1. Dynamic Dependence in Corporate Credit
Conference on Copulas and Dependence:
Theory and Applications
Columbia University
October 11-12, 2013
Peter Christoffersen, University of Toronto
Kris Jacobs, University of Houston
Xisong Jin, University of Luxembourg
Hugues Langlois, McGill University

2. Research Questions
Industry reports suggest that diversification benefits in corporate credit markets have gone down.
How do we model dynamic dependence in credit markets?
How do we measure diversification benefits?
Do credit spreads, volatility, and correlation have similar or separate dynamics?
Which economic variables drive credit and equity correlations?

3. Credit Default Swaps
Corporate credit can be measured using corporate bonds or credit default swaps.
Credit default swaps (CDS) can best be thought of as a simple insurance product, providing insurance against corporate default (or credit events more in general).
Periodic payments are exchanged against a lump sum payment contingent on default.
CDS offer many advantages over bonds for measuring corporate credit conditions and credit spreads.
Liquidity
Cleaner measure

4. Credit Default Swaps: Applications
Hedging
CDS allow capital or credit exposure constrained businesses (banks for example) to free up capacity.
CDS can be a short credit positioning vehicle. It is easier to buy credit protection than short bonds.
CDS may allow users to avoid triggering tax/accounting implications that arise from sale of assets.
Counterparty risk.
Investing
Investors take a view on deterioration or improvement of credit quality of a reference credit
CDS offer the opportunity to take a view purely on credit
CDS offer access to hard to find credit (limited supply of bonds)
Investors can tailor their credit exposure to maturity requirements, as well as desired seniority in the capital structure

5. Overview Data Conditional Mean and Volatility Models Copula Models
Credit Diversification Benefits
Economic Drivers of Dependence
(Tail) Dependence and Credit Spreads

6. 1. Data 5-year-CDS quotes each Wednesday.
From Markit: 215 individual firms included in the first 18 series of the CDX North American investment grade index.
Data range: from 01/01/2001 to 22/08/2012.
Equity data from CRSP

7. Some Market Events in our Sample
19/07/2002 WorldCom Bankruptcy
05/05/2005 Ford and GM Downgrade to Junk
08/10/2005 Delphi Bankruptcy
06/08/2007 Quant Meltdown
16/03/2008 Bear Stearns Bankruptcy
15/09/2008 Lehman Bankruptcy
10/03/2009 Stock Market Trough
05/08/2011 US Sovereign Debt Downgrade

8. Median CDS Spreads, IQR and 90% Range

9. CDS Spreads for 9 Industries: Industry Median and Industry 90% Range

10. Threshold Correlations
Use the weekly log differences in CDS premia and equity prices.
Standardize the weekly “returns” using sample mean and volatility.
Compute threshold correlations:
Where x is measured in standard deviations from the mean.

11. Bivariate Threshold Correlations. Median and IQR across Firm Pairs

12. 2. Dynamic Conditional Mean and Volatility Models
Univariate models on weekly log diffs for CDS spreads and equity on 215 firms.
Up to ARMA(2,2) for the conditional mean. Model selection by AICC.
Engle and Ng (1993) NGARCH(1,1) for the conditional variance.
Hansen (1994) asymmetric standardized t distribution for ARMA-NGARCH shocks.

13. Dynamic Conditional Mean and Volatility Models

14. Parameter Estimation (Univariate)

15. Threshold Correlations on Shocks.
Median and IQR

16. CDS Spreads and CDS Spread Volatility

17. CDS Spread Vols for 9 Industries: Industry Median and Industry 90% Range

18. CDS Spreads and Equity Volatility: Structural Credit Risk Models

19. 3. The Dynamic Asymmetric Copula (DAC)
Key Challenge: 215 firms and 25,000+ correlations that change week by week.
Crucial ingredients:
Parsimonious Dynamic Conditional Correlation model of Engle (2002).
Flexible Multivariate Skewed t Distribution in DeMarta and McNeil (2004).
Large-scale composite likelihood estimation as in Engle, Shephard and Sheppard (2008).
Allow for different start and end times for each firm. Patton (2006).
Unconditional moment matching.
Time-varying degrees of freedom.
DAC model based on Christoffersen and Langlois (JFQA, 2013) and Christoffersen, Errunza, Jacobs and Langlois (RFS, 2012).

20. Dynamic Asymmetric Copula
Use skewed t copula: three parameters

21. Dynamic Asymmetric Copula
Copula correlation dynamic
Time-varying degrees of freedom
Composite likelihood function

22. - Median, IQR, and 90% range of bivariate copula correlations
- Median, IQR, and 90% range of bivariate copula correlations. - CDS spread and equity log diffs. - Note shocks to credit and equity correlations occur at different times. - Note different time paths - Note different persistence

23. -Median, IQR, and 90% range of bivariate tail dependence
-Median, IQR, and 90% range of bivariate tail dependence. - Note differences with copula correlations - Note shift in credit and equity tail dependence occurs at different times. - Note different time path

24. CDS Spread and Equity Correlations for 9 Industries: Within Industry Median. Credit in black.

25. CDS Spread and Equity Tail Dependence for 9 Industries: Within Industry Median. Credit in black.

26. Parameter Estimation (Multivariate)

27. 4. Conditional Diversification Benefits (CDB)
Using Expected Shortfall (ES), We define CDB as
Upper bound on CDB is ES average across firms (no diversification benefits). Lower bound is portfolio VaR (no tail).
Gaussian version
(when p=50%):

28. - 5% CDB for EW credit portfolio (top) and EW equity portfolio
- 5% CDB for EW credit portfolio (top) and EW equity portfolio. (bottom). - Selling CDS and buying equity. - VIX on right-hand scale. Key dates in vertical bars. - Note: Deterioration in CDB in both markets. Began in credit in Decrease in CDB bigger for credit

29. 5. Economic Drivers of Credit and Equity Correlations
Macro and market variables considered
The CDX North American investment grade index level is used to proxy for the overall level of risk in credit markets.
The VIX index represents equity market risk.
The term structure is captured by a level variable, the 3-month US Constant Maturity Treasury (CMT), and a slope variable, the 10 year CMT index minus the 3-month CMT.
The crude oil price as measured by the West Texas Intermediate Cushing Crude Oil Spot Price
The inflation level as measured by breakeven inflation.
Economic Activity measured by the ADS business index.

30. Levels Regressions for Credit Copula Correlations (as well as Tail Dependence and Volatility)

31. Difference Regressions for Credit Copula Correlations (as well as Tail Dependence and Volatility)

32. 6. (Tail) Dependence and Credit Spreads
Is higher (tail) dependence associated with higher spreads?
Does dependence matter for spreads after taking the determinants from structural models into account (equity volatility, interest rates, leverage)?
Conduct analysis at the firm level.
Need to investigate time-series and cross-section separately.

33. Tail Dependence and Credit Spreads

34. Summary
We estimate a dynamic asymmetric copula model on 215 firms which each have different start and end dates.
Credit spread levels, volatility, dependence, and tail dependence are found to have separate dynamics.
Credit dependence appears to be permanently higher after Equity dependence not so.
Credit and equity tail dependence both increase throughout the sample
Diversification benefits have declined in both EW credit and EW equity portfolios, more so for credit.
We find some scope for economic drivers of credit and equity dependence.
We document the relation between (tail) dependence and credit spreads at the firm level.
Implications for portfolio credit risk, structured credit products, counterparty risk management.
Nice related (independent) work by Oh and Patton (2013).

35. Appendix: Credit Events in the Sample
CIT Group
Delphi
FHLMC
FNMA
Washington Mutual
Tribune
Lear
Eastman Kodak
Residential Cap
See: