Interest Rate Swaps and Agreements

1. Interest Rate Swaps and Agreements Chapter 28

2. 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

3. 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

4. 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

5. 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

6. Interest Rate Swaps • We depict this fixed-floating rate swap transaction in the following

7. Interest Rate Swaps • The expected net financing costs for the FIs are shown below

8. 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.

9. Interest Rate Swaps

10. 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%

11. Swaps

12. Swaps • trade date • effective date • maturity date • dates can differ for counterparties in same swap • terminology to describe position

13. 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

14. 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

15. 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

16. 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%

18. Swap Example • for the fixed-rate payment • suppose swap rate is 4.98% and quarter has 90 days

20. 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

22. Forward Discount Factors • for period 1 • for period 2 • for period 3

24. 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

26. Valuing a Swap • one year later, rates change so payments by floating rate side change – how does this affect value?

30. 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

31. 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?

32. 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

33. For the bank

34. For the insurance firm

35. 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