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

End of year One-Year LIBOR

LIBOR + 2%

Pmt by MCB

Pmt by thrift Net Pmt by MCB

1 9% 11% $11 $10 +$1 2 9% 11% $11 $10 +$1 3 7% 9% $9 $10 -$1 4 6% 8% $8 $10 -$2 TOTAL $39 $40 -$1

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

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

For the bank

For the insurance firm

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