Peter Christoffersen University of Toronto Kris Jacobs University of Houston Xisong Jin University of Luxembourg Hugues Langlois McGill University Conference on Copulas and Dependence ID: 683350
Download Presentation The PPT/PDF document "Dynamic Dependence in Corporate Credit" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Dynamic Dependence in Corporate Credit
Peter Christoffersen, University of TorontoKris Jacobs, University of HoustonXisong Jin, University of LuxembourgHugues Langlois, McGill University
Conference on Copulas and Dependence:
Theory and Applications
Columbia University
October 11-12, 2013Slide2
Research QuestionsIndustry 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?2Slide3
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.LiquidityCleaner measure3Slide4
Credit Default Swaps: Applications
HedgingCDS 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.InvestingInvestors take a view on deterioration or improvement of credit quality of a reference creditCDS offer the opportunity to take a view purely on creditCDS 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 structure4Slide5
OverviewData
Conditional Mean and Volatility ModelsCopula ModelsCredit Diversification BenefitsEconomic Drivers of Dependence(Tail) Dependence and Credit Spreads5Slide6
1. Data5-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 CRSP6Slide7
Some Market Events in our Sample19/07/2002 WorldCom Bankruptcy
05/05/2005 Ford and GM Downgrade to Junk08/10/2005 Delphi Bankruptcy06/08/2007 Quant Meltdown16/03/2008 Bear Stearns Bankruptcy15/09/2008 Lehman Bankruptcy10/03/2009 Stock Market Trough05/08/2011 US Sovereign Debt Downgrade7Slide8
8
Median CDS Spreads, IQR and 90% RangeSlide9
CDS Spreads for 9 Industries: Industry Median and Industry 90% Range
9Slide10
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.10Slide11
11
Bivariate Threshold Correlations. Median and IQR across Firm PairsSlide12
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.12Slide13
13
Dynamic Conditional Mean and Volatility ModelsSlide14
Parameter Estimation (Univariate)
14Slide15
15
Threshold Correlations on Shocks. Median and IQRSlide16
16
CDS Spreads and CDS Spread VolatilitySlide17
17
CDS Spread Vols for 9 Industries: Industry Median and Industry 90% RangeSlide18
18
CDS Spreads and Equity Volatility: Structural Credit Risk ModelsSlide19
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).19Slide20
20
Dynamic Asymmetric CopulaUse skewed t copula: three parametersSlide21
21
Dynamic Asymmetric CopulaCopula correlation dynamic
Time-varying degrees of freedom
Composite
likelihood functionSlide22
- 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 differentpersistence 22Slide23
-Median, IQR, and 90% range of bivariate tail dependence. - Note differences with copula correlations
- Note shift incredit and equity tail dependence occurs at different times.- Note different time path23Slide24
24
CDS Spread and Equity Correlations for 9 Industries: Within Industry Median. Credit in black. Slide25
25
CDS Spread and Equity Tail Dependence for 9 Industries: Within Industry Median. Credit in black. Slide26
Parameter Estimation (Multivariate)
26Slide27
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%):27Slide28
28
- 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 2007.- Decrease in CDB bigger for credit Slide29
5. Economic Drivers of Credit and Equity Correlations
Macro and market variables consideredThe 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 PriceThe inflation level as measured by breakeven inflation.Economic Activity measured by the ADS business index.29Slide30
30
Levels Regressions for Credit Copula Correlations (as well as Tail Dependence and Volatility)Slide31
31
Difference Regressions for Credit Copula Correlations (as well as Tail Dependence and Volatility)Slide32
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.32Slide33
33
Tail Dependence and Credit SpreadsSlide34
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 2007. 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).34Slide35
Appendix: Credit Events in the Sample
CIT GroupDelphiFHLMCFNMAWashington MutualTribuneLearEastman KodakResidential Cap See: http://creditfixings.com/CreditEventAuctions/fixings.jsp35