a. On what day would the 1% filter rule have issued its first signal? Was this a buy or a sell signal? At what price did the trade occur?

Transcription

1 Answers to Chapter #7 Exercises 1. Examine the daily closing price data on the DM/$ rate in file E07.WK1 that was used to construct Figure 7.5. Suppose you were using a 1% filter rule to trade the DM and US$. a. On what day would the 1% filter rule have issued its first signal? Was this a buy or a sell signal? At what price did the trade occur? b. On what day would the 1% filter rule have issued its second signal. Was this a buy or a sell signal? At what price did the second trade occur? c. Calculate the profit from the first trade. Assume that transaction costs are 0.02% and that the interest rates were constant over the period with i DM = 3.0% and i $ = 5.5%. a. The price on July 10, 1986 is So a 1% rule issues a buy signal at prices above DM/$ and a sell signal at prices below DM/$. The first signal occurs on July 11, It is a buy signal, that is Buy $ and Sell DM. The trade price is DM/$. b. On July 11, 1986, the interim high is 2.194, so a sell signal is issued at prices below DM/$. The second signal occurs on July 15, It is a sell signal, that is Sell $ and Buy DM. The trade price is DM/$. c. Profit has three components: (1) Gain on transaction = 2.150/2.194 = 0.98 => -2.0%. (2) Transaction costs = 2 x 0.02% = 0.04%. (3) Interest earned from long $ / short DM position at 2.5% per year for 4 days = 0.03%. Total = -2.0% % % = -1.99% in four days. 2. Examine the daily closing price data on the DM/$ rate in file E07.WK1 that was used to construct Figure 7.5. Suppose you were using a 1/200 moving average rule to trade the DM and US$. a. On what day would the 1/200 moving average rule have issued its first signal? Was this a buy or a sell signal? At what price did the trade occur? b. On what day would the 1/200 moving average rule have issued its second signal. Was this a buy or a sell signal? At what price did the second trade occur? c. Calculate the profit from the first trade. Assume that transaction costs are 0.02% and that the interest rates were constant over the period with i DM = 3.0% and i $ = 5.5%.

2 a. On August 3, 1987, the spot rate rises and exceeds the 200 day moving average creating a buy signal, that is Buy $ and Sell DM. The trade price is DM/$. b. On August 18, 1987, the spot rate falls below the 200 day moving average creating a sell signal, that is Sell $ and Buy DM. The trade price is DM/$. c. Profit has three components: (1) Gain on transaction = 1.843/1.875 = => -1.7%. (2) Transaction costs = 2 x 0.02% = 0.04%. (3) Interest earned from long $ / short DM position at 2.5% per year for 15 days = 0.10%. Total = -1.70% % % = -1.74% in 15 days. Answers to Chapter #9 Exercises 2. Atlantic Richfield, a big US oil and gas company, has a large amount of debt indexed to short-term Eurodollar rates. A $100 million facility at Bankers Trust is due in five months in mid-june Atlantic Richfield pays LIBOR + 1/4% and the Treasurer expects to "roll-over" the $100 million for another three months. The Treasurer is expecting interest rate to go up during the next three months. a. Use Table 9.3 to illustrate how Atlantic Richfield could hedge its interest rate exposure using futures traded on the CME. Show all the steps, now and in three months. [For convenience, assume that CME maturity dates coincide with the firm's roll-over dates.] b. Suppose in three months that LIBOR is 4.5%. Will the firm have a gain or a loss from its hedge? How large is the gain or loss in dollar terms? How much interest (in dollars) will the firm pay to Bankers Trust for the three-month period commencing in June? c. What if LIBOR is 5.25% in mid-june? Will the firm have a gain or a loss from its hedge? How large is the gain or loss in dollar terms? How much interest (in dollars) will the firm pay to Bankers Trust for the three-month period commencing in June? a. The firm hedges by selling $100 million worth of June Eurodollar futures at This locks in a LIBOR rate of 4.95%. In five months, Atlantic will establish a LIBOR rate of 4.95% for the next three months, either by making delivery of the Eurodollar deposits or by buying back the futures at the

3 current price. If rates go up, the firm will make a profit on its futures position that will compensate for the higher cost of funds. If rates go down, the firm will lose on its futures position. Loss on the futures will compensate gain from lower cost of funds. b. If LIBOR is 4.50% in five months, the futures will trade at 95.50, generating a loss of.45 for the firm. In dollar terms, the loss is *100,000,000/4 = $112,500. This loss offsets the decrease in market interest rates and gives the firm an effective LIBOR of 4.95%. The firm's interest payments to Bankers Trust are LIBOR+1/4% on $100 million for three months or *100,000,000/4 = $1,187,500. Net costs are $1,187,500 + $112,500 = $1,300,000. c. If LIBOR is 5.25% in three months, the futures will trade at 94.75, generating a gain of.30 for the firm. In dollar terms, the gain is *100,000,000/4 = $75,000. This gain offsets the increase in market interest rates and gives the firm an effective LIBOR of 4.95%. The firm's interest payments to Bankers Trust are LIBOR+1/4% on $100 million for three months or 0.055*100,000,000/4 = $1,375,000. Net costs are $1,375,000 -$75,000 = $1,300,000 just as we found in part (b) of this question. 3. General Motors finances itself, among other channels, by using one-year, floatingrate notes whose rates are re-calculated every three months at LIBOR+1/8. A new $250,000,000 issue is planned for mid-september 1997 with a one-year maturity. a. Describe how GM could hedge its interest payments for the year. [For convenience, assume that CME maturity dates coincide with the firm's rollover dates.] b. Using Table 9.3, what is the yearly rate that GM can secure if they hedge? c. Calculate GM's total costs for the $250,000,000 issue assuming that they hedge. a. On January 16, 1996 GM could sell 250 Eurodollar futures for every maturity where its interest payments are set initially or re-set; that is, September and December 1997 and March and June b. For the next year, GM can lock in LIBOR rates of 5.22% (Sept 1997 at 94.78); 5.40% (Dec 1997 at 94.60); 5.48% (Mar 98 at 94.52); and 5.60% (June 98 at 94.40). The annual LIBOR rate is : 5.22/ / / /4 = %

4 c. GM will pay $250,000,000*( ) = $13,875,000 in interest over the year on this borrowing. 4. The ABC firm is considering borrowing $50,000,000 for one year either at a fixed rate of 6.50% in the US domestic market or at a floating rate indexed to threemonth LIBOR+1/4 in the Eurocurrency market. Currently, 3-month LIBOR is 5.25% and expected to remain constant for the year. a. How much would ABC save if it uses the Euromarkets and these expectations are met? [For convenience, assume that CME maturity dates coincide with the firm's roll-over dates.] b. What are the risks in using a Euromarket loan? c. Calculate the eventual saving for ABC in the case where LIBOR increases by.50% every three months. a. Savings are 1% of the outstanding amount for one year, or $500,000. b. The risks are interest rate risk because the Euromarket loan is on floating rate terms, and roll-over risk if the bank has the option to refuse to renew or roll-over the loan. If ABC has a commitment for the year, then it has no rollover risk as long as the bank remains in operation. c. Fixed rate costs: 6.5% of $50,000,000 = $3,250,000 Floating rate costs: ( %/4) * ( %/4) * ( %/4) * ( %/4) = , or a cost of 6.25%. On $50,000,000 principal the interest bill will be $3,125,000; still better than a 6.5% fixed rate. 5. Suppose that three-month Eurodollars are quoted in the interbank markets at 6.0% % by London banks, and 6.25% % by Singapore banks. a. Explain how you could attempt to make arbitrage profits in the above case. b. How large is the profit from arbitraging $1,000,000 in this case? c. What risks and/or costs do you face in attempting the arbitrage? a. A trader would attempt to borrow dollars from a bank in London at 6.125% and then deposit them at a bank in Singapore for 6.25%.

5 b. The potential profit is * $1,000,000 / 4 = $ Remember, these are per annum interest rates for a three-month period. c. The trader carries the political risk of deposits in Singapore. If funds were blocked in Singapore, he might not be able to pay back his London loan. Time differences between London and Singapore may also increase the difficulty of this transaction.