1. 1 Chapter 8 – Problem 1 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)?

2. 2 Chapter 8 – Problem 1 TimeActionCash Flow Monday morningInvestor buys pound futures contract that matures in two days. Price is $1.78. none Monday closeFutures price rises to $1.79. Contract is marked-to-market. Investor receives 62,500 x (1.79 ‑ 1.78) = $625. Tuesday closeFutures price rises to $1.80. Contract is marked-to-market. Investor receives 62,500 x (1.80 ‑ 1.79) = $625. Wednesday closeFutures price falls to $1.785. (1) Contract is marked-to-market. (2) Investor takes delivery of £62,500. Net profit is $1,250 - 937.50 = $312.50. (1) Investor pays 62,500 x(1.80 -1.785) = $937.50 (2) Investor pays 62,500 x 1.785 = $111,562.50.

3. 3 Chapter 8 – Problem 2 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)? 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.

4. 4 Chapter 8 – Problem 7 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. 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? Going long on the 103 March put costs the trader 0.0281¢/¥ while going short on the 101 March put yields the trader 0.016¢/¥. The net cost is therefore 0.0121¢/¥ (0.0281- 0.016). On a contract of ¥6,250,000, this is equivalent to $756.25.

5. 5 Chapter 8 – Problem 7 b.What is the maximum amount the trader can make on the bear spread in the event the yen depreciates against the dollar? 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 to the trader 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.

6. 6 Chapter 8 – Problem 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? 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.

7. 7 Chapter 8 – Problem 8 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 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.

8. 8 Chapter 8 – Problem 8 Option premium 0.00015 x 125,000,000 = 18,750 USD If the yen settles at the minimum value, the company will not exercise the option. If the yen settles at the maximum value, the company will exercise at 0.00800 and earn (0.0084 – 0.00800)x 125,000,000 = 50,000 USD Net gain 50,000 – 18,750 = 31,250 USD

9. 9 Chapter 8 – Problem 8

10. 10 Chapter 8 – Problem 8 7579.481.584 Option inflow1,018,7501,050,000 Option premium -18,750 Exercise cost1,000,000 Profit-18,750 031,250 Futures inflow 937,500992,5001,000,0001,050,000 Futures outflow -992,500 Profit-55,00007,50057,500

11. 11 Chapter 8 – Problem 8 Apex can use a futures contract to lock in a price of $0.007940/¥ at a total cost of.007940 x 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 x 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 x 125,000,000 = $57,500.

12. 12 Chapter 8 – Problem 8 b.Calculate what Apex would gain or lose on the option and futures positions if the yen settled at its most likely value. 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. It will cost Apex $0.000040/¥, for a futures contract cost of 0.000040 x 125,000,000 = $5,000.

13. 13 Chapter 8 – Problem 8 c.What is Apex's break ‑ even future spot price on the option contract? On the futures contract? For the option 0.0080 + 0.00015 = 0.00815 For the futures 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. The sellers' profit and loss and break-even positions on the futures and options contracts will be the mirror image of Apex's position. 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.

14. 14 Chapter 9 – Problem 1 1.In May 1988, Walt Disney Productions sold to Japanese investors a 20 ‑ year stream of projected yen royalties from Tokyo Disneyland. The present value of that stream of royalties, discounted at 6% (the return required by the Japanese investors), was ¥93 billion. Disney took the yen proceeds from the sale, converted them to dollars, and invested the dollars in bonds yielding 10%. According to Disney's chief financial officer, Gary Wilson, "In effect, we got money at a 6% discount rate, reinvested it at 10%, and hedged our royalty stream against yen fluctuations ‑‑ all in one transaction." a.At the time of the sale, the exchange rate was ¥124 = $1. What dollar amount did Disney realize from the sale of its yen proceeds? Disney realized 93,000,000,000/124 = $750,000,000 from the sale of its future yen proceeds.

15. 15 Chapter 9 – Problem 1 b.Demonstrate the equivalence between Walt Disney's transaction and a currency swap. (Hint: A diagram would help.) In a currency/interest rate swap, one party trades a stream of payments in one currency, at one interest rate, for a stream of payments in a second currency, at a second interest rate. Disney's stream of yen royalties can be treated as a yen bond, which it traded for a dollar bond, with dollar payments. The only difference between the Disney swap and a traditional swap is that the latter usually involve cash outflows whereas the Disney swap involves cash inflows. c.Comment on Gary Wilson's statement. Did Disney achieve the equivalent of a free lunch through its transaction? Gary Wilson is committing the economist's unpardonable sin: He is comparing apples with oranges, in this case, a 6% yen interest rate with a 10% dollar interest rate. The international Fisher effect tells us that the most likely reason that the yen interest rate is 4 percentage points less than the equivalent dollar interest rate is because the market expects the dollar to depreciate by about 4% annually against the yen.

16. 16 Chapter 9 – Problem 2 2.Suppose that IBM would like to borrow fixed-rate yen, whereas Korea Development Bank (KDB) would like to borrow floating-rate dollars. IBM can borrow fixed-rate yen at 4.5% or floating-rate dollars at LIBOR + 0.25%. KDB can borrow fixed-rate yen at 4.9% or floating-rate dollars at LIBOR + 0.8%. a.What is the range of possible cost savings that IBM can realize through an interest rate/currency swap with KDB? BorrowerFixed-Rate Yen Available Floating-Rate Dollars Available Korea Development Bank4.9%LIBOR + 0.80% IBM4.5%LIBOR + 0.25% Difference0.4% 0.55% The two parties can achieve a combined 15 basis point savings through IBM borrowing floating-rate dollars at LIBOR + 0.25% and KDB borrowing fixed- rate yen at 4.9% and then swapping the proceeds. This could be accomplished by IBM providing KDB with floating-rate dollars at LIBOR + 0.25%, saving KDB 0.55%, which then passed these savings along to IBM by swapping the fixed-rate yen at 4.9% - 0.55% = 4.35%. Thus, the potential savings to IBM range from 0 to 0.15%.

17. 17 Chapter 9 – Problem 2 b.Assuming a notional principal equivalent to $125 million, and a current exchange rate of ¥105/$, what do these possible cost savings translate into in yen terms? At a current exchange rate of ¥105/$, IBM's borrowing would equal ¥13,125,000,000 (125,000,000*105). A 0.15% savings on that amount would translate into ¥19,687,500 per annum (¥13,125,000,000*0.0015). c.Redo Parts a and b assuming that the parties use Bank of America, which charges a fee of 8 basis points to arrange the swap. The potential savings from a swap net out to 7 basis points. IBM borrowing cost would be lowered to 4.43% (4.5% - 0.07%). The 7 basis point saving would translate into an annual saving of ¥9,187,500 (¥13,125,000,000*0.0007).

18. 18 Chapter 9 – Problem 5 5.Suppose that Skandinaviska Ensilden Banken (SEB), the Swedish bank, funds itself with three ‑ month Eurodollar time deposits at LIBOR. Assume that Alfa Laval comes to SEB seeking a one ‑ year, fixed ‑ rate loan of $10 million, with interest to be paid quarterly. At the time of the loan disbursement, SEB raises three ‑ month funds at 5.75%, but has to roll over this funding in three successive quarters. If it does not lock in a funding rate and interest rates rise, the loan could prove to be unprofitable. The three quarterly re ‑ funding dates fall shortly before the next three Eurodollar futures-contract expirations in March, June, and September.

19. 19 Chapter 9 – Problem 5 a.At the time the loan is made, the price of each contract is 94.12, 93.95, and 93.80. Show how SEB can use Eurodollar futures contracts to lock in its cost of funds for the year. What is SEB's hedged cost of funds for the year? The formula for the locked-in LIBOR, r, given a price P of a Eurodollar futures contract is r = 100 - P. Using this formula, the solution r for each of the contracts is 5.88%, 6.05%, and 6.2%. So SEB can lock in a cost for its $10 million loan equal to $10,000,000 x (1 + 0.0575/4)(1 + 0.0588/4)(1 + 0.0605)(1 + 0.062/4) = $10,610495, which is equivalent to a one-year fixed interest rate of 6.105%. Effectively, what this procedure does is to roll over the principal and cumulative interest payment each quarter until it is paid off in a lump sum at the end of the fourth quarter. If the bank does not roll over the interest, but makes cash payments every quarter, then we would use the arithmetic mean.

20. 20 Chapter 9 – Problem 5 b.Suppose that the settlement prices of the March, June, and September contracts are, respectively, 92.98, 92.80, and 92.66. What would have been SEB's unhedged cost of funding the loan to Alfa Laval? Given the stated prices at settlement, actual LIBOR on each rollover date was 7.02%, 7.2%, and 7.34%. The unhedged cost of the loan is $10,000,000 x (1 + 0.0575/4)(1 + 0.0702/4)(1 + 0.072/4)(1 + 0.0734/4) = $10,700,379. This is equivalent to an annual rate of 7.00%, or 90 basis points more than the hedged cost of the loan.