INSTRUCTOR’S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9TH ED.
CHAPTER 8
SUGGESTED ANSWERS TO CHAPTER 8 QUESTIONS
1.
On April 1, the spot price of the British pound was $1.86 and the price of the June futures contract was $1.85.
During April the pound appreciated, so that by May 1 it was selling for $1.91. 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.
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.
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 options 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.
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
1
CHAPTER 8: CURRENCY FUTURES AND OPTIONS MARKETS
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. But 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. In order 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 in order 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 x (actual spot rate - exercise price).
ADDITIONAL CHAPTER 8 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 particular 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 8.9, 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.
a.
Is there a paradox here? Explain.
ANSWER. There is no paradox here. 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.
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.
2
INSTRUCTOR’S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9TH ED.
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 8 PROBLEMS
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)?
ANSWER
Time
Action
Cash Flow
------------------------------------------------------------------------------------------------------------------------------------------Monday
Investor buys pound futures
None
morning
contract that matures in two
days. Price is $1.78.
Monday
close
Futures price rises to $1.79.
Contract is marked-to-market.
Investor receives
62,500 x (1.79 - 1.78) = $625.
Tuesday
close
Futures price rises to $1.80.
Contract is marked-to-market.
Investor receives
62,500 x (1.80 - 1.79) = $625.
Wednesday
close
Futures price falls to $1.785.
(1)
(1) Contract is marked-to-market.
(2) Investor takes delivery of £62,500. (2)
Investor pays
62,500 x (1.80 -1.785) = $937.50
Investor pays 62,500 x 1.785 = $111,562.50.
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.
3
CHAPTER 8: CURRENCY FUTURES AND OPTIONS MARKETS
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
(7,000,000/0.8952 - 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 (7,000,000/0.8952). This contrasts with a projected cost based on the spot rate on January 10th of
€7,823,851.57 (7,000,000/0.8947). However, the latter “cost” is irrelevant since VW had no opportunity to buy
March dollars at the January 10th spot rate of $0.8947/€. By not hedging, VW would have paid an extra €29,434.76
for the $7,000,000 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.
4
INSTRUCTOR’S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9TH ED.
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.
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?
ANSWER. 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¢/¥ (0.028- 0.016). On a contract of ¥6,250,000, this is
equivalent to $756.25.
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, it should be pointed out that 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.
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 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 125,000,000
5
CHAPTER 8: CURRENCY FUTURES AND OPTIONS MARKETS
= $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 125,000,000 = $50,000. Apex's net gain will be $50,000 - $18,750 = $31,250.
PROFIT (LOSS) ON APEX CORPORATION'S FUTURES AND OPTIONS POSITIONS
$60,000
$57,500
$40,000
$31,25
0
Profit (loss)
$20,000
79.4
81.5
$0
75
76
77
78
79
80
81
82
83
84
Yen price ($0.0000 omitted)
($20,000) ($18,750)
Profit (loss) on call option position
($40,000)
Profit (loss) on futures
($60,000)
OPTION
Inflow
Outflow
Call Premium
Exercise Cost
Profit
FUTURES
Inflow
Outflow
Profit
75
--
79.4
--
81.5
$1,018,750
84
$1,050,000
-$18,750
-___________
-$18,750
-$18,750
-__________
-$18,750
-18,750
-1,000,000
__________
$0
-1,000,000
-18,750
__________
$31,250
$937,500
-992,500
__________
-$55,000
$992,500
-992,500
__________
$0
$1,000,000
-992,500
__________
$7,500
$1,050,000
-992,500
__________
$57,500
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
125,000,000 = $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.
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 125,000,000 =
$5,000.
c.
What is Apex's break-even future spot price on the option contract? On the futures contract?
6
INSTRUCTOR’S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9TH ED.
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, breakeven 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.
ADDITIONAL CHAPTER 8 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-upon 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
Investor sells euro futures
None
morning
contract that matures in two
days. Price is $0.9370.
Monday
Futures price falls to $0.9315.
Investor receives
close
Contract is marked-to-market.
125,000 x (0.9370 - 0.9315) = $687.50.
Tuesday
Futures price falls to $0.9291.
Investor receives
close
Contract is marked-to-market.
125,000 x (0.9315 - 0.9291) = $300.
Wednesday
Futures price rises to $0.9420.
(1) Investor pays 125,000 x (0.9420 - 0.9291)
close
(1) Contract is marked-to-market.
= $1,612.50.
(2) Investor takes delivery of _125,000
(2) Investor pays 125,000 x 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.
a.
Calculate the daily cash flows on your account. Be sure to take into account your required performance
bond and any performance bond calls.
7
CHAPTER 8: CURRENCY FUTURES AND OPTIONS MARKETS
ANSWER
Time
Action
Cash Flow on Contract
------------------------------------------------------------------------------------------------------------------------------------August 6
Sell one IMM yen futures
Performance bond of $4,590.
morning
contract. Price is $0.00812.
August 6
close
Futures price falls to $0.00791.
Contract is marked-to-market.
You pay out
12,500,000 x (0.00812 - 0.00791) =
-$2,625.00
August 7
close
Futures price rises to $0.00845.
Contract is marked-to-market.
You receive
12,500,000 x (0.00845 - 0.00791) =
+$6,750.00
August 8
close
Futures price rises to $0.00894.
Contract is marked-to-market.
You receive
12,500,000 x (0.00894 - 0.00845) =
+$6,125.00
August 9
close
Futures price falls to $0.00857.
(1) Contract is marked-to-market.
(2) You close out the contract
You pay out
(1) 12,500,000 x (0.00894 - 0.00857) = -$4,625.00
(2) None
You pay out a round-trip commission = -$31.48
------------Net gain on the futures contract = $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.
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.
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 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.
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 8.6). Ignore transaction costs and margins.
8
INSTRUCTOR’S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9TH ED.
40000
$32,875
20000
Gain (loss) on futures position
1.6612
1.62
0
$1.62
-20000
GAIN (LOSS) ON BIOGEN'S FUTURES AND OPTIONS POSITIONS
$1.63
$1.64
$1.65
$1.66
1.701
$1.67
$1.68
$1.69
$1.70
$1.71
Pound price
Gain (loss) on put option position
($25,000)
-40000
-60000
($62,125)
-80000
1.6250
1.6400
1.6513
1.6612
1.7010
$2,076,500
$2,076,500
$2,076,500
--
--
-25,000
-2,031,250
________
$20,250
-25,000
-2,050,000
___________
$1,500
-25,000
-2,064,125
_________
-$12,625
-25,000
-25,000
__________
-$25,000
_________
-$25,000
$2,064,125
-2,031,250
_________
$32,875
$2,064,125
-2,050,000
__________
$14,125
$2,064,125
-2,064,125
________
$0
$2,064,125
$2,064,125
-2,126,250
__________
-$62,125
OPTION
Inflow
Outflow
Put premium
Exercise cost
Profit
FUTURES
Inflow
Outflow
_________
$7,500
Profit
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 x 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 x 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 x
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 x 1,250,000 = $32,875. On the other hand, if the pound
9
10
INSTRUCTORS MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 7TH ED.
appreciates to $1.70100, Biogen lose $1.7010 - $1.6513 = $0.0497/£ for a total loss on the futures contract of
0.0497 x 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 x 1,250,000 = $14,125.
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.
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.
SUGGESTED SOLUTIONS TO APPENDIX 8A PROBLEMS
1. Assume that the spot price of the British pound is $1.55, the annualized 30-day sterling interest rate is 10%, the
annualized 30-day U.S. interest rate is 8.5%, and the annualized standard deviation of the dollar:pound
exchange rate is 17%. Calculate the value of a 30-day PHLX call option on the pound at a strike price of $1.57.
ANSWER. To apply Equation 8.2 to value this option, we must first estimate B(t,0.0833) and B*(t,0.0833), since T
= 0.0833 (one month equal 0.0833 years). Given the annualized one-month interest rates of 8.5% and 10%, the
one-month U.S. and U.K. interest rates are 0.7083% (8.5/12) and 0.8333% (10/12), respectively. The associated
bond prices are
B(t,0.0833) =
*
B (t,0.0833) =
1
= 0.99297
1.007083
1
= 0.99174
1.008333
Substituting in the values for B and B* along with those for S (1.55), X (1.57), and σ (0.17) in Equation 7.2, we can
calculate
10
INSTRUCTOR’S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9TH ED.
d1=
ln( SB* /XB) + 0.5 σ 2 T ln(1.55 x0.99174/1.57 x0.99297) + 0.5(0.17 )2 (0.0833)
=
= - 0.26199
σ T
0.17 0.0833
d 2 = d 1 σ T = - 0.26199 0.17 0.0833 = - 0.31106
Using NORMDIST in Excel yields computed values of N(-0.26199) = 0.39667 and N(-0.31106) = 0.37788.
Applying Equation 7.2, we can now calculate the value of the one-month pound call option:
C(t) = N( d 1 ) x S(t) x B* (t,T) N( d 2 ) x X x B(t,T)
= 0.39667 x 1.55 x 0.99173 − 0.37788 x 1.57 x 0.99297
= $0.02066/ £
That is, the value of the one-month option to acquire pounds at an exercise price of $1.57 when the spot rate is
$1.55 is 2.066⊄/£. Given that the PHLX pound call option contract consists of £31,250, the value of the one-month
pound call option is $645.52 (31,250 x 0.02066). This figure is exact; the other figures are subject to rounding
error.
2. Suppose the spot price of the yen is $0.0109, the three-month annualized yen interest rate is 3%, the threemonth annualized dollar rate is 6%, and the annualized standard deviation of the dollar:yen exchange rate is
13.5%. What is the value of a three-month PHLX call option on the Japanese yen at a strike price of $0.0099/¥?
ANSWER. To apply Equation 8.2 to value this option, we must first estimate B(t,0.25) and B*(t,0.25), since T =
0.25 (three months equal 0.25 years). Given the annualized three-month interest rates of 6% and 3%, the threemonth U.S. and Japanese interest rates are 1.5% (6/4) and 0.75% (3/4), respectively. The associated bond prices
are
B(t,0.25) =
*
B (t,0.25) =
1
= 0.98522
1.015
1
= 0.99256
1.0075
Substituting in the values for B and B* along with those for S (0.0109), X (0.0099), and σ (0.135) in Equation 7.2,
we can calculate
11
INSTRUCTORS MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 7TH ED.
12
d1=
ln( SB* /XB) + 0.5 σ 2 T
σ
T
=
ln(0.0109 x0.99256/0.0099 x0.98522) + 0.5(0.135 )2 (0.25)
0.135 0.25
= 1.56923
d 2 = d 1 σ T = 1.56923 0.135 0.25 = 1.50173
Using NORMDIST in Excel yields computed values of N(1.56923) = 0.94170 and N(1.50173) = 0.93342.
Applying Equation 7.2, we can now calculate the value of the one-month pound call option:
C(t) = N( d 1 ) x S(t) x B* (t,T) N( d 2 ) x X x B(t,T)
= 0.94170 x 0.0109 x 0.99256 0.93342 x 0.0099 x 0.98523
= $0.00010839/¥
That is, the value of the three-month option to acquire yen at an exercise price of $0.0099 when the spot rate is
$0.0109 is 0.10839⊄/¥. Given that the PHLX yen call option con tract consists of ¥6,250,000, the value of the 90day yen call option is $6,774.31 (6,250,000 x 0.0010839). This figure is exact; the other figures are subject to
rounding error.
3. Suppose that the premium on March 20 on a June 20 yen put option is 0.0514 cents per yen at a strike price of
$0.0077. The forward rate for June 20 is ¥1 = $0.00787 and the quarterly U.S. interest rate is 2%. If put-call
parity holds, what is the current price of a June 20 PHLX yen call option with an exercise price of $0.0077?
ANSWER. We can apply the version of put-call option interest parity as expressed in Equation 6.5 to value this
option. According to this formula,
C=
f1 X
+P
1+ rh
Substituting in the numbers given in the question, we have
C=
f1 X
0.00787 - 0.0077
+ P=
+ 0.000514 = 0.0681¢/¥
1+ rh
1.02
Given that the size of the PHLX yen option contract is ¥6,250,000, the value of this contract is $4,254.17
(6,250,000 x 0.000681). This figure is exact; the other figures are subject to rounding error.
12