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