SYSTEMIC SOVEREIGN CREDIT RISK:

LESSONS FROM THE U.S. AND EUROPE

Andrew Ang

Francis A. Longstaff

Abstract. We study the nature of systemic sovereign credit risk using CDS spreads

for the U.S. Treasury, individual U.S. states, and major Eurozone countries. Using

a multifactor affine framework that allows for both systemic and sovereign-specific

credit shocks, we find that there is much less systemic risk among U.S. sovereigns

than among Eurozone sovereigns. Thus, systemic sovereign risk is not directly

caused by macroeconomic integration. We also find that both U.S and Eurozone

systemic sovereign risk is strongly related to financial market returns. These results

provide strong support for the view that systemic sovereign risk has its roots in

financial markets rather than in macroeconomic fundamentals.

Current draft: August 2011.

Andrew Ang is the Ann F. Kaplan Professor of Business, Columbia Business School,

3022 Broadway 413 Uris, New York NY 10025, email: aa610@columbia.edu. Francis A. Longstaff is the Allstate Professor of Insurance and Finance, UCLA Anderson School, 110 Westwood Plaza, Los Angeles CA 90095-1481, email: francis.longstaff@anderson.ucla.edu. We are grateful for helpful discussions with Navneet Arora, Ravi Mattu, David Mordecai, Mike Rierson, Eric Neis, Joel Silva, Ken

Singleton, Marcus Tom, Adalbert Winkler, and Vadim Yasnov. We are also grateful

for the comments of seminar and conference participants at Blackrock, the Federal

Reserve Bank of Chicago, the Federal Reserve Bank of New York, The Federal Reserve Board, the Milton Friedman Institute, and the Risks of Financial Institutions

Conference at the 2011 NBER Summer Institute. We acknowledge the capable

research assistance of Jiasun Li. All errors are our responsibility.
1. INTRODUCTION

Recent shocks in the European debt markets have given financial market participants deep concerns about the rapidly-growing amount of sovereign credit risk in

the global financial system. These concerns have increased with the rapid widening

of all sovereign credit spreads throughout Europe and with the recent downgrade

of the U.S. Treasury. These events have raised fears that sovereign credit risk may

be far more systemic in nature than previously anticipated. Given the massive size

of the sovereign debt markets, it is clear that understanding the systemic nature of

sovereign credit risk is of fundamental importance.1

Furthermore, studying systemic sovereign credit risk may also help resolve the

longstanding debate about the source of systemic risk in financial crises. In particular, one strand of the literature views systemic risk as arising from the effects of

common macroeconomic shocks on economic fundamentals. Key examples include

Gorton (1988), Calomiris and Gorton (1991), Allen and Gale (2000a), Calomiris

and Mason (2003), Reinhart and Rogoff (2008, 2009), and others. In contrast, the

other strand focuses primarily on the role that financial markets play in creating

systemic risk through channels such as capital flows, funding availability, risk premia, and liquidity shocks. Important examples include Diamond and Dybvig (1983),

Kaminski, Reinhart, and Vegh (2003), Allen and Gale (2000b), Kodres and Pritsker

(2002), Brunnermeier and Pedersen (2009), Allen, Babus, and Carletti (2009), and

others.

This paper provides an entirely new perspective on systemic sovereign credit

risk by contrasting the systemic credit risk of sovereigns within the U.S. with that

of sovereign issuers within Europe. For the U.S., we examine the systemic credit

risk of the U.S. itself and ten of the largest states by GDP such as California, Texas,

and New York. In Europe, our dataset consists of countries within the Euro area

(Eurozone). We examine the credit risk of both core countries, such as France and

the Netherlands, and periphery countries, such as Greece and Ireland.

In many ways, the relation between U.S. states closely parallels that of the

sovereigns in the Eurozone. First, under the U.S. Constitution, states are sovereign

entities and can repudiate their debts without bondholders being able to claim assets

in a bankruptcy process. In fact, several states have defaulted on and repudiated

debt in the past. Thus, states within the U.S. have sovereign immunity just as

1Standard and Poors downgraded the credit rating of the U.S. Treasury from AAA

to AA+ on August 5th, 2011. Furthermore, discussions about the possibility of

a default by the U.S. or by a U.S. state have become much more frequent in the

financial press. For example, see Samuelson (2009), Wessel (2010), Buttonwood

(2010), and Rampell (2011).

1
countries within the Eurozone. Second, each set of sovereigns is in a currency

union; U.S states share the dollar as a common currency, while Eurozone members

have the Euro as their common currency. For these reasons, we will often simply

refer to both states and Eurozone countries as sovereigns throughout this paper.

In addition, there are many economic, legal, and political linkages between states,

just as there are similar linkages among European countries. On the other hand,

sovereign debtors in the U.S. have much closer fiscal linkages than is the case in the

Eurozone. Thus, if systemic risk is driven by common shocks to macroeconomic

fundamentals, one would expect a higher level of systemic risk among U.S. states

than would be the case among European sovereigns.

In this study, we make use of a novel dataset of state and sovereign credit default

swap (CDS) spreads. An key advantage of using CDS data is that it provides a much

more direct measure of the credit risk of a sovereign than do sovereign debt spreads.

This is because sovereign debt spreads are driven not only by sovereign credit risk,

but also by interest rate movements, changes in the supply of the underlying bond,

illiquidity effects in sovereign debt prices, and other factors.

Since the term systemic risk is often loosely defined, it is important for us to

be clear about the sense in which we are using it. In studying sovereign credit risk,

we use the multivariate credit framework of Duffie and Singleton (2003) to model

both the systemic and sovereign-specific components of sovereign credit risk. In

this framework, nonsystemic shocks lead to individual sovereign defaults while the

realization of a systemic shock may trigger a cascade of defaults. Thus, systemic

credit risk arises because of the shared vulnerability of sovereigns in the U.S. or

Europe to a major adverse event. This definition of systemic credit risk closely

parallels the current situation in Europe where widespread losses in the banking

sector have weakened sovereign finances, and in the U.S. where large declines in the

housing markets have played a similar role.

We estimate the multivariate model using the full cross section of CDS term

structure data for U.S. sovereigns, and similarly for the Eurozone sovereigns. A

key advantage of this approach is that it provides us with a direct measure of the

sensitivity of sovereign debtors to systemic, or equivalently, common shocks.

A number of important empirical results emerge from this analysis. First, we

find that there is dramatic variation across sovereigns in terms of their exposure to

systemic or common shocks. For example, California has more than five times as

much systemic risk as the average for the other states in the sample, and nearly

three times as much as the U.S. Treasury. In stark contrast, New York has virtually

no systemic risk; New York’s credit risk appears to be almost entirely idiosyncratic

in nature. In Europe, Greece has about three times the systemic risk of other

vulnerable sovereigns such as Portugal, Ireland, Italy, Spain, and Belgium, which,

in turn, have roughly twice as much systemic risk as the remaining sovereigns in

2
the Eurozone.

Second, we show that there is much less systemic sovereign risk in the U.S.

than in the Eurozone. In particular, systemic credit risk represents only about 12

percent of the total credit risk of U.S. states. In contrast, systemic credit risk constitutes about 31 percent of the total credit risk of the Eurozone sovereigns. These

results provide direct evidence against the hypothesis that the tighter macroeconomic linkages should lead to higher levels of systemic risk in the U.S. than in

Europe.

Third, we find that systemic sovereign credit risk in both the U.S. and the

Eurozone is strongly related to financial market variables. Specifically, systemic

sovereign credit risk in the U.S. declines significantly when the S&P 500 increases,

and similarly for the Eurozone when the DAX increases. Systemic sovereign risk

in the U.S. is also significantly related to changes in interest rates and corporate

credit. Curiously, U.S. systemic risk is strongly negatively related to changes in the

VIX volatility index. This is consistent with the view that when global financial

markets experience turbulence, the U.S. may benefit from flight-to-quality-related

capital flows. These results provide new evidence that systemic risk has deep roots

in the flows and liquidity of financial markets.

There is an extensive literature on sovereign credit risk. Previous theoretical work focuses on the incentives faced by sovereign debtors to repay their debt.

Examples include Eaton and Gersovitz (1981), Grossman and Van Huyck (1988),

Bulow and Rogoff (1989a, b), Atkeson (1991), Dooley and Svenson (1994), Cole

and Kehoe (1996, 2000), Dooley (2000), and many others. A number of empirical studies focus on the factors that determine individual sovereign credit spreads.

These include Edwards (1984, 1986, 2002), Berg and Sachs (1988), Boehmer and

Megginson (1990), Duffie, Pedersen, and Singleton (2003), and Zhang (2003). Some

recent research provides evidence that sovereign credit spreads are related to common global and financial market factors. For example, see Kamin and von Kleist

(1999), Eichengreen and Mody (2000), Mauro, Sussman, and Yafeh (2002), Geyer,

Kossmeier, and Pichler (2004), Rozada and Yeyati (2005), Remolona, Scatigna, and

Wu (2008), Pan and Singleton (2008), Winkler (2011), and Longstaff, Pan, Pedersen, and Singleton (2011). This paper contributes to the literature by being the first

to focus on U.S. sovereign credit risk and to contrast it with sovereign credit risk

within the Eurozone. The paper also is the first to estimate the systemic component

of sovereign credit spreads from the cross section of CDS term structures.

The remainder of the paper is organized as follows. Section 2 discusses federal

and state credit risk within the U.S. and compares it with Eurozone sovereigns.

Section 3 describes the sovereign CDS data used in the study. Section 4 presents

the multivariate affine credit model. Section 5 discusses the estimation of the model.

Section 6 studies systemic credit risk of sovereigns in the U.S. and the Eurozone.

3
Section 7 explores the properties of the sovereign-specific portion of sovereign credit

risk. Section 8 provides concluding remarks.

2. U.S. FEDERAL, STATE, AND EUROZONE SOVEREIGNS

U.S. states are comparable to Eurozone member countries in many ways. First,

the GDP of states is roughly similar to the GDP of European countries. Second,

and probably less familiar, is that U.S. states have the same sovereign immunity

as countries in that states can repudiate debt, creditors have few, if any, rights to

claim assets, and there is no bankruptcy mechanism. Third, both U.S. states and

European nations have long histories of default.

2.1 Economic Size of U.S. States and Eurozone Sovereigns

The GDP of U.S. states is roughly comparable to the GDP of Eurozone countries

both in terms of levels and dispersion. Table 1 reports the 2009 nominal GDP of the

U.S. states and Eurozone countries used in our study. California’s economy is larger

than Spain and approximately 90 percent the size of Italy and 70 percent the size

of France. The dispersion of GDP across the largest states is also roughly similar

to the dispersion of GDP across Eurozone countries. Florida is roughly equivalent

to the Netherlands and Ohio has approximately the same GDP as Belgium. Michigan, despite its recent industrial decline, still has an economy greater than Greece,

Portugal, or Ireland taken separately. Thus, U.S. states are roughly comparable

economically to their Eurozone country counterparts.

2.2 Sovereign vs. Corporate Default

Sovereign default is different from corporate default in three important ways. First,

if a corporation decides not to repay its debts, bondholders would sue and the courts

would hand over assets held in collateral to the bond holders. The U.S. bankruptcy

code (Chapters 7 and 11) has both liquidation and restructuring mechanisms to

enforce creditor rights. In contrast, if a sovereign repudiates, most of the assets are

located domestically within a country and a sovereign cannot credibly commit to

handing these assets over in the event of default.

Second, the concept of sovereign immunity protects sovereign assets, even when

they are held outside the country. Sovereign immunity prevents individuals from

suing countries. Several court cases, international treaties, and legislative changes

have weakened the protection of sovereign immunity, but it remains the case that

4
in the U.S., the federal government cannot be sued by an individual unless it has

waived immunity or consented to a suit.2 The grounds for a suit, as specified for

example in the 1946 Federal Tort Claims Act, are very narrow and apply only when

a federal employee has committed a tort (and excludes breaches of contract).

Third, unlike corporate default, there is no recognized international process for

handling sovereign defaults. Certainly, there are international bodies such as the International Monetary Fund and consortiums of commercial banks and governments

which have helped restructure sovereign debt in the various international debt crises

in the 20th Century (see Reinhart and Rogoff (2009) for a detailed timeline), but

these have all been ad-hoc responses. Despite some economists showing that an

international bankruptcy regime for restructuring defaulted sovereign bonds would

be optimal (see, for example, Bolton and Jeanne (2007)), currently there is no such

mechanism for dealing with sovereign default.

State debt is similar to sovereign debt. The 11th Amendment to the U.S. Constitution guarantees that states are treated as sovereigns—no individual, domestic

or foreign, can bring suit against a state, with one exception. Suits can be brought

against states only with the consent of a state.3 Thus, just as individual investors

cannot claim the assets of the federal government, investors cannot seize state property. Furthermore, in the one case where another sovereign sued a state (Principality

of Monaco v. Mississippi), the Supreme Court ruled in 1934 that foreign countries

cannot sue U.S. states without their consent. Thus, states have sovereign status and

there is also no bankruptcy mechanism for handling state default in the U.S., just

as there is no international sovereign bankruptcy court.4 Thus, state and federal

debt have economically equivalent status.

In summary, state governments have sovereign protection. This makes U.S.

state debt similar to the sovereign debt of sovereign countries—individual investors

cannot claim state property or the property of sovereign nations, there is no ability

to force a state to pay in the even of repudiation, and there is no legal mechanism

to restructure defaulting state debts. The last would not be important if U.S. states

would never default – but they have in the past, and may in the future, as we now

describe.

2See Panizza, Sturzengger and Zettelmeyer (2009) for a recent summary of these

developments and a summary of the sovereign default literature.

3It is notable that despite the many attempts to collect money through the courts

from defaulted states, not one defaulting state has ever given consent (see McGrane

(1935) for a detailed account).

4Local municipalities in certain states can enter Chapter 9 of the Bankruptcy Code

similar to Chapter 11 for corporations. However, this does not apply to states.

5
2.3 U.S. Federal and State Default

Although the U.S. has legally never defaulted on its debt, it has unilaterally changed

the terms of its debt. The 1934 Gold Reserve Act changed the value of a U.S. dollar

from $20.67 per troy ounce to $35. Economically this is a default; the U.S. reduced

the value of its debt payments relative to an external measure of value and at that

time all major currencies were backed by gold. Reinhart and Rogoff (2008) classify

the U.S. abrogation of the gold clause in 1934 as a default.

In contrast to the implicit default on federal obligations during the Great Depression, the history of state debt in the U.S. is littered with episodes of explicit

defaults. Many states have defaulted. In the 1830s and 1840s, several states issued debt to finance canals and railroads. McGrane (1935) discusses these events

in detail and lists eight defaulting states and one territory: Arkansas, Florida Territory, Illinois, Indiana, Louisiana, Maryland, Michigan, Mississippi, Pennsylvania.

McGrane notes that most states resumed payment, but Florida Territory and Mississippi repudiated their debt completely (also see English (1996)).

These bonds were widely held in Europe, particularly in the United Kingdom.

Markham (2002) notes that the drop in value of these bonds and their credit risk

was the subject of a nightmare of Ebenezer Scrooge in Charles Dickens’ 1843 novel,

A Christmas Carol, in which Scrooge’s investments withered into a “mere United

States security.”

The partial or complete repudiation of these states’ debts was even placed

in states’ constitutions, or legislation was passed prohibiting payment. McGrane

(1935) recounts that when Florida achieved statehood, it wiped out its debt by legislative fiat and its legislature voted that it did not bear liability for debts incurred

while Florida was still a territory. Similarly, in 1875, Mississippi’s state constitution

was amended forbidding any payment on bonds issued on behalf of its two chartered

banks, Planters’ and the Union. Arkansas defaulted in 1841 and the first amendment to the Arkansas constitution in 1875, which was adopted by an overwhelming

popular vote of eight to one, made it illegal to ever pay the interest or principal on

the defaulted state railroad and levee bonds (see Bayliss (1964)).

Ten states also defaulted after the Civil War during the 1870s and 1880s: Alabama, Arkansas, Florida, Georgia, Louisiana, Minnesota, North Carolina, South

Carolina, Tennessee, and Virginia. All of these states with one exception, Minnesota, took on large debts during the period of Reconstruction and were unable

to service them. As McGrane (1935) describes, Minnesota’s case is particularly

interesting because it was a state untouched by the Civil War. Minnesota defaulted

on railroad bonds and although the Governor and other state officials were willing to make investors whole, they were stymied for over 20 years by constitutional

6
amendments passed by Minnesota repudiating the “swindling bonds”.

Arkansas has the dubious distinction of the only state to default three times.

Its last default, which was also the last default of any state, was in 1933 during the

Great Depression. Arkansas defaulted on highway bonds. Reaves (1943) describes

that the defaulting bonds were partially refunded in 1934, but it was only in 1943

that the majority of the defaulting issues were refinanced and the state returned to

good standing in debt markets.

Clearly, states have defaulted in the past. Investors in defaulted federal or state

debt have little redress to settle their claims. Furthermore, in all defaulting state

cases so far, the federal government did not step in to make investors whole.

2.4 Eurozone Country Default

There have also been defaults among countries which are currently members of the

Eurozone.5 Reinhart and Rogoff (2008) describe several of these episodes. During

the Great Depression, Greece went off the gold standard in 1932 and declared a

moratorium on all debt payments. Spain suspended interest payments on external

debt from 1936–1939 during the Spanish Civil War. Several nations defaulted on

debt raised to fight World War II, including Austria, which rendered many previous

bond issues worthless in 1945, and Germany, which instituted a brutal currency

reform in 1948 by introducing the Deutschmark and rendering most balances in

the previous currency, the Reichmark, close to worthless. However, an important

difference between these defaults and the situation of Eurozone member countries

today is that these defaults were done when each country had a separate currency. In

contrast, the previous defaults of the U.S. states happened under a currency union.

Future possible defaults of Eurozone sovereigns would occur with this feature.

3. THE DATA

As discussed in Duffie (1999), Longstaff, Mithal, and Neis (2005), Pan and Singleton

(2008), and many others, a CDS contract functions as an insurance contract against

the event that an entity such as a firm or a sovereign defaults on its debt. To

illustrate how a CDS contract works, consider the case of California. On January

5, 2011, the market premium or spread for a five-year CDS contract on California

was 295 basis points. If there was no default, the buyer would pay the equivalent of

5Other non-Eurozone countries within the European Union have also defaulted. For

example, the United Kingdom last defaulted in 1932 when most of its outstanding

debt incurred during World War I was consolidated into a 3.5 percent consol bond.

7
295 basis points per year for the full five-year horizon of the contract. If there was a

default, however, the buyer of credit protection could sell the defaulted debt to the

protection seller at its par value of 100, after which the contract would terminate.

In general, this default-linked cash flow is triggered by the default of a specific

reference obligation of the underlying entity.6

The data for the study include weekly midmarket CDS spreads for the term

structure of one-year, two-year, three-year, four-year, and five-year CDS contracts

on the U.S. Treasury and ten states. These states are California, Florida, Illinois,

Massachusetts, Michigan, Nevada, New Jersey, New York, Ohio, and Texas. The

data are obtained from the Bloomberg system which collects CDS market quotation

data from industry sources. The notional for the U.S. Treasury CDS contract is

specified in Euros. The notional for the state CDS contracts is specified in dollars.

The data for the study cover the 139-week period from May 14, 2008 to January 5,

2011. The beginning of this sample period is dictated by the availability of liquid

CDS data for all of the states in the study.

In addition to the U.S. data, we also collect the corresponding CDS term structure data for 11 of the largest sovereign borrowers within the Eurozone: Austria,

Belgium, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, and Spain. The data for the Eurozone sovereigns also cover the period from

May 14, 2008 to January 5, 2011. The notional amounts for the Eurozone data are

all specified in dollars.7

Table 2 provides summary statistics for the federal and state five-year CDS

spreads. All spreads are denominated in basis points.8 The average values of the

spreads range widely across the various sovereigns. The average CDS spread for the

U.S. Treasury is 38.52 basis points. The average spreads for the ten states are all

higher than for the U.S. Treasury, and range from a low of 86.82 basis points for

Texas to a high of 243.57 basis points for California.9

6For a detailed discussion of the characteristics of CDS contracts, see Longstaff,

Mithal, and Neis (2005) and Pan and Singleton (2008).

7For several of the Eurozone sovereigns, five-year CDS data is missing for a few

weeks. For these weeks, we use four-year CDS data to report summary statistics

and use the one-year to four-year term structure data to conduct the empirical

analysis.

8Recently, many CDS contracts are executed on the basis of the protection seller

paying points up front rather than a running spread. Despite this, however, the

market convention is to quote CDS contracts in terms of their equivalent running

spread. We adopt this standard market convention in this paper.

9Even though the notional for the CDS contract on the Treasury is denominated

8
Both the standard deviations and the minimum/maximum values indicate that

there is significant time-series variation in the CDS spreads. For example, the

five-year CDS spread for the U.S. Treasury reached a maximum of 99.26 basis

points in early 2009. Around the same time period, the CDS spreads for California

and Michigan reached maximum values of 402 basis points and 394 basis points,

respectively. The median values of the CDS spreads are typically fairly close to the

average values.

Table 2 also reports summary statistics for the five-year CDS spreads of the

Eurozone sovereigns in the sample. As shown, many of the average CDS spreads are

smaller than those for the states. On the other hand, many of the maximum values

for the Eurozone sovereigns are comparable to those for the states. The reason

for this is simply that while both U.S. and Eurozone sovereigns had similar CDS

spreads at the beginning of the sample periods, CDS spreads in the U.S. widened

more rapidly as the subprime/financial crisis unfolded than did European spreads.

After the Greek credit crisis of mid-2010, however, European CDS spreads quickly

increased to levels comparable to, or even in excess of, those in the U.S.

To provide some additional descriptive statistics, Table 3 reports the correlation

matrix of weekly changes in the five-year CDS spreads. The top panel reports the

correlations for the U.S. while the bottom panel reports the correlations for the

Eurozone.

Focusing first on U.S. sovereigns, the top panel of Table 3 shows that while

there is clearly significant cross-sectional correlation in spreads, the correlations are

far from perfect. Most of the correlations are less than 70 percent, and many are

less than 50 percent. The average correlation across all 11 U.S. sovereigns is only

55.6 percent.

Turning next to the Eurozone sovereigns, the bottom panel of Table 3 shows

that the cross-sectional correlations tend to be similar in magnitude or slightly

higher than those for the U.S. In particular, the average correlation across all 11

Eurozone sovereigns is 58.4 percent. This result is somewhat surprising given that

we would expect a stronger linkage within the U.S. since U.S. sovereigns would

presumably have stronger fiscal, political, and economic connections than would be

the case for the countries in the Eurozone. The stronger correlation among Eurozone

sovereigns, however, is consistent with the results in Longstaff, Pan, Pedersen, and

Singleton (2011) who report that the average correlation of changes in credit spreads

across 26 developed and emerging market sovereigns was 73 percent for the 2007–

2010 period.

in Euros, the CDS spread is expressed as a rate and is, therefore, free of units

of account. Thus, no currency translation is required for the U.S. Treasury CDS

contract.

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Although not shown, we note that the correlations between the U.S. and the

Eurozone are relatively weak compared to the correlations intra-U.S. and intraEurozone. For example, the average pairwise correlation between the U.S. sovereigns

and the Eurozone sovereigns is only 25.6 percent. These results, taken in context

with those previously documented in the literature for other sovereigns, hint that

the nature of U.S. sovereign credit risk may differ fundamentally from that of other

sovereigns.

Finally, Table 4 reports the results from a simple principal components analysis

for the U.S. sovereigns and for the Eurozone sovereigns. The analysis is based on the

correlation matrix of weekly changes in the five-year CDS spreads for the sovereigns

in the two regions.

The results indicate that there is greater commonality among the Eurozone

sovereigns than among the U.S sovereigns. In particular, the first principal component for the U.S. sovereigns explains slightly less than the first principal component for the Eurozone sovereigns. The first two principal components for the U.S.

sovereigns, however, explain only 70.28 percent of the variation, while the same

measure for the Eurozone sovereigns is 82.54 percent. The results for the first three

principal components are similar. As before, these results are very puzzling given

that we would expect credit risk within the U.S. to be more closely linked than

would be the case for credit risk within the Eurozone.

4. MODELING CDS SPREADS WITH SYSTEMIC RISK

There is an extensive literature on modeling sovereign credit spreads. Important

recent examples include Duffie, Pedersen, and Singleton (2003), Pan and Singleton

(2008), and Longstaff, Pan, Pedersen, and Singleton (2011). In this paper, we will

apply a framework proposed by Duffie and Singleton (2003) to the sovereign CDS

curves.10 A key advantage of this framework is that it introduces the possibility

that sovereign defaults may be triggered by the realization of a systemic shock.

Thus, in contrast to previous work that models sovereign CDS term structures in a

univariate setting, the Duffie and Singleton model is a multivariate model in which

joint defaults of sovereigns are explicitly captured.

Specifically, the model allows for two independent types of credit events to

trigger sovereign defaults. The first is an idiosyncratic shock that triggers the default

of an individual sovereign. This type of credit event is essentially the same as those

underlying standard reduced-form credit models such Duffie and Singleton (1997,

1999), Pan and Singleton (2008), and many others. In particular, the model treats

10This model is described in Section 10.7 of Duffie and Singleton, pp 247-249.

10
idiosyncratic default as being triggered by the first jump of a sovereign-specific

Poisson process. Let ξt denote the intensity of this Poisson process. Following

Longstaff, Mithal, and Neis (2005), we assume that this intensity process follows a

standard square-root process,

dξ = (a − bξ) dt + c

ξ dZ. (1)

These dynamics allow for mean reversion and conditional heteroskedasticity in the

intensity process and guarantee that the intensity process is nonnegative. The

constants a, b, and c and the Brownian motion Z are sovereign specific. We place no

restrictions on the correlation structure of the Brownian motions across sovereigns

or on the correlation of idiosyncratic defaults across sovereigns.11

The second type of credit event is different and can be viewed as a systemic

shock. This type of event has potential ramifications for all sovereigns within a

common area such as a monetary union. In particular, we assume that when a

systemic shock occurs, which is modeled as the arrival of a Poisson jump, each

sovereign has some probability of defaulting. The probability of default conditional

on the systemic shock, however, is sovereign specific and is denoted γ. Thus, some

sovereign borrowers may be more fragile or susceptible to systemic shocks than

others. Let λt denote the intensity of the Poisson process triggering a systemic

shock. This intensity also follows a standard square-root model,

dλ = (α − β λ) dt + σ √

λ dZλ, (2)

where α, β, and σ are constants, and Zλ is a Brownian motion that is uncorrelated

with the Brownian motions driving the idiosyncratic intensity processes.

Let us now consider the ways in which a sovereign default can occur in this

Duffie and Singleton (2003) framework. First, default occurs the first time that there

is an arrival of the sovereign-specific Poisson process. Second, default occurs with

probability γ the first time that there is an arrival of the systemic Poisson process

(provided, of course, that there has not been a previous idiosyncratic default).

Third, default occurs with probability (1 − γ)γ the second time that there is an

arrival of the systemic Poisson process. This follows since the sovereign has a 1 − γ

probability of surviving the first systemic shock, but then faces a γ probability of

succumbing to the second systemic shock. Fourth, default occurs with probability

11Since this framework allows idiosyncratic defaults to have some (although not

perfect) correlation across sovereigns, we are using the term idiosyncratic in the

broader sense of being nonsystemic.

11
(1 − γ)2γ the third time that there is an arrival of the systemic Poisson process,

and so forth. Thus, there is an infinite number of ways in which a sovereign default

can occur in this model. This contrasts sharply with the usual univariate modeling

framework in which default occurs the first time there is an arrival of the underlying

Poisson process.12

We note that it would be straightforward to extend this model to allow for

contagion-like effects. Specifically, the realization of a systemic Poisson shock could

trigger the default of an individual sovereign with probability γ as before, but

where the actual timing of the default was randomly distributed over some period

of time, say a year. In this situation, a systemic shock might be followed by a string

of defaults over the subsequent year, resulting in a contagion-like event. In this

paper, we will focus only on the simplest version of the model since the empirical

implications of the extended model for the properties of systemic credit risk are

very similar to those of the basic model.

Given the properties of Poisson processes, and conditional on the realized paths

of the intensity processes ξt and λt, the probability that no default occurs by time

t equals,

= exp −

 t

0

ξs ds 

∞

i=0

1

i! exp 

−

 t

0

λs ds (1 − γ)

 t

0

λs dsi



, (3)

= exp −

 t

0

ξs dsexp −

 t

0

λs dsexp  t

0

(1 − γ)λs ds, (4)

= exp −

 t

0

γ λs + ξs ds. (5)

Thus, we can now proceed to value credit derivatives using the standard reducedform framework, but with the twist that the instantaneous probability of a default

in this Duffie and Singleton (2003) model is proportional to γλ+ξ. We will designate

12It is important to recognize that this Duffie and Singleton (2003) framework differs

from the usual doubly stochastic credit framework. This is because multiple defaults

can occur simultaneously in this model, but not in the standard doubly stochastic setting. Recent evidence by Das, Duffie, Kapadia, and Saita (2007), however,

argues against the doubly stochastic model. Furthermore, the events surrounding

the Lehman default of 2008 provide support for the clustered default implication

of the Duffie and Singleton model we use. In the absence of defaults, however, the

two frameworks are essentially observationally equivalent. We are grateful to Ken

Singleton for this insight.

12
this value the total intensity. The total intensity can thus be interpreted as a default

probability arising from exposure to a systemic source λ, with exposure γ, and

from a sovereign-specific source, ξ. Perhaps in the more familiar terminology from

factor models or APT models, credit risk that is shared across sovereigns, where

each sovereign has a different exposure to the common shock, we term systemic

risk. Credit risk exposure that is idiosyncratic to an individual sovereign we term

sovereign-specific risk. Note that in this model, sovereign-specific shocks can be

correlated across countries.

Let rt denote the riskless rate. Although rt is stochastic, we assume that it

is independent of the intensity processes λt and ξt, and of the realizations of the

underlying Poisson processes. As we show later, this assumption greatly simplifies

the model, but has little effect on the empirical results. As in Lando (1998), we

make the assumption that a bondholder recovers a fraction 1 − w of the par value

of the bond in the event of default.

Given the independence assumption, we do not need to specify the risk-neutral

dynamics of the riskless rate to solve for CDS spreads. We require only that these

dynamics be such that the value of a riskless zero-coupon bond D(T) with maturity

T be given by the usual expression,

D(T) = E



exp 	−

 T

0

rt dt
 . (6)

Following Longstaff, Mithal, and Neis (2005), it is now straightforward to represent

the values of U.S. Treasury or state CDS spreads in terms of simple expectations

under the risk-neutral measure. Let s denote the spread paid by the buyer of default

protection. Assuming that the premium is paid continuously, the present value of

the spread leg of a sovereign CDS contract can be expressed as

E



s

 T

0

D(t) exp −

 t

0

γ λs + ξs dsdt. (7)

Similarly, the value of the protection leg of a CDS contract can be expressed as

E



w

 T

0

D(t) (γ λt + ξt) exp −

 t

0

γ λs + ξs dsdt. (8)

Setting the values of the two legs of the CDS contract equal to each other and

solving for the spread gives

13
s =

w E  T

0 D(t) (γ λt + ξt) exp 


−  t

0 γ λs + ξs ds

dt

E

 T

0 D(t) exp 


−  t

0 γ λs + ξs ds

dt . (9)

Given the square-root dynamics for the intensity processes, standard results such as

those in Duffie, Pan, and Singleton (2000) make it straightforward to derive closedform solutions for the expectations in Equation (9). The Appendix shows that the

sovereign CDS spread can be expressed as

s = w  T

0 D(t) (A(λ, t) C(ξ, t) + γ B(ξ, t) F(λ, t) dt

 T

0 D(t) A(λ, t) B(ξ, t) dt , (10)

where ξ and λ denote the current (or time-zero) values of the respective intensity

processes,

A(λ, t) = A1(t) exp(A2(t) λ), (11)

B(ξ, t) = B1(t) exp(B2(t) ξ), (12)

C(ξ, t)=(C1(t) + C2(t) ξ) exp(B2(t) ξ), (13)

F(λ, t)=(F1(t) + F2(t) λ) exp(A2(t) λ), (14)

and where,

14
A1(t) = exp α(β + ψ)t

σ2

  1 − ν

1 − ν eψt 2α/σ2

, (15)

A2(t) = β − ψ

σ2 +

2ψ

σ2(1 − ν eψt)

, (16)

B1(t) = exp a(b + φ)t

c2

  1 − θ

1 − θ eφt 2a/c2

, (17)

B2(t) = b − φ

c2 +

2φ

c2(1 − θ eφt)

, (18)

C1(t) = a

φ



eφt − 1



exp a(b + φ)t

c2

  1 − θ

1 − θ eφt 2a/c2+1

, (19)

C2(t) = exp a(b + φ)t

c2 + φt  1 − θ1 − θ eφt 2a/c2+2

, (20)

F1(t) = α

ψ



eψt − 1



exp α(β + ψ)t

σ2

  1 − ν

1 − ν eψt 2α/σ2+1

, (21)

F2(t) = exp α(β + ψ)t

σ2 + ψt  1 − ν1 − ν eψt 2α/σ2+2

, (22)

and finally,

ψ = β2 + 2γσ2, (23)

ν = (β + ψ)/(β − ψ), (24)

φ = b2 + 2c2, (25)

θ = (b + φ)/(b − φ). (26)

Several caveats of the model should be noted. First, the model treats default as

a simple arrival of a Poisson process–either through a process contingent on systemic

default, or a process capturing sovereign-specific default. In reality, default in a CDS

contract is triggered by a credit event. The precise legal definition of default, and

whether it corresponds to an actual economic default, is not captured in this model.

Second, the model is estimated under the risk-neutral measure. That is, our inferred

default processes and implied intensities are not actual probabilities of default in

the real world, but represent the default processes relevant for CDS pricing. We

cannot estimate actual default probabilities due to the lack of defaults in the data.

15
This does not mean that the risk-neutral probabilities are irrelevant; in fact, given

the high frequency of CDS data they are extremely informative real-time measures.

Moreover, most models specifying the link between real and risk-neutral measures

have simple transformations of probabilities between the two measures. Thus, we

expect our inference on real intensities to be qualitatively similar, particularly since

we focus on changes, not levels.13

5. MODEL ESTIMATION

With these closed-form solutions, we can now estimate the model using market CDS

spreads. Specifically, we will estimate the model using the term structure of one-,

two-, three-, four-, and five-year CDS spreads for each issuer for each date during

the sample period. This results in a vector λ ̄ of estimates of the systemic intensity

process for each date in the sample period as well as a vector  ̄ξ of estimates for

the sovereign-specific intensity process for each issuer. In addition, this estimation

approach provides estimates of the parameters of the systemic intensity process

and the sovereign-specific intensity processes, as well as the sensitivity coefficient

for each issuer.

In estimating the model for the U.S. issuers, we also impose two minor identifying restrictions. The first is that the sensitivity coefficient γ for the U.S. Treasury

is normalized to be one. Thus, the γ coefficients for the states have the interpretation as measuring systemic sensitivity relative to that of the U.S. Treasury. This

assumption is simply for convenience in scaling the results. Second, we make the

realistic assumption that a Treasury default can only occur in conjunction with a

systemic shock. This assumption makes intuitive sense since it is difficult to imagine a scenario in which the U.S. Treasury defaults without sending systemic shock

waves throughout the credit markets.

The values for the zero-coupon bonds D(t) that appear in the valuation formula

are bootstrapped from one-, three-, six-, and twelve-month LIBOR rates and two-,

three-, and five-year swap rates using a standard cubic spline interpolation algorithm. For a description of this algorithm, see Longstaff, Mithal, and Neis (2005).14

13Another concern may be the potential lack of integration across the CDS derivatives market and the underlying physical sovereign bond market. Fleckenstein,

Longstaff, and Lustig (2010) document that pricing in the physical market can imply mispricing in a derivative market, or vice versa. We do not examine underlying

bond markets.

14An alternative approach would be to bootstrap zero-coupon bond prices from the

Treasury constant maturity rates reported by the Federal Reserve Board’s H.15

release. The results, however, are not sensitive to the choice of the discounting

16
The LIBOR and swap data are obtained from the Bloomberg system. We will also

assume that the loss given default is 50 percent, implying w = 0.50.15

Let sijt denote the market spread for the i-th issuer for a CDS contract with

maturity j years as of date t. Let ˆsijt be the corresponding value implied by

substituting in the estimated values of the systemic intensity λ and the sovereignspecific intensity process ξi along with the estimated parameter vector θ into the

closed-form solution in Equation (10). The parameter vector and the time series of

the systemic intensity and sovereign-specific intensity processes are then estimated

by minimizing the objective function

min

λ,ξ1,ξ2,...,ξN ,θ



i



j



t

[ sijt − sˆijt ]

2 . (27)

We follow the same procedure in estimating the model for the Eurozone sovereigns,

with the exception that the identification conditions apply to Germany rather than

the U.S. Treasury.16

The upper part of Table 5 reports the estimated parameters a, b, and c for the

sovereign-specific processes for the individual states, and the estimated parameters

α, β, and σ for the systemic process. The lower part of the table gives the corresponding results for the Eurozone sovereigns. Table 5 also reports the asymptotic

standard errors for the parameters and the root mean squared error (RMSE) from

fitting the model to the term structure of CDS spreads for each issuer.

Table 5 shows that the speed of mean reversion parameter b or β is negative

for many of the U.S. and Eurozone sovereigns. This feature is not uncommon in

estimating affine models and does not pose a problem since we are estimating the

curve. Intuitively, this is because the discounting curve is applied symmetrically

to the cash flows from both legs of the CDS contract. Thus, bootstrapping zerocoupon bond prices from the Treasury curve rather than the swap curve would have

little effect on the fitted value of the CDS spread.

15Similarly, this assumption also has little effect on the fitted value of the CDS

spread since it is applied symmetrically to both legs of the CDS contract in the

estimation process.

16This assumption is innocuous. An alternative and much more complex econometric procedure would be to treat the systemic intensity as latent. This would

produce similar results to assuming the U.S. and Germany as systemic risks for

states and Eurozone nations, respectively, because these countries have the lowest

default intensities and treating them as latent would mostly assign systemic risk to

the lowest default intensity countries.

17
speed of mean reversion under the risk neutral measure rather than the objective

measure, and the speed of mean reversion parameter under the objective measure

is presumably positive.17 This argues that there might be a substantial difference

between the speed of mean reversion parameters across the two measures. In turn,

this implies that there could be a significant risk premium embedded into the pricing

of U.S. and Eurozone sovereign CDS contracts.

Table 5 also shows that the model fits the term structure of CDS spreads fairly

well. The RMSEs from fitting the model to U.S. sovereign issuers range from a low

of about one basis point for the term structure of U.S. Treasury CDS contracts, to

a high of roughly 16 basis points for Illinois. Six of the states have RMSEs of less

than ten basis points. Comparing these RMSEs to the average five-year CDS values

shown in Table 2 indicates that these RMSEs are a relatively small percentage of

the absolute level of CDS spreads for these issuers. Similar results hold for the

Eurozone sovereign issuers.

Finally, note that the systemic intensity process in the U.S. has parameters

that are very similar to those for the systemic intensity process in the Eurozone.

Similarly, the model fits both the term structure of U.S. Treasury CDS spreads

and the term structure of Germany CDS spreads very closely. The RMSEs from

fitting the U.S. Treasury and German CDS term structures are 1.179 and 2.528

basis points, respectively.

In Figure 1, we plot the total intensity γλ+ξ implied by the model for selected

states and Eurozone countries. These total intensities are not small and are of

roughly the same order of magnitude for these selected sovereigns. At the end

of the sample, January 5, 2011, the total intensity for Greece is 0.1201 and the

total intensity for California is 0.0530. If λ were constant, these total intensities

would represent risk neutral default probabilities of 1−exp(−0.01201) = 0.1132 and

1 − exp(−0.0530) = 0.0516 over the next year, respectively. Default probabilities

for California, Illinois, Greece, and Ireland all start off in May 2008 below 100

basis points and increase during the financial crisis of 2008. For most of 2009, the

total intensities of California and Illinois are higher than Greece and Ireland, with

California’s intensity being slightly higher than Illinois’. Sovereign credit risk for

Greece increases rapidly during early 2010 followed by Ireland in late 2010. Illinois’

default intensity also increases, but not to the same extent as Greece and Ireland.

The total default intensities shown in Figure 1 include both exposure to systemic

risk (either U.S. or Eurozone) and sovereign-specific default risk. We now separately

characterize each of these components of sovereign credit risk.

17For example, see Dai and Singleton (2002).

18
06−08 12−08 06−09 12−09 06−10 12−10

0

200

400

600

800

1000

1200

CA

IL

GRE

IRE

Figure 1. Selected State and Sovereign Total Default Intensities.

This figure plots the estimated time series of the total intensity processes

for the indicated states and sovereigns. The intensity process is measured

in basis points.

6. SYSTEMIC SOVEREIGN RISK

In this section, we examine the implications of the results for the systemic component of sovereign default risk. First, we focus on the systemic sensitivity measures

estimated from the multivariate credit model. Next, we decompose the default

spread for each sovereign into its systemic and sovereign-specific components. We

then contrast the nature of systemic sovereign risk in the U.S. with that in the

Eurozone. Finally, we explore the determinants of systemic sovereign risk using a

regression framework.

6.1 Systemic Credit Risk

Figure 2 plots the intensity λ of the systemic risk for the U.S. and the Eurozone.

The U.S. intensity has been, on average, higher than the Eurozone intensity. Thus,

the market perceives that a U.S. default is slightly higher than a German default.

The systemic default intensities of the U.S. and the Eurozone are highly correlated

at 0.9406. This high degree of commonality in systemic risk across the U.S. and

19
Euro market areas is consistent with Longstaff, Pan, Pedersen, and Singleton (2011),

who find that sovereign credit risk is highly correlated across countries. The high

correlation between the U.S. and Eurozone systemic intensities is also partly driven

by our sample period which covers the financial crisis. As is well known, correlations

tend to increase during market downturns and crisis periods (see, for example, Ang

and Bekaert (2002)).

06−08 12−08 06−09 12−09 06−10 12−10

0

20

40

60

80

100

120

US

Europe

Figure 2. U.S. and Eurozone Systemic Sovereign Credit Risk

Factors. This figure plots the estimated time series of the intensity process

for the two systemic sovereign credit risk factors. The intensity process is

measured in basis points.

The U.S. and Eurozone systemic intensities increase markedly during the last

quarter of 2008 after the default of Lehman Brothers (September 15, 2008). Both

systemic intensities reach their peaks of 102 and 90 basis points, respectively, at

the end of February 2009. The increases in default intensities during the financial

crisis come through two channels. First, there is an explicit increase of sovereign

liabilities by bringing onto sovereign balance sheets many of the liabilities of private

banks (in the U.S. through the Capital Purchase Program (CPP), the Troubled

Asset Relief Program (TARP), and loans and assistance to American International

Group (AIG) and auto manufacturers and in Germany the nationalization of Hypo

Real Estate and state support of banks through the Financial Market Stabilization

Fund). Second, there is an implicit increase in the riskiness of sovereign finances

20
through the deterioration of economic conditions and the fragility of the banking

sectors in each country.

Systemic default intensities for both the U.S. and the Eurozone decrease during

the first three quarters of 2009. The U.S. intensity starts to increase in November

2009, while the Eurozone intensity follows later in late December 2009. The U.S.

increase may reflect the large losses from Fannie Mae and increasing concerns about

large deficits during that quarter. The increase in Eurozone systemic sovereign

risk is likely due to the deteriorating finances of Greece and the downgrading of

Greek debt in December 2009. Since March 2010, the U.S. credit intensity has

averaged 39 basis points, representing a one-year probability of default of 0.0039

and has been fairly stable. Eurozone systemic sovereign risk has been a little more

volatile, increasing in April and May 2010 and in December 2010 and January

2011. This volatility reflects the sovereign debt crisis of Ireland, Spain, Portugal,

and other Eurozone periphery nations. Note that the Eurozone systemic default

intensity is not elevated through this period indicating that systemic Eurozone

risk has been relatively subdued even though the yields and default rates of other

European nations dramatically increase during this time.

6.2 Systemic Sensitivity

Recall from earlier discussion that the coefficient γ represents the probability that

a sovereign defaults conditional on the realization of a systemic credit event. By

normalizing the value of γ to one for the U.S. Treasury, the estimated values of γ

for the other sovereigns represent the ratio of the conditional probability of default

for the sovereign to that of the United States. Similarly, we normalize the Eurozone

sovereigns by the conditional default probability for Germany. Thus, the estimated

values of γ can be viewed as an index of relative systemic default risk.

Table 6 shows the estimated systemic default risk indexes. Surprisingly, nine

of the ten states studied actually have an systemic index of less than one. The

exception is California which has a systemic index of 2.647. The average value of

the systemic index taken over all ten states is 0.72; the median value of the systemic

index is 0.63. It is also interesting to observe that several of the states appear to have

little or no systemic default risk. In particular, Illinois, New York, and Ohio have

systemic indexes that are less than 0.10. These results have important implications

for the nature of state sovereign default risk in the U.S. since they imply that state

default risk is largely sovereign specific rather than systemic.

In stark contrast to the results for the states, Table 6 shows that systemic

default risk is far more important for the sovereigns in the Eurozone. In particular,

seven of the Eurozone sovereigns have systemic indexes in excess of one, implying

21
that their probability of a default given a systemic shock exceeds that of Germany.

The highest value of the systemic index is for Greece which has a value of 4.688.

The next highest values are for Italy, Portugal, Belgium, and Ireland with indexes

of 1.710, 1.674, 1.662, and 1.604, respectively. The smallest value for the index is

for Finland with a value of 0.356. The average value of the systemic index taken

over all ten Eurozone sovereigns is 1.597; the median value of the systemic index is

1.555.

6.3 How Large is the Systemic Component?

As an alternative way of looking at systemic risk, it is also interesting to decompose

the total default risk of each sovereign into its systemic and sovereign-specific components. Since the instantaneous default risk of each sovereign is γλ+ξ, the systemic

component is given simply by γλ while the sovereign-specific component is given

by ξ. Table 7 reports summary statistics for the systemic component expressed as

a percentage of the total default risk for each sovereign.

The results in Table 7 tell a similar story as the results for the systemic index. In

particular, the size of the systemic component for the states is typically very small.

The average systemic percentage taken over all ten states is only 12.21 percent.

Even for California, which has the highest systemic index of γ = 2.647, the average

systemic component is only 36.78 percent of the total credit risk. This reinforces

the earlier evidence that state credit risk in the U.S. is largely sovereign-specific in

nature rather than systemic.

The results for the Eurozone are again very different from those for the U.S.

The systemic component taken over all Eurozone sovereigns is 30.94 percent; the

median is 37.03 percent. The smallest average among Eurozone sovereigns is 16.77

percent for Ireland. The highest average among Eurozone sovereigns is 53.15 for

France. Thus, the results indicate that systemic default risk tends to be two to

three times as large a component of default risk in Europe as it is in the U.S.

6.4 What Drives Systemic Sovereign Risk?

We next explore the determinants of systemic sovereign credit risk. Specifically, we

study the extent to which a set of domestic and global variables explain changes

in the systemic intensity values estimated previously. There are several important

reasons for focusing on intensity values rather than on individual CDS spreads.

First, the intensities implied from the model are based on the full term structure

of CDS spreads. Thus, this approach allows us to use all of the information in the

market about systemic credit risk. Second, the intensity reflects the current prob22
ability of a systemic event rather than a long-term average. This means that this

measure has the potential to be more responsive and, therefore, more informative

about the underlying drivers of systemic default risk. Third, our approach parallels

that of Duffie and Singleton (1997, 1999), Longstaff, Mithal, and Neis (2005), Pan

and Singleton (2008), Longstaff, Pan, Pedersen, and Singleton (2011), and others

who study the properties of default intensities estimated from a model of the term

structure of credit spreads.

Since there is virtually an unlimited number of variables that could be related

to sovereign credit risk, it is important to be selective in the variables considered.

In particular, we will focus primarily on market-determined variables since we can

observe these at a higher frequency than other variables such as tax receipts or

budget deficits (which are generally only available on an annual or semiannual

basis).

The first set of four variables are taken from the domestic financial markets.

For the U.S., we use the weekly return on the S&P 500 index (excluding dividends),

the weekly change in the five-year constant maturity swap rate, the weekly change

in the VIX volatility index, and the weekly change in the CDX North American

Investment Grade Index of CDS spreads. For the Eurozone, we use the weekly

return on the DAX index, the weekly change in the five-year constant maturity

Euro swap rate, the weekly change in the VIX volatility index, and the weekly

change in the European ITraxx Index of CDS spreads. The data for these variables

are all obtained from the Bloomberg system.

The second set of explanatory variables consists of weekly changes in the fiveyear CDS spreads for three sovereigns or sovereign indexes. In particular, we include

the weekly change in the CDS contract for Japan, China, and for the CDX Emerging

Market (CDX EM) Index of sovereign CDS spreads. The data for these CDS spreads

are also obtained from the Bloomberg system.

Table 8 reports the results from the regressions of weekly changes in the default

risk for the issuers on the explanatory variables. Specifically, the table reports the

Newey-West t-statistics from the regressions along with the R2s.

Table 8 shows that U.S. systemic sovereign risk is strongly related to the financial market variables. In particular, the single most significant variable in the

regression is the return on the stock market, which has a t-statistic of −4.31. Thus,

U.S. systemic credit risk declines significantly as the stock market rallies, and vice

versa. This strongly suggests that the fortunes of the U.S. are closely linked to the

stock market. U.S. systemic risk is significantly positively related to changes in the

swap rate, indicating that the level of interest rates has an important effect on credit

risk. Interestingly, changes in the VIX index are significantly negatively related to

U.S. systemic credit risk. This is consistent with the view that Treasury bonds

23
may play the role of a “reserve investment” in the financial markets. Specifically,

that when uncertainty in the financial markets increases, the resulting global flight

to U.S. Treasury bonds makes it easier for the U.S. to finance its operations with

nominal debt. Finally, U.S. systemic credit risk is also positively related to changes

in investment grade corporate bond spreads (significant at the ten-percent level).

The results also show that U.S. systemic risk is related to the credit spreads

of the two largest holders of U.S. Treasury debt. In particular, the t−statistic for

the CDS spread of Japan is 1.64 (which just misses significance at the ten-percent

level), while the t-statistic for China is 1.80 which is significant at the ten-percent

level. The R2 for the regression is 0.352, indicating that a substantial proportion

of U.S. systemic credit risk can be explained in terms of the financial market and

global credit variables.

Turning now to the results for Eurozone systemic sovereign risk, we see a very

similar pattern. Eurozone systemic risk is again significantly negatively related

to stock market returns. As for the U.S., Eurozone systemic risk is significantly

positively related to changes in corporate credit spreads. Note that the coefficient

for changes in the VIX is not significant, consistent with the intuition of the unique

role played by U.S. Treasury debt discussed above. Finally, Eurozone systemic risk

is strongly positively related to the CDS spread of China. As before, the R2 of

0.431 for this regression indicates that much of the variation in Eurozone systemic

sovereign risk is captured by these financial market variables.

7. SOVEREIGN-SPECIFIC CREDIT RISK

In this section, we examine the properties of the sovereign-specific or idiosyncratic

component of sovereign default risk. We first explore whether there is a geographic

structure to sovereign-specific risk using a multivariate cluster analysis. We then

examine whether the extent to which the key financial and global variables are able

to explain variation in sovereign-specific credit risk.

7.1 Does Geography Matter?

To provide an alternative perspective on the cross-sectional structure of default

risk, we conduct a multivariate cluster analysis of the correlation matrix of weekly

changes in the estimated sovereign-specific components. In this cluster analysis, the

algorithm attempts to sort the states into groups where the members of each group

are as similar as possible. At the same time, the algorithm attempts to form the

groups to be as dissimilar from one another as possible. In effect, the algorithm tries

to create groupings in a way that maximizes the average correlation between coun24
tries in the same group, while minimizing the average correlation between countries

in different groups.18 Since the composition of clusters depends on the choice of the

number of clusters to be formed, we use a simple rule of thumb that the number of

clusters be roughly N/3, where N is the number of individual items to be grouped.

For the ten sovereigns in the U.S. and the ten in the Eurozone, this rule of thumb

suggests forming three clusters (we exclude the U.S. Treasury and Germany since,

by assumption, their default risk is due entirely to the systemic factor).

Table 9 reports the composition of the clusters. Although we present the clusters in order of the number of issuers each contains, there is no particular significance

to this ordering in cluster analysis. Similarly, the cluster analysis algorithm does not

place any restrictions on the number of items that can appear in any cluster (other

than the obvious requirement that a cluster has to contain at least one element).

The results illustrate that there is a strong regional flavor to state credit risk.

In particular, the first cluster contains five states, four of which are located in

Midwest/Central part of the U.S: Illinois, Michigan, Ohio, and Texas. The second

cluster consists primarily of states on the East and West Coasts such as New York,

New Jersey, and California. The third cluster consists only of Florida. This suggests

that the credit risk of Florida is sufficiently distinct from that of the other states

that the algorithm places it in a separate category altogether.

Turning to the results for the Eurozone, a somewhat different pattern emerges.

In particular, the largest cluster consists of the Eurozone periphery: Greece, Ireland, Italy, Portugal, and Spain – all countries that have experienced moderate or

severe financial distress recently. Thus, there is a clear “misery loves company”

structure to the correlation matrix of sovereign-specific spread changes. This pattern is also consistent with the second cluster which consists of Austria, Finland,

and the Netherlands, which have all represented strong credits through the global financial crisis. The third cluster shows the most geographical similarity since France

and Belgium are neighbors and share many common features such as language. We

will next examine in further detail the time series of the state-specific and countryspecific intensity processes.

7.2 State-Specific Sovereign Risk

18The cluster analysis is done using Ward’s method in which clusters are formed

so as to minimize the increase in the within-cluster sums of squares. The distance

between two clusters is the increase in these sums of squares if the two clusters were

merged. A method for computing this distance from a squared Euclidean distance

matrix is given by Anderberg (1973, pp. 142-145).

25
Figure 3 plots the states-specific intensities of the states in the various clusters

shown in Table 9. Panel A plots the state-specific ξ intensities of the states in the

first cluster: Illinois, Massachusetts, Michigan, Ohio, and Texas. The states in this

cluster all exhibit two large increases in credit risk, beginning with the start of the

financial crisis in 2008 when U.S. systemic credit risk also increases (see Figure 2)

and again in 2010. These state-specific intensities are large; Michigan’s intensity

reaches a peak of 740 basis points in April 2009 and Illinois’ maximum intensity is

680 basis points in June 2010.

The increase in default intensities during 2010 reflects different circumstances

for different states. Using data from the Bureau of Economic Analysis, Illinois has

the largest debt to GDP ratio, 20.6 percent, in 2009 of all the states considered in the

sample and financed the largest projected deficit to GDP ratio in 2011, 2.7 percent,

according to the Center on Budget and Policy Priorities. Massachusetts moved

from budget surpluses during the late 1990s to budget deficits during our sample

period, resulting from a combination of reducing taxes prior to the financial crisis

and increased demand for social services during the financial downturn. Similarly,

estimates of budget deficits for Texas started increasing dramatically in June 2010

to top $20 billion. In early January 2011, Texas legislators eventually cut spending

by more than $30 billion.

Panel B of Figure 3 graphs the state-specific intensities for the states in the

second cluster: California, Nevada, New Jersey, and New York. California’s statespecific default risk appears to be similar to these other states, so its overall high

default probabilities are due to California’s large loading on U.S. systemic risk

(see Table 6). The intensities for these four states are highly correlated with an

average cross-correlation of 90 percent. These states share a number of similarities:

California and Nevada have the highest state unemployment rates among the states

considered over the sample and California and Nevada have been very hard hit

by declining property prices. Although much smaller than its neighboring state

California, it is not surprising that Nevada is exposed to many of the same economic

forces facing California. Similarly, New Jersey and New York are adjoining states

and there is a high linkage of these economies. This may explain the increase

in the states’ intensities in February 2010 and June 2010. California and New

York’s fiscal years end in March 2010 and the challenges for both states in meeting

budget deficits could have spilled over to shared concerns in the neighboring states.

Similarly, the increase in intensities in June 2010 may reflect the difficulties in

financing deficits for the budget deadline of July 1 for California and the June 28

deadline for approving New York’s budget bill, which if not passed would have led

to a New York government shut down.

Finally, Panel C of Figure 3 graphs the default intensity of the third cluster,

which consists of just Florida. Unlike the first two clusters, Florida saw a very early

26
spike in its state-specific intensity in July 2008. This coincides with the bailouts

and credit lines provided to Fannie Mae and Freddie Mac to deal with deteriorating

conditions in the mortgage market, to which Florida was highly exposed.

7.3 Euro Country-Specific Sovereign Risk

In Figure 4, we plot country-specific intensities ξ for the Euro members. Panel A

graphs the intensities for the countries in the first cluster: Greece, Ireland, Italy,

Portugal, and Spain, all of which are Euro periphery countries. Policymakers have

been preoccupied in managing financing and avoiding default for these countries

since the financial crisis. Interestingly, all these countries, with the exception of

Greece, saw large increases in their sovereign-specific default risk from late 2008

through 2009. This mirrors the increase in German systemic risk and corporate

default rates over this time. It is only in January 2010 that Greek-specific intensities

start to rise, even though knowledge of Greece’s growing deficits and financing

problems were well known in 2009. The intensity for Greece rises from 187 basis

points at the end of December 2009 to close to ten percent at the beginning of

May 2010. This is when Ireland’s intensity starts to rapidly increase, also reaching

nearly ten percent at the end of the sample. This is due to market perceptions

that Ireland’s measures taken in 2008–2009 to fix the problems in its banking sector

are insufficient and additional measures, involving co-ordinated Euro action, are

necessary.

Panel B of Figure 4 plots the intensities for the countries in the second cluster: Austria, Finland, and the Netherlands. As is the case for the states (see

Figure 3) and the countries in the first cluster, default intensities rise during the

financial crisis. They remain elevated, and for the Netherlands also increase, after

2009. In contrast, the Belgian and French country-specific default risk shown in

Panel C barely changes during the financial crisis. Clearly, most of the variation

in the default risk of Belgium and France during the 2008–2009 period was due to

changes in systemic risk. Only towards the end of the sample do Belgian and French

sovereign-specific intensities start to increase.

7.4 What Drives Sovereign-Specific Credit Risk?

Given the evidence of common patterns in the country-specific default intensities

in Figures 3 and 4, we now investigate the determinants of sovereign-specific credit

risk. We regress weekly changes in the sovereign-specific intensity for each issuer

on the same set of financial market and global explanatory variables used in the

systemic regressions. Table 10 reports the results from these regressions.

27
06−08 12−08 06−09 12−09 06−10 12−10

0

200

400

600

800

US: Cluster 1

IL

MI

OH

MA

TX

06−08 12−08 06−09 12−09 06−10 12−10

0

200

400

600

800

US: Cluster 2

NY

NJ

NV

CA

06−08 12−08 06−09 12−09 06−10 12−10

0

200

400

600

800

US: Cluster 3

FL

Figure 3. State-Specific Credit Risk for the U.S. Clusters. The

upper, middle, and lower panels plot the state-specific intensity process

for the states in the first, second, and third clusters, respectively. The

intensities are measured in basis points.

A number of interesting patterns can be seen in these results. For example,

the explanatory power of these regressions is generally lower for the U.S. sovereigns

28
06−08 12−08 06−09 12−09 06−10 12−10

0

200

400

600

800

1000

Euro: Cluster 1

GRE

IRE

ITA

POR

SPA

06−08 12−08 06−09 12−09 06−10 12−10

0

200

400

600

800

1000

Euro: Cluster 2

NET

AUS

FIN

06−08 12−08 06−09 12−09 06−10 12−10

0

200

400

600

800

1000

Euro: Cluster 3

BEL

FRA

Figure 4. Country-Specific Credit Risk for the Eurozone Clusters. The upper, middle, and lower panels plots the country-specific intensity processes for the countries in the first, second, and third Eurozone

clusters, respectively. The intensities are measured in basis points.

than for the Eurozone sovereigns. In particular, the average R2 for the U.S. and

Eurozone sovereigns is 0.122 and 0.181, respectively.

29
One possible reason for the higher explanatory power in the Eurozone may be

that the ITraxx corporate index is significantly positive (at the ten-percent level)

for all but one of the Eurozone sovereigns. This result parallels the findings in

Longstaff, Pan, Pedersen, and Singleton (2011) that global sovereign CDS spreads

are strongly related to corporate spreads. In contrast, the corporate index is only

significant for several of the U.S. states.19

Another intriguing pattern in Table 10 is that stock market returns are significant for a number of states: Florida, New Jersey, New York, and Ohio. In contrast,

stock market returns are only significant for Austria. Thus, sovereign-specific risk

in the U.S. is more linked to equity markets than is the case in the Eurozone. One

reason for this might be that U.S. sovereigns have a greater reliance on capital gains

income tax receipts than do Eurozone sovereigns.

8. CONCLUSION

This paper studies the nature of systemic sovereign credit risk by examining the

pricing of CDS contracts on the U.S. Treasury, a number of key U.S. states, and

major Eurozone countries. An important advantage of comparing the U.S. with

the Eurozone is that the analysis can provide new insights into whether systemic

sovereign credit risk arises from common macroeconomic fundamentals or from the

influence of global financial markets.

By applying the multifactor credit model of Duffie and Singleton (2003), we are

able to decompose sovereign credit risk into a systemic component and a sovereignspecific component. We find that systemic risk represents a much smaller fraction of

total credit risk for U.S. states than is the case for members of the Eurozone. This

result is surprising since we would expect U.S. states to be more closely linked in

terms of their economic fundamentals. This result provides clear evidence against

the hypothesis that systemic risk is primarily an artifact of common macroeconomic

fundamentals.

We find that U.S. systemic sovereign credit risk is highly correlated with Eurozone systemic credit risk. Furthermore, we show that both are strongly related

19The increase in Eurozone sovereign-specific risk mirrors the increase in sovereign

liabilities in assuming banking sector liabilities, especially for Ireland. By itself

this should a priori predict a large sovereign-specific component in default risk for

Eurozone countries and a small sovereign-specific component in default risk for

states which did not assume any U.S.-based banking liabilities. The patterns of

sovereign-specific components in the Eurozone and the U.S. are the exact opposite

of this pattern.

30
to financial market variables such as stock returns. This argues that systemic risk

may arise largely through the global financial system.

One particularly intriguing result of our analysis is that U.S. systemic credit

risk is significantly negatively related to changes in the VIX index. Thus, as markets

become more volatile, the credit risk of the U.S. Treasury improves. This result is

consistent with the hypothesis that the financial position of the U.S. improves as

flights to quality occur in turbulent periods.

The results in this paper have at least two important implications for sovereign

credit risk. First, systemic risk is not directly caused by macro intergration. Second,

systemic risk is highly correlated with financial market variables. Clearly, future

work is needed to understand the deep reasons for the strong relation between

systemic sovereign risk and financial markets.

31
APPENDIX

After multiplying terms, taking expectations, and rearranging, the numerator of

Equation (9) can be expressed as,

w

 T

0

D(t) E



exp −

 t

0

γ λs ds E



ξt exp −

 t

0

ξs ds

+ γ E λt exp 

−

 t

0

γ λs ds E



exp −

 t

0

ξs ds dt. (A1)

Let A(λ, t) denote the first expectation in this expression. Standard results such as

Duffie, Pan, and Singleton (2000) imply that A(λ, t) satisfies the partial differential

equation

σ2

2

λAλλ + (α − βλ)Aλ − γλA − At = 0, (A2)

subject to the boundary condition A(λ, 0) = 1. Substituting the expression for

A(λ, t) given in Equation (11) into Equation (A2) shows that the partial differential

equation is satisfied provided that A1(t) and A2(t) satisfy the Riccati equations,

σ2

2

λA2

2 − βA2 − γ − A2 = 0, (A3)

αA2 − A

1

A1

= 0. (A4)

Integrating Equation (A3) for A2(t), and then substituting A2(t) into Equation

(A4) and integrating for A1(t) gives Equations (15) and (16) after using the initial

conditions A1(0) = 1 and A2(0) = 0 to determine the constants. The same procedure can be used to verify that the third expectation in Equation (A1) is given by

Equation (12) (where the parameters α, β, and σ are replaced by a, b, and c in the

partial differential equation and γ is set equal to one).

Let F(λ, t) denote the fourth expectation in Equation (A1). Standard results

can again be used to show that F(λ, t) satisfies the partial differential equation in

Equation (A2) with the boundary condition F(λ, 0) = λ. Substituting the expression for F(λ, t) into Equation (A2) shows that the partial differential equation is

satisfied provided that F1(t) and F2(t) satisfy the Riccati equations,

32
(α + σ2)A2 − β − F

2

F2

= 0, (A5)

αF2 + αF1A2 − F

1 = 0. (A6)

Integrating Equation (A5) for F2(t), and then substituting F2(t) into Equation

(A6) and integrating for F1(t) gives Equations (21) and (22) after using the initial

conditions F1(0) = 0 and F2(0) = 1 to determine the constants. The same procedure

can be used to verify that the second expectation in Equation (A1) is given by

Equation (13). The solution for the sovereign CDS spread s in Equation (10) is

then given by substituting the expressions for the respective expectations given in

Equations (11) through (14) into the numerator and denominator of Equation (9).

33
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38
Table 1

Nominal 2009 GDP in Millions of U.S. Dollars This table reports the 2009 Nominal GDP for the indicated States and Countries. GDP is measured in millions of U.S. dollars. Data from the

Bureau of Economic Analysis and the World Bank.

GDP

California 1,884,452

Florida 729,485

Illinois 621,101

Massachusetts 362,413

Michigan 361,126

Nevada 125,115

New Jersey 478,391

New York 1,085,131

Ohio 466,021

Texas 1,141,287

USA 14,119,000

Austria 384,908

Belgium 468,522

Finland 237,512

France 2,649,390

Germany 3,330,032

Greece 329,924

Ireland 227,193

Italy 2,112,780

Netherlands 792,128

Portugal 227,676

Spain 1,460,250
Table 2

cs for U.S. and Eurozone Sovereign CDS Spreads. This table reports summary statistics for the five-year CDS 

ated sovereigns. The sample consists of weekly observations for the May 14, 2008 to January 5, 2011 period.

Std. Serial

Mean Dev. Min. Med. Max. Corr. N

243.57 81.98 63.00 268.00 402.00 0.962 133

137.10 50.47 39.00 135.00 240.00 0.960 133187.61 87.32 25.00 191.00 369.00 0.982 130

ts 120.93 54.67 21.00 124.00 243.00 0.978 134

207.45 87.76 45.00 218.00 394.00 0.976 131

171.76 73.03 42.00 183.00 329.00 0.967 138

179.06 76.31 33.00 196.00 337.00 0.973 135

176.95 77.19 32.00 196.00 318.00 0.976 131

122.04 52.04 35.00 125.00 251.00 0.972 134

86.82 42.01 20.00 79.00 180.00 0.976 134

38.52 18.06 7.10 37.98 99.26 0.964 139

82.78 47.29 6.80 77.82 260.90 0.952 13675.63 48.76 10.00 62.01 227.68 0.977 13931.04 16.59 5.30 28.98 88.33 0.970 13947.49 26.95 6.75 43.78 108.84 0.975 139

33.56 17.16 4.40 33.75 90.61 0.959 139

353.34 316.99 32.19 230.25 1055.41 0.986 139205.94 143.40 17.30 162.48 613.43 0.982 139

121.86 58.34 24.75 113.68 241.03 0.963 139

44.58 26.38 6.30 41.27 123.33 0.970 139

155.43 133.54 21.33 93.84 500.02 0.978 139

126.61 80.54 24.25 98.83 349.90 0.977 139
Table 3

x of Weekly Changes in CDS Spreads. The top panel of this table reports the correlation matrix of weekly five-year 

for the U.S. sovereigns. The bottom panel reports the correlation matrix of weekly five-year CDS spread changes for the 

The sample consists of weekly observations for the May 14, 2008 to January 5, 2011 period.

CA FL IL MA MI NV NJ NY OH TX USA

1.0000.425 1.0000.657 0.529 1.000

0.595 0.410 0.653 1.000

0.678 0.323 0.691 0.773 1.0000.610 0.305 0.514 0.647 0.617 1.0000.726 0.352 0.615 0.665 0.683 0.630 1.0000.721 0.428 0.648 0.664 0.716 0.668 0.842 1.000

0.633 0.432 0.722 0.827 0.844 0.637 0.696 0.700 1.000

0.614 0.351 0.590 0.771 0.748 0.577 0.647 0.572 0.777 1.000

0.320 0.158 0.197 0.259 0.278 0.283 0.280 0.262 0.270 0.364 1.000

AUS BEL FIN FRA GER GRE IRE ITA NET POR SPA

1.0000.589 1.0000.816 0.649 1.0000.691 0.727 0.664 1.0000.745 0.713 0.720 0.820 1.0000.319 0.330 0.327 0.411 0.392 1.0000.650 0.529 0.542 0.544 0.533 0.559 1.0000.573 0.580 0.584 0.597 0.536 0.553 0.675 1.0000.716 0.668 0.785 0.587 0.665 0.325 0.548 0.554 1.0000.343 0.420 0.358 0.469 0.395 0.771 0.755 0.691 0.398 1.0000.503 0.567 0.493 0.563 0.485 0.727 0.738 0.808 0.560 0.845 1.000
Table 4

Principal Components Analysis Results. This table reports summary statistics for the principal components analysis of the correlation matrix of weekly changes in five-year CDS spreads for the U.S. and

Eurozone sovereigns. The correlation matrix is computed using all available overlapping observations

for each pairwise correlation.

Cumulative

Principal Percentage Percentage

Region Component Explained Explained

USA First 61.83 61.83

Second 8.45 70.28

Third 7.48 77.76

Eurozone First 62.40 62.40

Second 14.95 77.35

Third 5.19 82.54
Table 5

ts for the CDS Valuation Model Using Federal, State, and Eurozone CDS Spreads. This table reports the 

and their standard errors obtained by fitting the CDS valuation model to the term structure of CDS spreads for the 

ate, and Eurozone CDS contracts. For the systemic processes, the parameters reported are α, β, and σ. The RMSEs are 

oints. The sample consists of weekly observations for the May 14, 2008 to January 5, 2011 period.

Parameter Standard Error

a bc abc RMSE

0.00250 −0.1768 0.1064 0.00013 0.0114 0.0254 11.790

0.00306 0.1912 0.0268 0.00015 0.0187 0.2914 9.384

−0.00010 −0.0566 0.0096 0.00019 0.0094 0.2592 15.758

0.00140 0.0813 0.0174 0.00005 0.0068 0.1290 4.115

0.00214 0.0549 0.0440 0.00018 0.0151 0.1074 13.448

0.00171 −0.0508 0.1724 0.00012 0.0153 0.0246 10.218

0.00092 −0.0332 0.0253 0.00011 0.0135 0.1466 9.5050.00206 −0.1980 0.0607 0.00009 0.0064 0.0252 7.549

0.00108 −0.0796 0.2172 0.00004 0.0043 0.0049 3.595

0.00091 0.0914 0.0389 0.00007 0.0135 0.1213 5.419

0.00009 −0.4720 0.2868 0.00001 0.0041 0.0020 1.179

0.00006 −0.0976 0.0506 0.00005 0.0176 0.0901 5.592

−0.00019 −0.4646 0.2319 0.00002 0.0091 0.0070 4.181

0.00033 −0.1356 0.0228 0.00002 0.0188 0.1950 2.253

−0.00026 −0.4346 0.2013 0.00001 0.0065 0.0056 1.632

0.00081 −0.9786 0.5692 0.00022 0.0194 0.0083 51.6940.00115 −0.2562 0.3291 0.00010 0.0083 0.0076 12.742

0.00136 −0.1176 0.1623 0.00008 0.0166 0.0288 8.904

0.00041 0.0136 0.0954 0.00002 0.0175 0.0571 2.548

0.00063 −0.1926 0.2969 0.00012 0.0115 0.0126 16.556

0.00129 −0.0792 0.2232 0.00009 0.0118 0.0182 10.153

emic 0.00042 −0.4332 0.2672 0.00002 0.0161 0.0056 2.528
Table 6

Systemic Default Indexes This table reports the estimated value of the systemic default index

parameter γ and its standard error for the indicated sovereigns. The value of γ is constrained to be

1.000 for the USA and Germany. The sample consists of weekly observations for the May 14, 2008

to January 5, 2011 period.

Systemic Standard

Index Error

California 2.647 0.045

Florida 0.909 0.035

Illinois 0.000 0.031

Massachusetts 0.468 0.014

Michigan 0.731 0.054

Nevada 0.854 0.043

New Jersey 0.982 0.041

New York 0.000 0.022

Ohio 0.066 0.011

Texas 0.536 0.018

USA 1.000 −

Austria 1.173 0.028

Belgium 1.662 0.014

Finland 0.356 0.007

France 0.933 0.005

Germany 1.000 −

Greece 4.688 0.238

Ireland 1.604 0.049

Italy 1.710 0.037

Netherlands 0.668 0.011

Portugal 1.674 0.057

Spain 1.506 0.036
Table 7

cs for the Percentage Systemic Component of U.S. and Eurozone Sovereign Default Risk. This table reports 

or the percentage that the systemic component represents of the total credit risk of the indicated sovereigns. The sample 

bservations for the May 14, 2008 to January 5, 2011 period.

Std.

Mean Dev. Min. Med. Max. N

36.78 13.62 17.60 32.16 92.81 133

18.18 12.32 5.80 14.53 73.17 133

0.00 0.00 0.00 0.00 0.00 130

etts 10.59 6.02 3.46 9.49 40.07 134

8.83 4.33 3.35 7.71 26.76 131

13.63 6.24 6.27 12.11 47.64 138

y 15.05 5.55 7.15 13.59 36.72 135

0.00 0.00 0.00 0.00 0.00 131

1.28 0.38 0.62 1.22 2.50 134

17.73 9.73 5.58 15.42 60.01 134

100.00 0.00 100.00 100.00 100.00 139

34.31 16.16 0.00 30.76 100.00 13656.87 25.23 0.00 67.67 89.97 13939.75 22.20 0.00 33.49 100.00 13853.15 23.70 0.00 55.99 92.58 139

100.00 0.00 100.00 100.00 100.00 139

44.48 30.24 0.00 35.00 100.00 13816.77 9.82 0.00 15.30 45.71 139

31.84 15.36 0.00 31.32 71.60 139

ds 39.79 21.10 0.00 34.27 100.00 138

32.84 26.78 0.00 22.24 96.01 139

28.24 19.53 0.00 22.32 79.74 139
Table 8

for Systemic Risk. This table reports the t-statistics and other summary statistics from the regression of weekly 

c credit process on the indicated variables. Mkt denotes the return on the S&P500 for the US, and the return on the 

denotes the weekly change in the VIX volatility index. Corp denotes the weekly change in the CDX IG index for the 

ange in the ITraxx index for Europe. Japan, China, and EM denote the weekly changes in the CDS spreads for the 

r sovereign indexes. The sample consists of weekly observations for the May 14, 2008 to January 5, 2011 period.

Intercept Mkt Swap VIX Corp Japan China EM R2 N

0.55 −4.31∗∗ 2.60∗∗ −2.83∗∗ 1.80∗ 1.64 1.80∗ −0.50 0.352 138

0.56 −1.97∗∗ −0.61 −1.60 1.86∗ 1.44 2.67∗∗ 1.02 0.431 138
Table 9

his table reports the clusters formed on the basis of the correlation matrix of the weekly changes in the nonsystemic 

ses. The pairwise correlations in the correlation matrix are computed using all available overlapping observations for 

Cluster 1 Cluster 2 Cluster 3

Illinois California Florida

Massachusetts NevadaMichigan New JerseyOhio New YorkTexas

ne Greece Austria Belgium

Ireland Finland FranceItaly NetherlandsPortugalSpain
Table 10

for the Sovereign-Specific Credit Processes. This table reports the t-statistics and other summary statistics from 

y changes in the sovereign-specific credit processes on the indicated variables. Mkt denotes the return on the S&P500 

urn on the DAX for the Eurozone. VIX denotes the weekly change in the VIX volatility index. Corp denotes the weekly 

index for the US, and the weekly change in the ITraxx index for Europe. Japan, China, and EM denote the weekly 

reads for the respective sovereigns or sovereign indexes. The sample consists of weekly observations for the May 14, 2008 

iod.

Intercept Mkt Swap VIX Corp Japan China EM R2 N

0.48 −0.31 −2.51∗∗ −0.31 0.13 −0.50 −0.08 −1.11 0.094 132

0.14 −1.77∗ −2.11∗∗ −0.82 −2.07∗∗ 0.55 −3.52∗∗ −3.17∗∗ 0.136 1321.45 −1.64 −1.39 −0.07 −1.66∗ −0.84 0.81 −1.54 0.135 129

0.73 −1.50 −0.89 −1.50 −0.13 1.19 −0.40 −1.24 0.074 133

0.51 −0.63 −1.84∗ −1.44 0.08 0.66 −0.03 −1.57 0.113 130

0.70 −0.93 −0.19 −0.56 0.68 −0.47 −0.33 −1.41 0.089 137

0.44 −2.56∗∗ −1.62 −2.41∗∗ −0.99 0.05 0.19 −1.58 0.132 1340.33 −1.95∗ −1.13 −1.66∗ −1.75∗ 0.36 0.71 −3.19∗∗ 0.217 130

0.94 2.35∗∗ −0.80 1.83∗ 2.63∗∗ −0.58 2.81∗∗ 2.69∗∗ 0.144 133

0.31 −0.18 −1.10 −0.31 0.02 1.96∗∗ −0.11 −0.89 0.082 133

0.04 −2.21∗∗ −0.62 −2.49∗∗ 1.98∗∗ 1.36 0.76 0.12 0.336 1351.52 0.85 −0.97 −0.86 1.78∗ −0.51 −0.91 −0.97 0.061 138

−0.21 −0.83 −0.58 −0.85 1.99∗∗ 0.37 0.96 0.67 0.281 137

1.37 0.47 −1.52 0.74 2.01∗∗ −0.07 −2.83∗∗ −1.41 0.147 1381.42 1.34 −1.01 −1.69∗ 1.42 −0.72 −2.05∗∗ −1.73∗ 0.086 1371.70∗ −1.32 −2.20∗∗ −2.13∗∗ 2.24∗∗ 0.06 0.41 0.71 0.184 138

0.78 −0.63 −2.34∗∗ −0.74 2.71∗∗ −0.82 −1.17 −0.13 0.232 138

0.15 −0.52 0.05 −1.32 1.85∗ 1.03 1.22 0.53 0.177 137

0.94 0.96 −2.56∗∗ −0.55 1.87∗ −1.27 −1.03 0.65 0.161 138

1.33 −0.02 −1.84∗ −1.36 2.26∗∗ −0.98 −1.06 −0.59 0.146 138