CHAPTER 7: THE FOREIGN EXCHANGE MARKET1 SUGGESTED SOLUTIONS TO CHAPTER 7 PROBLEMS 1. The $: € exchange rate is €1 = $1.45, and the €/SFr exchange rate is SFr 1 = €0.71. What is the SFr/$ exchange rate? ANSWER. SFr1 = €0.71 x 1.45 = $1.0295. 2. Suppose the direct quote for sterling in New York is 1.9110-5. What is the direct quote for dollars in London? ANSWER. The direct quote for the dollar in London is just the reciprocal of the direct quote for the pound in New York or 1/1.9115 - 1/1.9110 = 0.5231-3. 3. Using the data in Exhibit 7.5, calculate the 30-day, 90-day, and 180-day forward discounts for the Canadian dollar. ANSWER. Here are the relevant rates for the Canadian dollar: Spot: C$1 = $1.0078 30-day forward: C$1 = $1.0073 90-day forward: C$1 = $1.0069 180-day forward: C$1 = $1.0066 The 30-day forward discount is: [($1.0073 - $1.0078)/$1.0078] x 12 = -0.60% The 90-day forward discount is: [($1.0069 - $1.0078)/$1.0078] x 4 = -0.36% The 180-day forward discount is: [($1.0066 - $1.0078)/$1.0078] x 2 = -0.24% In this case, the forward discounts at these maturities are relatively small, indicating that Canadian and U.S. interest rates are close to each other. 4. An investor wishes to buy euros spot (at $1.3908) and sell euros forward for 180 days (at $1.3996). a. What is the swap rate on euros? ANSWER. A premium of 88 points. b. What is the premium on 180-day euros? ANSWER. The 180-day premium is (1.3996 - 1.3908)/1.3908 x 2 = 1.27%. 5. Suppose Credit Suisse quotes spot and 90-day forward rates on the Swiss franc of $0.7957-60, 8-13. a. What are the outright 90-day forward rates that Credit Suisse is quoting? ANSWER. The outright forwards are: bid rate = $0.7965 (0.7957 + 0.0008) and ask rate = $0.7973 (0.7960 + 0.0013). b. What is the forward discount or premium associated with buying 90-day Swiss francs? ANSWER. The annualized forward premium = [(0.7973 - 0.7960)/0.7960]x 4 = 0.65%. c. Compute the percentage bid-ask spreads on spot and forward Swiss francs. ANSWER. The bid-ask spread is calculated as follows: 000 x 0.S. How many NT$ will Dow Chemical receive for U.S. dollars (which is the reciprocal of the ask rate for NT$.000.000 x 0. dollars at the bid rate and then use these dollars to buy yen at the ask rate. Use the euros to buy pounds for €1.009369-71 for the yen and $0. Suppose Dow Chemical receives quotes of $0.000 x 0.000. meaning it will receive from this sale of U.03676/0. Dow must sell at the bid rate for U. How many yen will Dow Chemical receive for NT$200 million? ANSWER. b. ANSWER.000? ANSWER.$500.1.000. 6. c.S.6259 .03675/0.15% (0.0.6080) in London. b. Dow must sell yen at the bid rate.334. dollars NT$13. meaning it will receive from this sale $468.450 (50. Compute the percentage bid-ask spreads on the pound and euro.09% euro bid-ask spread = (0.009369).6447). meaning it will cost Dow $9.0188/1. a.000.009369) 7.0. and the pound sterling is quoted at 1. The corresponding forward bid-ask spread is (0.000 x 0.6244-59 in Frankfurt.S.6080 .04%.000 (1.6259 = 0. d.6064)/0. What is the yen cost to Dow Chemical of buying NT$80 million? ANSWER.7957)/0. To buy yen. Percent spread = Ask price . There is a net profit of €0.009371).S.10%.6064-80 in London. dollars. dollars will Dow Chemical receive from the sale of ¥50 million? ANSWER.6447/£ (1/0. or 1/0.7960 .S.601. a.000/0.0188 per pound bought and sold–a percentage yield of 1.7973 .649. ANSWER.6080 = 0. How many U. The net result from these transactions is ¥784. Dow must buy at the ask rate.03676). Dow must sell the yen for dollars at the bid rate and then buy NT$ at the ask rate with the U.26% . 10TH ED.741 (500.886. Sell pounds for €1.220. Suppose the euro is quoted at 0. dollar cost to Dow Chemical of buying ¥1 billion? ANSWER.6244)/1.03675-6 for the Taiwan dollar (NT$).6259/£ in Frankfurt.000.S.7965)/0.Bid price x 100 Ask price Substituting in the numbers yields a spot bid-ask spread of (0.7960 = 0.45 (200.009371) to buy ¥1 billion. Is there a profitable arbitrage situation? Describe it. e.0. The percentage bid-ask spreads on the pound and euro are calculated as follows: £ bid-ask spread = (1. The net yen cost to Dow from carrying out these transactions is ¥313.03676). Dow must first sell the NT$200 million for U.51 (80. What is the U.2 INSTRUCTORS MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT.7973 = 0.371. 71. dollars for yen.S. it costs ¥101.2924 = ¥101.$1 A$1.$1 forward. With U.81. For the yen bid price for the Australian dollar.S. Buying and selling Australian dollars at the market price will leave you with no profit. Given the quotes above.22. The yen ask price for the Australian dollar can be found by first selling yen for U. one of your customers would like a yen quote on Australian dollars.2944 = ¥101. This is the yen ask price for the forward Australian dollar.$1.S.2944 = ¥101.2924. or A$1 = ¥78.72 to buy U.S. Hence.S.S.S.22-72/U. we can compute the outright forward direct quotes for the yen and Australian dollar by adding or subtracting the forward points as follows Spot ¥101. which can be sold for A$1. b.CHAPTER 7: THE FOREIGN EXCHANGE MARKET 8. we need to first sell Australian dollars for U.S. As a foreign exchange trader.22. you would try to buy Australian dollars at slightly less than ¥78. or A$1 = ¥78. dollars and then sell the U.2944.S.S.$1 By means of triangular arbitrage.S. Hence.37-85/U. dollars and then using the U. Given the swap rates. By means of triangular arbitrage.S.2924-44/U. What outright yen cross rates would you quote on 30-day forward Australian dollars? ANSWER.S.S.37. Hence.$1 a.04.2970 = ¥101.$1. This is the yen bid price for the Australian dollar.$1 we can buy ¥101.31.$1. How much better than the market prices you can do depends on the degree of competition you face from other traders and the extent to which your customers are willing to shop around to get better quotes. With U.S.31-81/A$1 These prices can be found as follows. A$1.2924-44/U. it costs ¥101.$1 A$1. Current market rates are: Spot ¥101.$1 we can buy ¥101.S.31 and sell them at slightly more than ¥78. dollars to buy Australian dollars. 3 30-day 15-13 20-26 What bid and ask yen cross rates would you quote on spot Australian dollars? ANSWER. we can calculate the market quotes for the Australian dollar in terms of yen as ¥78. For the yen bid price for the forward Australian dollar.2944 to buy U. Given the quotes above.S.37-85/U. dollars to buy forward Australian dollars. dollars forward for yen. It costs A$1. This is the yen ask price for the Australian dollar. which can be sold for A$1. dollars and then using the U.58.04-58/A$1 These prices can be found as follows. A$1.85.S. The yen ask price for the Australian dollar can be found by first selling yen forward for U. What is the forward premium or discount on buying 30-day Australian dollars against yen delivery? . we can then calculate the market quotes for the 30-day forward Australian dollar in terms of yen as ¥78.S. This is the yen bid price for the forward Australian dollar. As a foreign exchange trader at Sumitomo Bank.$1 30-day 15-13 20-26 30-day outright forward rates ¥101. or A$1 = ¥78. we need to first sell Australian dollars forward for U. Hence. or A$1 = ¥78. A$1. c.2970 to buy U.$1 A$1.37.2944-70/U. It costs A$1.S. dollars and then sell the U.81. A$1.85 to buy U. 81.64 x £0. 4 ANSWER.6957/ € or the ask rate is less than £0.22 $0. then from dollars to euros (at the bid rate).6957/ €.INSTRUCTORS MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT.99% .S.4762/£ or £0. As shown in parts a and b. it can earn an arbitrage profit. b.6774/ €. Air France would end up with the following amounts: (1) Euros to pounds = = = €/$ (ask) x 0.5. Given this exchange rate.19% a.78. Similarly.6774/ € (which is the equivalent of selling pounds for more than €0. what range of £/ € bid and ask quotes in Paris will permit arbitrage? ANSWER.43% Forward contract Spot rate 78. the ask rate for 30-day forward Australian dollars is ¥78. Yes. then from dollars to pounds (at the bid rate). So.726 .6774/£).58 .3 and £0.93 x € 1. which is the equivalent of selling euros at a rate of £0.81 30 number of days Suppose Air France receives the following indirect quotes in New York: €0. Triangular arbitrage can take place in either of two ways: (1) Convert from euros to dollars (at the ask rate).3.63 .81 360 x = x = .6957/€ or €1.63 (2) Pounds to euros = £/$ (ask) x 0.4762/£. computed as follows: Forward premium or discount 9.4375/£ $/ € (bid) 1/0.711 .58 and the spot ask rate is ¥78. On checking the Telerate screen. Thus. 10. or (2) convert from pounds to dollars (at the ask rate).6957/FF in Paris. Spot rates 90-day forward rates $0. dollars.6774/ €. Using the given rates. Air France can earn an arbitrage profit if it can sell these euros for more than £0.43%. 10TH ED. Given these quotes. Thus.32 Can you find an arbitrage opportunity? ANSWER. if Air France can buy euros in Paris for less than £0. = Forward rate Spot rate 360 78.6774/ € $/£ (bid) 1/0.92 = The import of the figures in method (1) is that Air France can buy pounds in New York for €1. The annualized discount equals -3.03% Swiss franc 3.14% .3.92 . the figures in method (2) tell us that Air France can buy euros in New York at a cost of £0. Air France can profitably arbitrage between New York and Paris if the bid rate for the euro in Paris is greater than £0. The first quote will give us the bid price for the euro in terms of the pound and the second quote will yield the ask price. The profitable arbitrage opportunity lies in the former: Lend Swiss francs financed by borrowing U.4. the Australian dollar is selling at a forward discount to the yen. you see the following exchange rate and interest rate quotes: Currency 90-day interest rates annualized Dollar 4. What steps must you take to capitalize on it? . There are two possibilities: Borrow dollars and lend in Swiss francs or borrow Swiss francs and lend in dollars. CHAPTER 7: THE FOREIGN EXCHANGE MARKET 5 ANSWER.14%/4).00785/0. and immediately sell the francs forward for dollars at the buy rate of $0.785% for 90 days (3.722.1.000.012575] = $858.726 . convert these dollars into francs at the ask rate of $0. What is the profit per $1.000 arbitraged? ANSWER.03%/4).726. . Borrow dollars at 1. lend the francs at 0.000.66.722) x 0. The profit is $1.000 x [(1.2575% for 90 days (5. c.