17-Swaps and Credit Derivatives

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?

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

A B9.95% (fixed)

Libor

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.

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.

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

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 -$95,000 -$95,000 -$95,000

Difference -$10,000 $0 $10,000 $20,000

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?

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

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.

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?

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%

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)

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.

Swaps and Comparative Advantage

One simple approach:

1. Each firm borrows in market (fixed or floating) in which it has a comparative advantage.

2. Swap Rates:1. Floating rate is same as floating rate of company

borrowing at floating rate.

2. Fixed Rate is same as fixed rate of company borrowing at floating rate less X%

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.

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.

Credit Default Swap

(Bank) (Speculator in credit derivatives)

Basic Contract terms

Reference Entity– 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

Example

Reference Entity– $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

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

Example: $10M 5 year CDS @ 500 basis points with Credit Event

Contract is terminated. No further payments.

and accrued interest

Growth of Underlying CDS Market

0

1

2

3

4

5

6

7

8

9

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

To

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ated

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Source: “Bear Sterns Structured Credit Products”, December 2005

Tril

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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

Example

Zero coupon bond– Matures in one year– Face value: 1000– Probability of default: 25%– Recovery rate: 60%– Price: 841.12

Risk-free rate: 5%

Swap rate: YTM – 5% = 18.89% - 5% = 13.89%

Example

Borrow 841.12, buy bond– Cost: 0– No default payoff: 1000 – 841.12*(1.05) = 116.82– Default payoff: 600 - 841.12*(1.05) = -283.18

Go short a swap on bond– Cost: 0– No default payoff: .1389*841.12 = 116.83– Default payoff: 600 – 1000 + .1389*841.12 = -283.18

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

Example

No 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: 126.17+883.18-1000 = 9.35

Default:– Short swap: get .15*841.12 =126.17– Short swap: pay out 1000– Short swap: get bond (use to close out short position)– Risk-free account: get 1.05*841.12=883.18– Total: 126.17-1000+883.18= 9.35

Example

In either state earn 9.35 Note: 9.35 = [(actual swap rate) – (no-arbitrage swap rate)]*P=(.15 - .1389)*841.12

If actual swap rate < no-arbitrage swap rate– Go long swap– Borrow money, buy bond

Example

Actual swap rate = 12%

No default:– long swap: pay out .12*841.12 = 100.94– Liability: pay out 1.05*841.12=883.18– Long bond: get 1000– Total: 1000-883.18-100.94= 15.88

Default:– long swap: pay out .12*841.12 = 100.94– Liability: pay out 1.05*841.12=883.18– Long swap: get 1000– Total: 1000-883.18-100.94 =15.88