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Chapter 13

Chapter 13. Forward Rate Agreements FRAs. If a deal was mathematically complex in 1993 and 1994, that was considered innovation. But this year, what took you forward with clients wasn’t the math – it was bringing them the most efficient application of a product. Mark Wells

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Chapter 13

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  1. Chapter 13 Forward Rate Agreements FRAs

  2. If a deal was mathematically complex in 1993 and 1994, that was considered innovation. But this year, what took you forward with clients wasn’t the math – it was bringing them the most efficient application of a product. Mark Wells Risk, January, 1996, p. R15

  3. A derivative on an interest rate: • The payoff of a derivative on a bond is based on the price of the bond relative to a fixed price. • The payoff of a derivative on an interest rate is based on the interest rate relative to a fixed interest rate. • In some cases these can be shown to be the same, particularly in the case of a discount instrument. In most other cases, however, a derivative on an interest rate is a different instrument than a different on a bond. • See Figure 13.1, p. 467 for notional principal of FRAs and interest rate options over time.

  4. Forward Rate Agreements • Definition • A forward contract in which the underlying is an interest rate • An FRA can work better than a forward or futures on a bond, because its payoff is tied directly to the source of risk, the interest rate.

  5. Forward Rate Agreements (continued) • Some possible payoffs. If LIBOR at expiration is 8 percent, • So the long has to pay $98,039. If LIBOR at expiration is 12 percent, the payoff is • Note the terminology of FRAs: A  B means FRA expires in A months and underlying matures in B months.

  6. Forward Rate Agreements (continued) • The Pricing and Valuation of FRAs • Let F be the rate the parties agree on, h be the expiration day, and the underlying be an m-day rate. L0(h) is spot rate on day 0 for h days, L0(h+m) is spot rate on day 0 for h + m days. Assume notional principal of $1. • To find the fixed rate, we must replicate an FRA: • Short a Eurodollar maturing in h+m days that pays 1 + F(m/360). This is a loan that can be paid off early or transferred to another party • Long a Eurodollar maturing in h days that pays $1

  7. Forward Rate Agreements (continued) • The Pricing and Valuation of FRAs (continued) • On day h, • Loan we owe has a market value of • Pay if off early. Collect $1 on the ED we hold. So total cash flow is

  8. Forward Rate Agreements (continued) • The Pricing and Valuation of FRAs (continued) • This can be rearranged to get • This is the payoff of an FRA so this strategy is equivalent to an FRA. With no initial cash flow, we set this to zero and solve for F: • This is just the forward rate in the LIBOR term structure. See Table 13.1, p. 471 for an example.

  9. Forward Rate Agreements (continued) • The Pricing and Valuation of FRAs (continued) • Now we determine the market value of the FRA during its life, day g. If we value the two replicating transactions, we get the value of the FRA. The ED we hold pays $1 in h – g days. For the ED loan we took out, we will pay 1 + F(m/360) in h + m – g days. Thus, the value is • See Table 13.2, p. 472 for example.

  10. Forward Rate Agreements (continued) • Applications of FRAs • FRA users are typically borrowers or lenders with a single future date on which they are exposed to interest rate risk. • See Table 13.3, p. 473 and Figure 13.2, p. 474 for an example. • Note that a series of FRAs is similar to a swap; however, in a swap all payments are at the same rate. Each FRA in a series would be priced at different rates (unless the term structure is flat). You could, however, set the fixed rate at a different rate (called an off-market FRA). Then a swap would be a series of off-market FRAs.

  11. A forward rate agreement (FRA) • The buyer of a FRA agrees to pay a fixed-rate coupon payment (at the exercise rate) and receive a floating-rate payment against a notional principal amount at a specified future date. • The buyer of a FRA will receive (pay) cash when the actual interest rate at settlement is greater than the exercise rate (specified fixed-rate). • The seller of a FRA agrees to make a floating-rate payment and receive a fixed-rate payment against a notional principal amount at a specified future date. • The seller of a FRA will receive (pay) cash when the actual interest rate at settlement is less than the exercise rate.

  12. Forward rate agreements (FRA) • While futures and forward contracts are similar, forward contracts differ because • they are negotiated between counterparties • there is no daily settlement or marking-to-market • no exchange guarantees performance

  13. Notional principal amounts • The two counterparties to a FRA agree to a notional principal amount that serves as a reference figure in determining cash flows. • the principal does not change hands, but is only used to calculate the value of interest payments. • The buyer agrees to pay a fixed-rate coupon payment and receive a floating-rate payment against the notional principal at some specified future date. • The seller agrees to pay a floating-rate payment and receive the fixed-rate payment against the same notional principal.

  14. Example of an FRA: • ABC Bank would refer to this as a “3 vs. 6” FRA at 7 percent on a $1 million notional amount from XYZ Bank. • a 6-month maturity • based on a $1 million notional principal amount • floating rate is 3-month LIBOR and the fixed (exercise) rate is 7 percent • The phrase “3 vs. 6” refers to a 3-month interest rate observed three months from the present, for a security with a maturity date six months from the present. • The only cash flow will be determined in six months at contract maturity by comparing the prevailing 3-month LIBOR with 7 percent.

  15. Example of FRA (cont’d). • In three months the 3-month LIBOR equals 8 percent. • In this case, ABC Bank would receive from XYZ Bank $2,451. • The interest settlement amount is $2,500: • interest = (.08 - .07)(90/360) $1,000,000 = $2,500. • Because this represents interest that would be paid three months later at maturity of the instrument, the actual payment is discounted at the prevailing 3-month LIBOR: • actual interest = $2,500/[1+(90/360).08]=$2,541 • If instead, LIBOR equals 5 percent in three months. ABC Bank would pay XYZ Bank: • interest = (.07 -.05)(90/360) $1,000,000 = $5,000 • or $5,000 /[1 + (90/360).05] = $4,938

  16. Similarities to a futures contract… • In this example, XYZ Bank would pay fixed-rate/receive floating-rate as a hedge if it was exposed to loss in a rising rate environment. • This is the same effect as a short futures position • ANC Bank would take its position as a hedge if it was exposed to loss in a falling (relative to forward rate) rate environment. • This is the same effect as a long futures position

  17. Comparing Futures, Swaps and FRAs. • Futures are standardized contracts based on fixed principal amounts. • Parties negotiate the notional principal amount with FRAs and interest rate swaps. • Financial futures require daily marking-to-market, which is not required with FRAs and swaps. • The market for FRAs is not too liquid and most contracts are short-term.

  18. The case of Tridant Corp From Chapter 14 Interest Rate & Currency Swaps Fundamentals of Multinational Finance Michael H. Moffett, Arthur I. Stonehill, David K. Eiteman

  19. Trident’s Floating-Rate Loans • Example using Trident corporation’s loan of US$10 million serviced with annual payments and the principal paid at the end of the third year • The loan is priced at US dollar LIBOR + 1.50%; LIBOR is reset every year • When the loan is drawn down initially (at time 0), an up-front fee of 1.50% is charged • Trident will not know the actual interest cost until the loan has been completely repaid

  20. Trident’s Floating-Rate Loans

  21. Trident’s Floating-Rate Loans • If Trident had wished to manage the interest rate risk associated with the loan, it would have a number of alternatives • Refinancing – Trident could go back to the lender and refinance the entire agreement • Forward Rate Agreements (FRAs) – Trident could lock in the future interest rate payment in much the same way that exchange rates are locked in with forward contracts • Interest Rate Futures • Interest Rate Swaps – Trident could swap the floating rate note for a fixed rate note with a swap dealer

  22. Forward Rate Agreements (FRAs) • A forward rate agreement is an interbank-traded contract to buy or sell interest rate payments on a notional principal • Example: If Trident wished to lock in the first payment it would buy an FRA which locks in a total interest payment at 6.50% • If LIBOR rises above 5.00%, then Trident would receive a cash payment from the FRA seller reducing their LIBOR payment to 5.0% • If LIBOR falls below 5.00% then Trident would pay the FRA seller a cash amount increasing their LIBOR payment to 5.00%

  23. Interest Rate Futures • Interest Rate futures are widely used; their popularity stems from high liquidity of interest rate futures markets, simplicity in use, and the rather standardized interest rate exposures firms posses • Traded on an exchange; two most common are the Chicago Mercantile Exchange (CME) and the Chicago Board of Trade (CBOT) • The yield is calculated from the settlement price • Example: March ’03 contract with settlement price of 94.76 gives an annual yield of 5.24% (100 – 94.76)

  24. Interest Rate Futures • If Trident wanted to hedge a floating rate payment due in March ’03 it would sell a futures contract, or short the contract • If interest rates rise, the futures price will fall and Trident can offset its interest payment with the proceeds from the sale of the futures contracts • If interest rates rise, the futures price will rise and the savings from the interest payment due will offset the losses from the sale of the futures contracts

  25. Exposure or Position Futures Action Interest Rates Position Outcome Sell a futures (short) Buy a futures (long) Paying interest on futures date Earning interest on futures date If rates go up If rates go up Futures price falls; Short earns profit Futures price falls; Long earns a loss If rates go down If rates go down Futures price rises; short earns a loss Futures price rises; Long earns profit Strategies Using Interest Rate Futures

  26. Interest Rate Swaps • Swaps are contractual agreements to exchange or swap a series of cash flows • If the agreement is for one party to swap its fixed interest payment for a floating rate payment, its is termed an interest rate swap • If the agreement is to swap currencies of debt service it is termed a currency swap • A single swap may combine elements of both interest rate and currency swap • The swap itself is not a source of capital but an alteration of the cash flows associated with payment

  27. Interest Rate Swaps • If firm thought that rates would rise it would enter into a swap agreement to pay fixed and receive floating in order to protect it from rising debt-service payments • If firm thought that rates would fall it would enter into a swap agreement to pay floating and receive fixed in order to take advantage of lower debt-service payments • The cash flows of an interest rate swap are interest rates applied to a set amount of capital, no principal is swapped only the coupon payments

  28. Trident Corporation:Swapping to Fixed Rates • Maria Gonzalez (Trident’s CFO) is concerned about the floating rate loan • Maria thinks that rates will rise over the life of the loan and wants to protect Trident from an increased interest payment • Maria believes that an interest rate swap to pay fixed/receive floating would be Trident’s best alternative • Maria contacts the bank and receives a quote of 5.75% against LIBOR; this means that Trident will receive LIBOR and pay out 5.75% for the three years

  29. Trident Corporation:Swapping to Fixed Rates • The swap does not replace the original loan, Trident must still make its payments at the original rates; the swap only supplements the loan payments • Trident’s 1.50% fixed rate above LIBOR must still be paid along with the 5.75% as per the swap agreement; however, Trident now receives LIBOR thus offsetting the floating rate risk in the original loan • Trident’s total payment will therefore be 7.25% (5.75% + 1.50%)

  30. Trident Corporation:Swapping to Fixed Rates

  31. Trident Corp:Swapping Dollars into Swiss francs • After raising the $10 million in floating rate financing and swapping into fixed rate payments, Trident decides it would prefer to make its debt-service payments in Swiss francs • Trident signed a 3-year contract with a Swiss buyer, thus providing a stream of cash flows in Swiss francs • Trident would now enter into a three-year pay Swiss francs and receive US dollars currency swap • Both interest rates are fixed • Trident will pay 2.01% (ask rate) fixed Sfr interest and receive 5.56% (bid rate) fixed US dollars

  32. Trident Corp:Swapping Dollars into Swiss francs

  33. Trident Corp:Swapping Dollars into Swiss francs • The spot rate in effect on the date of the agreement establishes what the notional principal is in the target currency • In this case, Trident is swapping into francs, at Sfr1.50/$. • This is a notional amount of Sfr15,000,000. Thus Trident is committing to payments of Sfr301,500 (2.01%  Sfr15,000,000 = Sfr301,500) • Unlike an interest rate swap, the notional amounts are part of the swap agreement

  34. Trident Corp:Swapping Dollars into Swiss francs

  35. Trident Corporation:Unwinding Swaps • As with the original loan agreement, a swap can be entered or unwound if viewpoints change or other developments occur • Assume that the three-year contract with the Swiss buyer terminates after one year, Trident no longer needs the currency swap • Unwinding a currency swap requires the discounting of the remaining cash flows under the swap agreement at current interest rates then converting the target currency back to the home currency

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