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 Libor A B 9.95% (fixed)

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 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: 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%

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 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

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

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

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

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

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 Risk-free rate: 5% 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 Go short a swap on 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 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: 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) 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: 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: get 1000 Total: 1000-883.18-100.94 =15.88