Certain Selected Problems Chapter 8 1 On Monday
Certain Selected Problems Chapter 8
• 1. On Monday morning, an investor takes a long position in a pound futures contract that matures on Wednesday afternoon. The agreed‑upon price is $1. 78 for £ 62, 500. At the close of trading on Monday, the futures price has risen to $1. 79. At Tuesday close, the price rises further to $1. 80. At Wednesday close, the price falls to $1. 785, and the contract matures. The investor takes delivery of the pounds at the prevailing price of $1. 785. Detail the daily settlement process (see Exhibit 8. 3). What will be the investor's profit (loss)?
Net profit is $1, 250 - 937. 50 = $312. 50.
• 2. Suppose that the forward ask price for March 20 on euros is $0. 9127 at the same time that the price of IMM euro futures for delivery on March 20 is $0. 9145. 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 $0. 9145 and buy euro forward in the same amount at $0. 9127. The arbitrageur will earn 125, 000(0. 9145 - 0. 9127) = $225 per euro futures contract arbitraged.
• 3. Suppose that DEC buys a Swiss franc futures contract (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 x. 005 = $625.
• 4. On January 10, Volkswagen agrees to import auto parts worth $7 million from the United States. 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 $0. 8947/€ and the March futures price is $0. 9002/€.
• a. Calculate the number of futures contracts that VW must buy to offset its dollar exchange risk on the parts contract.
• Answer. Volkswagen can lock in a euro price for its imported parts by buying dollars in the futures market at the current March futures price of € 1. 1109/$1 (1/0. 9002). This is equivalent to selling euro futures contracts. At that futures price, VW will sell € 7, 776, 050 for $7 million. At € 125, 000 per futures contract, this would entail selling 62 contracts (7, 776, 050/125, 000 = 62. 21) at a total cost of € 7, 750, 000.
• b. On March 4, the spot rate turns out to be $0. 8952/€, while the March futures price is $0. 8968/€. 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, Volkswagen has agreed to sell € 7, 750, 000 and receive $6, 976, 550 (7, 750, 000 x 0. 9002). On March 4, VW can close out its futures position by buying back 62 March euro futures contracts (worth € 7, 750, 000). At the current futures rate of $0. 8968/€, VW must pay out $6, 950, 200 (7, 750, 000 x 0. 8968). Hence, VW has a net gain of $26, 350 ($6, 976, 550 - $6, 950, 200) on its futures contract. At the current spot rate of $0. 8952/€, this translates into a gain of € 29, 434. 76 (26, 350/0. 8952). Upon closing out the 62 futures contracts, VW will then buy $7 million in the spot market at a spot rate of $0. 8952/€. Its net cost is € 7, 790, 046. 92 (7, 000/0. 8952 - 29, 434. 76).
• If VW had not hedged its import contract, it could have bought the $7 million on March 10 at a cost of € 7, 819, 481. 68 (7, 000/0. 8952). This contrasts with a projected cost based on the spot rate on January 10 th of € 7, 823, 851. 57 (7, 000/0. 8947). However, the latter “cost” is irrelevant since VW had no opportunity to buy March dollars at the January 10 th spot rate of $0. 8947/€. By not hedging, VW would have paid an extra € 29, 434. 76 for the $7, 000 to satisfy its dollar liability, the difference between the cost of $7 million with hedging (€ 7, 790, 046. 92) and the cost without hedging (€ 7, 819, 481. 68).
• 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 $0. 91 and the spot price of the euro at date of expiration is $0. 93, what is Citigroup's profit (loss) on the call option?
• Answer. Since the spot price of $0. 93 exceeds the exercise price of $0. 91, 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. 02 x 500, 000 = $10, 000. •
• 6. Suppose you buy three June PHLX call options with a 90 strike price at a price of 2. 3 (¢/€). • 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 therefore 187, 500 x $0. 023 = $4, 312. 50.
• 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 x 187, 500). Brokerage fees totaled $10 per contract or $30 overall. The opportunity cost would be $4, 312. 50 x 0. 08 x 60/365 = $56. 71. After deducting these expenses (which total $86. 71), the net profit is $2, 725. 79.
• 7. 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 in order 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.
• 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 all 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 x 125, 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. 0004 x 125, 000 = $50, 000. Apex's net gain will be $50, 000 ‑ $18, 750 = $31, 250.
• As the diagram shows, Apex can use a futures contract to lock in a price of $0. 007940/¥ at a total cost of. 007940 x 125, 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 x 125, 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 x 125, 000 = $57, 500.
• 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 x 125, 000 = $5, 000.
• 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.
• 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.
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