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How inter-related is the American and European Credit Default Swap indices market? A search for transatlantic kinship.

Executive Summary

This paper is aimed at analyzing the interdependency between American and European Credit Default Swap (CDS) Indices markets from June 2004 to April 2009. For this exercise, the author has chosen the two most liquid Investment-Grade (IG) CDS indices: CDX. NA.IG of North America and iTraxx.Europe of Europe. Both 5Y and 10Y CDS spreads were considered for this study. A granger-causality test was employed to test the direction of granger-causation between CDX.NA.IG and iTraxx.Europe spreads. In addition, the Chow test was employed to test for sensitivity of the underlying interdependency (if any) between the American and European CDS indices, to the onset of the 2007 financial crisis.

The study's findings reveal the prevalence of unidirectional granger-causality between 5Y CDX.NA.IG and 5Y iTraxx.Europe. In other words, 5Y CDX.NA.IG spread movements granger-cause iTraxx.Europe spread movements. Further, this underlying dependency is found to be sensitive to the onset of the 2007 financial crisis. On the other hand, 5Y iTraxx.Europe spread movements fail to granger-cause 5Y CDX.NA.IG. Also, this lack of dependency is found to be insensitive to the onset of the 2007 financial crisis.

On the 10Y front, the study's findings reveal the prevalence of bi-directional granger-causality between 10Y CDX.NA.IG and 10Y iTraxx.Europe spread movements. Also, the underlying bi-directional causality between 10Y CDX.NA.IG and 10Y iTraxx.Europe was found to be sensitive to the onset of the 2007 financial crisis.

Section 1 constitutes the significance of this study, while section 2 offers a brief overview of the relevant literature on CDS and CDS indices. Section 3 details the data utilized for the study. The author discusses the methodology employed and presents the findings pertaining to this study in section 4. The author concludes in section 5.

1. Significance of this study

Credit default swaps, as the name indicates, are credit instruments used by banks, non-banking financial institutions, hedge funds and investors, so as to shift risk from one party to another (Mengle, 2007, p.1). These instruments have been in the news in recent times for their role in the 2007-2008 financial crisis that originated in United States, which then paved the way for the acute credit crunch and synchronized global recession. In 2007-2008, reckless risk-taking by financial market participants led to a cardiac arrest in the credit markets. This caused an immense liquidity crunch and macro-economic uncertainty at a global level, thereby bringing about a vicious cycle of reduced lending by banks on the one hand and lack of economic growth (in many cases, acute contraction) on the other hand (Bank of England, 2008). It became evident that the market participants, such as global investment banks, institutional investors, insurance companies and hedge funds had taken on immense exposure to credit risks based on unrealistic analytical models, which had utilized historical data. It is notable that the historical data used in such models was not a true representation of the recent industry scenario, which has been characterized by poor lending standards and collapsing home prices (Jarrow, Mester and van Deventer, 2007; van Deventer, 2008).

Amidst such a chaotic environment, central bankers in the U.S. and Europe were forced to take policy actions overnight before the markets opened in other parts of the world, in order to provide the requisite signal to the markets during a time of immense and unprecedented economic distress. Such sudden policy actions by central bankers were guided by a sense of urgency to contain global repercussions of regional financial distress. Although this urgency was understandable, not much is known on exactly how the global markets are intertwined. Consequently, the author believes that it is of utmost importance for both policy makers and market participants to better understand the interdependency of global credit markets. It would be easier to gain such much-needed understanding by examining a section of credit markets that is most liquid and transparent, namely Investment Grade (IG) Credit Indices of U.S. (CDX.NA.IG) and Europe (iTraxx.Europe).

2. Literature Review

Early research works in the Credit Default Swap market were aimed at understanding the interrelationship between the CDS and Bond Markets (Zhu, 2004) and co-movements of CDS, Bond and Equity Markets (Norden and Weber, 2004). Such research excursions in the CDS markets involved data pertaining to individual reference entities, and they were undertaken to identify arbitrage opportunities owing to possible lead-lag relationship in price discovery mechanism between the equity, bond and CDS markets.

According to FitchRatings' global credit markets survey (FitchRatings, 2004, 3; FitchRatings, 2006, 6), the growth rate of CDS Indices had skyrocketed from 49% in 2003 to 900% in 2005. The British Bankers Association (BBA) predicted that the share of index-related products in the credit-derivative markets would rise from 11% to 17% in 2006 as compared to the fall in share of single-name CDS from 51 to 42 percent (Meng and ap Gwilym, 2007, 196). Consequently, overtime, research on CDS indices gained traction.

Prior works on CDS indices were aimed at understanding the contemporaneous and serial correlation between a credit and equity index of the same region (Bystrom, 2005; Fung, Sierra, Yau, and Zhang, 2008). Such efforts were aimed at understanding the capital structure arbitrage opportunities between equities, and CDS index markets pertaining to U.S. or Europe. Also, there have been studies that compare the empirical CDS spreads of European iTraxx markets and the model-induced spreads wherein the model predictions are based on prevalent bond data (Longstaff, Mithal and Neis, 2003; Zhu, 2004) or equities data (Bystrom, 2006). Moody's KMV model and Credit Grades model are some of the current industry models that predict the default probability of a reference entity and the consequent expected default spreads based on the underlying equity and asset characteristics of the reference entity.

Also, a 2007 study by Hans Bystrom attempts to understand the instantaneous credit risk correlation amidst regional and sector-level iTraxx indices (Bystrom, 2007). The different indices considered in this study were iTraxx Europe, iTraxx Japan, iTraxx Australia, iTraxx Korea, iTraxx Greater China, and iTraxx Rest of China.

However, not much is known about the interdependency (if any) between CDS Indices of U.S. and Europe. It is notable that the most liquid of the CDS indices is the North American investment grade index (CDX.NA.IG) and its European cousin (iTraxx.Europe). These two indices also offer the most opportunities for dynamic hedging, speculating and investment (McManus, Ray, and Preston, 2006, 14). Since the onset of the 2007 financial crisis, triggered by the near-collapse of Bear Stearns in August 2007, a lot of unpleasant events took place in the credit markets that include but are not limited to the insolvency of a prime-broker, a run on money-market funds, immense injection of liquidity, concurrent interest rate cuts, and an unprecedented amount of government subsidies and bailouts for financial and non financial firms owing to economic and political reasons. In light of such turbulence, it is all-the-more critical for us to understand how interdependent these supposedly most liquid and most transparent credit indices, CDX.NA.IG and iTraxx.Europe are. Accordingly, this paper is an attempt to do so.

3. Data

Both CDX.NA.IG and iTraxx.Europe trade in spreads. Buying and selling the indices is similar to buying and selling portfolios of loans or bonds. CDX.NA.IG and iTraxx.Europe comprise 125 equally-weighted reference entities each. Each entity in the index is referenced to an underlying bond/obligation. As a result, the buyer the of the CDS index gains exposure to the 125 underlying obligations. Therefore, the buyer of the CDS index, who takes on the credit risk of the 125 reference obligations, is the protection seller. On the other hand, the seller of the CDS index who offloads his/her credit risk exposure to underlying reference obligations is the protection buyer.

Both CDX and iTraxx indices roll every six months. In other words, a new series is created every six months. The first series of CDX.NA.IG came into effect on 21st October '03, while the first series of iTraxx Europe came into effect on 21st June '04. Although the old series continue trading, liquidity is concentrated on the most recent series at any point of time. Accordingly, this study takes into account data pertaining to only the most recent CDX.NA.IG and iTraxx. Europe series, starting from 21st June '04 to 2nd April '09.

CDX.NA.IG is available in 1, 2, 3, 5, 7, and 10 year tenor (maturity), while iTraxx.Europe is available in 3, 5, 7 and 10 year tenor. 5Y tenor remains the most liquid and frequently quoted part of the credit curve, while other tenors such as 10Y are becoming more common (Markit, 2008, p.31). For this study, the author considers daily CDX.NA.IG and iTraxx.Europe spreads pertaining to 5Y and 10Y maturities. CDX. NA.IG data was obtained from a Bloomberg terminal, while iTraxx.Europe data was obtained at www.indexco.com

With regard to pricing mechanism, licensed dealers determine the spread for each index and maturity. This is done through a dealer call in Europe (iTraxx). In North America (CDX), the licensed dealers send Markit - the company that owns and administers these indices - an average spread and the median becomes the fixed spread of the index.

4. Methodology and Findings

To start with, the mid-value of daily closing bid and ask spreads pertaining to CDX.NA.IG and iTraxx.Europe from 21st June 2004 to 2nd April 2009 were considered. Saturdays and Sundays were removed from the American and European datasets. Also, no methodology was used to impute missing values. In short, missing values were treated as missing for all statistical tests. RATS (Regression Analysis of Time Series) software was used by the author to conduct the statistical tests. The descriptive statistics pertaining to the different time series are shown below.

Before employing the granger-causality test, the Phillips-Perron test was employed to test for stationarity of all time series. The test outcomes revealed the prevalence of non-stationarity in all time series. Consequently, all time-series were first-differenced to ensure stationarity.

Before subjecting the first-differenced time-series variables to granger-causality tests, the author employed Akaike Information Criterion (AIC) to choose the optimal lag length pertaining to each of the first-differenced time series variables series variables1. For instance, a regression test was run, with the current value of iTraxx10Y as the dependent variable and 15 lagged values of iTraxx10Y as independent variables. The AIC for such a regression was recorded. Then, the most distant time period was dropped from the model and the regression was re-run to calculate the new AIC. This procedure was repeated until there was only one independent variable in the regression model. Then the AICs pertaining to each of the regressions were compared and the lag length that resulted in the minimum AIC was chosen as the optimal lag-length for iTraxx10Y. The optimal lag-length for the CDX10Y, iTraxx5Y, and CDX5Y time series was arrived at by employing the same procedure. The optimum lag-length for CDX5Y, iTraxx5Y, CDX10Y and iTraxx10Y was found to be 14, 4, 11 and 14 respectively.

At this juncture, the author would like to first present the granger-causality models and their associated findings pertaining to iTraxx5Y and CDX5Y datasets.

Model 1:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The null hypothesis for Model 1 is that iTraxx5Y does not granger-cause CDX5Y. Put simply, [delta]11 = [delta]12 = [delta]13 = [delta]14 = 0. The regression test outcomes offered sufficient grounds to reject the null hypothesis.

Having said so, the Durbin-Watson statistic was found to be 2.01. Generally speaking, a Durbin-Watson statistic of 2 would imply lack of serial correlation of error terms. But model specifications such as ours, wherein the lagged values of dependent variables occur as independent variables, will lead to a reduction in serial correlation of residuals and an increase in Durbin-Watson statistic (Nerlove and Wallis, 1966, 235). Further, the author tested for homoscedasticity of the regression outcomes by employing White's test. The test-outcomes indicated prevalence of heteroscedasticity.

Consequently, Heteroscedasticity and Autocorrelation Consistent (HAC) standard errors were generated using Newey-West methodology, and the F-test was reemployed to see if the rejection of null hypothesis persists. Once statistical properties such as heteroscedasticity and autocorrelation were identified and dealt with, test outcomes revealed that iTraxx5Y fails to granger-cause CDX5Y. Having established lack of granger-causation in one direction, the following model was employed to test if CDX5Y granger-causes iTraxx5Y.

Model 2

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The null hypothesis for Model 2 is that CDX5Y does not granger-cause iTraxx5Y. The test outcomes offered sufficient grounds to reject the null hypothesis. At this juncture, the author tested for homoscedasticity of the regression outcomes by employing White's test. The test-outcomes indicated prevalence of heteroscedasticity. Consequently, Heteroscedasticity and Autocorrelation Consistent (HAC) standard errors were generated using Newey-West methodology, and the F-test was reemployed to see if the rejection of null hypothesis persists. Despite identifying and dealing with statistical properties such as heteroscedasticity and autocorrelation, test outcomes revealed that CDX5Y's granger-causation of iTraxx5Y persisted. This implies that 5-year CDX.NA.IG spread movements in North America impacts successive spread movements of iTraxx.Europe across the Atlantic.

To understand the sensitivity of test-outcomes to the onset of the recent financial crisis that was triggered by the near-collapse of Bear Stearns in August 2007, the Chow test was employed to test for a structural break in models 1 and 2. Since the preliminary test outcomes pertaining to models 1 and 2 warranted heteroscedasticity and autocorrelation consistent (HAC) error correction, a separate dummy variable was created in RATS environment for each regressor in each subsample, beyond the first sample. In total, (n-1)*k dummies were created. In our case, n equals 2, and k equals 18. Then the Chow test was estimated over the whole sample, including regressors and dummies, and the joint significance of all dummies was tested. Chow test outcomes reveal absence of any structural breaks in model 1, and prevalence of a structural break in model 2.

To summarize, iTraxx5Y fails to granger-cause CDX5Y. Further, this lack of dependency was found to be insensitive to the onset of the 2007 financial crisis. On the other hand, CDX5Y granger-causes iTraxx5Y, and this underlying causation was found to be sensitive to the onset of the 2007 financial crisis. (2)

Having presented the different test outcomes pertaining to CDX5Y and iTraxx5Y time series, the following models were employed to test for inter-dependency between iTraxx10Y and CDX10Y time series.

Model 3:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Model 4:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The same methodology that was employed to test for granger-causation and structural break in models 1 and 2, was employed by the author to test for granger-causality and structural break in models 3 and 4.

Unlike 5Y indices, test outcomes revealed prevalence of bi-directional granger-causality between CDX10Y and iTraxx10Y. Further, Chow test outcomes reveal a structural break in models 3 and 4 since the onset of recent financial crisis in August 2007. (3)

5. Conclusion and Avenues for Future Research

There exists unidirectional granger-causality between 5Y CDX.NA.IG and 5Y iTraxx.Europe. In other words, 5Y iTraxx.Europe spread movements fail to granger-cause 5Y CDX.NA.IG spread movements (model 1), while 5Y CDX.NA.IG spread movements granger-cause iTraxx.Europe spread movements (model 2). Further, granger-causality evidenced in model 2 is found to be sensitive to the onset of the 2007 financial crisis. On the other hand, in the case of model 1, neither granger-causality, nor sensitivity to the onset of the 2007 financial crisis exists.

On the 10Y front, there exists bi-directional granger-causality between 10Y CDX.NA.IG and iTraxx.Europe. Put differently, both 10Y iTraxx.Europe and 10Y CDX.NA.IG granger-cause one another. Further, the underlying bi-directional interdependency is found to be sensitive to the onset of the 2007 financial crisis.

Based on test outcomes pertaining to 5Y and 10Y IG CDS Indices, it is evident that regional financial distress in the U.S. is bound to have transatlantic repercussions in Europe. This is because CDX.NA.IG granger-causes iTraxx.Europe in both 5Y and 10Y tenors. However, the reverse is untrue. To be more specific, distress in 5Y European IG CDS indices market is bound to have no statistically significant effect on its American counterpart, while a regional distress in 10Y European CDS IG market would have transatlantic repercussions on its 10Y American counter-part.

Further, the study clearly proves that the underlying interdependency or lack-thereof between American and European IG CDS indices is bound to be different for different maturities/tenors. Consequently, any generalization of this study's findings to IG CDS indices of other maturities that were not part of this study would be wrong.

Also, it is notable that all models (1 to 4) assumed linear relationship between the dependent and independent variables, while testing for granger-causality. Taking cognizance of this fact, the author introduced additional second order regressors to all 4 models to see a) if there is any change in the direction of granger-causality being captured by the models, and b) to see if there is any noticeable improvement in the strength of the granger-causal relationship being captured by the models. The revised models are shown below.

Model 5:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Model 6:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Model 7:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Model 8:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Test outcomes (4) pertaining to revised models revealed no change in the direction of granger-causality being captured by the models. However, there was considerable improvement in the strength of dependence relationship being captured by the models. To be more specific, addition of second order regressors enhanced the goodness-of-fit (R square value adjusted for degrees of freedom) of model 7 to 45.71% (model 3 [R.sup.2] was 28.62%) and of model 8 to 47.25% (model 4 [R.sup.2] was 25.71%). In the case of models 5 and 6, addition of second-order regressors improved the goodness-of-fit to 20.15% and 31.17% respectively.

Also, the following second-order terms were found to have a statistically significant impact on the dependent variable.

Further, the covariance-correlation matrices (5) generated for each of the above 4 models reveal cross-correlations between second-order regressors and other regressors in the model. Put simply, the models suffer from Omitted Variable Bias owing to non-linear higher-order properties not being captured by models 1 to 4. These findings are in line with author's findings pertaining to another study that tests for non-linearity in 10Y CDX.NA.IG and iTraxx.Europe datasets by employing BDS and close-returns tests (Madhavan, 2010, p.22). Future studies should employ sophisticated non-linear models to a) capture all of the non-linearity prevalent in these models and b) to enhance the strength of the inter-dependence relationship being captured. Finally, this study takes into account only the daily closing spreads of the CDS indices. Not much is known about intra-day spread movements in CDS markets. The author foresees huge potential for future research on this front.

ENDNOTES

(1.) All subsequent times series references in this paper such as and limited to iTraxx10Y, CDX10Y, iTraxx5Y and CDX5Y correspond to the first-differenced stationary values pertaining to 10Y iTraxx.Europe, 10Y CDX.NA.IG, 5Y iTraxx.Europe, and 5Y CDX.NA.IG spreads respectively.

(2.) Owing to space constraints, Model 1 and 2 test outcomes are not made available in this paper. A copy of the test outcomes pertaining to a) preliminary granger-causality estimations, b) Subsequent HAC Standard Error estimations, and c) Chow Tests can be obtained in the form of an appendix (Appendix 1, exhibits A1.1 to A1.6) from the author.

(3.) Owing to space constraints, Model 3 and 4 test outcomes are not made available in this paper. A copy of the test outcomes pertaining to a) preliminary granger-causality estimations, b) subsequent HAC Standard Error estimations, and c) Chow Tests can be obtained in the form of an appendix (Appendix 2, exhibits A2.1 to A2.6) from the author.

(4.) Owing to space constraints, test outcomes are not shown here. Test outcomes pertaining to Models 7 and 8 can be obtained in the form of an appendix (Appendix 3, exhibits A3.1 and A3.2) from the author.

(5.) Owing to space constraints, these matrices were not made available. Readers interested in obtaining these matrices are urged to contact the author.
Exhibit 1:
Descriptive Statistics: iTraxx10Y, CDX10Y, iTraxx5Y. CDX5Y

Series Obs Mean Std Error Minimum Maximum

ITRAXX10Y 1201 71.346 33.303 39.560 186.250

CDX10Y 1113 85.657 34.475 53.417 247.448

ITRAXX5Y 1218 58.327 45.389 20.095 215.915

CDX5Y 1172 76.803 56.314 29.030 279.313

Exhibit 2
Model Dependent Variable Second-Order Terms that were
# found to be significant

5 [(CDX5Y).sub.t] [[(CDX5Y).sub.t-5].sup.2],
 [[(CDX5Y).sub.t-11].sup.2],
 [[(CDX5Y).sub.t-14].sup.2]

6 [(iTraxx5Y).sub.t] [[(CDX5Y).sub.t-1].sup.2],
 [[(CDX5Y).sub.t-7].sup.2]

7 [(CDX10Y).sub.t] [[(CDX10Y).sub.t-2].sup.2],
 [[(CDX10Y).sub.t-3].sup.2],
 [[(CDX10Y).sub.t-7].sup.2],
 [[(CDX10Y).sub.t-9].sup.2],
 [[(iTraxx10Y).sub.t-3].sup.2],
 [[(iTraxx10Y).sub.t-4].sup.2],
 [[(iTraxx10Y).sub.t-8].sup.2]

8 [(iTraxx10Y).sub.t] [[(CDX10Y).sub.t-7].sup.2],
 [[(CDX10Y).sub.t-10].sup.2],
 [[(iTraxx10Y).sub.t-3].sup.2],
 [[(iTraxx10Y).sub.t-4].sup.2]


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Vinodh Madhavan, Vinod Gupta School of Management, Indian Institute of Technology, Kharagpur, India vinodh.madhavan@vgsom.iitkgp.ernet.in
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Date:Dec 22, 2011
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