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Abstract
This paper investigates potential contagion among the major financial institutions in developed economies. Using Credit Default Swaps (CDS) premia as a measure of both credit and counterparty risks, our analysis focuses on the extreme co-movements of financial institutions’ default swap contracts during the high level of stress undergone by the CDS markets in the aftermath of the 2007 sub-prime crisis. Our approach is twofold. First, under different tail dependence scenarios, we calibrate several multivariate linear models of constant correlation. Our Monte Carlo simulation study finds evidence of contagion for financial institutions, notably in the U.S., and captures a non-normal dependence structure in the tails for the traded contracts. Second, we estimate a multivariate Dynamic Conditional Correlation-GARCH (DCC-GARCH) model, and demonstrate significant ARCH and GARCH effects, as well as time-varying correlations in CDS spread variations. Our overall analysis rejects the assumption of constant correlation. More importantly, it advocates changing structures in the tail dependence for CDS returns series during times of financial turmoil as an important feature of banks’ increased fragility.
Notes
1 Downside returns or losses apply to equity and/or bond negative returns and consequently involve for the latter an increase in credit spreads. Because CDS premia are quoted and traded in basis points of a notional amount, extreme downside, indicating the deterioration of the credit or counterparty risk profile of a financial institution, is associated with an increase in CDS premia.
2 The analytical framework presented in this paper uses a simulation methodology to describe CDS returns’ tail dependence breaks and thus differs from models that aim, by means of copulas, to characterize market returns’ cumulative distribution functions and provide quantitative measures of their dependence structure.
3 The contagion literature has primarily made use of stock and bonds markets indices. See Baig and Goldfajn (Citation1998), Ramchand and Susmel (Citation1998), Chesney and Jondeau (Citation2000), Longin and Solnik (Citation2001), Ang and Bekaert (Citation2002), Bae et al. (Citation2003), Hartman et al. (Citation2004) and Rodriguez (Citation2007), among others. On the other hand, empirical research using firm-specific CDS premia has focused on the study of lead–lag relationships between several asset classes and credit derivatives markets (Norden and Weber Citation2004), on the investigation of the default and non-default components of bond spreads (Longstaff et al. Citation2005) or the market reaction of industry competitors surrounding credit events (Jorion and Zhang Citation2007). Contagion analysis, as captured by significant correlation breakdowns in the auto industry, was carried out by Coudert and Gex (Citation2008).
4 Bae et al. (Citation2003) explore whether contagion based on observed excess co-movements can stem from a relative increase in the volatility of stock market indices’ returns. They compute a time-varying variance–covariance matrix, identify two sub-periods of low and high volatility and study the returns’ multivariate distribution parameters conditioning on those two sub-periods. They simulate returns for the entire sample period based on the high volatility sample’s parameters and find evidence of contagion. Our approach is different in that it simulates CDS price variations while accounting for continuously dynamic conditional volatilities and correlations over the entire study period.
5 A CDS premium thus incorporates both the issuer’s probability of default and the recovery rate in the event of default. The probability of weighted expected loss on a given obligation is equal to Protection Notional∗(1–Recovery rate)∗Probability of Default of the issuer.
6 From an accounting standpoint, financial institutions’ CDS cash flows and CDS marked-to-market gains/losses are treated as ordinary income. Therefore, premia paid are included in the protection seller’s income and deducted from the protection buyer’s income. This symmetrical tax treatment for both legs of the contract reduces potential tax effects on CDS short/long positions and prices. Bond spreads over the risk-free rate, on the other hand, embed a non-default component, which stems from tax treatment differentials. This is all the more relevant in the U.S. where interest on Treasury bonds are exempt from both local and federal government tax, whereas coupon payments on corporate bonds are not. Furthermore, Elton et al. (Citation2004) have shown that this non-default component varies depending on the coupons the bonds pay, even when the tax rate on interest income remains unchanged over time.
7 Despite their contractual nature, CDS premia could include a non-default component, as recent investigations of a possible liquidity effect in the CDS market indicated positively priced liquidity risk. Liquidity risk for less actively traded CDS could be particularly large for short-term (less than 5 year) CDS contracts. See Tang and Yan (Citation2007).
8 Single-name CDSs are all denominated in local currency, U.S. Dollar and Euro for American and European entities, respectively, except for Spanish Bancaja, for which we choose USD CDS on a USD-denominated free-float bond for quote accuracy purposes.
9 Augmented Dickey–Fuller tests also reject both trend and intercept in CDS return series, except for Old Mutual PLC, for which we included a significant deterministic time trend.
10 Under the null hypothesis, the Jarque–Bera test statistic follows a chi-square distribution with two degrees of freedom.
11 Moors’ (Citation1988) robust kurtosis coefficient is computed as where
is the ith octile for each of the CDS returns’ series. Because it is an octile-based measure, the coefficient is robust to outliers, especially in the case of a large number of observations. For a normally distributed variable with zero mean and unit variance, Moors’ robust kurtosis is equal to 1.23. Our excess robust kurtosis is thus centered around that value. For a survey of robust third and fourth moments and their applications, see Kim and White (Citation2004).
12 Counterparty risk directly relates to the probability of the counterparty of a CDS contract failing to meet its payment obligations if the reference entity were to default, whereas credit risk refers to the failure to meet payment obligations on debt issued by a given obligor.
13 For a detailed introduction to copula functions, see Nelsen (Citation2006).
14 For a detailed presentation of hyperbolic distributions and their applications in finance, see Eberlein and Keller (Citation1995).
15 As mentioned above, we chose the multivariate normal and Student-t distributions for their elliptical properties. The multivariate Student-t is introduced to capture a non-normal dependence in the tails of the series. Each marginal distribution is symmetric with zero mean, unit variance, zero skewness and a kurtosis equal to It is important to note that the multivariate Student-t is elliptically contoured when all the marginal distributions have the same degrees of freedom v. For a detailed presentation of elliptical distributions, see Jondeau et al. (Citation2007).
16 We are grateful to Mr. Abdelaziz Rouabah from Banque Centrale du Luxembourg for his guidance in implementing the test’s code on Eviews.
17 The DCC-GARCH model assumes conditionally multivariate returns with zero expected mean or de-meaned residuals obtained beforehand by fitting a conditional mean process such as a vector AR or ARMA (see equations (1) to (3)). An examination of the CDS return autocorrelation and partial autocorrelation functions did not point to any significant lags in the series. We also performed a zero mean hypothesis test and found that all means for our CDS return series are not statistically different from zero. We therefore did not filter the series prior to the DCC-GARCH estimation. The lag orders p and q are equal to 1 as the analysis of squared returns’ autocorrelation and partial autocorrelation functions evidenced a significant first order lag. The choice of first-order ARCH and GARCH lags also made sense due to the computational difficulties of estimating higher-order models as the number of parameters increases.
18 This feature of CDS returns also explains the presence of extreme outliers, which we pointed out in section 2.
19 Under the null hypothesis that U.S. and European financial institutions’ CDS premia changes are drawn from a multivariate normal distribution, the Monte Carlo simulation evaluates the number of co-exceedances within each sample. We use the simulated p-value to accept or reject the null hypothesis. Consecutively and for each of the four envisaged scenarios, p-values give the proportion of replications with co-exceedances in a given sample exceeding the actual number of co-exceedances.
20 See Haldane (Citation2009) for a presentation of the concept of ‘Disaster Myopia’ resulting in banks’ failed risk management practices prior and during the 2007 financial crisis.