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### Interest Rate Swaps and Agreements

Chapter 28

Swaps

- CBs and IBs are major participants
- dealers
- traders
- users
- regulatory concerns regarding credit risk exposure
- five generic types of swaps
- interest rate swaps
- currency swaps
- credit swaps
- commodity swaps
- equity swaps

Interest Rate Swaps

- OTC instruments
- investors can go through securities firm or commercial bank
- firms can act as brokers or dealers for investor
- counterparty risk can be significant
- Swap can be viewed as
- package of forward/future contracts
- package from CFs from buying and selling cash market instruments
- fixed rate payer has position similar to long position in floating rate bond and short in fixed rate (borrowing by issuing fixed rate bond)
- floating payer has position like purchasing fixed rate bond and financing purchase at floating rate

Interest Rate Swaps

- counterparties agree to exchange periodic interest payments with dollar amount based on notional principal
- plain vanilla – fixed-rate payer and floating-rate payer
- reset frequency
- reference rates

Plain Vanilla Interest Rate Swap Example

- Consider money center bank that has raised $100 million by issuing 4-year notes with 10% fixed coupons. On asset side: C&I loans linked to LIBOR. Duration gap is negative.

DA - kDL < 0

- Second party is savings bank with $100 million in fixed-rate mortgages of long duration funded with CDs having duration of 1 year.

DA - kDL > 0

Interest Rate Swaps

- We depict this fixed-floating rate swap transaction in the following

Interest Rate Swaps

- The expected net financing costs for the FIs are shown below

Interest Rate Swaps

- Assume that the realized path of LIBOR over the 4 year life of the contract would be as follows 9%, 9%, 7%, and 6% at the end of each of the 4 years. The money center bank’s variable payments to the thrift are indexed to these rates by the formula:

(LIBOR + 2%) * $100m

- The annual payments made by the thrift were the same each year

10% * $100m.

Interest Rate Swaps

- example
- notional of $50m where X is fixed rate payer and Y is floating rate payer – X pays 10% per year and Y pays the 6-month LIBOR – payments every 6 months for next 5 years
- what will payments be if 6-month LIBOR is 7%

Swaps

- trade date
- effective date
- maturity date
- dates can differ for counterparties in same swap
- terminology to describe position

Swaps

- fixed rate payer is short the bond market – explain
- fixed rate payer – position that is exposed to the price sensitivities of a longer-term liability and a floating-rate bond
- floating rate payer – position that is exposed to the price sensitivities of a fixed-rate bond and a floating-rate liability

Swaps

- dealer quotes fixed payer to pay 8.85% and receive LIBOR “flat” – bid price dealer quotes floating payer is to pay LIBOR flat and receive 8.75% - spread is 10bp
- fixed rate is spread above Treasury yield curve – say 10 year Treasury yield is 8.35% - offer price dealer quoted is 10 year Treasury plus 50bp vs. receiving LIBOR flat
- bid price dealer quoted for floating payer is LIBOR flat vs. 10 year Treasury plus 40bp
- dealer quotes swap as 40-50 – dealer willing to enter into swap to receive LIBOR and pay fixed rate equal to 10-yr Treas. plus 40bp – willing to enter into swap to pay LIBOR and receive fixed rate equal to 10-yr. Treas. plus 50bp

Swap Rate

- to determine rate, remember that no upfront CFs are made, so PV of payments must be equal
- swap rate for floating payer must be rate that makes PV of payments on fixed-rate side equal to payments on floating rate side
- what rate do we use to discount CFs to find PV?
- example
- swap settlement date is January 1 at year 1
- floating-rate payments made quarterly based on actual/360
- reference rate is 3-month LIBOR
- notional amount is $100m
- term of swap is 3 years

Swap Example

- today 3-month LIBOR is 4.05%
- floating payment is
- fixed rate payer receives payment on March 31 of
- next payment from April 1 to June 30 – 91 days
- 3 month Eurodollar CD futures contract for settlement on June 30 of year 1 is 95.85 so Eurodollar futures rate is 4.15%

Swap Example

- for the fixed-rate payment
- suppose swap rate is 4.98% and quarter has 90 days

Swap Rate

- key principle in finding swap rate is no arbitrage opportunity – PV of payments received must equal PV of payments made
- rate used for discounting?
- forward discount factor is PV of $1 received at period t
- find forward discount factor for period using forward rates – but adjust rates for number of days in quarter

Forward Discount Factors

- for period 1
- for period 2
- for period 3

Swap Rate

- no arbitrage – PV of fixed = PV of floating
- fixed rate pmt for period t
- PV of fixed rate payment for period t is
- PV of fixed rate payments
- no arbitrage so

Valuing a Swap

- one year later, rates change so payments by floating rate side change – how does this affect value?

Asset/Liability Management

- bank has portfolio of $50m of 5-year loans with fixed rate of 10% - loans are interest only with semiannual pmts and principal due at end of 5 yrs – CF is $2.5m every 6 months
- to fund, bank will issue 6 month CDs on which it pays 6-month LIBOR plus 40bp
- at what LIBOR rate is bank in trouble?
- bank wants to lock in spread over cost of funds

Asset/Liability Management

- life insurance firm pays 9% over next 5 years on GIC – amount is $50m
- firm can invest $50m in 5 year floating rate security on which rate is 6-month LIBOR plus 160bp with coupon reset every 6 months
- risk for insurance firm?

Asset/Liability Management

- swap available in market has terms:
- every 6 months bank pays 8.45% (annual rate)
- every 6 months bank receives LIBOR
- every 6 months insurance firm pays LIBOR
- every 6 months insurance firm receives 8.40%
- what does swap do for each party?
- bank locks in spread of 155bp
- insurance firm locks in spread of 100bp

Asset/Liability Management

- bank – alters CF of assets from fixed to floating
- life insurance firm – alters CF of assets from floating to fixed
- asset swap – in above example
- liability swap

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