessen (2009) argue that expected returns for CDS contracts depend on expected
transaction costs in the CDS market. Acharya, Schaefer and Zhang (2008) show that heightened
liquidity risk in the bond market increased comovement in CDS returns around the downgrade of
spreads from a fixed point, the grand (pooled) mean, whereas Pearson’s correlation measures comovement relative
to the contract-specific mean.
4
Bekaert et al. (2005) study contagion in international equity markets. However, their observations regarding the
variance of fundamental factors and correlations are directly applicable to the CDS market.
5
Some of the factors used to control for credit risk can also be subject to non-fundamental effects. This may
complicate their interpretation as pure measures of credit risk.
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Ford and GM in 2005. Tang and Yan (2008) find that CDS spreads covary with liquidity proxies.
However, some authors have argued that CDS contracts are relatively immune to liquidity risk [see
Longstaff, Mithal and Neis (2005)]. In this paper, I focus on a set of highly liquid CDS contracts
with the purpose of isolating changes in correlations that are unrelated to liquidity premiums.
However, given the extreme conditions that persisted during the crisis, liquidity cannot be ignored
as a possible source of correlation.
To evaluate the role of liquidity risk, I add several liquidity proxies into the fundamental regressions. The average contract bid-ask spread, over all CDS contracts in the sample, captures
changes in transaction costs [see Stoll (1989); Huang and Stoll (1997); Amihud and Mendelson
(1986); Amihud (2002)]. To proxy for systematic liquidity premiums [see Pastor and Stambaugh
(2003); Acharya and Pedersen (2005)], I include the yield difference between the off and on-therun five-year Treasury notes, the spread between the three-month overnight index swap rate and
the three-month constant maturity Treasury rate [see Eichengreen, Nedeljkovic, Mody and Sarno
(2009)], and the spread between the general collateral repo rate and the three-month constant maturity Treasury rate [see Liu, Longstaff, and Mandell (2006)]. Further, Brunnermeier and Pedersen
(2009) argue that speculators’ access to external financing is an important determinant of asset
liquidity. Therefore, I include an index of lagged hedge fund returns to capture speculators’ funding
liquidity. Finally, Pu (2009) shows that CDS and bond liquidity are linked. To measure the effect
of bond liquidity, I use TRACE transaction data to calculate liquidity proxies (Amihud, volume,
and the number of trades per day) for bonds issued by reference entities (firms) in the sample.
Results of these tests show that liquidity contributed to the increase in correlations; however, it is
not the main source of contagion.
Next, I consider counterparty risk as a source of contagion. Eichengreen et al. (2009) show
that the credit risk of major U.S. and U.K. banks varied more during the crisis than in the period
leading up to it. These banks are major dealers in the CDS market. Therefore, if CDS spreads
carry a common counterparty risk premium, then the increased volatility of credit risk among CDS
dealers may have amplified correlations. Counterparty risk has been shown to be a significant
determinant of CDS spreads; however, there is controversy on the size of the effect [see Jorion
and Zhang (2009); Coval, Jurek and Stafford (2009); Arora, Gandhi and Longstaff (2009)]. To
investigate whether changes in counterparty risk increased correlations, I construct four measures
of banking sector credit risk. First, the overnight index swap spread (OIS) captures the credit
risk component of the TED spread. Second, the asset-backed commercial paper spread proxies for
banks’ access to short-term funding. Next, the return on a value-weighted portfolio of licensed
market-makers (CPstock) in the CDX.NA.IG index measures the financial health of CDS dealers.
Finally, I include two measures of dealer risk dispersion. CPDIF is the difference between the
maximum and median equity return among licensed market-makers in the CDX.NA.IG index,
and EXCPDIF is equal to CPDIF on days when it is above its 95th percentile. These variables
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capture potential concentrations in the demand for credit protection from a small group of high
quality dealers, which could lead to a reduction in market-making services. After controlling for
counterparty risk, I reevaluate the change in excess correlation. These results provide no evidence
that counterparty risk was a significant source of contagion.
Finally, I investigate the impact that risk premiums had on CDS correlations. Risk premiums are
an important component of the corporate credit spread [see Duffee (1999); Elton, Gruber, Agarwal
and Mann (2001); Driessen (2005)] and can vary drastically over time [see Berndt, Douglas, Duffie,
Ferguson, and Schranz (2008) - hereafter (“BDDFS”)]. Taken together, these findings suggest that
an increase in the volatility of changes in the default risk premium, which would likely occur as
investors adjust their risk appetites, can amplify the correlations between CDS spread changes. To
measure this effect, I estimate the time-varying default risk premium following BDDFS. Adding
changes in this measure back into the fundamental regression, I find that it explains approximately
18% of the time-series variation in CDS spread changes. More importantly, controlling for changes
in the default risk premium explains the majority of the increase in inter-industry excess correlation,
which suggests that risk premiums were the main source of contagion. This important result shows
that a systematic re-pricing of credit risk, rather than changes in market frictions, was the main
factor that amplified correlations during the crisis.
This paper contributes to three strings of literature. First, several authors have documented
a time-varying latent component in credit spreads [see Collin-Dufresne et al. (2001); Ericsson
et al. (2009); Collin-Dufresne, Goldstein and Helwege (2003); Giesecke (2004); Duffie, Eckner,
Horel, and Saita (2009)]. I contribute to this literature by investigating how this latent component
affected correlations in CDS spread changes during the credit crisis. Second, credit contagion
studies investigate how negative shocks propagate over credit spreads [see Giesecke and Weber
(2004); Allen and Carletti (2006); Jorion and Zhang (2007); Acharya et al. (2008); Longstaff
(2008); Jorion et al. (2009)]. This paper adds to the literature on credit contagion by considering
whether shocks were transmitted to investment grade corporate CDS spreads during the 2007-2009
turmoil. Finally, the literature on default correlation seeks to estimate and model the correlations
between default probabilities, losses given default, and defaults over time [see Zhou (2001); Allen
and Saunders (2003); de Servigny and Renault (2004); Das, Duffie, Kapadia and Saita (2007)]. To
the extent that CDS spreads reflect compensation for credit risk, this paper documents an increase
in the correlations between default probabilities and/or losses given default during the crisis.
The remainder of this paper proceeds as follows: Section 2 describes the data. Section 3 discusses
comovement and tests for contagion. In Section 4, I investigate liquidity risk, counterparty risk
and risk premiums as channels of contagion. In Section 5, I discuss the robustness of the results.
Finally, Section 6 concludes the paper.
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2
Data
2.1
Timing the Crisis
Most observers agree that the credit crisis began in the summer of 2007 [see Reinhart and
Rogoff (2008); Brunnermeier (2009); Beltratti and Stulz (2011)]. However, an exact date is difficult
to define. Fortunately, Figure 2 provides convincing visual evidence of a shift in the state of the
economy that occurred at the end of July 2007. Therefore, I define July 31, 2007 as the first day
of the crisis.6
[INSERT Figure 2]
The graph is even more specific in identifying the date when credit markets began to recover.
On March 9, 2009 there is a sharp drop in the average credit spread. Given the pronounced reversal
in CDS spreads, I define March 9, 2009 as the end of the crisis.
2.2
Credit Default Swap Premiums
A single name credit default swap is simply a contract that insures against deteriorations
in the credit-worthiness of a reference entity (bond issuer). The insurance purchaser (protection
buyer) pays a fixed quarterly premium (CDS spread or premium), which is quoted as a percent of
the notional value and can be directly interpreted as a credit spread [see Duffie(1999)]. End-of-day
CDS premium quotes, on five-year contracts, are obtained from Markit and Credit Market Analysts
(CMA). Mayordomo, Peña and Schwartz (2010) find a high degree of consistency between CMA
and Markit quotes. They also provide details on the data screening procedures for each database.
Because CDS contracts are flexible, it is important to ensure that CDS spreads, are quoted
on the same contract specification. Therefore, I choose to focus on the five-year maturity, which
is widely considered the most liquid, and has become standard practice in academic literature.
Furthermore, I use premiums on contracts that trade under the North American convention, which
standardizes many technical features of these contracts [see Casey(2009)].
To construct the sample, I begin by obtaining CDS premiums for all contracts included in
the CDX.NA.IG index rolls 8, 9, 10, 11 and 12. The CDX.NA.IG is constructed or “rolled”
every six months. Each roll includes 125 CDS contracts that dealer surveys determine to be
the most liquid contracts on the market. This criterion yields 159 unique contracts. Further,
I require that all contracts remain active for the duration of the sample period. This restriction
prevents changes in the sample composition from producing spurious changes in correlations, which
is especially problematic as credit events become imminent. In this case, the growing volatility of the
6
This date corresponds to the liquidation of Bear Stearns High-Grade Structured Credit Strategies Master Fund and
the Bear Stearns High-Grade Structured Credit Strategies Enhanced Leverage Master Fund. I also test different
crisis dates and find the results are robust to different specifications in July and June.
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affected contract premium gradually dominates the volatility of the portfolio, causing correlations to
decrease leading up to the credit event. After the event, there is a sharp correction in correlations
as the affected contract exits the sample. Freddie Mac, Fannie Mae, Washington Mutual and
Interactive Corporation are eliminated because they stop trading prior to the end of the sample.
Embarq, Expedia, ERP, and Time Warner Cable are also eliminated because their premiums are
not available until after the beginning of the sample period. Finally, I drop Residential Capital
Corp because the volatility of its contract premiums is an extreme outlier (it exceeds the 75th
percentile by 25 times the interquartile range). This leaves 150 CDS contracts.
2.3
Sample Characteristics
Panel A of Table I reports the average market-to-book ratio, cash holdings, profitability, total
assets, book leverage, and size over all firms in the sample for each year between 2005 and 2009.
These variables were found to be important determinants of credit-quality by Campbell, Hilscher,
and Szilagyi (2008). To gain a basic understanding of how these companies relate to other commonly
studied firms, I test whether each of the sample means, reported in the table, is equal to the
corresponding average over all firms in the CRSP/Compustat universe. These results suggest
that, on average, the firms in my sample are not remarkably levered or profitable, nor do they
have extraordinary growth prospects when compared to firms in the CRSP/Compustat merged
universe. In contrast, firms in the sample are relatively large cash-rich entities with high total asset
values relative to firms in the CRSP/Compustat universe. Interestingly, companies in the sample
maintained large cash reserves and high total asset values throughout the crisis, which may provide
some support for the argument that correlations increased for reasons other than changes in credit
risk.
[INSERT Table I]
Panel B of Table I shows the distribution of S&P long-term issuer credit ratings over time
(obtained from Compustat). These distributions are centered between BBB and BBB+ with a
slight shift toward speculative grade in 2009. This suggests that these firms are relatively high
quality issuers and remained so throughout the crisis.7
3
Comovement and Excess Correlation
In this section, I document an increase in the comovement between CDS spread changes during
the crisis and investigate whether that increase can be explained by changes in the fundamental
factors that drive credit risk. The discussion is split into four subsections: First, I formally test
7
Long-Term issuer credit ratings can drop below investment grade. This is because the index is constructed using
specific credits; whereas, the issuer ratings evaluate the credit quality of the company.
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for an increase in the comovement between CDS spread changes. Second, I develop a simple factor
model approach to decompose the raw correlation into fundamental and excess components. Third,
I describe the variable specification of the factor model. Finally, I review the results of the excess
correlation analysis, which includes the test for contagion.
3.1
Measuring Comovement
As a first step, I establish that raw CDS correlations increased during the crisis by evaluating
three different measures of aggregate association. Intraclass correlation extends Pearson’s pairwise
correlation to measure the degree of association among a set of random variables. Therefore, this
statistic can be interpreted as an aggregate Pearson’s correlation coefficient. Next, I evaluate the
average Spearman’s correlation (over all firm pairs). Lastly, I estimate the average fraction of firms
that move together each week following Morck et al. (2000). Formally, I test the null hypothesis that
the aggregate comovement statistic (intraclass correlation, Spearman’s correlation, or the fraction
of firms that move together each week), represented by ρ̄ below, prior to the crisis is greater than
or equal to the aggregate comovement statistic during the crisis:
Ho : ρ̄pre−crisis ≥ ρ̄crisis
Ha : ρ̄pre−crisis < ρ̄crisis
The results of these tests are reported in Table II. Columns one and two (respectively) of
Panel A show that intraclass correlation increased from 0.20 prior to the crisis to 0.44 during the
crisis, which is a significant increase at the 1% level. To ensure that this result is not driven by
a small group of firms that become highly correlated during the turmoil, I repeat the test within
each industry group. Intraclass sector correlations range from 0.14 to 0.30 prior to the crisis and
increase to between 0.40 and 0.54 during the crisis. The change, for each sector, is significant at the
1% level, indicating that correlations increased uniformly within the sample. However, intraclass
correlation is subject to distributional assumptions that may influence the outcome of these tests
[see Fisher (1921); Donner and Zou (2001)]. Therefore, I also include two nonparametric tests
[see Kendall and Smith (1939); Schucany and Frawley (1973)]. First, the change in the average
Spearman’s correlation coefficient, which is reported in Panel B yields similar results for the full
sample and at the industry level. Second, the average fraction of firms with CDS spreads that
move in the same direction each week increased from 73% prior to the crisis to 83% during the
crisis (columns one and two of Panel C respectively); the increase is statistically significant at the
1% level. At 73% (83%) the fraction seems relatively high when compared to an average Pearson’s
correlation of 0.20 (0.44). This is easily resolved by noting that the Morck et al. (2000) fraction is
bounded between 0.50 and 1.00, and therefore will naturally produce larger values.
[INSERT Figure 3]
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Finally, some additional evidence of a uniform increase in Pearson’s and Spearman’s correlation is provided in Figure 3, which shows a shift in the cross-sectional densities of Pearson’s and
Spearman’s correlation during the crisis.
[INSERT Table II]
3.2
Measuring Excess Correlation
To estimate excess correlation, I aggregate to the industry level, which reduces the noise
from firm-level CDS spreads and produces a clearer decomposition of CDS correlations. Moreover,
focusing on industry portfolios (described above) provides an additional control for the influence
of fundamentals. Jorion et al. (2007) document a significant intra-industry contagion effect in
daily CDS spreads around distress events. They argue that commonality in the expected future
cash flows among industry cohorts causes this contagion. Focusing on inter-industry correlations
mitigates the concern that fundamental intra-industry contagion increased correlations.
Unreported results show that industry CDS spread changes are autocorrelated and heteroskedastic, which can artificially inflate correlations. Therefore, I standardize portfolio spread changes
using autoregressive GARCH filters prior to examining inter-industry correlations. Similarly, all
economic factors used in subsequent tests are standardized using the same approach.
As a first step, I test for an increase in the raw correlations between CDS spread changes
of industry portfolios. These results, reported in Panel A of Table III, show that inter-industry
correlations increased significantly across all industry pairs.
Next, I decompose raw correlations into fundamental and excess correlations by assuming that
industry CDS spread changes follow a linear factor structure. Given this framework, the correlation
between spread changes can be decomposed as shown below:
h
0 i
E ∆S∆S 0 = E βF 0 + βF 0 + = βE F 0 F β 0 + E 0
(1)
∆S is an Nx1 vector of industry CDS spread changes. β is an NxK matrix of factor exposures, F
is a 1xK vector of factors, and is an Nx1 vector of model errors. The decomposition yields two
covariance matrices βE [F 0 F ] β 0 and E [0 ]. The excess correlation is obtained by extracting the
correlation matrix from E [0 ].
Equation 1 suggests that, all else equal, correlations can increase for three reasons: (i) an
increase in the exposure of industry CDS spread changes to a common factor, (ii) an increase in
the correlation between factors, and (iii) an increase in the correlation between unexplained CDS
spread changes (contagion).
An important implication of Figure 1 is that correlations remained high over the full crisis
period. A one-time shock to factor exposures, factor correlations, or excess correlation would not
explain this result. Therefore, it is more likely that a sustained increase in the exposure to a
common factor or a sustained increase in the variance of a common factor increased correlations.
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In the first case, if a single industry’s CDS spread changes become more exposed to changes in a
common factor, this will increase the correlation between the CDS spread changes of the affected
industry and those of all other industries.
Under the framework described above, an increase in the variance of a common factor is observed
through an increase in excess correlations. This is because all economic factors are standardized
using a GARCH autoregressive filter. Therefore, the variance of economic factors cannot increase
over the sample period. Although the factor standardization implies that the residual variance
is also constant, the composition of these variances can change. Therefore, a component of the
residual, for example a liquidity premium, can experience an increase in variance while the series
itself remains homoscedastic. In this case, a larger proportion of the residual variance is common
across industries, which increases excess correlation.
The decomposition in Equation 1 requires estimates of all factor exposures for each industry
portfolio, which are obtained from the standard feasible generalized least squares (FGLS) estimation of the system of seemingly unrelated regressions (SUR). The SUR estimation relaxes the
assumption of zero excess correlation implicit in the OLS implementation. From this estimation,
the excess correlation is calculated as the correlation between factor model residuals [see Kallberg
et al. (2008)].
After extracting factor model residuals, I perform three tests for a change in excess correlation.
Following Goetzmann, Li, and Rouwenhorst (2005), the first two test the null hypotheses that the
excess correlation matrix and the average excess correlation remain constant over the full sample
period. The third tests for an increase in the pairwise Pearson’s correlations between unexplained
CDS spread changes of industry portfolios.
3.3
Factor Model Specification
The factor model approach requires a strong stance on fundamentals, as well as the form
by which fundamentals effect changes in CDS spreads. Fortunately, prior research has uncovered
several factors that determine changes in corporate yield spreads. Because CDS spreads are closely
related to corporate yield spreads [see Duffie (1999); Blanco, Brennan, and Marsh (2005)], these
factors can also be used to explain changes in CDS spreads. Therefore, I base the factor model
specification on the work of Collin-Dufresne et al. (2001) who investigate the determinants of
bond yield spreads changes implied by Merton (1974).
8
In addition, I include several systematic
variables designed to capture changes in loss given default, which is largely a function of the state
of the economy [see Altman and Kishore (1996); Allen et al. (2003); Schuermann (2004); Altman,
Brady, Resti, and Sironi (2005)]. The final specification is shown below.
8
Colin-Dufresne et al. (2001) argue that the model does not perform well in explaining changes in bond yield spreads.
However, Ericsson et al. (2009) show that a similar model performs well in explaining CDS spread changes. Their
specification includes leverage, which is not available daily. Instead, I use daily equity returns to proxy for the
overall financial health of the industry.
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∆S = α + β1 (∆RF 3M ) + β2 (∆SLOP E) + β3 (V IX) + β4 (SP 500) + β5 (HB)
+β6 (∆DEF ) + β7 (SM B) + β8 (HM L) + β9 (IN DRET ) + β10 (∆IN DV OL)
(2)
+Icrisis [αc + β1,c (∆RF 3M ) + β2,c (∆SLOP E) + β3,c (V IX) + β4,c (SP 500)
+β5,c (HB) + β6,c (∆DEF ) + β7,c (SM B) + β8,c (HM L) + β9,c (IN DRET )
+β10,c (∆IN DV OL)] + Where RF3M is the three-month constant maturity treasury rate from the Federal Reserve,
SLOPE is the difference between the five year constant maturity treasury rate and RF3M, VIX
is the option-implied volatility index from the Chicago Board of Exchange (CBOE), SP500 is the
daily return on the S&P 500 index from the Center of Research in Securities Prices (CRSP), HB
is the daily return on a value weighted portfolio of major U.S. home builders (SIC code 1521)
from CRSP, SMB and HML are the small cap and value premiums respectively obtained from the
French data library, INDRET is the daily equity return on an equally weighted industry portfolio
constructed from firms in the sample (the six industry classifications are discussed above), INDVOL
is the daily industry equity return volatility calculated using a GARCH model.
To explain the change in CDS spreads, I take the change in each of the variables defined above
with the exception of return series. This is consistent with Collin-Dufresne et al. (2001). Because
many of these variables are highly correlated, I orthogonalize all market variables (SMB, HML,
HB, VIX, and INDRET) to the S&P 500 return and focus on their relative effects. Finally, I allow
factor exposures to shift during the crisis to avoid biasing the estimated excess correlation; the final
model specification is given in Equation 2. Following the notation from Equation 1, βj and βj,c (j
= 1:10) are Nx1 vectors of factor exposures for factor j prior to the crisis and its marginal change
during the crisis respectively.
For brevity, estimates of the factor model are left unreported. However, some key results are
worth discussing. First, The S&P 500 return is negative and significant and becomes more so during
the crisis, for all industry portfolios, which is consistent with its interpretation as a state variable
(as the state of the economy deteriorates, credit risk increases, and CDS spreads widen). Second,
the change in the default premium (∆DEF) is positive and significant for all industry portfolios
prior to the crisis and does not change significantly during the crisis.
The value premium (HML) is a significant determinant of CDS spread changes for four of the
six industry portfolios prior to the crisis. However, during the crisis HML is not a significant
determinant of CDS spread changes. This may provides some evidence that the CDS market
detached from the equity market over this period.
Finally, R squareds imply that changes in the fundamental factors that drive credit risk account
for approximately 20% of the time-series variation in CDS spread changes. Importantly, when the
model is estimated on each sub-period, R squareds increase from approximately 10% to 26% during
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the crisis. This suggests that the increase in excess correlation is not driven by a breakdown of the
fundamental model.
3.4
Contagion Results
Having controlled for credit risk, I now investigate whether inter-industry excess correlation
increased during the crisis; results of these tests are reported in Table III. First, I test the pairwise excess correlations between industry portfolios individually. These results show that excess
correlation between all industry pairs increased significantly. Next, I test the null hypotheses that
the excess correlation matrix and average excess correlation remained constant over the full sample
period. P-values reported in the lower panel show that these hypotheses are both rejected at the
1% level. The factor model specification is critical to this investigation. Therefore, I repeat the
analysis for several different models, which are described in Section 5, and find no notable change
in the result.
The uniform increase in inter-industry excess correlation provides sufficient evidence to conclude
that contagion occurred. Moreover, this result supports the argument that a common non-credit
component amplified correlations during the crisis. Therefore, I investigate potential channels of
contagion in the next section.
[INSERT Table III]
4
Channels of Contagion
The evidence presented in the previous section shows that approximately 80% of the increase
in correlations cannot be explained by the fundamental determinants of credit risk. Furthermore,
and of particular interest to this paper, the tests indicate that the excess correlation increased
across all industries, which is consistent with the influence of a common non-credit component.
In this section, I explore how changes in liquidity risk, counterparty risk, and the default risk
premium increased the correlations between CDS spread changes. Furthermore, I formally test
each channel of contagion, which allows me to comment on the degree to which each channel
increased correlations.
4.1
Liquidity Contagion
The premise of this argument is that a sustained increase in the volatility of common liquidity
premiums can increase CDS correlation.9 Liquidity premiums in the CDS market can vary for
9
If bonds are perfectly liquid, an exact arbitrage relation with CDS contracts would prevent liquidity premiums from
entering CDS spreads. However, bonds are not perfectly liquid [see Dick-Nielsen, Feldhutter and Lando (2009)]
and an exact arbitrage between bonds and CDS contracts can rarely be achieved.
12
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several reasons. First, changes in the supply of or demand for credit protection can cause transaction
costs to become more volatile. This is because market-makers will attempt to hedge their exposure
to inventory risk and asymmetric information risk by adjusting the bid-ask spread [see Stoll (1989);
Huang et al. (1997)]. During the crisis, investors and dealers likely experienced increased volatility
in their need to hedge credit risk, which may have increased the variance of liquidity premiums.
Bongaerts et al. (2009) propose a model in which CDS expected (synthetic) returns depend on
transaction costs in the CDS market. Moreover, they argue that this effect can be captured in the
bid-ask spread. Therefore, I include daily changes in the average bid-ask spread, over all contracts
(BIDASK), to measure changes in market-wide CDS liquidity and changes in the average industry
bid-ask spreads (IBIDASK) to control for changes in industry-specific liquidity. The direction
of this relation depends on differences in the characteristics of protection buyers and sellers [see
Bongaerts et al. (2009)].
Second, the liquidity of CDS contracts may depend on liquidity in the bond market. This
is because CDS contracts can be used as a substitute for bonds to trade credit risk. Therefore,
when bonds become difficult to trade, the CDS market may experience increased volatility in the
quantity of credit protection supplied or demanded [see Acharaya et al. (2008)].10 To capture this
effect, I obtain transaction prices and volumes, from TRACE, for each firm’s bonds that traded
over the sample period (these data are filtered according to Dick-Nielsen (2009)). I consider only
those bonds with a minimum maturity greater than five years and a maximum maturity of less than
twenty years over the sample period. This eliminates bonds that would not likely be hedged using
a five-year CDS contract. I then calculate daily Amihud measures for each bond [see Pu (2009);
Dick-Nielsen, Feldhtter and Lando (2009)] in the sample and create an aggregate index (AMIHUD),
which increases with illiquidity.11 Next, I count the number of bond transactions that occurred
each day in each industry and average these counts to obtain the variable NTRADE. Using the
same procedure, I also calculate the average principal amount (VOLUME) traded each day across
industries. Changes in these measures proxy for changes in bond trading activity, which can be
either positively or negatively related to CDS spread changes. For example, an increase in volume
may suggest that bonds are easier to trade; this could relieve hedging pressure and reduce liquidity
premiums in CDS spreads. Alternatively, the increased volume may relate to higher expected
inventory costs, which could lead dealers to reduce their market-making services in both the CDS
and bond market.
10
This requires dealers to be more willing to trade in the CDS market than in the bond market, which could
occur because of differences in transparency. Bond trades require mandatory disclosure but CDS trades do not.
Transparency of bond trading reduces transaction costs. Therefore, dealers may be able to charge higher transaction
costs in the CDS market than in the bond market, which would make them more willing to trade CDS contracts.
11
I calculate the Amihud measure for bonds that trade more than 100 times over the sample period. Bond-days
with fewer than 2 trades are replaced with missing values. To arrive at the final measure, I first average bond
measures to the firm-level. Then I average firm measures to the industry-level. Finally, I average over industries.
This procedure ensures that each industry is equally represented in the final aggregation.
13
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Third, authors have argued that liquidity is a state variable, which suggests that CDS spreads
should contain a component that compensates for systematic liquidity risk [see Pastor et al. (2003);
Acharya et al. (2005)]. The high level of uncertainty regarding liquidity during this period likely
increased the volatility of systematic liquidity premiums. Therefore, I include three measures of
market-wide liquidity. The first is the difference between the yield of the off and on-the-run fiveyear Treasury notes (ONOFF), which is calculated using yields on end of day quotes obtained from
Datastream [see Fleming (2003)]. A difficulty with this measure is that it may contain “flight-toquality” premiums or be subject to specialness effects that arise from the supply of or demand
for the on/off-the-run five-year Treasury note. Therefore, I include the repo spread (ONREPO),
which Liu et al. (2006) argue is less sensitive to these effects. The repo spread is constructed by
subtracting the three-month constant maturity Treasury rate (RF3M) from the three-month general
collateral repo rate obtained from Bloomberg. The third measure is the liquidity component of the
TED spread (OISTB), which is the difference between the overnight index swap rate (OIR) and
RF3M [see Eichengreen et al. (2009)].
Finally, liquidity in the CDS market can suffer if speculators reduce their trading activity [see
Brunnermeier et al. (2009)], which can increase and sustain correlations at a higher level for two
reasons. First, speculative trading in the CDS market depends on investors’ access to funding
(funding liquidity). This is because CDS contracts commonly contain collateral agreements, which
require the exchange of capital at inception.12 Therefore, an increase in the volatility of speculators’
funding liquidity can magnify correlations by increasing the volatility of liquidity premiums. Second,
collateral agreements provide for incremental payments (collateral calls) throughout the life of the
contract, which are contingent on the credit quality of the counterparty and value of the contract.
Collateral calls can represent substantial costs to speculators.13 Therefore, speculative trading may
have varied more during the crisis as investors attempted to manage their growing mark-to-market
risk.
To capture the effects of funding liquidity, I identify hedge funds as the major speculators in the
CDS market. According to the 2007 estimates from Bank of America, banks and hedge funds are
the largest participants in the CDS market with 40% and 31% (59% and 28%) respectively of buy
(sell) side trading activity [see Duffie (2008)]. However, banks mainly trade as dealers. Therefore,
hedge funds are clearly the largest non-dealer participants in the market, making up approximately
50% of non-dealer buy and sell side trading activity. Therefore, I focus on measuring hedge funds’
access to capital.
One measure of hedge funds ability to obtain external financing is the hedge fund return itself.
12
The initial payment, which is referred to as the Independent Amount, is outlined in the 2005 ISDA Collateral
Guidelines. According to the 2009 ISDA Margin Survey, 74% of contracts executed in 2008 were subject to
collateral agreements. Further, the dollar value of collateral used increased from approximately $2 trillion to $4
trillion in 2008
13
An example of such a shock to funding liquidity can be found in the downgrade of AIG in September 2008, which
triggered collateral calls that exceeded $30 billion by the end of October.
14
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Boyson, Stahel and Stulz (2010) argue that extreme negative hedge fund returns are associated with
funding liquidity shocks. Dudley and Nimalendran (2009) show that increased correlations between
hedge fund returns relates to a decrease in funding liquidity as measured by margins on futures
contracts. Therefore, I obtain daily index returns for the Equity Market Neutral, Fixed Income
Arbitrage and Relative Value Arbitrage hedge fund styles from Hedge Fund Research (HFR) and
Bloomberg, and create an equally weighted return index. Since raw returns are a noisy measure of
hedge funds’ funding liquidity, I calculate the excess return as the residual from a market model
regression. Although the results are robust to the choice of raw or excess hedge fund returns, the
excess return is likely a stronger measure of funding liquidity. The final measure, HEDGE, is lagged
one period to limit the influence of hedge funds’ CDS holdings.
As with other potential explanations, I evaluate the role of liquidity in two steps. First, I
control for liquidity in the fundamental regression. Second, I reevaluate the correlation between
factor model residuals to test if liquidity was a significant channel of contagion.
Results of the test for liquidity contagion are reported in Panel A of Table IV. These results show
that changes in systematic liquidity, as measured by ∆ONOFF, ∆OISTB, and ∆ONREPO, as well
as changes in bond market liquidity, as measured by ∆AMIHUD, ∆VOLUME, and ∆NTRADES,
do not determine CDS spread changes prior to the crisis. In contrast, I find that CDS spread changes
are significantly related to changes in the average bid-ask spread over this period for four of the six
industry portfolios. This is consistent with the findings of Tan et al. (2008) and Bongaerts et al.
(2009). During the crisis, industry specific liquidity may have played a larger role in determining
CDS spread changes, which is evidenced by a significant change in regression coefficients for three of
the industry portfolios. These industry effects could either increase or decrease excess correlations.
AMIHUD coefficients also changed significantly in the crisis, which reflects a shift in the relationship
between CDS and bond market liquidity. However, the absolute value of these coefficients remained
constant. Therefore the change should not affect excess correlations.
CDS spread changes became significantly more positively related to lagged hedge fund returns
during the crisis. The positive coefficient indicates that a negative hedge fund return is associated
with a negative change, or decrease, in the CDS spread. This suggests that a reduction in hedge
funds’ access to capital lowers the liquidity premium for protection buyers and increases the liquidity
premium for protection sellers. Such a shift is consistent with an increase in the quantity of
protection supplied relative to the quantity of protection demanded [see Bongaerts et al. (2009)].
Therefore, the positive sign supports a funding liquidity argument if, all else equal, a decrease
in hedge funds’ speculating activity reduces the quantity of protection demanded by more than
the quantity of protection supplied. When faced with funding constraints, hedge funds will likely
decrease their buy and sell side activity equally due to the collateral requirements (the independent
amount) that must be posted on either side of the trade. Given that hedge funds were net protection
buyers at the time, a shock to their funding liquidity (negative return) will likely create a surplus
15
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in the supply of credit protection and decrease the CDS premium.14
The period following the failure of Lehman Brothers is generally considered a time of severe
illiquidity in financial markets. Therefore, I reestimate the above regressions, with an additional
interaction term that allows liquidity exposures to change in the month following the Lehman
Brothers bankruptcy (Sept. 15, 2008 - Oct. 15, 2008 - hereafter “the Lehman Brothers month”).
Surprisingly, unreported results show that the exposures to liquidity proxies do not change significantly, relative to their crisis values, in the Lehman Brothers month. To better understand this
result, I reestimate the regressions, in the same SUR setting, using each liquidity proxy individually
as the only explanatory variable. These univariate regressions show that BIDASK, NTRADES, and
VOLUME are significant determinates of CDS spread changes prior to the crisis. Moreover, the
regression coefficients, for each of these variables, increased significantly during the crisis across all
industries in the Lehman Brothers month. These regressions recover the expected result that CDS
contracts carried a larger liquidity premium after the failure of Lehman Brothers. However, this
effect is largely subsumed by the fundamental model, which is not surprising given that liquidity
across several markets suffered in response to the Lehman Brothers event.
[INSERT Table IV]
The above analysis shows that changes in the bid-ask spread, hedge fund returns and bond
liquidity are significant determinants of CDS spread changes, but systematic liquidity is not. It is
important to interpret the reported results relative to liquidity in other markets. This is because
market-based proxies for fundamentals can carry liquidity premiums, which may absorb the effect
of liquidity in CDS contracts. The presence of such an effect is apparent from the results of the
unreported univariate regressions.
I now turn to liquidity contagion. To address this question, I reevaluate the increase in excess
correlation using residuals from the fundamental model with liquidity controls. These results are
reported in Panel B of Table IV and show that pairwise excess correlations still increase significantly
across all firm pairs. Furthermore, the tests for a constant excess correlation matrix and for constant
average correlation both reject the null hypothesis at the 1% level. This suggests that changes in
liquidity do not explain the full increase in excess correlation documented above. However, it
may still make a marginal contribution. Therefore, I calculate a difference-in-difference matrix by
subtracting the matrix in Panel B of Table III from the matrix in Panel B of Table IV. If there
is a significant reduction in the change in excess correlation after controlling for liquidity, then
values in the difference-in-difference matrix will be positive and significant. The results of this test
show that controlling for liquidity offers no significant reduction in the increase in inter-industry
excess correlations across most industry pairs. The financial sector is an exception. Its CDS spread
14
Hedge funds are required to post the Independent Amount on either side of the trade. Therefore, it is reasonable
to assume that hedge funds would decrease buy and sell side activity by roughly equal amounts if they became
impaired.
16
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changes experienced a significantly smaller increase in excess correlation with three of the five other
industry portfolios after controlling for liquidity. This suggests that financial sector CDS contracts
became less liquid during the crisis.
Next, I repeat the tests described above using residuals from the fundamental model with
marginal changes on liquidity variables estimated in the Lehman Brothers month and several other
time intervals. Unreported results are equivalent to those of the previous tests. The important
conclusion from the liquidity analysis is that changes in liquidity premiums, particularly for the
financial sector, (in excess of what may be implied by equity markets) are important determinants
of CDS spread changes and can effect correlations. However, changes in liquidity alone cannot
explain the full increase in excess correlation documented above.
4.2
Counterparty Risk Contagion
The risk that counterparties will not be able to uphold contractual obligations can system-
atically affect CDS spreads for at least three reasons. First, an increase in the credit risk of a
CDS protection seller decreases the value of the insurance guarantee they can provide [see Arora
et al. (2009)] and, therefore, reduces the CDS premium they are able to charge. I refer to this
effect as the “insurance value mechanism”. Second, an increase in counterparty risk can reduce
market participants’ willingness to trade with each other; a condition that Brunnermeier (2009)
refers to as “gridlock”. Gridlock is a side effect of the CDS market structure (over-the-counter),
which transfers credit risk from the seller to the final bearer of the risk through a series of offsetting transactions. This creates a complex and fragile network of interdependence among dealers.15
In gridlock, dealers’ refusal to trade with each other causes this network to breakdown, making
contracts more difficult to offset and increasing liquidity premiums.
Both gridlock and the insurance value mechanism suggest that an increase in the volatility
of credit risk among dealers can increase excess correlation. Eichengreen et al. (2009) argue
that the credit risk of large investment banks, who are major dealers in the CDS market, varied
substantially more throughout the crisis. To evaluate the effect that the gridlock and insurance
value mechanisms had on correlations, I relate CDS spread changes to four measures of bank sector
credit risk. First, I include the credit risk component of the TED spread. Eichengreen et al. (2009)
argue that the Overnight Index Swap Rate (OIR) can be used to decompose the TED spread into
its credit risk and liquidity risk components. In this decomposition, TED = (LIBOR - OIR) +
(OIR - TBILL), the difference between LIBOR and OIR is the Overnight Index Swap Spread (OIS),
which measures banking sector credit risk. Hence, the difference between OIR and the three-month
constant-maturity Treasury yield captures the liquidity component of the TED spread.
Banks’ access to short-term funding is also an important determinant of dealers’ credit risk.
15
Some evidence is provided in the March 10, 2009 testimony of Robert Pickel, CEO of ISDA, to Congress that 86%
of the Depository Trust & Clearing Corporation (DTCC) trades were dealer-to-dealer trades.
17
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Prior to 2007 banks took on large positions in long-term structured finance products, such as
residential mortgage backed securities (RMBS), which they financed using short-term asset-backed
commercial paper. This maturity mismatch caused banks to rely heavily on the asset-backed
commercial paper market to meet short-term funding requirements [see Kashyap, Rajan, and Stein
(2009); Brunnermeier (2009); Acharya and Richardson (2009)]. To capture changes in the cost
of short-term funding, I construct my second measure, the asset-backed commercial paper spread
(ABCP), which is the spread between the yield on 90 day asset-backed commercial paper obtained
from Bloomberg and RF3M.
Third, I create a value-weighted index of dealers’ stock returns (CPstock), which is a direct
measure of dealers’ financial health. I define dealers as the sixteen banks that are licensed by the
index administrator (Markit) to make the market in the CDX.NA.IG index. The data used to
construct the dealer stock return index is obtained from Datastream for each dealer as long as
equity returns are available.
Finally, CDS correlations can increase if credit risk increased inconsistently across dealers. In
the extreme, this would produce a group of high-quality dealers and a group of low-quality dealers.
In this case, the demand for protection from participants seeking to enter new positions will be
concentrated with high-quality dealers. This is because, even with collateral agreements, protection
buyers can experience losses from the failure of a CDS counterparty.16 Hence, they have incentives
to deal with low-risk dealers. Moreover, if protection buyers hold existing contracts with high-risk
counterparties, they may choose to novate (transfer) their contracts to a more stable dealer. This
would further increase the quantity of protection demanded from a small group of high-quality
market-makers. The additional strain would likely cause dealers to reduce the extent of their
market-making services. Therefore, CDS spread changes may have become more related to the
degree of risk dispersion among dealers. To capture the cross-sectional variation in dealers’ credit
risk, I create a measure of risk dispersion among CDS market-makers. I use individual equity
returns for the sixteen dealers defined above (for as long as equity returns are available) to measure
the credit risk of each dealer. Next, I take the log of the difference between the maximum and
median daily return as a measure of dealer risk dispersion (CPDIF). The median return measures
the “normal” credit risk in the pool and the maximum return measures the risk of the highest
quality dealer. The effect of dealer risk dispersion will be most severe on days when risk dispersion
is large. Hence, I include an interaction dummy variable (EXCPDIF) that is equal to CPDIF on
days when the difference between the median and maximum return is above its 95th percentile.
[INSERT Table V]
16
Losses can occur for two reasons. First, the protection buyer may have to pay to reestablish a comparable contract
with another dealer. In this case, if the value of the collateral posted does not fully cover these costs, the protection
buyer must seek compensation from the bankruptcy estate. Second, if the contract triggers at the same time the
protection seller defaults, then additional costs (over the value of collateral posted) must be claimed from the
bankruptcy estate.
18
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Regression coefficients for counterparty risk variables, which are added to the fundamental
model, are reported in Panel A of Table V. They show that changes in counterparty risk are not
significant determinants of CDS spread changes prior to the crisis. Furthermore, the marginal
change in the exposure of CDS spread changes to counterparty risk is insignificant for all proxies.
This result suggests that counterparty risk is not a significant determinant of CDS spread changes,
which is consistent with the findings of Arora et al. (2009).17
Having controlled for counterparty risk, I now turn to the question of contagion. The results
of these tests are reported in Panel B of Table V. Tests of pairwise excess correlation between
industry portfolios show that controlling for counterparty risk does not explain the increase in excess
correlation. Further, the null hypotheses of constant average excess correlation and a constant
correlation matrix are both rejected at the 1% level. Moreover, the difference-in-difference matrix,
reported in Panel B, shows that, relative to fundamentals, counterparty risk offered no significant
contribution to the increase in correlations. As with the liquidity analysis, I repeat these tests on
the month following the Lehman Brothers Bankruptcy with no notable change in the results. This
suggests that counterparty risk contagion did not significantly affect CDS spread changes during
the crisis.
4.3
Risk Premium Contagion
In this subsection I investigate whether changes in default risk premiums amplified CDS cor-
relations. Prior work has shown that risk premiums make up a substantial portion of corporate
credit spreads [see Duffee (1999); Elton et al. (2001); Driessen (2005)] and can vary drastically
over time [see BDDFS]. These empirical findings suggest that a prolonged increase in the volatility
of changes in the default risk premium is capable of explaining the observed increase in excess
correlation. The volatility of changes in the default risk premium would likely increase if investors
continually adjusted their risk appetites, perhaps in response to large mark-to-market losses, over
the crisis period. Hence, the default risk premium provides a likely explanation for the higher level
of correlation.
Some evidence that default risk premiums varied more in the crisis can be found in the December
2008 Financial Stability Review issued by the European Central Bank (ECB). According to the
ECB, the market price of default risk was low (at approximately 5 basis points) and remained
relatively constant prior to the crisis. However, in August of 2007 the risk premiums began to
increase and became much more volitile. The volatility remained high throughout the end of 2008.
An increase in the volatility of changes in the default risk premium alone is not sufficient
to explain the observed increase in excess correlation. In addition, risk premiums in the CDS
17
They find evidence of statistically significant counterparty risk in the cross section of dealer quotes; however, the
effect only appears in quotes from U.S. issuers and is not economically large. Therefore, counterparty risk is not
likely to be present in the dealer-averages.
19
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market must vary independently from those in the equity market, which may be captured by the
fundamental model. There are at least two reasons why risk premiums in the CDS market can
differ from those in the equity market. First, if the CDS market is segmented or became segmented
during the crisis, then risk premiums in the CDS market would be determined independently from
those in other markets. Second, CDS spreads contain a jump-to-default risk premium that is not
present in equity returns [see Saita (2006); Berndt, Lookman, and Obreja (2007)].18
Recent investigations of the credit crisis suggest that risk premiums may play a role in amplifying
correlations in credit derivatives. For example, Longstaff (2008) shows that contagion spread from
the subprime market, represented by the ABX index, to different asset classes such as stocks,
corporate bonds and Treasuries during the credit crisis. In a related paper, Kim, Loretan and
Remolona (2009) use Moody’s EDF and principal components (extracted from various CDS indices)
to argue that changes in risk premiums were responsible for a general widening of CDS spreads in
Asian credit markets (38 foreign references) between 2007 and 2009.
The default risk premium compensates investors for bearing exposure to two basic sources of
risk. The first is diffusion or systematic risk [see Duffee (1999)], which is the non-diversifiable risk
associated with macroeconomic conditions. This component of the default risk premium is closely
related to the premiums demanded by investors in the equity market [see Elton et al. (2001)].
Second, investors require a premium for bearing exposure to the default event itself (the jump-todefault risk premium) [see Jarrow, Lando and Yu (2005); Driessen (2005); BDDFS (2008)].19 This
is measured as the ratio of the risk neutral to the physical probability of default and is exclusive to
defaultable securities. A ratio in excess of one indicates that investors require a positive premium
for exposure to event risk. This can be justified in two ways. First, if the default event is specific
to a particular firm, the associated risk can be priced if event risk is not fully diversifiable [see
Jarrow et al. (2005)]. Alternatively, the jump-to-default risk premium can compensate investors
for exposure to contagious events [see Collin-Dufresne, et al. (2010)]. In either case, an increase in
the variance of this premium is capable of amplifying correlations.
To investigate whether an increase in the variance of the jump-to-default risk premium increased
CDS correlation, it is necessary to obtain a time-varying measure of this premium. To do this,
I follow BDDFS who use Moody’s Expected Default Frequency (EDF) to measure the physical
probability of default. Moody’s KMV provide a firm’s EDF, which is an estimate of the firm’s
default probability, for most publicly traded companies over several horizons. I use the five-year
horizon to match the CDS maturities. Crosbie and Bohn (2002) and Kealhofer (2003) provide more
details on the KMV model and fitting procedure for the EDF.
18
The default spread used in the fundamental model may also capture some of the influence from risk premiums.
However, the default spread is mainly a measure of aggregate business conditions and not a proxy for jump to
default risk [see Chen (1989); Chen Roll Ross (1986); Fama and French (1989) and Keim and Stambaugh (1986)].
19
I am aware that recovery risk will also command a premium. However, research has shown that recovery is closely
associated with macroeconomic conditions. Therefore, this premium is likely captured by the systematic component
of the default risk premium.
20
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Daily EDF data is available beginning on June 1, 2006. Therefore, I adjust the pre-crisis
period, for the risk premium analysis, to begin on this date. I then reevaluate the change in excess
correlation using the adjusted sample periods. Unreported results show that pairwise correlations
still increase significantly across all industry pairs.
Following BDDFS, I estimate the panel regression model shown in Equation 3. I modify the
original estimation slightly by adding firm fixed effects, which offer stronger controls for the crosssectional variation in expected loss given default.20 Consistent with their specification, Dt is a time
fixed effect, which is equal to one on day t. This yields estimates γˆj for each day j; the inverse log
of these parameters eγ̂j is an estimate of the proportional risk premium (RP). That is, eγ̂j is the
ratio of the fitted CDS spread for a firm on day j to that of the average firm on June 1, 2006 (the
reference time period).21
ln(CDSi ) = α̂ + β̂ln(EDFi ) +
X
γ̂j Dt + zi
(3)
j
The object of this estimation is to obtain an accurate measure of the jump-to-default risk
premium in CDS spreads. Intuitively, one can think of this as the ratio of the risk neutral to the
physical probability that a systematic jump will occur.22 The most direct method of obtaining
this premium is to estimate Equation 3 using all contracts in the sample. However, this assumes
that all CDS spreads are unaffected by other non-credit risk factors, which is inconsistent with the
results from the liquidity contagion analysis. The presence of additional premiums could bias the
estimation. For example, evidence presented in Section 4.1 suggests that CDS spreads for firms
in the financial sector became more exposed to liquidity risk during the crisis. Because this effect
is concentrated in the financial sector, it will not uniformly increase correlations. However, the
presence of a contaminated CDS spread in the estimation of Equation 3 could bias estimates of the
jump-to-default risk premium.
Alternatively, one could estimate the jump-to-default risk premium using a subset of contracts.
This is because the premium associated with a systematic jump will be present in the CDS spreads
of all contracts if the event is priced. This follows directly from the definition of a priced event.
20
This justification for fixed effects is valid to the extent that expected loss given default has a component that varies
over industries or firms and is constant over time.
21
Jarrow et al. (2005) show that, under no-arbitrage conditions, the jump-to-default risk premium is equal to the
ratio of the risk neutral to the physical probability of default. This assumption may have been violated in the
months following the failure of Lehman Brothers. However, the results still hold after dropping September and
October 2008 from the sample.
22
This interpretation violates the conditions outlined by Jarrow, Lando, and Yu (2005) by linking firms’ default
intensities to a single unpredictable event, which is a special case of the Jarrow and Yu (2001) model. Alternatively,
one can think of this as a contagion premium. This is modeled by Collin-Dufresne, Goldstein, and Helwege (2010).
A systematic jump-to-default risk premium could arise from the risk that a major counterparty defaults. This would
be more adequately classified as counterparty risk. However, in Section 5, I find that the increase in correlations is
not driven by extreme events, which minimizes concerns about this potential contaminate.
21
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Following this intuition, I choose a subset of firms that is likely to yield the most precise
estimate of the jump-to-default risk premium. To construct this subsample, I begin by removing
firms that are in relatively poor financial health at the beginning of the crisis. This improves the
performance of the EDF by eliminating firms that are likely to experience a large jump in their
default probabilities. Healthy firms are defined as the seventy five firms with the lowest conditional
five-year default probabilities (EDF) at the end of July 2007.
Next, I identify healthy firms with CDS spreads that are relatively robust to liquidity risk. To
do this, I estimate a pre-crisis liquidity beta for each healthy firm by regressing individual CDS
spreads (levels) against the average daily bid-ask spread (over all contracts in the sample) prior to
the onset of the crisis. This yields seventy five pre-crisis liquidity betas.
Finally, the jump-to-default risk premium is estimated using the twenty CDS spread series,
referencing healthy firms, which have the smallest pre-crisis liquidity betas. To avoid a hardwired
result, I estimate the risk premium individually for each industry by omitting members of the
relevant industry.
After estimating the risk premium, I return to the question of excess correlation. This requires a control for the influence of risk premiums on CDS spread changes. To remain consistent
with prior explanations, I add the change in the estimated risk premium ∆eγ̂j back into the
fundamental regression, which achieves the desired control. To illustrate, note that Equation 3
implies
a proportional relation
between the fitted CDS spread and both the EDF and risk premium
β̂
α̂
CDSi,t = e EDFi,t (RPt ) . Therefore, by holding the EDF constant over time, I can isolate the
relationship between the CDS spread and the risk premium. In this setting, a change in the risk
premium is clearly proportional to a change in the CDS spread (∆CDSi,t = δ∆RPt ) over time,
which still holds after CDS spreads are aggregated to the industry level.
Results of the fundamental regression with risk premium controls are reported in panel A
of Table VI. As with other tests, I allow the exposures to change during the crisis. A significant
increase in the exposure across industries indicates that a larger portion of the common variation in
CDS spread changes can be attributed to an increase in the variance of the default risk premium.
The first row of Table VI reports the exposures of CDS spread changes to changes in the risk
premium. Not surprisingly, I find that risk premiums are both statistically and economically
important determinants of CDS spread changes prior to and during the crisis. The estimated
regression coefficients imply that, after controlling for factors that determine expected loss and
holding all else constant, on average 20% of the change in CDS spreads can be explained by changes
in risk premiums. This number increases to approximately 45% during the turmoil. R-squared for
each regression shows a strong improvement in the model fit increasing by approximately 0.23
relative to the fundamental regression. This suggests that approximately 23% of the time-series
variation in CDS spread changes can be explained by changes in the risk premium.
[INSERT Table VI]
22
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Panel B of Table VI shows the results of the test for risk premium contagion. Strikingly, the
increase in pairwise inter-industry excess correlation is entirely explained by controlling for changes
in the default risk premium. This result suggests that daily adjustments in investors’ tolerance for
bearing risk increased the correlations between industry CDS spread changes.
5
Robustness
5.1
Factor Model Specification
At this point, I explore the robustness of the above results beginning with the fundamental
model. It is important to ensure that the finding of contagion is not driven by model misspecification. Therefore, I have considered several different specifications. In addition to the fundamental
variables outlined above, I have investigated: (i) different maturities of the risk free rate ranging
from the (one month -20 year); (ii) different combinations of maturities in constructing the SLOPE
variable; (iii) lagged fundamental variables; (iv) square and cubed changes in the risk free rate;
(v) the percent change in the trade weighted U.S. dollar exchange rate index from the Federal
Reserve Board; (vi) daily changes in three-month financial and non-financial commercial paper,
when available; (vii) the daily return from Lehman Brothers bond indices AAA-Ca and the High
Yield as well Investment Grade index.
Next, I investigate different model specifications. These specifications include: (i) the Acharya
and Johnson (2007) model, which provides a stronger control for non-linearity; (ii) a hypothetical
credit spread, constructed from Moody’s EDF (this credit spread is subtracted from the CDS
spread); (iii) a firm-level estimation of the fundamental model. Finally, I allow factor exposures to
vary through time. This is achieved by first estimating the fundamental model on sixty-day rolling
windows. In addition, I allow factor exposures to change at the beginning of the crisis, at the
Bear Stearns merger and at the Lehman brothers Failure. The second technique is repeated for the
liquidity and counterparty risk analysis as well. The original results hold for all of the alternative
specifications above.
5.2
Liquidity and Counterparty Risk
I now turn to the results for liquidity and counterparty risk. The proxies developed in these
sections are designed to measure changes in liquidity and counterparty risk. However, one could
argue that they do not adequately capture the desired effect during periods of turmoil or that
the microstructure noise present in high frequency data obscures their power. To address these
concerns, I simplify the approach and focus on events that occurred during the crisis that could
have constrained liquidity or amplified counterparty risk. At this point, I do not attempt to separate
these two effects as both are susceptible to sudden short-lived spikes. This is distinctly different
23
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from risk premiums, which will likely change gradually over time as investors adjust their risk
preferences.
If shocks to liquidity/counterparty risk significantly affected CDS correlation during the crisis,
then spread changes, across all portfolios, should respond to liquidity/counterparty risk enhancing
and deteriorating events. To test this, I begin by collecting a list of 87 events that occurred during
the crisis. The majority of these events are taken from the St Louis Federal Reserve financial
timeline. I then split these into distress events, which constrain liquidity or increase counterparty
risk, and recovery events with the opposite effect. I then include two dummy variables “DISTRESS”
and “RECOVERY” into the fundamental regressions. Each dummy variable equals one on a window
around the distress or recovery date and zero elsewhere. For distress or recovery events, a positive
coefficient suggests that CDS spread changes increased, which is consistent with an increase in
liquidity risk or a decrease in counterparty risk. The opposite is true for a negative coefficient.
[INSERT Table VII]
Table VII reports the estimated shift in the constant around the specified event dates. Because
each fundamental regression already contains a crisis dummy, this marginal change is relative to the
crisis fixed effect. However, the results hold if the crisis dummy is omitted. In Panel A, the distress
and recovery indicators are set equal to one on all event dates and zero elsewhere. Using the event
date only eliminates overlapping windows. Results show that, on average, CDS spread changes
do not increase significantly on distress event dates, nor do they decrease significantly on recovery
event dates. This result could arise if a number of insignificant events, included in this first pass,
obscure the larger effect, which is concentrated on more severe event dates. Therefore, I repeat the
test after eliminating several events that I classify as “less severe”. This leaves 10 distress events
and 21 recovery events. These results are reported in Panel B. This adjustment does not change
the above result. Finally, I investigate only the most severe distress events, which include the Bear
Stearns merger, the collapse of Lehman Brothers, and the closure of Washington Mutual. I define a
four-day observation window around each of these events (one day prior and two days after; several
windows were used with no change in the result). In this last regression, I find that industry CDS
spread changes jointly increase over a short window around these extreme events, which could
explain the sustained increase in the rolling average correlation observed Figure 1. However, after
controlling for extreme events, I find that excess correlations still increase significantly across all
industry pairs.23
Controlling for extreme events cannot explain the increase in excess correlation. After including
the distress and recovery indicators in the fundamental regression, I repeat the tests for a change in
inter-industry excess correlation. These results, which are left unreported, show that the correlation
23
It is important to remember that these dummy variables are estimated relative to fundamental factors. Therefore,
CDS spreads may have reacted to these events, but these results suggest that the reaction was not remarkably
different from what occurred in other markets.
24
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between model residuals still increases significantly across all industry pairs. Thus confirming the
original result.
5.3
Default Risk Premium
Finally, I provide further analysis of the risk premium results. A potential difficulty in estimating
the risk premium is that the market may not have known the contemporaneous probability of
default. This could bias the estimated risk premium if the contemporaneous CDS spread is based
on prior realizations of the EDF. To explore this possibility, I re-estimate the risk premium using
the contemporaneous EDF, as well as, the one to five day lagged EDF. Although in many cases
lagged EDF are significant, substituting the change in this more robust measure of the default risk
premium into the fundamental model does not affect the results. The change in the default risk
premium still absorbs the full increase in excess correlation.
The results of the default risk premium analysis are compelling. However, estimates of the risk
premium obtained from Equation 3 may also capture liquidity premiums, which previous tests have
shown to be important determinants of CDS spread changes. Therefore, it is plausible that the
risk premium control is in fact a more powerful estimate of the liquidity premium.
To address this concern, I regress the estimated risk premium on the liquidity proxies discussed
in Section 4.1. These results suggest that the estimated risk premium may capture some component
of liquidity risk, particularly with respect to transaction costs, funding liquidity and bond liquidity.
Therefore, I reestimate the risk premium with liquidity controls.24 That is, I include the log of the
individual contract bid-ask spread on the right-hand side of equation three. After obtaining the
risk premium (in its first differenced form), it is orthogonalized with respect to all liquidity proxies
and reintroduced, as a liquidity adjusted risk premium, into the fundamental model.
[INSERT Table VIII]
Results of the risk premium robustness tests are reported in Panels B and C of Table VIII. As
one would expect, purging liquidity from the estimated jump-to-default risk premium decreases its
ability to explain the increase in excess correlation. This is evidenced by a slight reduction in the
magnitude of regression coefficients on changes in the risk premium. R-squareds also drop slightly
to approximately 0.36, which is an improvement of approximately 0.18 over the fundamental model
alone. This suggests that daily changes in the default risk premium account for approximately
18% of the time-series variation in CDS spread changes. Panel C shows the results of the test
24
One may question the power of daily liquidity proxies in this setting. Therefore, I also run the regressions at the
weekly frequency. These results confirm those of the daily regressions in that funding liquidity and transaction
costs are important determinants of CDS spread changes. The one notable difference is that proxies for systematic
liquidity ∆OISTB and ∆ONREPO are significant determinants of CDS spread changes prior to the crisis but become
insignificant during the crisis. This provides additional evidence that systematic liquidity is not a significant channel
of contagion.
25
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for risk premium contagion using the liquidity adjusted risk premium. These results confirm that
controlling for the risk premium, even in its liquidity adjusted form, explains the majority of
the increase in inter-industry excess correlation. However, the remaining increase in correlations,
though sparse, indicates that transaction costs, funding liquidity and bond liquidity may have also
played a role in increasing correlations.
6
Conclusion
This paper investigates contagion and excess correlation in daily CDS spread changes during
the 2007-2009 credit crisis. I construct a sample of liquid corporate single-name credit default swap
contracts, which includes constituents of the CDX North American Investment Grade index roles
8-12. Using simple measures of association, I show that the comovement between CDS spread
changes increased significantly after July 2007.
Having established that correlations increased, I turn to the question of contagion. The correlation between CDS spread changes can increase simply because of an increase in the variance
of common factors that drive credit risk. Alternatively, correlations can increase because of an increase in the influence of non-credit risk factors. To test whether credit risk increased correlations,
I build six equally weighted industry portfolios based on the Fama and French five industry classifications (the six is Financials which is extracted from Other). In the spirit of Bekaert et al. (2005),
I decompose the raw inter-industry CDS correlations into fundamental and excess correlation using
a factor model. Finally, I test for contagion by evaluating whether the correlations between factor
model residuals increased during the crisis. I find strong evidence that an increase in the volatility
of common factors that drive credit risk was not fully responsible for amplifying correlations during
the crisis, which establishes that contagion occurred.
Next, I investigate whether liquidity risk, counterparty risk, or the jump-to-default risk premium
contributed to the increase in excess correlation. First, I investigate liquidity risk. To do this, I add
several liquidity proxies, which control for changes in transaction costs, funding liquidity, systematic
liquidity, and bond market liquidity, into the fundamental model and repeat the test for contagion.
The results of these tests show that liquidity is an important factor, especially in determining the
CDS spreads of financial institutions. However, it cannot explain the full and uniform increase in
excess correlations. Therefore, I turn to counterparty risk. To control for changes in counterparty
risk, I add several proxies of aggregate dealer credit risk into the factor model. However, controlling
for changes in counterparty risk offers no significant improvement over the fundamental model alone.
Therefore, I conclude that counterparty risk was not a significant source of contagion during the
crisis.
Finally, I evaluate whether changes in risk premiums increased the excess correlation. To do
this, I estimate the jump-to-default risk premium from a sample of healthy firms whose CDS spreads
have low exposure to liquidity risk. Adding the change in this measure into the factor model, I find
26
Electronic copy available at: https://ssrn.com/abstract=1937998
that changes in the risk premium account for approximately 18% of the time-series variation in CDS
spread changes. Furthermore, controlling for changes in the risk premium completely explains the
increase in excess correlation, which suggests that an increase in the variance of the jump-to-default
risk premium was the main channel of contagion. This important result shows that a systematic
re-pricing of credit risk, rather than market frictions, amplified CDS correlations during the credit
crisis.
27
Electronic copy available at: https://ssrn.com/abstract=1937998
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Figure 1: Average CDS Spread & Rolling 60 day correlations
The Average CDS spread is an equally weighted average over all 150 firms in the sample. To get the average correlation for a particular
day, I calculate pairwise correlations for each of the 11,175 possible firm pairs using 60 days of trailing data. I then take an equally
weighted average over all pairwise correlations. This calculation is rolled daily to obtain the correlations graphed above.
32
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Figure 2: Average CDS Spread & Sample Periods
The graph shows the daily equally weighted average CDS spread for all 150 firms between July 5, 2005 and March 9, 2009. The time period
labeled pre-crisis ranges from July 1, 2005 to July 30, 2007 and the period labed crisis ranges from July 31, 2007 to March 9, 2009.
33
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Figure 3: S&P Long-Term Issuer Ratings
Pairwise correlations for all 11,175 possible firm pairs are calculated prior to and during the crisis and are shown above. In tan (right) is the
cross-sectional density of pairwise correlation during the crisis and in blue (left) is the cross-sectional density of pairwise correlation prior to the
crisis.
34
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Table I
Descriptive Statistics: Panel A presents the average Book Leverage Profitability, Book to Market
Ratio Cash holdings, Total Asset values and Market Capitalization over all firms in the sample for each
year (2005-2009). Descriptive variables are calculated using the accounting data from the reporting period
(Compustat datadate) that is nearest to December 31 of each year and not more than a half of a year from
this date. Each variable is calculated as follows (Notation is taken directly from the Compustat variable
definitions): Book Leverage = ((AT - (AT - LT - PSTLK + TXDITC + DCVT))/AT), Profitability =
NI/AT, Market-To-Book =(CSHO PRCC C + AT - (AT - LT - PSTLK + TXDITC + DCVT))/AT, Cash
= CH, Total Assets = AT, and Market Capitalization = CSHO PRCC C. Cash, Total Assets and Market
Capitalization are reported in Billions. Sample means that are significantly different (at the 1% level)
from the mean of the CRSP/Compustat merged universe are reported in bold. Panel B: Reports the
distribution of S&P long-term issuer credit ratings by year for all firms in the sample whenever the Longterm issuer credit rating is available. The Long-term issuer credit rating is taken as the first monthly
observation of each year. The last row in the table shows the number of firms for which Long-Term issuer
credit ratings are available in each year.
2005
2006
2007
2008
2009
0.60
0.05
1.49
1.89
59.51
34.34
0.66
0.01
1.24
2.58
60.92
21.92
0.64
0.03
1.34
2.86
61.95
25.53
Panel A: Sample Characteristics
Book Leverage
Profitability
Market to Book
Cash
Total Assets
Market Cap
0.59
0.06
1.58
1.64
50.73
31.80
0.59
0.06
1.59
1.67
55.83
35.34
Panel B: S&P Long-Term Issuer Ratings
AAA
AA+
AA
AAA+
A
ABBB+
BBB
BBB< BBB-
4
0
3
2
9
25
19
28
33
18
3
3
0
4
1
9
25
20
31
33
16
3
3
0
4
0
10
23
20
32
36
15
1
2
1
2
2
11
20
20
30
27
21
6
2
0
2
1
10
18
19
29
25
20
16
N
144
145
144
142
142
35
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Table II
Changes in comovement: The table reports the values of three measures of aggregate comovement in CDS spread changes: Intraclass
Correlation, Average Pearson’s Correlation and the average fraction of firms whose CDS spreads move in the same direction each week;
reported in panels A,B and C respectively. Columns one and two report the value prior to and during the crisis respectively. Columns
three and four show the change in each measure and the associated p-value respectively for each measure. The pre-crisis period ranges
from July 1, 2005 to July 30, 2007 and the crisis period ranges from July 31, 2007 to March 9, 2009. Industries are the Fama and
French five industry classifications with the sixth industry, Financials, extracted from the Other category. The significance of the
change in intraclass correlation is evaluated using a modified Fisher Z-test for equality of the intraclass correlation coefficient. Details
of this test are provided in Donner and Zou (2002). Because intraclass correlation is sensitive to changes in variance, CDS spread
changes are standardized in the pre-crisis and crisis period separately. Significance of the change in Average Spearman’s correlations
is evaluated using Kendall’s concordance coefficient (W), which is a simple transformation of the average pairwise Spearman’s rank
correlation. The test follows Schucany
and Frawley
(1973). The
fraction of firms that move together each week is calculated from
up
up
up
Morck et al. (2000) ft = max nt , ndown
/ nt + ndown
. Their proposed asymptotic variance ft (1 − ft )/(nt + ndown
) is
t
t
t
used to assess the statistical significance of the increase in this fraction. *, **, *** indicate significance at the 10%, 5% and 1% levels
respectively.
Pre-Crisis
Crisis
Diff
P-Value
0.44
0.50
0.45
0.48
0.42
0.54
0.40
0.24***
0.29***
0.23***
0.24***
0.29***
0.23***
0.20***
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.46
0.51
0.47
0.50
0.47
0.54
0.43
0.28***
0.32***
0.28***
0.28***
0.35*
0.27***
0.27***
0.00
0.00
0.00
0.00
0.08
0.00
0.00
0.83
0.85
0.85
0.84
0.83
0.85
0.82
0.10***
0.11***
0.11***
0.08***
0.08***
0.08***
0.07***
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Panel A: Intraclass Correlation
Full Sample
Consumer
Manufacturing
HiTech
Health
Other
Financials
0.20
0.21
0.22
0.24
0.14
0.30
0.20
Panel B: Average Spearman Correlation
Full Sample
Consumer
Manufacturing
HiTech
Health
Other
Financials
0.18
0.19
0.19
0.22
0.12
0.27
0.16
Panel C: Comovement Fraction
Full Sample
Consumer
Manufacturing
HiTech
Health
Other
Financials
0.73
0.73
0.74
0.76
0.76
0.77
0.75
36
Electronic copy available at: https://ssrn.com/abstract=1937998
Table III
Change in correlations: This table reports the results of three tests for an increase in correlation during the crisis. The first is a
one-sided test for an increase in the average pairwise Pearson’s correlation coefficient between industry CDS spread changes (industries
are defined in the caption of Table II). The change in pairwise correlations is shown in the upper subpanel. Significance for these tests
is determined using the Fisher transformed correlation coefficients. The next two tests are tests of the null hypotheses for a constant
correlation matrix and constant average correlation. Significance for these joint tests is determined using the χ2 statistics developed by
Goetzmann et al. (2005). These Statistics are based on the asymptotic distribution of the covariance matrix derived in Browne and
−1 h
i
iT 1
h
1
d
vec Pˆ1 − Pˆ2
−
−−−−
→ χ2 [rk (Ω)]
+
Ω
Shapiro (1986) and Neudecker and Wesselman (1990): vec Pˆ1 − Pˆ2
n1
n2
where Ω is the covariance matrix defined by Neudecker et al. (1990), and Pˆ1 and Pˆ2 are estimates of the vectorized correlation
matrix. Results for these tests are reported in the lower subpanel. Panel A shows the results for each of the three tests described
above applied to correlations in raw industry CDS spread changes. Panel B shows the results of the main tests for contagion, which
test for an increase in pairwise excess correlation. Excess correlation is the correlation between factor model residuals from the
fundamental model. Outliers (observations above the 99.5 percentile and below the .5 percentile) are eliminated prior to calculating
correlations. *,**,*** indicate significance at the 10%, 5%, and 1% level respectively.
Panel A: Change in Inter-industry Pairwise Correlations
Consumer
Manufacturing
HiTech
Health
Other
Financials
Consumer
Manuf.
HiTech
Health
Other
Financials
0.00
0.17***
0.24***
0.26***
0.21***
0.20***
0.00
0.25***
0.30***
0.19***
0.24***
0.00
0.36***
0.21***
0.20***
0.00
0.29***
0.37***
0.00
0.22***
0.00
Statistic
Matrix Test
Average Correlation
0.2480***
P-Value
0.00
0.00
Panel B: Contagion Change in Inter-industry Excess Correlations
Consumer
Manufacturing
HiTech
Health
Other
Financials
Consumer
Manuf.
HiTech
Health
Other
Financials
0.00
0.11***
0.17***
0.19***
0.14***
0.09*
0.00
0.25***
0.26***
0.20***
0.21***
0.00
0.31***
0.18***
0.12***
0.00
0.23***
0.30***
0.00
0.15***
0.00
Statistic
Matrix Test
Average Correlation
0.1927***
P-Value
0.00
0.00
37
Electronic copy available at: https://ssrn.com/abstract=1937998
Table IV
Liquidity contagion Panel A: shows the estimated liquidity parameters along with their marginal changes during the crisis.
The standard set of fundamental variables are included but not reported. The dependant variable is the standardized change in
industry CDS spreads. Liquidity proxies include: ONOFF - the yield difference between the on-the-run and directly off the run
five-year Treasury note; OISTB - the spread between the three-month overnight index swap rate and RF3M; BIDASK & IBIDASK
- the change in the average bid-ask spread and industry average bid-ask spread respectively (each IBIDASK is orthogonalized to
BIDASK); ONREPO - The difference between the general collateral repo rate and RF3M; HEDGE - the lagged hedge fund return
index (orthogonal to the market return); AMIHUD - the aggregate Amihud Measure over bonds in the sample; VOLUME - the average
principal amount traded each day over industries; NTRADE - average number of daily trades over industries. Constants are omitted
because they are insignificant Panel B: The change in excess pairwise correlations are reported in the upper subpanel below the
diagonal. Significance is assessed using the Fisher transformation. The difference-in-difference (marginal increase in correlations from
liquidity) for each pairwise correlation is reported above the diagonal. Standard errors are bootstrapped (non-parametric) with 1000
replications and re-sampling size equal to the size of the original data set. Diagonal values are always equal to zero and are omitted.
The lower panel reports the tests for a constant correlation matrix and constant average correlation. Significance is assessed using
the Goetzmann et al. (2005) χ2 statistics. There are 899 observations for each industry and *,**,*** indicates significance at 10%,
5% and 1% respectively.
Panel A: Liquidity Factor Exposures
Consumer
Manuf.
HiTech
Health
Other
Financials
-0.02
(-0.47)
-0.01
(-0.20)
-0.06
(-1.06)
0.12**
(2.34)
0.02
(0.56)
0.06
(0.88)
0.02
(0.58)
-0.06
(-0.83)
0.04
(0.54)
-0.03
(-0.91)
-0.05
(-0.61)
0.02
(0.37)
0.09*
(1.80)
-0.02
(-0.50)
-0.03
(-0.41)
0.02
(0.58)
0.05
(0.59)
-0.09
(-1.25)
0.00
(0.10)
-0.01
(-0.17)
-0.02
(-0.29)
0.09**
(1.97)
-0.06**
(-1.90)
0.06
(1.04)
0.04
(1.12)
0.03
(0.38)
-0.05
(-0.68)
0.00
(0.08)
0.04
(0.47)
0.02
(0.28)
0.07
(1.47)
0.13***
(3.63)
-0.08
(-1.18)
0.03
(0.70)
0.04
(0.44)
-0.02
(-0.26)
0.01
(0.41)
0.04
(0.53)
-0.03
(-0.61)
0.00
(0.09)
0.05*
(1.74)
-0.03
(-0.47)
0.05
(1.25)
0.00
(-0.05)
-0.09
(-1.25)
0.01
(0.21)
0.01
(0.16)
-0.02
(-0.32)
0.09**
(1.98)
0.04
(1.25)
-0.09
(-1.54)
0.08*
(1.92)
0.01
(0.19)
-0.10
(-1.34)
0.06
(1.00)
0.02
(0.14)
0.10
(1.25)
-0.09
(-1.32)
0.04
(0.86)
0.17*
(1.77)
-0.05
(-0.87)
0.14
(1.25)
-0.21*
(-1.93)
0.04
(0.71)
0.10
(0.92)
-0.11
(-1.34)
-0.01
(-0.16)
0.16***
(3.00)
0.34***
(3.54)
-0.10*
(-1.75)
0.00
(0.04)
-0.05
(-0.42)
0.02
(0.33)
0.03
(0.31)
-0.05
(-0.66)
0.04
(0.52)
0.10**
(2.10)
0.24**
(2.51)
-0.11*
(-1.82)
-0.04
(-0.39)
-0.05
(-0.47)
0.06
(0.99)
-0.04
(-0.33)
-0.02
(-0.19)
0.03
(0.42)
-0.08*
(-1.46)
0.34***
(3.34)
-0.09
(-1.38)
0.08
(0.66)
-0.17
(-1.45)
0.02
(0.29)
-0.03
(-0.33)
-0.01
(-0.17)
0.13*
(1.93)
0.01
(0.33)
0.31***
(3.40)
-0.12**
(-2.16)
0.06
(0.60)
-0.08
(-0.81)
-0.02
(-0.32)
0.02
(0.21)
-0.01
(-0.14)
-0.10
(-1.27)
0.14**
(2.22)
0.35***
(3.78)
-0.14**
(-2.43)
-0.05
(-0.44)
0.06
(0.57)
0.2307
0.2091
0.2085
0.1284
0.3153
0.2568
Pre-Crisis
∆ONOFF
∆OISTB
∆ONREPO
∆BIDASK
∆IBIDASK
HEDGE
∆AMIHUD
∆NTRADE
∆VOLUME
Marginal Crisis Effects
∆ONOFF
∆OISTB
∆ONREPO
∆BIDASK
∆IBIDASK
HEDGE
∆AMIHUD
∆NTRADE
∆VOLUME
R-Squared
Panel B: Liquidity Contagion - Change in Inter-industry Excess Correlations
Consumer
Manufacturing
HiTech
Health
Other
0.12***
0.16***
0.19***
0.12***
-0.01
0.24***
0.25***
0.19***
0.01
0.01
0.33***
0.15***
0.00
0.01
-0.02
0.22***
0.02
0.01
0.03
0.01
-
0.03
0.05*
0.06**
0.03
0.07**
Financials
0.05
Statistic
0.17***
P-Value
0.00
0.00
0.06
0.27***
0.08
-
Matrix Test
Average Correlation
0.1726***
38
Electronic copy available at: https://ssrn.com/abstract=1937998
Table V
Counterparty risk contagion Panel A: shows the regression coefficients for counterparty risk proxies prior to the crisis and
their marginal changes during the crisis. The standard set of fundamental variables are included but not reported. The dependant
variable is the standardized change in industry CDS spreads. Counterparty risk variables include the spread between the three-month
overnight index swap rate and three-month LIBOR; ABCP - the spread between the yield on three-month asset-backed commercial
paper and RF3M ( ABCP is orthogonal to RF3M); CPstock - The value-weighted return from a portfolio of 16 licensed market-makers
in the CDX index (CPstock is orthogonal to the market return); CPDIF- the log of the difference between the maximum and median
daily return of the 16 licensed market-makers in the CDX Index; EXCPDIF - an interaction variable that equals CPDIF on days
when risk dispersion is above its 95th percentile. The dummy variable corresponding to EXCPDIF is estimated but not reported
because it is always insignificant. Regression constants are also estimated but omitted as they too are insignificant. Panel B: The
change in excess pairwise correlations are reported in the upper subpanel below the diagonal. Significance is assessed using the Fisher
transformation. The difference-in-difference (marginal increase in correlations from counterparty risk) for each pairwise correlation
is reported above the diagonal. Standard errors are bootstrapped (non-parametric) with 1000 replications and re-sampling size equal
to the size of the original data set. Diagonal values are always equal to zero and are omitted. The lower panel reports the tests
for a constant correlation matrix and constant average correlation. Significance is assessed using the Goetzmann et al. (2005) χ2
statistics. There are 905 observations for each industry and *,**,*** indicates significance at 10%, 5% and 1% respectively.
Panel A: Counterparty Risk Factor Exposures
Consumer
Manuf.
HiTech
Health
Other
Financials
-0.03
(-0.62)
-0.07
(-0.81)
-0.06
(-0.85)
0.01
(0.18)
0.06
(1.34)
-0.14*
(-1.74)
-0.02
(-0.29)
-0.03
(-1.06)
0.05
(1.24)
-0.03
(-0.41)
0.01
(0.14)
-0.03
(-0.89)
0.02
(0.42)
-0.06
(-0.75)
-0.03
(-0.37)
-0.02
(-0.50)
0.02
(0.41)
-0.13
(-1.60)
-0.06
(-0.81)
-0.02
(-0.63)
0.00
(0.07)
-0.01
(-0.13)
-0.03
(-0.44)
-0.01
(-0.29)
0.09
(1.47)
0.09
(0.83)
-0.10
(-0.80)
-0.06
(-0.40)
-0.06
(-0.86)
0.17
(1.63)
-0.10
(-0.76)
-0.03
(-0.18)
0.00
(0.04)
-0.02
(-0.21)
-0.13
(-1.08)
0.05
(0.36)
0.05
(0.71)
0.04
(0.34)
-0.12
(-0.91)
-0.12
(-0.75)
0.00
(-0.01)
0.11
(1.14)
0.01
(0.08)
0.02
(0.13)
0.03
(0.52)
-0.03
(-0.31)
0.07
(0.53)
0.14
(0.87)
0.2150
0.1761
0.1869
0.1016
0.2883
0.2011
Pre-Crisis
∆OIS
∆ABCP
CPstock
CPDIF
Marginal Crisis Effects
∆OIS
∆ABCP
CPstock
EXCPDIF
R-Squared
Panel B: Counterparty Risk Contagion - Change in Inter-industry Excess Correlations
Consumer
Manufacturing
HiTech
Health
Other
Financials
Matrix Test
Average Correlation
0.12***
0.20***
0.26***
0.15***
0.10**
0.00
0.23***
0.32***
0.20***
0.17***
Statistic
P-Value
0.00
0.00
0.2151***
-0.01
0.03
0.39***
0.16***
0.12***
-0.04
-0.05
-0.08*
0.31***
0.26***
0.01
-0.02
0.01
-0.06
0.14***
-0.02
0.00
0.00
0.03
-0.03
-
Panel C: Liquidity & Counterparty Risk Contagion - Change in Inter-industry Excess Correlations
Consumer
Manufacturing
HiTech
Health
Other
Financials
Matrix Test
Average Correlation
0.12***
0.15***
0.23***
0.13***
0.11**
0.00
0.22***
0.29***
0.19***
0.20***
Statistic
P-Value
0.00
0.00
0.1995***
0.03
0.03
0.36***
0.15***
0.12**
-0.02
-0.05
-0.06
0.28***
0.31***
0.02
-0.02
0.05
-0.04
0.14***
39
Electronic copy available at: https://ssrn.com/abstract=1937998
-0.02
0.00
0.01
-0.03
-0.02
-
Table VI
Risk Premium Contagion: Reported in Panel A below are the regression results for the risk premium analysis. The dependent
variable for each regression is the change in industry CDS spreads; industries are defined in the caption of Table II and are listed
in column headers. The risk premium (RP) for each industry is estimated from the 20 CDS spread series of healthy (non-industry
members) firms which are least sensitive to liquidity. I follow the panel regression methodology outlined by BDDFS to obtain estimates
of the daily default risk premium. Changes in the estimated risk premium are then included in the fundamental regression (defined in
the caption of Table IV) as explanatory variables. Coefficients of the fundamental controls are omitted for brevity. The row labeled
∆RP shows the pre-crisis risk premium regression coefficient for each industry. The row labeled ∆RP c shows the marginal change in
that coefficient during the crisis. Due to EDF data limitations, the pre-crisis period was shortened to 3/1/2006 - 7/30/2007. Panel
B shows the change in excess correlation after controlling for the risk premium. Tests of pairwise correlations are based on the Fisher
transformed correlation coefficients. Tests of the average correlation and correlation matrix are based on the asymptotic χ2 tests
derived in Goetzmann et al. (2005). Tests of pairwise correlations are one-sided. Z-statistics are reported in parentheses. There are
746 observations for each industry portfolio and *,**,*** indicate statistical significance at the 10%, 5% and 1% level respectively.
Panel A: Risk Premium Controls
Consumer
Manuf.
HiTech
Health
Other
Financials
0.18***
(4.31)
0.21***
(5.41)
0.18***
(4.93)
0.30***
(6.38)
0.17***
(4.55)
0.14***
(3.27)
0.24***
(4.38)
0.32***
(6.00)
0.36***
(6.97)
0.26***
(4.13)
0.26***
(5.13)
0.21***
(3.64)
0.4089
0.4376
0.4671
0.3371
0.4921
0.3404
Consumer
0.00
-0.09
-0.10
0.03
0.01
-0.13
Manuf.
HiTech
Health
Other
Financials
0.00
-0.03
-0.01
0.01
-0.08
0.00
-0.01
-0.05
-0.14
0.00
0.03
0.03
0.00
-0.10
0.00
Statistic
P-Value
0.00
0.00
Pre-Crisis
∆RP
Marginal Crisis Effects
∆RP c
R-Squared
Panel B: Risk Premium Contagion
Consumer
Manufacturing
HiTech
Health
Other
Financials
Matrix Test
Average Correlation
-0.0426***
40
Electronic copy available at: https://ssrn.com/abstract=1937998
Table VII
Liquidity & Counterparty Risk Shocks: This table reports the results of the tests for liquidity/counterparty risk shocks during
the crisis. The dependant variables are CDS spread changes for industry portfolios listed in the column headers. The independent
variables include the standard set of fundamental variables and two indicator variables, “DISTRESS” and “RECOVERY”, which
equal one on or surrounding significant event dates, and zero everywhere else. Panel A shows the results using all events. In this
case, the indicator variables, “DISTRESS” and “RECOVERY”, equal one on the event date only. Panel B reports results for more
severe events. For this regression, I define a three “calendar” day window which includes the event date and one day pre and post.
Panel C includes the results of the most severe distress events, which include the Bear Stearns merger (3/14/2008), the collapse of
Lehman Brothers (9/15/2008), and the closure of Washington Mutual (9/25/2008). I define the window around these events to be 1
observation prior to the event and 2 observations after. As with other tests, these regressions are estimated using SUR. Z-statistics
are reported in parentheses. There are 912 observations for each industry portfolio and *,**,*** indicate statistical significance at
the 10%, 5% and 1% level respectively.
Consumer
Manuf.
HiTech
Health
Other
Financials
Panel A: All Distress and Recovery Events (event date only)
DISTRESS
-0.01
(-0.04)
-0.06
(-0.19)
-0.21
(-0.63)
0.25
(0.72)
-0.13
(-0.43)
-0.07
(-0.22)
RECOVERY
-0.16
(-0.78)
0.05
(0.26)
-0.07
(-0.34)
0.15
(0.69)
-0.17
(-0.88)
0.01
(0.05)
R-Squared
0.2111
0.1855
0.1869
0.1009
0.2760
0.1939
Panel B: Level 2 and 3 Distress and Recovery Events (1 calendar day around the event)
DISTRESS
-0.07
(-0.36)
-0.07
(-0.34)
-0.07
(-0.37)
0.17
(0.81)
-0.07
(-0.39)
0.01
(0.07)
RECOVERY
0.04
(0.29)
-0.08
(-0.57)
-0.18
(-1.32)
-0.02
(-0.13)
-0.04
(-0.28)
-0.10
(-0.75)
R-Squared
0.2107
0.1859
0.1881
0.1006
0.2755
0.1945
Panel C: Level 3 Distress Events (1 - 2 observations prior to and after the event)
DISTRESS
0.66**
(2.20)
0.53*
(1.72)
0.58*
(1.89)
0.57*
(1.76)
0.42
(1.43)
0.58*
(1.87)
R-Squared
0.2147
0.1881
0.1896
0.1031
0.2769
0.1970
Electronic copy available at: https://ssrn.com/abstract=1937998
Table VIII
Risk Premium Contagion Robustness: Reported in Panel A are the regression results which test the relation between the estimated risk premium
and different proxies for liquidity. The dependant variable in each regression is the change in the estimated risk premium. Models are listed from 1 to 5
in the column headers. Model 1 includes all market-wide liquidity measures, Model 2 test CDS transaction costs, Model 3 tests bond liquidity, Model 4
tests funding liquidity and Model 5 combines all liquidity proxies. The panel labeled Pre-Crisis/Crisis test show the marginal change at the beginning
of the crisis (7/31/2007). The Panel labeled Pre/Post Lehman shows the marginal change after the collapse of Lehman Brothers (9/15/2008). Panel
B reports the results of the risk premium controls in the fundamental model. The standard set of fundamentals is included in the regression but
coefficients are not reported. In this case, the risk premium is estimated with controls for transaction costs. That is, I add the log of the contract
bid-ask spread into Equation 3 and reestimate the risk premium. Additionally, I orthogonalize the change in the risk premium to all liquidity variables
using Model 5. The risk premium (RP) for each industry is estimated from the 20 CDS spread series of healthy (non-industry members) firms which
are least sensitive to liquidity. The estimated risk premium is then included in the fundamental regression to control for potential contamination
from transaction costs in the estimation of the risk premium. The row labeled ∆RP shows the pre-crisis risk premium regression coefficient for
each industry. The row labeled ∆RP c shows the marginal change in that coefficient during the crisis. Due to EDF data limitations, the pre-crisis
period was shortened to 3/1/2006 - 7/30/2007. Panel C reports the change in excess correlation after controlling for variations in the fundamental
factors that drive credit risk and the liquidity adjusted risk premium. Tests of pairwise correlation are based on the Fisher transformed correlation
coefficients. Tests of the average correlation and correlation matrix are based on the asymptotic Chi Squared tests derived in Goetzmann et al.
(2005). Tests of pairwise correlations are one-sided. Z-statistics are reported in parentheses. There are 747 observations for each industry portfolio
and *,**,*** indicate statistical significance at the 10%, 5% and 1% level respectively.
Panel A: Estimated Risk Premium and Liquidity
(1)
Pre-crisis
constant
∆ONOFF
∆OISTB
∆ONREPO
0.07
(1.40)
-0.01
(-0.15)
0.01
(0.11)
0.09
(1.27)
∆BIDASK
Pre-Crisis/Crisis
(2)
(3)
0.05
(0.93)
0.07
(1.34)
(4)
0.08
(1.61)
0.20***
(3.94)
∆AMIHUD
0.11*
(1.90)
0.12
(1.16)
-0.12
(-1.16)
∆NTRADE
∆VOL
HEDGE
-0.21***
(-2.64)
(5)
0.07
(1.41)
-0.03
(-0.52)
0.02
(0.27)
0.06
(0.83)
0.17***
(3.24)
0.08
(1.57)
0.14
(1.41)
-0.11
(-1.14)
-0.17**
(-2.14)
Marginal Changes
constant
∆ONOFF
∆OISTB
∆ONREPO
-0.04
(-0.59)
0.10
(1.27)
0.10
(1.06)
-0.10
(-1.02)
∆BIDASK
-0.04
(-0.52)
0.00
(-0.01)
-0.01
(-0.17)
Pre/Post Lehman
(3)
(4)
0.04
(1.04)
0.07*
(1.89)
0.07*
(1.79)
0.21***
(4.80)
0.03
(0.78)
-0.01
(-0.07)
-0.06
(-0.79)
0.02
(0.37)
-0.23
(-0.29)
1.05
(1.12)
-1.01*
(-1.70)
-0.91
(-1.33)
0.51***
(4.60)
-0.04
(-0.56)
0.11
(1.52)
0.10
(1.08)
-0.10
(-1.10)
0.06
(0.85)
-0.13*
(-1.80)
-0.25*
(-1.94)
0.11
(0.83)
0.46***
(4.30)
0.0289
0.1079
0.0244
0.11
(1.51)
-0.11
(-1.56)
-0.35***
(-2.62)
0.19
(1.43)
∆NTRADE
∆VOL
HEDGE
0.0154
Pre-crisis
0.06
(1.51)
0.07*
(1.71)
0.06
(1.06)
0.02
(0.26)
(2)
(5)
0.05
(1.36)
0.04
(0.96)
0.10*
(1.84)
-0.01
(-0.21)
0.20***
(4.39)
0.02
(0.53)
0.02
(0.33)
-0.05
(-0.69)
0.03
(0.52)
Marginal Changes
∆AMIHUD
R-Squared
(1)
0.0725
0.0265
-0.24
(-0.34)
0.40
(0.53)
-0.15
(-0.20)
2.67**
(2.40)
1.61*
(1.86)
-0.10
(-0.09)
-0.52
(-0.79)
-0.07
(-0.09)
-1.32
(-1.54)
-0.16
(-0.23)
2.14
(1.41)
-4.30***
(-3.05)
2.91**
(2.17)
0.0111
0.0965
-1.05
(-1.41)
-1.06*
(-1.81)
1.17
(0.88)
-3.86***
(-2.90)
0.0502
0.0338
42
Electronic copy available at: https://ssrn.com/abstract=1937998
Panel B: Liquidity Adjusted Risk Premium Controls
Consumer
Manuf.
HiTech
Health
Other
Financials
0.16***
(3.69)
0.18***
(4.32)
0.17***
(4.38)
0.24***
(4.90)
0.14***
(3.54)
0.10**
(2.23)
∆RP c
0.26***
(4.28)
0.31***
(5.35)
0.33***
(5.93)
0.29***
(4.20)
0.24***
(4.34)
0.19***
(2.96)
R-Squared
0.3774
0.3848
0.4128
0.2831
0.4428
0.2998
Pre-Crisis
∆RP
Marginal Crisis Effects
Panel C: Liquidity Adjusted Risk Premium Contagion
Consumer
Manufacturing
HiTech
Health
Other
Financials
Matrix Test
Average Correlation
Consumer
0.00
-0.02
-0.03
0.04
0.05
-0.04
Manuf.
HiTech
Health
Other
Financials
0.00
0.10*
0.06
0.09**
0.04
0.00
0.09
0.05
-0.02
0.00
0.09
0.13*
0.00
0.05
0.00
Statistic
P-Value
0.00
0.00
0.0466***
43
Electronic copy available at: https://ssrn.com/abstract=1937998