Sovereign - Bank Default Risk Linkages During the Greek Financial Crisis and the Role of the Italian Debt

The Greek crisis has brought to light the strong nexus between the credit risks of European banks and their sovereign. We study this phenomenon in Germany, France, Italy and Spain by estimating the conditional correlations between sovereign and bank CDS bond spreads over the period 2006-2015. Trivariate time-varying regime switching correlation analyses, such as the STCC-GARCH and DSTCC-GARCH, are implemented to associate causally the state shifts to the dynamics of the so-called “transition variables”. We find evidence of significant changes in the correlation structures due to the evolution of both the Greek and Italian crises.


Introduction
We focus on the time varying correlation between the credit default swap (CDS) spreads of the bonds of major international banks and of sovereign issuers over the period 2006-2015. From here onwards, we use the term nexus to define the link between the default risk of a sovereign issuer and the default risk of banks or the reverse. Acharya et al. (2015) and De Bruyckere et al. (2013) analyze the feedback loops between sovereign risk and bank risk. The direction of causality can run from bank to sovereign risk in countries with sound public finances and weak banking sector or the other way around, i.e. from sovereign to banks, when an over-indebted public sector jeopardizes the solvency of domestic banks. Gennaioli et al. (2014) investigate the repercussions of a sovereign debt crisis on the banking system and on the real economy via the banks' holdings of sovereign debt (assets side).
Indeed, the unsustainability of public debt affects sovereign creditworthiness and, depending on the exposure of banks' portfolios to government loans, bank's balance sheets. The overall effects, i.e. the strength of the nexus, will depend on the degree of portfolio diversification. (Note 1) It is noteworthy that, in response to the Lehman crisis, governments often provided explicit guarantees to bank bond issuers in order to restore transactions on the wholesale funding market (liabilities side). Recently, Leonello (2018) shows that guarantees link banks and sovereign stability even in absence of banks sovereign's exposure and that under certain conditions a larger size of the guarantee can be beneficial to the nexus as it enhances financial stability.
As is well known a sovereign downgrade will increase the cost of funding, which in turn will affect credit availability and economic growth, determining spillovers on credit quality and thus raising the default probability of banks (Davies andNg, 2011, Panetta, 2011).
Both sides can be at work at the same time. Podstawski and Velinov (2018) find heterogenous and time varying effects of bank exposure on sovereign credit risk in the Euro area. (Note 2) A destabilizing impact -running from bank exposure to sovereign default risk -characterizes Spain, Italy and Portugal, especially during phases of financial turmoil, whereas a stabilizing effect characterizes the EMU core countries. Gomez-Puig et al. (2018), using three different interconnection measures, find evidence of bidirectional linkages between country-level banking and sovereign risk indicators for Spain and Italy during the European debt crisis. Similarly, Buchholz and Tonzer (2016), study the EU sovereign credit risks interconnections and find that the correlation/contagion structure varies across time and countries, requiring therefore a dynamic approach.
Since the inception of the Greek crisis in 2010, several papers have attempted to address the issue of contagion from the Greek sovereign bonds to the European sovereign markets and national financial systems. This kind of contagion is far from undisputed, however, as the mechanism behind is hazy. Mink and De Haan (2016), for example, find that news about Greek public finance, per se, do not generate abnormal bank stock returns, with the exception of Portuguese, Irish and Spanish banks, while news related to the likelihood of a bail-out affect both the European bank abnormal returns and the sovereign bond prices of Portugal, Ireland and Spain. Similarly, Buchel (2013), analyzing the impact of communications on rescue of indebted countries on PIIGS' CDS and bond yield spreads, find that statements from German, French, EU officials and ECB governing members exert an immediate (asymmetric) influence.
An insignificant economic effect of Greek CDS spread changes on the stock returns of banks of other countries is also detected by Beltratti and Stulz (2017), who find that shocks from larger countries or multiple peripheral countries, instead, have a substantial impact.
According to their analysis the relation between contagion and the holdings of peripheral country bonds by banks from other countries is weak. Similarly, Pradigis et al. (2015), using a corrected Dynamic Conditional Correlation model, and Philippas and Siriopoulos (2013), using a regime switching model and a time varying copula, do not find an overall contagion effect from the Greek crisis to other countries.
Recently, Koutmos (2018) analyzes CDS spreads in the EU to test for contagion and finds not only a heterogenous and time-varying pattern of interdependence but also that the role of Greece, as catalyst for the shocks cannot be statistically proved. (Note 3) About the nature of the Greek contagion, Gomez-Puig and Sosvilla-Rivero (2016) detect both pure and fundamentals-based bond yield spread co-movements. Arghyrou and Kontonikas (2012), instead, find that evidence of contagion during the European sovereign crisis is restricted mostly to the peripheral countries.
Using a conditional value-at-risk (CoVaR) measure based on copulas and vine copulas, Roboredo and Ugolini (2015) investigate the systemic risk implications of a potential Greek debt default before and after the onset of the financial turmoil. Sovereign debt was found to imply a homogeneous positive systemic risk for domestic financial systems across Europe before the crisis. With the onset of the Greek crisis, however, the systemic impact of sovereign debt increased for countries like Greece, Italy and Portugal, and remained stable or even decreased in other countries.
R-vine copulas have been used by Zhang et al. (2018) to explore the tail dependence between financial stress indicators (including an index of vulnerability of the public and financial sector) of 11 European countries. They find that Spain, Italy, Belgium and France are the most interconnected.
Our investigation deals with the strength and the nature of the nexus between domestic sovereign and bank bond CDS spreads over the decade 2006-2015. The within country analysis is complemented by cross country (contagion) considerations via the transition variables. The domestic nexus correlation structure varies, at first, according to the dynamics of the Greek-German sovereign bond spread, and later onin the case of Germany and France -also in reaction to the behavior of the Italian-German sovereign bond spread. Analyses of the nexus based on standard techniques, which posit a priori causality linkages, are likely to be distorted during crises since the direction of causality may vary.
We implement thus a correlation analysis procedure and -in order to avoid biases due to volatility shifts (see Forbes and Rigobon, 2002, among many others) -we use a dynamic conditional correlation approach: the smooth transmission constant correlation STCC-GARCH of Berben and Jansen (2005) and Silvennoinen and Terӓsvirta (2005) and its two transition functions extension, the DSTCC-GARCH by Silvennoinen and Terӓsvirta (2009). These techniques -along with a preliminary probit analysis of the factors that bring about shifts in DCC-GARCH conditional correlations -allow us to identify two transition variables that determine changes in the correlation regime status. as a significant increase in the co-movement of the rates of return of the sovereign and bank bonds CDS spreads, in the following ways. First, by focusing on correlation analysis we avoid the indeterminacy of ad hoc causality assumptions. Second, the use of a complex trivariate STCC-GARCH methodology allows to by-pass most of the shortcomings that affect the effectiveness of previous empirical investigations. Indeed, we upgrade the heteroskedasticity consistent procedure of Forbes and Rigobon (2002) by avoiding any ad hoc assumption on the timing of the crisis and the subsequent sub-sample selection bias. Third, we date when correlations among returns increase and, in this way, identify contagion events more precisely. Fourth, the transition variables help us to detect which factor brings about contagion. We avoid in this way the causal indeterminacy of the extreme events/copula contagion analyses. Finally, we assess both the minimal dimension of the shocks required to generate a reaction of CDS investors (and thus a shift in the nexus) and the speed of their reaction, which reflects the relative heterogeneity of their expectations.
The paper is structured as follows. Section 2 presents an overview of the empirical methodology. In Section 3 we focus on the relation between the Greek financial turmoil and the domestic nexuses whereas in Section 4, considering a larger perspective, we include in the analysis the concerns about the sustainability of the Italian public debt as a risk magnifying factor. Finally, Section 5 concludes the paper.

Trivariate Parameterizations of Time-Varying Correlations via STCC-GARCH (1, 1) and DSTCC-GARCH (1, 1)
In a time-varying context, conditional correlations are usually estimated with the help of the DCC-GARCH of Engle (1992). The STCC-GARCH implemented in this paper extends this procedure by linking the shifts of the correlations to specific explanatory transition variables.
Consider a 3x1 vector of CDS daily rates of change, with the following conditional mean dynamics = 01 + ∑ is the rate of change of a sovereign bond CDS, where C is a country index, and , = 1, 2, is the rate of change of a bank bond CDS, where denotes a domestic bank.
is a 3x1 vector of residuals ( 1 2 3 )′ such that where −1 is the relevant information set.
The conditional variance matrix of the residuals has the following time-varying structure Bollerslev (1990) posits in the CCC-GARCH parameterization that the conditional variance of each residual time series , = 1, … , 3, follows a GARCH(1,1) process and that the International Journal of Accounting and Financial Reporting ISSN 2162-3082 2018 correlations are constant. The conditional second moments are thus modeled as Denoting as a 3x3 diagonal matrix with diagonal elements given by (ℎ ) 0.5 and as a constant 3x3 correlation matrix, the conditional covariance matrix reads as = and can be rewritten in extended form as Berben and Jansen (2005) and Silvennoinen and Terӓsvirta (2005) modify the CCC-GARCH model and introduce smoothly time-varying conditional correlations. The latter are assumed to switch over time from one (extreme) constant correlation regime to the other according to the distance from a threshold value of a transition variable. The shifts in turn depend on the dynamics of a continuous logistic function.
In this case, at time t the 3x3 conditional correlation matrix can be written as where 1 and 2 are assumed to be constant 3x3 positive definite correlation matrices. The logistic function is defined as − is a transition variable with delay d. The coefficient γ and the threshold c determine, respectively, the speed of adjustment and the location of the transition between the two regimes.
is, indeed, a mixture of the two correlation matrices 1 and 2 . When ( − − ) is large and positive, is close to 1 and nears 2 , and when ( − − ) is large and negative, is close to 0, and nears 1 .
In the DSTCC-GARCH(1,1) model the conditional correlations vary according to two transition variables. They are parameterized as follows with, as transition functions, the logistic functions International Journal of Accounting and Financial Reporting ISSN 2162-3082 2018 For each k (k = 1, 2), − are transition variables with delay ,. The coefficients and the thresholds determine, respectively, the speed of adjustment and the location of the transitions between regimes.

The Impact of the Greek Financial Turmoil on Domestic Nexuses
We use a data set of daily observations on sovereign and banks CDS 5 year spreads (the corresponding contract being the most liquid of the CDS market) and on the Greek and Italian sovereign spread, i.e. the differential between the yields of the Greek and Italian 10 year sovereign bonds and of the German 10 year bund. The latter are our selected transition variables.
The panel consists of four large European countries, Germany, France, Italy and Spain, which accounted, in recent years, for 75% of the GDP of the EMU. Their net sovereign debt to GDP ratios differ significantly and rangein 2015 -from 119% in the case of Italy, to 89% for France, 65% for Spain and to 48% in the case of Germany. As we shall see the order of these ratios coincides with the ranking of the severity of the estimated impact of the Greek financial crisis on the national banks -sovereign nexuses.
The graphs of Figure 1 are highly informative. CDS premia vary substantially over the sample period and reflect the shifts in the probabilities of bond potential defaults that are priced by the market. The series in level are not stationary. (Note 4) In France and Germany sovereigns are perceived as substantially less risky than banks whereas in Spain and, especially in Italy, the CDS levels are alike. (Note 5) The sheer dimension of the financial disequilibria hinders, in these countries, any public intervention in favor of distressed banks. The co-movements between CDS spreads on sovereign and bank bonds too change over time, and justify the stochastic correlation approach adopted hereafter.
The statistics set out in Table 1 deal with the rates of change of the CDS spreads on sovereign bonds and on bonds issued by eight major banks, two each for Germany, France, Italy and Spain. They reflect the turbulence of the sample period, since all the time series are strongly serially correlated and are affected by nonlinearities.
Indeed, the BDS test statistics of Brock et al. (1987) strongly reject, with embedding dimension 2, the null hypothesis that the rates of return, filtered for first order serial dependence, are iid. (Analogous results are obtained for the unfiltered returns, and with embedding dimensions varying from 2 to 6.) The standard tests, moreover, suggest that their distributions are non-normal (mostly leptokurtic) and conditionally heteroskedastic. An analysis of the co-movement of these time series requires, therefore, the use of a multivariate GARCH procedure such as the STCC-GARCH(1,1).
In order to corroborate the selection of the transition variables, we perform a probit analysis of first step estimates of DCC-GARCH parameterizations of the conditional correlations of International Journal of Accounting and Financial Reporting ISSN 2162-3082 2018 each trivariate system. In every relationship, the dependent variable takes value 1, if the magnitude of the conditional correlation at time t is larger than its average value, and 0 otherwise. The probit specification includes, besides a Lehman dummy, two additional dummies obtained from abnormal shifts of the selected transition variables. The empirical evidence suggests that they have a clear-cut and highly significant impact. (Note 6) Figure 1. CDS spreads International Journal of Accounting and Financial Reporting ISSN 2162-3082 2018  GGsp: daily change in the spread between the yields of Greek and German 10 years bonds; ∆ + : positive daily change in the spread between the yields of Greek and German 10 years bonds; ∆ + : positive daily change in the spread between the yields of Italian and German 10 years bonds; Probability values in square brackets; Skew: Skewness; Kurt: Excess Kurtosis; JB: Jarque-Bera normality test; AR(n): Ljung-Box test statistic for n-th order serial correlation of the time series; ARCH(n): Ljung-Box test statistic for n-th order serial correlation of the squared time series; BDS(k): z-test statistic, with embedding dimension k and Є value =.9, of the null that the time series, filtered for a first order autoregressive structure, is independently and identically distributed.   ISSN 2162-3082 2018 test; ARCH(n): Ljung-Box test statistic for n-th order serial correlation of the squared time series; BDS(k): z-test statistic, with embedding dimension k and and Є value =.9, of the null that the standardized residuals are independently and identically distributed. Table 2 presents the conditional correlations and the smooth transition parameters of equations (7) and (8), where the transition variable is the Greek-German sovereign 10 year bond spread first difference. Strongly significant from a statistical point of view, they have the appropriate size and the expected sign. (Note 7) The usual misspecification tests performed using the standardized residuals, suggest that the quality of fit is adequate (E( ) = 0, E( 2 ) = 1 and conditionally homoskedastic and serially uncorrelated, for = 1, … , 3).
Indeed, the BDS(2) and BDS(3) test statistics, resulting from BDS tests with embedding dimensions 2 and 3, fail to reject (with one exception only) the null that the standardized residuals are iid. The nonlinearities detected in the return time series of Table 1 are filtered away by the model. However, since the Jarque-Bera statistics systematically reject the null of normality, we compute the estimates using the robust QMLE procedure developed by Bollerslev and Wooldridge (1992). Note: For each country, the sovereign-bank bonds CDS correlations are simple averages of the correlations between the rates of change of the spreads of sovereign bonds CDS and the rates of change of the spreads of the CDS of the bonds issued by the corresponding national banks.
To extract additional useful insights, in Table 3 we label as "contagious" the regime in which the transition function is larger than 0.5 and the conditional correlation -the nexus -is closer to its high extreme value 2 (regime 2) than to its low extreme value 1 (regime 1). The relative number of days spent in each regime and the relative dimension of the corresponding conditional correlations differ among countries.
In Germany and France, the number of days in the "no contagion" regime is from 6 to 7 times larger than the number of days in the "contagion" regime. In the latter, the size of the nexus rises by 65 percent in Germany and by 90 percent in France. In the peripheral countries of the sample, the results are less homogeneous.
The number of days in the "no contagion" regime is only 3 times larger than the number of days in the "contagion" one in Italy and 24 times larger in Spain. In the same way, the nexus in Italy increases by 60 percent in the "contagion" regime, in line with the increases in the core countries of the sample. This is not the case in Spain, where the rise in the nexus is huge (larger than 90 percent). It is noteworthy that the estimates repeated over the Greek-crisis subsample are qualitatively similar to the full sample ones, as the contagion phenomena turn out to occur mostly during the Greek financial turmoil.
Additional information is provided by the graphs of Figure 2, where the nexuses are related to changes in the differences between Greek and German bond yields (the values of the selected transition variable). The shape of the curves depends upon the values of the coefficient gamma (speed of adjustment variable) and c (threshold parameter) estimates in Table 2. (Note 8) In Germany and France we detect a similar market psychology, since the dynamics of the nexuses (i.e. the conditional correlations between banks and sovereign bond CDS) displays a strong similarity.
This is not the case for Spain and Italy. Agents' reactions are strong and homogenous in Italy whereas they are slow and highly heterogeneous in Spain. In Italy, the nexuses fluctuate frequently and abruptly from one regime to the other, while in Spain they change more slowly and tend to be persistent.
In Italy traders have a common risk perception and react to small variations of the Greek German yield spread, in Spain an opposite behavior holds; the dimension of the public (rather than of banks') debt seems to be the discriminating factor in the risk assessment of bond traders.
The larger the stock of sovereign debt the faster and more homogeneous is the positive shift in the pricing of risk and the smaller the absolute value of the Greek-German sovereign risk differential that triggers it. The differing patterns of reaction, detected in Figure 2, reveal that the focus of the markets is on sovereign financial equilibrium, in line with the major policy recommendations of the European institutions.   Figure 2. Speed/homogeneity of the reaction of the nexus to shifts of the Greek-German yield differential

The Role of the Italian Public Debt
On the basis of the above considerations and taking into account the relevance of the systemic risk channel pointed out by Beltratti and Stultz (2017), who notice that holdings of peripheral country bonds by core banks may not be a statistically and economically significant contagion channel, we extend our analysis introducing a second transition variable, the positive changes of the BTP Bund sovereign bond spread. (Note 9) To give substance to the Italian channel hypothesis, we compute -using data from the BIS quarterly review -the share of the outstanding claims on Greek and Italian official sectors by German and French banks with respect to their total claims on the foreign official sector.
The findings, set out in Table 4, support the view that, after 2011, Greece should not be International Journal of Accounting and Financial Reporting ISSN 2162-3082 2018 viewed as the unique source of contagion. The share of the Italian official sector claims reported by French and German banks seems to have magnified the effect of the Greek turmoil; the sheer size of the Italian public debt being able to transform tensions in the Italian sovereign sector into a threat to the survival of the euro area. Note: Raw data are obtained from the BIS quarterly report statistics.
In order to account for the role of an additional highly indebted peripheral country, such as Italy, the STCC-GARCH(1,1) model has been extended by adding a second transition variable, the daily positive changes in the difference between the yields of the Italian 10 year BTP and of the German 10 year Bund. The DSTCC-GARCH(1,1) model parameterized by equations (9), (10) and (11) of Section 2 is therefore estimated, where 1 and 2 are, respectively, the positive changes in the differentials between the Greek-German and Italian-German 10 year sovereign bonds yields, ∆ + and ∆ + .
The conditional correlations and the smooth transition parameters are set out in Table 5. The estimates are significant from a statistical point of view and have the appropriate size and the expected sign. (Note 10) The usual misspecification tests, performed using the standardized residuals, suggest that the quality of fit is adequate and the BDS(2) and BDS(3) tests fail to reject (with one exception only) the null that the standardized residuals are iid. The nonlinearities of the return time series of Table 1 are filtered away by the DSTCC-GARCH(1,1) model. The estimates are performed using the robust QMLE procedure developed by Bollerslev and Wooldridge (1992), since the Jarque-Bera statistics systematically reject the null of normality. ISSN 2162-3082 2018 Table 5. System 2 = (1 − 1 ) 1 + 1 2 , = (1 − 2 ) 1 + 2 2 k = 1,2 (14) ; Probability values in square brackets; JB: Jarque-Bera normality test; ARCH(n): Ljung-Box test statistic for n-th order serial correlation of the squared time series; BDS(k): z-test statistic, with embedding dimension k and and Є value =.9, of the null that the standardized residuals are independently and identically distributed.

International Journal of Accounting and Financial Reporting
The interaction of regimes 1 and 2 for the Greek-German and Italian-German transition variables produces the correlation tree sketched below.
The positive shifts of the Greek-German yield differential determine two regimes according to the positive changes of the sovereign spread being below or above a threshold value c1, each of which, in turn, can be associated with two regimes generated by positive shifts of the Italian-German yield differentials. We obtain in this way the four regime paths above, where the transitions from one regime to the other are modeled by smooth transmission mechanisms.
A perusal of the estimates of Table 5 shows that when both transition variables are in regime 1, the nexuses ( 12 11 , 13 11 ) are quite small. They increase substantially when the transition  ISSN 2162-3082 2018 variable associated with the Italian debt is in regime 2 ( 12 12 , 13 12 ). The correlations of Table 2 ( 12 1 , 13 1 ), for Germany and France, thus, are likely to be the by-product of a combination of shocks, which have to be disentangled. We find an analogous result when the Greek-German bonds yield differential is in regime 2. On average, the association with a contagion regime in Italy determines a significant increase in the nexuses ( 12 22 , 13 22 ) both in Germany and France with respect to 12 21 and 13 21 . Here too, the size of the single transition variable correlations estimates of Table 2 ( 12 2 , 13 2 ) seems to be due to multiple causes.
The seventy days centered moving averages of the conditional correlations obtained from historical simulations of the estimates of the STCC and DSTCC -GARCH models of Tables 2 and 5, set out in Figure 3, support the hypothesis of an amplifying effect of the Italian financial stress. In each graph, the blue lineassociated with the DSTCC-GARCH modellies above the black STCC-GARCH line whenever the Italian-German yield differential is large and below it whenever this differential is small even if the absolute value of the shifts of the latter are much smaller than those of the correspond Greek-German bond yield differential. (Note 11) As for the estimated speed of convergence, 1 is always lower than 2 , which suggests that the Italian default risk is likely to trigger a much faster reaction of market agents. As for the threshold values c, they are not comparable since in Table 5 they refer only to positive changes of the Greek and Italian sovereign bond yields spread whereas in Table 2 both positive and negative changes are considered.

Germany
International Journal of Accounting and Financial Reporting ISSN 2162-3082 2018 France Figure 3. 70 days MA of the STCC and DSTCC GARCH conditional correlations The results suggest that the two transition variables matter in both core countries, since concomitant positive changes of sovereign bond spreads determine a significant rise in the conditional correlations. In France, however, the behavior of the estimated correlation coefficient through regimes suggests that the role of the Italian debt be dominant, a result in line with the size of the outstanding claims of French banks towards Italian official counterparties (see Table 4).

Conclusions
The interconnections between sovereign and banks CDS spreads are highly informative and provide new insights on the financial contagion triggered by the Greek crises. Using the STCC-GARCH methodology we find similar patterns of behavior in core countries (Germany and France) and strong dissimilarities in the so called peripheral ones (Italy and Spain). In the peripheral countries, the main driver of contagion is the perceived default risk of the sovereign issuer, which is linked to the size of the outstanding public debt for a well know debt sustainability issue. Actually, the Italian banks are hit by the Greek turmoil more severely than the Spanish ones.
We extend, therefore, the model introducing a second transition variable related to the Italian public debt. We find that core countries nexuses are affected and increase in a significant way whenever the Italian-German 10 year bond spread change rises above a regime threshold. This highlights the key role of the Italian sovereign debt on the tenability of the EMU project. However, it is the concomitant occurrence of tensions on the Italian and Greek sovereign bond markets that matters. Indeed, positive changes of the Italian spread exert a magnifying effect on the nexuses of core countries, especially in the case of France. changes in the Greek German bond yields spread) and the threshold c from zero. We report the former on the vertical axis and the latter on the horizontal one. For the sake of clarity, we have interpolated the scatter plots using local first order polynomial regressions with bandwidth based on the nearest neighbor approach. The local regressions are performed on a sub sample selected according to the Cleveland (1993) procedure and involves about 100 evaluation points. Tricube weights are used in the weighted regressions aimed at minimizing the weighted sum of squared residuals. The bandwidth span of each local regression is set to 0.3. Note 9. Beltratti and Stultz (Table 2, 2017), find that core country banks' net holding of bonds issued by Greece accounted for 4.99% of banks' market capitalization in 2010 (5.88% if normalized by banks' tangible equity). A year later these percentages were respectively 5.89% and 2.97%. As for bonds issued by Italy, the percentages were 18.45% and 19.69% in 2010, whereas in 2011 the figures rose to 27.15% in terms of market capitalization and fell to 9.19% in terms of tangible equity. The figures for Greece are quite small if compared to the severe turmoil generated by the so called "Greek crisis".
Note 10. The full set of mean and variance equations parameters of the GARCH estimates are not reported here for the sake of parsimony and are available from the authors upon request.