Michał Adam – Spillovers and contagion in the sovereign CDS market

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Bank i Kredyt 44 (6), 2013, 571–604

www.bankandcredit.nbp.pl www.bankikredyt.nbp.pl

Spillovers and contagion in the sovereign

CDS market

Michał Adam*

Submitted: 20 December 2012. Accepted: 20 May 2013.

Abstract

This paper focuses on the relationship between sovereign credit default swaps (SCDS) referencing a group of selected developed and emerging economies during the recent sovereign debt crisis. Interdependence and contagion are found on the market dominated by a small number of big international participants. The results show that: (i) a strong commonality exists between global credit spreads (almost half of their variance can be attributed to a single component) with important regional resemblances, (ii) intra-regional spillovers are even more significant, as up to 80% of the forecast error variance of SCDS spreads comes from spillovers, (iii) there is a significant time-variation in spillovers, with contagion from distressed countries gradually diminishing over time as they lose access to bond markets, (iv) the impact of a country’s credit spread on the system appears to be largely liquidity-driven (up to 67% is explained by various liquidity measures). Keywords: sovereign debt crisis, sovereign credit default swap, sunspot, contagion, spillover index

JEL: C32, C38, F34, G01, G15

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572 1. Introduction

With the transformation of the global financial crisis into a sovereign debt crisis in the Eurozone, starting from Greece in late 2009, an insight into the nature of credit risk has become crucial. A number of countries have experienced intense debt price pressures and have withdrawn from international bond markets. Furthermore, the concerns about contagion among group of countries have appeared. As suggested by Longstaff et al. (2011), the complex nature of sovereign credit risk affects the ability of market participants to diversify risk internationally. Given the large size of sovereign debt markets, the emergence and rapid development of credit derivatives as a means of insuring sovereign debt is not surprising.

The most popular derivative security for managing sovereign debt exposure is a credit default swap (CDS). An in-depth description of CDS contracts has been provided e.g. by Duffie and Singleton (2004). A CDS is an OTC contract that offers insurance against credit event (in particular sovereign default). The protection buyer pays a fixed premium, called the CDS spread, to the seller until the time of the credit event or until the maturity date of the CDS, whichever is first. If the credit event occurs prior to maturity, the protection seller pays compensation to the protection buyer. The contingent amount is most often specified to be the difference between the face value of a bond and its market value, paid at the time of the credit event. It is equal to the notional principal multiplied by one less the recovery rate, where the recovery rate is equal to the ratio of the post- -default value of the bond to its face value (Hull 2009).

Sovereign CDS contracts have been traded actively on emerging country and recently also on developed country debts. Longstaff et al. (2011) argue that an important advantage of using SCDS data (rather than sovereign bond data) for measuring credit risk is that the sovereign credit swap market is often more liquid than the corresponding sovereign bond market. As a result, SCDS contracts provide more accurate estimates of credit spreads. The increasing attractiveness of SCDS has also been caused by the fact that investors frequently buy protection even if they do not necessarily own the referencing bond at the time of agreement (the so-called uncovered, or naked SCDS). By that means banks can proxy hedge the exposure to a counterparty, which operates in the reference country. Global regulatory standards also have contributed to the increasing demand for such insurance. For instance, Basel rules require banks to hold capital against changes in the market price of protecting against the risk of a credit event. Such a situation takes place for example when a bank enters into the interest rate swap transaction with the sovereign.

International financial markets are closely integrated worldwide. Also, a number of factors have integrated markets at the regional level. These developments include the rise of the regional initiatives like the European Union (with the emergence of the common currency itself), the liberalisation of capital flows or the tendency to diversify the portfolios of financial institutions. In this context, the focus of investors shifted from individual sovereign spreads in isolation to the co-movements across countries and regions. Ehrmann, Fratzscher and Rigobon (2011) find that asset prices react the strongest to other domestic asset price shocks, but that there is also a substantial international spillover. Therefore, they conclude that it is necessary to model international financial linkages in order to gain a better understanding of the financial transmission process across various assets. Moreover, Pan and Singleton (2008) show that during some periods a substantial portion of the co-movement among the term structures of sovereign

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Spillovers and contagion in the sovereign...

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spreads across countries is induced by changes in investors’ appetites for credit exposure at the global level. These results become of crucial importance during crises, when financial market volatility generally increases sharply and spills over across markets. In bear markets, as found by Longin and Solnik (2001), co-movements increase the most. Those periods emphasise the systemic importance of certain countries in a group. A market is systemic if it both sends and receives shocks from all other markets (ECB 2011). Hence, systemic sovereigns are those that do not only suffer most individually during a crisis, but also contribute most to overall market losses. Systemic events spread from one market to another such that the overall stability of the system may be impaired.

In this paper I show that the Masson’s topology (1999) of reasons why crises can occur contemporaneously over time is valid for countries’ credit risk. To this end I use the SCDS dataset of developed and emerging markets from the latest debt crisis period, during which the banking sector risk was transferred to sovereign borrowers. First, using a principal components analysis, I document a strong resemblance between global credit spreads and confirm that almost half of their variance can be attributed to a single component. Loadings of the first components suggest that regional factors play a significant role in determining changes in sovereign spreads and validate the subsequent regional approach, in which countries are clustered into the Eurozone, Asia, EMEA (Europe, Middle East and Africa) and Latin America groups. I then study the interdependence and contagion among pre-specified regions. I employ a recent method of spillover index (Diebold, Yilmaz 2009). In this method results are not derived from a partial equilibrium assumption, in which foreign conditions cause domestic changes. Conversely, the method fully accounts for the feedback of domestic markets to international markets. Spillover indices allow for the aggregation of spillover effects across markets, distilling a wealth of information into a single spillover measure. In this method spillovers are defined in terms of forecast error variance decompositions. The results show that intra-regional spillovers are important, as only 20% to 31% of forecast error variance is explained by domestic factors and region-specific linkages are clearly visible. In general, larger countries in terms of the size of debt markets have a more pronounced impact on the regional SCDS spread returns. 67% of the net spillovers is explained by liquidity measures.

The intensity of spillovers may of course vary over time and the nature of any time-variation should be of great interest. Therefore, I use rolling estimations to detect the potential intra-regional contagion, following Forbes and Rigobon (2002) being defined as a sharp surge in spillovers across markets. I find that contagion spills from distressed countries. The influence of the countries loosing access to the bonds markets, however, gradually diminishes over time. For instance, Greek SCDS spreads appear to be systemically important only during the specific early phase of the European sovereign debt crisis.

The remainder of the paper is organised as follows. In the next section the related subject literature is reviewed. The third section gives a thorough description of the employed methods. The fourth section contains details concerning the data set at hand. The results from a factor analysis are presented in the fifth section. The sixth and seventh section deal with spillover and contagion analysis, also in the time-varying framework. The last section concludes.

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574 2. Studies on spillovers, contagion and the SCDS market

There is a vast literature concerning co-movements across financial markets. Most of the studies, however, focus on stock markets. The early work of Hamao, Masulis and Ng (1990) finds evidence of short-run interdependence of prices across three major international stock markets located in New York, London and Tokyo. Bekaert, Hodrick and Zhang (2009) find a significant upward trend for developed stock return correlations during the period 1980−2005. Their findings are the strongest in relation to the European countries. Regional contagion was also found for East Asia by Caporale, Cipollini and Spagnolo (2005), running from Thailand, Taiwan, Hong Kong, the Philippines and Korea. Evidence was also presented by Hashimoto and Ito (2004), where contagion was detected to be originating primarily in Hong Kong, or by Gębka and Serwa (2007), who find all intra-regional markets influence each other. The latter study confirms, also for Central and Eastern Europe and Latin America, that both intra-regional spillovers are more pronounced than the inter-regional dependencies, which underlines the importance of regional financial markets analysis.

The substantial increase in the co-movement among corporate CDS spreads during the GM/Ford rating downgrade in 2005 has been documented by Acharya, Schaefer and Zhang (2008), as well as by Coudert and Gex (2010). The intra-industry information transfer effect of credit events was studied by Jorion and Zhang (2007) and illustrated by a strong co-movement across corporate CDS spreads. The authors also distinguished between contagion effects (positive correlations across credit events) and competitive effects (negative correlations). The first one occurs when the default (reorganisation) of one firm causes financial distress on other firms with which the first firm has close business ties. Assuming a fixed demand for the product, the second effect occurs because remaining firms may capture new clients from the displaced firms, or gain market power generally.

The literature on SCDS contagion is rather scant. The Argentinian sovereign crisis has been studied by Chen, Wang and Tu (2011), who using copulas find a significant increase in correlation and tail dependence between Argentinian and other Latin American SCDS spreads. Arghyrou and Kontonikas (2011) observe contagion running from Greece to several EMU countries since late 2009, although their analysis concludes in early 2010. Using a similar to this study’s technique, Alter and Beyer (2013) find two kinds of linkages: in a group of European sovereigns and between the sovereigns and European banks. Calani’s study (2012) also uses SCDS data set and spillover index method. Kliber (2011), on the other hand, focuses on the causality between Central European sovereign spreads during the recent financial crisis. Most of the analysis is however performed on the alternative measures of sovereign risk. Caceres, Guzzo and Segoviano (2010) measure euro area spreads as spreads of sovereign bond yields to the yield on a 10-year euro swap and identify Greek, Portuguese, Spanish and Italian spreads to be main sources of euro-wide contagion. Claeys and Vasicek (2012) examine data for 10-year sovereign bond yield spreads of 16 European Union countries over the corresponding German bond yield to find the systemic importance of the Spanish bond market.

Other studies focus mainly on documenting a strong commonality across sovereign credit spreads. Pan and Singleton (2008) emphasise the co-movement among the term structures of SCDS. Longstaff et al. (2011) find, that the first principal component explains 64% of the variation in global sovereign spreads during the 2000–2010 sample period. Furthermore, this value increases

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to 75% during the 2007–2010 crisis period in the global financial markets. Augustin and Tedongap (2011) present similar results. These studies use a large sample of both developed, high-grade countries as well as emerging economies, finding that loadings of the first principal component are roughly uniform. On this backdrop the interpretation of Bernd and Obreja (2010) would suggest, that such a phenomenon needs to be associated with the risk of economic catastrophe, as countries with the lowest credit risk usually are expected to fulfil the payments they promise to their debt holders except in the worst economic states.

Augustin and Tedeongap (2011) quote macroeconomic fundamentals in the United States to be among the primary drivers of global sovereign CDS spreads and conclude that theoretical determinants are insufficient to explain sovereign risk premia (embedded in SCDS prices). They find that common variation is driven more by global events rather than by the reassessments of the fundamental strengths of sovereign entities (in particular at short-term horizons). Longstaff et al. (2011) point to global market factors, risk premia and investment flows. Upon decomposing sovereign credit risk into a systemic component and a sovereign-specific component, Ang and Longstaff (2011) argue that systemic risk represents a much smaller fraction of total credit risk for U.S. states than is the case of members of the euro area, maintaining that systemic risk is primarily an artefact of common macroeconomic fundamentals.

The literature finds also non-negligible role for the liquidity of financial instruments. The explanations of contagion given by Kodres and Pritsker (2002) take into account major global financial institutions, which facing a loss in one market, turn to other markets in order to realise liquidity, so that a crisis in one market triggers crises in others. Investors specialised in a certain region who for instance face losses as a result of a crisis in one country may be forced to liquidate

in a number of countries. In these explanations liquidity risk1_{plays a nontrivial role. The liquidity}

premium is less volatile in liquid markets. Thus, high levels of liquidity should stabilise sovereign spreads. Furthermore, the literature acknowledges that there is a high degree of co-linearity between empirical measures of liquidity and the global risk factor (Arghyrou, Kontonikas 2011). Liquidity-related explanations possibly play a significant role in the SCDS market, where the

10 largest dealers now account for 90% of trading volume by gross notional amounts.2_{Concentration}

is even higher in the US market, where the five biggest investment banks account for more than 99% of gross notional amounts. In such a homogenous market microstructure, it is more plausible for the agents to coordinate their decisions on market sentiment (particularly concerning pricing of the sovereign risk). Gomez-Puig (2006) finds a stabilising role for liquidity premium for the large Eurozone countries (Italy, France and Spain) after the introduction of the common currency. Eichengreen et al. (2009) argue that the rising importance of common factors from the outbreak of the subprime crisis was due to rising funding risk, while Acharya, Schaefer and Zhang (2008) notice, that the increase in the co-movement among CDS spreads during the GM/Ford rating downgrade in May occurred when dealer funding was stretched. Theoretical foundations to link an asset’s market liquidity and traders’ funding liquidity has been provided by Brunnermeier and Pedersen (2009). Funding shocks experienced by leveraged investors may translate into declines in the market liquidity of securities. From an empirical perspective, these types of funding-

1_{Liquidity risk refers to the size and depth of the sovereign bonds market. Additionally, it captures the risk of capital} losses in the event of early liquidation or significant price changes resulting from a small number of transactions. 2_{Since 2004 the share of 10 largest dealers in trading volume increased more than 15 percentage points (Duquerroy,}

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-induced liquidity shocks could represent a common factor driving the values of affected securities. Specifically, if the marginal investor holding sovereign debt (or being long a SCDS contract) were to be subject to these funding shocks, sovereign credit spreads might display a common pattern in liquidity.

Adopting Masson’s topology (1998), one may discern three reasons for which crises may occur contemporaneously in time. Firstly, they may be due to a common cause, for instance policies undertaken at a global level, e.g. by supranational initiatives, or by developed countries (“monsoonal effects”). Secondly, a crisis in one market may affect the macroeconomic fundamentals in other markets, for instance because a slowdown in growth in one country reduces the potential for other countries’ exports in a trade union, or because lack of liquidity in one market leads financial intermediaries to liquidate other emerging market assets. With respect to this category the term interdependence is often applied. Finally, a crisis in one country may conceivably trigger a crisis elsewhere for reasons unexplained by macroeconomic fundamentals, likely because it leads to shifts in market sentiment or changes the interpretation given to existing information. For instance, a crisis might lead investors to reassess the fundamentals of other countries, even if they have not changed, or lead to a change in the risk tolerance among investors. This category is often called contagion, as it involves changes in expectations that are not related to changes in a country’s macroeconomic fundamentals. It is most natural to think of this in a context where financial markets are subject to multiple equilibria, or self-fulfilling expectations (Masson 1999). It gives a prominent role to what is commonly called “market sentiment” in the determination of asset prices, or, in economic literature, “sunspots”, that is irrelevant variables that nevertheless coordinate investors’ expectations. Self-fulfilling expectations can introduce extrinsic volatility that substantially exceeds the volatility generated by the macroeconomic fundamentals alone. When crisis occurs, jumps between equilibria are triggered by extraneous events. Macroeconomic linkages are simply insufficient to explain dynamic changes, as they typically take time to operate.

Forbes and Rigobon (2002) also define contagion as significant cross-market co-movement increasing after a shock. Therefore, one would expect bursts in dependence measures of sovereign risk across countries as a sign of contagion, while any continued high levels of co-movement would only suggest strong linkages between sovereign entities.

Vector autoregressive (VAR) models and forecast error variance decompositions (FEVD) are already well understood and widely used both by researchers and practitioners. Chen, Firth and Rui (2002) apply the variance decomposition to the stock markets of Latin America to find that a large proportion of stock market indices variance is attributable to shocks from regional markets. FEVD has been applied by Leitão and Oliveira (2007), who found Portugal to be a stock market volatility absorber. Sari and Malik (2000) use the generalised FEVD and conclude that the growth rate of the money supply contains significant information for predicting the variance of future forecast errors of stock returns. The method of Diebold and Yilmaz (2009) was originally applied to a wide range of global stock markets and generalised by Diebold and Yilmaz (2012) on a sample of US stock, bond, foreign exchange and commodities markets. Recently, this method has been employed to analyse the Central European (CE) exchange and money markets inter alia. Bubak, Kocenda and Zikes (2011) discover that along with the increasing market uncertainty, CE foreign exchange rates and US dollar volatilities co-move closely. The spillover effects increase most for the countries with troubled financial sector developments (e.g. Hungary). Kliber (2010) studies

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spillovers in a range of Central European money markets and exchange rates, finding evidence of close intra-regional relationships between the Czech Republic, Poland, Slovakia, and Hungary. The study of Calani (2012) also uses Spillover index method in assessing SCDS spreads, finding signs of contagion in the second moment (volatility) of the European SCDS spreads.

3. The spillover index method

The spillover index (SI) method, first introduced by Diebold and Yilmaz (2009), is based on a VAR model. The focus is on the forecast error variance decomposition (FEVD), which allows both to aggregate spillover measures across SCDS spreads and to split forecast error variances of each variable into portions attributable to individual system shocks. Consider a covariance stationary,

N-variable VAR(p) process of the following form:

= = = × = = = = = = = = = = _ = = = = = = + + + + = _ _ _ _ _ p i i t t t x x φ φ φ φ ε ε ε σ ξ θ ξ ∞ ε 1 i ) , 0 ( ~ 0 i i ti t A x p i p i i i A A A A 1 2 2 ... _ _ 1 1 0

A being an N N identity matrix and with Ai 0 for

i

<0.

+ − H h h t H h t H A 0 ) ( h h t H A A Cov[ ( )] ' 2 1 ) ' ' ( ) ' ( ) ( i h h i j h i jj g ij θg ij θg ij θg ij e A A e e A e H N j H H H 1 ) ( ) ( ) ( ~ H) 1 ( ~ _and N H ) ( 100 100 ) ( N H SIg i j ) (H SIg ₁₀₀ ₁₀₀ N i ) (H SIg i 100 _N 100 ) ( ) ( ) (H SI H SI H SI g i g i g i

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

∑ (1) where = = = × = = = = = = = = = = _ = = = = = = + + + + = _ _ _ _ _ p i i t t t x x φ φ φ φ ε ε ε σ ξ θ ξ ∞ ε 1 i ) , 0 ( ~ 0 i i t i t A x p i p i i i A A A A 1 2 2 ... _ _ 1 1 0

A being an N N identity matrix and with A_i 0 for i<0.

+ − H h h t H h t H A 0 ) ( h h t H A A Cov[ ( )] ' 2 1 ) ' ' ( ) ' ( ) ( i h h i j h i jj g ij θg ij θ g ij θg ij e A A e e A e H N j H H H 1 ) ( ) ( ) ( ~ H) 1 ( ~ _and N H ) ( 100 100 ) ( N H SIg i j ) (H SIg ₁₀₀ ₁₀₀ N i ) (H SIg i 100 _N 100 ) ( ) ( ) (H SI H SI H SI g i g i g i

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

∑ is a vector of independently and identically distributed disturbances.

The VAR can be rewritten in its moving average representation:

= = = × = = = = = = = = = = _ = = = = = = + + + + = _ _ _ _ _ p i i t t t x x φ φ φ φ ε ε ε σ ξ θ ξ ∞ ε 1 i ) , 0 ( ~ 0 i i t i t A x p i p i i i A A A A 1 2 2 ... _ _ 1 1 0

i

<0.

+ − H h h t H h t H A 0 ) ( h h t H A A Cov[ ( )] ' 2 1 ) ' ' ( ) ' ( ) ( i h h i j h i jj g ij θg ij θ g ij θg ij e A A e e A e H N j H H H 1 ) ( ) ( ) ( ~ H) 1 ( ~ _and _{H )} _N ( 100 100 ) ( N H SIg i j ) (H SIg ₁₀₀ ₁₀₀ N i ) (H SIg i 100 _N 100 ) ( ) ( ) (H SI H SI H SI g i g i g i

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

∑ (2)

where the N × N coefficient matrices A_i obey the recursion

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

∑ with A0

being an N × N identity matrix and with A_i = 0 for i < 0.

The error in forecasting x_tH steps ahead conditional on information available at t – 1 is given by:

= = = × = = = = = = = = = = _ = = = = = = + + + + = _ _ _ _ _ p i i t t t x x φ φ φ φ ε ε ε σ ξ θ ξ ∞ ε 1 i ) , 0 ( ~ 0 i i ti t A x p i p i i i A A A A 1 2 2 ... _ _ 1 1 0

i

<0.

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

∑ (3) with the covariance of:

(4) = = = × = = = = = = = = = = _ = = = = = = + + + + = _ _ _ _ _ p i i t t t x x φ φ φ φ ε ε ε σ ξ θ ξ ∞ ε 1 i ) , 0 ( ~ 0 i i ti t A x p i p i i i A A A A 1 2 2 ... _ _ 1 1 0

i

<0.

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

The decomposition of the forecast error variance allows to parse the variance of each variable in (4) into parts attributable to the various system shocks. The FEVD allows then to assess the fraction of the H step ahead error variance in forecasting x_ithat is due to shocks to x_jfor each i.

The FEVD based on Cholesky factorisation is presented in Diebold and Yilmaz (2009). As the variance decomposition using Cholesky factorisation depends on the ordering of variables in the VAR, Diebold and Yilmaz (2012) adopt the generalised VAR framework of Pesaran and Shin (1998).

In this framework the H step ahead forecast error variance decompositions, for H = 1, 2,… are

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578 i

< 0.

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

∑ (5)

where Σ is the variance matrix for the error vector ε, σ_jj is the standard deviation of the error term

for the j-th equation, and e_i is the selection vector, with one as the i-th element and zeros otherwise.

The larger is the fraction of the H step ahead forecast error variance in forecasting the asset i

due to shocks to market j, relative to the total forecast error variance, the larger will be the measure

of spillovers. Since the historical shocks are not orthogonal, the sum of forecast error variance decompositions does not sum up to 100%. Diebold and Yilmaz (2012) normalise each entry of the variance decomposition matrix by the row sum as:

(6) = = = × = = = = = = = = = = _ = = = = = = + + + + = _ _ _ _ _ p i i t t t x x φ φ φ φ ε ε ε σ ξ θ ξ ∞ ε 1 i ) , 0 ( ~ 0 i i t i t A x p i p i i i A A A A 1 2 2 ... _ _ 1 1 0

i

<0.

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

∑ By construction, = = = × = = = = = = = = = = _ = = = = = = + + + + = _ _ _ _ _ p i i t t t x x φ φ φ φ ε ε ε σ ξ θ ξ ∞ ε 1 i ) , 0 ( ~ 0 i i t i t A x p i p i i i A A A A 1 2 2 ... _ _ 1 1 0

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

∑ and = = = × = = = = = = = = = = _ = = = = = = + + + + = _ _ _ _ _ p i i t t t x x φ φ φ φ ε ε ε σ ξ θ ξ ∞ ε 1 i ) , 0 ( ~ 0 i i t i t A x p i p i i i A A A A 1 2 2 ... _ _ 1 1 0

A being an N N identity matrix and with Ai 0 for i<0.

+ − H h h t H h t H A 0 ) ( h h t H A A Cov[ ( )] ' 2 1 ) ' ' ( ) ' ( ) ( i h h i j h i jj g ij θg ij θg ij θg ij e A A e e A e H N j H H H 1 ) ( ) ( ) ( ~ H) 1 ( ~ and (H ) N 100 100 ) ( N H SIg i j ) (H SIg ₁₀₀ ₁₀₀ N i ) (H SIg i 100 _N 100 ) ( ) ( ) (H SI H SI H SI g i g i g i

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

. For each asset i, the shares of its H step

ahead forecast error variance coming from shocks to asset j, j ≠ i are added. Then these sums are

added across all i = 1,..., N. The spillover index (SI) can be written as:

i

<0.

+ − H h h t H h t H A 0 ) ( h h t H A A Cov[ ( )] ' 2 1 ) ' ' ( ) ' ( ) ( i h h i j h i jj g ij θg ij θ g ij θg ij e A A e e A e H N j H H H 1 ) ( ) ( ) ( ~ H) 1 ( ~ _and _{H )} _N ( 100 100 ) ( N H SIg i j ) (H SIg ₁₀₀ ₁₀₀ N i ) (H SIg i 100 _N 100 ) ( ) ( ) (H SI H SI H SI g i g i g i

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

∑ ₍₇₎

when there are no spillovers, the SI equals zero.

The index is therefore not a simple measure of co-movement of markets that reflects a similar response to a common shock, but it measures the importance of idiosyncratic shocks of all variables included in an unrestricted VAR on other markets (Claeys, Vasicek 2012).

As mentioned before, in contrast to the Cholesky factorisation of the VAR model, the generalised approach is invariant to ordering. Instead, the analysis describes how the system behaves taking into account the historical patterns of correlations among the shocks. Elyasiani, Kocagil and Mansur (2007) show that the generalised variance decomposition framework provides a more accurate and realistic description of market linkages, also because it does not impose any a priori restrictions in the VAR, which might be difficult to defend based on economic theory.

The Diebold and Yilmaz (2012) method also facilitates the identification of directional spillovers using the normalised elements of the generalised variance decomposition matrix.

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579 i

<0.

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

while the directional spillovers transmitted by market i to all other markets j are calculated as:

i

<0.

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

The net contribution to a system of CDS spreads is obtained by simply subtracting, for

a variable i, the shares of its H step ahead forecast error variance coming from shocks to asset j,

j ≠ i, from its sum of shocks to other variables:

i

<0.

+ − H h h t H h t H A 0 ) ( h h t H A A Cov[ ( )] ' 2 1 ) ' ' ( ) ' ( ) ( i h h i j h i jj g ij θg ij θ g ij θg ij e A A e e A e H N j H H H 1 ) ( ) ( ) ( ~ H) 1 ( ~ _and ₍_{H )} _N 100 100 ) ( N H SIg i j ) (H SIg ₁₀₀ ₁₀₀ N i ) (H SIg i 100 _N 100 ) ( ) ( ) (H SI H SI H SI g i g i g i

∑

∑ ∑ ∑ = H h 0

∑

= H h 0

∑

_₁ = = H h 0

∑

θg ij N j 1=

∑

θ~g ij N i, j 1=

∑

H ) ( ~ θg ij N j 1= j 1= ≠

∑

j i H ) ( ~ θg ij N ≠

∑

j i i H ) ( ~ θg ji N j 1= ≠

∑

j H ) ( ~ θg ji N j 1= ≠

∑

H ) ( ~ θg ji N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1

∑

= j i H ) ( ~ θg ij N ≠

∑

H ) ( ~ θg ij N i, j 1= i, j 1= i, j 1=

∑

∑ (10) This group of measures (equations 8−10) is important, because it describes the degree of connectedness, and the degree to which various credit spreads are systemic. The directional measures elucidate how much of the total spillover comes from, or goes to a particular source. From an economic point of view, the statistics facilitate identifying the sources (i.e. transmitters) and the receivers of spillovers, serving as an instrument for the input-output analysis. Against this background, the statistics provide a synthetic indication on the mechanism of transmission and a possibility of identifying contagious elements of a given system. Obviously, a SCDS spread may be both a transmitter and a receiver of spillovers. It is the net measure which allows to quantify the net impact of a SCDS spread, i.e. if it is more of a source than a receiver of spillovers. For that reason the net measure helps to identify systemic countries.

The intensity of spillovers may of course vary over time and the nature of any time-variation is of potentially great interest, as it may help in determining contagion. To allow for time-variation of SI, I calculate them in a rolling window of 260 observations, which corresponds to the 1-year period in the data I use.

4. Data

The daily pricing data for 5-year SCDS3_{used in this study is provided by CMA datavision via}

Bloomberg terminal. The SCDS spreads are New York end-of-day quotes. It allows to avoid the possible problem of synchronicity of the data. To maintain uniformity in the contracts, I only use SCDS quotations for senior debt and denominated in US dollars. The sample covers the period from January 2008 to January 2012 in the case of Latin American and Asian countries and from

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580

September 2008 to January 2012 in the case of the Eurozone and EMEA countries. The difference is driven by the availability of data and the routine of gradually adding new quotations to the Bloomberg system. An advantage of using such a sample is that only the recent financial crisis period is examined. Since the time span covers the transformation from an initial subprime crisis in the United States to the sovereign debt crisis in the Eurozone, any possible caveats stemming from the use of both crisis and non-crisis subsamples are avoided.

Liquidity is widely acknowledged to be particularly difficult to measure. Two different sources of liquidity proxies for SCDS are used in this study. First, it is calculated as a standard bid-ask spread, where the data is obtained from Bloomberg. Alternatively, I also employ the Depository Trust & Clearing Corporation’s (DTCC) data containing volumes of transactions with a weekly frequency. This data is provided by Reuters and is used to check the robustness of the results. DTCC data comes as net notional values, which are the sum of the net protection bought/sold by net buyers/sellers. Net notional positions generally represent the maximum possible net funds transfer between net sellers of protection and net buyers of protection that could be required under the occurrence of a credit event. By contrast, gross notional values are the sum of all SCDS contracts, do not take into account the offsetting positions and are not very reflective of a true market size. It is the net notional amount, which reflects the actual size of the SCDS market, even if it can be meaningfully smaller than the gross notional amount outstanding (constituting around 10% of the gross amounts).

The series used as inputs for VAR models are SCDS spread daily log-returns for selected developed and emerging markets in Asia (China, Indonesia, South Korea, Malaysia, Philippines, Thailand, Vietnam), EMEA (Bulgaria, Croatia, Czech Republic, Hungary, Israel, Latvia, Lithuania, Poland, Romania, Russia, South Africa, Turkey, Ukraine), the Eurozone (Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Portugal, Slovakia, Slovenia, Spain) and Latin America (Argentina, Brazil, Chile, Colombia, Mexico, Panama, Peru, Venezuela). The dimension of the models can grow large for such a number of markets, but the use of daily data and the sample of 260 observations (in a rolling window analysis) allows to avoid estimation problems occurring in small samples. Three criteria were used to include a country’s SCDS spread in the sample. First, data availability. The availability of SCDS data is usually high for the big corporates, but much narrower for sovereign entities. Also, time-series data for developed economies is shorter than for the majority of emerging markets. Second, only liquid markets are analysed, as indicated by DTCC’s top 1,000 most liquid entities. Therefore, for instance, Malta and Luxembourg, which are members of the Eurozone, are not included in the sample. Moreover, quotation precision is closely associated to liquidity of the SCDS market. The regional division follows a standard market convention, according to which investors group countries according to their geographical location and economic development (see also Section 5 for more arguments for the regional approach). Additionally, regional similarities, due to cultural links and both economic as well as political integration, make these countries particularly suitable for a comparative study.

Usually, studies regarding sovereign risk (e.g. Longstaff et al. 2011; Augustin, Tedongap 2011) use data samples containing a considerably large number of pre-crisis observations. This approach facilitates a comparison of crisis and non-crisis periods. On the other hand, one needs to deal with structural breaks in the data, which pose obvious estimation problems. Using a sample from January 2008 onwards, this study avoids the aforementioned problems. The period I cover includes the onset of the financial crisis, as well as its transformation into the sovereign risk

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581

phase. Table 1 provides a summary of sovereign CDS premia. The average values of the spreads range widely across countries. The lowest is 33.8 basis points for Finland. The highest average is 1,293.7 basis points for Argentina. Both the standard deviations and the minimum/maximum values indicate that there is also a significant time-series variation in sovereign CDS spreads. For example, the spread for Greece ranges from 17.7 basis points to 11,310.0 basis points during the sample period. Table 2 provides similar information for the liquidity measures used in the study. The largest average transaction costs (bid-ask spread) are observed in Cyprus (20.1%), Finland (14.8%) and Chile (12.5%) with the lowest in Brazil (2.3%), Mexico (2.8%), South Africa and Turkey (both 2.9%). The largest weekly SCDS volume is observed in Italy (USD 23.2 billion), Spain (USD 14.9 billion), Germany (USD 14.1 billion) and Brazil (USD 13.6 billion), while the countries with the lowest volumes are Estonia, Chile (both USD 0.5 billion) and Vietnam (USD 0.6 billion). Some distortions in the data are observed, for example, bid-ask spreads are sometimes negative,

but these observations are not frequent in the sample.4_{Standard deviations are relatively lower in}

the credit swap volumes sample.

5. Similarities between sovereign CDS spreads

In this section, a principal components analysis (PCA) is applied to determine whether SCDSs exhibit a similar degree of commonality. As an input for the analysis, 43 times series of logarithmic rates of return of the SCDS premia are used. The sample is balanced in that each series consists of

886 observations beginning in September 2008. As indicated by the correlation matrix,5_pairwise

correlations vary across countries, which suggests that different sovereigns may have similar credit risk profiles conditional on their geographical, economic, cultural or historical similarities. The lowest pairwise correlation is observed between Israel and Vietnam (11%), while the highest is between Brazil and Colombia (96%). The strongest correlation patterns are found within the regions: Bulgaria and Romania (84%), Korea and Philippines (80%) or Hungary and Poland (79%). It must be stressed, however, that the signs of all pairwise correlations are positive and the average value is 43%. Hence, sovereign spreads tend to display similar dynamics.

Table 3 contains the results of the PCA for the period September 2008 to January 2012. Again, a strong resemblance in the performance of sovereign CDS spreads is found. In particular, the first component explains 46% of the variation in premia. In addition, the first three components explain nearly 60% of the variation over the entire sample period. Taking into account the fact

that the sample consists of both low and high risk countries,6_{it is consistent with the hypothesis}

of economic catastrophe risk embedded in the CDS premia, advocated by Bernd and Obreja (2010). Alternatively, it may exacerbate a feature of the CDS market, according to which the market is driven by a limited number of traders, as noted by Duquerroy, Gex and Gauthier (2009).

4 _{In fact, they constitute half a percent of the bid-ask spread sample. Also, only average measures are used, controlling} for the possible influence of negative ask spreads. The calculations using adjusted samples (without negative bid--ask spreads) do not change the results of the study.

5_{The correlation matrix for 43 sovereign CDS spreads is very large and therefore available upon request.}

6_{E.g. Germany is a low risk, high investment grade sovereign with AAA rating, while Greece is a high risk, low or even} non-investment grade sovereign. Following a series of downgrades by major rating agencies, Greece gradually lost its investment grade rating in late 2010.

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Loadings of the first component support these results. Figure 1 shows that the first component consists of a roughly uniform weighting of credit spreads for most of the sovereigns. It is also positive for all of the countries in the sample. On the other hand, the second component places substantial positive weight on members of the euro area. The third component is heavily positively weighted towards Asian countries and heavily negatively weighted towards Latin American countries at the same time. The PCA therefore clearly suggests that geographical and economic factors might play a significant role in determining changes in sovereign spreads. Strong regional linkages justify clustering the sovereign entities in the subsequent analysis into the following regions: the Eurozone, Asia, EMEA and Latin America with the three last regions being usual market convention for grouping emerging market economies. This clustering is consistent with the financial market agents’ approach to specifying regional divisions. The agents often analyse a market from the perspective of its regional peers, which display similar economic patterns (e.g. similar growth perspective, economy structure or market organisation). Also, many investment decisions, including fund allocations, are made solely on the basis of geographical distance of two or more markets. To sum up, a significant intra-regional spillovers are expected upon employing this approach to clustering subjects of the study.

6. Spillovers and contagion between SCDS spreads: the role of liquidity

In this section VAR models are estimated on the four sets of SCDS premia referencing countries constituting pre-defined regions. Next, FEVDs are performed to obtain estimates of the SI.

The chosen models for the SCDS spread returns are first-order VAR models.7_{However, as shown}

by Diebold and Yilmaz (2009), the proper order of the VAR models is of secondary importance. Different orders do not change the overall results in terms of spillover patterns and dynamics, which is also true for the rolling window analysis. I compute FEVDs at a 5-day horizon, which corresponds to one business week. It is sufficient to capture the horizon at which spillover across markets occurs.

Spillover indices for the Eurozone, Asia, EMEA and Latin America regions are presented in Tables 4−7. The analysis is performed on the full samples of September 2008 – January 2012 in the case of the Eurozone and EMEA and January 2008 – January 2012 in the case of Asia and Latin America. Spillover indices are reported in the lower right corner of each of the spillover tables. For example, in Table 4 one can see that the estimated contribution to the forecast error variance of Portugal coming from changes into Spain, equals 12.6%. The off-diagonal column sums (labelled Contribution to others) and row sums (labelled Contribution from others) are the “to” and “from” directional spillovers. In this context, SI are approximately the off-diagonal column sums (or row sums) relative to the column sums including diagonals (or row sums including diagonals), expressed as a percentage.8_{Therefore, the spillover tables provide an approximate input-output}

decomposition of the total SI.

7_{I follow the indications of information criteria (both Schwarz and Hannan-Quinn) to select the optimal lag length.} 8_{As noted by Diebold and Yilmaz (2012), if Cholesky ordering was used in the variance decomposition procedure, the}

spillover indices would be exactly the off-diagonal column sums (or row sums) relative to the column sums including diagonals (or row sums including diagonals).