The Single Name Corporate CDS Market. Alan White

Transcription

1 The Single Name Corporate CDS Market Alan White

2 CDS Structure Single Name DJ Index Products CDS Notional x [ ] bp p.a. Buyer Credit Risk of ABC Seller 125 Equally Weighted Names Buyer Delivery 10MM Principal ABC Sr. Unsecured Debt $10 MM Cash Seller

3 Market Growth Notional Outstanding 7,000 6,000 5,000 4,000 US Corp. Debt Global CDS CDS Index 3,000 2,000 1,

4 CDX-IG Index Industry Composition 18.9% 19.7% 15.6% 14.8% 10.7% 7.4% 4.9% 5.7% 2.5% Materials Consumer, Cyclical Consumer, NonCyc. Energy Financial Industrial Tech. Comm. Utilites

5 CDX-IG Index Moody s Ratings 27.2% 16.0% 16.8% 17.6% 12.0% 3.2% 0.8% 1.6% 0.8% 4.0% Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3

6 End Users Hedge Funds, 15% Insurance Companies, 20% Protection Sellers Securities firms, 16% Hedge Funds, 16% Insurance Companies, 7% Protection Buyers Securities firms, 16% Corporations, 2% Mutual Funds, 4% Other, 4% Banks, 38% Corporations, 3% Mutual Funds, 3% Other, 3% Banks, 51%

7 Risk and Return

8 Corporate Bonds vs. CDS ABC Corporate Bond Return ABC Corporate CDS Credit Risk Credit Risk Interest Rate Risk Allows direct trading of credit risk

9 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

10 Comparing with Treasury and Swap Rates Spreads In Basis Points r r T r r S Rating Mean S.E. Mean S.E. Aaa / Aa A Baa All Ratings

11 Ratings and CDS Spreads

12 CDS Spreads and Ratings Events Conditioning on Ratings Event Average CDS Spread Change (bp) Window (days relative to event) Event n 90, 61 60, 31 30, 1 1, 1 1, 10 Downgrade ** 8.4** 15.0** Review for Downgrade * ** 9.9** -1.0 Negative Outlook * 17.7** * 5% significance ** 1% significance

13 CDS Spreads and Ratings Events Conditioning on CDS Spread Changes Percent of events in following 30 days in the subset of firms with the top p% of credit spreads p Downgrade Review for Downgrade Negative Outlook 50 80** 72** 68** 25 59** 46** 48** 10 37** 28** 15 * 5% significance ** 1% significance

14 Recovery Rates and Probability of Default

15 CDS Structure 1 PD(0.25) P(s / 4) Accrual LGD = P(1 R) PD(1.75) PD(1.50)

16 Extracting Hazard Rates I Fixed Recovery Model CDS value is the PV of payments weighted by the probability that the payment occurs Often set PD( t) = 1 exp( λt) Find the hazard rate λ that sets the CDS value to zero Implied λ is sensitive to assumed recovery rate, R

17 Implied Hazard Rates 5% Implied Hazard Rate CDS Spread = 50 bp 4% 3% 2% 1% 0% 0% 20% 40% 60% 80% 100% Recovery Rate

18 A Recovery Model Hamilton, Varma, Ou, and Cantor 2005

19 Gaussian Copula Latent variable Conditioning on x x N ( 0,1) ( ) PD t x 1 N ( PD() t ) ρx = N 1 ρ 1 N ( PD() 1 ) ρx Rx= N 1 ρ

20 Conditional 1-Year PD Unconditional PD(1) = 0.02 Probability rho = rho = 0.1 rho = 0.2 rho = PD(1 x)

21 Conditional Recovery Rate Unconditional PD(1) = 0.02 Probability rho = rho = 0.1 rho = 0.2 rho = R x Rho Exp. Recovery 38.2% 38.4% 39.3% 40.5%

22 Extracting Hazard Rates II Variable 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 λ IC (s, ρ) is the copula implied hazard rate, V C (s, λ IC (s, ρ), ρ) = 0

23 Extracting Recovery Rates E C [R(λ, ρ)] is the expected recovery rate under the copula model found by integrating over the latent variable R IF (s, λ IC ) is the implied fixed recovery rate based on the copula implied hazard rate

24 Copula Implied Hazard Rate 1.0% 0.9% 0.8% CDS spread = 50 bp CDS spread = 200 bp 3.0% 2.8% 2.6% 0.7% 2.4% 0.6% 2.2% 0.5% Copula Correlation 2.0%

25 Recovery Rates Implied R s=50 E(R) s=50 Implied R s=200 E(R) s= Copula Correlation

26 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