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Questions Practice on ED Futures Updated 5 March 2003 Question 1. Suppose that on 8 February, exactly at the close of trading, you opened a futures position consisting of long 100 June Eurodollar contracts. The 8 February settlement price was 95.03, and this was the price at which you established the position. The settlement prices on 9, 10, and 11 February were 94.89, 94.76, and 94.95. What cash flows did you pay and receive? (The payments would actually be made into or withdrawn from your margin account.) Solution: The changes in the implied ED interest rate were 14 basis points, 13 basis points, and 19 basis points. Using the fact that the DV01 of the ED contract is 25, your daily cash flows are 100( 25)(14) = 35,000, 100( 25)(13) = 32,500, and 100( 25)( 19) = 47,500. Question 2. The last trading day for the Eurodollar futures contract is Monday, 15 June. The current price of this contract is 94.38. Suppose that you enter into a long position in a single June Eurodollar contract (long 1 ED contract) at the price of 94.38, and hold the position until the end of the last trading day. On that day (15 June), 3-month LIBOR is 4.00%, and 1-month LIBOR is 3.75%. How much money did you make or lose? Solution: The daily cash flows can be computed using the formula 1,000,000(1 0.25i ) , where on the last day i is 3-month LIBOR and prior to the last day i is the implied interest rate i = 1 P / 100 , where P is the price. The current price is P = 94.38, so the current implied interest rate is 0.0562. The final (15 June) interest rate is 0.04. Thus, the profit on the position is profit = 1,000,000(1 0.25(.04)) 1,000,000(1 0.25(.0562)) = 4,050. Alternatively, you could just remember that the DV01 is 25, and use the fact that the implied interest rate changed by 162 basis points. The total profit is then 25( 162) = 4,050. Question 3. Today is time 0, and time is measured in years. The price of the June ED futures contract is based on the forward rate f0(0.1, 0.35), the price of the September ED futures contract is based on the forward rate f0(0.35, 0.6), and the price of the December ED futures contract is based on the forward rate f0(0.6, 0.85). You have computed the DV01 s of your swap book with respect to the forward rates underlying the various Eurodollar futures contracts, that is you have computed the DV01 s of your swap book with respect to f0(0.1, 0.35), f0(0.35, 0.6), f0(0.6, 0.85), etc. You have found that the first three DV01 s are as follows: Underlying Forward Rate f0(0.1, 0.35) f0(0.35, 0.6) f0(0.6, 0.85) DV01 1,000 1,800 1,400 a. What will be the gain or loss if these three forward rates simultaneously increase by 1 basis point and all other rates are unchanged? b. What will be the gain or loss if the forward rate f0(0.35, 0.6) decreases by 10 basis point and the other two forward rates (and all other rates) are unchanged? c. How many of the first ED futures contract (the contract based on f0(0.1, 0.35)) should be bought/sold in order to eliminate the exposure to the forward rate f0(0.1, 0.35)? Solution: Be serious. You don t need me to provide the solution to this question. Question 3. Suzy Lee, a fixed income portfolio manager at Quantum Capital Management, expects the US dollar yield curve to make a parallel shift upward. (That is, she expects that the interest rates for different maturities will all increase by the same amount.) Lee s portfolio includes two USD-denominated corporate bonds. Both have a face value of $100 million, mature on 15 June 2002, and pay interest twice a year on 15 June and 15 December. One of the bonds pays interest at a fixed rate of 7 percent, while the other is a floating rate bond paying interest based on 6-month USD LIBOR. Lee wishes to enter into an interest rate swap transaction to take advantage of her belief that USD interest rates will increase. a. Describe an rate interest swap based on 6-month USD LIBOR that would allow Lee to take advantage of her beliefs that USD interest rates will increase. Should she pay floating or fixed? What should be the notional amount of the swap? Will the market value of the swap increase or decrease if interest rates increase? (No calculations are required for part a.) Solution: If Suzy thinks that interest rates will increase, she should swap the fixed rate note to floating. Thus, Suzy should receive floating and pay fixed on a swap with a notional amount of $100 million. Payment dates of swap should be 15 June and 15 December. If interest rates increase, the market value of the swap will increase. b. Lee is also considering using a strip of Eurodollar futures contracts instead of the interest rate swap. Assuming that Lee s beliefs about future changes in interest rates are correct, what portfolio of Eurodollar futures contracts would have approximately the same cash flows as the interest rate swap? (Hint: Notice that the question asked for a portfolio of ED futures with approximately the same cash flows. There is no portfolio of ED futures with exactly the same cash flows.) Solution: There are three things you need to know to correctly answer this question. (1) First, a short position in the ED contract benefits from increases in interest rates, so the portfolio will involve short positions in ED futures. (2) The swap payment is based on LIBOR 6 months before, but the ED contract is based on LIBOR quoted on the maturity of the ED contract. For example, the December swap payment is based on LIBOR in June, and the June ED contract is based on LIBOR in June. Also, the ED contract is based on 3-month LIBOR, while the swap contract is based on 6 month LIBOR. One way to deal with this is to recognize that six month LIBOR quoted in June is related to 3month LIBOR quoted in June and the forward rate from September to December. Combining these ideas, the December swap payment would be approximated by a portfolio of the June and September ED contracts. Also, the first June payment does not need to be hedged, though because I didn t tell you what is the current date it is ok if you hedge it. (3) Second, the ED contract has a size of 1 million. This will determine the number of ED contracts. Combining all of these ideas, the hedge would involve short (see point (1)) positions in 10 (see point (3)) of each of the following ED contracts (see point (2)): June 2000, Sept 2000 (to approximate Dec 2000 payment); Dec 2000, March 2001 (to approximate June 2001 swap payment); June 2001, Sept 2001 (to approximate Dec 2001 payment); Dec 2001, March 2002 (to match June 2002 swap payment); June 2002, Sept 2002 (to approximate Dec 2002 payment). c. Please briefly explain how the cash flows of the portfolio of ED futures contracts will differ from the cash flows of the interest rate swap. Solution: Two points should be made: (1) the ED contracts are on 3-month LIBOR, while the swap is on 6-month LIBOR; and (2) the timing of the cash flows in the ED contract is different due to both the daily resettlement of futures and the fact that the futures mature before the swap payment date. Remark: Note that (1) is not really relevant for this problem, because the assumption of the problem is that all rates move together. Thus, the 3 and 6-month rates move together. As a result, students who omit the first reason and mention the fact that rates move together should receive full credit. The same issue appears in part (b). Because the question assumes that all rates move together, the issue of which ED contracts to use to hedge which swap payment does not matter. All rates move together, so any ED contract can be used to hedge any swap payment. A student who makes this point should receive full credit for a portfolio that is short the correct number of ED contracts, regardless of which contracts are used.

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