1. Interest Rate & Currency Swaps

2. Swaps Swaps are introduced in the over the counter market 1981, and 1982 in order to: restructure assets, obligations mitigate and transfer risk for those who wish to avoid it to those who are equipped to take it for profit. Reduce volatility of earnings

3. Motivations for Swaps To transform floating rate obligations synthetically to fixed rate. -To write off tax loss carry forward before they expire. -To manage interest rate risk at a lower cost relative to any other derivatives in its class as reflected in its enormous volume. - To Reduce volatility of earnings

5. Synthetic Fixed Rate via FRA Suppose 1 year LIBOR is currently at 3.75%. XYZ corporation wishes to borrow $100 over a three year period. She wishes to have fixed rate liability. Can borrow at the floating rate as follows: Borrow at floating rate of LIBOR+2% Enter into a 12X24 FRA, paying 5 percent receiving LIBOR. Enter into a 24X36 FRA, paying 6 percent and receiving LIBOR

6. Continued XYZ can mitigate interest rate risk by entering into FRA. By entering into a 12X24 FRA, she can fixes its interest rate at 7 percent for the second year. By entering into a 24X36 FRA, she can fixes its interest rate at 8 percent for the third year. Year 1 pay 5.7% Year 2 pay 6% Year 3 pay 8 %

7. Interest rate convention

8. Fixed for Floating rate Swap In the following swap, the construction company initially borrows at L+1%, and convert the variable rate into fixed rate of 6 percent. Construction Company Bank of America 5% Fixed rate LIBOR LIBOR+1%

14. Valuation of Swap

15. Interest rate caps are call options on interest rates where the buyer of the cap pays to the seller of the cap, usually an intermediary or insurance company, a fee upfront so that the buyer gets protection from rising interest rates above the strike price (the cap rate) agreed by both parties. Interest Rate Caps, Floors, Collars

16. Interest rate Cap

18. All in-cost of cap Example: Suppose six-month LIBOR is equal to 9.25 percent in the next reset date, the borrower pays the LIBOR+1.25 percent on the outstanding balance of $5 million and receives 1 percent from the seller of the cap on scheduled semiannual payment dates as follows: Borrower pays: (.1050)x ½ x $5,000,000 = $262,500 Borrower receives: (.01) x1/2 x $5,000,000 = $25,000 Borrower pays cap insurance premium of = $15,220.167 All in-cost of cap = $252,720.16

19. Floors are the put option that provides downside protection on the underlying instrument with an unknown payoff in the future, which provides insurance that the return will be no less than the minimum rate, “floors rate “ of say 5 percent over the life of the option. Floors

20. Behavior of Floors Payments, Market Rate for a 5 Percent Floor

21. 5.09 5.5 % Annualized Floors premium =MAX (R C –R f, 0) LIBOR over time Interest Earned Unhedged Pay off Floors pay off Floors Premium

22. Example Fabulous Fund has invested $10 million in a portfolio of bonds promising investors a minimum return of 3.5 percent guaranteed over a five year investment horizon and the potential for high returns is tied to the performance of the Lehman Brothers government/credit index. The portfolio manager has purchased floors at the strike price of 5.5 percent in the over the counter market for the life of the portfolio by paying an upfront fee at the offer rate of 1.75 percent on the notional principal of $10 million.

23. Floors premium =.0175 x $10,000,000 = $175,000 Amortized floors premium = 175,000[(1+.06/2)^10 -1]/ [(1+.06/2)^10 x.06/2] =$20,515.33 The annualized floors premium is equal to $41,030.66 that translates to 41 basis points per year on the notional principal of $10 million assuming the fixed rate for a five- year debt is equal to 6 percent per annum. A summary of the cash flow assuming the return in the portfolio is equal to the return in the benchmark of 4.5 percent in the first six months is presented as follows: $10,000,000 x.045/2 = $225,000 Cash flow Received on Floors Protection: Since the rate has fallen below the floors rate of 5.5 percent, the floors are activated and the buyer of the floors receives the interest rate differentials from the seller as follows: Cash Flow Received on Floors Protection: $10,000,000 x (.055-.045)/2 = $50,000 Amortized Premium Paid for the Floors: $20,515.33 Total Net Semiannual Cash flow = $254,484.67 The annualized return = $508,969.34/$10,000,000 =.0509

24. Buying the cap (call option) or the floor (put option), and simultaneously selling the floor or the cap creates collars. The motivation for such a transaction is to finance some or all of the cost of the purchase of the caps or floors by selling the floors or caps and foregoing the potential of a decrease in floating rate borrowing or an increase in investment return that could improve the performance of the portfolio of floating rate notes. Interest Rate Collars

27. Example: A U.S. Money Manager buying three-year collars can finance the purchase of three-year 4 percent floors at the offer price of 62 basis points by selling 6 percent cap at the bid price of 69 basis points as shown in the following exhibit. 4.025 % 6.025 % Interest rate Collar 64 LIBOR Over time % Interest Earned

28. Cap premium = 69 bps/[(1+.05/2)^6 -1]/[(1+.05/2)^6 x.05/2] = 12.5 bps Floor premium= 62 bps/[(1+.05/2)6-1]/[(1+.05/2)^6 x.05/2] = 11.25 bps The collar has two pay-offs, depending on whether the cap or floor is activated. The cap is activated over and above the strike price of 6%, when floor is worthless, while the floor is activated below 4%, when the cap is worthless. 1. Pay-off of Collar = (6% + 25bps -22.5bsp)=6.025% 2. Pay-off of Collar = (4% - 22.5bps +25bps)=4.025%

29. Interest Rate Corridor Corridor is a portfolio of two caps; the borrower buys one cap at a certain strike price and simultaneously sells the second cap at a higher strike price to offset some of the cost of the cap purchased.

30. A swaption provides the right not an obligation to enter into an n-year swap agreement say in the next six months. For an upfront premium Mercury Inc. in Illustration 7.1 can enter into a swaption that is an option on the swap, to swap floating rate for fixed rate of 6 percent in the next six months over the swap period of say three years. If in the next six months the fixed interest rate on a three-year loan increases to 8 percent Mercury exercises its right to enter into the swap agreement. However, if the interest rates on a three-year fixed rate loan drops to 5 percent, the swaption is worthless and expires without being exercised and Mercury can secure better terms in the market.

32. There are several risks that need to be considered in the interest rate and currency swaps. They are: The basis risk due to the mismatch of the cash flow created, The counterparty or credit exposure, and, The sovereign risk Swaps Risks

33. To mitigate the counterparty risk to the financial institution engaged in derivative transactions such as swaps the Bank for International Settlement (BIS) has imposed a minimum capital requirement to provide a buffer against large unexpected losses. The amount of capital for financial institutions exposed to interest rate and currency risks has to be equal to three times the ten-day value at risk with 99 percent confidence interval.

34. Currency Swaps In a simple plain vanilla currency swap two parties agree to exchange periodic interest in two different currencies over specific periods of time as well as to exchange the notional principal at the maturity at the agreed rate.

37. The break-even swap rate The annualized swap rate is estimated from the above equation to be 7.7039 percent. This is the rate that IBM’s treasurer uses as a benchmark to compare the rate on the pound denominated loan in the Eurocredit market. If the rate in the Europound (pound loan offshore) for a five-year loan is greater than 7.7039 percent, then swapping dollars with pounds in the above example makes economic sense. Otherwise IBM may be better off directly borrowing in the Europound market.

38. For example, in the currency swap the British Petroleum decides to terminate the swap at the end the third year. The pound has depreciated to $1.42/pound and the two year debt in dollars and pounds are rated to yield 4 and 5 percent, respectively. Termination fee = -$158.5674 + 148.6776 = -$9.8899 million Unwinding Currency Swaps