“Unveiling trading patterns: iTraxx Europe financials from the great financial crisis to ECB monetary easing”

Financial stability is a statutory concern of the European Central Bank. Spreads of bank credit default swaps (CDS) indices are a reference for financial stability, but the literature is scarce in this respect. This paper poses the novel research question of which characteristics of investors in these derivatives are implied by the volatility behavior of the returns of financial CDS indices. Daily spread returns for the 5-year maturity iTraxx Europe Financials (subordinated and senior), for the period between June 2004 and March 2015, are used to estimate a GJR-M model with Student t innovations, and two MGARCH models (one with constant and the other with dynamic conditional correlations). The results show that investors in the index referring to subordinated debt are risk averse (risk premium estimate of 0.688) and liable to leverage effects, while investors in the index for senior debt do not have such characteristics. The degrees of freedom of the Student t innovations are estimated to be 4 for both indices, implying that returns have distributions with very fat tails. Population excess kurtosis diverges to infinity. The results show that the conditional correlation between the indices is dynamic. Although correlations vary widely, most of that variation occurs before the Euro Area crisis. It is concluded that the inclusion of both indices in a portfolio would be misadvised for bear markets with distressed financial entities: the correlations are always positive, above 0.75 since 2010. Moreover, both indices prove to be sensitive to the varying surrounding conditions as investors share market sentiments.


INTRODUCTION 1
Credit Default Swaps (CDS) are credit derivatives concerning a single reference entity.The protection buyer pays periodic coupons during the lifetime of the agreement, while the seller makes no payments unless a credit event occurs.Multi-name CDS (CDS indices) provide protection against credit events in any of a list of reference single-name CDS.The choice of these varies with different criteria (liquidity, business sector, geographical location, etc.).
Bank credit default swaps (CDS) 1 have been at the core of the debate surrounding the Great Financial Crisis (GFC) and the Euro Area (EA) sovereign debt crisis.In the latter, the nexus between financial instability and the sovereign crisis is well established in the literature, particularly in the bank bailout period.The concern with financial stability was such that, from 2012 onwards, the European Central Bank (ECB) has changed monetary policy radically, from inflation targeting to quantitative easing.Notwithstanding, although bank CDS indices are a benchmark for financial stability, and in spite of some studies trying to focus on them to assess policy measures in highly volatile periods, the literature concerning the characteristics and motivations of the behavior of investors in these synthetic Over-The-Counter (OTC) derivatives is scarce.This paper seeks to fill that gap.Its research motif is to understand the behavior of the volatility of returns from these in-dices, retrieving the investors' behavioral parameters from such volatility models.The aim is to achieve a better understanding of the characteristics of these investors.This is done for both subordinated and senior debt bank indices, as subordinated debt is deemed to be quite relevant in the EA.In fact, as it shall be shown, the behavior of investors differs, with respect to some fundamental reactions, between these two segments of the bank multi-name CDS market.Nonetheless, it is similar in other behavioral features, namely the roles of shared market sentiments and trading momentum. 2 The CDX refers to North America.3 The iTraxx Europe Financials index includes presently 30 institutions, most of which are bank groups, although there are some insurance providers as well.

LITERATURE REVIEW AND HYPOTHESES
CDS indices emerged in 2002, when J. P. Morgan launched the synthetic indices JECI and Hydi, while Morgan Stanley launched the TRACERS index (Markit, 2019).With the two firms merging in 2003, the consolidated TRAC-X indices have appeared.The TRAC-X consisted of US single names only.IHS Markit® has acquired both indices, now owning iTraxx and CDX 2 , as well as other families of indices (Markit, 2019).It should be noticed that Markit® may vary the constituents of an index (e.g., iTraxx Financials) 3 , every six months, depending mainly on the rating of the underlying reference entities.As in single name CDS, a spread increase in the index indicates deteriorating credit conditions (Markit, 2021).
The relevance of looking both at the CDS index for banks subordinated debt and at the index for banks senior debt should be clear, when the concern is financial stability.The nexus between the EA sovereign debt crisis and banks default likelihood, as well as the connectedness between bank CDS spreads and sovereign CDS spreads, are well documented in the finance literature (see, inter alia, Alter & Schüller, 2012).In fact, the addition of government-initiated bail-ins to the credit events list (ISDA, 2014) was the result of an attempt to solve the EA debt crisis (Oliveira & Santos, 2015).In short, the EA crisis comprised a bail outs period, in which banks were deemed too big to fail, thus ultimately being saved by governments.However, bailing out banks increased the pressure over the financially distressed EA periphery, rising sovereign CDS.Given the EA banks' high exposure to public debt (Covi & Eydam, 2020), there was an increased likelihood of bank defaults after a public bail out, with a new surge in banks CDS spreads.Covi and Eydam (2020) estimate the two-way effect between sovereign and bank CDS to be of a non-negligible magnitude: an increase in sovereign CDS of 10% would lead to an increase of 0. Katsompoxakis (2022) seeks to assess the relevance of the monetary policy shift to the nexus between EA sovereign CDS spreads and bank CDS spreads.He concludes that the radical change to quantitative easing, that the ECB has adopted from 2012 onwards, has succeeded in increasing financial stability, since the nexus between sovereign and bank spreads appears to have been broken.The author also points out that bank CDS spreads do not appear to be reacting to the deteriorating government deficits 4 .However, the paper does leave the question of which would be the reaction of the bank CDS spreads to a possible reversal in the ECB monetary policy 5 .The analysis in Katsompoxakis (2022) does not make use of CDS indices (either financial or sovereign).
As In conclusion, the research question addressed in this paper seeks to fill such a gap in the literature, and it is clearly defined: Which characteristics of investors in these derivatives are implied by the volatility behavior of the returns of financial CDS indices?
In particular, the paper shall address this goal through the following research hypotheses: H 1 : There exists volatility clustering in the returns of financial CDS indices, for both subordinated and senior debt.
The conditional volatility of both series of returns exhibits long memory.
H 3 : Investors in financial CDS indices are risk averse.Therefore, they demand a risk premium in the returns.

4
These rose in many EA countries, well above the 3% maximum for the deficit to the GDP ratio, during the pandemic years.The average EA government deficit was 7.2% in 2020 and 5.1% in 2021 (Eurostat, 2021(Eurostat, , 2022)).5 We are beginning to observe that policy reversal (Financial Times, 2022b), as the ECB rose its interest rate by half a percentage point in June 2022.
H 4 : Investors in financial CDS indices are prone to react to negative news in a way that amplifies the variance, in comparison to their reaction to positive news, which will have a smaller variance.
H 5 : Given the heterogeneous sample period, one expects the distribution of returns to be non-normal, with fat tails.
H 6 : The correlation between the two series of returns is time varying.

METHODS
This paper uses two series of spreads: that for the 5-year maturity iTraxx for subordinated debt of European financial institutions, and that for the corresponding iTraxx for senior debt of such financial institutions.Firstly, the daily returns of each spread will be modelled independently, using a specification that allows for non-normal innovations, volatility clustering, long memory, risk aversion and leverage effects (as defined in Glosten et al., 1993).As such, for each series of returns the GARCH (1,1)_t-M model shall be estimated, with the following equations defining the mean and the conditional variance.Equation (1) refers to the returns and is known as the mean equation, and equation (2) refers to the conditional variance of the returns and is known as the conditional volatility equation: It is assumed that i = 1, 2. That is, there will be an equation for the mean and one equation for the conditional variance, for i = 1, referring to a GARCH (1,1)_t-M for the returns of the CDS index defined for subordinated debt of financial reference entities.There will also be a mean and a conditional variance equation for the returns of the CDS index referring to senior debt, in which case i = 2.
Banks and Bank Systems, Volume 17, Issue 3, 2022 http://dx.doi.org/10.21511/bbs.17(3).2022.16 In equations ( 1) and (2): and t(v i ) is a Student t distribution with v i degrees of freedom, where v i is a parameter to be estimated.The model above is also known as the GJR-M specification with t(v i ) distributed random errors.Most of the behavioral hypotheses outlined in the previous section will be answered from testing certain parameters in the specification above.
Notwithstanding, multivariate joint models for the returns and conditional volatilities of both series shall also be estimated: a multivariate GARCH with dynamic conditional correlations (MGARCH-DCC) as suggested by Engle (2002), and a multivariate GARCH with constant conditional correlations (MGARCH-CCC), suggested by Bollerslev (1990).
The MGARCH-DCC starting point is the definition of a conditional correlation matrix: where J t is a diagonal square matrix, of the form { } 11 11, , , ., Q t is a square matrix of dimensions (k x k), satisfying ( ) 1' , , , , , where ε t is the standardized vector of innovations with elements, Q ̅ is the unconditional covariance matrix of ε t , and θ 1 , θ 2 are nonnegative scalar parameters satisfying 0 < θ 1 + θ 2 < 1. J t is a normalization matrix to guarantee that the correlation matrix R t exists and is properly defined.
The MGARCH-DCC is a common choice when modelling jointly two or more series of returns.Tsay (2010) discusses other alternatives.It should become clear, from the outline of the hypotheses to be tested, provided in the previous section, that the purpose of such models, in this paper, is solely to compare a time-varying correlations output with that of a model with constant correlations, such as the one developed by Bollerslev (1990), where ρ 21,t = ρ 2,1 .In practice, only one output from the MGARCH-DCC will be relevant for this research: the plot of conditional correlations between returns of the two series.With respect to the MGARCH-CCC, the only relevant estimate is that of the correlation coefficient.As such, it makes no sense to derive the MGARCH-CCC with the detail used above for the MGARCH-DCC.
The plot of the dynamic conditional correlations shall be confronted with the constant correlation estimate obtained, so that conclusions about H 6 are drawn.The plot of the time-varying correlations shall also allow drawing conclusions for portfolios containing these indices, in different sample periods.
The next section shall be concluded by a detailed inspection of the plot of the spreads themselves, from which additional insights on traders' behavior can be gained.
The sample consists of two daily series of spreads for 5-year maturity financial CDS: the iTraxx Europe Financials Sub (for subordinated debt) and the iTraxx Europe Financials Senior (for senior debt).The data comprises the period from the 24 th of June 2004 to the 20 th of March 2015 (2,740 observations).Data was obtained under an academic license directly from the creators and managers of the index: Markit ®.The GJR version of the GARCH_t-M model for each series, as well as the MGARCH models were estimated using the Oxmetrics Professional 8 software.This software uses the BFGS algorithm to estimate the parameters of these models.

RESULTS
The estimation results for equations ( 1) and ( 2), for both indices, are displayed in Table 1.
The first two columns of Table 1 report the estimation results for the subordinated debt CDS index.The third refers to the p-value obtained when conducting an individual significance test on each of the equations' parameters.On the right-hand side of the table, columns 4 and 5 report estimates of the same parameters for the senior debt index.Column 6 presents the p-value obtained when conducting individual significance tests on each parameter, for the series pertaining senior debt.
To test the hypothesis H 0 : α 1 = 0, the p-value for both models is approximately 0. Hence, at a 1% significance level, the p-value is smaller than 0.01.As such, the null hypothesis is rejected, for both subordinated and senior debt.The reasoning with respect to β is very similar.A test, at a significance level of 1%, of the hypothesis H 0 : β = 0, leads to rejection of the null.Table 1 indicates p-value < 0.01 for both series, with respect to this hypothesis.
For the null hypothesis H 0 : c = 0, a p-value of 0.0085 is obtained for the model concerning subordinated debt.Hence, at a significance level of 1%, the null hypothesis is rejected.In fact, the evidence in Table 1 implies that if the conditional variance of returns increases by one, investors will want an average increase in the returns of 0.687778.However, when running the same test on the model for senior debt CDS index, the p-value is 0.1153.The hypothesis 0 : c = 0 cannot be rejected in this model, since, even considering a much higher significance level of 10%, 0.1 < p-value.
For the sample consisting of returns from the subordinated debt bank CDS index, a test of the hypothesis H 0 : γ = 0, at a 10% significance level, rejects the null: p-value = 0.0853.When looking at the right part of table 1 (results for the senior debt sample), the hypothesis H 0 : γ = 0 is not reject-6 The excess kurtosis for a Student t distribution with v degrees of freedom is given by 6/(v-4).Hence, it is not defined for v < 4, and when v converges to 4, the excess kurtosis diverges to infinity (Johnson et al., 1995).
ed.Even at a significance level of 10%, the relevant p-value is 0.777 > 0.1.
In both cases v̂ is such that there is support for a t(4).In fact, the hypothesis H 0 : v = 4 is not rejected.For subordinated debt, the observed test statistic is Given that the test statistic is asymptotically normal N(0; 1), the observed value is inside the non-rejection region with 90% confidence: [-1.96;1.96].
The same is true for senior debt (observed test statistic of -0.3546).
A t(4) has indeed very fat tails.Although variance is defined (since v > 2), population excess kurtosis in a t distribution can only be computed for v > 4 (Johnson et al., 1995).The implication is that excess kurtosis of spread returns diverges to infinity as v → 4, in both cases 6 .
The bivariate MGARCH, both with constant conditional correlations and with dynamic conditional correlations, was estimated.As discussed in the methodology section, this paper is only interested in the constant correlation estimate obtained from the first model, and in the plot of estimated dynamic correlations obtained from the second model.There is no need to report other results.The estimate of a constant conditional correlation is 0.773506 (the sample correlation between the returns of the two indices).When confronting this constant correlation with Figure 1 (the plot of the estimated dynamic correlations), one may argue, along the lines of Tsay (2010), that the CCC as- sumption would be absurd.In fact, Figure 1 shows that the correlation coefficients between returns of the two indices vary widely, taking all possible values in the interval [0,1] during the sample period 7 .
An interesting fact suggested by the plot in Figure 1 is that correlations between returns of the iTraxx Europe Financials, for subordinated debt and for senior debt, vary more widely before the EA crisis.In fact, before 2008 it was possible to observe conditional correlations differing by 0.5 or 0.6, for relatively close days.Indeed, since 2010, the maximum observable difference between correlations was approximately 0.3.Moreover, the plot in Figure 1 clearly suggests the conditional correlation of returns for the two CDS indices is almost always systematically high (above 0.75) from 2010 onwards.not resulting from any hypothesis raised in the previous section, the plot of the spreads of the two indices for the sample period is provided in Figure 2. It clearly shows common patterns in the two indices, with simultaneous, or almost simultaneous, peaks and troughs for all major events in the period.There are common surges in the indices' spreads: from July to September 2007, the year of the crash in the US housing market (on the 20 th of June of 2007 the Bear Sterns investment bank bailed out two of its mortgage backed securities  2 also shows that the index for subordinated debt has always had a higher spread, which was to be expected given the riskier nature of subordinated debt.

DISCUSSION
In this section, the findings of section 3 shall be interpreted in connection with the research hy-Source: Results from Oxmetrics Professional 8.

Figure 1. Dynamic conditional correlations from MGARCH-DCC
potheses raised at the end of section 1, and in relation to the main research question of this paper.It shall also be argued whether such findings were to be expected.A discussion on the reasons for some more intriguing results shall also be provided.
Comparisons with existing literature results will be provided when possible.
The rejection of the null H 0 : α 1 = 0, in the two cases, implying that both returns series have volatility clustering, means that research hypothesis H 1 is confirmed.This was to be expected, since volatility clustering is a stylized fact of most financial returns time series (Tsay, 2010).The same should be said of the confirmation of long memory in both series, resulting from the individual significance of the parameter β.H 2 is also confirmed.
The results obtained with respect to the risk premium, c in equation ( 1), are interesting.The rejection of the null hypothesis related to c implies that the buyers of iTraxx for subordinated debt of European financial institutions have significant risk aversion.In the previous section, it was also shown that in the model for the senior debt returns, the risk premium term is not significant.Contrary to buyers of iTraxx for subordinated bank debt in the EU, the buyers of iTraxx for senior debt do not demand an increase in returns when conditional volatility rises.Hence, they do not exhibit statisti-cally significant risk aversion behavior, when buying this CDS index.Thus, H 3 cannot be validated.
If the conflicting evidence does not allow to confirm hypothesis H 3 it must be said a market behavior has been uncovered.One possible explanation, assuming buyers of iTraxx Financials for subordinated debt, in fact, own subordinated debt from the reference financial institutions, and the same assumption holding for senior debt holders, is that the baseline exposure to risk is already higher for the first group, given the nature of subordinated debt.As such, they are more prone to demand risk premium, than investors with a lower baseline risk exposition.Notice that this explanation, assuming no short positions of index holders, is just an hypothesis.
For buyers of the index pertaining subordinated debt, the leverage effects studied by the estimated effect of a positive shock is α̂1 + γ̂ = 0.26349 -0,062042 = 0.201448.Therefore, the investors in subordinated bank CDS indices react to news differently, depending on whether they are good or bad, and bad news have a bigger effect on volatility than good news, increasing it.
In the previous section, it was noticed that, despite having the correct sign for leverage effects, γ̂ = -0.009464< 0, in the sample referring to senior debt financial CDS indices, the coefficient γ was not statistically significant.Hence, the behavior of investors in bank CDS indices referring to subordinated debt differs from that of investors in this product for senior debt.H 4 is not Despite not concluding in favor of H 4 , another behavioral characteristic of market participants is uncovered.Given the relevance of CDS bank indices as a reference for financial stability, it is important to know that the subordinated segment is subject to leverage effects.Again, the fact that this market may possibly be dominated by agents who are really hedging, with an already high (as creditors) baseline exposure to risk, might be the reason for the stronger volatility reaction to negative shocks.
With respect to H 5 , one should bear in mind that as the degrees of freedom of a Student t distribution lower, its kurtosis rises, with tails getting increasingly fat (Johnson et al., 1995).A sample of financial CDS index spread returns that comprises periods of tranquility (pre-2007), the GFC, the EA sovereign debt crisis in the bail outs and the post bail outs periods, and a drastic shift in ECB's monetary policy as a support to financial stability, is heterogeneous enough to support the idea behind H 5 .In fact, Table 1 provides support for this intu-ition, as explained in section 3, since the hypothesis H 0 : v = 4 could not be rejected, both for subordinated and for senior debt.As shown in that section, the returns from both CDS indices have very fat tails, confirming H 5 .
The conclusion that the time-varying correlation model is preferred, in section 3, shows that research hypothesis H is confirmed.The two regimes in the dynamic conditional correlations found in the results lead to an interesting implication for portfolio management: the DCC plot suggests that in bearish market periods, with threats to bank stability, one should not include both indices in the same portfolio, since the correlation of their returns is not only positive, but very high.
In conclusion, Figure 2  the discussion in this section is original, filling a gap in the literature.No other study had looked at bank CDS indices per se, nor at the behavioral characteristics of market participants, namely with the division between types of debt.Notwithstanding, the study should be deepened, namely considering whether investors behavior varied at other indices maturities.Moreover, the experience of Covid lockdowns and the departure from quantitative easing by the ECB, would make it interesting, in the future, to extend the analysis until 2022.

CONCLUSION
In this paper, a novel research question was posed: Which characteristics of investors in these derivatives are implied by the volatility behavior of the returns of financial CDS indices?The GJR_t-M was used, as well as two MGARCH variations.The data used referred to the EU and included senior and subordinated debt separately.It was shown that market participants for the subordinated debt segment have a distinct behavioral profile.They are risk averse, demanding a risk premium for increases in returns' conditional volatility.This segment also exhibits leverage effects, as the impact of bad news in the previous day has the consequence of increasing conditional volatility above the level that would exist otherwise.In contrast, investors in the senior segment do not show risk aversion nor asymmetric suggests that investors shared market sentiments, and that these drove the spreads for CDS indices.The highly leveraged nature of the indices (Oliveira & Santos, 2015) is likely to have facilitated some herding behavior.These conclusions are in line with those of Bruneau et al. (2014) for single name bank CDS.Chiarella et al. (2015) also conclude that trading momentum plays a fundamental role in sovereign CDS.
Tamakoshi and Hamori (2014)indices to portfolios containing stock and sovereign bonds indices.The authors conclude that, in the long run, the risk-return features of the CDS indices are such that these are more appealing to institutional investors.Therefore, they tend to partially substitute sovereign bonds by corporate indices in their portfolios.Despite the relevance of the paper, it is not concerned with financial CDS indices.One of the closest studies to this paper, in terms of focusing on financial CDS indices alone, is provided byTamakoshi and Hamori (2014).The authors use daily data covering the period be-The authors constructed the ABX as an index of Collateralized Debt Obligations (CDO) related to asset backed securities (ABS).Choe et al. (2020) develop a tool to assess systemic risk during the EA debt crisis.The authors study the simultaneous default risk and the contagion-default risk during the crisis, by using the iTraxx Europe and the Marshall-Olkin copula.
Fenech et al. (2014)s concerned with the liquidity differences between the two markets: single-name CDS and CDS indices.The paper compares the relative liquidity for corporate CDS markets and CDS indices pertaining comparable reference entities.The indices used are the iTraxx Europe and CDX North America.This choice of variables is sufficient to distinguish hers from this paper: her concern is not the financial sector.Wang and Zhong (2022) study CDS indices alone, trying to understand the features of their OTC trade.Notwithstanding, the concern is with the role of dealer's inventories on the price and liquidity of CDS indices markets.Hippert et al. (2019) provide an insightful study on CDS indices from the perspective of financial management.They explore the effect on the mean and variance of returns, resulting from adding investment grade US tween January 2004 and June 2013.However, they are only interested in the insurance sector, leaving banks aside.Furthermore, differently from this paper, they are interested in the dependence structure between the US, the EU and the UK CDS indices.Their copula analysis shows particularly strong dependence between the UK and the US, suggesting simultaneous losses, in the period prior to the GFC.From 2008 onwards, the authors find low dependence between each pair, suggesting low systemic risk in the global insurance sector.Calice (2014) investigates the connectedness between bank CDS indices and the equity returns, for a sample of systemically important financial institutions (SIFIs).He uses both the 5-year maturity investment grade iTraxx Europe and the matching CDX North America.He concludes in favor of a negative correlation between both CDS indices and the corresponding equity returns, for SIFIs.This relationship appears to be stronger in Europe.The author assumes explicitly he is not interested in behavioral parameters.King (2019)studies the effects of bank bail outs on bank stock prices, and bank CDS spreads.He looks at the GFC, particularly at data from October 2008, referring to US banks and banks from 5 European countries.Fenech et al. (2014)also focus on the GFC, using Archimedean copulas to study the dependence between the Australian iTraxx CDS index and the price of the corresponding firms in the stock market.Fang and Lee (2011) study the GFC, using a measure of the impact of the ABX index on the CDX-US index.
Glosten et al. (1993)this section, no papers provide behavioral insights into the agents acting in the market for financial CDS indices.Even the very rare studies that model indices' returns volatility are not concerned with traders' behavior as foundations for modelling, but rather with spillovers to other markets.In particular, models of indices' returns that include behavioral parameters, namely the GJR model ofGlosten et al. (1993), which allows positive and negative surprises to have different impacts on conditional volatility (leverage effects), are not used in this literature.Models checking if the expected returns on CDS indices are increasing with their conditional variance, a sign of risk aversion, are also missing (GARCH variations of the ARCH-M of Engle et al. (Bollerslev et al., 1988)ights gained from looking jointly at subordinated and senior bank CDS indices have never been studied (using, inter alia, MGARCH models(Bollerslev et al., 1988)).