Contagion and Excess Correlation in Credit Default Swaps
Mike Anderson1
May 2010
This paper documents an increase in the correlation of credit default swap (CDS) spread changes
during the credit crisis and investigates the source of that increase. One possible explanation is that
correlations increased because fundamental values became more correlated during the crisis.
Alternatively, correlations may have increased because of contagion, rather than because of an
increase in the correlation of fundamental values. I find that fluctuations in fundamental credit risk
account for only a small fraction of the increase in correlation. Furthermore, I find no evidence that
correlations increased due to liquidity or counterparty risk. Lastly, I show that a systematic re-pricing
of credit risk, as evidenced by variations in the default risk premium, amplified correlations during
the crisis.
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. I also thank the Dice Center for research support.
1
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 increase in comovement
[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 of 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.3 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 correlation increased during the credit crisis.4 In particular, I
investigate whether the increase in correlation was a function of fundamental values or nonfundamental factors.
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 variations in the fundamental factors that determine credit risk.
Therefore, I turn to non-credit risk explanations. In particular, I examine whether liquidity risk,
counterparty risk, or risk premiums increased correlations during the crisis. Empirical results show
no evidence that CDS correlation increased because of liquidity risk or counterparty risk. In contrast,
I find convincing evidence that an increase in the variance of the default risk premium amplified
CDS correlation during the crisis.
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.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
2
The definition of fundamentals, in any market, is usually a point of debate. For the purpose of this paper, I define
fundamentals as those factors implied by Merton (1974) that determine credit risk. 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
Global Credit Derivatives Survey: Surprises, Challenges and the Future, Fitch Ratings, August 20, 2009.
4
Throughout this paper I use the term “CDS correlation” to refer to the correlation between daily changes in CDS
spreads.
2
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 of CDS spread changes during the
crisis. To do this, I test the average Pearson’s and Spearman’s correlation coefficients as well as the
average fraction of firms that move together each week [see Morck, Yeung and Yu (2000)]. Average
pairwise Pearson’s correlation increased from 20% prior to the crisis (July 31, 2007) to 44% during
the crisis (from July 31, 2007 to March 3, 2009). A similar result holds for average Spearman’s
correlation, which more than doubled during the crisis. Finally, the average fraction of firms whose
CDS spreads 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 correlation 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, which as
noted by Bekaert et al. (2005) will always be a point of controversy.5 Therefore, I rely on the
extensive credit risk literature to specify the model. I define a linear factor structure to control for
changes in the fundamental values of CDS contracts; this model is similar to those employed by
Collin-Dufresne, Goldstein and Martin (2001) and Ericsson, Jacobs and Oviedo (2009). Under this
framework, I define the excess correlation as the correlation between factor model residuals.
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. To test for contagion, I begin with a firm
level analysis, which shows that the average pairwise correlation of OLS residuals, over the full
sample and within industry categories, increased significantly during the crisis. 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
common variations in credit risk, on average, reduces the increase in inter-industry correlation from
5
Bekaert et al. (2005) study contagion in international equity markets. However, their observations regarding the
influence of variations in fundamental factors are directly applicable to the CDS market.
3
0.26 to 0.20.6 However, credit risk cannot fully explain the increase in correlations, which is
evidenced by a significant contagion effect between 14 of the 15 industry pairs. This provides
additional support for the argument that common, non-credit factors amplified correlations during the
crisis.
After documenting contagion, I investigate why it occurred. Specifically, I examine whether
variations in 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 on 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 the comovement in CDS returns during the correlation
crisis. Tang and Yan (2008) find that CDS spreads covary with liquidity proxies.7 In contrast, 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 (changes) 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 the run 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
6
It is important to note that some of the factors used to measure credit risk may be subject to non-fundamental
effects, which will complicate their interpretation as credit risk proxies. However, these measures will still respond
to changes in fundamental values. Therefore, they will still control for changes in credit risk. Unfortunately, to the
extent that non-fundamental effects are common across markets, these factors will also capture changes in noncredit risk factors. As long as the commonality of non-fundamentals increases during the crisis, this will bias
against finding an increase in excess correlation. In this respect, the increase in excess correlation is a conservative
estimate.
7
The correlation crisis refers to the downgrade of Ford and GM in 2005; specifically, the downgrade of Ford on
May 5, 2005.
4
liquidity. Therefore, I include an index of hedge fund returns to capture speculators’ funding
liquidity. Finally, Pu (2009) shows that CDS and bond liquidity is linked. To measure the effect of
bond liquidity, I use TRACE transaction data to calculate liquidity proxies (Amihud, volume, and the
number of trades) for bonds issued by firms in the sample. Results from these tests show that
liquidity was not a significant source of contagion during the turmoil.
Next, I consider counterparty risk contagion. Eichengreen et al. (2009) show that the credit
risk of major U.S. and U.K. banks varied drastically during the crisis. These banks are major dealers
in the CDS market. Therefore, an increase in the common variation of counterparty risk premiums
may have amplified CDS correlation. 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 variations 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.8 Next, the return on a value weighted portfolio of licensed marketmakers (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 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 variations in counterparty
risk, I reevaluate the change in excess correlation.
As with liquidity, I find 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”)]. Therefore, an increase in the
common variation of risk premiums, which likely occurs as investors adjust their risk appetites, can
increase CDS correlation. To measure this effect, I estimate the time varying risk premium following
BDDFS. Adding the change in the risk premium back into the fundamental regression, I find that
variations in the default risk premium account for approximately 20% of the time series variation in
8
This is taken as the difference between the yield on 90 day asset-backed commercial paper and the three-month
constant maturity Treasury yield.
5
CDS spread changes. More importantly, controlling for changes in the risk premium completely
explains 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, amplified CDS correlation 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 [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 of default probabilities,
losses given default, and defaults over time [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 correlation of 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. Finally, Section 5 concludes.
2. Data
2.1 Credit Default Swap Contracts Overview
A single-name corporate credit default swap is simply an insurance contract that protects
against deteriorations in the credit worthiness of a single reference entity (bond issuer).9 There are
two parties to each contract, the protection seller and the protection buyer. The protection buyer
agrees to make fixed payments, which are usually quarterly, to the protection seller. These payments
are based on the CDS spread or premium, which is quoted as a percent of the notional value of the
contract and can be directly interpreted as a credit spread [see Duffie (1999)]. In return, the
9
It should be noted that contract specific issues, such as what legally constitutes a credit event, can greatly
complicate this simple explanation. For example, the Bear Stearns merger did not qualify as a credit event while
placing Fannie Mae and Freddie Mac into government conservatorship did.
6
protection seller agrees to make a one-time payment, equal to the difference between the face value
of the bond and its recovery value, if a credit event occurs. Credit events are defined in the standard
contracts published by the International Swaps and Derivatives Association (ISDA). Specifically, the
2003 ISDA Credit Derivatives Definitions outline five classes of credit events (failure to pay, default
or acceleration, bankruptcy, moratorium/remuneration and restructuring), which are designed to
trigger CDS contracts when the credit worthiness of an issuer reaches a critical level. It should be
noted that ISDA contracts are flexible and can be used to construct many different types of CDS
contracts for a particular reference. Therefore, when comparing CDS premiums, it is important to
make sure that all contracts are identically specified.
2.2 Timing the Crisis
Most observers agree that the credit crisis began in the summer of 2007. However, an exact
date is difficult to define. Fortunately, Figure 2 provides convincing visual evidence of a shift in
economic states that occurred at the end of July 2007. Therefore, I define July 31,2007 as the first
day of the crisis.10
[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. I define this date as the end of
the crisis.
2.3 Credit Default Swap Premiums
End-of-day CDS premium quotes, on five-year contracts, are obtained from Markit and
Credit Market Analysts (CMA). Each of these companies collects quotes from a wide range of
contributors who are active in the CDS market. Quotes are first screened and then averaged over
dealers to produce the daily mid-quotes used in this study. A comparison of Markit and CMA quotes,
on overlapping periods, shows a high degree of consistency between the two sources with a mean
and median correlations of .995 and .998 respectively.
10
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. Finally, further evidence is
provided by a Chow test for parameter stability, which rejects the null hypothesis at the 1% level. The test is run
using changes or returns of fundamental variables on changes in the equally weighted average of CDS spreads
7
Given the above discussion, it is important to ensure that CDS spreads, for all firms in the
sample, are quoted on the same contract specification. Therefore, I choose to focus on five-year
contracts, which are widely considered the most liquid, and should convey the most accurate pricing
information. Furthermore, I use premiums on contracts that trade under the North American
convention, which standardizes many technical issues. Importantly, this convention defines a set of
triggering events, which include all the ISDA credit events (mentioned above) except
moratorium/remuneration, which is exclusive to sovereign contracts.11
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 an investment grade CDS index that
is “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. Furthermore, I
require all contracts to remain active throughout the sample period, which eliminates changes in
correlation due to contracts entering and exiting the sample. Freddie Mac, Fannie Mae, Washington
Mutual and Interactive Corporation are dropped because they stop trading prior to the end of the
sample. Embarq, Expedia, ERP, and Time Warner Cable are also dropped 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.
The sample period begins on July 1, 2005 and ends on March 9, 2009. This period isolates
two distinct economic states. The first, which is characterized by low volatility and high economic
growth, was a tranquil period in U.S. credit markets. In contrast, the months following August 2007
represent a time of severe economic turmoil. This abrupt shift in economic climate provides an ideal
setting to investigate sudden changes in credit correlation.12
This paper is mainly concerned with the correlation between credit default swap spread
changes, which is directly linked to the common variation in different components of the CDS
spread. Therefore, a brief overview of what credit spreads represent will offer clarity on the
economic meaning of these correlations. From a fundamental perspective, in frictionless markets
with no arbitrage opportunities credit spreads arise for two reasons: (i) because investors are exposed
to default risk and (ii) because, in default, bondholders receive only a fraction of the bond’s face
11
Restructuring was recently removed from the North American Convention. However, this change did not take
effect until April 2009, which is after the end of my sample period. O’Kane, Pedersen and Turnbull (2003) and
Berndt, Jarrow and Kang (2007) provide detailed discussion of the restructuring clause in CDS contracts.
12
I exclude the correlation crisis because it resulted from a liquidity shock to the bond market [see Acharya et al.
(2008)] and the focus of this paper is to explain why correlations increased during the credit crisis.
8
value. These risks reduce the value of corporate bonds relative to their risk-free counterparts creating
a positive credit spread, which, in theory, equals the CDS spread [see Duffie (1999)]. In addition to
fundamental credit risk, CDS spreads may also compensate for non-fundamental risks [see BDDFS;
Bongaerts et al. (2009); Arora et al. (2009)], which, if common to all contracts, can alter CDS
correlation. The table below provides an initial overview of the behavior of CDS spread changes
during the sample period.
[INSERT TABLE I]
Panel A of Table I describes the time series of daily changes in spreads for seven portfolios
of CDS contracts. Statistics for the full sample portfolio, constructed using all 150 CDS contracts, are
reported in row one; subsequent rows show descriptive statistics for each of the six industry
portfolios. In the construction of industry portfolios, I assume that all contracts have equal notional
amounts; that is, they are equally weighted portfolios. Figure 3 shows that CDS spreads for all
portfolios increased during the crisis, which is consistent with a heightened concern of default risk.
These increases in CDS spreads translate into larger daily changes during the crisis as seen in Panel
A of Table I. For example, the premium for the full sample portfolio increased, on average, 0.05%
per day prior to the crisis; during the crisis, the average daily change increased by more than a full
percentage point to 1.07%, which is a significant change at the 1% level. The industry breakdown
shows that, on average, CDS spreads experienced larger movements during the crisis across all
industry groups, although the change is insignificant for both the Healthcare and Other industries.
This is not surprising for the Healthcare industry given that it is commonly thought of as “recession
proof”. However, the Other industry category is mainly composed of homebuilders and
entertainment companies, which one would have expected to be among the hardest hit. A closer
investigation reveals that entertainment companies, on average, suffered a significant increase in
CDS spreads, whereas home builders did not. This result seems counter-intuitive; however, at the
beginning of the crisis most homebuilders held large cash reserves, which along with the
homebuyers’ tax credit may have helped these companies’ weather the turmoil.13
[INSERT FIGURE 3]
The volatility of CDS spread changes increased significantly during the crisis across all
portfolios, which is not surprising given the increased uncertainty in the market over this period. The
last two sections of Panel A of Table I show that spread changes are positively skewed with fat tails
prior to the crisis and approach normality during the turmoil. Again, this result is somewhat counter13
It is important to note that CDS spread levels increased for all industries; however, the average incremental
changes were smaller for Healthcare and Other.
9
intuitive because, in times of crisis, one would expect to see a higher probability of tail events
(kurtosis). This outcome is more easily understood with a closer investigation of the CDS spread
distributions in each period. Prior to the crisis, CDS spread changes are tightly clustered around zero.
Therefore, a large idiosyncratic or industry shock could push observations into the tail of the
distribution, which is evidenced by the positive pre-crisis skew. If these events occur frequently
enough, in the two years preceding the crisis, the distribution would be characterized by high excess
kurtosis. In contrast, during the turmoil extreme events became common place, which widened the
distribution of credit spread changes, making it more difficult for tail events, in relation to the crisis
distribution, to occur. Intuitively, the probability of seeing an event capable of producing outlying
observations in the midst of such a turbulent economic climate is very small.
Panel B shows the progression in average pairwise correlation within the full sample and
within each industry group over the sample period. This shows that the average correlation is low at
approximately 0.20 in each half year prior to the second half of 2007 and doubled during the crisis.
Importantly, this analysis also reveals that the increase in correlation is not concentrated within any
particular sub-period of the turmoil. Lastly, Ljung-Box tests for autocorrelation, in Panel C, show
that daily CDS spread changes are significantly autocorrelated for all industries in both periods.
2.4 Sample Characteristics
Figure 4 shows the distributions of the market-to-book ratio, cash holdings, profitability, total
assets, book leverage, and size, for the full sample (used in this paper) and for the CRSP/Compustat
merged universe. These variables, which are important determinants of credit worthiness [see
Campbell, Hilscher, and Szilagyi (2008)], are calculated using annual data obtained from the
CRSP/Compustat merged data base.14 Distributions of firm characteristics, from 2005 to 2008, are
shown in box plots, which provide a convenient visual representation of the sample heterogeneity.
For each year and characteristic there are two box plots, one (left) describes the distribution of a firm
characteristic for the full sample, the second (right) describes the distribution of the same
characteristic for the CRSP/Compustat merged universe. From Figure 4, it is (visually) apparent that
these firms 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
14
Book Leverage = ((AT - book equity)/AT) [see Baker and Wurgler (2002)]; book equity = AT – LT – PSTLK +
TXDITC + DCVT (or PSTKRV if PSTLK is not available); profitability = (NI/AT); cash holdings = CH; total assets
= AT; size = CSHO*PRCC_F; Market-to-book = (CSHO*PRCC_F + AT – book equity)/AT
10
CRSP/Compustat universe. This is apparent from the fact that the mass of each sample distribution
occurs in the tail of the corresponding CRSP/Compustat merged distribution for each firm
characteristic.
[INSERT FIGURE 4]
The figure also provides preliminary insight into why correlations increased. For example,
firms in the sample maintained large cash reserves and high total asset values throughout the crisis,
which may have limited large fluctuations in expected loss. However, there is some evidence of a
potential increase in the comovement of fundamentals. In 2008, firms in the sample experienced
what appears to be a joint increase in book leverage and decrease in profitability. These movements
in fundamentals could translate into higher CDS correlation. However, the full increase in CDS
correlation will depend on the increased comovement of non-credit risk components of the CDS
spread as well.
Finally, Figure 5 shows the distribution of S&P long term issuer credit ratings through time
(obtained from Compustat). The mass of these distributions is centered around BBB and BBB+,
although observations range from BB- to AAA.15 The distributions remain relatively constant over
time, with a slight shift toward speculative grade in 2008 and 2009. This suggests that these
companies were relatively high grade issuers and remained so throughout the crisis.
[INSERT FIGURE 5]
3. Comovement and Excess Correlation
In this section, I document an increase in the comovement of CDS spread changes during the
crisis and investigate whether that increase can be explained by variations in the fundamental factors
that drive credit risk. The discussion is split into four subsections. First, I formally test for an increase
in the comovement of CDS spread changes. Second, I develop a simple factor model approach to
decompose the raw correlation into fundamental and excess components. Third, I describe and justify
the variable specification of the factor model. Finally, I review the results of the excess correlation
analysis, which includes the base test for contagion.
15
Some ratings drop below the investment grade threshold (BBB-), which can occur because the long term issuer
rating is a composite rating meant to judge a firm’s long term credit worthiness; whereas, the CDX.NA.IG index is
constructed using specific credits. Therefore, firms with speculative long term credit ratings can be included in the
sample if they issued investment grade bonds that are included in the CDX.NA.IG index.
11
3.1 Measuring Comovement
The first step is to establish that CDS correlation increased during the crisis. To do this, I test
for an increase in the average pairwise Pearson’s and Spearman’s correlation coefficients over all
firm pairs, as well as an increase in the average fraction of firms that moved together each week
during the crisis [see Morck et al. (2000)]. Formally, I test the null hypothesis that the aggregate
comovement statistic (Pearson’s correlation, Spearman’s correlation, or the fraction of firms that
move together each week), represented by ρ below, prior to the crisis is greater than or equal to the
aggregate comovement statistic during the crisis:
Ho: ρ pre −crisis ≥ ρ crisis
Ha: ρ pre − crisis < ρ crisis
The results of these tests are reported in Table II. Columns one and two (respectively) of
Panel A show that the average Pearson’s correlation, taken over all 11,175 pairwise
combinations, is 0.20 prior to the crisis and increases to 0.44 during the crisis, which is a
significant increase of 0.24 (reported in column 3) 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. Average 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 Pearson’s correlation increased uniformly within the
sample. However, Pearson’s correlation is subject to distributional assumptions that may
influence the outcome of these tests. Therefore, I also include two nonparametric tests. First, the
change in the average Spearman’s correlation coefficients (reported in Panel B) yields similar
results for the full sample and at the industry level.16 Additional evidence of a uniform increase
in Pearson’s and Spearman’s correlation is provided in Figure 6, which shows a shift in the
cross-sectional densities of Pearson’s and Spearman’s correlation during the crisis.
16
The sampling distribution of Pearson’s correlation coefficients becomes skewed as the true correlation approaches
1 or -1. Fisher (1921) proposes a simple transformation, which under certain conditions ensures normality (as the
number of observations gets large). Moreover, pairwise correlations are measured repeatedly for each firm pair.
These conditions satisfy the assumptions of a two sample paired t-test, which is the appropriate test for a change in
Pearson’s correlation. The large number of pairwise combinations will mechanically inflate t-statistics. Therefore, I
repeat the paired test using the asymptotic distribution implied by the Fisher transformation. Tests based on the
Fisher transformation, can be misleading if CDS spread changes do not approximately follow a bivariate normal
distribution. Descriptive statistics in Table I show that, prior to the crisis, spread changes were positively skewed
with a high degree of excess kurtosis. Spearman’s rank correlation is robust to these distributional assumptions.
Further, it can be directly tested using the Friedman statistic [see Friedman (1937)], which is distributed
asymptotically Chi squared with T-1 degrees of freedom (as n goes to infinity).
12
[INSERT FIGURE 6]
Second, the average fraction of firms whose CDS spreads 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. The change in the
fraction and its corresponding p-value are reported in columns three and four, respectively. The
within-sector changes range from 7% to 11% and are all 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 TABLE II]
3.2 Measuring Excess Correlation
To estimate excess correlation, I build six equally weighted industry portfolios based on the
Fama and French five industry classifications. Given the increased attention on the financial sector, I
choose to extract financials from the Other industry classification.17 Aggregating to the industry level
reduces the noise from firm level CDS spreads and produces a clearer decomposition of CDS
correlation.
Next, I assume that industry CDS spread changes follow a linear factor structure. Given this
framework, and assuming all variables are standardized, the correlation between spread changes can
be decomposed as shown below:
[
]
[ ]
′
E ∆S∆S ′ = E (β F + ε )(β F + ε )  = β E [FF ′]β ′ + E εε ′


(1)
∆S is an Nx1 vector of CDS spread changes. β is an NxK matrix of factor exposures, F is a Kx1
vector of factors, and ε is an Nx1 vector of model errors.
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, (iii) an increase in the correlation of unexplained CDS spread changes
(contagion). In the first case, an increase in the exposure of CDS spread changes, for a single
industry, to even one common factor, will increase the correlation of that industry’s CDS spread
changes with those of all other industries.
17
Although the industry classification is coarse, further refinement reduces the power of the correlation
decomposition. This classification may limit the explanatory power of industry variables in the factor model.
Further, if refined industry components, that are not capture by industry controls, become more correlated in the
crisis, tests may be bias in favor of contagion. However, given the results hold at the firm-level as well (with
industry controls-see Appendix A), it is unlikely that this limitation bias the tests of contagion.
13
An important implication of Figure 1 is that correlations remained high throughout the crisis
period. Therefore, a onetime shock to factor exposures, factor correlations, or excess correlation,
would not explain this observed outcome. A more likely explanation is that a sustained increase in
the variance of a common factor increased correlations.
An increase in the variance of a common factor, in the context of Equation 1, is counterintuitive. This is because variables are standardized, using GARCH filters that correct for
heteroskedasticity, prior to estimating Equation 1. Therefore, the variance of observed common
factors is constant over the sample period. Two important observations will help to clarify this
contradiction. First, the factor covariance component of the decomposed correlation ( β E [FF ′]β ′ )
can change with changes in the regression coefficient. Hence, an increase in the regression
coefficient represents an increase in the variance of an observed common factor. Furthermore, an
increase in the variance of common non-credit factors in the CDS spread, which have not been
standardized, can also increase the correlation between CDS spread changes by increasing excess
correlation. To illustrate, suppose CDS spreads contain a common non-credit premium that is not
controlled for by fundamental variables. Because the variation in this premium is common across
contracts, it will induce correlation between industry CDS spread changes, which results in excess
correlation. Further, since the premium is not standardized, it can experience an increase in variance,
which would increase correlations. Hence, excess correlation, and therefore, CDS correlation can
increase with the variance of a common non-credit factor. By identifying these factors, I can add
them to the factor model in their standardized form, which effectively removes the increase in
common variation from the excess correlation matrix. This procedure is employed in Section 4 to
study the channels of contagion.
The decomposition in Equation 1 requires estimates of all factor exposures for each industry
portfolio, which are obtained from a standard feasible generalized least squares (FGLS) estimation of
the system of seemingly unrelated regressions (SUR). From this estimation, the excess correlation is
calculated as the correlation between factor model residuals [see Kallberg and Pasquariello (2008)].18
After extracting factor model residuals, I perform three tests for a change in excess
correlation. First, I test the null hypotheses that the excess correlation matrix and the average excess
18
Equation 1 holds only if all independent variables are the same across equations. If variables differ across
equations, then the decomposition should also include the covariance between equation residuals and off-equation
specific variables. For example, the covariance of industry i’s residuals with industry j’s stock returns. However,
there is no fundamental justification for why the unexplained CDS spread changes of industry i should be correlated
with the stock returns of industry j. Therefore, I assume these covariances are non-fundamental and allow them to be
absorbed into the residual covariance matrix.
14
correlation remain constant over the full sample period. Statistical significance for these tests is
assessed using the Chi-Squared statistics developed by Goetzmann, Li, and Rouwenhorst (2005),
which are based on the asymptotic distribution of the correlation matrix.19 The third test is a test of
the individual pairwise Pearson’s correlations between unexplained CDS spread changes of industry
portfolios.
3.3 Factor Model Specification
A disadvantage of the factor model approach is that it 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 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 using factors implied by Merton (1974).20 In
addition, I include several systematic variables designed to capture fluctuations 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)]. Variable definitions are
provided in Table III along with data sources and the expected sign.
[INSERT TABLE III]
To explain CDS spread changes, I transform all variables that are not returns into first
differences, which is consistent with Collin-Dufresne et al. (2001). Results reported in Table I show
that the variance of CDS spread changes increased significantly for all industry portfolios during the
crisis; unreported results indicate that factor variances increased significantly as well. Therefore, I
19
They base their statistic on the asymptotic distribution of the covariance matrix derived in Browne and Shapiro
(1986) and Neudecker and Wesselman (1990):
) )
vec P1 − P2
[ (
)]
T
 1
1  
 + Ω
 n1 n 2  
−1
[vec(P) − P) )] → χ [rk (Ω)]
d
1
2
2
)
)
where Ω is the covariance matrix defined by Neudecker et al. (1990), and P1 and P2 are estimates of the
vectorized correlation matrix.
20
Colin-Dufresne et al. (2001) show 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 specifications include leverage, which is not available daily. Instead, I use daily equity returns to
proxy for the overall financial health of the industry. To evaluate the performance of the model, I replicate the
Principal Component Analysis used in these papers and find that the common component in factor model residuals
is comparable to what Ericsson et al. (2009) find. Prior to (during) the crisis the first PCA explains 19% (37%) of
the common variation in factor model residuals.
15
standardize all variables using autoregressive GARCH filters prior to estimating the fundamental
model. In addition, I orthogonalize all market variables (SMB, HML, HB, VIX, and INDRET) to the
S&P 500 return since these variables are all highly correlated. 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.
∆S = α + β1 (∆RF 3M ) + β 2 (∆SLOPE) + β 3 (∆VIX ) + β 4 ( SP500) + β 5 ( HB) + β 6 (∆DEF ) + β 7 (SMB)
+ β 8 ( HML) + β 9 ( INDRET ) + β10 (∆INDVOL) + α c + β1,c (∆RF 3M ) I crisis + β 2,c (∆SLOPE) I crisis
(2)
+ β 3,c (∆VIX ) I crisis + β 4,c ( SP500) I crisis + β 5,c ( HB) I crisis + β 6,c (∆DEF ) I crisis + β 7,c ( SMB) I crisis
+ β 8,c ( HML) I crisis + β 9,c ( INDRET ) I crisis + β10,c (∆INDVOL) I crisis + ε
3.4 Factor Model Results
Before discussing excess correlation, I briefly review results from the factor model
estimation. SUR estimates of the pre-crisis factor exposures, for each of the six industry portfolios,
are reported in the upper half of Table IV and marginal contributions during the crisis are shown
below. Not surprisingly, the S&P500 return is negative and significant, for all industry portfolios.
This is consistent with the interpretation of the S&P 500 return as a state variable (as the state of the
economy improves, credit risk decreases, and CDS spreads become less sensitive to changes in
economic conditions). Estimated pre-crisis coefficients range from -0.11 to -0.36. This suggests that
a one standard deviation increase in the S&P 500 return relates to approximately a 0.20 standard
deviation decrease in CDS spread changes. Interest rate variables, ∆SLOPE and ∆RF3M, have
relatively little explanatory power in the full regression. However, univariate regressions recover the
well-known negative relation between the short-term risk-free rate and portfolio credit spread
changes.21 Not surprisingly, the change in the default premium (∆DEF) is positive and significant for
all industry portfolios.
The value premium (HML) is a significant determinant of CDS spread changes for four of
the six industry portfolios prior to the crisis. However, the negative sign is inconsistent with its
interpretation as a measure of default risk. Vassalou and Xing (2004) find that HML increases with
default risk; however, the effect is small for high credit quality firms. Given the large cash reserves
and long-term credit ratings of firms in this sample, it is safe to assume that they are at relatively low
21
Longstaff and Schwartz (1995), Duffee (1998), and Collin-Dufresne et al. (2001) all document this relation.
16
risk of default. Therefore, a more plausible explanation is that HML captures systematic risk
premiums imbedded in CDS spreads prior to the crisis. Elton et al. (2001) show that a negative
exposure is consistent with this interpretation. Interestingly, during the crisis, CDS spreads become
less exposed to HML and unreported results show that the absolute exposure is insignificant for all
industries. This result provides some evidence that the CDS market detached from the equity market
during the crisis.
Marginal changes in factor exposures are, for the most part, insignificant with the exception
of the marginal change in exposure to the S&P 500 return, which becomes significantly more
negative during the crisis for five of the six industry portfolios. This is consistent with the shift in
economic conditions observed at the beginning of August 2007.
[INSERT TABLE IV]
3.5 Contagion Results
Having controlled for credit risk, I now explore whether inter-industry excess correlation
increased during the crisis; results of these tests are reported in Table V. First, I test the pairwise
excess correlation 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 and find that these results are robust to the model specification.22 For
brevity and consistency, I choose to report results for the base model only. 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
22
Other variable specifications include non-linear transformations of interest rate variables to control for the effects
of convexity. A transformation of equity returns to account for the non-linear relation between equity and debt
implied by Merton (1974). I also include different bond indices of various rating categories as well as different riskfree rates of varying maturities. Lagged stock returns up to a five day lag were also explored with no change in the
result. From Figure 1, correlation jumped at the Bear Stearns merger and the Lehman Brothers bankruptcy.
Therefore, I split the crisis into three sub periods: July 31, 2007 – March 15, 2008, March 15, 2008 - September 15,
2008, and September 15, 2008 – March 9, 2009. I allow exposures to change in each period. Regression results
show very little variation in factor exposures. Further, excess correlation still increases across industries. Next, I
repeat the tests after estimating the factor model once prior to the crisis and once in the crisis. This explicitly allows
factor correlations to change. However, there is no change in the main result. Next I re-estimate the model on the
crisis sub-periods described above with no change in the main result. The last three tests are performed for each
channel of contagion as well, with no notable change in the results.
17
correlations during the crisis. Therefore, I investigate potential channels of contagion in the next
section.
[INSERT TABLE V]
4. Channels of Contagion
The evidence presented in the previous section shows that a large increase in the
comovement of daily CDS spread changes, during the crisis, cannot be explained by changes in
fundamental 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 variations in liquidity risk,
counterparty risk, and the default risk premium increase the correlation in CDS spreads. Furthermore,
I formally test each channel of contagion to see if it can resolve the increase in excess correlation
documented above. These tests allow me to comment on the degree to which each channel increased
excess correlation.
4.1 Liquidity Contagion
The premise of this argument is that a sustained increase in the variance of common liquidity
premiums can increase CDS correlation.23 Liquidity risk in the CDS market can vary for several
reasons. First, fluctuations in the supply of or demand for credit protection can lead to variations in
transaction costs. 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 larger fluctuations in their need to
hedge credit risk, which may have increased the common variation in the liquidity related component
of the change in CDS spread. 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
This argument requires some clarification on the relation between bonds and CDS contracts. If bonds are perfectly
liquid, an exact arbitrage relation with CDS contracts would prevent liquidity premiums from entering CDS spreads.
However, the single name contracts in the study do not specify a particular reference obligation (bond), which
makes this an approximate arbitrage. Furthermore, bonds are notoriously illiquid and became more so during the
crisis [see Dick-Nielsen, Feldhütter and Lando (2009)]. These limits to the arbitrage relation could allow liquidity
premiums to enter CDS spreads.
18
in the average industry bid-ask spreads (IBIDASK) to control for changes in industry specific
liquidity.24 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 more variation in the supply of or
demand for credit protection [see Acharaya et al. (2008)]. 25 To capture variation in bond liquidity, 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 then calculate daily
Amihud measures for each bond [see Pu (2009); Dick-Nielsen, Feldhütter and Lando (2009)] in the
sample and create an aggregate index (AMIHUD).26 AMIHUD increases with illiquidity, which
implies a positive relation with CDS spread changes. To measure variation in the ability of investors
to trade in the bond market, I use the TRACE data described above to count the number of bond
transactions that occurred each day in each industry and average these counts to obtain the variable
NTRADES. Using the same procedure, I also calculate the average principal amount (VOLUME)
traded each day across industries. These variables control for variations in bond trading activity,
which could 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 in
the CDS market and decrease CDS liquidity premiums. Alternatively an increase in volume could
relate to higher expected inventory costs, which could lead dealers to reduce liquidity in both the
CDS and bond market.
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 risk that persisted during the
24
Changes in Industry bid-ask spreads are orthogonalized with respect to changes in the average bid-ask spread
BIDASK.
25
This would require 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.
26
Bond level Amihud measures require at least two trades per day; days with one or no trades are replaced with
missing values. The index is constructed by building firm level Amihud measures, which are averages of bond-level
measures. Next, I aggregate to the industry level by averaging over firms in the industry. The final index is an
equally weighted average of industry liquidity measures. This procedure ensures that each industry is equally
represented in the final aggregation. I also tested industry level measures but this did not change the result. TRACE
variables measure intra-day activity which affects the daily (close-to-close) change and are therefore included as
levels.
19
crisis may have increased the volatility of systematic liquidity premiums. Therefore, I include three
measures of market-wide liquidity, which are designed to capture fluctuations in aggregate liquidity
premiums. The first is the difference between the yield of the off the run and on the run five-year
Treasury note (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.27 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 their access to funding (funding
liquidity). This is because CDS contracts commonly contain collateral agreements, which require the
exchange of capital at inception.28 Therefore, increased variation in speculators funding liquidity can
magnify CDS correlation by increasing the variation in speculators ability to trade.29 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.30 Therefore, trading activity likely
varied more during the crisis due to the management of mark-to-market risk.
To measure speculators’ ability to transact, I construct an index of hedge fund returns.
According to the British Bankers’ Association (BBA) 2006 Credit Derivatives Report, banks and
27
The three-month constant maturity risk-free rate (RF3M), from the Federal Reserve, is constructed from a
composite of on-the-run Treasury Bills. Therefore, it can be used as a proxy for the “liquid” risk-free rate. The repo
rate is basically the interest rate on a short-term loan collateralized by Treasury bills. Repo rates are usually over
collateralized making them effectively a risk-free rate. Moreover, since they are contracts, they are not subject to the
same supply and demand issues that result in specialness or flight-to-quality premiums that are present in bonds.
28
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
29
The increased uncertainty surrounding the value of hedge fund collateral, along with measures taken by the
federal government to maintain a liquid market during the crisis could have induced substantial variations in hedge
funds’ ability to trade.
30
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
20
hedge funds are the largest participants in the CDS market with 59% and 28% (44% and 32%)
respectively of buy (sell) side trading activity as of the end of 2006.31 Assuming that banks mainly
trade as dealers, hedge funds are clearly the largest speculators in the market, making up
approximately 70% (60%) of non-dealer buy (sell) side trading activity. Therefore, I focus on
measuring hedge funds’ access to capital, which depends on the performance of their returns [see
Boyson, Stahel and Stulz (2008)]. As a direct measure I obtain eight series of daily hedge fund style
index returns from Hedge Fund Research (HFR).32 From these data, I calculate an aggregate hedge
fund return index (HEDGE) by taking the equally weighted average across all eight return series.
Hedge fund returns are lagged one day to limit the influence of hedge fund 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 of factor
model residuals to test whether liquidity was a significant channel of contagion.
Results of the test for liquidity contagion are reported in Panel A of Table VI. The main
result, for the role of liquidity prior to and during the crisis, is reported in the subpanel labeled PreCrisis/Crisis. These results show that prior to the crisis changes in systematic liquidity as measured
by ∆ONOFF, ∆OISTB, and ∆ONREPO do not determine CDS spread changes. Furthermore, bond
market liquidity is not a significant determinant of CDS spread changes prior to the crisis, which is
evidenced by insignificant estimated regression coefficients for AMIHUD, NTRADES, and
VOLUME. The change in the average bid-ask spread is significant, in the pre-crisis period, for four
of the six industry portfolios. Moreover, CDS spread changes become significantly more positively
related to lagged hedge fund returns during the crisis, which is counter intuitive if hedge funds are
liquidity providers (this result is discussed in more detail below). Various industries become more
exposed to changes in the bid-ask spread and bond liquidity measures during the crisis. However,
these changes are not consistent across industries.
For robustness, I repeat these tests on the month following the collapse of Lehman Brothers
(Sept. 15, 2008 - Oct. 15, 2008), which is widely thought of as a time when contagion gripped credit
markets. The results of these tests are reported in Panel A of Table VI in the subpanel labeled
Lehman/Non-Lehman. These results show that liquidity effects, as measured by changes in the bid31
Banks participation is further split into trading activity (39% buy side and 35% sell side) and loan portfolio (20%
buy side and 9% sell side), which makes banks market making activity comparable to hedge funds speculating
activity.
32
HRF includes over 1,600 funds with no required minimum track record or asset value. Their series are equallyweighted averages of domestic and offshore fund returns. Daily returns are available for eight style indices: Equal
Weighted, Equity Hedge, Equity Market Neutral, Event Driven, Global, Macro, Market Directional, Merger
Arbitrage, and Relative Value Arbitrage
21
ask spread and HEDGE, are concentrated outside of the Lehman Brothers month. A closer
investigation shows that the change in the average bid-ask spread, when run independently of other
proxies is positive and significant over the full sample period and becomes more so during the
Lehman Brothers month. The hedge fund effect is strongest between August 2007 and May 2008.
One possible explanation for this is that bonds were difficult to sell during this period. Therefore,
hedge funds may have effectively sold the illiquid bond in the CDS market by purchasing CDS
protection, which could lead to a positive return. However, this would also increase the amount of
protection demanded in the CDS market, which could increase the liquidity premium. This would
explain the positive sign. An asset substitution explanation is supported by a significant negative
relation between bond volume and CDS spread changes for four of the six industry portfolios over
this period.
[INSERT TABLE VI]
The above analysis shows that changes in the bid-ask spread and hedge fund returns are
significant determinants of CDS spread changes, but systematic liquidity and bond liquidity (with the
exception of VOLUME) are not. However, these results must be interpreted relative to liquidity in
the equity market. This is because market based proxies for fundamentals, such as the S&P 500
return, can carry liquidity premiums, which could absorb the effect of liquidity in CDS contracts.
I now turn to the question of liquidity contagion. To determine whether liquidity risk was a
significant source of contagion, I reevaluate the increase in excess correlation using residuals from
the fundamental model with liquidity controls. Panel B of Table VI reports results for the tests of
excess correlation. The increase in pairwise excess correlation between industry portfolios ranges
from 0.09 to 0.33 and is significant for all industry pairs. Furthermore, the tests for a constant excess
correlation matrix and for constant average correlation both reject the null hypothesis at the 1% level.
These results suggest that liquidity contagion cannot explain the full increase in excess correlation
documented above. To investigate the marginal contribution of liquidity, I calculate a difference-indifference matrix by subtracting the matrix in Table V from the matrix in Panel B of Table VI. If
there is a significant reduction in correlation after controlling for liquidity, then values in the
difference-in-difference matrix will be positive and significant. However, the results show that
liquidity controls offer no significant reduction in excess correlation. Additionally, I repeat these tests
using residuals from the fundamental model with liquidity contagion parameters 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, fluctuations in
22
liquidity premiums (in excess of what may be implied by equity markets) do not significantly
increase the correlation in CDS spread changes during the crisis.
4.2 Counterparty Risk Contagion
The risk that counterparties will not be able to uphold contractual obligations can
systematically 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. Hence, a common
increase in the variation of credit risk among CDS dealers can increase the comovement of CDS
spreads. 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;33 a condition that
Brunnermeier (2009) refers to as “Gridlock”. Gridlock is a side effect of CDS market structure (overthe-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.34 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 the Gridlock and the insurance value mechanisms suggest that variations in dealers’
credit risk 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 test if an increase in the variation of counterparty risk amplified correlations during the
crisis, I relate CDS spread changes to four measures of bank sector credit risk. First, I include the
credit risk component of the TED spread, which is calculated using the overnight index swap rate
(OIR) [see Eichengreen et al. (2009)]. In this decomposition, TED = (LIBOR – OIR) + (OIR –
TBILL), the first term (the overnight index swap spread (OIS)) measures banking sector credit risk
and the second term measures liquidity risk.
Banks’ access to short-term funding is also an important determinant of dealers’ credit risk.
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
33
Some evidence that dealers became more reluctant to trade with each other during the crisis can be found in
Global Credit Derivatives Survey: Surprises, Challenges and the Future, Fitch Ratings, August 20, 2009.
34
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.
23
commercial paper market to meet short-term funding requirement [see Kashyap, Rajan, and Stein
(2009); Brunnermeier (2009); Acharya and Richardson (2009)]. Therefore, to capture changes in the
cost of short-term funding, I construct a 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 construct a measure of dealers’ financial health, which is a
value weighted index of dealers’ stock returns (CPstock). 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.35
Finally, CDS correlation 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.36 Hence, they have incentives
to deal with low-risk dealers. Moreover, protection buyers who hold existing contracts with high-risk
counterparties may choose to novate (transfer) these contracts to a more stable dealer. This would
further increase the quantity of protection demanded from a small group of high-quality marketmakers. The additional strain would likely cause dealers to reduce the extent of their market making
services. Therefore, an increase in the time variation of dealer risk dispersion may have increased
CDS correlation during the crisis.37 In this case, CDS spread changes would 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 return series for the sixteen dealers
defined above (for as long as equity returns are available) to measure the credit risk of each dealer.
35
The counterparty risk variables are mainly designed to capture changes in liquidity brought on by changes in
dealers’ credit risk. It is likely that this form of liquidity will not be captured by changes in the bid-ask spread
because it stems from dealers refusal to trade with each other. This would manifest as a symmetric increase in the
bid-ask spread, in which case, changes in the mid price would not become more correlated with changes in the bid
ask spread.
36
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.
37
Some evidence of the time variation in risk dispersion can be seen in the Bear Stearns and Lehman Brothers
events. Also variation in the timing an degree to which various banks accepted government aid provides additional
evidence of an increase in the time variation of dealer risk dispersion.
24
Next, I calculate the degree of risk dispersion (CPDIF) by subtracting the maximum return from the
median return on each day. The median return measures the “normal” credit risk in the pool and the
maximum return measures the risk of the highest quality dealer.38 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 VII]
Regression coefficients for counterparty risk variables, which are added to the fundamental
model, are reported in Panel A of Table VII. 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).39
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 VII. 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 counterparty risk proxies do not provide any significant
improvement, over the fundamental model alone, in explaining the increase in excess correlation. As
with the liquidity analysis, I repeat these tests on the month following the Lehman Brothers
Bankruptcy with no notable change in the results. These results suggest that counterparty risk
contagion did not significantly affect CDS spread changes during the crisis.
4.3 Liquidity and Counterparty Risk Robustness
Before investigating risk premiums, I explore the robustness of the above results. Although
proxies are designed to measure changes in liquidity and counterparty risk, one could argue that they
do not adequately capture the desired effect during periods of turmoil or that the microstructure noise
38
To correct for the large skewness of this variable I take the natural log of dealer risk dispersion, which is the final
measure.
39
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.
25
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 which 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 from risk premiums, which likely
changed gradually over this period as investors adjusted their risk appetites.
For shocks to liquidity risk or counterparty risk to produce a sustained increase in
correlations, multiple events would need to be spaced throughout the crisis period. From appendix A
it is apparent that this requirement was sufficiently satisfied.
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 85 events that occurred
during the crisis. I then split these into distress events, which constrain liquidity or increase
counterparty risk, and recovery events with the opposite effect. This list is included as Appendix B. I
then implement a calendar time event study by including two dummy variables DISTRESS and
RECOVERY in 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 spreads 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 VIII]
Table VIII 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.40 In Panel A, the distress and recovery indicators are set equal to one
on all event dates listed in Appendix B and zero elsewhere.41 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, Panel B reports the estimated
recovery and distress indicator variable coefficients for more severe events, which are labeled 2 and
3 in the Severity column of Appendix B. This adjustment does not change the above result. Finally, I
40
To ensure that these effects are not subsumed by the crisis fixed effect, I repeat the estimation without a crisis
dummy. The results do not change.
41
Most events are obtained from the St. Luis Federal Reserve timeline. If events fall on a weekend, I define the next
available trading date as the event date.
26
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).42 Again, I find that the reaction in
CDS spread changes around these events is insignificant.43
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 between model residuals still increases significantly for most industry pairs. Taken
together, the results of the examination to this point provide convincing evidence that CDS
correlation increased for reasons other than liquidity or counterparty risk.
4.4 Risk Premium Contagion
In this subsection I investigate whether variations in default risk premiums amplified CDS
correlation. Prior work has shown that the default risk premium is an important component of
corporate credit spreads [see Duffee (1999); Elton et al. (2001); Driessen (2005)] and can vary
drastically over time [see BDDFS]. Therefore, a sustained increase in the common variation of risk
premiums may have increased CDS correlation over the crisis period. This could occur if investors
continually adjusted their risk appetites, perhaps in response to large mark-to-market losses, over the
crisis period. Hence, an increase in the common variation of risk premiums is 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. In August 2007 there is a notable change in the behavior of risk
premiums, which increased drastically up to the Bear Stearns merger and continued to vary through
the end of 2008.
An increase in the common variation of default risk premiums alone is not sufficient to
explain the observed increase in excess correlation. Additionally, risk premiums in the CDS market
must vary independently from those in the equity market, which may be captured by the fundamental
42
Several different windows were specified the 1 and 2 day combination was chosen because it performed best in
the regression.
43
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.
27
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 risk premiums in other
markets. Second, CDS spreads contain a jump-to-default risk premium that is not present in equity
returns.44
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 Duffie (1999)], which is the risk associated with
non-diversifiable variations in 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-to-default risk premium) [see Jarrow, Lando and Yu (2005); Driessen (2005); BDDFS
(2008)].45 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 systemic or contagious events [see Collin-Dufresne, Goldstein, and Helwege
(2010)]. In either case, common variations in this premium are capable of amplifying correlations.
To investigate whether variations in the jump-to-default risk premium increased CDS
correlation, it is necessary to obtain a time varying measure of this risk premium. To do this, I
follow BDDFS who use Moody’s Expected Default Frequency (EDF) to measure the physical
44
The default spread used in the fundamental model may also capture some of the influence from risk premiums.
However, this does not preclude changes in risk premiums from increasing excess correlation because, as previously
discussed, the arbitrage relation between CDS contracts and bonds is approximate.
45
I am aware that recovery risk will also command a premium. However, research has shown that recovery is
closely associated with macroeconomic conditions. Therefore, these premiums are likely captured by the systematic
component of the default risk premium.
28
probability of default. 46 Moody’s KMV provides EDF, which are firm-level estimates of conditional
default probabilities, 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.
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 for 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 crosssectional variations in expected loss given default. 47 Consistent with their specification, Dt is a time
fixed effect, which is equal to one on day t. This yields estimates γ for each day j; the inverse log of
these parameters e is an estimate of the proportional risk premium (RP). That is, e 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).
ln ln γ D z
(3)
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 premium associated with a systemic
event that is capable of increasing default probabilities for a substantial number of firms. In this case,
the risk associated with such an event would be priced. Hence, the estimated jump-to-default risk
premium can be interpreted as the ratio of the risk neutral to the physical probability that a systemic
event occurs.
48
The most direct method to obtain this premium is to estimate Equation 3 using all
contracts in the sample. However, this assumes that all CDS spreads are unaffected by other noncredit risk factors. If this is not the case, then these factors could bias the estimation. For example,
46
This can also be achieved using equity returns [see Elkamhi and Ericsson (2007)]. However, I focus on the jumpto-default risk premium, which is inherently difficult to measure using equity returns. Moreover, if markets became
segmented during the crisis this technique would not be appropriate. BDDFS, to my knowledge provides the only
time varying estimate of the jump-to-default risk premium.
47
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. An f-test of the fixed effects and a Hausman for fixed vs.
random effects confirms that this is the appropriate model.
48
This interpretation violates the conditional independence assumption of Jarrow, Lando, and Yu (2005) by linking
firms’ default intensities to a single unpredictable event. Therefore, it is closely related to the counterparty risk
pricing model of Jarrow and Yu (2001) where many firms share a single counterparty. Alternatively, one can think
of this as a contagion premium where firm’s default intensities are linked. This is modeled by Collin-Dufresne,
Goldstein Helwege (2010).
29
suppose contracts in a particular industry carry a liquidity premium that is not common across
industries. Although variations in this premium would not affect correlations, its presence in the CDS
spread 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 only a priced event is capable of producing premiums that can alter
correlations. Therefore, if contagion occurred because of an increase in the variance of the jump-todefault risk premium, then, by definition, this premium would be present in the CDS spreads of all
contracts.
Following this intuition, I choose the set of firms that have the lowest volatility in their
contract premiums over the sample period. The basic reasoning behind this choice is that contracts
with relatively low CDS spread volatility are not likely to be heavily exposed to other non-credit risk
factors such as liquidity or counterparty risk. Further, if event risk is priced then the CDS spreads of
these firms, which I refer to as well-behaved firms, should vary with variations in the jump-to-default
risk premium. Therefore, focusing on well-behaved firms may offer the most precise estimate of the
risk premium.
Additionally, Moody’s EDF likely performed best during the crisis for firms that did not
experience large variations in credit risk, which, by definition, would include well-behaved firms.
This will also add precision to the estimated risk premium.
Specifically, I define well-behaved firms using a double sort. First, I sort CDS contracts by
the volatility of their contract spreads prior to the crisis and eliminate all firms with pre-crisis
volatilities that fall above the median. Second, I repeat the sort using the volatility of their contract
spreads during the crisis. This ensures that contract premiums have low volatility in both periods.
Finally, I take the 10 firms with the lowest crisis CDS spread volatility as my base subsample of
well-behaved firms.49
After estimating the risk premium using well-behaved firms, 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 ∆e back into the fundamental regression, which achieves the desired control. To see this, note that
Equation 3 implies a proportional relation between the fitted CDS spread and both the EDF and risk
49
I chose 10 firms to avoid a hardwired result. As more firms are added to the set, there is higher likelihood that the
risk premium measure is significant because it captures residual variations from firms that are also in the industry
portfolios. To address this issue I also construct risk premium estimates using the 20 most well-behaved firms that
are not included in each of industry.
30
%
$
premium ,! " # ,! &'! (. Therefore, by holding the EDF constant over time, I can isolate
the relation 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 ∆,! )∆&'! over time, which
still holds after CDS spreads are aggregated to the industry level.
Results of the fundamental regression with risk premium controls, estimated using the
subsample of 10 well-behaved firms, are reported in panel A of Table IX. As with other tests, I allow
the exposures to vary 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
variation in the default risk premium. The first row of table IX 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 40% of the change in CDS spreads can be
explained by changes in risk premiums. This number increases slightly during the crisis to
approximately 60%, which is consistent with an increase in excess correlation. R-squared for each
regression shows a strong improvement in the model fit increasing by approximately 0.30 relative to
the fundamental regression. This suggests that approximately 30% of the time series variation in
CDS spread changes can be explained by changes in the risk premium.50
Panel C of Table IX shows the results of the test for risk premium contagion. Strikingly, the
increase in pairwise inter-industry excess correlation is almost entirely explained by controlling for
changes in the default risk premium. This result suggests that risk premiums were the main source of
contagion during the crisis. The one notable exception is the healthcare industry, which still shows a
significant increase in excess correlation with the other and financial sectors. This could result from a
noisy estimate of the risk premium given that only 10 firms are used to construct this measure.
Therefore, I repeat the test using estimates of the risk premium constructed from 20 firms. To avoid a
hardwired result, each industry’s risk premium proxy is estimated using the 20 most well-behaved
firms that are not members of that particular industry. The results of the factor model estimation
using the modified risk premium are reported in Panel B of table IX and show similar results to those
50
Adding the estimated risk premium back into the fundamental model means that the SUR regression suffers from
errors in variables. This is done to remain consistent with other tests. To alleviate such econometric concerns, I also
extract additive errors from equation 3 and repeat the tests for a change in excess correlation. These results are
consistent with what is reported in Table IX
31
in panel A. The tests for contagion are reported in Panel D and show that increasing the precision of
the risk premium estimate explains any residual 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 re-estimate the risk premium using the 20 most well-behaved non-industry firms and
control for liquidity using bid-ask spreads for each firm.51
Results of the risk premium robustness tests are reported in Table X. They show that
controlling for transaction costs in the estimation of the jump-to-default risk premium reduces its
explanatory power in the fundamental regression. This is evidenced by a reduction of approximately
0.08 in r-squared relative to the results reported in Table IX. Therefore, variations in the risk
premium explain approximately 20% rather than 30% of the time series variation in CDS spread
changes. The remaining 10% is likely due to variations in the liquidity premium. With respect to risk
premium contagion, Panel B shows that the results of risk premium contagion are not driven by
variations in liquidity risk.
5. 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.NA.IG index roles 8-12. Using simple measures of
association, I show that the comovement of CDS spread changes increases significantly after July
2007.
Having established that correlations increased, I turn to the question of contagion. CDS
correlation 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 noncredit risk factors. To test whether common variations in 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 correlation into fundamental and excess correlation using a factor model.
Finally, I test for contagion by evaluating whether the correlations of factor model residuals
51
Specifically, I add the natural of the bid-ask spread for each firm into the panel regression in Equation 3. The bidask spread was show to be the most significant determinant of CDS liquidity in Section 4.1
32
increased during the crisis. I find strong evidence that common variations in credit risk were not fully
responsible for the higher correlations observed during the crisis, which establishes that contagion
occurred.
Next, I investigate whether an increase in the variance of liquidity premiums, counterparty
risk premiums, or the jump-to-default risk premium can explain the increase in excess correlation.
First, I investigate liquidity risk. To do this, I add several liquidity proxies, which control for
variations 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
risk was not a significant channel of contagion during the crisis. Therefore, I turn to counterparty
risk. To control for variations in counterparty risk, I add several proxies of aggregate dealer credit
risk into the factor model. However, as with liquidity, controlling for variations 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 variations in risk premiums increased the excess correlation. To
do this, I estimate the jump-to-default risk premium from a sample of well-behaved firms using
Moody’s EDF and the panel regression procedure developed in BDDFS. Adding the change in this
measure into the factor model, I find that changes in the risk premium account for approximately
30% 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 risk premium was the main channel for contagion. This important result shows
that a systematic re-pricing of credit risk, rather than increased variations from market frictions,
amplified CDS correlation during the credit crisis.
33
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37
Appendix A
Firm-by-Firm Excess Correlation
Testing for excess correlation proceeds in two steps, first I control for changes in credit risk
using firm-level OLS estimations of the factor model. Independent variables include firm specific
equity returns and equity volatility (when equity data is available). Systematic and industry variables
are defined in Table III (firm-level factor models do not include industry equity volatility). For
robustness, I estimate three additional models. The time varying model allows for time variation in
factor exposures.52 The Acharya and Johnson (2007) (A&J) model controls for the non-linear relation
between equity returns and CDS returns [see Acharya and Johnson (2007)],53 The time varying
Acharya and Johnson model allows for time varying parameters in the A&J model. This produces
150 series of regression residuals for each model. After controlling for credit risk I implement three
tests for an increase in excess correlation. The first is a principal component analysis of the model
residuals, which is similar to that of Collin-Dufresne et al. (2001). In this analysis, a decrease in the
number of principal components required to explain a certain level of common variation indicates an
increase in comovement [see Kaminsky et al. (2002)]. Additionally, I include tests of average
Pearson’s and Spearman’s correlations, which are identical to those carried out on raw CDS spread
changes.
The results of these tests are reported in Table A1. Panel A shows the factor exposures of the
average firm; the percent of firms for which the factor is significant at the 10% level is reported in
square brackets. Panel B shows that the number of principal components required to explain 37% of
the common variation in residuals, for the base model, decreased from twelve prior to the crisis to
one during the crisis. This result is consistent across all model specifications. Furthermore, the
average Pearson’s and Spearman’s correlations increased significantly during the crisis for all model
residuals and within each industry. These results support the argument that correlations increased due
to the heightened influence of a common non-credit component.
52
This is achieved, using OLS, by estimating interaction terms for each factor along with a constant dummy variable
for sixty day intervals, which is the same as running OLS on 60 day windows throughout the sample period. The 60
day window is arbitrary and reduces the precision of OLS estimates. Therefore, I also use 90 and 120 day windows,
which do not change the results.
53
Acharya et al. (2007) exploit the approximate linear elasticity between CDS returns and equity returns to capture
the non- linear relation implied by Merton (1974). Their model relates CDS returns, which are different from spread
changes, to stock returns. However, CDS returns, as defined by Longstaff, Pan, Pedersen and Singleton (2007), on
average have a correlation of -.94 with spread changes.
38
Table A1
Equation – by – equation excess correlation: This table reports the results from the firm-by-firm analysis of
excess correlation. In the fundamental model, shown below, β i is a vector of coefficients on economic variables
for firm i and γ i is a vector of marginal changes during the crisis, Dcrisis is an indicator variable equal to one during
the crisis. Finally, F is the vector of economic factors listed in Table III with the addition of firm specific equity
returns (FRET) and equity GARCH volatility (FVOL) for each firm with available equity prices.
Ri = β i F + γ i FDcrisis + ε i
The average regression coefficients from the equation-by-equation OLS estimation are reported in Panel A. The
column labeled β contains the average regression coefficient for each fundamental variable and the panel labeled
γ contains the average marginal change during the crisis. In square braces is the percent of times the variable is
significant at the 10% level, significance is determined using the Huber/White/sandwich robust variance estimator.
Market variables ∆VIX, HML SMB and HB are orthogonalized to the S&P 500 returns. Panel B reports the
cumulative explained variation for components 1 through 4 and 12 of the principal components analysis of OLS
residuals. Columns 1 and 2 show the pre-crisis and crisis principal components for the base model, time varying
factor exposure model, the Acharya and Johnson Model and the time varying Acharya and Johnson Model. Panel
C shows the results of the test for a change in the average correlations (Pearson’s and Spearman’s) of OLS
residuals from each of the four different models. The first column gives the number of firms in each group.
Column two reports the average difference in Pearson’s correlation from the pre-crisis to the crisis period. The tstatistic is for a paired two sample t-test of Fisher transformed correlation coefficients, the z-statistic is calculated
from the asymptotic variance of the difference in transformed correlations (assuming independence). Columns five
and six report results of the test for a change in average Spearman’s Rho. Significance of the change is assessed
using an F-test based on the ratio of Friedman (1937) statistics in the pre-crisis and crisis periods. Correlations are
tested using one sided tests for an increase. *, **, *** indicate significance at the 10% 5% and 1% levels
respectively.
Panel A: Firm Regression Coefficient Summary
β
-0.24
SP500
0.00
∆VIX
-0.03
∆RF3M
-0.01
∆SLOPE
-1.19
HB
0.07
∆DEF
0.04
SMB
-0.26
HML
-0.07
FVOL
0.00
FRET
0.01
INDRET
0.19
R Squared
Panel B: Principal Components
Base Model
Pre-Crisis
Crisis
Component 1
0.19
0.37
Component 2
0.22
0.41
Component 3
0.24
0.43
Component 4
0.26
0.45
Component 12
0.37
0.58
γ
[0.44]
[0.27]
[0.18]
[0.30]
[0.14]
[0.49]
[0.11]
[0.31]
[0.19]
[0.19]
[0.15]
-0.86
-0.04
0.01
0.10
0.78
0.17
0.17
0.39
-4.36
-0.18
-0.08
[0.27]
[0.43]
[0.19]
[0.09]
[0.07]
[0.22]
[0.03]
[0.20]
[0.17]
[0.25]
[0.11]
Time Varying
Pre-Crisis
Crisis
0.18
0.36
0.21
0.40
0.23
0.42
0.25
0.44
A&J
Pre-Crisis
Crisis
0.20
0.37
0.23
0.40
0.25
0.43
0.27
0.45
Time Varying AJ
Pre-Crisis
Crisis
0.15
0.33
0.18
0.37
0.20
0.39
0.22
0.41
0.37
0.57
0.38
0.57
0.34
0.53
39
Time Varying AJ
A&J
Time Varying
Base Model
Panel C: Excess Correlation
Full Sample
Consumer
Manufacturing
HiTech
Health
Other
Financials
Full Sample
Consumer
Manufacturing
HiTech
Health
Other
Financials
Full Sample
Consumer
Manufacturing
HiTech
Health
Other
Financials
Full Sample
Consumer
Manufacturing
HiTech
Health
Other
Financials
N
150
36
43
20
7
18
26
150
36
43
20
7
18
26
150
36
43
20
7
18
26
150
36
43
20
7
18
26
pre
0.17
0.18
0.19
0.21
0.13
0.27
0.18
0.17
0.17
0.18
0.19
0.12
0.26
0.16
0.17
0.19
0.20
0.22
0.13
0.28
0.19
0.17
0.15
0.15
0.18
0.12
0.22
0.10
Pearson’s Correlation
crisis
Diff
t-stat
0.36
0.18***
154.81
0.40
0.22***
42.54
0.37
0.19***
47.15
0.44
0.23***
23.45
0.42
0.29***
17.57
0.44
0.17***
10.24
0.31
0.13**
16.46
0.36
0.18***
154.81
0.40
0.22***
44.17
0.37
0.19***
47.77
0.44
0.25***
26.64
0.38
0.26***
15.88
0.44
0.18***
11.94
0.31
0.15***
17.24
0.36
0.18***
154.81
0.41
0.22***
45.15
0.37
0.17***
43.10
0.44
0.21***
20.92
0.41
0.28***
20.17
0.43
0.15***
10.06
0.30
0.11**
14.40
0.36
0.18***
154.81
0.37
0.22***
47.12
0.34
0.18***
49.73
0.40
0.23***
25.62
0.35
0.23***
13.86
0.39
0.17***
13.70
0.26
0.16***
23.48
z stat
3.02
3.67
3.16
3.98
4.72
2.79
2.18
3.02
3.72
3.16
4.20
4.17
2.97
2.51
3.02
3.74
2.89
3.69
4.67
2.47
1.87
3.02
3.61
3.01
3.78
3.67
2.73
2.53
pre
0.16
0.18
0.18
0.21
0.11
0.26
0.16
0.16
0.15
0.16
0.18
0.10
0.24
0.13
0.16
0.17
0.17
0.21
0.11
0.25
0.15
0.16
0.13
0.14
0.16
0.08
0.20
0.10
Spearman’s Rho
crisis
Ratio
0.37
1.70***
0.41
1.65***
0.40
1.60***
0.43
1.42***
0.41
1.59***
0.43
1.20**
0.33
1.46***
0.37
1.70***
0.38
1.70***
0.38
1.72***
0.40
1.49***
0.36
1.50***
0.41
1.21**
0.31
1.58***
0.37
1.70***
0.41
1.71***
0.38
1.57***
0.41
1.37***
0.40
1.61***
0.42
1.21**
0.31
1.37***
0.37
1.70***
0.34
1.74***
0.32
1.64***
0.34
1.44***
0.33
1.53***
0.36
1.26***
0.26
1.61***
p-val
0.00
0.00
0.00
0.00
0.00
0.03
0.00
0.00
0.00
0.00
0.00
0.00
0.02
0.00
0.00
0.00
0.00
0.00
0.00
0.02
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.00
40
Appendix B
List of Events: This table shows a list of significant distress and recovery events that occurred during the crisis. The event number is listed in the left most
column, the date it occurred is in column two. Column three contains the type of event, which is defined as follows: D = distress event, F = action by the Federal Reserve, R = the
rescue of a distressed company or companies, P = a government implemented policy to aid the economy, CI = a capital infusion where the government purchased stock via the
Capital Purchase Program. Panel B lists interest rate reduction events (IR) and Panel C lists dates that are omitted due to two or more confounding events that took place on a single
day. Finally, Swap identifies days when swap lines with other countries were established or increased. I also classify the events into three categories by the severity of the event.
These classifications, 1-3, are reported in the column labeled Severity. In determining severity of an event both the timing and significance of the event are taken into account. For
example Capital Infusions during the most severe part of the crisis (Sept. 2008 to Dec. 2008) are classified as 2; after Dec. they are classified as 1.
Date
Type
Severity
Event
1
7/31/2007
D
2
2
3
8/6/2007
8/9/2007
D
D
2
1
4
8/16/2007
D
1
5
1/11/2008
D
2
6
1/18/2008
D
1
7
8
9
10
11
2/17/2008
3/5/2008
3/14/2008
6/5/2008
7/11/2008
D
D
D
D
D
2
1
3
1
2
12
7/15/2008
D
1
13
9/7/2008
D
2
14
9/15/2008
D
3
15
16
9/25/2008
10/24/2008
D
D
3
2
17
11/17/2008
D
1
18
1/13/2009
D
1
19
8/10/2007
F
1
Distress Events
Bear Stearns Liquidates two hedge funds that specialize in subprime securitizations. American Home Mortgage announces inability to
fund lending obligations
American Home Mortgage Investment Corporation files for bankruptcy.
BNP Paribas halts redemptions on three investment funds.
Fitch Ratings downgrades Countrywide Financial Corporation to BBB+. Countrywide borrows the entire $11.5 billion available in its
credit lines with other banks.
Bank of America announces that it will purchase Countrywide Financial for approximately $4 billion.
Fitch Ratings downgrades Ambac Financial Group’s insurance financial strength rating to AA, Credit Watch Negative. Standard and
Poor’s place Ambac’s AAA rating on CreditWatch Negative.
Northern Rock is taken over by the Treasury of the United Kingdom.
Carlyle Capital Corporation begins receiving default notices after failing to meet margin calls on mortgage securities.
JPMorgan Chase announces the purchase of Bear Stearns
Standard and Poor’s downgrades monoline bond insurers AMBAC and MBIA from AAA to AA.
The Office of Thrift Supervision closes IndyMac Bank
The Securities Exchange Commission (SEC) temporarily prohibits naked short selling in the securities of Fannie Mae, Freddie Mac, and
primary dealers at commercial and investment banks.
The Federal Housing Finance Agency (FHFA) places Fannie Mae and Freddie Mac in government conservatorship. The U.S. Treasury
Department announces three additional measures to provide additional support to Fannie Mae and Freddie Mac.
Lehman Brothers Holdings Incorporated files for bankruptcy. Bank of America announces its intent to purchase Merrill Lynch & Co. for
$50 billion.
The Office of Thrift Supervision closes Washington Mutual Bank and JPMorgan Chase acquires its banking operations.
PNC Financial Services Group Inc. purchases National City Corporation
Three large U.S. life insurance companies seek TARP funding: Lincoln National, Hartford Financial Services Group, and Genworth
Financial.
The Federal Home Loan Bank of Seattle reports a risk-based capital deficiency and suspend its dividend because of a decline in the
market value of its mortgage-backed securities portfolio. Royal Bank of Scotland forced to reveal that it had leant 3.47 billion dollars to
bankrupt Lyondell Chemical
Recovery Events
The Federal Reserve Board announces that it “will provide reserves as necessary…to promote trading in the federal funds market at rates
41
20
21
9/14/2007
10/15/2007
R
R
2
2
22
12/12/2007
F
2
23
2/13/2008
P
2
24
3/7/2008
F
1
25
3/11/2008
F
2
26
3/16/2008
F
3
27
5/2/2008
F
1
28
7/13/2008
F
1
29
7/30/2008
F/P
1
30
31
9/14/2008
9/16/2008
F
R
1
3
32
9/19/2008
F
2
33
10/3/2008
P
3
34
10/7/2008
F
2
35
10/8/2008
R
1
36
10/14/2008
F/P
1
37
10/21/2008
F
2
38
10/28/2008
CI
2
close to the FOMC’s target rate of 5.25 percent.”
The Chancellor of the Exchequer authorizes the Bank of England to provide liquidity support for Northern Rock.
Citigroup, Bank of America, and JPMorgan Chase announce plans for an $80 billion Master Liquidity Enhancement Conduit.
The Federal Reserve Board announces the creation of the Term Auction Facility (TAF) in which fixed amounts of term funds will be
auctioned to depository institutions. The FOMC authorizes temporary swap lines with the European Central Bank (ECB) and the Swiss
National Bank (SNB).
President Bush signs the Economic Stimulus Act of 2008 (Public Law 110-185) into law.
The Federal Reserve Board announces $50 billion TAF auctions on March 10 and March 24 and extends TAF for at least 6 months. The
Board also initiates a series of term repurchase transactions, expected to cumulate to $100 billion, conducted as 28-day term repurchase
agreements with primary dealers.
The Federal Reserve Board announces the creation of the Term Securities Lending Facility (TSLF). The FOMC increases its swap lines
with the ECB by $10 billion and the Swiss National Bank by $2 billion.
The Federal Reserve Board establishes the Primary Dealer Credit Facility (PDCF), which extends credit to primary dealers at the primary
credit rate (against investment grade securities). The Federal Reserve Board reduces the primary credit rate 25 basis points to 3.25
percent.
The FOMC expands the list of eligible collateral for Schedule 2 TSLF auctions. The FOMC also increases existing swap lines with the
ECB and with the Swiss National Bank by $6 billion. The Federal Reserve Board expands TAF auctions from $50 billion to $75 billion.
The Federal Reserve Board authorizes the Federal Reserve Bank of New York to lend to Fannie Mae and Freddie Mac, should such
lending prove necessary. The U.S. Treasury Department announces a temporary increase in the credit lines of Fannie Mae and Freddie
Mac and a temporary authorization for the Treasury to purchase equity in either GSE if needed.
The Federal Reserve Board extends the TSLF and PDCF. It also introduces auctions of options on $50 billion of draws on the TSLF, and
introduces 84-day TAF loans. The FOMC increases its swap line with the ECB to $55 billion. President Bush signs into law the Housing
and Economic Recovery Act of 2008 (Public Law 110-289).
The Federal Reserve Board expands the list of eligible collateral for the PDCF and TSLF.
The NY Fed is authorized to lend up to $85 billion to American International Group (AIG).
The Federal Reserve Board announces the creation of the Asset-Backed Commercial Paper Money Market Mutual Fund Liquidity
Facility (AMLF) facilitating the purchase of high-quality asset-backed commercial paper from money market mutual funds. The Federal
Reserve Board also announces plans to purchase federal agency discount notes from primary dealers. The U.S. Treasury Department
makes $50 billion available, which will guarantee investments in participating money market mutual funds.
Congress passes and President Bush signs into law the Emergency Economic Stabilization Act of 2008 (Public Law 110-343), which
establishes the $700 billion Troubled Asset Relief Program (TARP).
The Federal Reserve Board announces the creation of the Commercial Paper Funding Facility (CPFF) providing liquidity backstops to
U.S. issuers of commercial paper. The FDIC announces an increase in deposit insurance coverage to $250,000 per depositor.
NY Fed is authorized to borrow up to $37.8 billion in investment-grade, fixed-income securities from American International Group
(AIG) in return for cash collateral.
The FOMC increases its swap line with the Bank of Japan. The FDIC creates a new Temporary Liquidity Guarantee Program to
guarantee the senior debt of all FDIC-insured institutions and their holding companies, as well as deposits in non-interest-bearing deposit
transactions through June 30, 2009. U.S. Treasury Department announces that TARP funds will be used to purchase equity in financial
institutions under the authority of the Emergency Economic Stabilization Act of 2008.
The Federal Reserve Board announces creation of the Money Market Investor Funding Facility (MMIFF). The facility provides senior
secured funding to special purpose vehicles for the purchase of U.S. dollar-denominated certificates of deposit and commercial paper,
issued by highly rated financial institutions, with a maturity of 90 days or less.
The U.S. Treasury Department purchases $125 billion in preferred stock in nine U.S. banks (Capital Purchase Program). The FOMC and
42
Reserve Bank of New Zealand establish a $15 billion swap line.
Federal Reserve adds $21 billion to loans for AIG
Restructuring of AIG financial support. Treasury purchased 40 billion in AIG preferred stock under TARP. AIG will use 25 billion to
40
11/10/2008
CI
1
pay down Federal Reserve Board Loans leaving $15 billion in new support to AIG. Also NY Fed establishes new lending facility with
AIG
41
11/14/2008
CI
2
Treasury purchase $33.5 billion in preferred stock of 21 U.S. banks (Capital Purchase Program)
42
11/21/2008
CI
2
Treasury purchase $3 billion in preferred stock of 23 U.S. banks (Capital Purchase Program)
The U.S. Treasury Department, Federal Reserve Board, and FDIC jointly announce an agreement provide Citigroup with protection
43
11/23/2008
R
1
against losses on commercial residential securities. In exchange Citigroup will issue preferred shares to the Treasury and FDIC.
The Federal Reserve Board announces the creation of the Term Asset-Backed Securities Lending Facility (TALF). The Federal Reserve
44
11/25/2008
F
2
Board announces a new program to purchase direct obligations of GSEs — Fannie Mae, Freddie Mac and Federal Home Loan Banks. Up
to $100 billion in GSE direct obligations and $500 billion in MBS.
45
12/2/2008
F
2
The Federal Reserve Board announces that it will extend three liquidity facilities, PDCF, AMLF, TSLF through April 30, 2009.
46
12/5/2008
CI
2
Treasury purchase $4 billion in preferred stock of 35 U.S. banks (Capital Purchase Program)
Treasury purchase $27.9 billion in preferred stock of 49 U.S. banks (Capital Purchase Program) The U.S. Treasury Department
47
12/19/2008
CI
2
authorizes loans of up to $13.4 billion for General Motors and $4.0 billion for Chrysler from the TARP.
48
12/23/2008
CI
2
Treasury purchase $15.1 billion in preferred stock of 43 U.S. banks (Capital Purchase Program)
The U.S. Treasury Department announces that it will purchase $5 billion in equity from GMAC and agrees to lend up to $1 billion to
49
12/29/2008
R
2
GM.
50
12/31/2008
CI
2
Treasury purchase $1.91 billion in preferred stock of 7 U.S. banks (Capital Purchase Program)
51
1/9/2009
CI
1
Treasury purchase $4.8 billion in preferred stock of 43 U.S. banks (Capital Purchase Program)
Treasury purchase $1.4 billion in preferred stock of 39 U.S. banks (Capital Purchase Program). The U.S. Treasury Department, Federal
52
1/16/2009
CI
1
Reserve, and FDIC announce a support package for Bank of America including a loss-sharing arrangement ($118 billion), in exchange
for preferred stock. The U.S. Treasury Department announces that it will lend $1.5 billion from the TARP to Chrysler Financial.
53
1/23/2009
CI
1
Treasury purchase $326 million in preferred stock of 23 U.S. banks (Capital Purchase Program)
The National Credit Union Administration (NCUA) Board announces that the NCUA will guarantee uninsured shares at all corporate
54
1/28/2009
CI
1
credit. The Board also approves a $1 billion capital purchase in U.S. Central Corporate Federal Credit Unions.
55
1/30/2009
CI
1
Treasury purchase $1.15 billion in preferred stock of 23 U.S. banks (Capital Purchase Program)
56
2/3/2009
F
1
The Federal Reserve announces the extension of existing liquidity programs.
57
2/6/2009
CI
1
Treasury purchase $238.5 million in preferred stock of 28 U.S. banks (Capital Purchase Program)
The Federal Reserve Board announces that it is prepared to expand the Term Asset-Backed Securities Loan Facility (TALF). U.S.
58
2/10/2009
F
1
Treasury announces a Financial Stability Plan involving purchases of preferred stock in eligible banks. Expansion of the Federal
Reserve’s TALF.
59
2/13/2009
CI
1
Treasury purchase $429 million in preferred stock of 29 U.S. banks (Capital Purchase Program)
Treasury
purchase $365.4 million in preferred stock of 23 U.S. banks (Capital Purchase Program)
60
2/24/2009
CI
1
President Obama signs into law the "American Recovery and Reinvestment Act of 2009", which includes a variety of spending measures
61
2/17/2009
P
1
and tax cuts intended to promote economic recovery.
Treasury purchase $394.9 million in preferred stock of 28 U.S. banks (Capital Purchase Program)
62
2/27/2009
CI
1
The U.S. Treasury Department and the Federal Reserve Board announce the launch of the Term Asset-Backed Securities Loan Facility
63
3/3/2009
F
1
(TALF).
64
3/6/2009
CI
1
Treasury purchase $284.7 million in preferred stock of 22 U.S. banks (Capital Purchase Program)
Panel B: Interest Rate Reductions and Swap Agreements
39
10/30/2008
R
1
43
64
65
66
67
68
69
70
71
72
8/17/2007
9/18/2007
10/31/2007
12/11/2007
1/22/2008
1/30/2008
3/18/2008
4/30/2008
10/8/2008
IR
IR
IR
IR
IR
IR
IR
IR
IR
1
1
1
1
1
1
1
1
1
73
12/16/2008
IR
1
73
9/18/2008
Swap
1
74
9/24/2008
Swap
1
75
9/26/2008
Swap
1
76
10/13/2008
Swap
1
77
10/29/2008
Swap
1
Panel C: Multiple Event Dates
78
12/21/2007
D
79
12/21/2007
F
80
9/17/2008
D
81
9/17/2008
P
82
9/29/2008
F
83
9/29/2008
D
84
85
12/12/2008
12/12/2008
CI
D
The Federal Reserve Board reduces the primary credit rate 50 basis points to 5.75 percent.
FMOC reduces target federal funds rate 50 basis points to 4.75 percent. Fed reduces primary credit rate50 basis points to 5.25 percent.
FMOC reduces target federal funds rate 25 basis points to 4.50 percent. Fed reduces primary credit rate25 basis points to 5.00 percent.
FMOC reduces target federal funds rate 25 basis points to 4.25 percent. Fed reduces primary credit rate25 basis points to 4.75 percent.
FMOC reduces target federal funds rate 75 basis points to 3.5 percent. Fed reduces primary credit rate75 basis points to 4 percent.
FMOC reduces target federal funds rate 50 basis points to 3 percent. Fed reduces primary credit rate50 basis points to 3.5 percent.
FMOC reduces target federal funds rate 75 basis points to 2.25 percent. Fed reduces primary credit rate75 basis points to 2.50 percent.
FMOC reduces target federal funds rate 25 basis points to 2 percent. Fed reduces primary credit rate25 basis points to 2.25 percent.
FMOC reduces target federal funds rate 50 basis points to 1.50 percent. Fed reduces primary credit rate50 basis points to 1.75 percent.
The FOMC votes to establish a target range for the effective federal funds rate of 0 to 0.25 percent. Fed reduces primary credit rate75
basis points to 0.50 percent.
The FOMC expands existing swap lines by $180 billion and authorizes new swap lines with the Bank of Japan, Bank of England, and
Bank of Canada.
The FOMC establishes new swap lines with the Reserve Bank of Australia, the Sveriges Riksbank, the Danmarks National bank and the
Norges Bank.
The FOMC increases existing swap lines with the ECB by $10 billion and the Swiss National Bank by $3 billion.
The FOMC increases existing swap lines with foreign central banks. The Bank of England, European Central Bank, and Swiss National
Bank announce that they will conduct tenders of U.S. dollar funding at 7-, 28-, and 84-day maturities at fixed interest rates.
The FOMC also establishes swap lines with the Banco Central do Brasil, Banco de Mexico, Bank of Korea and the Monetary Authority
of Singapore for up to $30 billion. The FOMC reduces its target for the federal funds rate 50 basis points to 1.00 percent. The Federal
Reserve Board reduces the primary credit rate 50 basis points to 1.25 percent.
Citigroup, JPMorgan Chase, and Bank of America abandon plans for the Master Liquidity Enhancement Conduit.
The Federal Reserve Board announces that TAF auctions will be conducted every two weeks as long as financial market conditions
warrant.
The SEC bans short selling of stock for all companies in the financial sector.
The U.S. Treasury Department announces a Supplementary Financing Program consisting of a series of Treasury bill issues that will
provide cash for use in Federal Reserve initiatives.
The FOMC authorizes a $330 billion expansion of swap lines with Bank of Canada, Bank of England, Bank of Japan, Danmarks
Nationalbank, ECB, Norges Bank, Reserve Bank of Australia, Sveriges Riksbank, and Swiss National Bank. The Federal Reserve Board
expands the TAF.
The FDIC announces that Citigroup will purchase the banking operations of Wachovia Corporation. The FDIC agrees to a loss-sharing
arrangement with Citigroup. In return, Citigroup would grant the FDIC $12 billion in preferred stock and warrants. The U.S. House of
Representatives rejects legislation submitted by the Treasury Department requesting authority to purchase troubled assets from financial
institutions.
Treasury purchase $6.25 billion in preferred stock of 28 U.S. banks (Capital Purchase Program)
Bernard Madoff arrested for over alleged Ponzi scheme
44
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 equ
equally
ally weighted average over all
pairwise correlations. This calculation is rolled daily
ily to obtain the correlations graphed above.
45
Figure 2
Average CDS Spread & Sample Per
Periods
The graph shows the daily equally weighted average CDS spread for all 150 firms between July 5, 2005 and March 9,
2009. Numbers on the graph represent significant events that occurred during the crisis aand correspond to event numbers
in Appendix A.. The time period between the two vertical bars (labeled crisis period) defines the crisis period. To the left
of the left-most vertical bar is the pre-crisis
crisis period.
46
Figure 3
S&P Long Term Issuer Ratings
Over Time
Industry groups are defined using the Fama and French 5 industry classifications with the sixth industry, Financials, extract
extracted from Other. Each
industry CDS spread represents the CDS premium on an equally weighted portfolio of contracts.
47
Figure 4
Sample Characteristics
Box plots show the distributions of firms’ characteristics through time (2005-2008) for the sample of the full sample of firms used in this study against the
CRSP/Compustat universe. Book Leverage = ((AT - (AT – LT – PSTLK + TXDITC + DCVT))/AT), Profitability = NI/AT, Market–To– Book = (CSHO*PRCC_F
+ AT - (AT – LT – PSTLK + TXDITC + DCVT))/AT, Cash = CH, Total Assets = AT, and Market Capitalization = CSHO * PRCC_F. The book leverage and book
value of equity are calculated as in Baker and Wurgler (2002).The Box plots omit outliers.
48
Figure 5
S&P Long Term Issuer Ratings
Over Time
The graph above shows the number of firms in the sample with S&
S&P long-term
term issuer ratings in a given
category by year from 2005 to 2009. The investment grade threshold for S&P ratings is BBB
BBB- and several firms
in the CDX.NA.IG fall below that. This is because the long term issuer rating is an aggregate measure of the
firm’s ability to meet all debt obligations. In contrast, the CDX.NA.IG index is constructed using investment
grade bonds. Monthly S&P long term issuer ratings are obtained from Compustat and yearly ratings are
constructed using the rating on the first ava
available month of the year.
49
Figure 6
Pairwise Correlations of CDS Spread Changes
Pairwise correlations for all 11,175 possible firm pairs are calculated prior to and during the crisis and are shown
above. In red is the cross-sectional density of pairwise correlation during the crisis and in blue is the crosssectional density of pairwise correlation prior to the crisis.
50
Table I
Descriptive statistics for the sample of CDS spread changes prior to and during the crisis are reported below. The pre-crisis period begins on July 5, 2005 and ends on July 30 2007; the crisis period begins on July 31, 2007 and
ends on March 9, 2009. Each panel describes the changes in raw CDS premiums for seven equally weighted portfolios of CDS contracts. The Full Sample portfolio is constructed using daily premiums for all CDS contracts in
the sample. Similarly, industry portfolios are constructed using daily spreads for industry groups defined using the Fama and French five industry portfolio classifications. The sixth industry, Financials, is extracted from the
Other industry classification, which yields the following industry groups. Consumer: Consumer Durables and Non-Durables, Wholesale, Retail, and Laundry and Repair shop services. Manufacturing: Manufacturing, Energy and
Utilities. HiTech: Business Equipment and Telephone & Television Transmission. Other: Mining, Construction, Building Materials, Transportation, Hotels, Business Services, and Entertainment. In Panel A, the first two
columns give portfolio labels and the number of firms in each portfolio. Columns labeled Pre-Crisis report statistics calculated prior to the crisis and columns labeled Crisis report statistics calculated during the crisis. Statistics
include the mean, standard deviation, skewness and kurtosis of CDS spread changes. The difference in the average spread change and standard deviations are reported in columns labeled Diff and Ratio respectively. The column
labeled Ratio reports the ratio of the variance in spread changes during the crisis to that prior to the crisis. Panel B shows the average Pearson’s correlations for the full sample and within each industry over different sub periods.
Column one reports the average correlations over the full sample period. Columns two and three give correlations for the pre-crisis and crisis periods respectively. The remaining columns show the average correlation calculated
on half year intervals where H1 and H2 indicate the first and second half of each year. Significance of correlation coefficients is assessed using a standard t-test. Panel C reports results for the tests of autocorrelation using the
standard Ljung Box test with five lags. Bold statistics represent significance at the 5% level.
Panel A: Descriptive Statistics
Mean Spread Changes
Standard Deviations
Skewness
Excess Kurtosis
Pre-Crisis
Crisis
Diff
Pre-Crisis
Crisis
Ratio
Pre-Crisis
Crisis
Pre-Crisis
Crisis
Full Sample
150
0.05%
0.01
0.08
4.45
0.39
40.95
4.79
1.07%
1.02%
146.08
Consumer
36
0.02%
0.01
0.09
3.09
-0.07
21.46
5.47
1.00%
0.98%
153.13
Manufacturing
43
0.01%
0.01
0.06
3.34
0.78
25.88
4.62
0.88%
0.86%
113.54
HiTech
20
0.07%
0.01
0.07
3.14
0.17
20.73
5.09
0.69%
0.62%
57.96
Health
7
0.11%
0.04%
0.01
0.03
5.91
0.01
62.13
2.53
0.07%
13.95
Other
18
0.56%
0.45%
0.01
0.07
3.81
0.04
32.38
2.37
0.11%
31.64
Financials
26
0.01
0.22
4.51
0.32
42.36
10.09
0.07%
2.38%
2.30%
763.98
Panel B: Pre-Crisis and Crisis Correlations
N
Full Period Pre-Crisis
Crisis
2005 H2
2006 H1
2006 H2
2007 H1
2007 H2
2008 H1
2008 H2
2009 H1
Full Sample
150
0.22
0.16
0.22
0.12
0.20
0.41
0.43
0.41
0.52
0.47
0.42
Consumer
36
0.20
0.14
0.22
0.11
0.21
0.47
0.50
0.45
0.53
0.56
0.44
Manufacturing
43
0.22
0.23
0.14
0.21
0.42
0.24
0.43
0.45
0.58
0.46
0.44
HiTech
20
0.27
0.20
0.27
0.15
0.26
0.47
0.51
0.49
0.52
0.53
0.55
Health
7
0.13
0.04
0.09
0.07
0.13
0.33
0.40
0.41
0.44
0.53
0.54
Other
18
0.32
0.28
0.32
0.22
0.31
0.52
0.54
0.51
0.59
0.58
0.58
Financials
26
0.26
0.20
0.22
0.12
0.21
0.34
0.36
0.37
0.37
0.47
0.43
Panel C: Autocorrelation
Pre-Crisis
Crisis
Full
Full
Sample Consumer Manuf.
HiTech
Health
Other
Financials Sample Consumer Manuf.
HiTech
Health
Other
Financials
Ljung-Box
Test (1-5)
205.88
122.26
158.33
114.80
159.55
148.37
246.39
37.49
36.40
72.54
52.18
37.84
60.81
11.34
p-value
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.04
N
51
Table II
Changes in comovement are reported below. The table shows three measures of aggregate comovement in CDS spread changes prior to and
during the crisis. It also includes the results of tests for an increase in each of these measures. Spread changes have all been filtered for
autocorrelation. The pre-crisis and crisis periods are defined in Table I. Industries are the Fama and French five industry classifications with
the sixth industry, Financials, extracted from Other; category details are given in Table I. In each panel the column labeled Pre-Crisis shows
the aggregate association statistic calculated prior to the crisis and the column labeled Crisis shows the aggregate association statistic during
the crisis. Aggregate association statistics include the average pairwise Pearson’s correlation, the average pairwise Spearman’s correlations
and the average fraction of firms that move together each week reported in panels A,B and C respectively. Panel A: the t-statistic for a two
sample paired t-test of Fisher transformed Pearson’s correlations (z = ½ ln[(1+ρ)/ (1-ρ)]) is reported in the column labeled t-statistic. The
column labeled z-statistic reports the z-statistic for the paired two sample test based on the asymptotic distribution implied by the Fisher
transformation. Panel B: The average change in Rho is tested using the ratio of Friedman statistics (FR = (T-1)[(N-1) ρ +1]) ~ χ2(T-1)),
which are shown in column labeled Ratio. P-values for these ratios, taken from the F distribution, are reported in column labeled P-Value.
Panel C The fraction of firms that move together each week is calculated from Morck et al. (2000)
up
t
Their proposed asymptotic variance ( f t (1 − f t ) /(n
down
t
+n
(
)
f t = max ntup , ntdown ntup + ntdown
.
) ) is used to assess the statistical significance of the increase in this fraction
(assuming independence over time). The change in this fraction is reported in the column labeled Difference and the associated p-values for
the change are reported in the column labeled P-Value. All tests are one sided for an increase in comovement. *, **, *** indicate significance
at the 10% 5% and 1% levels respectively.
Panel A: Average Pearson’s Correlation
Full Sample
Consumer
Manufacturing
HiTech
Health
Other
Financials
Pre-Crisis
0.20
0.21
0.22
0.24
0.14
0.30
0.21
Crisis
0.44
0.50
0.45
0.51
0.46
0.54
0.40
Diff
0.24***
0.29***
0.23***
0.27***
0.32***
0.23***
0.19***
t-statistic
194.75
56.64
53.04
27.39
22.87
14.60
22.33
z-statistic
4.16
5.20
4.07
4.90
5.42
4.12
3.32
Panel B: Average Spearman Correlation
Full Sample
Consumer
Manufacturing
HiTech
Health
Other
Financials
Pre-Crisis
0.18
0.19
0.19
0.22
0.12
0.27
0.16
Crisis
0.46
0.51
0.47
0.50
0.47
0.54
0.43
Ratio
1.96***
1.88***
1.77***
1.56***
1.72***
1.40***
1.80***
P-Value
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Difference
0.10***
0.11***
0.11***
0.08***
0.08***
0.08***
0.07***
P-value
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Panel C: Fraction of Common Co-movement
Full Sample
Consumer
Manufacturing
HiTech
Health
Other
Financials
Pre-Crisis
0.73
0.73
0.74
0.76
0.76
0.77
0.75
Crisis
0.83
0.85
0.85
0.84
0.83
0.85
0.82
52
Table III
Variable Definitions for the fundamental model are shown below. The specification is based on Collin-Dufresne et al. (2001) who base their
intuition on Merton (1974). The upper panel labeled Default Probabilities lists variables that are included to capture changes in default
probabilities. The lower panel labeled Loss Given Default lists systematic variables, which capture changes in loss given default. The
column labeled “Source” gives the data source which are: The Center for Research in Security Prices (CRSP), The Federal Reserve (FED),
and The Chicago Board of Exchange (CBOE).
Name
Variable Description
Default Probabilities
INDRET
The equally weighted industry equity return. It proxies for leverage or
the overall financial health of firms in the industry
Source
Ex-Sign
CRSP
-
INDVOL
The GARCH equity return volatility. It measures the aggregate risk
of firms in each industry
CRSP
+
RF3M
The three-month constant maturity treasury rate (CMT). Measures the
risk neutral drift of the firm value process. Increases in the risk free
rate decrease default probabilities.
FED
-
SLOPE
The spread between the three-month and 5 year CMT rates. The slope
of the yield curve contains information about the expected future
short rate [Litterman and Scheinkman (1991)], which may affect the
short term risk free rate.
FED
-
VIX
The S&P 500 option implied volatility. Measures expected future
volatility
CBOE
+
SMB & HML
Fama and French small cap and value premiums. Vassalou and Xing
(2004) argue that they contain default risk information
French Data
Library
+
CRSP
-
Loss Given Default
SP500
The daily return on the S&P 500 index. Measures the economic state.
Higher returns are associated with good economic states and lower
CDS spreads
HB
Value weighted return index of major U.S. homebuilders (SIC code
of 1521). The index excludes homebuilders in the sample. This
variable measures variations in the real estate market.
Datastream
-
DEF
Yield spread between Baa and Aaa Moody's bond indices. DEF
measures the general state of credit markets.
FED
+
53
Table IV
SUR parameter estimates of the fundamental model are reported in this table. The dependant variable in each regression is the daily change in CDS spreads for
each of the six industry portfolios (for industry group classifications and sub-period definitions, see the caption in Table I). Independent variables are defined in
Table III. Regression estimates of factor exposures, for the pre-crisis period, are reported in the section of the table labeled Pre-Crisis. Their marginal changes,
during the crisis period, are reported in the section of the table labeled “Marginal Change in the Crisis”. ∆ indicates that the variable is first differenced; all
other variables are percent changes. All variables are corrected for serial correlation and standardized using autoregressive GARCH filters. Changes in
volatilities are winsorized at 99%. ∆VIX, HB, SMB, HML, INDRET are all orthogonalized to SP500. Constants were estimated, though not reported, for the
pre-crisis and crisis periods. The z-statistics are reported in parentheses. There are 912 observations for each industry and *,**,*** represent significance at the
10%, 5% and 1% levels respectively.
Pre-Crisis
SP500
∆RF3M
∆SLOPE
∆VIX
HB
∆DEF
SMB
HML
INDRET
∆INDVOL
Consumer
Manuf.
HiTech
Health
Other
Financials
-0.21***
(-5.26)
0.01
(0.14)
-0.01
(-0.14)
0.05
(0.77)
-0.07
(-1.37)
0.14***
(3.49)
-0.02
(-0.55)
-0.15***
(-3.82)
0.01
(0.27)
-0.03
(-1.29)
-0.20***
(-5.05)
-0.04
(-0.95)
-0.05
(-1.25)
-0.02
(-0.28)
-0.02
(-0.31)
0.12***
(3.12)
-0.03
(-0.59)
-0.09*
(-2.07)
0.00
(0.00)
-0.05
(-1.95)
-0.14***
(-3.57)
-0.06
(-1.49)
-0.05
(-1.16)
0.05
(0.80)
-0.09
(-1.81)
0.14***
(3.54)
-0.01
(-0.14)
-0.05
(-1.40)
0.07
(1.38)
-0.06*
(-2.27)
-0.11**
(-2.49)
0.05
(1.18)
0.01
(0.13)
-0.03
(-0.46)
0.07
(1.24)
0.10**
(2.39)
0.02
(0.43)
-0.07
(-1.71)
-0.10*
(-1.97)
0.02
(0.65)
-0.36***
(-9.35)
-0.05
(-1.26)
-0.12***
(-3.11)
0.06
(0.86)
-0.24***
(-4.28)
0.08*
(2.23)
0.04
(0.98)
-0.10***
(-2.66)
0.05
(0.86)
0.00
(0.20)
-0.19***
(-4.79)
-0.10**
(-2.51)
-0.07
(-1.75)
0.03
(0.47)
-0.10*
(-1.98)
0.10***
(2.61)
0.02
(0.46)
-0.19***
(-4.82)
-0.13*
(-2.12)
0.05
(1.59)
-0.23***
(-3.40)
-0.09
(-1.31)
-0.02
(-0.25)
0.18
(1.60)
-0.01
(-0.16)
-0.05
(-0.79)
0.03
(0.45)
0.12
(1.89)
0.04
(0.41)
0.06
(1.54)
0.1684
-0.32***
(-4.72)
-0.11
(-1.64)
-0.01
(-0.21)
0.08
(0.74)
0.07
(0.77)
-0.07
(-1.17)
-0.04
(-0.60)
0.09
(1.43)
-0.09
(-1.07)
0.04
(0.90)
0.1781
-0.19***
(-2.67)
-0.18**
(-2.50)
-0.07
(-0.99)
0.19
(1.58)
-0.10
(-1.04)
-0.12
(-1.88)
-0.01
(-0.19)
0.14*
(2.05)
0.02
(0.23)
-0.04
(-0.89)
0.0913
-0.11
(-1.72)
-0.17**
(-2.50)
-0.01
(-0.11)
0.01
(0.11)
0.20*
(2.04)
-0.06
(-1.14)
-0.01
(-0.15)
0.13*
(2.14)
-0.32***
(-3.21)
0.04
(1.07)
0.2822
-0.24***
(-3.51)
0.00
(0.05)
0.05
(0.67)
0.10
(0.92)
0.10
(1.18)
-0.03
(-0.44)
0.01
(0.10)
0.24***
(3.83)
-0.17
(-1.74)
-0.05
(-1.03)
0.1974
Marginal change during the crisis
SP500
-0.29***
(-4.27)
∆RF3M
-0.15*
(-2.13)
∆SLOPE
-0.05
(-0.69)
∆VIX
0.08
(0.76)
HB
0.09
(0.98)
∆DEF
-0.06
(-1.01)
SMB
-0.02
(-0.23)
HML
0.14*
(2.29)
INDRET
-0.11
(-1.28)
∆INDVOL
0.03
(0.74)
R Squared
0.2084
54
Table V
Change in excess correlation: Reported below are estimates of the increase in excess correlation between industry portfolios. After
estimating the SUR system shown in Table IV, I extract regression residuals for the pre-crisis and crisis periods (defined din the caption of
Table I). Using these residuals, I implement three tests for a change in excess correlation. The first two, test for a change in the correlation
matrix and a change in the average pairwise correlation using the χ2 statistics developed by Goetzmann et al. (2005); p-values for these tests
are reported in Panel B. In Panel A I report the results of the test for a change in pairwise correlations ρ crisis − ρ pre −crisis the significance
of the change is determined using z-scores from the fisher transformation. Outliers are eliminated prior to calculating correlations. *,**,***
indicate significance at the 10%, 5%, and 1% level respectively.
Panel A: Pairwise Excess Correlation Difference Matrix
Consumer
Manuf.
HiTech
Consumer
0.00
Manufacturing
0.09**
0.00
HiTech
0.17***
0.21***
0.00
Health
0.22***
0.30***
0.36***
Other
0.12***
0.18***
0.15***
Financials
0.08
0.19***
0.14***
Panel B: Correlation Matrix & Average Correlation
Statistic
P-Value
Matrix Test
0.00
Average Correlation
0. 1963***
0.00
Health
Other
Financials
0.00
0.27***
0.32***
0.00
0.14***
0.00
55
Table VI
Liquidity contagion parameter estimates are reported below. Panel A shows the estimated liquidity parameters along with their marginal changes during the crisis, which are estimated by adding liquidity proxies back into
the fundamental model. The specification below contains all fundamental variables defined in Table III (∆S = βiF+γiFDcrisis), and liquidity proxies (L).
∆S i = β i F + γ i FDcrisis + δ i L + δ ic LDcrisis + ε i
Liquidity proxies include the yield spread between the on-the-run and off-the-run five-year treasury note (ONOFF). The spread between the three-month overnight index swap rate and RF3M (OISTB). The average bid-ask
spread over all contracts in the sample (BIDASK) and by industry (IBIDASK); the industry bid-ask spreads are orthogonalized to the average bid-ask spread. The difference between the general collateral repo rate and RF3M
(ONREPO) and the hedge fund index (HEDGE), which is the equally weighted average of hedge fund style returns. Bond market liquidity proxies include the daily average Amidhud measure (AMIHUD), the average
industry principal amount traded each day (VOLUME), and the average number of trades per industry each day (NTRADE). All bond market proxies are constructed using TRACE transaction prices for all firms’ bonds that
traded over the sample period. HEDGE is orthogonalized to the S&P 500 return. I re-estimate the marginal changes in liquidity parameters on the month following the collapse of Lehman Brothers (9/15/2008-10/15/2008)
these results are reported in the panel labeled Non-Lehman/ Lehman. Panel B reports the results of the tests for an increase in excess correlation. The subpanel labeled “Change in Excess Correlation” shows the results of the
tests for a change in the correlation matrix and a change in the average correlation (lower panel); p-values are calculated using the χ2 statistics developed by Goetzmann et al. (2005). ∆ indicates that the variable is first
differenced; all other variables are percent changes. All variables are corrected for serial correlation and standardized using autoregressive GARCH filters. The upper half of the panel shows the increase in correlation between
industry pairs; significance is assessed using Fisher transformed correlations. Finally, the subpanel labeled “Excess Correlation Diff-in-Diff” shows the marginal reduction in excess correlation relative to the fundamental
model without liquidity controls. Positive values indicate a reduction in excess correlation. z-statistics are reported in parentheses. There are 899 observations for each industry and *,**,*** indicates significance at 10% 5%
and 1% respectively.
56
Panel A: Liquidity Factor Exposures
Pre-Crisis/Crisis
Consumer
Manuf.
HiTech
Health
Pre-Crisis
∆ONOFF
-0.01
-0.03
0.00
0.00
(-0.35)
(-0.69)
(0.11)
(0.05)
∆OISTB
-0.01
-0.04
-0.02
0.04
(-0.13)
(-0.60)
(-0.26)
(0.45)
∆ONREPO
-0.06
0.01
-0.02
0.01
(-1.13)
(0.25)
(-0.40)
(0.26)
∆BIDASK
0.10*
0.08
0.10**
0.09*
(2.21)
(1.83)
(2.54)
(2.02)
∆IBIDASK
0.02
-0.01
-0.07*
0.13***
(0.64)
(-0.29)
(-2.30)
(3.65)
HEDGE
0.16*
0.08
0.08
0.00
(2.06)
(1.02)
(1.05)
(-0.05)
AMIHUD
0.01
-0.04
-0.01
-0.02
(0.16)
(-1.04)
(-0.26)
(-0.53)
NTRADES
-0.02
0.02
-0.01
-0.02
(-0.36)
(0.42)
(-0.29)
(-0.35)
VOLUME
0.00
-0.07
0.00
0.06
(0.04)
(-1.45)
(-0.04)
(1.15)
Marginal Crisis Effects
∆ONOFF
0.06
0.05
0.04
0.08
(1.10)
(0.93)
(0.67)
(1.29)
∆OISTB
0.04
0.12
0.07
-0.01
(0.36)
(1.12)
(0.64)
(-0.09)
∆ONREPO
0.11
-0.09
-0.04
-0.01
(1.36)
(-1.14)
(-0.48)
(-0.15)
∆BIDASK
-0.03
0.07
0.08
0.07
(-0.45)
(1.06)
(1.23)
(1.01)
∆IBIDASK
0.04
0.14***
0.12**
-0.10
(0.77)
(2.65)
(2.45)
(-1.68)
HEDGE
0.07
0.23*
0.28***
0.30**
(0.62)
(2.03)
(2.62)
(2.49)
AMIHUD
-0.10
-0.07
-0.09
-0.04
(-1.65)
(-1.25)
(-1.56)
(-0.70)
NTRADES
0.11
-0.01
-0.01
0.08
(1.47)
(-0.11)
(-0.10)
(0.99)
VOLUME
-0.18**
-0.07
-0.09
-0.21***
(-2.47)
(-0.94)
(-1.24)
(-2.69)
R-Squared
0.2366
0.2184
0.2216
0.1371
Other
Financials
0.02
(0.54)
0.03
(0.50)
-0.03
(-0.66)
0.01
(0.25)
0.05
(1.77)
0.07
(0.94)
0.00
(-0.10)
-0.07
(-1.42)
-0.05
(-1.16)
0.02
(0.48)
0.01
(0.10)
-0.02
(-0.45)
0.09*
(2.28)
0.06
(1.63)
0.06
(0.82)
0.02
(0.55)
-0.07
(-1.47)
-0.02
(-0.47)
0.03
(0.50)
-0.01
(-0.13)
0.00
(-0.04)
0.14*
(2.25)
0.03
(0.66)
0.22*
(2.13)
-0.08
(-1.47)
0.10
(1.36)
-0.09
(-1.27)
0.3178
-0.01
(-0.24)
0.03
(0.30)
0.01
(0.10)
-0.03
(-0.50)
0.10
(1.74)
0.20
(1.88)
-0.17***
(-2.87)
0.02
(0.25)
-0.07
(-0.96)
0.2642
Consumer
Manuf.
Non-Lehman
0.01
-0.01
(0.43)
(-0.18)
0.02
0.01
(0.45)
(0.11)
-0.03
-0.03
(-0.65)
(-0.84)
0.08*
0.11***
(2.28)
(3.18)
0.04
0.03
(1.54)
(1.26)
0.19***
0.19***
(3.44)
(3.35)
-0.04
-0.08***
(-1.42)
(-2.72)
0.02
0.02
(0.53)
(0.41)
-0.07*
-0.10***
(-2.00)
(-2.74)
Marginal Lehman Effects
0.25
0.21
(0.90)
(0.78)
0.04
-0.03
(0.14)
(-0.09)
0.18
0.10
(0.96)
(0.54)
0.30
0.25
(0.84)
(0.63)
0.58
1.14
(0.90)
(1.79)
0.43
0.04
(0.96)
(0.09)
0.55
0.10
(0.88)
(0.15)
-0.37
-0.09
(-0.47)
(-0.11)
0.02
0.19
(0.07)
(0.76)
0.2346
0.2118
Non-Lehman/Lehman
HiTech
Health
Other
Financials
0.02
(0.73)
0.01
(0.22)
-0.04
(-0.95)
0.13***
(4.20)
-0.02
(-1.02)
0.22***
(3.99)
-0.05
(-1.74)
-0.01
(-0.39)
-0.04
(-1.15)
0.04
(1.36)
0.04
(0.62)
0.01
(0.13)
0.11***
(3.38)
0.09***
(3.35)
0.15**
(2.56)
-0.05
(-1.49)
0.01
(0.17)
-0.02
(-0.64)
0.04
(1.28)
0.03
(0.64)
-0.05
(-1.39)
0.07*
(2.25)
0.05*
(2.21)
0.18***
(3.41)
-0.05
(-1.76)
-0.02
(-0.64)
-0.09**
(-2.57)
0.02
(0.58)
0.02
(0.39)
-0.04
(-1.10)
0.09***
(2.61)
0.09***
(3.23)
0.17***
(3.14)
-0.07*
(-2.31)
-0.06
(-1.78)
-0.05
(-1.55)
0.47
(1.66)
0.02
(0.06)
0.04
(0.20)
0.26
(0.69)
1.21
(1.90)
0.22
(0.53)
-0.40
(-0.68)
-0.03
(-0.03)
-0.23
(-0.95)
0.2183
0.12
(0.42)
-0.03
(-0.09)
0.03
(0.12)
0.23
(0.63)
0.13
(0.15)
0.08
(0.12)
0.21
(0.33)
-0.19
(-0.21)
0.20
(0.33)
0.1209
0.15
(0.56)
-0.09
(-0.30)
0.24
(0.94)
0.25
(0.76)
0.84
(1.26)
0.37
(0.60)
0.28
(0.43)
-0.40
(-0.36)
0.21
(0.64)
0.3178
0.34
(1.29)
-0.36
(-1.19)
0.25
(1.32)
0.58
(1.57)
0.40
(0.66)
0.64
(1.62)
0.69
(1.09)
0.20
(0.25)
0.46
(1.21)
0.2631
57
Panel B: Liquidity Contagion
Consumer
Manufacturing
HiTech
Health
Other
Financials
Matrix Test
Average Correlation
Consumer
0.00
0.11***
0.15***
0.18***
0.12***
0.09*
Statistic
0. 1680***
Change in Excess Correlation
Manuf.
HiTech
Health
Other
0.00
0.21***
0.22***
0.16***
0.17***
P-Value
0.00
0.00
0.00
0.33***
0.14***
0.10*
0.00
0.21***
0.23***
0.00
0.10**
Financials
0.00
Consumer
0.00
-0.03
-0.05
0.00
-0.05
-0.06
Excess Correlation Diff-in-Diff
Manuf.
HiTech
Health
Other
0.00
-0.05
0.12
0.04
-0.03
0.00
0.00
0.03
0.02
0.00
0.06
-0.01
0.00
0.03
Financials
0.00
58
Table VII
Counterparty risk contagion parameter estimates are reported below. Panel A shows the regression coefficients for counterparty risk proxies prior to the crisis and their marginal changes during the crisis. The
specification below contains all fundamental variables defined in Table III (∆S = βiF+γiFDcrisis),along with counterparty risk proxies (CP).
∆S i = β i F + γ i FDcrisis + ϑCPi + ϑic CPi Dcrisis + ε i
Counterparty risk variables include the spread between the three-month overnight index swap rate and three-month LIBOR (OIS). The spread between the yield on three-month asset-backed commercial paper and RF3M
(ABCP). The change in ABCP is orthogonalized to the change in RF3M. The return on the value weighted portfolio of 16 licensed market-makers in the CDX index (CPstock). CPstock is orthogonalized to SP500. Finally,
CPDIF measures risk dispersion between counterparties. The interaction variable EXCPDIF equals CPDIF on days when risk dispersion is above its 95th percentile. I also include the dummy variable corresponding to
EXCPDIF but do not report it because it is always insignificant. I re-estimate the marginal changes on the month following the collapse of Lehman Brothers (9/15/2008-10/15/2008) these results are reported in the panel
labeled Non-Lehman/ Lehman. Panel B reports the results of the tests for an increase in excess correlation after controlling for counterparty risk. The subpanel labeled “Change in Excess Correlation” shows the results of
the test for a change in the correlation matrix and the average correlation (lower panel) p-values are calculated using the χ2 statistics developed by Goetzmann et al. (2005). The upper half of the panel shows the increase in
correlation between industry pairs; significance is assessed using Fisher transformed correlations. Finally, the subpanel labeled “Excess Correlation Diff-in-Diff” shows the marginal reduction (positive values) in excess
correlation relative to the fundamental model without counterparty risk controls. ∆ indicates that the variable is first differenced; all other variables are percent changes. All variables are corrected for serial correlation and
standardized using autoregressive GARCH filters. z-statistics are reported in parentheses. There are 905 observations for each industry and *,**,*** indicates significance at 10% 5% and 1% respectively.
Panel A: Counterparty Risk Factor Exposures
Pre-Crisis/Crisis
Consumer
Manuf.
HiTech
Health
Pre-Crisis
∆OIS
-0.03
0.06
0.05
0.02
(-0.62)
(1.34)
(1.24)
(0.42)
∆ABCP
-0.07
-0.14
-0.03
-0.06
(-0.81)
(-1.74)
(-0.41)
(-0.75)
CPstock
-0.06
-0.02
0.01
-0.03
(-0.85)
(-0.29)
(0.14)
(-0.37)
CPDIF
0.01
-0.03
-0.03
-0.02
(0.18)
(-1.06)
(-0.89)
(-0.50)
Marginal Crisis Effects
∆OIS
0.09
-0.06
0.00
0.05
(1.47)
(-0.86)
(0.04)
(0.71)
∆ABCP
0.09
0.17
-0.02
0.04
(0.83)
(1.63)
(-0.21)
(0.34)
CPstock
-0.10
-0.10
-0.13
-0.12
(-0.80)
(-0.76)
(-1.08)
(-0.91)
EXCPDIF
-0.06
-0.03
0.05
-0.12
(-0.40)
(-0.18)
(0.36)
(-0.75)
R-Squared
0.2150
0.1761
0.1869
0.1016
Other
Financials
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)
0.00
(-0.01)
0.11
(1.14)
0.01
(0.08)
0.02
(0.13)
0.2883
0.03
(0.52)
-0.03
(-0.31)
0.07
(0.53)
0.14
(0.87)
0.2011
Consumer
Manuf.
Non-Lehman
0.01
0.04
(0.27)
(1.23)
-0.01
-0.05
(-0.26)
(-0.92)
-0.10
-0.05
(-1.62)
(-0.81)
0.01
-0.04
(0.22)
(-1.08)
Marginal Lehman Effects
0.22
-0.32
(1.11)
(-1.61)
0.42
0.26
(0.67)
(0.42)
-0.12
-0.82
(-0.23)
(-1.57)
-0.08
-0.08
(-0.48)
(-0.50)
0.2153
0.1764
Non-Lehman/Lehman
HiTech
Health
Other
Financials
0.05
(1.65)
-0.05
(-1.06)
-0.03
(-0.54)
-0.03
(-0.91)
0.04
(1.31)
-0.05
(-0.96)
-0.07
(-1.10)
-0.02
(-0.52)
0.02
(0.50)
-0.05
(-1.14)
-0.05
(-0.94)
-0.02
(-0.61)
0.02
(0.72)
-0.03
(-0.63)
-0.01
(-0.16)
-0.01
(-0.29)
-0.10
(-0.53)
0.18
(0.29)
-0.59
(-1.16)
0.02
(0.12)
0.1880
-0.35
(-1.69)
0.85
(1.32)
-0.83
(-1.55)
-0.18
(-1.07)
0.1082
0.01
(0.05)
-0.17
(-0.28)
-0.29
(-0.59)
0.00
(-0.01)
0.2879
-0.40*
(-2.08)
0.19
(0.30)
-0.77
(-1.52)
0.08
(0.52)
0.2045
59
Panel B: Counterparty Risk Contagion
Consumer
Manufacturing
HiTech
Health
Other
Financials
Matrix Test
Average Correlation
Consumer
0.00
0.12***
0.20***
0.26***
0.15***
0.10**
Statistic
0.2151***
Excess Correlation Difference Matrix
Manuf.
HiTech
Health
Other
0.00
0.23***
0.32***
0.20***
0.17***
P-Value
0.00
0.00
0.00
0.39***
0.16***
0.12***
0.00
0.31***
0.26***
0.00
0.14***
Panel C: Liquidity & Counterparty Risk Excess Correlation
Excess Correlation Difference Matrix
Consumer
Manuf.
HiTech
Health
Other
Consumer
0.00
Manufacturing
0.10***
0.00
HiTech
0.13***
0.19***
0.00
Health
0.16***
0.22***
0.28***
0.00
Other
0.10***
0.17***
0.11***
0.18***
0.00
Financials
0.08
0.16***
0.08
0.24***
0.10*
Statistic
P-Value
Matrix Test
0.00
Average Correlation
0.1544***
0.00
Financials
0.00
Financials
0.00
Consumer
0.00
-0.04
-0.10
-0.08
-0.08
-0.08
Consumer
0.00
-0.03
-0.03
0.02
-0.03
-0.06
Excess Correlation Diff-in-Diff
Manuf.
HiTech
Health
Other
0.00
-0.06
0.02
0.00
-0.04
0.00
-0.07
0.02
0.00
0.00
-0.04
-0.05
0.00
-0.01
Excess Correlation Diff-in-Diff
Manuf.
HiTech
Health
Other
0.00
-0.03
0.12
0.02
-0.03
0.00
0.04
0.07
0.04
0.00
0.08
-0.03
Financials
0.00
Financials
0.00
0.03
0.00
60
Table VIII
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 all
the controls for fundamental credit risk defined in the caption of Table V and two indicator variables DISTRESS and RECOVERY, which
equal one on the day of, or surrounding, events listed in Appendix B and zero everywhere else.
∆S i = β i F + γ i FDcrisis + λ R DRECOVERY + λ D DDISTRESS + ε i
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 the level 2 and 3 severity events only. Again these events are listed in the table in Appendix B. They
include all dates corresponding to events with 2 or 3 listed in the column labeled Severity. 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
RECOVERY
R-Squared
-0.01
-0.06
-0.21
0.25
-0.13
-0.07
(-0.04)
(-0.19)
(-0.63)
(0.72)
(-0.43)
(-0.22)
-0.16
0.05
-0.07
0.15
-0.17
0.01
(-0.78)
(0.26)
(-0.34)
(0.69)
(-0.88)
(0.05)
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
RECOVERY
R-Squared
-0.07
-0.07
-0.07
0.17
-0.07
0.01
(-0.36)
(-0.34)
(-0.37)
(0.81)
(-0.39)
(0.07)
0.04
-0.08
-0.18
-0.02
-0.04
-0.10
(0.29)
(-0.57)
(-1.32)
(-0.13)
(-0.28)
(-0.75)
0.2107
0.1859
0.1881
0.1006
0.2755
0.1945
Panel C: Distress and Recovery Events (1 - 2 observations prior to and after the event)
DISTRESS
R-Squared
0.66*
0.53
0.58
0.57
0.42
0.58
(2.20)
(1.72)
(1.89)
(1.76)
(1.43)
(1.87)
0.2147
0.1881
0.1896
0.1031
0.2769
0.1970
61
Table IX
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 I and are listed in column headers. The risk
premium (RP) is estimated from the 10 most well-behaved firms using the panel regression approach outlined by BDDFS. 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 ∆RPC shows the marginal change in that coefficient during the crisis. Panel B shows the coefficients from the factor model estimation
using the risk premium estimated from the 20 most well-behaved (non-industry) firms. Due to EDF data limitations, the pre-crisis period was
shortened to 3/1/2006 – 7/30/2007. Panel C shows the change in excess correlation after controlling for the risk premium. Panel D shows the
change in excess correlation after controlling for the risk premium (estimated using the 20 most well-behaved (non-industry) firms). 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: Risk Premium Using the 10 Most Well-behaved Firms
Consumer
Manuf.
HiTech
Pre-Crisis
∆RP
0.47***
0.53***
0.37***
(10.60)
(13.10)
(8.83)
Health
Other
Financials
0.45***
(9.19)
0.40***
(9.47)
0.34***
(7.23)
Marginal Crisis Effects
∆RPC
0.10
(1.63)
0.20***
(3.69)
0.27***
(4.74)
0.16**
(2.50)
0.14**
(2.56)
0.14*
(2.26)
R-Squared
0.4698
0.5477
0.4729
0.3475
0.5158
0.3718
Panel B: Risk Premium Using the 20 Most Well-behaved Non-Industry Firms
Consumer
Manuf.
HiTech
Health
Pre-Crisis
∆RP
0.30***
0.41***
0.26***
0.30***
(7.49)
(11.28)
(7.04)
(6.15)
Other
Financials
0.29***
(7.89)
0.28***
(6.42)
Marginal Crisis Effects
∆RPC
0.15***
(2.76)
0.20***
(4.12)
0.30***
(5.97)
0.25***
(3.95)
0.16***
(3.12)
0.12*
(2.11)
R-Squared
0.4606
0.5519
0.4995
0.3280
0.5340
0.3906
Panel C: Risk Premium Contagion: 10 Most Well-behaved Firms
Consumer
Manuf.
HiTech
Health
Consumer
0.00
Manufacturing
-0.09
0.00
HiTech
-0.05
0.03
0.00
Health
0.10
0.07
0.11
0.00
Other
-0.02
0.03
-0.01
0.16**
Financials
-0.10
-0.02
-0.03
0.13*
Statistic
P-Value
Matrix Test
0.00
Average Correlation
0.0170***
0.00
Panel D: Risk Premium Contagion: 20 Most Well-behaved Firms Non-Industry Firms
Consumer
Manuf.
HiTech
Health
Consumer
0.00
Manufacturing
-0.11
0.00
HiTech
-0.10
-0.03
0.00
Health
0.02
0.04
0.10
0.00
Other
-0.05
0.08
-0.05
0.09
Financials
-0.17
0.07
-0.07
0.09
Statistic
P-Value
Matrix Test
0.00
Average Correlation
-0.008***
0.00
Other
Financials
0.00
-0.03
0.00
Other
Financials
0.00
-0.04
0.00
62
Table X
Risk Premium Contagion Robustness: Reported in Panel A reports the results of the risk premium controls in the fundamental model. The
standard set of fundamentals is included in the regression but coefficients for not reported. In this case, the risk premium is estimated with controls
for transaction costs. That is, I add the bid-ask spread into Equation 3 and re-estimate the risk premium. The risk premium is estimated from the
CDS spreads of the 20 most well-behaved non-industry firms. 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 ∆RPC 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 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: Liquidity Adjusted Risk Premium Controls Using the 20 Most Well-behaved Non-industry Firms
Consumer
Manuf.
HiTech
Health
Other
Financials
Pre-Crisis
∆RP
0.12***
0.20***
0.14***
0.15***
0.16***
0.16***
(3.12)
(5.25)
(3.62)
(3.02)
(4.22)
(3.58)
Marginal Crisis Effects
∆RPC
0.21***
(3.93)
0.26***
(5.09)
0.30***
(5.77)
0.32***
(4.96)
0.17***
(3.36)
0.17***
(2.83)
R-Squared
0.3723
0.4207
0.4017
0.2795
0.4576
0.3388
Panel B: Risk Premium Contagion: 20 Most Well-behaved Non-Industry Firms
Consumer
Manuf.
HiTech
Health
Consumer
0.00
Manufacturing
-0.06
0.00
HiTech
-0.01
0.00
0.00
Health
0.03
-0.05
0.03
0.00
Other
0.04
0.08
0.00
0.05
Financials
-0.07
0.06
-0.08
0.09
Statistic
Matrix Test
Average Correlation
0.0074***
Other
Financials
0.00
0.03
0.00
P-Value
0.00
0.00
63