The Single Name Corporate CDS Market

Alan White

CDS StructureSingle Name DJ Index Products

CDS

Buyer SellerNotional x [ ] bp p.a.

Credit Risk of ABC

Buyer Seller

Delivery 10MM Principal ABC Sr. Unsecured Debt

$10 MM Cash

125 Equally Weighted Names

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

CDS CDS CDS CDS CDS

Market Growth Notional Outstanding

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

US Corp. DebtGlobal CDSCDS Index

CDX-IG Index Industry Composition

7.4%

18.9%

15.6%

4.9%

19.7%

10.7%

2.5%

14.8%

5.7%

Materials Consumer,Cyclical

Consumer,NonCyc.

Energy Financial Industrial Tech. Comm. Utilites

CDX-IG Index Moody’s Ratings

3.2%0.8% 1.6% 0.8%

4.0%

12.0%

16.0% 16.8%

27.2%

17.6%

Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3

End Users

Banks, 38%

Securities firms, 16%

Insurance Companies,

20%

Other, 4%

Hedge Funds, 15%

Corporations, 2%

Mutual Funds, 4%

Protection Sellers

Insurance Companies, 7%

Banks, 51%

Hedge Funds, 16%

Other, 3%

Corporations, 3%

Securities firms, 16%

Mutual Funds, 3%

Protection Buyers

Risk and Return

Corporate Bonds vs. CDS

Credit Risk

ABC Corporate CDS

Allows direct trading of credit risk

Credit Risk

Interest Rate Risk

ABC Corporate Bond Return

Arbitrage Trade

• Buy the bond, buy protection earn the risk-free rate of interest

• Make a riskless investment, sell protection earn the bond yield

⇒ CDS spread, s ≈ y – r

⇒ return on trade, r ≈ y – s

Comparing with Treasury and Swap Rates

1.06–6.511.3862.97All Ratings

2.79–2.213.6384.93Baa

1.59–5.831.8264.33A

1.31–9.55 1.9751.30Aaa / Aa

S.E.MeanS.E.Mean

r – rSr – rT

Rating

Spreads In Basis Points

Ratings and CDS Spreads

CDS Spreads and Ratings EventsConditioning on Ratings Event

Negative Outlook

Review for Downgrade

Downgrade

Event

0.62.017.7**7.0*4.069

-1.09.9**14.6**3.26.0*114

8.23.815.0**8.4**14.1**83

1, 10–1, 1–30, –1–60, – 31–90, – 61n

Window (days relative to event)

Average CDS Spread Change (bp)

* 5% significance** 1% significance

CDS Spreads and Ratings EventsConditioning on CDS Spread Changes

1528**37**10

48**46**59**25

68**72**80**50

Negative Outlook

Review for DowngradeDowngradep

* 5% significance** 1% significance

Percent of events in following 30 days in the subset of firms with the top p% of credit spreads

Recovery Rates and Probability of Default

CDS Structure

0.00 0.25 1.000.50 1.501.250.75 1.75

P(s / 4) Accrual

1 – PD(0.25) … ……

PD(1.75) – PD(1.50)

LGD = P(1 – R)

… … … … …

… …

Extracting Hazard Rates – IFixed Recovery Model

• CDS value is the PV of payments weighted by the probability that the payment occurs

• Often set• Find the hazard rate λ that sets the CDS value to

zero • Implied λ is sensitive to assumed recovery rate, R

( ) ( )1 expPD t t= − −λ

Implied Hazard Rates

Implied Hazard RateCDS Spread = 50 bp

0%

1%

2%

3%

4%

5%

0% 20% 40% 60% 80% 100%

Recovery Rate

A Recovery ModelHamilton, Varma, Ou, and Cantor 2005

Gaussian Copula

• Latent variable• Conditioning on x

( )0,1x N

( ) ( )( )

( )( )

1

1

1

10.52 6.9

1

N PD t xPD t x N

N PD xR x N

−

−

⎡ ⎤− ρ= ⎢ ⎥

−ρ⎢ ⎥⎣ ⎦⎡ ⎤− ρ

= − × ⎢ ⎥−ρ⎢ ⎥⎣ ⎦

Conditional 1-Year PDUnconditional PD(1) = 0.02

0 0.02 0.04 0.06 0.08 0.1PD(1|x)

Pro

babi

lity

rho = 0.0001rho = 0.1rho = 0.2rho = 0.3

Conditional Recovery RateUnconditional PD(1) = 0.02

40.5%39.3%38.4%38.2%Exp. Recovery

0.30.20.10.0001Rho

0.2 0.25 0.3 0.35 0.4 0.45 0.5

R | x

Prob

abili

ty rho = 0.0001rho = 0.1rho = 0.2rho = 0.3

Extracting Hazard Rates – IIVariable Recovery Model

• For CDS with spread s, hazard rate λ, copula correlation ρ, and latent variable value x, the probabilities of default are known and the conditional CDS value can be computed

• Integrating the conditional values over x produces the unconditional CDS value

• λIC(s, ρ) is the copula implied hazard rate,

VC(s, λIC(s, ρ), ρ) = 0

Extracting Recovery Rates

• EC[R(λ, ρ)] is the expected recovery rate under the copula model found by integrating over the latent variable

• RIF(s, λIC) is the implied fixed recovery rate based on the copula implied hazard rate

Copula Implied Hazard Rate

0.5%

0.6%

0.7%

0.8%

0.9%

1.0%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Copula Correlation

2.0%

2.2%

2.4%

2.6%

2.8%

3.0%

CDS spread = 50 bp

CDS spread = 200 bp

Recovery Rates

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1Copula Correlation

Implied R s=50 E(R) s=50

Implied R s=200 E(R) s=200

Conclusion

• If CDS quotes reflect a recovery model in which probability of default and recovery are negatively related, and

• A fixed recovery rate model is used to infer probabilities of default

• The appropriate recovery rate needed to determine the probability of default is much lower than intuition would suggest