the term structure of cds spreads and sovereign credit risk

The Term Structure of CDS Spreads and Sovereign Credit Risk1

Patrick Augustina∗

a McGill University - Desautels Faculty of Management.

April 3, 2018

2

Abstract3

The shape of the term structure of credit default swap spreads is an informative signal about4

the importance of global and domestic risk factors to the time variation of sovereign credit spreads.5

Exploiting cross-country heterogeneity among 44 countries, I document that the importance of6

global and country-specific risk in explaining sovereign credit risk varies with the sign of the slope7

of the term structure and the duration of its inversion. A model is used to show that global8

uncertainty shocks determine spread changes when the slope is positive, and that domestic shocks9

are more important when the slope is negative.10

Keywords: Credit Default Swaps, Default Risk, Sovereign Debt, Term Structure11

JEL classification: C1, E43, E44, G12, G1512

∗Correspondence to: McGill University, Desautels Faculty of Management, 1001 Sherbrooke Street West,Montreal, Quebec H3A 1G5, Canada; Tel.: +1 514 398 4726; E-mail address: [email protected].

The Term Structure of CDS Spreads and Sovereign Credit Risk 2

1. Introduction1

The defaults of several emerging market economies over the last two decades and the2

multiple recent European government bailouts have fueled the interest in understanding3

the pricing of sovereign credit risk.1 Yet the literature is inconclusive as to the relative4

importance of global and country-specific risk factors to the time variation in sovereign5

credit spreads. Until the end of the 2007-09 financial crisis, there appeared to be some6

consensus that sovereign credit risk is driven by global factors (Pan and Singleton, 2008;7

Borri and Verdelhan, 2016; Ang and Longstaff, 2013) and that it is better explained by U.S.8

financial market factors than by country-specific fundamentals (Longstaff et al., 2011). Since9

the start of the sovereign debt crisis in Europe in 2009, Gennaioli et al. (2012) and Acharya10

et al. (2014), among others, establish a tight link between sovereign risk and the performance11

of the domestic financial sector.12

Such differences in findings are intriguing and beg the question of what could explain13

the divergence in emphasis among these results, and, perhaps, reconcile both parties? One14

possible explanation could be the focus of the above studies on the level of credit spreads.15

For many asset classes, the entire term structure has been shown to convey valuable economic16

information on the pricing of risk, including U.S. government bonds (Cochrane and Piazzesi,17

2005), equity and dividend derivatives (Binsbergen et al., 2012, 2013), currencies (Lustig18

et al., 2017; Zviadadze, 2017), inflation (Fleckenstein et al., 2017), and volatility (Gruber19

et al., 2017), among many others. Thus, incorporating the information from the slope of20

the term structure (henceforth the “slope”) may help us understand why researchers reach21

different conclusions in the sovereign credit risk literature. The examination of the term22

structure of credit default swap (CDS) spreads of different countries across time suggests,23

indeed, that the slope conveys differences in information that cannot be distinguished by24

the level of spreads. Russia, for example, exhibits an identical 5-year CDS spread in three25

1For example, Greece was bailed out three times (2010, 2011, and 2015) and officially defaulted in 2012.Explicit or implicit bailouts were implemented for Ireland (2010), Portugal (2011), Spain (2012), and Cyprus(2013).


separate months, despite significant differences in the slope. It is 418 and 270 basis points1

(bps) in January and June 2002, respectively, and -106 bps (inverted) in March 2009, when2

many countries had upward sloping term structures.2 This suggests that dependence on a3

common (level) factor alone is insufficient to explain country-specific heterogeneity in the4

term structure of CDS spreads, and that the shape of the slope may be informative about5

the underlying sources of risk.6

I show that the shape of the term structure of sovereign CDS spreads conveys useful in-7

formation on the importance of global and domestic risk factors for the dynamics of sovereign8

credit risk. In particular, global shocks are the primary source of time variation for spreads9

when the term structure is upward-sloping. A negative slope, in contrast, indicates that10

local shocks dominate. Importantly, for each country, the relative influence of global and11

country-specific risk factors can be inferred in real time, as CDS spreads are observable at12

a daily frequency. These empirical findings are supported by a general equilibrium asset13

pricing model for CDS spreads with recursive preferences and long-run risk. This model can14

be used to explore the time-varying dynamics and cross-country heterogeneity of the term15

structure of sovereign credit risk in relation to common and country-specific shocks.16

The informational power of the term structure of sovereign CDS spreads is documented17

in three ways, using a novel data set on six maturities of sovereign CDS spreads for 4418

countries from January 2001 to February 2012. The level of CDS spreads is defined as the19

5-year spread, and the slope as the difference between the 10-year and the 1-year spreads.20

The focus is on the sign of the slope and the number of months that the slope is negative (the21

duration of inversion). First, using a simple cross-sectional analysis, it is shown that country-22

specific fundamentals explain a significantly greater fraction of the variation in monthly CDS23

spread changes for countries with term structure inversions, compared to countries that have24

never had a negative slope. More importantly, the fraction of variation in spreads due to25

domestic risk increases monotonically with the duration of the inversion.26

2These empirical observations are illustrated graphically in the Online Appendix.


Second, the slope is explicitly used as an interaction term in panel regressions to show its1

power in identifying the importance of global and domestic risk factors in driving the time2

variation of sovereign credit risk. Country stock market returns proxy for domestic risk, as3

they are the most significant domestic determinant of CDS spreads in the empirical analy-4

sis. The magnitude of the impact of domestic stock market returns on CDS spread changes5

increases fifteenfold when the slope is negative. It is also greater for larger spread changes,6

and these impacts are statistically significant primarily for spread innovations that are asso-7

ciated with a flattening of the slope. Furthermore, the slope is shown to significantly explain8

quarterly real GDP growth, a country-specific measure, only when the slope is negative.9

An examination of the factor structure of changes in the slope of spreads across countries10

suggests that the slope exhibits little commonality, in contrast to the strong factor structure11

documented for the levels (Pan and Singleton, 2008; Longstaff et al., 2011). One factor12

influences only about 22% of changes in the slope of spreads, while it influences about 57%13

of changes in the level of spreads, i.e., almost three times as much. Overall, these findings14

support the view that the slope contains country-specific information not accounted for by15

the level of CDS spreads, and that this information is useful for understanding cross-country16

heterogeneity related to the dynamics of sovereign credit spreads.17

I next demonstrate that a model with recursive preferences and long-run risk has im-18

plications for time variation in the term structure of CDS spreads that are consistent with19

the observed dynamics of the term structure of spreads. Given the well-documented role of20

time-varying macroeconomic uncertainty (Jurado et al., 2015) and its impact on asset prices21

(Lettau et al., 2008), global macroeconomic uncertainty is the common risk factor in each22

country’s default process, which depends both on global macroeconomic uncertainty and on23

country-specific shocks. Both types of shocks impact the CDS term structure all the time.24

Common shocks work in two counteracting directions, but the dominating effect is to steepen25

the slope. Country-specific shocks work in the opposite direction to the global shock. The26

differential impact on the term structure is due to a differential impact of the shocks on de-27


fault probabilities and risk premia. Domestic shocks only affect default probabilities because1

they are unpriced. A negative country-specific shock increases default probabilities more2

for short maturities and less for long maturities, as conditions are expected to improve over3

time. As a result, the term structure inverts. Priced uncertainty shocks also command a risk4

premium, which increases more for longer maturities, due to preference for early resolution of5

uncertainty. Thus, the term structure steepens, as the increase in the term structure of risk6

premia outweighs the decrease in the term structure of default probabilities. The mechanism7

underlying the term structure inversions is consistent with my findings that country-specific8

shocks have greater explanatory power when the slope is negative.9

The model is calibrated to the unconditional moments of all 44 countries in sample.10

Countries, which, on average, have upward-sloping term structures, load heavily on aggregate11

risk. For countries that, on average, have downward-sloping term structures, the leverage12

factor on global risk is small, and the default intensity depends more on idiosyncratic shocks.13

Simulations suggest that the model describes the data well, as the 5-year spread level always14

lies within the 5th and the 95th percentiles of the small sample distribution. The model15

qualitatively fits the slope patterns and, importantly, the frequency of the term structure16

inversion. The simulated panel also closely matches the factor structure of high commonality17

in the levels, despite little commonality in the slopes. Model-implied risk premia rise with18

maturity, and represent a smaller proportion of the level of the spreads when the term19

structure is inverted.20

The model has two testable predictions, which bear out in the data. First, the ratio of21

risk premia relative to expected default losses is lower for countries when the term structure22

is inverted. Second, expected excess returns are greater when global economic uncertainty23

is high. The confirmation of both predictions validates the model and supports the findings24

that the shape of the CDS term structure conveys useful information on the importance of25

global and domestic risk for the dynamics of sovereign credit risk.26

My findings provide support for several conclusions in the literature, despite an apparent27


disagreement about the importance of global and country-specific risk. As the influence of1

global and domestic risks on sovereign credit risk is varying over time, the results may be2

linked to the evidence on a tight relation between sovereign default risk and the domestic3

financial sector observed during times of distress (Gennaioli et al., 2012; Acharya et al.,4

2014). My findings may also be linked to the evidence on the relation between sovereign CDS5

spreads and U.S. financial factors during benign times (Pan and Singleton, 2008; Longstaff6

et al., 2011; Ang and Longstaff, 2013). Remolona et al. (2008) provide evidence that global7

risk aversion is unconditionally the dominant determinant of sovereign risk premia, while8

country-specific fundamentals and market liquidity matter more for expected credit losses.9

In contrast to these papers, I examine the interactions between global and country-specific10

risk factors and study their implications for the dynamics of the CDS term structure.311

Duffie et al. (2003) and Zhang (2008) use an exogenous default intensity to study the12

credit risk of Russia and Argentina. The presented framework embeds such a reduced-form13

default intensity into a recursive utility framework, similar to Augustin and Tedongap (2016)14

and Chernov et al. (2017), although the latter endogenize sovereign default to examine the15

size of U.S. CDS premia. While these two papers focus on aggregate moments of the CDS16

term structure, this paper focuses on the dynamics of the CDS term structure. Hence, cross-17

sectional differences in the term structure of CDS spreads may be related to the importance18

of global and local risk. Contagion is not modeled. This distinguishes the paper from Benzoni19

et al. (2015), who use the fragile beliefs framework to study how a hidden factor generates20

contagion in the cross-section of sovereign default probabilities.21

Importantly, among the above papers, almost none use the information embedded in22

the CDS term structure. Notable exceptions are Pan and Singleton (2008) and Longstaff23

et al. (2011), who use the cross-sectional information in the term structure to estimate the24

risk-neutral parameters of the default process. Arellano and Ramanarayanan (2012), on the25

3Augustin (2014) surveys the role of global and local risk factors for sovereign CDS spreads. Other relatedreferences are Mauro et al. (2002), Geyer et al. (2004), Uribe and Yue (2006), Reinhart and Rogoff (2008),Obstfeld and Rogoff (2009), Hilscher and Nosbusch (2010), Dieckmann and Plank (2011), Jeanneret (2015),and Kallestrup et al. (2016).


other hand, illustrate how the endogenous choice of debt maturity may lead to an inverted1

sovereign yield curve. Jotikasthira et al. (2015) show that world inflation and the U.S. yield2

curve are a source of co-movement of the yield curves of the U.S., the U.K., and Germany.3

My focus is on the empirical findings that the slope of the CDS term structure is a useful4

real-time market indicator of the country-specific sources of sovereign credit risk, which is5

explained using a general equilibrium asset pricing model.6

The rest of this paper proceeds as follows. In Section 2., the data is described and stylized7

facts about the term structure of sovereign CDS spreads are presented. The development of8

the model and a discussion of the asset pricing implications follows in Section 3. The model9

is validated in Section 4. The conclusion is presented in Section 5.10

2. The Term Structure of Sovereign CDS Spreads11

In this section, I present stylized facts about the term structure of sovereign CDS spreads.12

After an overview of the data, I provide cross-sectional and time series evidence on how the13

slope relates to global and domestic risks, and country-specific economic growth. The section14

ends with a statistical analysis of the factor structure of the level and the term structure of15

CDS spreads.16

2.1. Data17

The study of the term structure of sovereign CDS spreads is based on daily spreads from18

Markit for maturities of 1, 3, 5, 7, and 10 years. All swaps are denominated in USD, apply19

to senior foreign debt, and contain the full restructuring credit event clause. Monthly CDS20

spreads are derived from the last available observation in each month. The slope of the CDS21

term structure is defined as the difference between the 10- and 1-year spreads. With 4422

countries from Europe/Eastern Europe, Asia, Latin America, and the Middle East/Africa,23

the panel spans a broad geographical area and exhibits significant time series and cross-24

sectional heterogeneity in both the level and the slope.25


Table 1 presents summary statistics. The earliest starting period is January 2001, and1

all observations end in February 2012. For any country, the market typically charges higher2

spreads over longer horizons to compensate for greater uncertainty about future default risk.3

Plotted against progressively longer maturities, this produces a smooth, upward-sloping4

curve. In contrast to the findings in Pan and Singleton (2008), I find that the average5

term structure in column (7) is not always upward-sloping; it is negative for four countries:6

Greece, Ireland, Portugal, and Uruguay. The mean slope is as negative as -382 bps in the7

case of Greece, and Colombia has the largest positive slope at 234 bps. The average 5-year8

spread, reported in column (5), ranges from 13 bps for Finland to 868 bps for Venezuela.9

Columns (8) and (9) display the number and frequency of months during which the term10

structure was inverted. Twenty countries had a negative slope for at least one month, while11

six countries had an inverted term structure for more than twelve months, with the frequency12

of inversion ranging up to 20% of the sample period. There are 198 (monthly) inversions,13

staggered across countries and across time.4 The term structure of individual countries14

inverts (and consequently reverts) up to four times during the sample period. The fact that15

inversions (and reversals) occur for different countries at different points of time creates rich16

panel dynamics that are key to identifying the stylized facts highlighted in the following17

subsections.18

2.2. Cross-sectional explanatory power of domestic and global risk19

To understand the relative role of domestic and global risk factors, I first examine whether

the sign of the slope and the duration of inversion can be related to cross-sectional differences

in the explanatory power of common risk factors and country-specific fundamentals. To this

end, for each country i, the changes in the monthly 5-year sovereign CDS spreads (∆CDSit)

are projected on the changes of three local factors and changes of three groups of global

4Due to space limitations, additional summary statistics are in the Online Appendix. The Appendix alsoprovides examples of countries with low CDS spread levels and an inverted CDS term structure that arecompared to countries which contemporaneously have high CDS spread levels and a positive term structureof spreads.


factors. The regression output is used to construct “local ratios” that proxy for the amount

of the explanatory power of the country-specific risks. Specifically, the following regression

model is estimated:

∆CDSit = αi + β>i ∆Lit + γ>i ∆Gt + εit, εit ∼ N (0, 1) , (1)

where Lit denotes a vector of domestic factors and Gt refers to the vector of global factors.1

The three local factors are the domestic stock market return in local currency, the ex-2

change rate relative to the USD, and the USD-denominated foreign currency reserves.5 The3

first set of global factors are financial market indicators from the U.S.: the U.S. excess stock4

market return, changes in the 5-year constant maturity Treasury yield, and changes in the5

spreads of U.S. investment-grade and high-yield bond indices. The second set of global fac-6

tors comprises proxies for international risk premia, based on the intuition that risk premia7

should correlate across asset classes. The equity risk premium is proxied by changes in the8

earnings-price ratio of the S&P 500 Index. Changes in the spread between the implied and9

realized volatility of index options are used for the volatility premium, and changes in the10

expected excess returns on five-year Treasury bonds approximate the term premium. Val-11

uation effects based on international capital flows are captured using net global flows into12

equity and bond mutual funds. Finally, to account for any residual economic sources of risk,13

the predictor variables also include a regional and a global sovereign spread. The regional14

spread is computed as the mean spread of all other countries in the same region, whereas the15

global spread is measured as the mean spread of the countries in all other regions, except16

the region being analyzed. Only the residual part orthogonal to all other regressors is used17

in the regressions. Data sources and details about variable constructions are provided in the18

Online Appendix.19

The local ratio (LR) statistic captures cross-sectional differences in the explanatory power20

5While exchange rates may contain a systematic component (Verdelhan, 2018), they are classified as localfollowing Longstaff et al. (2011). All conclusions remain unchanged if the local variation in spread changesis associated with the component unexplained by all global risk factors.


of local risk. The LR is computed as the ratio of the adjusted R2 from a restricted regression,1

which includes domestic variables only, to that of an unrestricted regression, which includes2

all variables. The metric is thus increasing in the importance of country-specific factors.3

Longstaff et al. (2011) show, using a sample of 26 countries, that spread changes are related4

primarily to global determinants, in particular U.S. equity returns, volatility, and bond5

market risk premia. I document cross-sectional differences in the explanatory power of local6

and global risk factors, which I relate to the sign of the slope and the duration of inversion.7

All 44 countries are separated into two groups: those that never had an inverted slope8

(G1) and those that had an inverted slope during at least one month (G2). Table 2 reports9

the mean and median LR for both groups, which are highly statistically different.6 The10

median (mean) LRs for the two groups are 38% (40%) and 63% (61%). The set of individual11

country LRs contains three outliers. In G1, the LR for Venezuela is roughly 5%. This12

country arguably plays a special role, given its importance for global oil production. In G2,13

Mexico and Egypt, two countries with a high LR, never have an inverted term structure14

yet experienced significant financial or political trouble. Mexico underwent an economic15

downturn in connection with the drug cartel wars, while Egypt suffered as a result of the16

Arab Spring. Their LRs are 77% and 65%, respectively. Excluding the outliers, the difference17

in the mean and median LRs between the two groups widens further, both the mean and18

median LRs being 36% for G1 and 64% for G2. The LRs for Portugal, Greece, and Ireland19

are 109%, 76% and 100%. Overall, these findings suggest that country-specific risk factors20

explain more variation in the CDS spreads of countries with inverted term structures.21

Figure 1 shows that the LR is monotonically increasing in the months when the term22

6Inference is obtained by block-bootstrapping 10,000 times a sample size of 36 months for each country.A one-sided t-test on the equality of means, assuming paired data, against the alternative that G1 has asmaller mean, is rejected at the 1% significance level. The Wilcoxon matched-pairs signed-rank test rejectsthe null hypothesis that both distributions are the same, while the one-sided sign test rejects the equality ofthe medians against the alternative that the median of G1 is lower. Note that in this inference, I assume thatthe correlation between local and global factors is the same for each country. Adjusting for this correlationwould lower the LR. If the local economies of distressed countries are more highly correlated with globalfactors than are those with non-distressed countries (the most unlikely case), the results would be evenstronger.


structure is inverted. The relation between the duration of inversion and how much variation1

the domestic factors explain is depicted in the upper panel of Figure 1 for countries in G22

(excluding Venezuela). A linear regression fitted to the scatter plot yields an R2 statistic of3

32%, with a statistically significant t-statistic of 3.11. The regression fit further improves if4

countries from both G1 and G2 are considered, as is illustrated in the lower graph in the5

figure. The R2 increases to 45% and the t-statistic is 5.76. These results are not driven6

by the European sovereign debt crisis, nor by a clustering of events over time. Excluding7

Europe from the sample yields an R2 of 32% with a t-statistic of 3.16. The explanatory8

power decreases slightly to 23% using the full sample that includes Venezuela, and the9

relation remains significant with a t-statistic of 3.12. These findings support the view that10

the explanatory power of country-specific risk is monotonically increasing in the duration11

of term structure inversion.7 The results in Figure 1 suggest that the LR, imputed from12

CDS spread levels, yields similar cross-country rankings of the importance of local risk to13

those obtained from the term structure of spreads. The estimation of LRs requires a long14

time series for an important number of observables. The slope is model-independent and15

observable in real time.16

2.3. The role of the slope for the dynamics of sovereign credit risk17

I next use panel regressions and augment the empirical model from equation (1) with an18

indicator variable that is equal to one if the term structure is negative, and zero otherwise.19

This indicator variable is interacted with both the local and global risk factors, but the20

focus is on the domestic and U.S. stock market returns, as these are the most significant21

determinants in country and panel regressions. In other words, the information in the slope22

is used to distinguish the importance of global and local risk factors as a function of the23

sign of the slope. For the sake of brevity, Panel A of Table 3 only reports the coefficients of24

7Detailed results of individual country regressions are available upon request. The most significant globalrisk factors are the U.S. stock returns, the U.S. equity premium, and global and regional spreads, consistentwith Longstaff et al. (2011). The most significant local risk factor is the domestic stock market return.


interest.1

All specifications indicate that an increase in both the domestic and global stock market2

return reduces sovereign CDS spreads, as demonstrated by the statistically significant nega-3

tive coefficient on both risk factors. The unconditional effect of the U.S. equity return is, on4

average, three times as large as that of the country-specific stock market return. The coeffi-5

cient on the interaction term between the negative slope indicator and the local stock market6

return is negative. It has a magnitude of 0.15, suggesting that the impact of domestic stock7

market returns on sovereign CDS spreads is fifteen times larger when the term structure8

is inverted, and five times larger than the unconditional impact of the U.S. stock market9

performance. The coefficient on the negative slope indicator multiplied by the U.S. equity10

return suggests, likewise, a stronger dependence in times of term structure inversion. The11

coefficient is, however, not robust, and mostly statistically insignificant. The specifications12

presented in columns (2) to (8) of Table 3 successively feature controls, country fixed effects,13

and different standard error corrections.8 In column (8), the full set of interaction effects14

between all risk factors and the negative slope indicator is included. Importantly, none of15

the specifications change the statistical significance or economic magnitude of the coefficient16

for the interaction term between the domestic stock market return and the negative slope17

indicator.18

The sample is next split conditional on positive and negative changes in the CDS spread19

slopes. While the relation between changes in CDS spreads and domestic stock market20

returns is consistently negative in Panel B of Table 3, it is asymmetric. The dependence is21

about two to three times greater for changes that flatten the slope (column (2)), as opposed22

to changes that steepen it (column (1)). Importantly, the correlation between domestic23

equity returns and sovereign credit risk increases in months when the slope is negative, in24

8Regression specifications are reported with and without country fixed effects, clustering by country,month, time and month, and with Driscoll-Kraay standard errors with country fixed effects, accounting forcross-sectional correlation and time series correlation of up to three lags. Results are similar for specificationsthat use the component of local shocks that is orthogonal to global shocks, as reported in the OnlineAppendix.


an economically significant way, only when the slope is flattening, as demonstrated by the1

significant regression coefficient in column (2) of Panel B. In contrast, the impact of U.S.2

equity returns on spread changes is of equal economic magnitude for shocks that flatten the3

slope, than for shocks that steepen the slope. In both cases, the negative coefficient has a4

magnitude of 0.027. In addition, the regression that conditions on a flattening of the slope5

has an R2 of 24%, compared to a weaker fit of 18% for the regression that conditions on a6

steepening of the slope. The results in column (3) corroborate the finding that the relation7

between domestic stock market returns and changes in CDS spreads significantly increase8

when the slope is flattening, while this is not the case for the relation with U.S. equity9

returns. For the specification in column (3), in which the full panel and dynamics of the10

slope are exploited, the explanatory power increases to 39%.11

I provide even more granular results in Panel C of Table 3, which reports the impact of12

local stock market performance on CDS spread changes at different quantiles of the distri-13

bution of 5-year CDS spread changes. Given that the interaction term with the U.S. equity14

return is insignificant, only the coefficient of the domestic stock market return and its inter-15

action with the negative slope indicator are reported. The magnitude of the coefficient of the16

local stock market return increases monotonically from 0.003 (in absolute value) for the 50th17

to 0.009 for the 95th percentile of the distribution of CDS spread changes, corresponding18

to a multiplicative factor of three. Similarly, the magnitude of the beta coefficient on the19

interaction term increases monotonically from a magnitude of 0.04 to 0.27, but the increase20

is more pronounced, given that the impact at the 95th percentile is more than six times as21

large as that at the 50th percentile. These findings jointly underscore that the contempora-22

neous impact of domestic stock market returns on sovereign CDS spread changes is greater23

when the slope is negative, for shocks that flatten the slope, and for larger spread changes.24


2.4. The slope of CDS spreads and economic growth1

In this section, I examine the relation between the term structure of sovereign CDS2

spreads and macroeconomic fundamentals. If a negative slope truly signals the impact of3

domestic risks, then we should observe a significant relationship between the slope and4

country-level economic growth (country-specific measure) only when the slope is negative.5

Quarter-on-quarter seasonally adjusted GDP growth data is sourced for 42 countries from6

the OECD, Oxford Economics, IHS Global Insight, Thomson Reuters Datastream, IMF7

International Financial Statistics, and the national statistical offices or central banks of8

Uruguay, Peru, Egypt, South Africa, Slovenia, and Cyprus.9 Merging the data results in an9

unbalanced panel of 42 countries from 2001:Q1 to 2012:Q1 with a total of 4,951 observations.10

First, all 4,951 observations are ranked in ascending order based on the size of the slope,11

and grouped into sliding windows of 100 observations. Within each window, the fraction of12

observations with negative real GDP growth relative to the previous quarter is computed,13

as well as the average slope of the term structure of CDS spreads.10 The resulting relation14

between real GDP growth and the slope of CDS spreads, plotted in Panel A of Figure 2,15

illustrates a visible discontinuity at the threshold of a flat slope. Once the slope shifts from16

being positive to negative, there is a sharp drop in the average level of growth, as well as17

a sharp increase in the number of countries with negative growth. Panel B in Figure 218

illustrates the same relation between real GDP growth and the magnitude of the slope for19

values above -250 bps.20

One valid concern is that the slope is highly correlated with the level of CDS spreads,21

which, would capture the relation between the dynamics of the CDS spreads and the ex-22

planatory power of domestic risk. Panels C and D of Figure 2 depict the proportion of23

countries with an inverted term structure and the average slope, respectively, against the24

9No reliable information was found for Panama and Russia. The information for Lebanon is availableonly at a yearly frequency.

10If the ranked CDS spreads are indexed with integer numbers starting from 1, then the first windowprovides the average slope of the term structure and real GDP growth for observations 1 to 100; the secondfor observations 2 to 101; the third for observations 3 to 102, and so forth.


average level of spreads. The figures show, however, that such concerns are unfounded. Even1

though the level and the slope are positively correlated, almost 40% of the countries do not2

have a negative slope at spread levels as high as 1,000 bps. This confirms that the slope3

captures information different from that captured by the level of CDS spreads.4

The “slope-growth” relation is formally validated using panel regressions, whereby the5

seasonally adjusted quarter-on-quarter real GDP growth is projected on the level and the6

slope of CDS spreads, as well as the interaction between the slope and a negative slope7

indicator, which is equal to one if the slope is negative in a quarter, and zero otherwise. The8

results in Table 4 suggest that the slope is contemporaneously predictive of the quarterly real9

GDP growth only when it is negative. The level of spreads is negatively predictive of growth,10

and growth is, on average, 2.07 percentage points lower when the slope is negative, based on11

the most conservative results in column (5). A steeper slope, on the other hand, is positively12

predictive of growth, but the unconditional effect is not statistically significant. The slope13

is a significant predictor of economic growth only in those quarters when the term structure14

is inverted. Adding the interaction term to the regression increases the explanatory power15

of GDP growth from 2.49% to 3.01%, in terms of adjusted R2. Excluding Greece from the16

sample (column (6)) does not affect the results. Similar regression results at the monthly17

frequency are provided in the Online Appendix; the interaction between the slope and the18

negative slope indicator is consistently significant at either the 5% or 1% significance level,19

depending on the specification.20

2.5. Principal component analysis21

I next evaluate the statistical content of the slope by examining its factor structure. Table22

5 reports the results of a principal component analysis (PCA) on the covariance matrix of23

changes in both CDS spread levels and slopes. The results of the PCA are reported for the24

whole sample period, the pre-crisis period of 2003-2006, the financial crisis of 2007-2009, and25


the sovereign debt crisis of 2010-2012.11 Over the whole sample period, the first principal1

component provides explanatory power, on average, for 57% of the variation in monthly2

5-year CDS spread changes (Panel A). In line with the literature, this number varies from3

43% in the pre-crisis period (with sovereign defaults) to 75% during the financial meltdown4

(with no sovereign defaults).12 This suggests that the drop in correlation is driven by the5

countries in distress. Panel B shows that similar results are found for a PCA performed on6

pooled spreads of all maturities, as in Pan and Singleton (2008).137

The results in Panels A and B contrast sharply with those in Panel C, which show8

that the first principal component has relatively little explanatory power for changes in9

the slope. On average, the first factor provides explanatory power for only about 22%10

of the variation. Conditional values change from 24% to 38%, and back to 31% over the11

three time periods. The first three common factors combined provide explanatory power12

for only about 39% of the slope variation. Thus, the high degree of commonality in spread13

levels contrasts with the low degree of commonality in the slope. This reflects a significant14

degree of heterogeneity in the behavior of the slope in the cross-section and over time. This15

heterogeneity is symptomatic of the slope’s ability to capture cross-sectional differences in16

the importance of domestic and global risk over time.17

Even though liquidity is more balanced across contract maturities for sovereign than for18

corporate CDS contracts (Pan and Singleton, 2008), idiosyncratic liquidity shocks, which19

affect separate maturities differently, could explain a lower co-movement of the term struc-20

tures. Such shocks should, however, also reduce the co-movement in the level of spreads.21

Thus, idiosyncratic liquidity shocks are unlikely to affect the difference in explanatory power22

provided by the first principal components from a PCA on the level and slope of CDS spreads.23

11To perform the PCA, balanced panel dataset is needed, which is why the starting year of the analysis is2003. The analysis is conducted for standardized spread changes.

12During the sovereign debt crisis, one might expect spreads to co-move even more. However, the fractionexplained by the first factor falls back to the long-run average of 58%. Such a result is not found if thesample is limited to the 26 countries used in Longstaff et al. (2011), who examine no country in distress,apart from Hungary and Venezuela. These results are available upon request.

13The requirement of a balanced panel for the full term structure reduces the sample to 30 countries.


Note that 42 out of 44 countries in the sample rank among the 1,000 most liquid CDS refer-1

ence entities, as reported by the Depository Trust & Clearing Corporation (Augustin, 2014).2

This should somewhat mitigate concerns about liquidity in these contracts.3

The difference in the factor structures implied by the PCAs of CDS spread levels and4

slopes is a fourth stylized fact about the slope of the term structure of sovereign CDS5

spreads. In addition, it has been documented that in the cross-section, the explanatory6

power of country-specific risk is increasing in the duration of term structure inversion; the7

contemporaneous impact of domestic stock market returns on spread changes is greater in8

times when the slope is negative, for larger spread changes, and for changes that attenuate9

the slope; the slope contemporaneously predicts quarterly real GDP growth only when the10

slope is negative.11

3. A Preference-based Model for Credit Default Swaps12

I now turn to rationalize my findings using one of the workhorse equilibrium asset-pricing13

models. The challenge is to link the dynamics in the term structure to the dynamics of both14

global and country-specific risk factors, such that the slope is an informative signal about15

the relative importance of each source of risk. To this end, a reduced-form default process is16

embedded into a consumption-based asset pricing framework with recursive preferences and17

a long-run risk economy. The results rely on three key assumptions: persistent shocks to18

the volatility of aggregate consumption growth (Jurado et al., 2015), a preference for early19

resolution of uncertainty (a standard assumption in the literature), and integrated capital20

markets.21

3.1. Pricing credit default swaps22

The proposed CDS pricing framework is conceptually standard. The difference from

reduced-form models is that default dynamics are impacted by economic fundamentals,

which, together with investor preferences, define the pricing kernel used to discount ex-


pected cash flows. The general equilibrium valuation of CDS spreads builds on Augustin

and Tedongap (2016). Without loss of generality, the trading frequency is monthly. Each

coupon period contains J trading months, thus a K-period swap has a time to maturity of

KJ months.14 The buyer’s leg πpbt is defined as:

πpbt = CDSt (K)

(K∑k=1

Et [Mt,t+kJI (τ > t+ kJ)] + Et

[Mt,τ

(τ − tJ−⌊τ − tJ

⌋)I (τ ≤ t+KJ)

]),

(2)

where CDSt (K) is the constant time t (annualized) premium of a K-period CDS, quoted1

as a percentage of the insured face value, and expected to be paid until the earlier of either2

maturity (month t+KJ) or a credit event occurring at a random month τ . Mt,t+j denotes3

the stochastic discount factor that values in month t any financial payoff to be claimed at4

a future month t + j. Note that b·c rounds a real number to the nearest lower integer, and5

I (·) is an indicator function taking the value 1 if the condition is met, and 0 otherwise. The6

protection leg in equation (2) is the sum of two parts. The first relates to payments made7

by the protection buyer if there is no credit event. The second defines accrual payments for8

default occurring between two payment dates.9

The seller’s leg πpst is defined as the net present value (NPV) of expected losses incurred

by the buyer when there is a credit event. πpst is described by:

πpst = Et [Mt,τ (1−R) I (τ ≤ t+KJ)] , (3)

where R represents the constant post-default recovery rate. A fairly priced CDS at date t is10

thus obtained by equating at inception the NPVs of cash flows for the buyer and the seller,11

which yields the K-period CDS spread12

14For example, an annual (bi-annual, quarterly) payment frequency for a 5-year swap implies that J =12 (6, 3) and K = 5 (10, 20) with 60 months to maturity.


CDSt (K) =

KJ∑j=1

Et [Mt,t+j (1−R) (St+j−1 − St+j)]

K∑k=1

Et [Mt,t+kJSt+kJ ] +KJ∑j=1

(jJ− b j

Jc)Et [Mt,t+j (St+j−1 − St+j)]

, (4)

where the process St ≡ Prob (τ > t | It) denotes the survival probability conditional on the

time-t information set It. Survival probabilities depend on an hazard rate ht:

St = S0

t∏j=1

(1− hj) for t ≥ 1, (5)

which defines the instantaneous probability of default conditional on no earlier default, i.e.,1

ht ≡ Prob (τ = t | τ ≥ t; It). Equation (4) contains two main ingredients: the pricing kernel2

Mt,t+j and the survival probabilities St. These are defined in terms of investor preferences3

and the dynamics of the aggregate economy.4

Counterparty risk is not modeled, as Arora et al. (2012) and Du et al. (2017) show5

that while counterparty risk is statistically priced, its economic significance is negligible.6

The framework also does not account for the introduction of the Big Bang and Small Bang7

protocols in the U.S. and Europe, respectively, as the standardization of coupon payments8

with up-front settlements has little quantitative pricing implications (Collin-Dufresne et al.,9

2012). Finally, accounting for differential liquidity across different contract maturities would10

most likely only affect the convexity of the slope, at the expense of making the model11

substantially more cumbersome.12

3.2. Preferences13

I assume the existence of U.S.-based representative investor selling USD-denominated

insurance contracts. This view is consistent with the strong concentration of CDS trading


in the OTC dealer market for CDS.15 The utility-maximizing marginal investor has Epstein

and Zin (1989)-Weil (1989) recursive preferences. This implies that the logarithm of the

stochastic discount factor can be written as a function of consumption growth ∆ct+1 =

ln (Ct+1/Ct), the natural logarithm of the gross return on a claim to aggregate wealth rc,t+1,

and preferences:

mt,t+1 = θ ln δ − θ

ψ∆ct+1 − (1− θ) rc,t+1, (6)

where θ = 1−γ1− 1

ψ

, with both the coefficient of relative risk aversion γ ≥ 0 and the elasticity1

of intertemporal substitution (EIS) ψ ≥ 0 being non-negative, and where δ defines the time2

preference. I assume that the agent prefers early resolution of uncertainty, i.e., γ > 1ψ

, which3

is necessary to obtain an upward-sloping term structure of CDS spreads.4

3.3. Economy5

As in Bansal and Yaron (2004), and supported by Hansen et al. (2008) and Bansal et al.

(2012), aggregate consumption growth ∆ct+1 embeds a slowly mean-reverting predictable

component xt, which determines the conditional expectation of consumption growth,

∆ct+1 = xt + σtεc,t+1

xt+1 = µx + φx (xt − µx) + νxσtεx,t+1,

(7)

where the short- and long-run consumption shocks εc,t+1 and εx,t+1 are independent and6

identically distributed normal errors with zero mean and unit variance. The parameter φx7

modulates the persistence of expected growth, whose long-run mean is defined by µx, and8

whose sensitivity to long-run shocks is guided by νx. While persistent shocks to expected9

growth help matching the moments of other asset classes (risk-free bonds, equity, etc.), they10

are not necessary for generating any of the implications for the CDS term structure, which11

depends crucially on the persistence of shocks to the volatility of aggregate consumption12

15See Giglio (2017) and Augustin (2014), among others. Sovereign CDS are priced in USD. Thus, resultswould carry through for a foreign investor as long as markets are complete and all shocks are spanned byexchange rates (Borri and Verdelhan, 2016).


growth.1

Consumption growth and its conditional mean inherit the same stochastic volatility pro-

cess σ2t , modeled as an autoregressive gamma process (Gourieroux and Jasiak, 2006; Le et al.,

2010),

σ2t+1 ∼ ARG

(νσ, φσσ

2t , cσ

), (8)

where the parameter φσ modulates the persistence of volatility. The parameters νσ > 0 and

cσ > 0 define the shape and scale of the distribution, and are related to the unconditional

mean µσ and variance ωσ of the volatility process by µσ = (νσcσ) / (1− φσ) and ωσ =

(νσc2σ) / (1− φσ)2. Thus, consumption growth has conditionally time-varying first and second

moments, given by:

Et[σ2t+1

]= φσσ

2t + νσcσ and Vt

[σ2t+1

]= 2cσφσσ

2t + νσc

2σ, (9)

consistent with empirical evidence of conditional volatility in consumption growth (Kandel2

and Stambaugh, 1990; Stock and Watson, 2002), and the co-movement between macroe-3

conomic volatility and asset prices (Bansal et al., 2005; Lettau et al., 2008). With this4

specification, the model remains nested in the class of general affine equilibrium models de-5

scribed by Eraker (2008) and it ensures that consumption volatility is a positive process.6

More importantly, it allows me to easily introduce aggregate macroeconomic uncertainty as7

a proxy for global risk into the underlying default process to generate dynamics in the term8

structure of CDS spreads.9

The primary modeling contribution of this paper is the specification of the dynamics for

sovereign default risk. In Equation (5), I describe how survival probabilities depend on the

hazard rate ht, which is driven by the country-specific default intensity λit+1 through the

following relation:

hit+1 = 1− exp(−λit+1

), (10)


where the superscript i will subsequently be dropped for ease of exposition. To ensure

that the hazard rate is bounded between zero and one, the default process must be positive.

Furthermore, it should inherit both global and country-specific shocks. To attain these goals,

the default process λt+1 is modeled as a bivariate autoregressive gamma process:

λt+1 ∼ ARG(νλ, φλσσ

2t + φλλt, cλ

), (11)

where the parameters φλσ > 0 and 0 < φλ < 1 modulate the sensitivity of the default

process to the global factor and its own past, respectively, while the νλ > 0 and cλ > 0

define the shape and scale parameters of the distribution. Thus, macroeconomic uncertainty

σ2t may feed directly into expectations about future defaults. The default process features

time-varying conditional first and second moments, given by:

Et [λt+1] = φλσσ2t + φλλt + νλcλ and Vt [λt+1] = 2cλ

(φλσσ

2t + φλλt

)+ νλc

2λ, (12)

where time-varying second moments generate time-varying correlations in CDS spreads

across countries. These expressions reflect that the conditional first and second moments are

high when macroeconomic uncertainty σ2t is high and the exposure φλσ is large, or when the

default process is very persistent, that is φλ is close to one.16 It is useful to illustrate the

autoregressive form of the default intensity:

λt+1 = νλcλ + φλσσ2t + φλλt + ηλ,t+1, (14)

which highlights the unpriced country-specific innovations ηλ,t+1 (zero mean shocks). The1

mean-reverting common factor σ2t introduces co-movement into spreads across countries.2

16This is also well illustrated based on the unconditional first and second moments of the default process,defined as:

E [λ] =φλσµσ + νλcλ

1− φλand V [λ] =

2cλ (φλσµσ + φλµλ) + φ2λσωσ + νλc2λ

1− φ2λ. (13)


Each country’s default process is driven by shocks to macroeconomic uncertainty through1

its dependence on σ2t . However, it also inherits idiosyncratic shocks ηλ,t+1, which are uncor-2

related across countries. Sensitivity to global shocks is modulated through φλσ. If φλσ is3

zero, the default process becomes purely idiosyncratic.174

The process driving default risk differs here from the literature in four respects. First,5

the default intensity is specified under the objective probability measure and describes the6

actual default process underlying sovereign default risk. This contrasts with the common7

reduced-form pricing framework of Duffie (1999), in which default intensities are specified8

under the risk-neutral probability measure. Second, the default process describes the risk9

attributed to unpredictable variation in the probabilities of triggering CDS credit events,10

which does not include default or bankruptcy.18 The default process therefore appeals to11

distress risk, which influences the market’s perception of sovereign default risk. This is12

relevant from an investment perspective for marking-to-market portfolios of government debt13

and CDS positions. It does not capture jump-at-default risk, in line with Pan and Singleton14

(2008) and Longstaff et al. (2011). Third, the functional form of the default process, i.e.,15

autoregressive gamma, converges in the limit to a square-root process, which is used to16

study the default risk of Argentina in Zhang (2008) or corporate default risk in Longstaff17

et al. (2005). Berndt et al. (2008) and Longstaff et al. (2011) settle on a lognormal process.18

Fourth, while the previous papers use a one-factor model, which can be sufficient to capture19

the strong commonality in spreads, I specify a two-factor process, which incorporates both20

global and idiosyncratic shocks. Two factors are necessary to capture differences in the shape21

of the slope across countries and over time.22

17Default risk does not feed back into the pricing kernel, nor into the consumption process of the marginalinvestor, consistent with recent multi-country no-arbitrage approaches as in Jotikasthira et al. (2015). Suchalternative specifications would be interesting avenues for future research.

18Standard ISDA documentation for sovereign CDS contracts list four different credit events: obligationacceleration, restructuring, failure to pay, and repudiation/moratorium, but not default, due to the inexis-tence of a formal international bankruptcy court for sovereign issuers (Pan and Singleton, 2008).


3.4. Calibration of preferences and of the endowment economy1

The parameters for preferences and aggregate consumption growth, based on a monthly2

decision interval, are summarized in Table 6. The subjective discount factor δ is set to 0.9987,3

while the EIS ψ and the coefficient of relative risk aversion γ are 1.7 and 10 respectively. In4

line with Bansal et al. (2012), consumption dynamics are calibrated to have an annualized5

growth rate of 1.8% and a volatility of 2.5%. The mean of expected consumption growth µx6

is 0.0015. The process has a persistence φx of 0.975 and a volatility leverage coefficient νx7

equal to 0.034. The level of stochastic volatiliy√µσ is calibrated to 0.00725, with the uncon-8

ditional volatility of volatility√ωσ given by 2.8035e-005. Shocks to consumption volatility9

are persistent, with the value of φσ set at 0.9945. Table 6 shows that the dynamics reproduce10

the moments in the data well, both in-population and out-of-sample. The calibrated values11

are fixed for the subsequent analysis. To support the calibration, it is shown in the Online12

Appendix that the model provides reasonable results for the first and second moments of the13

equity premium, the risk-free rate, the real and nominal term structures of interest rates,14

the variance risk premium, and the wealth-consumption and price-dividend ratios.1915

3.5. Time variation in the term structure of CDS spreads16

I next discuss how the tension between global and country-specific shocks generates time17

variation in the slope of the term structure of CDS spreads in the model. Such dynamics18

arise through the joint evolution of risk premia and expected losses. In normal times, the19

term structure of expected losses is flat or slightly decreasing. Risk aversion introduces20

a risk premium and raises the level of CDS spreads. However, the increase is higher for21

longer maturities, provided the Epstein-Zin agent prefers early resolution of uncertainty.22

Following a series of negative shocks, expectations about future default rates become more23

uncertain and more volatile. As a consequence, expected losses increase dramatically around24

19Processes for dividends and inflation are specified in the Online Appendix to examine price-dividendratios and the nominal term structure of interest rates.


short maturities. Because of mean reversion in prices, the term structure of expected losses1

becomes steeply downward-sloping. Yet, a flat or increasing term structure of risk premia2

is insufficient to offset the strongly inverted shape of expected losses. The net outcome is3

a negative term structure of spreads. Thus, the joint dynamics of global and local shocks4

together with investor preferences are responsible for time variation in the term structure.5

Global shocks are the dominant force underlying spread variation when the slope is positive.6

An inverted term structure nevertheless indicates that domestic shocks are more important.7

These dynamics are in addition modulated by the sensitivity of countries to each risk factor.8

Figure 3 illustrates the mechanism graphically for a simulated sample path of 600 months9

for a hypothetical country.20 In Panel 3.A, I plot the evolution of the 1-year and 10-year10

spreads. While on average the long-maturity spread is higher, it occasionally falls below11

the short spread. Panel 3.B depicts the slope and the volatility of the default process. It12

is straightforward to see that the term structure inverts when uncertainty about default13

rises sharply. In these situations, expected losses rise more quickly than risk premia, as is14

shown for the 5-year spread in Panel 3.C. Finally, Panel 3.D illustrates that risk premia are15

strongly correlated with global macroeconomic uncertainty. Also note that risk premia are16

only weakly correlated with the country-specific default process.17

The comparative statics depicted in Figure 4 provide deeper insights into the mechanics of18

the model. I plot the difference between the model-implied 10-year and 1-year CDS spreads19

for perturbed values of φλσ and φλ, keeping the mean (µλ) and volatility (ωλ) of default risk20

constant at 0.005 and 5e-04, respectively.21 Panel 4.A shows that, for small values of φλσ,21

the slope becomes more negative as the default process becomes more persistent. Panel 4.B,22

in contrast, shows that, for high values of φλσ, raising the persistence has a positive effect on23

the slope. Thus, all else equal, the slope tends to be more negative for low loadings on the24

global factor and a high persistence of past idiosyncratic shocks. Panel 4.C depicts the effect25

20The default parameters for the simulated path are φλσ = 1.84, φλ = 0.9871, νλ = 1.60e-03, andcλ = 1.59e-04.

21Keeping the mean and volatility constant requires an adjustment to νλ > 0 and cλ > 0. The lines onlydepict the values remaining in their domains.


of default volatility on the slope for a constant mean default rate of 0.0039. The outcome is1

reproduced for various combinations of φλσ and φλ. Overall, volatility decreases the slope of2

the term structure.223

One feature of the model is that macroeconomic uncertainty positively contributes to the4

volatility of the default process, which itself impacts the inversion. The global shock thus5

works in two counteracting directions, but the impact on the risk premium channel dominates6

for realistic levels of CDS spreads. Local shocks impact the term structure in the opposite7

direction to the global shock. Depending on the cross-sectional variation in the exposures8

to these two types of shocks, and the intensity of their realizations, one or the other could9

dominate. The Online Appendix contains additional empirical evidence, which suggests10

that both global and local shocks impact the term structure all the time, which generates11

heterogeneity in the cross-section and time series. The observed dynamics are consistent12

with the theoretical properties of the model, which in turn improve the interpretation of the13

evidence.14

3.6. Calibration of the default process15

The default process is calibrated to fit the unconditional moments of the term struc-16

ture for all 44 countries in the sample. The vector of the default parameters is defined by17

Θ = [φλσ, φλ, νλ, cλ]> and note that the CDS spread is a function of expected consump-18

tion growth xt, macroeconomic uncertainty σ2t , and the latent default process λt, that is19

CDS = f (xt, σ2t , λt (Θ)). Like Longstaff et al. (2011), the 5-year CDS spread is assumed to20

be perfectly priced. Assuming that all state variables are at their steady state, and condi-21

tional on a set of starting values for Θ, one can back out λ, which becomes a function of22

the observed mean of the 5-year CDS spread CDS (5) and the steady state values µx and23

µσ, i.e., λ = f(CDS (5) , µx, µσ; Θ

). The implied mean hazard rate λ can be injected back24

22Note that if the slope is very negative, raising volatility increases the slope (it becomes less negative).This reflects an option-type feature in the term structure of CDS spreads. A severely distressed country hasa strongly downward-sloping curve. If the country is close to default, the seller’s position behaves like a deepout-of-the money put. Raising volatility increases the likelihood of a positive payoff and increases the slope.


into the pricing equation (4) to generate the term structure of credit spreads. This two-step1

iterative procedure is repeated until the distance between the implied CDS spreads of dif-2

ferent maturities and the observed sample moments is minimized. The recovery rate is kept3

constant at 25%, consistent with industry practice and the findings by Pan and Singleton4

(2008). Due to the structural break in sovereign spreads in the summer of 2007, with spreads5

even for “safe” countries like Finland jumping from an average 5-year CDS spread of 3 to 326

bps, i.e., an increase of 967%, the calibration is separated for the periods before and after7

July 2007.23 The results for the pre-crisis period are not reported, but are available upon8

request.9

The calibration outcomes for the period after July 2007 are reported in Table 7 (columns10

(2) to (5)). The parameter φλσ modulates the sensitivity of the default process to global11

shocks, while φλ determines the persistence of the process. When the global leverage factor12

φλσ is small and the persistence φλ is large, the process is mainly driven by contemporaneous13

and past country-specific shocks, as illustrated in equation (14). If φλσ is large, global shocks14

dominate the behavior of the default process. In addition, the higher its value, the higher15

is the correlation with the stochastic discount factor. Common dependence on the global16

factor also introduces co-movement of spreads across countries. The results indicate that17

there is a systematic difference in the parameter values of countries that exhibit positive or18

negative slopes, on average. For countries with a positive slope, the leverage coefficient on19

the global factor φλσ is large and above 1, ranging between 3.63 for Finland and 91.16 for20

Venezuela. At the same time, the persistence of the default process φλ tends to be smaller21

and below 1, with a maximum of 0.5343 for France. For countries with a negative slope,22

the global leverage factor is below one, while the persistence is larger, ranging from 0.449023

for Cyprus to 0.9797 for Greece. The shape and scale parameters, νλ and cλ, determine24

the density of the default process. The results suggest that countries that have a negative25

slope, on average, exhibit a lower sensitivity to the common risk factor, as well as a greater26

23As another example, spreads jumped from 10 to 300 bps in the case of Malaysia, an increase of 2,900%.


sensitivity to lagged idiosyncratic shocks.1

3.7. Asset pricing implications2

For each country, a time series of 120,000 months is simulated to examine the asset3

pricing implications of the general equilibrium model. The CDS pricing model is evaluated4

along three dimensions: (i) the ability to match the factor structure in the levels and slopes5

of CDS spreads; (ii) the ability to fit the moments of the level and slope of CDS spreads;6

and (iii) the frequency of term structure inversion.7

To examine the first dimension, I report in Panel D of Table 5 the results from a PCA8

conducted on the simulated panel data. These results are compared to the factor structure9

of the observed data, which are reported in Panels A, B, and C of Table 5. While the first10

principal component provides explanatory power for about 81% of the variation in the level11

of spreads, it provides explanatory power for only 25% in the slope. This closely resembles12

the factor structure observed in the data, although, unconditionally, the variation in the13

level of spreads identified by the first principal component is a bit lower, with a value of14

56%. Overall, this exercise confirms that the model is able to reconcile the high degree of15

commonality in the level of spreads, despite little commonality in the slope.16

Columns (6) to (8) in Table 7 report the population values of the average 5-year spread17

and the average slope (in bps), along with the fraction of simulated observations with an18

inverted term structure of CDS spreads, respectively. Columns (12) to (13) report the small19

sample moments (5th and 95th percentiles) of the 5-year CDS spread and the slope of spreads,20

based on 1,000 simulations of 100 years (1,200 months). Five-year CDS spreads are close to21

the data (column (9)). Other than Greece, the average difference between the simulated and22

observed spread is 15 bps, or 9% of the observed level of spreads. Across countries, these23

differences range from 0 bps to 59 bps, the latter corresponding to 18% of the 5-year CDS24

spread. Only the fit for Greece is less satisfactory, as the simulated spread of 1,644 bps is25

too high, compared to the observed average of 1,214 bps. Importantly, for all 44 countries,26


the sample moment always lies within the 5th and the 95th percentiles of the small sample1

distribution. Thus, the model is able to quantitatively fit the level of the CDS spreads of all2

44 countries in the sample.3

In Table 7, the slope of the term structure tends to be underestimated, with simulated4

averages (column (7)) that are mostly below the observed sample moments reported in col-5

umn (10). For five countries (Lithuania, Venezuela, Cyprus, Greece, and Portugal), the6

average observed slope lies within the 5th and the 95th percentiles of the small sample dis-7

tributions (column (13)), but, in general, the simulated slope of the term structure is too8

flat. The challenge to quantitatively fit the magnitude of the slope of CDS spreads is pri-9

marily attributable to the difficulty in matching short-term spreads, a challenge that is also10

faced by reduced-form credit spread models (Pan and Singleton, 2008). Even though the11

model underestimates the magnitude of the slope, it qualitatively fits the difference between12

10-year and 1-year spreads well, despite the restriction of a unique stochastic discount factor13

imposed for all countries. Reduced-form specifications typically link the risk-adjusted de-14

fault dynamic under the risk-neutral and historical pricing measures through an exogenously15

defined price of risk, whose coefficients are estimated country by country, using both time16

series and term structure data. This is equivalent to assuming a different functional form for17

the stochastic discount factor of each country. Note that the stochastic discount factor is an-18

imated by fundamental macroeconomic shocks and the marginal investor’s attitude towards19

these risks. It provides an economic interpretation of how aggregate shocks feed into the20

term structure of CDS spreads and it enables a study of comparative statics. Although the21

former specification is statistically more flexible, it provides less insight into the economic22

mechanism.23

The third dimension along which I examine the asset pricing implications is with respect24

to the frequency of term structure inversion. The inversion of the term structure of CDS25

spreads is a rare occurrence. Therefore, for some countries in the sample, it could be true26

that we do not have a time series long enough to observe it. On the other hand, for other27


countries, we may have too many observations with an inverted curve with respect to long1

run averages. Given that the simulation for some countries yields, on average, an inverted2

term structure, one may raise the concern that the model-implied inversion is, in fact, not3

a rare event. This is, however, not the case. The results in column (8) show that safe4

countries, like Germany, exhibit term structure inversions for 0.10% of all observations in5

the simulated sample. Two countries, Ireland and Portugal, which have a negative mean6

slope in the sample, exhibit an inversion frequency of the term structure of only 3.34% and7

3.24%, respectively (column (11)). The frequency of inversion for Venezuela, on the other8

hand, is 6.33%, higher than for Ireland and Portugal, despite a mean positive slope. The9

highest inversion frequency after Venezuela is accounted for by Greece, as 35.72% of the10

observations in the simulated data have a negative slope. This inversion frequency in the11

simulated data compares to 46.43% in the observed data. The model-implied outcomes12

align reasonably with the ranking of the frequencies of term structure inversions, although13

the ranking is not absolutely perfect. Overall, there is a greater frequency of inversion for14

countries that have a greater sensitivity of the default intensity to local shocks. The model15

qualitatively captures the dynamics of the slope in the data well.16

Finally, column (14) in Table 7 reports model-implied risk premia as a percentage of the 1-17

year and 10-year level of spreads. The term structure of risk premia is upward-sloping. Their18

magnitude hovers around 3% for short maturities up to approximately 10% for 5-year spreads19

(unreported), and 18% at the 10-year maturity.24 Another pattern is that risk premia are20

proportionally smaller for countries that load weakly on the global factor, even though their21

absolute risk premium may be larger. This is due to two reasons: lower values for φλσ imply22

lower correlations with the stochastic discount factor. In addition, countries with a negative23

slope are marked by higher expected losses, which rise more quickly than risk premia. While24

24Longstaff et al. (2011) report 5-year CDS risk premia of 30%, on average. While they allow for a differentstochastic discount factor for each country, I impose a unique pricing kernel for all countries. Note also thatthe autoregressive gamma specification for consumption volatility implies smaller risk premia compared togaussian dynamics, as the practice of assigning positive outcomes to negative realizations of the varianceincreases the correlation with the pricing kernel.


it may seem counterintuitive that riskier countries command lower risk premia, it is rational1

from the perspective of a global investor, who, given integrated markets, can diversify away2

idiosyncratic country risk. Only aggregate risk is priced. When the dependence on the global3

factor is low, default risk becomes mainly country-specific. At those times, speculators who4

bet on default are only compensated for expected losses.5

3.8. Fundamental versus uncertainty shocks6

Many countries experienced term structure inversions during the global financial crisis.7

This raises the question whether a global fundamental shock could also lead to an inversion8

of the term structure, challenging the unique association of term structure inversions with9

local fundamental shocks. I therefore explore the distinct impact of global fundamental and10

uncertainty shocks on the term structure of sovereign CDS spreads. Details of this analysis11

are reported in the Online Appendix.12

The data suggest that term structure inversions and reversals occur almost always in13

isolated fashion, staggered across countries and over time. Such patterns are difficult to14

reconcile with the interpretation that common fundamental shocks are responsible for an15

inversion of the term structure, as such shocks would necessarily lead to contemporaneous16

inversions and reversals all the time.17

As a formal test, I examine the cross-sectional relation between the slope and both global18

fundamental and uncertainty shocks using Fama-MacBeth regressions. Global fundamental19

risk is proxied by U.S. consumption growth and global uncertainty risk by the Baker et al.20

(2016) U.S. economic policy uncertainty index. In robustness tests, filtered U.S. expected21

growth and consumption growth volatility serve as additional proxies for global fundamental22

and uncertainty shocks. Unconditional risk loadings (cash flow and uncertainty betas) from23

first-stage regressions of changes in 5-year CDS spreads on fundamental (uncertainty) shocks24

are negative (positive). Coefficients from the projection of the slope on fundamental cash-flow25

betas (uncertainty betas) are negative (positive). Thus, a more negative (positive) exposure26


to fundamental shocks (uncertainty shocks) is associated with a steeper slope. This suggests1

that negative fundamental and positive uncertainty shocks have a similar positive impact on2

the term structure. These results hold both at the country level and for 10 portfolios sorted3

monthly on the 5-year CDS spread.4

Economic uncertainty is the only source of global risk affecting default in the baseline

model. I therefore examine an extension that incorporates common fundamental shocks into

the default process. Specifically, the economy in equation (7) is augmented with large drops

in consumption growth (disasters) as proxy for global fundamental shocks:

∆ct+1 = xt + σtεc,t+1 − zt+1, (15)

where the jumps zt+1 are drawn from an independent Poisson-Gamma mixture distribution5

and arrive with time-varying probability πt+1.25 Thus, disasters (or disaster probabilities)6

are allowed to impact each country’s default process, possibly with heterogeneity in the7

sensitivities to common disaster shocks. Asset pricing implications from the augmented8

model suggest that disasters or their probabilities have an even stronger positive impact on9

the term structure than uncertainty shocks.2610

In sum, the additional analysis supports the interpretation that term structure inver-11

sions are more likely driven by country-specific shocks, rather than by common fundamental12

shocks. A negative shock to a (mean-reverting) country-specific source of risk will only im-13

pact default probabilities, which increase more for short-dated tenors and less for long-dated14

tenors, as conditions are expected to normalize over time. This leads to an inversion of15

the term structure of CDS spreads. A large drop in consumption growth, in contrast, will16

also command a risk premium, which is increasing more for longer maturities, because of17

25Specifically, the jump arrival rate jt+1 follows a Poisson distribution with disaster intensity πt+1, jt+1 ∼P(πt+1), and zt+1|jt+1 ∼ Gamma(jt+1, α). The disaster probability follows autoregressive gamma dynamics,similar to those of consumption growth volatility: πt+1 = νπcπ + φππt + ηπ,t+1.

26An alternative source of fundamental shocks could be short-run or long-run consumption shocks. Suchan extension of the model does not allow for term structure inversions either, unless I allow for negative CDSspread levels, a violation of no-arbitrage conditions.


preference for early resolution of uncertainty. Global fundamental shocks have thus opposite1

effects on the term structure, similar to uncertainty shocks. The risk premium effect domi-2

nates as the increase in the term structure of risk premia outweighs the decrease in the term3

structure of default probabilities, leading to a steepening of the slope.4

4. Model Validation5

The results of the CDS pricing model suggest two testable predictions for a validation of6

the model. First, risk premia represent a lower fraction of spreads when the slope is negative.7

Second, excess returns are greater when U.S. economic uncertainty is high. The validity of8

these predictions is tested in the following subsections.9

4.1. Risk premia and the slope10

The first asset pricing implication of the model is that, while the relative risk premia11

(rel.RPt), as a fraction of spreads, should be lower, the absolute risk premia (RPt) should12

be higher when the slope is negative. To test this prediction, I estimate the country-specific13

measures of credit risk premia as a linear combination of forward CDS spreads following14

Friewald et al. (2014), who rely on the intuition of Cochrane and Piazzesi (2005) that forward15

spreads contain information about future excess returns.2716

Panel A in Figure 5 depicts the relation between the slope of the term structure of CDS17

27The computation of relative and absolute risk premia involves several steps. First, for a given predictionhorizon τ and a T -year CDS contract STt+τ , I compute forward CDS spreads F τ×Tt , which at time t containinformation about expected future T -year CDS spreads starting at time t+τ . Second, for each CDS contractmaturity Tk ∈ T = {1, 3, 5, 7}, I compute CDS excess changes, defined as RXTk

t+τ = STkt+τ −Fτ×Tkt , and CDS

excess returns, i.e., rel.RXTkt+τ = logSTkt+τ − logF

τ×Tkt . Third, for each country, I construct the cross-maturity

CDS excess change, RXt+τ = 14

∑Tk∈T

RXTkt+τ , and excess return rel.RXt+τ = 1

4

∑Tk∈T

rel.RXTkt+τ . Fourth, I

regress the average excess return and excess change, respectively, on a constant and the term structure of CDSspreads, defined by the current one-year CDS spread and forward CDS spreads of contracts starting in one,three, five, and seven years, and effective for one year. Define the vector Ft =

(1, S1

t , F1×1t , F 3×1

t , F 5×1t , F 7×1

t

)and the corresponding regression coefficients γ = (γ0, γ1, γ2, γ3, γ4, γ5). The estimated absolute and relativerisk premia are then obtained using the relation RPt = −(γRX)>Ft and rel.RPt = −(γrel.RX)>Ft. I maprelative risk premia from percent into a ratio using the transformation erel.RPt , such that I can interpretrelative risk premia as the ratio of CDS spreads under the risk-neutral Q measure and the physical P measure.Results are robust when we use a simpler calculation of excess returns from holding long over short CDS.


spreads and relative CDS risk premia in the upper panel; Panel B depicts the absolute1

level of the risk premia. A regression line separately fitted to the right side of the figure2

(corresponding to data points when the slope is positive), and to the left side of the figure3

(corresponding to data points when the slope is negative), highlights a significant drop in4

relative risk premia when the slope becomes inverted. Panel B shows, however, that the level5

of risk premia is increasing in the inversion of the term structure, despite a lower relative risk6

premium. This confirms the model’s implications that expected losses (risk premia) represent7

a greater (lower) fraction of the level of spreads when the slope of the term structure of CDS8

spreads is negative.9

4.2. Excess returns and economic uncertainty10

The CDS pricing model uses U.S. economic uncertainty as a global risk factor. Moreover,11

the findings in column (14) in Table 7 suggest an upward-sloping term structure of risk12

premia. The second testable prediction is, thus, that excess returns should be greater when13

U.S. economic uncertainty is high. To test this conjecture, it is preferable to use a longer14

time series of excess returns, computed using bond prices from an unbalanced panel of 2515

countries starting in December 1985. Specifically, one-year holding period excess returns are16

projected on the Baker et al. (2016) U.S. economic policy uncertainty index, which serves as17

a proxy for U.S. economic uncertainty.18

I collect data on the monthly Citigroup world government bond total return indices in19

USD (former Salomon Smith Barney Indices) from Datastream for five different maturity20

brackets (1-3, 3-5, 5-7, 7-10, 10+ years), and compute yearly holding period returns in excess21

of the return on the JP Morgan one-month total return cash index. For each country c, the22

annual return on an n-period bond in excess of the risk-free yield is defined as rxnc,t+12 =23

pn−1c,t+12 − pnc,t − y1

t , where p denotes the log bond price and y denotes the log yield defined24

as ync,t = −pnc,t/n. Then, for each country and maturity bracket, the regression rxnc,t+12 =25

ac + bcEPUt + εnc,t+12 is evaluated, where rxnc,t+12 denotes the annual excess return for an26


n-period bond of country c and EPUt is the economic policy uncertainty index.1

The results in Table 8, by and large, confirm that (i) excess returns are greater in mag-2

nitude for larger contract maturities, and (ii) that excess returns are positively predicted by3

the economic policy uncertainty index. For almost all countries, the average excess return is4

greater for the maturity bucket that contains longer-term bonds. For a few select countries,5

the returns decrease for very long-term bonds (above ten years), which is primarily related to6

significant illiquidity in the long-term maturity brackets (Chaieb et al., 2014). The average7

annual excess bond return across countries ranges from 2.94% for bonds of one to three years,8

to 4.47% for bonds with maturities above ten years. The average coefficient is approximately9

0.06 to 0.07 in panel regressions, and ranges from 0.01 to 0.19 in country regressions. It is10

almost always positive and significant for more than half of all coefficients. Only Poland and11

Singapore load negatively on economic uncertainty, but the coefficients are not statistically12

significant. In addition, the explanatory power is meaningful, on average around 6% to 7%13

percent, ranging up to 28% for New Zealand. In the Online Appendix, it is shown that14

results are robust across a large range of different measures of economic uncertainty taken15

from Gilchrist and Zakrajsek (2012), Bekaert et al. (2013), Jurado et al. (2015), Baker et al.16

(2016). While the results are also robust against measures of financial uncertainty, such as17

the S&P500 option-implied volatility index VIX and the 1-year swaption-implied volatility18

for 10-year USD interest rate swaps, they tend to be weaker. Overall, these results also19

provide validation of the model, and support for the informativeness of the slope about the20

relative importance of global and local risk.21

5. Conclusion22

A country’s term structure of CDS spreads conveys useful information to market partici-23

pants with which to pinpoint the importance of global and domestic risk. Global shocks are24

the primary source of a country’s CDS spread variation when its term structure is upward-25

sloping. In contrast, a country’s spreads are primarily influenced by domestic shocks when26


its term structure is downward-sloping. Thus, both global and country-specific risk factors1

impact the dynamics of sovereign credit risk. As the slope of the CDS term structure is2

available at high frequencies, it improves the identification of the importance of local and3

global risk across countries in real time.4

The findings in this paper document several new stylized facts about the slope of the5

term structure of CDS spreads, based on a panel of 44 countries from January 2001 to6

February 2012. Country-specific risk factors explain cross-sectionally a greater fraction of7

the variation in spreads for countries that have had inverted slopes. More importantly, there8

exists a monotonic relation between the duration of term structure inversion and how much9

CDS spread variation is due to domestic risk factors. In addition, the contemporaneous10

impact of domestic stock market returns on spread changes is greater for larger spread11

changes, stronger for shocks that flatten the slope, and fifteen times greater when the slope12

is negative. Finally, the slope is shown to be contemporaneously predictive of quarterly real13

GDP growth, but only when the slope is negative. Consistent with the findings that the slope14

contains information about the cross-sectional differences in the importance of domestic risk15

over time, the dynamics of the slope are found to exhibit a weak factor structure, in contrast16

to the strong commonality documented for the dynamics of the level of spreads.17

I develop a recursive preference-based model with long-run risk for CDS spreads, where18

the underlying default process depends both on aggregate macroeconomic uncertainty and19

domestic risk. The joint dynamics of global uncertainty and country-specific shocks, com-20

bined with investor preferences, economically explain time variation in the slope of the term21

structure. Two empirical tests support the model’s implications. While absolute risk premia22

are greater when the term structure is inverted, they represent a lower fraction of the level23

of CDS spreads compared to when the slope is positive. In addition, excess bond returns24

are positively predicted by U.S. economic uncertainty. Overall, my analysis reconciles differ-25

ences in conclusions in the literature favoring either local or global risk as an unconditionally26

dominant source of sovereign credit risk.27


A Acknowledgements1

I am grateful for constructive comments and suggestions from the editor Urban Jermann,2

an anonymous referee, Adrian Alter, David Backus, Laurent Barras, Nicola Borri, Nina3

Boyarchenko, Ines Chaieb, Mike Chernov, Magnus Dahlquist, Itamar Drechsler, Wenxin4

Du, Mathieu Fournier, Nils Friewald, Jean Helwege, Alexander Herbertsson, Jens Hilscher,5

Alexandre Jeanneret, Bige Kahraman, Leonid Kogan, Rajnish Mehra, Sergei Sarkissian,6

Olivier Scaillet, Paolo Sodini, Valeri Sokolovski, Marti G. Subrahmanyam, Saskia ter Ellen,7

Romeo Tedongap, Stijn van Nieuwerburgh, Michael Weber, Fan Yu, Stanley Zin, Irina Zvi-8

adadze; from seminar participants at the University of Melbourne, the University of Sydney,9

the University of New South Wales, the University of Geneva, McGill (Economics), HEC10

Liege, the Amsterdam Business School, HEC Paris, the University of Hong Kong, the Univer-11

sity of Toronto, the Federal Reserve Board of Governors, the University of Virginia McIntire12

School of Commerce, McGill (Finance), Bocconi University, the European Central Bank, the13

Bank of France, Nova Lisbon, Warwick Business School, LUISS Guido Carli, the Stockholm14

School of Economics, the Luxembourg School of Finance; from participants at the 2015 Fixed15

Income Conference, the 2014 NFA, the IFSID 3rd Conference on Derivatives, the 2014 IFM216

Mathematical Finance Days, the 2013 WFA, the 2013 FMA Europe, the Marie Curie ITN17

Conference on Financial Risk Management & Risk Reporting. Feng Jiao provided excellent18

research assistance. I acknowledge outstanding hospitality offered by the Swedish House of19

Finance, and financial support from the Jan Wallander and Tom Hedelius Foundation, the20

Nasdaq-OMX Nordic Foundation, the Bank Research Institute in Stockholm, the Institute of21

Financial Mathematics of Montreal, the Fonds de Recherche du Quebec - Societe et Culture22

grant 2016-NP-191430, the Canada Social Sciences and Humanities Research Council grant23

435-2016-1504.24


B Supplementary Material1

Supplementary material can be found in the Online Appendix at http://dx.doi.org/10.1016/j.jmoneco.2

xxxx.xx.xxx.3

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Figure 1: The Slope of the CDS Term Structure and Local Ratios

The local ratio (LR) denotes the ratio of the adjusted R2 from the restricted regression of changes in 5-year

CDS spreads on local variables only to that from the unrestricted regression on local and global variables.

In the figure, I plot the LRs for the countries that have had inverted term structures against the number

of months for which the term structure was inverted. For illustration purposes, Venezuela is excluded from

the graphs. It has a LR of 0.05 and its term structure was inverted for 26 months. Figure 1.A (Figure 1.B)

excludes (includes) the countries that did not have an inverted slope.

(Figure 1.A)

Korea

Slovakia

Bulgaria

Brazil

Portugal

Hungary

Philippines

Ireland

Italy

Spain

Romania

Greece

Uruguay

Cyprus

Russia

Croatia

Czech Rep.

Lithuania

Turkey

.2.4

.6.8

11.

2E

xpla

ined

by

Loca

l Ris

k (L

R)

0 5 10 15 20 25# Months of Inverted Slope

linear fit 95% CIR2 = 32% t-stat = 3.11

Local Risk and Negative Slope

(Figure 1.B)

Sweden

France

PeruThailandBelgiumColombia

Morocco

Panama

Austria

Lebanon

Poland

Germany

China

JapanFinlandSlovenia

Malaysia

Qatar

Denmark

Chile

Israel

Korea

SlovakiaBulgaria

Brazil

Portugal

Hungary

Philippines

Ireland

Italy

Spain

Romania

Greece

UruguayCyprus

Russia

Croatia

Czech Rep.

Lithuania

Turkey

Sth. Africa

0.3

.6.9

1.2

Exp

lain

ed b

y Lo

cal R

isk

(LR

)

0 5 10 15 20 25# Months of Inverted Slope

linear fit 95% CIR2 = 45% t-stat = 5.76

Local Risk and Negative Slope


Figure 2: Real GDP Growth and the Term Structure of CDS Spreads

In Figure 2.A, I plot the average real quarter-on-quarter GDP growth (left axis, dashed line) and the

proportion of observations with negative real seasonally adjusted quarter-on-quarter GDP growth (right

axis, solid line) as a function of the average slope of the CDS term structure, in sliding windows of 100

growth-slope observations. The observations are ranked according to their slope in ascending order. For

instance, the left-most point reflects the average real GDP growth (or the proportion of countries with

negative growth) against the average CDS slope among the 100 observations with the lowest (most negative)

slope. The next point reflects the averages for observations 2 to 101, and so forth. The right-most points

will be computed based on fewer than 100 observations. In Figure 2.B, I restrict the average slope to be

more than -250 bps. In Figures 2.C and 2.D, I plot the fraction of observations with a negative slope and

the average slope as a function of the average 5-year CDS spread level in sliding windows of 100 level-slope

observations, where the observations are ranked according to their 5-year CDS spread in ascending order.

(Figure 2.A)

0.2

.4.6

.8F

ract

ion

of o

bser

vatio

ns w

ith n

egat

ive

grow

th

-20

24

6A

vera

ge r

eal G

DP

gro

wth

(%

), q

oq

-1000 -500 0 500Mean 10y-1y CDS (Slope), in bps

Real GDP growth (%) Negative Growth (Fraction)

(Figure 2.B)

0.2

.4.6

.8F

ract

ion

of o

bser

vatio

ns w

ith n

egat

ive

grow

th

-20

24

6A

vera

ge r

eal G

DP

gro

wth

(%

), q

oq

-200 0 200 400 600Mean 10y-1y CDS (Slope), in bps

Real GDP growth (%) Negative Growth (Fraction)

(Figure 2.C)

0.2

.4.6

.8#

Neg

ativ

e S

lope

- F

ract

ion

(%)

0 500 1000 1500 2000Mean 5-year CDS (conditional on CDS<2,000 bps)

(Figure 2.D)

-600

-400

-200

020

0M

ean

Slo

pe (

CD

S10

y-C

DS

1y)

0 500 1000 1500 2000Mean 5-year CDS (conditional on CDS<2,000 bps)


Figure 3: Time Variation in the Term Structure

In this figure, I plot model-implied metrics for a simulated sample path of 600 months. The default pa-

rameters used for the simulation are the calibrated values for Uruguay, that is φλσ = 1.84, φλ = 0.9871,

νλ = 1.60e-03 and cλ = 1.59e-04. In Panel 3.A, I plot the evolution of the 1-year (dash-dotted line) and

10-year (solid line) CDS spreads in bps. Panel 3.B illustrates the slope of the CDS curve in bps (solid line,

left scale) versus the conditional volatility of the default process (dash-dotted line, right scale). Panel 3.C

shows the simulated time series for the risk premium (solid line, right axis) and expected loss (dash-dotted

line, left axis) in bps. In Panel 3.D, I plot the evolution of aggregate macroeconomic uncertainty (solid

line, left axis), annualized and in %, against the risk premium in bps (dash-dotted line, right axis), and the

default process λt (solid line with dotted markers, right axis). The default process is multiplied by 1,000 for

better visualization.

(Figure 3.A)

0 100 200 300 400 500 6000

500

1000

1500

2000

2500

CDS Spread (bps)

Time Series - Hypothetical Sample Path

1-year and 10-year CDS Spread

CDS1y

CDS10y

(Figure 3.B)

0 100 200 300 400 500 600-600

-400

-200

0

200

400

600Slope 10y-1y CDS Spread (bps)


Slope 10y-1y

0 100 200 300 400 500 600

0

1

2

3

4

5

6

7

8

x 10-6

Dynamics of the Slope

Conditional Volatility of default risk

Default Risk Volatility

(Figure 3.C)

0 100 200 300 400 500 6000

200

400

600

800

1000

1200

1400

1600

1800

5-year Expected Loss (bps)


Expected Loss 5y

0 100 200 300 400 500 600

10

15

20

25

30

35

Expected Loss and Risk Premium

5-year Risk Premium (bps)

Risk Premium 5y

(Figure 3.D)

0 100 200 300 400 500 6000.6

0.8

1

1.2

1.4


Global Volatility, Risk Premia and Default Risk

Glo

bal V

ola

tility

(%

)

0 100 200 300 400 500 6000

10

20

30

40

Ris

k P

rem

ium

(b

ps)

an

d D

efa

ult

Ris

k (

x 1

000)Consumption Volatility

Default Risk

Risk Premium 5y


Figure 4: Comparative Statics of the CDS Term Structure

Panels 4.A and 4.B illustrate the sensitivity of the slope of the CDS term structure (in bps) when φλ and φλσ

are perturbed, keeping the mean µλ and volatility of default ωλ constant at 0.005 and 5e-04, respectively. In

Panel 4.A, I perturb φλ for different values of φλσ equal to 1 (dotted red line), 2.6 (solid line), 42 (dash-dotted

line), and 66 (dashed line). In Panel 4.B, I perturb φλσ for different values of φλ equal to 0.1 (dotted line),

0.25 (dash-dotted line), 0.5 (dashed line), and 0.75 (solid line). Keeping the mean and volatility constant

requires an adjustment to νλ > 0 and cλ > 0. The lines are plotted for values remaining in their respective

domains. Panel 4.C illustrates a similar analysis for the slope of the CDS term structure by perturbing the

volatility of the default process ωλ and keeping the mean default rate µλ constant at 0.0039. The outcome

is reproduced for different combinations of φλ and φλσ, that is 0.90 and 7.5 (dotted line), 0.50 and 37.5

(dashed-dotted line line), 0.20 and 60 (dashed line), 0.01 and 74.25 (solid line).

(Figure 4.A)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-30

-20

-10

0

10

20

30

40

50

60

CD

S10y

-CD

S1y

(bps

)

= 0.005,

= 5e-4

= 1

= 2.6

= 42

= 66

(Figure 4.B)

10 20 30 40 50 60 70 800

10

20

30

40

50

60

CD

S10y

-CD

S1y

(bps

)

= 0.005,

= 5e-4

= 0.1

= 0.25

= 0.5

= 0.75

(Figure 4.C)

0.001 0.01 0.02 0.03 0.04 0.05

-30

-20

-10

0

10

20

30

40

50

CD

S10y

-CD

S1y

(bps

)

= 0.0039

= 7.5, = 0.90

= 37.5, = 0.5

= 60, = 0.20

= 74.25, = 0.01


Figure 5: Relation between Risk Premia and the Term Structure

In Panels 5.A and 5.B, I plot the relation between the slope of the term structure of CDS spreads (CDS10y-

CDS1y) and either the relative CDS risk premia (Panel 5.A) or the absolute level of risk premia (Panel

5.B). The computation of relative and absolute risk premia follows Friewald et al. (2014). First, for a

prediction horizon τ and a T -year CDS contract STt+τ , I compute forward CDS spreads F τ×Tt , which at

time t contain information about expected future T -year CDS spreads starting at time t + τ . Second, for

each maturity Tk ∈ T = {1, 3, 5, 7}, I compute CDS excess changes RXTkt+τ = STkt+τ − F τ×Tkt , and CDS

excess returns rel.RXTkt+τ = logSTkt+τ − logF

τ×Tkt . Third, for each country, I construct the cross-maturity

CDS excess change RXt+τ = 14

∑Tk∈T

RXTkt+τ , and excess return rel.RXt+τ = 1

4

∑Tk∈T

rel.RXTkt+τ . Fourth, I

regress the average excess return and excess change on a constant and the term structure of CDS spreads,

defined by the current one-year CDS spread and forward CDS spreads of contracts starting in one, three,

five, and seven years, and effective for one year. Define the vector Ft =(1, S1

t , F1×1t , F 3×1

t , F 5×1t , F 7×1

t

)and

the corresponding regression coefficients γ = (γ0, γ1, γ2, γ3, γ4, γ5). The estimated absolute and relative risk

premia are obtained using RPt = −(γRX)>Ft and rel.RPt = −(γrel.RX)>Ft. I map relative risk premia

from percentage into a ratio using the transformation erel.RPt , such that I can interpret relative risk premia

as the ratio of CDS spreads under the risk-neutral Q and the physical P measures.

(Figure 5.A)

.99

.995

11.

005

1.01

CD

S R

elat

ive

Ris

k P

rem

ia (

~C

DS

(Q)/

CD

S(P

))

-1000 -500 0 500 1000Slope CDS10y-CDS1y (bps)

(Figure 5.B)

-100

0-5

000

500

Leve

l CD

S R

isk

Pre

mia

-500 0 500Slope CDS10y-CDS1y (bps)


Table 1: Summary Statistics of Sovereign CDS Spreads

This table presents summary statistics for sovereign CDS spreads. In columns (1) to (3), I report the namesof the 44 countries in the sample, the first monthly observation in the panel, and the number of observations,respectively. All series end in February 2012. In columns (4) to (6), I report the sample average (in bps)CDS spread levels, for swap maturities of 1, 5, and 10 years. The average slope of the CDS term structure,measured as the difference between 10- and 1-year CDS spreads, is documented in column (7). I report thenumber and frequency of months during which the term structure was inverted in columns (8) and (9).

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Country Information Spread Levels Slope < 0 Slope

Country Start Obs 1y 5y 10y 10y-1y N Freq

Austria 2001-10 125 22 37 41 19 0 0.00Belgium 2001-2 133 29 44 47 19 0 0.00Brazil 2001-1 134 318 498 530 212 7 0.05Bulgaria 2001-4 131 113 203 233 120 5 0.04Chile 2002-2 121 34 80 101 67 0 0.00China 2001-1 134 29 58 75 46 0 0.00Colombia 2001-4 131 140 329 374 234 0 0.00Croatia 2001-2 133 107 161 183 76 4 0.03Cyprus 2002-7 116 129 133 133 3 10 0.09Czech Rep. 2001-4 131 30 49 58 28 2 0.02Denmark 2003-1 110 14 26 30 16 0 0.00Egypt 2002-4 119 150 251 290 140 0 0.00Finland 2002-9 114 9 17 21 12 0 0.00France 2002-8 115 17 33 38 20 0 0.00Germany 2002-10 113 9 21 26 17 0 0.00Greece 2001-1 134 814 515 433 -382 26 0.19Hungary 2001-2 133 99 136 147 48 5 0.04Ireland 2003-1 110 162 155 139 -23 22 0.20Israel 2001-11 124 47 95 115 68 0 0.00Italy 2001-1 134 51 69 74 23 4 0.03Japan 2001-2 133 12 32 45 33 0 0.00Korea 2001-3 132 58 89 106 48 1 0.01Lebanon 2003-3 108 300 413 460 159 0 0.00Lithuania 2002-9 114 125 150 157 32 15 0.13Malaysia 2001-4 131 43 85 108 66 0 0.00Mexico 2001-1 134 66 152 187 122 0 0.00Morocco 2001-4 131 101 201 242 141 0 0.00Panama 2002-7 116 77 212 256 179 0 0.00Peru 2002-2 121 94 260 306 212 0 0.00Philipp. 2001-3 132 138 307 369 231 4 0.03Poland 2001-1 134 44 78 92 48 0 0.00Portugal 2002-2 121 170 155 139 -31 22 0.18Qatar 2001-9 126 44 79 102 58 0 0.00Romania 2002-7 116 139 218 239 100 6 0.05Russia 2001-10 125 137 226 261 124 7 0.06Slovakia 2001-11 124 37 63 74 37 1 0.01Slovenia 2002-2 121 36 55 62 27 0 0.00Sth. Afr. 2001-3 132 70 141 173 103 0 0.00Spain 2001-7 128 55 72 73 18 4 0.03Sweden 2001-5 130 11 20 23 13 0 0.00Thailand 2001-5 130 47 92 115 68 0 0.00Turkey 2001-1 134 251 397 440 188 8 0.06Uruguay 2002-4 119 790 731 712 -78 19 0.16Venezuela 2001-2 133 695 868 865 170 26 0.20


Table 2: Local Ratios

The local ratio (LR) denotes the ratio of the adjusted R2 from the restricted regression of changes in 5-yearCDS spreads on local factors to that from the unrestricted regression on local and global factors. Countriesare grouped into two categories. G1 contains all countries that never had an inverted slope. G2 containsall countries with at least one month of inverted slope. The restricted sample excludes outliers Egypt andMexico in G1 and Venezuela in G2. Inferences are obtained by block-bootstrapping 10,000 times a samplesize of 36 months for each country. A one-sided t-test on the equality of means, assuming paired data,against the alternative that G1 has a smaller mean, is rejected at the 1% significance level. The Wilcoxonmatched-pairs signed-rank test rejects the null hypothesis that both distributions are the same, while theone-sided sign test rejects equality of medians against the alternative that the median of G1 is lower.

Full Sample (44 countries) Restricted Sample (41 countries)Mean LR (%) Median LR (%) Mean LR (%) Median LR (%)

Group 1: Slope was never inverted 40 38 36 36Group 2: Slope was inverted 61 63 64 64

t-test p < 0.01 p < 0.01Sign test p < 0.01 p < 0.01Wilcoxon signed-rank test p < 0.01 p < 0.01


Table 3: Dynamics of Sovereign Credit Risk - Panel and Quantile Regressions

Panel A reports the coefficients of interest (for brevity) from equation (1), augmented with interaction termsbetween the risk factors and an indicator variable equal to one, if the term structure is negative, and zerootherwise. Column (1) reports the results of a restricted specification that uses the 5 reported variables.Column (2) includes all controls. The specifications in columns (3) to (6) contain country fixed effects, and Isuccessively introduce clustering by country, by month, and by time and month. In column (7), I use Driscoll-Kraay standard errors with country fixed effects, accounting for cross-sectional and time series correlationof three lags. The specification in column (8) includes the full set of interaction terms. Columns (1) and (2)in Panel B report results from sample splits for a specification similar to that of column (3) in Panel A. Thesample is split for CDS spread changes that steepen the slope (column (1): ∆CDS · I(∆Slope > 0)) andthat flatten the slope (column (2): ∆CDS · I(∆Slope < 0)). Column (3) in Panel B includes the full sampleand an interaction term that is equal to one if the slope flattens, and zero otherwise. Panel C reports thecoefficients for the local stock market return and its interaction with the indicator variable from quantileregressions with a specification similar to that of column (3) in Panel A. *, ** and ***, denote significanceat the 1%, 5%, and 10% levels.

Panel A: 5-year CDS Spread Changes

Variables (1) (2) (3) (4) (5) (6) (7) (8)

LocalRet -0.01*** -0.01*** -0.01*** -0.01*** -0.01*** -0.01*** -0.01*** -0.01***LocalRet× I(Slope < 0) -0.15** -0.15** -0.15** -0.15** -0.15** -0.15** -0.15** -0.16**I(Slope < 0) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01USret -0.03*** -0.03*** -0.03*** -0.03*** -0.03*** -0.03*** -0.03*** -0.03***USret× I(Slope < 0) -0.11 -0.10 -0.11* -0.11* -0.11 -0.10* -0.11 -0.10

Country FE No No Yes Yes Yes Yes Yes YesFcluster No No No Yes No Yes 3lags 3lagsTcluster No No No No Yes Yes Yes YesControls No Yes Yes Yes Yes Yes Yes YesControls×I(Slope < 0) No No No No No No No YesAdj.R2 0.17 0.19 0.19 0.19 0.18 0.19 0.19 0.24N 5476 5456 5456 5456 5456 5456 5456 5456

Panel B: Conditional 5-year CDS Spread Changes

Variables (1) (2) Variables (3)

LocalRet -0.0057*** -0.0125*** LocalRet -0.0060**LocalRet× I(Slope < 0) -0.0701 -0.1785** LocalRet× I(∆Slope < 0) -0.0151**I(Slope < 0) -0.0085* 0.0078*** I(∆Slope < 0) -0.7084***USret -0.0277*** -0.0270*** Usret -0.0391***USret× I(Slope < 0) -0.0282 -0.1117* USret× I(∆Slope < 0) -0.0005

Adj.R2 0.18 0.24 Adj.R2 0.39N 2805 2651 N 5456

Panel C: Quantiles of 5-year CDS Spread Changes

Quantile 0.5 0.75 0.9 0.95

LocalRet -0.0030*** -0.0045*** -0.0064 -0.0087LocalRet× I(Slope < 0) -0.0441*** -0.0811*** -0.1536*** -0.2700***


Table 4: Growth Regressions

This table presents the results from regressions of seasonally adjusted quarter-on-quarter real GDP growth

on the level (CDS5y) and the slope (CDS10y-CDS1y) of CDS spreads, as well as their interactions. The level

is defined as the quarterly 5y CDS spread, where the quarterly spread is defined as the average spread over

all monthly observations. The slope is defined as the difference between the 10y and the 1y CDS spreads.

I(Slope< 0) is equal to one if the slope is negative in a quarter, and zero otherwise. The frequency of the

regressions is quarterly. All regressions are clustered at the country level, and the regressions for the results

in columns (4) to (6) contain country fixed effects. In the regression for the results in column (5), I use

Driscoll-Kraay robust standard errors that account for arbitrary spatial dependence and serial correlation

up to four quarters. The results in column (6) exclude Greece. *, ** and ***, denote significance at the 1%,

5%, and 10% levels. Source: Markit, OECD, Thomson Reuters Datatsream, IHS Global Insight, Oxford

Economics.

Variables (1) (2) (3) (4) (5) (6)

Level(CDS5y) -27.46*** -31.20*** -38.83** -53.40*** -53.40*** -54.89***(7.76) (9.25) (15.06) (15.74) (16.21) (15.99)

Slope(CDS10y − CDS1y) 45.01* 61.51* 10.23 10.23 15.08(24.55) (34.02) (23.12) (19.62) (22.89)

I(Slope < 0) -2.41* -2.07* -2.07** -1.81(1.30) (1.21) (0.96) (1.17)

I(Slope < 0)× Slope -142.79** -135.51* -135.51* -155.92**(69.41) (67.24) (74.84) (71.89)

Constant 2.86*** 2.58*** 2.58*** 3.21*** 3.21*** 3.20***(0.40) (0.40) (0.41) (0.20) (0.43) (0.20)

Observations 1,672 1,672 1,672 1,672 1,672 1,632Country FE No No No Yes Yes YesCluster Country Yes Yes Yes Yes No YesDK No No No No Yes NoLags – – – – 4 –Greece Yes Yes Yes Yes Yes NoAdj.R2(%) 1.69 2.49 3.01 3.59 3.82 3.27


Table 5: Principal Component Analysis

This table reports the variation in CDS spread changes explained by the first three principal components.Panel A presents results from a principal component analysis (PCA) conducted on 5-year CDS spreads. PanelB presents results from a PCA conducted on the level of spreads, using the maturities of 1, 2, 3, 5, 7, and 10years. Panel C presents results from a PCA conducted on the slope of the term structure of CDS spreads.The slope is defined as the difference between the 10-year and 1-year spreads. The column Full Samplerefers to the results from the entire sample period from January 2003 to February 2012. The subperiodsrefer to the time before the financial crisis (Jan2003-Dec2006), the financial crisis (Jan2007-Dec2010) andthe sovereign debt crisis (Jan2011-Feb2012). Panel D reports the results from a PCA conducted on changesin the 5-year CDS spread levels and on changes in the slope of spreads obtained from a simulated panel of44 countries over 120,000 months.

Full Sample 2003-2006 2007-2010 2011-2012

Panel A: 44 countries - 5-year spreads

% Cumulative

PC1 56.52 56.52PC2 8.14 64.66PC3 4.44 69.10

% Cumulative

42.63 42.6315.25 57.8811.95 69.83

% Cumulative

75.36 75.366.05 81.414.74 86.15

% Cumulative

57.96 57.9613.33 71.297.56 78.85

Panel B: 30 countries - Term structure of spreads

% Cumulative

PC1 54.59 54.59PC2 10.04 64.63PC3 5.03 69.66

% Cumulative

54.60 54.6012.74 67.347.43 74.77

% Cumulative

75.84 75.845.71 81.553.70 85.26

% Cumulative

62.70 62.7012.82 75.529.26 84.78

Panel C: 30 countries - Slope of spreads

% Cumulative

PC1 21.79 21.79PC2 9.26 31.06PC3 7.92 38.98

% Cumulative

24.20 24.2016.35 40.5510.38 50.93

% Cumulative

38.00 38.0012.85 50.8510.22 61.07

% Cumulative

31.30 31.3018.32 49.6212.43 62.05

Panel D: Model (120,000 months of simulated data)

44 countries - 5-year spreads 44 countries - Slope of spreads

% Cumulative

PC1 80.58 80.58PC2 2.30 82.87PC3 2.28 85.15

% Cumulative

PC1 25.06 25.06PC2 16.22 41.28PC3 2.32 43.61


Table 6: Model Parameter Calibration

Panels A and B in this table reports model and preference parameter values, which are calibrated at amonthly decision interval. Panel C reports the endogenous coefficients of the wealth-consumption ratio.Panels D and E present moments of consumption dynamics from the data and the model. The data are real,sampled at an annual frequency, and cover the period 1929 to 2011. Standard errors are Newey-West withone lag. For the model, I report percentiles of these statistics based on 10,000 simulations of 600 months,equalling 50 years of data. The column Pop reports population statistics based on a long simulation of 1.2million months. All statistics are time-averaged. Data for consumption growth are taken from the Bureauof Economic Analysis National Income and Product Accounts Tables. The parameters νσ > 0 and cσ > 0are linked to the unconditional mean µσ and variance ωσ of the volatility process by µσ = (νσcσ) / (1− φσ)

and ωσ =(νσc

2σ

)/ (1− φσ)

2.

Panel A: Preference Parameter Values

Subjective discount factor δ 0.9987Intertemporal elasticity of substitution ψ 1.7

Coefficient of relative risk aversion γ 10

Panel B: Consumption Growth Dynamics

Mean consumption growth µx 0.0015Persistence of expected consumption growth φx 0.975

Sensitivity to long-run risk shocks νx 0.034Persistence of volatility φσ 0.9945

Volatility level√µσ 0.00725

Volatility of volatility√ωσ 2.8035e-005

Panel C: Coefficients of the wealth-consumption ratio - Model

Ac0 Ac1 Ac2

6.85 15.80 -1085.18

Panel D: Consumption - Model

Mean (%) 1% 5% 50% 95% 99% Pop

E [∆c] 1.79 0.40 0.83 1.78 2.77 3.20 1.80σ [∆c] 2.30 0.24 1.61 2.26 3.13 3.50 2.38AC1 [∆c] 0.34 -0.01 0.11 0.35 0.57 0.65 0.41

Panel E: Consumption - Data

Estimate SE

E [∆c] (%) 1.97 0.28σ [∆c] (%) 2.02 0.38AC1 [∆c] 0.48 0.12


Tab

le7:

Def

ault

Par

amet

ers

and

CD

SP

rici

ng

Implica

tion

s(a

fter

July

2007

)

Th

ista

ble

rep

orts

the

calib

rate

dp

aram

eter

sof

the

def

ault

pro

cess

Θλ

=(φλσ,φλ,νλ,cλ)>

inco

lum

ns

(2)

to(5

)fo

rth

e44

cou

ntr

ies

inth

esa

mp

le.

Th

em

od

elis

sim

ula

ted

over

ati

me

seri

esof

120,

000

mon

ths.

Colu

mn

s(6

)to

(8)

rep

ort

the

pop

ula

tion

valu

esof

the

aver

age

5-y

ear

spre

ad

an

dth

eav

erag

esl

ope

(in

bp

s),

and

the

frac

tion

ofsi

mu

late

dob

serv

ati

on

sw

ith

an

inve

rted

term

stru

ctu

reof

CD

Ssp

read

s.C

olu

mn

s(9

)to

(11)

rep

ort

the

obse

rved

sam

ple

equiv

alen

tsfo

rth

ep

erio

dJu

ly20

07u

nti

lF

ebru

ary

2012.

Colu

mn

s(1

2)

to(1

3)

rep

ort

small

sam

ple

mom

ents

base

don

1,0

00

sim

ula

tion

sof

100

year

s(1

,200

mon

ths)

.C

olu

mn

(12)

rep

ort

sth

e5th

and

95th

per

centi

les

of

the

dis

trib

uti

on

of

the

5-y

ear

CD

Ssp

read

(in

bp

s),

wh

ile

colu

mn

(13)

rep

orts

the

5th

and

95th

per

centi

les

ofth

ed

istr

ibu

tion

of

the

10y-1

ysl

op

eof

spre

ad

s(i

nb

ps)

.C

olu

mn

(14)

rep

ort

sm

od

el-i

mp

lied

risk

pre

mia

for

1-ye

aran

d10

-yea

rC

DS

spre

ads

(in

%)

asa

fract

ion

of

tota

lsp

read

sb

ase

don

the

sim

ula

ted

valu

esof

120,0

00

month

sof

data

.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

Defa

ult

Param

eters

Sim

.in

Popula

tio

nD

ata

SS

CD

S5y

SS

Slo

pe

Risk

Prem

iaΘλ

(bps)

(%

)(bps)

(%

)(bps)

(bps)

(%

)C

ountr

yφλσ

φλ

νλ

cλ

CD

S5y

Slo

pe

Fra

c<

0C

DS5y

Slo

pe

Fra

c<

0[5

th,9

5th

][5

th,9

5th

][1

y,1

0y]

Aust

ria

Belg

ium

Bra

zil

Bulg

ari

aC

hile

Chin

aC

olo

mbia

Cro

ati

aC

ypru

sC

zech

Rep.

Denm

ark

Egypt

Fin

land

Fra

nce

Germ

any

Gre

ece

Hungary

Irela

nd

Isra

el

Italy

Japan

Kore

aL

ebanon

Lit

huania

Mala

ysi

aM

exic

oM

oro

cco

Panam

aP

eru

Philip

p.

Pola

nd

Port

ugal

Qata

rR

om

ania

Russ

iaSlo

vakia

Slo

venia

Sth

.A

fric

aSpain

Sw

eden

Thailand

Turk

ey

Uru

guay

Venezuela

10.4

211.9

226.0

530.2

411.8

113.3

320.9

821.5

90.0

115.6

24.8

339.0

43.6

34.9

111.9

30.1

936.9

90.7

216.8

422.9

112.4

814.1

735.1

738.8

614.5

023.0

123.4

725.3

823.4

527.4

017.7

00.0

414.3

235.5

629.5

127.8

433.9

926.3

446.2

04.0

521.6

722.0

234.8

891.1

6

0.2

244

0.3

025

0.0

234

0.3

367

0.2

422

0.1

346

0.2

987

0.5

220

0.4

490

0.0

278

0.4

102

0.3

050

0.3

329

0.5

343

0.0

003

0.9

794

0.2

720

0.7

787

0.1

970

0.1

740

0.0

001

0.4

119

0.5

274

0.1

598

0.2

458

0.1

192

0.1

894

0.0

968

0.1

549

0.2

351

0.2

757

0.8

325

0.2

390

0.3

207

0.2

793

0.0

083

0.0

177

0.1

352

0.0

263

0.4

173

0.0

375

0.4

605

0.2

120

0.5

196

4.1

8e-0

41.5

6e-0

35.1

1e-0

41.3

0e-0

21.4

9e-0

37.9

2e-0

42.3

6e-0

35.0

5e-0

25.3

8e-0

33.5

9e-0

23.6

0e-0

11.1

8e-0

22.4

2e-0

15.2

2e-0

13.4

6e-0

61.6

6e-0

15.4

9e-0

34.9

2e-0

31.9

9e-0

36.6

2e-0

41.2

8e-0

61.5

0e-0

31.7

4e-0

25.3

7e-0

21.2

0e-0

48.7

9e-0

42.4

9e-0

35.0

4e-0

35.2

4e-0

44.0

6e-0

33.3

6e-0

34.5

8e-0

36.6

3e-0

11.1

0e-0

21.4

6e-0

21.0

0e-0

61.0

3e-0

51.9

3e-0

33.5

3e-0

54.0

2e-0

12.0

8e-0

39.9

7e-0

38.1

4e-0

45.0

7e-0

1

2.2

1e-0

27.8

7e-0

38.0

0e-0

46.5

2e-0

43.8

1e-0

32.0

7e-0

33.5

6e-0

41.3

2e-0

44.9

6e-0

11.0

0e-0

61.0

0e-0

69.2

9e-0

61.0

0e-0

61.0

0e-0

68.9

8e-0

12.8

9e-0

31.0

5e-0

45.0

9e-0

12.7

9e-0

32.5

8e-0

22.5

3e-0

11.1

8e-0

31.1

6e-0

44.4

9e-0

35.9

8e-0

32.4

9e-0

35.7

7e-0

44.0

5e-0

42.5

5e-0

45.8

0e-0

58.2

4e-0

46.5

4e-0

11.0

0e-0

69.3

5e-0

41.0

2e-0

36.3

2e-0

19.2

0e-0

11.5

2e-0

46.8

2e-0

11.0

0e-0

61.5

5e-0

31.2

8e-0

41.0

1e-0

68.1

9e-0

4

69

89

139

238

81

80

155

235

257

84

43

292

28

55

33

1644

264

338

109

141

52

125

386

265

99

136

151

146

144

186

127

387

98

273

214

89

93

158

146

36

117

212

230

1056

12

15

24

38

14

14

26

38

-10

15 8

46 5

10 6

-493

42

-80

19

24 9

22

57

38

17

23

26

25

25

31

22

-105

17

43

35

16

16

27

25 7

20

35

38

103

2.4

75.4

20.2

31.0

64.0

80.6

50.4

81.0

43.0

00.1

40.1

00.6

00.0

90.1

10.1

035.7

20.5

63.3

41.7

83.0

30.1

14.9

91.2

61.2

34.4

80.4

70.3

70.2

40.2

70.3

30.8

93.2

40.1

51.3

10.9

50.2

70.2

90.2

70.5

00.1

00.2

10.7

50.4

06.3

3

78

100

154

256

93

90

173

253

257

92

48

315

32

63

38

1214

283

300

124

153

61

135

409

278

111

151

165

163

161

206

142

328

107

291

226

98

101

177

158

41

131

235

243

1096

38

37

104

76

67

58

109

76 -7 43

28

111

21

38

29

-933

73

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73

39

56

51

119

41

67

89

76

103

104

122

69

-76

56

77

61

44

43

98

36

26

76

133

125

101

0.0

00.0

00.0

08.9

30.0

00.0

00.0

07.1

417.8

63.5

70.0

00.0

00.0

00.0

00.0

046.4

38.9

339.2

90.0

07.1

40.0

01.7

90.0

026.7

90.0

00.0

00.0

00.0

00.0

07.1

40.0

039.2

90.0

010.7

112.5

01.7

90.0

07.1

40.0

00.0

00.0

08.9

30.0

025.0

0

[47,1

00]

[61,1

30]

[95,2

03]

[162,3

48]

[56,1

19]

[55,1

17]

[106,2

28]

[161,3

44]

[252,2

61]

[57,1

23]

[29,6

3]

[199,4

27]

[19,4

2]

[37,8

0]

[23,4

8]

[763,3

404]

[180,3

87]

[283,4

32]

[75,1

60]

[97,2

06]

[36,7

6]

[86,1

83]

[262,5

65]

[189,3

76]

[68,1

45]

[93,1

99]

[103,2

21]

[100,2

14]

[99,2

12]

[127,2

73]

[87,1

86]

[306,6

54]

[67,1

44]

[186,3

99]

[147,3

13]

[61,1

31]

[64,1

36]

[108,2

32]

[100,2

13]

[25,5

3]

[80,1

72]

[144,3

11]

[157,3

37]

[735,1

504]

[10,1

4]

[13,1

8]

[19,2

8]

[30,4

6]

[12,1

7]

[12,1

6]

[21,3

1]

[29,4

5]

[-30,1

][1

2,1

7]

[6,9

][3

5,5

5]

[4,6

][8

,11]

[5,7

][-

1222,-

17]

[32,5

1]

[-253,1

][1

5,2

2]

[19,2

8]

[8,1

1]

[17,2

5]

[42,7

1]

[30,4

6]

[14,2

0]

[19,2

7]

[20,3

0]

[20,2

9]

[20,2

9]

[24,3

7]

[18,2

6]

[-355,-

1]

[14,2

0]

[33,5

2]

[27,4

1]

[13,1

8]

[13,1

9]

[21,3

2]

[19,2

9]

[5,8

][1

6,2

4]

[27,4

1]

[29,4

5]

[60,1

41]

[2.7

9,1

8.1

6]

[2.7

4,1

7.9

9]

[2.9

0,1

8.1

7]

[2.7

3,1

7.5

4]

[2.7

9,1

8.2

2]

[2.8

6,1

8.3

7]

[2.7

7,1

7.9

9]

[2.5

5,1

7.4

0]

[0.7

5,0

.51]

[2.9

0,1

8.4

2]

[2.6

8,1

8.4

3]

[2.7

6,1

7.4

1]

[2.7

5,1

8.5

5]

[2.5

5,1

8.2

6]

[2.9

0,1

8.5

5]

[0.6

4,0

.98]

[2.7

8,1

7.5

4]

[0.7

6,0

.76]

[2.8

2,1

8.1

5]

[2.8

1,1

7.8

9]

[2.9

1,1

8.5

7]

[2.6

9,1

8.0

4]

[2.5

5,1

6.8

3]

[2.5

7,1

5.8

9]

[2.8

1,1

8.2

7]

[2.8

6,1

8.1

3]

[2.8

3,1

8.0

5]

[2.8

7,1

8.1

0]

[2.8

5,1

8.1

1]

[2.8

1,1

7.8

9]

[2.7

8,1

8.1

0]

[0.7

4,0

.54]

[2.8

0,1

8.2

8]

[2.7

4,1

7.3

9]

[2.7

6,1

7.6

0]

[2.9

1,1

8.4

0]

[2.8

9,1

8.2

7]

[2.8

6,1

8.0

5]

[2.8

7,1

7.9

4]

[2.6

8,1

8.4

5]

[2.8

9,1

8.2

2]

[2.6

3,1

7.6

4]

[2.8

2,1

7.7

1]

[2.3

6,1

3.2

6]


Tab

le8:

Exce

ssB

ond

Ret

urn

san

dE

conom

icP

olic

yU

nce

rtai

nty

Col

um

ns

(2)

to(1

1)in

this

tab

lere

por

tth

eco

effici

ent

esti

mate

san

dR

2fr

om

the

pro

ject

ion

of

on

e-ye

ar

hold

ing

per

iod

exce

ssb

on

dre

turn

s(c

olu

mn

s(1

2)to

(16)

)on

the

Bak

eret

al.

(201

6)ec

onom

icp

olic

yu

nce

rtain

tyin

dex

.S

tati

stic

al

sign

ifica

nce

isb

ase

don

stan

dard

erro

rsth

at

acc

ou

nt

for

seri

al

corr

elat

ion

up

totw

elve

lags

asin

New

eyan

dW

est

(198

7).

Ies

tim

ate

the

regre

ssio

ns

for

five

matu

rity

ban

ds

an

d25

cou

ntr

ies.

Th

em

atu

rity

ban

ds

are

1-3

years

,3-

5ye

ars,

5-7

year

s,7-

10ye

ars

and

over

10ye

ars

.T

he

cou

ntr

ies

are

Au

stra

lia,

Au

stri

a,

Bel

giu

m,

Can

ad

a,

Den

mark

,F

inla

nd

,F

ran

ce,

Ger

man

y,G

reec

e,Ir

elan

d,

Ital

y,Jap

an,

Kor

ea,

Mal

aysi

a,

Mex

ico,

Net

her

lan

ds,

New

Zea

lan

d,

Norw

ay,

Pola

nd

,P

ort

ugal,

Sin

gap

ore

,S

pain

,S

wed

en,

Sw

itze

rlan

d,

and

the

U.K

.B

ond

retu

rns

are

com

pu

ted

bas

edon

the

Cit

igro

up

Worl

dG

over

nm

ent

Bon

dU

SD

Tota

lR

etu

rnIn

dic

es(f

orm

erS

alo

mon

Sm

ith

Bar

ney

Ind

ices

).T

he

retu

rns

are

inex

cess

ofth

esh

ort

-ter

mJP

Morg

an

Cash

on

e-m

onth

Tota

lR

etu

rnIn

dex

.T

he

earl

iest

start

ing

per

iod

for

the

dat

ais

Dec

emb

er19

85.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

1-3

years

3-5

years

5-7

years

7-1

0years

10+

years

AverageExcess

Retu

rns

Cou

ntr

yβ

R2

βR

2β

R2

βR

2β

R2

1−

33−

55−

77−

10

+10

Au

stra

lia

0.1

1***

15.0

70.1

2***

16.1

70.1

2***

16.6

20.1

2***

16.5

80.1

2***

16.4

85.1

45.8

86.4

76.7

47.2

2A

ust

ria

0.0

9**

8.8

00.1

0***

9.7

70.1

0***

9.6

90.1

0***

9.1

20.1

0***

8.7

21.5

42.6

13.1

83.6

45.2

4B

elgiu

m0.1

0***

10.3

70.1

1***

10.8

10.1

1***

10.4

00.1

0***

9.4

90.1

0***

8.5

21.7

92.7

43.3

73.8

14.3

6C

an

ad

a0.0

4*

5.0

80.0

4*

5.0

00.0

4*

4.5

60.0

4*

3.7

70.0

42.2

93.1

43.9

74.6

54.9

75.9

8D

enm

ark

0.0

6*

4.3

40.0

6*

5.2

90.0

6**

5.3

00.0

6**

5.2

90.1

0***

9.2

42.9

63.8

64.5

55.1

66.6

2F

inla

nd

0.1

0***

11.1

10.1

1***

12.4

50.1

1***

11.6

80.1

***

10.7

80.0

7***

5.7

60.3

81.3

42.5

13.7

11.5

8F

ran

ce0.0

53.5

50.0

6*

4.6

90.0

6*

4.7

80.0

6**

4.7

50.0

6**

4.6

32.6

33.5

64.0

84.4

95.3

8G

erm

any

0.0

53.4

50.0

6*

3.8

60.0

6*

4.1

50.0

6*

3.6

20.1

0***

5.8

62.0

92.8

63.5

23.5

35.6

2G

reec

e0.0

5*

3.8

10.0

52.1

30.0

51.5

40.0

51.4

40.0

61.7

14.2

03.2

02.7

92.4

92.6

1Ir

elan

d0.0

7*

8.0

80.0

9***

11.3

50.0

7**

6.3

20.0

6*

3.3

20.0

7*

3.5

92.0

82.2

91.7

03.6

12.9

6It

aly

0.0

41.6

90.0

31.2

10.0

20.3

90.0

41.5

70.0

8**

3.4

33.3

03.8

02.8

72.8

56.4

6Jap

an

0.1

0***

11.0

20.1

1***

11.5

00.1

1***

10.9

50.1

0***

9.9

60.1

2**

11.2

00.7

81.7

82.5

73.1

16.2

0K

ore

a0.1

2**

12.6

80.1

3***

13.9

40.1

4***

15.0

20.1

4***

14.2

60.1

5***

14.9

10.7

10.9

91.3

81.5

41.5

8M

ala

ysi

a0.0

4*

6.1

60.0

4**

5.5

70.0

4*

4.5

80.0

32.0

20.0

10.3

64.4

85.0

95.5

25.6

06.7

9M

exic

o0.0

53.1

10.0

53.2

10.0

52.4

40.0

51.8

60.0

20.3

54.5

65.7

56.5

77.1

88.8

5N

eth

erla

nd

s0.0

63.7

70.0

6*

4.3

20.0

6*

4.5

90.0

6*

4.3

50.0

52.7

02.3

03.0

63.5

93.7

64.2

4N

ewZ

eala

nd

0.1

9***

27.8

00.1

9***

24.3

60.1

6***

22.3

70.1

8***

21.3

00.1

6***

18.8

76.1

34.2

33.2

25.4

06.1

5N

orw

ay

0.1

3***

17.8

70.1

3***

16.2

20.1

0***

11.9

60.1

2***

14.1

70.0

2***

8.5

71.5

22.6

72.9

43.9

1-2

.66

Pola

nd

-0.0

20.2

4-0

.01

0.0

6-0

.01

0.0

30.0

00.0

1-0

.05

1.5

49.6

310.4

65.6

711.0

65.5

9P

ort

ugal

0.0

55.0

70.0

53.7

30.0

52.4

90.0

52.2

30.0

74.6

54.3

34.0

43.7

53.6

50.5

7S

ingap

ore

0.0

21.8

40.0

22.0

30.0

10.5

2-0

.01

0.1

9-0

.01

0.1

72.3

44.0

35.0

55.3

54.6

6S

pain

0.0

53.2

10.0

53.3

40.0

7**

5.9

20.0

52.6

50.0

30.7

11.6

82.5

83.4

53.7

22.9

8S

wed

en0.0

63.1

60.0

63.0

30.0

52.5

70.0

51.9

00.0

41.4

41.6

32.5

93.3

74.2

25.0

1S

wit

zerl

an

d0.0

41.9

60.0

52.3

60.0

52.2

10.0

52.5

20.0

63.0

51.4

52.0

42.4

62.8

93.4

4U

.K.

0.0

20.7

10.0

21.0

00.0

31.0

80.0

31.1

20.0

30.9

02.7

73.3

73.8

44.0

64.3

3

Pan

el0.0

6***

5.1

50.0

7***

5.5

30.0

7***

5.1

50.0

7***

4.5

50.0

6***

3.8

2

Aver

age

0.0

77.1

30.0

77.1

60.0

76.6

40.0

76.0

50.0

65.5

92.9

43.5

53.7

24.4

24.4

7

the term structure of cds spreads and sovereign credit risk

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