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This Document Contains Chapters 6 to 7 CHAPTER 6 THE FOREIGN EXCHANGE MARKET Chapter 6 is basically institutional in nature, although it opens by discussing the rationale for a foreign exchange market, namely to facilitate the transfer of purchasing power denominated in one currency to purchasing power denominated in another currency. Like other financial markets, the foreign exchange market facilitates trading in financial assets by lowering transaction costs. The balance of the chapter provides the institutional framework of the foreign exchange market, both spot and forward transactions. It discusses pricing conventions, costs, size, and participants, and goes through some of the mechanics of foreign exchange trading. I always illustrate this subject matter with quotes found in The Wall Street Journal. Every issue of the Journal (Section C) contains a story on the foreign exchange market, providing spot quotations for the Canadian dollar, pound sterling, Swiss francs, euros, and Japanese yen. The financial section also carries a more extensive listing of spot and forward prices for about forty currencies. SUGGESTED ANSWERS TO “ARBITRAGING CURRENCY CROSS RATES” 1. Do any triangular arbitrage opportunities exist among these currencies? Assume that any deviations from the theoretical cross rates of 5 points or less are due to transaction costs. Answer: Unfortunately, there are no shortcuts here. It is necessary to try out each possibility. Here are the 4 arbitrage opportunities that I found. If anyone finds any additional ones, please contact me at my email address: ashapiro@marshall.usc.edu. 1) Convert dollars to SFr, SFr to DKr, and DKr back to dollars. The profit per dollar equals $1 * 1.2250 * 4.5570/5.5485 - $1 = $0.0061. 2) Convert dollars to DKr, DKr to pounds, and pounds back to dollars. The profit per dollar equals $1 * 5.5475 * 0.0910/.5012 - 1 = $0.0072. 3) Convert dollars to SFr, SFr to pounds, and pounds back to dollars. The profit per dollar equals $1 * 1.2250 * 0.4122/.5012 - 1 = $0.0055. 4) Convert dollars to yen, yen to pound, and pound back to dollars. The profit per dollar equals $1 * 121.33 * 0.0042/0.5012 - 1 = $0.0167. 2. Compute the profit from a $5 million transaction associated with each arbitrage opportunity. Answer: All answers are based on rounding the arbitrage profit per dollar to the fourth decimal place. 1) The profit for the $/SFr/DKr/$ arbitrage will be $5,000,000 * 0.0061 = $30,500. 2) The profit from the $/DKr/£/$ arbitrage will be $5,000,000 * 0.0072 = $36,000. 3) The profit from the $/£/DKr/$ arbitrage will be $5,000,000 * 0.0055 = $27,500. 4) The profit from the $/¥/DKr/$ arbitrage will be $5,000,000 * 0.0167 = $83,500. SUGGESTED ANSWERS TO CHAPTER 6 QUESTIONS 1. Answer the following questions based on data in Exhibit 6.5. 1.a. How many Swiss francs can you get for one dollar? Answer: The indirect quote is $1 = SFr 1.2297. 1.b. How many dollars can you get for one Swiss franc? Answer: The direct quote is SFr1 = $0.8132. 1.c. What is the three month forward rate for the Swiss franc? Answer: The three month forward rate is SFr1 = $0.8192. 1.d. Is the Swiss franc selling at a forward premium or discount? Answer: At a forward premium. 1.e. What is the 90 day forward discount or premium on the Swiss franc? Answer: The 90 day forward premium is 60 points (pips), which translates into an annualized forward premium of 2.95% (4 * (0.8192 – 0.8132)/0.8132). 2. What risks confront dealers in the foreign exchange market? How can they cope with these risks? Answer: Foreign exchange dealers must cope with exchange risk, because of the foreign currency positions they take. They also bear credit risk since the counterparties to the trades they enter into may not honor their obligations. They can cope with currency risk by using forward contracts and currency options, widening their bid-ask quotes, and limiting the position they are willing to take in any one currency. They can limit credit risk by restricting the position they are willing to take with any one customer and by setting margin requirements that vary with the riskiness of their customers (banks will generally not do this). 3. Suppose a currency increases in volatility. What is likely to happen to its bid ask spread? Why? Answer: As a currency’s volatility increases, it becomes riskier for traders to take positions in that currency. To compensate for the added risks, traders quote wider bid ask spreads. 4. Who are the principal users of the forward market? What are their motives? Answer: The principal users of the forward market are currency arbitrageurs, hedgers, importers and exporters, and speculators. Arbitrageurs wish to earn risk free profits; hedgers, importers and exporters want to protect the home currency values of various foreign currency denominated assets and liabilities; and speculators actively expose themselves to exchange risk to benefit from expected movements in exchange rates. 5. How does a company pay for the foreign exchange services of a commercial bank? Answer: Companies compensate banks for foreign exchange services through the bid-ask spread. The bank will buy foreign exchange at the bid rate (low) and sell at the ask rate (high). SUGGESTED SOLUTIONS TO CHAPTER 6 PROBLEMS 1. The $: € exchange rate is €1 = $1.35, and the €/SFr exchange rate is SFr 1 = €0.61. What is the SFr/$ exchange rate? Answer: SFr1 = €0.61 * 1.35 = $0.8235. 2. Suppose the direct quote for sterling in New York is 1.9880 5. 2.a. How much would £500,000 cost in New York? Answer: To buy £500,000 would cost £500,000 * 1.9885 = $99,425. 2.b. 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 1/1.9880 1/1.9885 = 0.5029 0.5030. 3. Using the data in Exhibit 6.5, 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: 4. An investor wishes to buy euros spot (at $1.3480) and sell euros forward for 180 days (at $1.3526). 4.a. What is the swap rate on euros? Answer: A premium of 46 points. 4.b. What is the premium on 180 day euros? Answer: The 180 day premium is (1.3526 1.3480)/1.3480 * 2 = 0.68%. 5. Suppose Credit Suisse quotes spot and 90-day forward rates of $0.7957-60 and 8-13, respectively. 5.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) 5.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] * 4 = 0.65%. 5.c. Compute the percentage bid-ask spreads on spot and forward Swiss francs. Answer: The bid-ask spread is calculated as follows: Substituting in the numbers yields a spot bid-ask spread of (0.7960 - 0.7957)/0.7960 = 0.04%. The corresponding forward bid-ask spread is (0.7973 - 0.7965)/0.7973 = 0.10%. 6. Suppose Dow Chemical receives quotes of $0.008242-45 for the yen and $0.03023-27 for the Taiwan dollar (NT$). 6.a. How many U.S. dollars will Dow Chemical receive from the sale of ¥50 million? Answer: Dow must sell yen at the bid rate, meaning it will receive $412,100 (50,000,000 * 0.008242). 6.b. What is the U.S. dollar cost to Dow Chemical of buying ¥1 billion? Answer: Dow must buy at the ask rate, meaning it will cost Dow $8,245,000 (1,000,000,000 * 0.008245) to buy ¥1 billion. 6.c. How many NT$ will Dow Chemical receive for U.S.$500,000? Answer: Dow must sell at the bid rate for U.S. dollars (which is the reciprocal of the ask rate for NT$, or 1/0.03027), meaning it will receive from this sale of U.S. dollars NT$16,518,005 (500,000/0.03027). 6.d. How many yen will Dow Chemical receive for NT$200 million? Answer: To buy yen, Dow must first sell the NT$200 million for U.S. dollars at the bid rate and then use these dollars to buy yen at the ask rate. The net result from these transactions is ¥733,292,905 (200,000,000 * 0.03023/0.008245). 6.e. What is the yen cost to Dow Chemical of buying NT$80 million? Answer: Dow must sell the yen for dollars at the bid rate and then buy NT$ at the ask rate with the U.S. dollars. The net yen cost to Dow from carrying out these transactions is ¥293,812,182 (80,000,000 * 0.03027/0.008242) 7. Suppose the euro is quoted at 0.6786-98 in London, and the pound sterling is quoted at 1.4724-70 in Frankfurt. 7.a. Is there a profitable arbitrage situation? Describe it. Answer: Buy euros for £0.6798/€ in London. Use the pounds to buy euros for €1.4770/£ in Frankfurt. This is equivalent to buying pounds for £0.6770. There is a net profit of £0.0028 per pound bought and sold – a percentage yield of 0.41% (0.0028/0.6798). 7.b. Compute the percentage bid ask spreads on the pound and euro. Answer: The percentage bid-ask spreads on the pound and euro are calculated as follows: £ bid-ask spread = (1.4770 - 1.4724)/1.4770 = 0.31% € bid-ask spread = (0.6798 - 0.6786)/0.6798 = 0.18% 8. As a foreign exchange trader at Sumitomo Bank, one of your customers would like a yen quote on Australian dollars. Current market rates are: Spot 30-day ¥121.37-85/U.S.$1 15-13 A$1.1878-98/U.S.$1 20-26 8.a. What bid and ask yen cross rates would you quote on spot Australian dollars? Answer: By means of triangular arbitrage, we can calculate the market quotes for the Australian dollar in terms of yen as ¥102.00-58/A$1 These prices can be found as follows. For the yen bid price for the Australian dollar, we need to first sell Australian dollars for U.S. dollars and then sell the U.S. dollars for yen. It costs A$1.1898 to buy U.S.$1. With U.S.$1 we can buy ¥121.37. Hence, A$1.1898 = ¥121.37, or A$1 = ¥102.00. This is the yen bid price for the Australian dollar. The yen ask price for the Australian dollar can be found by first selling yen for U.S. dollars and then using the U.S. dollars to buy Australian dollars. Given the quotes above, it costs ¥121.85 to buy U.S.$1, which can be sold for A$1.1878. Hence, A$1.1878 = ¥121.85, or A$1 = ¥102.58. This is the yen ask price for the Australian dollar. 8.b. What outright yen cross rates would you quote on 30-day forward Australian dollars? Answer: Given the swap rates, we can compute the outright forward direct quotes for the yen and Australian dollar by adding or subtracting the forward points as follows Spot 30-day 30-day outright forward rates ¥121.37-85/U.S.$1 15-13 ¥121.22-72/U.S.$1 A$1.1878-98/U.S.$1 20-26 A$1.1898-1.1924/U.S.$1 By means of triangular arbitrage, we can then calculate the market quotes for the 30-day forward Australian dollar in terms of yen as ¥101.66-102.30/A$1 These prices can be found as follows. For the yen bid price for the forward Australian dollar, we need to first sell Australian dollars forward for U.S. dollars and then sell the U.S. dollars forward for yen. It costs A$1.1924 to buy U.S.$1 forward. With U.S.$1 we can buy ¥121.22. Hence, A$1.1924 = ¥121.22, or A$1 = ¥100.82. This is the yen bid price for the forward Australian dollar. The yen ask price for the Australian dollar can be found by first selling yen forward for U.S. dollars and then using the U.S. dollars to buy forward Australian dollars. Given the quotes above, it costs ¥121.72 to buy U.S.$1, which can be sold for A$1.1898. Hence, A$1.1898 = ¥121.72, or A$1 = ¥102.30. This is the yen ask price for the forward Australian dollar. 8.c. What is the forward premium or discount on buying 30-day Australian dollars against yen delivery? Answer: As shown in 8.a and 8.b, the ask rate for 30-day forward Australian dollars is ¥102.30 and the spot ask rate is ¥102.58. Thus, the Australian dollar is selling at a forward discount to the yen. The annualized discount equals -0.27%, computed as follows: 9. Suppose Air France receives the following indirect quotes in New York: €0.92-3 and £0.63-4. Given these quotes, what range of £/€ bid and ask quotes in Paris will permit arbitrage? Answer: Triangular arbitrage can take place in either of two ways: (1) Convert from euros to dollars (at the ask rate), then from dollars to pounds (at the bid rate), or (2) convert from pounds to dollars (at the ask rate), then from dollars to euros (at the bid rate). The first quote will give us the bid price for the euro in terms of the pound and the second quote will yield the ask price. Using the given rates, Air France would end up with the following amounts: i) Euros to pounds = €/$ (ask) * $/£ (bid) = 0.93 * 1/0.63 = € 1.4762/£ or £0.6774/ € ii) Pounds to euros = £/$ (ask) * $/ € (bid) = 0.64 * 1/0.92 = £0.6957/€ or €1.4375/£ The significance of the figures in method (i) is that Air France can buy pounds in New York for €1.4762/£, which is the equivalent of selling euros at a rate of £0.6774/ €. So, if Air France can buy euros in Paris for less than £0.6774/€ (which is the equivalent of selling pounds for more than €0.6774/£), it can earn an arbitrage profit. Similarly, the figures in method (ii) tell us that Air France can buy euros in New York at a cost of £0.6957/€. Given this exchange rate, Air France can earn an arbitrage profit if it can sell these euros for more than £0.6957/FF in Paris. Thus, Air France can profitably arbitrage between New York and Paris if the bid rate for the euro in Paris is greater than £0.6957/€ or the ask rate is less than £0.6774/€. 10. On checking the Telerate screen, you see the following exchange rate and interest rate quotes: Currency 90-Day Interest Rates Annualized Spot Rates 90-Day Forward Rates Dollar 4.99% - 5.03% Swiss franc 3.14% - 3.19% $0.711-22 $0.726-32 10.a. Can you find an arbitrage opportunity? Answer: Yes. There are two possibilities: Borrow dollars and lend in Swiss francs or borrow Swiss francs and lend in dollars. The profitable arbitrage opportunity lies in the former: Lend Swiss francs financed by borrowing U.S. dollars. 10.b. What steps must you take to capitalize on it? Answer: Borrow dollars at 1.2575% for 90 days (5.03%/4), convert these dollars into francs at the ask rate of $0.722, lend the francs at 0.785% for 90 days (3.14%/4), and immediately sell the franc’s forward for dollars at the buy rate of $0.726. 10.c. What is the profit per $1,000,000 arbitraged? Answer: The profit is $1,000,000 * [(1.00785/0.722) * 0.726 - 1.012575] = $858.66. ADDITIONAL CHAPTER 6 PROBLEMS AND SOLUTIONS 1. Suppose the quote on pounds is $1.624-31. 1.a. If you converted $10,000 to pounds and then back to dollars, how many dollars would you end up with? Answer: For $10,000, you would buy pounds at the price of $1.631, giving you £6,131.21 ($10,000/1.631) and resell them at the bid price of $1.624. The latter transaction would yield $9,957.08, resulting in a round-trip cost of $42.92. 1.b. Suppose you could buy pounds at the bid rate and sell them at the ask rate. How many dollars would you have to transact in order to earn $1,000 on a round-trip transaction (buying pounds for dollars and then selling the pounds for dollars)? Answer: For every pound you could buy at the bid and sell at the ask, you would earn the spread of $0.007. To earn $1,000, you would have to transact £142,857.14 ($1,000/$0.0007). At the current bid rate of $1.624, this is equivalent to $232,000 (142,857.14 * $1.624). 2. Using the following data, calculate the 30 day, 90 day, and 180 day forward premiums for the British pound. Answer: Here are the relevant calculations for the pound: 3. The spot and 90 day forward rates for the pound are $1.1376 and $1.1350, respectively. What is the forward premium or discount on the pound? Answer: The forward premium (discount) on the British pound is [(f1 e0)/e0] * (360/n) = [(1.1350 1.1376)/1.1376] * 4 = 0.91% which is a forward discount of 0.91%. 4. Suppose the spot quote on the euro is $0.9302 18, and the spot quote on the Swiss franc is $0.6180 90. 4.a. Compute the percentage bid ask spreads on the euro and franc. Answer: The percentage bid-ask spreads on the euro and franc are calculated as follows: Euro bid-ask spread = (0.9318 - 0.9302)/0.9318 = 0.17% SFr bid-ask spread = (0.6190 - 0.6180)/0.6190 = 0.16% 4.b. What is the direct spot quote for the franc in Frankfurt? Answer: To sell one franc for euros, first sell the franc for $0.6180 and then convert $0.6180 into euros at the ask rate of $0.9318. Thus the bid rate for the franc is 0.6180/0.9318 = €0.6632. Similarly, to acquire one franc, sell euros for dollars and then sell dollars for francs. Specifically, it costs $0.6190 to buy €1. Because €1 can be converted into $0.9302, it takes €0.6190/0.9302 = €0.6654 to buy $0.6190. Thus the ask rate for francs is €0.6654. The bid ask quote on the franc in Frankfurt is therefore €0.6632 54. 5. Suppose you observe the following direct spot quotations in New York and Toronto, respectively: 0.8000 50 and 1.2500 60. What are the arbitrage profits per $1 million? Answer: Converting the direct quotes in Toronto into indirect quotes yields bid ask rates for the Canadian dollar in terms of the U.S. dollar of U.S.$.7962 .8000. Hence, there is no arbitrage opportunity. 6. Assuming no transaction costs, suppose £1 = $2.4110 in New York, $1 = FF 3.997 in Paris, and FF 1 = £0.1088 in London. How could you take profitable advantage of these rates? Answer: Sell pounds in New York for $2.4110 apiece. Sell the dollars in Paris for FF 3.997, and sell the francs in London for £.1088. This sequence of transactions yields 2.4110 * 3.997 * 0.1088 pounds or £1.0485 per pound initially traded. 7. Suppose the euro is quoted at $0.8782-92, while the yen is quoted at $0.001760-69. 7.a. Given these quotes for the euro and yen, what is the maximum bid-ask spread in the ¥/DM rate for which there is no arbitrage? Answer: The ¥/€ bid rate based on triangular arbitrage is ¥496.44/€1 (0.8782/0.001769). Similarly, the ¥/€ ask rate based on triangular arbitrage is ¥499.55/€1 (0.8792/0.001760). Hence, the bid-ask spread based on triangular arbitrage is ¥499.55 - ¥496.44 = ¥3.11. This spread is the maximum one would expect. Beyond this spread, it would be profitable to engage in triangular arbitrage. 7.b. What is the maximum bid-ask spread in percentage terms? Answer: The maximum bid-ask spread in percentage terms equals the maximum spread divided by the bid price or 3.11/496.44 = 0.63%. Relative to the ask price, this percentage is 0.62% (/499.55). 8. Assume that back in 1995 the pound sterling is worth FF9.80 in Paris and SFr5.40 in Zurich. 8.a. Show how British arbitrageurs can make profits given that the Swiss franc is worth two French francs. What would be the profit per pound transacted? Answer: Sell pounds in Zurich for SFr5.40. Sell Swiss francs in Zurich for FF2. Then buy pounds in Paris for FF9.80. This yields (5.40 * 2)/9.8 = £1.102. 8.b. What would be the eventual outcome on exchange rates in Paris and Zurich given these arbitrage activities? Answer: The Swiss franc price of the pound would decline in Zurich. The Swiss franc would depreciate relative to the French franc. The pound would appreciate relative to the French franc in Paris. 8.c. Rework 8.a, assuming that transaction costs amount to 0.6% of the amount transacted. What would be the profit per pound transacted? Answer: Each transaction costs 0.6%. Thus, at each stage the arbitrageur receives 99.4% of what he previously received. Thus after the three transactions undertaken in part a, the arbitrageur receives 1.102 * (.994)3 = £1.0823 for a profit per pound sold equal to £0.0823. 8.d. Suppose the Swiss franc is quoted at FF2 in Zurich. Given a transaction cost of 0.6% of the amount transacted, what are the minimum/maximum French franc prices for the Swiss franc that you would expect to see quoted in Paris? Answer: With a transaction cost of 0.6%, an arbitrageur will receive 99.4% of what she would receive absent these costs. To find the maximum and minimum French franc prices for the Swiss franc that would be quoted in Paris, it is sufficient to invoke the following no arbitrage conditions: Converting FF1 into Swiss francs in Zurich and then converting the Swiss francs back into French francs in Paris should yield no more than one FF1. ii) Converting SFr1 into French francs in Zurich and then converting the French francs back into Swiss francs in Paris should yield no more than SFr1. If e is the direct quote for the Swiss franc in Paris, the first no arbitrage condition says that 0.5 * 0.994 * e * 0.994 < 1 or e < 2.0242 According to the second no arbitrage condition, 2 * 0.994 * (1/e) * 0.994 1.9761 Combining these inequalities yields the minimum and maximum exchange rates or 1.9761 < e < 2.0242. 9. On checking the Reuters screen, you see the following exchange rate and interest rate quotes: Currency 90-Day Interest Rates Spot Rates 90-day Forward Rates Pound 7 7/16 - 5/16% ¥159.9696-9912/£ ¥145.5731-8692/£ Yen 2 3/8 - 1/4% 9.a. Can you find an arbitrage opportunity? Answer: There are two alternatives: (1) Borrow yen at 2 3/8%/4, convert the yen into pounds at the spot ask rate of ¥159.9912/£, invest the pounds at 7 5/16%/4, and sell the expected proceeds forward for yen at the forward bid rate of ¥145.5731/£; or (2) borrow pounds at 7 7/16%/4, convert the pounds into yen at the spot bid rate of ¥159.9696/£, invest the yen at 2 1/4%/4, and sell the proceeds forward for pounds at the forward ask rate of ¥145.8692/£. The first alternative will yield a loss of -¥7.94 per ¥100 borrowed, indicating that this is not a profitable arbitrage opportunity: (100/159.9912) * (1.0183) * 145.5731 - 100 * 1.0059 = -7.94 Switching to alternative 2, the return per £100 borrowed is £8.42, indicating that this is a very profitable arbitrage opportunity: 100 * 159.9696 * 1.0056/145.8692 - 100 * 1.0186 = 8.42 9.b. What steps must you take to capitalize on it? Answer: The steps to be taken have already been outlined in the answer to part a. To capitalize on an opportunity, whether in business, personal development, or any other area, follow these steps: 1. Identify the Opportunity: • Clearly define what the opportunity is. • Understand its potential benefits and impact. 2. Conduct Research: • Gather relevant information and data. • Analyze market trends, customer needs, and competitive landscape. 3. Evaluate Feasibility: • Assess the resources required (time, money, skills). • Evaluate risks and potential obstacles. • Consider the alignment with your goals and strategy. 4. Develop a Plan: • Set clear objectives and goals. • Create a detailed action plan with timelines and milestones. • Identify key performance indicators (KPIs) to measure success. 5. Secure Resources: • Allocate necessary resources (financial, human, technological). • Seek additional funding or partnerships if needed. 6. Build a Team: • Assemble a team with the skills and expertise required. • Assign roles and responsibilities. 7. Execute the Plan: • Implement the action plan. • Monitor progress and make adjustments as needed. 8. Market the Opportunity: • Develop a marketing strategy to promote the opportunity. • Use appropriate channels to reach your target audience. 9. Monitor and Evaluate: • Continuously track progress against KPIs. • Collect feedback and make necessary improvements. 10. Scale and Expand: • If successful, look for ways to scale up and expand the opportunity. • Explore additional markets or segments. 11. Review and Reflect: • Conduct a post-mortem analysis to understand what worked and what didn’t. • Document lessons learned for future opportunities. 9.c. What is the profit per £1,000,000 arbitraged? Answer: Based on the answer to part a, the profit is £84,200 (8.42 * 10,000). Arbitrage involves profiting from price discrepancies across different markets. In this scenario, the profit per £1,000,000 arbitraged is £84,200, based on an 8.42% profit rate. This means that for every £1,000,000 arbitraged, the trader earns £84,200. Successful arbitrage requires swift execution to capitalize on fleeting opportunities. It plays a crucial role in market efficiency by helping to equalize prices and reduce discrepancies. NOTES ON FOREIGN EXCHANGE QUOTES 1. Spot rate rate at which foreign exchange can be bought or sold for immediate delivery. €1 = $0.9107 SFr1 = $0.6340 1.a. Actual rates are given in pairs: a bid (buy) rate and ask (sell) rate €1 = $0.9107 10 SFr1 = $0.6340 42 1.b. Cross rates: €1 = SFr 1.4364 (0.9107/0.6340) €1 = SFr 1.4360 9 (0.9107/0.6342 0.9110/0.6340) 1.c. Measuring currency changes • Year 2: €1 = $0.9107 or $1 = €1.0981 • Year 1: €1 = $0.8163 or $1 = €1.2250 • The euro is said to have appreciated against the dollar by (0.9107 0.8163)/0.8163 = 11.56%. • Alternatively, the dollar is said to have depreciated against the euro by (1.0981 1.2250)/1.2250 = 10.37%. • Thursday, January 9, 1986: Cr$1 = $0.00009615 or $1 = Cr$10400 • Thursday, January 31, 1985: Cr$1 = $0.0002899 or $1 = Cr$3449.50 • The Brazilian cruzeiro has depreciated against the dollar by (.00009615 .0002899)/.0002899 = 66.83%. • Alternatively, the dollar has appreciated against the cruzeiro by (10400 3449.5)/3449.5 = 201.49%. Note: The new Brazilian currency is now the real. This example dates back to a time when the Brazilian currency was running a very high rate of inflation and so was continually devaluing 2. Forward rate rate at which foreign exchange can be bought or sold today for delivery at a fixed future date, typically in multiples of 30 days, e.g., 30, 60, 90, or 180 days. 2.a. Forward quotations 30 day forward rates €1 = $0.9120 SFr1 = $0.6338 2.b. Forward premium (+) or discount ( ) (annualized) = [(forward rate spot rate)/spot rate] * (360/n) where n is the number of days in the forward contract. Thus, the euro is selling at an annualized forward premium of 1.71% against the dollar: [(0.9120 0.9107)/0.9107] * 12 = 1.71%. The Swiss franc is selling at an annualized forward discount of 0.38% against the dollar: [(0.6338 0.6340)/0.1340] * 12 = 0.38%. 2.c. Swap rates Spot rates: €1 = $0.9107 10 SFr1 = $0.6340 42 30 day forward rates: €1 = $0.9120 25 SFr1 = $0.6338 41 Expressed as: €1 = $0.9107 10 13 15 SFr1 = $0.6340 42 2 1 2.d. Cross rates on a 30 day forward contract: €1 = SFr1.4383 97 (0.9120/0.6341 0.9125/0.6338) CHAPTER 7 CURRENCY FUTURES AND OPTIONS MARKETS This chapter describes foreign currency futures and options contracts and shows how they can be used to manage foreign exchange risk or take speculative positions on currency movements. It also shows how to read the prices of these contracts as they appear in the financial press. SUGGESTED ANSWERS TO CHAPTER 7 QUESTIONS 1. On April 1, the spot price of the British pound was $1.96 and the price of the June futures contract was $1.95. During April the pound appreciated so that by May 1 it was selling for $2.01. What do you think happened to the price of the June pound futures contract during April? Explain. Answer: The price of the June futures contract undoubtedly rose. Here’s why. The June futures price is based on the expectations of market participants as to what the spot value of the pound will be at the date of settlement in June. Since the spot value of the pound has risen in during April, the best prediction is that the future level of the pound will also be higher than it was on April 1. This expectation will undoubtedly be reflected in a June pound futures price that is higher on May 1 than it was on April 1. 2. What are the basic differences between forward and futures contracts? Between futures and options contracts? Answer: The basic differences between forward and futures contracts are described in Section 3.1. The most important difference between these two contracts and an options contract is that a buyer of a forward or futures contract must take delivery, while the buyer of an options contract has the right but not the obligation to complete the contract. 3. A forward market already existed, so why was it necessary to establish currency futures and currency options contracts? Answer: A currency futures market arose because private individuals were unable to avail themselves of the forward market. Currency options are partly a response to individuals and firms who would like to eliminate some currency risk while at the same time preserving the possibility of earning a windfall profit from favorable movements in the exchange rate. Options also enable firms bidding on foreign projects to lock in the home currency value of their bid without exposing themselves to currency risk if their bid is rejected. 4. Suppose that Texas Instruments must pay a French supplier €10 million in 90 days. 4.a. Explain how TI can use currency futures to hedge its exchange risk. How many futures contracts will TI need to fully protect itself? Answer: TI can hedge its exchange risk by buying euro futures contracts whose expiration date is the closest to the date on which it must pay its French supplier. Given a contract size of €125,000, TI must buy 10,000,000/125,000 = 80 futures contracts to hedge its euro payable. 4.b. Explain how TI can use currency options to hedge its exchange risk. How many options contracts will TI need to fully protect itself? Answer: TI can hedge its exchange risk by buying euro call option contracts whose expiration date is the closest to the date on which it must pay its French supplier. Given a contract size of €62,500, TI must buy 10,000,000/62,500 = 160 options contracts to hedge its payable. 4.c. Discuss the advantages and disadvantages of using currency futures versus currency options to hedge TI’s exchange risk. Answer: A futures contract is most valuable when the quantity of foreign currency being hedged is known, as in the case here. An option contract is most valuable when the quantity of foreign currency is unknown. Other things being equal, therefore, TI should use futures contracts to hedge its currency risk. However, TI must honor its futures contracts even if the spot rate at settlement is less than the futures price. In contrast, TI can choose not to exercise currency call options if the call price exceeds the spot price. Although this feature is an advantage of currency options, it is fully priced out in the market via the call premium. Hence, options are not unambiguously better than futures. In this case, since the quantity of the future French franc outflow is known, TI should use currency futures to hedge its risk. 5. Suppose that Bechtel Group wants to hedge a bid on a Japanese construction project. Because the yen exposure is contingent on acceptance of its bid, Bechtel decides to buy a put option for the ¥15 billion bid amount rather than sell it forward. To reduce its hedging cost, however, Bechtel simultaneously sells a call option for ¥15 billion with the same strike price. Bechtel reasons that it wants to protect its downside risk on the contract and is willing to sacrifice the upside potential to collect the call premium. Comment on Bechtel’s hedging strategy. Answer: The combination of buying a put option and selling a call option at the same strike price is equivalent to selling ¥15 billion forward at a forward rate equal to the strike price on the put and call options. That is, Bechtel is no longer holding an option; it is now holding a forward contract. If the yen appreciates and Bechtel loses its bid, it will face an exchange loss equal to 15 billion * (actual spot rate exercise price). ADDITIONAL CHAPTER 7 QUESTIONS AND ANSWERS 1. What is the last day of trading and the settlement day for the IMM Australian dollar futures for September of the current year? Answer: The last day of trading for the IMM Australian dollar futures for September will be the third Wednesday of September. The specific date depends on the year. For 2001 it is September 19 and for 2002 it is September 18. Settlement takes place each day. 2. Which contract is likely to be more valuable, an American or a European call option? Explain. Answer: The American call option is likely to be more valuable since it can be exercised at any time prior to maturity, unlike the European option which can be exercised only at maturity. The option to exercise early is valuable when interest rates on the two currencies differ. 3. In Exhibit 7.9, the value of the call option is shown as approaching its intrinsic value as the option goes deeper and deeper in the money or further and further out of the money. Explain why this is so. Answer: As the call option moves further out of the money, the chances that it will expire unexercised and worthless increase, bringing it closer to its intrinsic value of 0. Alternatively, as the option goes deeper in the money, the chance that the exchange rate will fall below the exercise price declines, increasing the probability that the option will be exercised eventually at a profit equal to its intrinsic value. 4. During September 1992, options on ERM currencies with strike prices outside the ERM bands had positive values. At the same time, actual currency volatility was close to zero. 4.a. Is there a paradox here? Explain. Answer: There is no paradox. Although current volatility was almost zero, currency traders were betting that the ERM could not be maintained, which would lead to a jump in currency volatility. If the ERM broke up, there was a positive probability that ERM currency values would move outside the bands. Hence, it is not surprising that options on ERM currencies with strike prices outside the ERM bands had positive values. 4.b. Why might actual currency volatility have been close to zero? What does a zero volatility imply about the value of currency options? Answer: Actual currency volatility was close to zero because of government intervention to maintain currency values within the established bands. However, a zero current volatility implies nothing about the value of currency options. What matters in pricing an option is the underlying asset’s projected volatility over the life of the contract. If future volatility is expected to differ from current volatility, option prices will not reflect current volatility. 4.c. What does the positive values of ERM options outside the bands tell you about the market’s perceptions of the possibility of currency devaluations or revaluations? Answer: The market was clearly expecting currency movements beyond the established ERM bands. In other words, traders believed that currency devaluations or revaluations had a positive probability of occurring. Otherwise, the value of options with strike prices outside the ERM bands would have been insignificantly different from zero. SUGGESTED SOLUTIONS TO CHAPTER 7 PROBLEMS 1. On Monday morning, an investor takes a long position in a pound futures contract that matures on Wednesday afternoon. The agreed on price is $1.95 for £62,500. At the close of trading on Monday, the futures price has risen to $1.96. At Tuesday close, the price rises further to $1.98. At Wednesday close, the price falls to $1.955, and the contract matures. The investor takes delivery of the pounds at the prevailing price of $1.955. Detail the daily settlement process (see Exhibit 7.3). What will be the investor's profit (loss)? Answer: Time Action Cash Flow Monday Open Investor buys a pound futures contract that matures in two days None. Price is $1.95 Monday Close Futures price rises to $1.96. Contract is marked-to-market. Investor receives 62,500 * (1.96 – 1.95) = $625 Tuesday Close Futures price rises to $1.98. Contract is marked-to-market. Investor receives 62,500 * (1.98 – 1.96) = $1,250 Wednesday Close Future price falls to $1.955. 1) Contract is marked-to-market 2) Investor takes delivery of £62,500. 1) Investor pays 62,500 * (1.98 – 1.955) = $1,562.50 2) Investor pays 62,500 * 1.955 = $122,187.50 Net profit is $1,785 – $1,562.5 = $312.50. 2. Suppose that the forward ask price for March 20 on euros is $1.3327 at the same time the price of IMM euro futures for delivery on March 20 is $1.3345. How could an arbitrageur profit from this situation? What will be the arbitrageur’s profit per futures contract (size is €125,000)? Answer: Since the futures price exceeds the forward rate, the arbitrageur should sell futures contracts at $1.3345 and buy euro forward in the same amount at $1.3327. The arbitrageur will earn 125,000(1.3345 - 1.3327) = $225 per euro futures contract arbitraged. 3. Suppose DEC buys a Swiss franc futures contract (size is SFr 125,000) at a price of $0.83. If the spot rate for the Swiss franc at the date of settlement is SFr 1 = $0.8250, what is DEC’s gain or loss on this contract? Answer: DEC has bought Swiss francs worth $0.8250 at a price of $0.83. Thus, it has lost $0.005 per franc for a total loss of 125,000 * 0.005 = $625. 4. On January 10, Volkswagen agrees to import auto parts worth $7 million from the U.S. The parts will be delivered on March 4 and are payable immediately in dollars. VW decides to hedge its dollar position by entering into IMM futures contracts. The spot rate is $1.3447/€ and the March futures price is $1.3502. 4.a. Calculate the number of futures contracts that VW must buy to offset its dollar exchange risk on the parts contract. Answer: VW can lock in a euro price for its imported parts by buying dollars in the futures market at the current March futures price of €0.7406/$1 (1/1.3502). This is equivalent to selling euro futures contracts. At that futures price, VW will sell €5,184,200 for $7 million. At €125,000 per futures contract, this would entail selling 42 contracts (5,184,200/125,000 = 41.47) at a total cost of €5,250,000. 4.b. On March 4, the spot rate turns out to be $1.3452/€, while the March futures price is $1.3468/€. Calculate VW’s net euro gain or loss on its futures position. Compare this figure with VW’s gain or loss on its unhedged position. Answer: Under its futures contract, VW has agreed to sell €5,250,000 and receive $7,088,550 (5,250,000 * 1.3502). On March 4, VW can close out its futures position by buying back 42 March euro futures contracts (worth €5,250,000). At the current futures rate of $1.3468/€, VW must pay out $7,070,700 (5,250,000 * 1.3468). Hence, VW has a net gain of $17,850 ($7,088,550 - $7,070,700) on its futures contract. At the current spot rate of $1.3452/€, this translates into a gain of €13,269.40 (17,850/1.3452). On closing out the 42 futures contracts, VW will then buy $7 million in the spot market at a spot rate of $1.3452/€. Its net cost is €5,190,417.78 (7,000,000/1.3452 - 13,269.4). If VW had not hedged its import contract, it could have bought the $7 million on March 10 at a cost of €5,203,687.18 (7,000,000/1.3452). In contrast, the projected cost based on the spot rate on January 10 is €5,252,494.94 (7,000,000/1.3327). However, the latter “cost” is irrelevant since VW had no opportunity to buy March dollars at the January 10 spot rate of $1.3327/€. By not hedging, VW would have paid an extra €13,269.4 for the $7,000,000 to satisfy its dollar liability, the difference between the cost of $7 million with hedging (€5,190,471.78) and the cost without hedging (€5,203,687.18). 5. Citigroup sells a call option on euros (contract size is €500,000) at a premium of $0.04 per euro. If the exercise price is $1.34 and the spot price of the euro at expiration is $1.36, what is Citigroup’s profit (loss) on the call option? Answer: Since the spot price of $1.36 exceeds the exercise price of $1.34, Citigroup’s counterparty will exercise its call option, causing Citigroup to lose 2¢ per euro. Adding in the 4¢ call premium it received gives Citigroup a net profit of 2¢ per euro on the call option for a total gain of 0.02 * 500,000 = $10,000. 6. Suppose you buy three June PHLX call options with a 90 strike price at a price of 2.3 (¢/€). 6.a. What would be your total dollar cost for these calls, ignoring broker fees? Answer: With each call option being for €62,500, the three contracts combined are for €187,500. At a price of 2.3¢/€, the total cost is 187,500 * $0.023 = $4,312.50. 6.b. After holding these calls for 60 days, you sell them for 3.8 (¢/€). What is your net profit on the contracts assuming that brokerage fees on both entry and exit were $5 per contract and that your opportunity cost was 8% per annum on the money tied up in the premium? Answer: The net profit would be 1.5¢/€ (3.8 - 2.3) for a total profit before expenses of $2,812.50 (0.015 * 187,500). Brokerage fees totaled $10 per contract or $30 overall. The opportunity cost would be $4,312.50 * 0.08 * 60/365 = $56.71. After deducting these expenses (which total $86.71), the net profit is $2,725.79. 7. A trader executes a “bear spread” on the Japanese yen consisting of a long PHLX 103 March put and a short PHLX 101 March put. 7.a. If the price of the 103 put is 2.81 (100ths of ¢/¥), while the price of the 101 put is 1.6 (100ths of ¢/¥), what is the net cost of the bear spread? Answer: Going long on the 103 March put costs 0.0281¢/¥ while going short on the 101 March put yields 0.016¢/¥. The net cost is therefore 0.0121¢/¥ (0.028 - 0.016). On a contract of ¥6,250,000, this is equivalent to $756.25. 7.b. What is the maximum amount the trader can make on the bear spread in the event the yen depreciates against the dollar? Answer: To begin, the 103 March put gives the trader the right but not the obligation to sell yen at a price of 1.03¢/¥. Similarly, the 101 March put gives the buyer the right but not the obligation to sell yen at a price of 1.01¢/¥. If the yen falls to 1.01¢/¥ or below, the trader will earn the maximum spread of 0.02¢/¥. After paying the cost of the bear spread, the trader will net 0.079¢/¥ (0.02¢ - 0.0121¢), or $493.75 on a ¥6,250,000 contract. 7.c. Redo your answers to parts a and b assuming the trader executes a “bull spread” consisting of a long PHLX 97 March call priced at 0.0321¢/¥ and a short PHLX 103 March call priced at 0.0196¢/¥. What is the trader's maximum profit? Maximum loss? Answer: In this case, the trader will pay 0.0321¢/¥ for the long 97 March call and receive 0.0196¢/¥ for the short 103 March call. The net cost to the trader, therefore, is 0.0125¢/¥, which is also the trader’s maximum potential loss. At any price of 1.03¢/¥ or greater, the trader will earn the maximum possible spread of 0.06¢/¥. After subtracting off the cost of the bull spread, the trader will net 0.0475¢/¥, or $2,968.75 per ¥6,250,000 contract. 8. Apex Corporation must pay its Japanese supplier ¥125 million in three months. It is thinking of buying 20 yen call options (contract size is ¥6.25 million) at a strike price of $0.00800 to protect against the risk of a rising yen. The premium is 0.015 cents per yen. Alternatively, Apex could buy 10 three month yen futures contracts (contract size is ¥12.5 million) at a price of $0.007940 per yen. The current spot rate is ¥1 = $0.007823. Suppose Apex’s treasurer believes that the most likely value for the yen in 90 days is $0.007900, but the yen could go as high as $0.008400 or as low as $0.007500. 8.a. Diagram Apex’s gains and losses on the call option position and the futures position within its range of expected prices (see Exhibit 8.4). Ignore transaction costs and margins. Answer: In the following calculations, note that the current spot rate is irrelevant. When a spot rate is referred to, it is the spot rate in 90 days. If Apex buys the call options, it must pay a call premium of 0.00015 * 125,000,000 = $18,750. If the yen settles at its minimum value, Apex will not exercise the option and it loses the call premium. But if the yen settles at its maximum value of $0.008400, Apex will exercise at $0.008000 and earn $0.0004/¥1 for a total gain of 0.0004 * 125,000,000 = $50,000. Apex’s net gain will be $50,000 $18,750 = $31,250. Contract Yen Price Option 75 79.4 81.5 84 Inflow --- --- $1,018,750 $1,050,000 Outflow Call Premium -$18,750 -$18,750 -$18,750 -$1,000,000 Exercise Cost --- --- -$1,000,000 -$18,750 Profit -$18,750 -$18,750 $0 $31,250 Futures Inflow $937,500 $992,500 $1,000,000 $1,050,000 Outflow -$992,500 -$992,500 -$992,500 -$992,500 Profit -$55,000 $0 $7,500 $57,500 As the diagram and table show, Apex can use a futures contract to lock in a price of $0.007940/¥ at a total cost of 0.007940 * 125,000,000 = $992,500. If the yen settles at its minimum value, Apex will lose $0.007940 $0.007500 = $0.000440/¥ (remember it is buying yen at 0.007940, when the spot price is only 0.007500), for a total loss on the futures contract of 0.00044 * 125,000,000 = $55,000. On the other hand, if the yen appreciates to $0.008400, Apex will earn $0.008400 $0.007940 = $0.000460/¥ for a total gain on the futures contracts of 0.000460 * 125,000,000 = $57,500. 8.b. Calculate what Apex would gain or lose on the option and futures positions if the yen settled at its most likely value. Answer: If the yen settles at its most likely price of $0.007900, Apex will not exercise its call option and will lose the call premium of $18,750. If Apex hedges with futures, it will have to buy yen at a price of $0.007940 when the spot rate is $0.0079. This will cost Apex $0.000040/¥, for a total futures contract cost of 0.000040 * 125,000,000 = $5,000. 8.c. What is Apex’s break even future spot price on the option contract? On the futures contract? Answer: On the option contract, the spot rate will have to rise to the exercise price plus the call premium for Apex to break even on the contract, or $0.008000 + $0.000150 = $0.008150. In the case of the futures contract, break-even occurs when the spot rate equals the futures rate, or $0.007940. 8.d. Calculate and diagram the corresponding profit-and-loss and break even positions on the futures and options contracts for the sellers of these contracts. Answer: The sellers’ profit-and-loss and break-even positions on the futures and options contracts will be the mirror image of Apex’s position on these contracts. For example, the sellers of the futures contract will breakeven at a future spot price of ¥1 = $0.007940, while the options sellers will breakeven at a future spot rate of ¥1 = $0.008150. Similarly, if the yen settles at its minimum value, the options sellers will earn the call premium of $18,750 and the futures sellers will earn $55,000. But if the yen settles at its maximum value of $0.008400, the options sellers will lose $31,250 and the futures sellers will lose $57,500. ADDITIONAL CHAPTER 7 PROBLEMS AND SOLUTIONS 1. On Monday morning, an investor takes a short position in a euro futures contract that matures on Wednesday afternoon. The agreed on price is $0.9370 for €125,000. At the close of trading on Monday, the futures price has fallen to $0.9315. At Tuesday close, the price falls further to $0.9291. At Wednesday close, the price rises to $0.9420, and the contract matures. The investor delivers the euros at the prevailing price of $0.8420. Detail the daily settlement process (see Exhibit 8.2). What will be the investor's profit (loss)? Answer: Time Action Cash Flow Monday Open Investor sells euro futures contract that matures in two days None. Price is $0.9370 Monday Close Futures price falls to $0.9315. Contract is marked-to-market. Investor receives 125,000 * (0.9370 - 0.9315) = $687.50 Tuesday Close Futures price falls to $0.9291. Contract is marked-to-market. Investor receives 125,000 * (0.9315 - 0.9291) = $300 Wednesday Close Future price rises to $0.9420. 1) Contract is marked-to-market 2) Investor takes delivery of €125,000. 1) Investor pays 125,000 * (0.9420 - 0.9291) = $1,612.50 2) Investor pays 125,000 * 0.9420 = $117,750 Net loss is -$1,612.50 + $987.50 = -$625. 2. On August 6, you go long one IMM yen futures contract at an opening price of $0.00812 with a performance bond of $4,590 and a maintenance performance bond of $3,400. The settlement prices for August 6, 7, and 8 are $0.00791, $0.00845, and $0.00894, respectively. On August 9, you close out the contract at a price of $0.00857. Your round-trip commission is $31.48. 2.a. Calculate the daily cash flows on your account. Be sure to take into account your required performance bond and any performance bond calls. Answer: Time Action Cash Flow August 6 Open You sell one IMM yen futures contract Performance bond of $4,590. Price is $0.00812. August 6 Close Futures price falls to $0.00791. Contract is marked-to-market. You pay 12,500,000 * (0.00812 - 0.00791) = -$2,625 August 7 Close Futures price rises to $0.00845. Contract is marked-to-market. You receive 12,500,000 * (0.00845 - 0.00791) = $6,750 August 8 Close Future price rises to $0.00894. Contract is marked-to-market. You receive 12,500,000 * (0.00894 - 0.00845) = $6,125 August 9 Close Futures price falls to $0.00857. 1) Contract is marked-to-market. 2) You close out the contract. 1) You pay 12,500,000 * (0.00894 - 0.00857) = -$4,625 2) None. You pay round-trip commission -$31.48 Net gain on the futures contract = -$2,625 + $6,750 + $6,150 - $4,625 - $31.48 = $5,593.52 Your performance bond calls and cash balances as of the close of each day were as follows: August 6 With a loss of $2,625, your account balance falls to $1,965 ($4,590 -$2,625). You must add $2,625 ($4,590 - $2,625) to your account to restore it to the performance bond requirement of $4,590. With subsequent gains on the futures contract, you have no further margin calls. 2.b. What is your cash balance with your broker on the morning of August 10? Answer: As shown in part a, your net profit was $5,593.52. Add to this the $4,590 performance bond and the further margin of $2,625 paid in on August 6 and the amount in your account on the morning of August 10 is $12,808.52 ($5,593.52 + $4,590 + $2,625). 3. Biogen expects to receive royalty payments totaling £1.25 million next month. It is interested in protecting these receipts against a drop in the value of the pound. It can sell 30 day pound futures at a price of $1.6513 per pound or it can buy pound put options with a strike price of $1.6612 at a premium of 2.0 cents per pound. The spot price of the pound is currently $1.6560, and the pound is expected to trade in the range of $1.6250 to $1.7010. Biogen’s treasurer believes that the most likely price of the pound in 30 days will be $1.6400. 3.a. How many futures contracts will Biogen need to protect its receipts? How many options contracts? Answer: With a futures contract size of £62,500, Biogen will need 20 futures contracts to protect its anticipated royalty receipts of £1.25 million. Since the option contract size is half that of the futures contract, or £31,250, Biogen will need 40 put options to hedge its receipts. 3.b. Diagram Biogen’s profit and loss associated with the put option position and the futures position within its range of expected exchange rates (see Exhibit 7.6). Ignore transaction costs and margins. Contract Pound Price Option 1.6250 1.6400 1.6513 1.6612 1.7010 Inflow $2,076,500 $2,076,500 $2,076,500 --- --- Outflow Put Premium -$25,000 -$25,000 -$25,000 -$25,000 -$25,000 Exercise Cost -$2,031,250 -$2,050,000 -$2,064,125 Profit $20,250 $1,500 -$12,625 -$25,000 -$25,000 Futures Inflow $2,064,125 $2,064,125 $2,064,125 $2,064,125 $2,064,125 Outflow -$2,031,250 -$2,050,000 -$2,064,125 -$2,056,625 -$2,126,250 Profit $32,875 $14,125 $0 -$7,500 -$62,125 3.c. Calculate what Biogen would gain or lose on the option and futures positions within the range of expected future exchange rates and if the pound settled at its most likely value. Answer: If Biogen buys the put options, it must pay a put premium of 0.02 * 1,250,000 = $25,000. If the pound settles at its maximum value, Biogen will not exercise and it loses the put premium. But if the pound settles at its minimum of $1.6250, Biogen will exercise at $1.6612 and earn $0.0362/£or a total of 0.0362 * 1,250,000 = $45,250. Biogen's net gain will be $45,250 $25,000 = $20,250. With regard to the futures position, Biogen will lock in a price of $1.6513/£ for total revenue of $1.6513 * 1,250,000 = $2,064,125. If the pound settles at its minimum value, Biogen will have a gain per pound on the futures contracts of $1.6513 $1.6250 = $0.0263/£ (remember it is selling pounds at a price of $1.6513 when the spot price is only $1.6250) for a total gain of 0.0263 * 1,250,000 = $32,875. On the other hand, if the pound appreciates to $1.70100, Biogen lose $1.7010 $1.6513 = $0.0497/£ for a total loss on the futures contract of 0.0497 * 1,250,000 = $62,125. If the pound settles at its most likely price of $1.6400, Biogen will exercise its put option and earn $1.6612 $1.6400 = $0.0212/£, or $26,500. Subtracting off the put premium of $25,000 yields a net gain of $1,500. If Biogen hedges with futures contracts, it will sell pounds at $1.6513 when the spot rate is $1.6400. This will yield Biogen a gain of $0.0113/£ for a total gain on the futures contract equal to 0.0113 * 1,250,000 = $14,125. 3.d. What is Biogen’s break even future spot price on the option contract? On the futures contract? Answer: On the option contract, the spot rate will have to sink to the exercise price less the put premium for Biogen to break even on the contract, or $1.6612 $0.02 = $1.6412. In the case of the futures contract, breakeven occurs when the spot rate equals the futures rate, or $1.6513. 3.e. Calculate and diagram the corresponding profit-and-loss and break even positions on the futures and options contracts for those who took the other side of these contracts. Answer: As in the case of Apex, the sellers’ profit-and-loss and break-even positions on the futures and options contracts will be the mirror image of Biogen’s position on these contracts. For example, the sellers of the futures and options contracts will break even at future spot prices of $1.6513/£ and $1.6412/£, respectively. Similarly, if the pound falls to its minimum value, the options sellers will lose $20,250 and the futures sellers will lose $32,875. But if the pound hits its maximum value of $1.7010, the options sellers will earn $25,000 and the futures sellers will earn $62,125. Solution Manual for Foundations of Multinational Financial Management Atulya Sarin, Alan C. Shapiro 9780470128954
