Credit Default Swaps (CDS)

Introduction to

Introduction to

CDS Market

„ CDS provide investors with the ability to

easily and efficiently short credit

„ Shorting allows positions to be taken in

f d dit i k forward credit risk

„ CDS allow hedgers or speculators to take an

unfunded position solely on credit risk unfunded position solely on credit risk

„ The market has grown from $180 billion in

notional in 1997 to $5 trillion by 2004 and the notional in 1997 to $5 trillion by 2004 and the current estimate of the market size is $17 trillion in notional**

trillion in notional

CDS Cashflows

„ A Credit Default Swap (CDS) is an insurance „ A Credit Default Swap (CDS) is an insurance

policy between two parties that protects the buyer against the loss of principal on a bond y g p p in case of a default by the issuer

Protection Protection Quarterly Premium otect o Buyer Seller Protection on Default

CDS Cashflows

„ $5MM PPL CDS, Price: 49bps $6,125 $6,125 $6,125 $6,125 $6,125 Protection Buyer Default $6, 5 $6, 5 $6, 5 $6, 5 $6, 5 3m 6m 9m 12m 15m _60m Protection Seller $3,000,000

Default Events

Cash Settlement in Case of Default

Protection Par – Recovery Protection

Cash Settlement in Case of Default

Buyer Value Seller

Deliverable Obligation

Physical Settlement in Case of Default

Protection Buyer Protection Seller Obligation Par Par

Credit Events

„ A CDS is triggered by an event that has a

material impact on the cashflows of the debt material impact on the cashflows of the debt obligation.

„ A credit event may include: „ A credit event may include:

„ Bankruptcy

„ Issuer becoming insolventg „ Failure to pay a coupon „ Obligation acceleration „ Repudiation

„ Moratorium

R t t i (if CDS i t “R” “M d R”) „ Restructuring (if CDS is type “R” or “Mod-R”)

Contract Details

„ The contract specifically references the „ The contract specifically references the

precise name of the legal entity in which it provides protection

p p

„ It is important to know the exact legal entity

and seniority of the capital structure as and seniority of the capital structure as covered by the CDS

„ Change in ownership of the bonds can „ Change in ownership of the bonds can

change the underlying reference entity of the CDS

Contract Details (cont.)

„ Since 2002 in order to increase liquidity a „ Since 2002, in order to increase liquidity, a

vast majority of CDS contracts have

standardized quarterly payments on the 20q y p y th of March, June, September and December

„ Credit events and settlement procedures in „ Credit events and settlement procedures in

case of default can be specifically defined within the contract

„ CDS contracts have become increasingly

Valuation

„ The exposure of any investment in a given issuer’sThe exposure of any investment in a given issuer s credit is defined by the equation:

)

(D

P

LGD

EAD

EL

EL=Expected Loss

)

(D

P

LGD

EAD

EL

=

×

×

EAD=Exposure at Default LGD=Loss Given Default P(D) P b bilit f D f lt P(D)=Probability of Default

Valuation (Cont.)

„ We can use a binomial model to value a simple one period CDS where protection was sold

period CDS where protection was sold C1 No Default

(1-P1)

R = Recovery Rate P1 = Probability of P1 = Probability of

Default in Period One

C1 = CDS Spread (Coupon)

f O P i d

-(1-R)

P1 for One Period

Default

Valuation (Cont.)

„ Two Periods C2 (1-P2) C1 (1-P2) (1-P1) P2 -(1-R) P2 (1 ) P1 -(1-R)

Valuation (Cont.)

„ At the inception of the swap the present „ At the inception of the swap, the present

value of the coupon payments (spread) is equal to the present value of the expected q p p default cashflow ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( P ×C P × P ×C R ×P R × P ×P 2 2 2 1 1 1 2 2 2 2 1 1 1 1 ) 1 ( ) 1 ( ) 1 ( 1 ) 1 ( ) 1 ( ) 1 ( ) 1 ( 1 ) 1 ( r P P R r P R r C P P r C P + × − × − + + × − = + × − × − + + × −

Example Calculation 1

„ Issuer: IBM

„ Issuer: IBM

„ One Year Spread: 7 bps

Assumed Recovery Rate: 40%

„ Assumed Recovery Rate: 40% „ One Year Libor Rate: 5.64%

Example Calculation 1 (Cont.)

1 1 1) (1 ) 1 ( P C − R × P = × −

Solving the equation for P1 we get:

1

1 1

1+ r = + r

Solving the equation for P1 we get:

R C C P − + = 1 1 1 1+ C₁ R 1 % 1165 . 4 0007 1 0007 . 1 = + − = P 4 . 0007 . 1+ % 88 . 99 %) 1165 . 1 ( ) 1 ( Pr obability = − P₁ = − = Survival

Example Calculation 2

„ Deal Spread: 12 bps I IBM „ Issuer: IBM „ CDS Notional: $100M „ Term: 1 Year

„ Assumed Recovery Rate: 40% „ One Year Libor Rate: 5.64% „ Par Curve Implied

„ Par Curve Implied

Survival Probability: 99.88%

Calculate the PV of a sell protection position Calculate the PV of a sell protection position

Example Calculation 2 (Cont.)

1 1 1) (1 ) 1 ( P C R P PV − × − × 1 1 1 1 1 1 ) ( 1 ) ( r r PV + − + = 0564 . 1 000 , 000 , 100 $ 001165 . ) 4 . 1 ( 0564 . 1 0012 . 000 , 000 , 100 $ ) 001165 . 1 ( + × × − − + × × − = PV Present Value = $47,275.40

*You will notice that if you replace the .0012 with .0007, the value of this t t i l t

Recovery Rates

„ An underlying assumption in the valuation of „ An underlying assumption in the valuation of

a credit default swap is the recovery rate, or the value of the bond issue after a default occurs

„ The valuation can be altered significantly if „ The valuation can be altered significantly if

the recovery rate is different from a market average of approximately 40%g pp y

Recovery Rates (Cont.)

„ Let us create a fictitious example in which the

survival probability for year one is 93% (GM). We will p y y ( ) value a contract with a spread of 400 bps with a

recover rate of both 40% and 60%

0564 . 1 000 , 000 , 100 $ 07 . ) 4 . 1 ( 0564 . 1 04 . 000 , 000 , 100 $ ) 07 . 1 ( + × × − − + × × − = PV 000 , 000 , 100 $ 07 . ) 6 . 1 ( 04 . 000 , 000 , 100 $ ) 07 . 1 ( − × × − × × − = PV Present Value = -$454,373 0564 . 1 0564 . 1+ − + = PV Present Value = +$870,882 Difference = $1,325,260

Recovery Rates and PAR CDS Spreads

„ Consider the market value of a 5 yr. $100M CDS with a

Recovery Rate

Consider the market value of a 5 yr. $100M CDS with a deal spread of 400 bps under different scenarios:

20% 30% 40% 50% 60% 70% 100 bps $11.5 $12.2 $12.9 $13.6 $14.4 $15.1 200 b $ $ $ $ $ $ Recovery Rate a te 200 bps $5.5 $6.9 $8.3 $9.7 $11.0 $12.4 300 bps $0.0 $2.0 $4.0 $6.0 $8.0 $9.9 400 bps ($5.1) ($2.6) $0.0 $2.6 $5.1 $7.7 C DS R a ( ) ( ) 500 bps ($9.8) ($6.8) ($3.7) ($0.6) $2.5 $5.5 600 bps ($14.2) ($10.6) ($7.1) ($3.5) $0.0 $3.6 700 bps ($18 2) ($14 2) ($10 3) ($6 3) ($2 3) $1 7 M arket C 700 bps ($18.2) ($14.2) ($10.3) ($6.3) ($2.3) $1.7 M

Trade Example

„ Deal Spread: 2,000 bps „ CDS Notional: $100M

„ Term: 5 Years

„ Assumed Recovery Rate: 50% „ Yearly Payment:y y $20M$ „ Default Payout: $50M

„ Breakeven Point: $50M/$20M „ Breakeven Point: $50M/$20M

Summary

„ Credit Default Swaps have increased the „ Credit Default Swaps have increased the

efficiency of the lending market while giving investors an option to easily take on long or p y g short credit exposure

„ The CDS market also provides investors the „ The CDS market also provides investors the

opportunity to create excess returns by

forecasting both recovery rates and survival g y probabilities