1. 17-Swaps and Credit Derivatives

2. Questions What is an interest rate swap?
How is it used to hedge interest rate risk?
How does comparative advantage create swap opportunities?
What is a credit default swap?
What is the no arbitrage CDS rate?

3. Swaps
An agreement between two parties to exchange cash flows in the future.
Cash flows and dates when cash is exchanged are specifically defined.
Example:
A agrees to pay B the Libor rate at the end of each
“B” agrees to give “A” 9.95%
Both rates are a percentage of some notional amount
Libor A B
9.95% (fixed)

4. Swaps: What is the Purpose?
Example:
Banks have a natural mismatch between the durations of assets and liabilities.
As a result, equity takes a hit when rates go up.

5. Example: Asset & Liability Management
Risk Management Techniques
Reduce the duration of the assets.
Increase the duration of the liabilities.
Take a short position on treasury futures
Buy a put on treasury bonds or treasury futures.
Use an interest rate swap.

6. Interest Rate Swaps Example: An interest rate swap
principal value of $1M
exchanges annually
Floating cash flow: one-year LIBOR rate plus 5.5%
Fixed cash flow: 9.5% interest rate
Maturity: thirty years.
The Bank may want to pay fixed and receive floating

7. Cash Flows of Floating for Fixed Swap
The swap does not cost anything upfront.
This swap is equivalent to going long in floating-rate bonds (lending money at a floating rate) and going short in fixed-rate bonds (borrowing money at a fixed rate).
LIBOR Rate 3% 4% 5% 6%
Floating Cash Flow
$85,000
$95,000
$105,000
$115,000
Fixed Cash Flow
-$95,000
Difference
-$10,000 $0
$10,000
$20,000

8. Swaps and Comparative Advantage
A bank has a small client called “the firm”
Suppose the banks and the firm can borrow at rates:
Fixed Floating
Bank 10% Libor+0.3%
Firm 12% Libor+1.0%
Who has the better credit rating?

9. Swaps and Comparative Advantage
Note that the firm pays 2% more in fixed markets and only .7% more in floating markets.
If the default risk of the firm increases:
Floating rate lenders can charge higher rates, or refuse to roll-over loans
Fixed-rate lenders are stuck and will likely be stuck with losses

10. Swaps and Comparative Advantage
Relative to the bank, the firm has a comparative advantage in floating markets
Relative to the firm, the bankhas a comparative advantage in fixed markets.

11. Swaps and Comparative Advantage
Suppose the bank has more tolerance for bearing the default risk of the firm than the market
Since the firm is a client of the bank, the bank has “insider information” about the financial health of the firm
Suppose the firm wants to borrow at fixed
wants to avoid interest rate risk
Can the two enter a swap and be better off than borrowing at market rates?

12. Swaps and Comparative Advantage
Suppose the firm borrows from outside lenders at L+1%
Suppose the bank borrows from outside lenders at 10%
The bank and the firm can then enter a swap with
The firm paying the bank a fixed rate 11.35
The bank paying the firm a floating rate L + 1%

13. Swaps and Comparative Advantage
The firm
Pays Libor +1% (outside lenders)
Receives Libor + 1% (from the bank)
Pays 11.35% (to the bank)
Net: Paying 11.35% Fixed
(.65% better than at fixed market rates)
The bank
Pays 10% (outside lenders)
Receives 11.35% (from the firm)
Pays Libor + 1 %
Net: Paying Libor – 0.35%
(.65% better than at floating market rates)

14. Swaps and Comparative Advantage
Cost to bank: bears default risk of firm
May be willing to do so if it wants to maintain the firm as a client and is generating fees from other services it is offering the client.
Bank has insider information
Firm pays 11.35% fixed only if it can continue to borrow floating at 1% over Libor.
If default risk increases, firm could lose benefit of swap.

15. Swaps and Comparative Advantage
One simple approach:
Each firm borrows in market (fixed or floating) in which it has a comparative advantage.
Swap Rates:
Floating rate is same as floating rate of company borrowing at floating rate.
Fixed Rate is same as fixed rate of company borrowing at floating rate less X%

16. Swaps and Comparative Advantage
How to find X
Find total possible gain
Difference in fixed rates minus difference in floating rates
Divide this difference by 2
Setting up the swap in this way will allow the bank and firm to split the gain.

17. Credit Derivatives
Credit derivatives are financial contracts designed to reduce or eliminate credit risk exposure by providing insurance against losses suffered due to credit events.
Banks can repackage and parcel out credit risk while retaining assets on balance sheet and thus maintain client relationships.
Bank can transfer the credit risk of illiquid assets if it cannot transfer the assets themselves.

18. Credit Default Swap
(Bank)
(Speculator in credit derivatives)

19. Basic Contract terms Reference Entity Notional Amount Maturity
The underlying asset (e.g., a bond)
Notional Amount
Value of reference entity at swap origination
Maturity
Date when swap contract matures
Credit events
Bankruptcy, failure to pay, debt restructuring
Price
Fixed-rate to be paid/received

20. Example Reference Entity Notional Amount Maturity Credit events Price
$10 million dollar bond
Notional Amount
$10 million (par value)
Maturity
5 years
Credit events
Bankruptcy, failure to pay, debt restructuring
If a credit event occurs, protection seller pays par value of bond
Note that protection seller bears interest-rate risk
Price
500 basis points

21. Example: $10M 5 year CDS @ 500 basis points with No Credit Event

22. Example: $10M 5 year CDS @ 500 basis points with Credit Event
and accrued interest
Contract is terminated. No further payments.

23. Growth of Underlying CDS Market
Trillions
Source: “Bear Sterns Structured Credit Products”, December 2005

24. Credit Default Swap - Pricing
Swap Rate = Default risk premium
Short Swap: Sell protection in the default swap market and earn the swap rate or
Borrow at risk-free, buy bond, and earn the spread

25. Example Zero coupon bond Risk-free rate: 5%
Matures in one year
Face value: 1000
Probability of default: 25%
Recovery rate: 60%
Price:
Risk-free rate: 5%
Swap rate: YTM – 5% = 18.89% - 5% = 13.89%

26. Example Borrow 841.12, buy bond Go short a swap on bond Cost: 0
No default payoff: 1000 – *(1.05) =
Default payoff: *(1.05) =
Go short a swap on bond
No default payoff: * =
Default payoff: 600 – * =

27. Example
If swap rate is not 13.89%, then an arbitrage opportunity exists.
Suppose swap rate is 15%
Go short swap
Short bond (assuming its possible)
Invest proceeds at risk-free rate

28. Example No default: Default: Short swap: get .15*841.12 = 126.17
Risk-free account: get 1.05*841.12=883.18
Short bond: must pay out 1000
Total: = 9.35
Default:
Short swap: get .15* =126.17
Short swap: pay out 1000
Short swap: get bond (use to close out short position)
Total: = 9.35

29. Example In either state earn 9.35 Note: 9.35 =
[(actual swap rate) – (no-arbitrage swap rate)]*P
=( )*841.12
If actual swap rate < no-arbitrage swap rate
Go long swap
Borrow money, buy bond

30. Example Actual swap rate = 12% No default: Default:
long swap: pay out .12* =
Liability: pay out 1.05*841.12=883.18
Long bond: get 1000
Total: = 15.88
Default:
Long swap: get 1000
Total: =15.88