1. Interest Rate & Currency Swaps The numbers in the table is in trillions of dollars. By second half of 2008, interest rate swap amounted to $328.11 trillion, while currency swap was over $14 trillion.

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

4. L+1.25% LIBOR Converting variable rate into fixed rate via FRA In the above structure, buyer of FRA who has variable rate liability at the rate of LIBOR plus 1.25 percent buys 3-year FRA, paying 7 percent while receiving LIBOR. This structure converts variable rate into fixed rate of 8.25 percent.

5. Synthetic Fixed Rate via FRA Suppose 1 year LIBOR is currently at 3.75%. XYZ corporation wishes to borrow $100 millions over a three year period. She wishes to have fixed rate liability. XYZ can take the following course of action to synthetically convert variable rate into fixed 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 % A 12X24 FRA begins in 12 months and ends in 24 months. Other FRAs are defined the same way.

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%

9. The semi-annual settlement in the above structure allows the conterparties to exchange cash flows based on the 3-month LIBOR prevailing 6 months earlier. This is the grace period in which parties are aware of their obligations. For example, the first settlement due in August 11,02 is based on LIBOR rate prevailing in Feb 11, 02, and other periods likewise.

10. In the above swap, party A has absolute advantage in both fixed and floating rate. However, relatively speaking A enjoys comparative advantage in the fixed rate only, while B having absolute disadvantage in both rates, enjoys comparative advantage in the variable rate. The counterparties are instructed to borrow where they enjoy comparative advantage. The gains in the above swap is equal to fixed rate differential and variable rate differential, that is 50 basis points to be divided among three parties, the party A, party B and the swap dealer.

11. In the above structure, there is no swap dealer and both parties borrow where they have comparative advantage. Namely, party A borrows fixed rate, while party B borrowing at the floating rate, then they swap. As can be verified from the exhibit, party A pays 5% for fixed rate, receiving 5.75%, while assuming variable rate at LIBOR plus 2 percent which effectively locks party A at LIBOR plus 1.25% basis points which is better than LIBOR +1.5% by 25 basis points in the previous slide. Party B on the other hand borrowing at L+2, receiving L+2 for swap, while paying 5.75 % for assuming fixed rate obligation that is 25 bps better than borrowing 6 % without swap in the previous slide.

12. In the above 5 year interest rate swap with semi-annual settlement, where Mercury Inc pays L+2 while receiving fixed rate of 5.75 percent on notional principal of $10 millions based on stripes of forward LIBOR implied from the IMM index as reported by Wall Street Journal. The implied LIBOR is equal to 100-IMM index. The interest paid is equal implied LIBOR+2 percent.

13. The gains in the above swap is equal to 50 basis points to be divided among three parties, the party A, party B and the swap dealer. As can be verified party A is paying and receiving fixed rate of 5 %, while assuming variable rate at L+1.35%, that saves A, 15 bps. Party B, borrowing and lending (paying and receiving L+2%), while paying 5.85%, for a saving of 15bps. Swap dealer for taking counter party risk, receiving net 85 bps in the fixed rate market, while paying net 65 bps for a net profit of 20 bps. These spreads to all three adds up to 50 bps, that is equal to the gains from the swap.

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

25. For example, the buyer of 3-years cap, pays 79 bps, while the seller of the 3-years cap receiving at the bid 69 bps.

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. Value at Risk Notional amount Sensitivity Analysis, Duration ignores non- linearity in the price yield relationship Scenario Analysis, allows investor to investigate nonlinear extreme effect on price, but fails to associate risk with a probability. Both sensitivity and scenario analysis do not allow for the aggregation of risk across different markets. Value at risk achieves all of the above.

35. Value at Risk (VAR) VAR provides a framework for the analysis of potential unexpected loss over a specific horizon and a given confidence interval. VAR estimate recognizes various sources of risk and expresses loss in terms of probability. VAR= amount of exposure*volatility*confidence interval VAR (dP) = D.P x VAR(dy)

36. VAR Consider a hedge fund is contemplating on Japanese yen devaluation against US dollar. The hedge funds sells $5 billion worth of Japanese yen at the CME. Using 10 years of data from 1985-1994, we estimated VAR at 95 percent confidence Interval. 2512 observations of daily returns are used to generate estimate of VAR. VAR=$47,401,685

37. Distribution of Losses Left Tail

38. Distribution of Losses and Gains

39. Margin Setting CME or CBOT has set as of March 12, 2007, the initial margin in JPY/USD futures at $1350. The size of contract is ¥ 12,500,000. The spot exchange on march 12 was ¥116/$. The volatility of the exchange rate is estimated to be 8.4%. What is the 1-day VAR at 99% confidence interval? VAR=2.33(8.4%/ )x 12,500000/116= $1300 In the OTC market the level of margin is related to the amount of volatility and exchange rate.

40. VAR: Caveats Shortcomings: VAR does not define the worst loss VAR does not describe the losses on the left tail, it does not say anything about the distribution of the losses. VAR is measured with some error VAR(T days)=VAR(1-day)*T^1/2

41. 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 prevailing rates. Currency swap for mitigating foreign exchange rate risk, as both IBM and British Petroleum derives revenue in pound and US dollar. IBM assumes pound exposure, and BP assumes dollar exposure. Then IBM and BP enters into currency and interest rate swaps that naturally hedges their foreign currency earnings. Pound earnings for IBM hedges pound payables in pound denominated loan. Likewise, dollar earnings for BP hedges dollar payables as BP assumes dollar exposure by borrowing dollar denominated loan.

43. The gains in the above swap structure is 75 bps, to be divided say equally among three parties. As can be verified IBM borrowing dollar where it has comparative advantage, where it pays and receives 6% for dollar denominated loans, while paying 6.75 percent for pound loan, a saving of 25 bps as compared to no swap at 7 %. BP also does the same as borrows pound where she has comparative advantage, paying 7.5%, receiving the same in the swap while paying 7 for dollar loan that saves her 25 bps. Swap dealer nets 25 bps assuming dollar and pound basis points are the same value. The book explains in some detail how to convert correctly basis points in foreign currency to the US dollar.

44. 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.

45. 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. How much is the termination fee? Termination fee = -$158.5674 + 148.6776 = -$9.8899 million Unwinding Currency Swaps