Dynamic Dependence in Corporate Credit

Peter Christoffersen, University of TorontoKris Jacobs, University of Houston

Xisong Jin, University of LuxembourgHugues Langlois, McGill University

Conference on Copulas and Dependence: Theory and Applications

Columbia UniversityOctober 11-12, 2013

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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?

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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

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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

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Overview

1. Data2. Conditional Mean and Volatility Models3. Copula Models4. Credit Diversification Benefits5. Economic Drivers of Dependence6. (Tail) Dependence and Credit Spreads

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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

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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

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Median CDS Spreads, IQR and 90% Range

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CDS Spreads for

9 Industries: Indus

try Medi

an and

Industry

90% Rang

e

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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.

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Biva

riate

Thr

esho

ld C

orre

latio

ns.

Med

ian

and

IQR

acro

ss F

irm P

airs

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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.

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Dynamic Conditional Mean and Volatility Models

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Parameter Estimation (Univariate)

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Thre

shol

d Co

rrel

ation

s on

Sho

cks.

M

edia

n an

d IQ

R

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CDS Spreads and CDS Spread Volatility

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CDS

Spre

ad V

ols

for 9

Indu

strie

s:

Indu

stry

Med

ian

and

Indu

stry

90%

Ran

ge

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CDS Spreads and Equity Volatility: Structural Credit Risk Models

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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).

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Dynamic Asymmetric Copula

Use skewed t copula: three parameters

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Dynamic Asymmetric Copula• Copula correlation dynamic

• Time-varying degrees of freedom

• Composite likelihood function

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- 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

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-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 path

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CDS

Spre

ad a

nd E

quity

Cor

rela

tions

for 9

Indu

strie

s:

With

in In

dust

ry M

edia

n. C

redi

t in

blac

k.

25CDS

Spre

ad a

nd E

quity

Tai

l Dep

ende

nce

for 9

Indu

strie

s:

With

in In

dust

ry M

edia

n. C

redi

t in

blac

k.

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Parameter Estimation (Multivariate)

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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%):

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- 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

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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.

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

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

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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.

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Tail Dependence and Credit Spreads

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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).

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Appendix: Credit Events in the Sample

• CIT Group• Delphi• FHLMC• FNMA• Washington Mutual• Tribune• Lear• Eastman Kodak• Residential Cap See: http://creditfixings.com/CreditEventAuctions/fixings.jsp