37. Bullspreads and Bearspreads. Two British pound (₤) put options are available with exercise prices
of $1.60 and $1.62. The premiums associated with these options are $.03 and $.04 per unit,
respectively. (See Appendix B in this chapter.)
a. Describe how a bullspread can be constructed using these put options. What is the difference
between using put options versus call options to construct a bullspread?
b. Complete the following worksheet.
Value of British Pound at Option Expiration
$1.55 $1.60 $1.62 $1.67
Put @ $1.60
Put @ $1.62
Net
a. At option expiration, the spot rate of the pound is $1.60. What is the bullspreader’s total gain or
loss?
b. At option expiration, the spot rate of the pound is $1.58. What is the bearspreader’s total gain or
loss?
ANSWER:
b.
Value of British Pound at Option Expiration
$1.55 $1.60 $1.62 $1.67
c.
Per Unit Per Contract
d. A bearspread using these put options would be constructed by writing the $1.60 put option and
buying the $1.62 put option.
Per Unit Per Contract
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Currency Derivatives 2
38. Profits from Using Currency Options and Futures. On July 2, the two-month futures rate of the
Mexican peso contained a 2 percent discount (unannualized). There was a call option on pesos with
an exercise price that was equal to the spot rate. There was also a put option on pesos with an exercise
price equal to the spot rate. The premium on each of these options was 3 percent of the spot rate at
that time. On September 2, the option expired. Go to the oanda.com website (or any site that has
foreign exchange rate quotations) and determine the direct quote of the Mexican peso. You exercised
the option on this date if it was feasible to do so.
a. What was your net profit per unit if you had purchased the call option?
b. What was your net profit per unit if you had purchased the put option?
c. What was your net profit per unit if you had purchased a futures contract on July 2 that had a
settlement date of September 2?
d. What was your net profit per unit if you sold a futures contract on July 2 that had a settlement
date of September 2?
39. Uncertainty and Option Premiums. This morning, a Canadian dollar call option contract has a $.71
strike price, a premium of $.02, and expiration date of one month from now. This afternoon, news
about international economic conditions increased the level of uncertainty surrounding the Canadian
dollar. However, the spot rate of the Canadian dollar was still $.71. Would the premium of the call
option contract be higher than, lower than, or equal to $.02 this afternoon? Explain.
40. Uncertainty and Option Premiums. At 10:30 a.m., the media reported news that the Mexican
government’s political problems were reduced, which reduced the expected volatility of the Mexican
peso against the dollar over the next month. The spot rate of the Mexican peso was $.13 as of 10 a.m.
and remained at that level all morning. At 10 a.m., Hilton Head Co. purchased a call option at the
money on 1 million Mexican pesos with an expiration date one month from now. At 11:00 a.m.,
Rhode Island Co. purchased a call option at the money on 1 million pesos with a December expiration
date one month from now. Did Hilton Head Co. pay more, less, or the same as Rhode Island Co. for
the options? Briefly explain.
41. Speculating with Currency Futures. Assume that one year ago, the spot rate of the British pound
was $1.70. One year ago, the one-year futures contract of the British pound exhibited a discount of
6%. At that time, you sold futures contracts on pounds, representing a total of 1,000,000 pounds.
From one year ago to today, the pound’s value depreciated against the dollar by 4 percent. Determine
the total dollar amount of your profit or loss from your futures contract.
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Currency Derivatives 3
42. Speculating with Currency Options. The spot rate of the New Zealand dollar is $.77. A call option
on New Zealand dollars with a one-year expiration date has an exercise price of $.78 and a premium
of $.04. A put option on New Zealand dollars at the money with a one-year expiration date has a
premium of $.03. You expect that the New Zealand dollar’s spot rate will decline over time and will
be $.71 in one year.
a. Today, Dawn purchased call options on New Zealand dollars with a one-year expiration date.
Estimate the profit or loss per unit at the end of one year. [Assume that the options would be
exercised on the expiration date or not at all.]
b. Today, Mark sold put options on New Zealand dollars at the money with a one-year expiration
date. Estimate the profit or loss per unit for Mark at the end of one year. [Assume that the options
would be exercised on the expiration date or not at all.]
ANSWER:
43. Impact of Expected Volatility on Currency Option Premiums. Assume that Australia’s central
bank announced plans to stabilize the Australian dollar (A$) in the foreign exchange markets. In
response to this announcement, the expected volatility of the A$ declined immediately. However, the
spot rate of the A$ remained at $.89 on this day, and was not affected by the announcement. The one-
year forward rate of the A$ remained at $.89 on this day and was not affected by the announcement.
Do you think the premium charged on a one-year A$ currency option increased, decreased, or
remained the same on this day in response to the announcement? Briefly explain.
CRITICAL THINKING
Pricing of Currency Options Review the logic regarding how currency options are priced. Consider a
speculator who plans to purchase currency options for the option at the money on whatever currency has
the lowest premium. He also who plans to sell currency options for the option at the money on whatever
currency has the highest premium. Another speculator uses a strategy of purchasing call options on
Australian dollars at the money whenever the premium is relatively low (compared to the historical
premiums that existed for this type of option), and sells call options at the money on Australian dollars at
the money. Write a short essay describing your opinion about the likely success of these strategies.
ANSWER
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Currency Derivatives 4
Solution to Continuing Case Problem: Blades, Inc.
1. If Blades uses call options to hedge its yen payables, should it use the call option with the exercise
price of $0.00756 or the call option with the exercise price of $0.00792? Describe the tradeoff.
2. Should Blades allow its yen position to be unhedged? Describe the tradeoff.
3. Assume there are speculators who attempt to capitalize on their expectation of the yen’s movement
over the two months between the order and delivery dates by either buying or selling yen futures now
and buying or selling yen at the future spot rate. Given this information, what is the expectation on
the order date of the yen spot rate by the delivery date? (Your answer should consist of one number.)
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Currency Derivatives 5
4. Assume that the firm shares the market consensus of the future yen spot rate. Given this expectation
and given that the firm makes a decision (i.e., option, futures contract, remain unhedged) purely on a
cost basis, what would be its optimal choice?
5. Will the choice you made as to the optimal hedging strategy in question 4 definitely turn out to be the
lowest-cost alternative in terms of actual costs incurred? Why or why not?
Alternative 1—Remain Unhedged
Expected Spot Rate $ 0.006912
Amount of Yen
Payables 12,500,000
Cost in Two Months ($.006912 × 12,500,000 units) $ 86,400.00
Alternative 2—Purchase One Futures Contract
Futures Price per Unit $ 0.006912
Units in Contract 12,500,000
Cost in Two Months ($.006912 × 12,500,000) $ 86,400.00
Alternative 3—Purchase Two Options
Options Information Option 1 Option 2
Exercise Price $0.0075600 $0.0079200
Premium per Unit $0.0001512 $0.0001134
Units in Contract 6,250,000 6,250,000
Calculations Column A Column B Column C Column D
Amount Paid
Total Premium Exercise? for Yen Total Paid
(Premium per (Is Spot Rate > (Exercise Price (Column A +
unit Units) Exercise Price?) Units) Column C)
Two Options, Exercise
Price of $.00756 $1,890.00 No $86,400.00 $88,290.00
Two Options, Exercise
Price of $.00792 $1,417.50 No $86,400.00 $87,817.50
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Currency Derivatives 6
One Option of Each
Exercise Price $1,653.75 O1-No; O2-No $86,400.00 $88,053.75
6. Now assume that you have determined that the historical standard deviation of the yen is about
$0.0005. Based on your assessment, you believe it is highly unlikely that the future spot rate will be
more than two standard deviations above the expected spot rate by the delivery date. Also assume that
the futures price remains at its current level of $0.006912. Based on this expectation of the future spot
rate, what is the optimal hedge for the firm?
ANSWER: (See spreadsheet attached.) Although the spreadsheet is required, the answer to this
Calculation of Highest Forecasted Spot Rate
Alternative 1—Remain Unhedged
Alternative 2—Purchase One Futures Contract
Alternative 3—Purchase Two Options
Options Information Option 1 Option 2
Calculations Column A Column B Column C Column D
Amount Paid
Total Premium Exercise? for Yen Total Paid
(Premium per (Is Spot Rate > (Exercise Price (Column A +
unit Units) Exercise Price?) Units) Column C )
Two Options, Exercise
One Option of Each
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Currency Derivatives 7
Solution to Supplemental Case: Capital Crystal, Inc.
This case is designed to give students more insight on the advantages and disadvantages of currency
futures and options. More comprehensive questions on this subject are offered in Chapter 11.
a. To hedge with futures, the cost of the imports will be $795 million ($1.59 × £500 million). To hedge
with call options, the cost per unit (including the premium paid) is $1.61, so that the cost of the
imports if the option is exercised is $805 million. Since the pound’s spot rate is expected to be above
the call option’s exercise price, the call option would likely be exercised. In this case, hedging with
futures will cost $10 million less than hedging with call options.
b. Since the future spot rate is likely to exceed the futures price, hedging with futures would likely be less
costly than not hedging. Even if it was more costly, it might be wise to hedge in keeping with the
conservative management style of Capital Crystal, Inc.
Small Business Dilemma
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Currency Derivatives 8
Use of Currency Futures and Options by the Sports Exports Company
1. How can the Sports Exports Company use currency futures contracts to hedge against exchange rate
risk? Are there any limitations of using currency futures contracts that would prevent the Sports
Exports Company from locking in a specific exchange rate at which it can sell all the pounds it
expects to receive in each of the upcoming months?
2. How can the Sports Exports Company use currency options to hedge against exchange rate risk? Are
there any limitations of using currency options contracts that would prevent the Sports Exports
Company from locking in a specific exchange rate at which it can sell all the pounds it expects to
receive in each of the upcoming months?
3. Jim Logan, owner of the Sports Exports Company, is concerned that the pound may depreciate
substantially over the next month, but he also believes that the pound could appreciate substantially if
specific situations occur. Should Jim use currency futures or currency options to hedge the exchange
rate risk? Is there any disadvantage of selecting this method for hedging?
Part 1—Integrative Problem
The International Financial Environment
Mesa Company specializes in the production of small fancy picture frames, which are exported from the
U.S. to the United Kingdom. Mesa invoices the exports in pounds and converts the pounds to dollars
when they are received. The British demand for these frames is positively related to economic conditions
in the United Kingdom. Assume that British inflation and interest rates are similar to the rates in the U.S.
Mesa believes that the U.S. balance-of-trade deficit from trade between the U.S. and the United Kingdom
will adjust to changing prices between the two countries, while capital flows will adjust to interest rate
differentials. Mesa believes that the value of the pound is very sensitive to changing international capital
flows, and is moderately sensitive to international trade flows. Mesa is considering the following
information:
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Currency Derivatives 9
The U.K. inflation rate is expected to decline, while U.S. inflation rate is expected to rise.
British interest rates are expected to decline, while U.S. interest rates are expected to increase.
1. Explain how the international trade flows should initially adjust in response to the changes in
inflation (holding exchange rates constant). Explain how the international capital flows should adjust
in response to the changes in interest rates (holding exchange rates constant).
2. Using the information provided, will Mesa expect the pound to appreciate or depreciate in the future?
Explain.
ANSWER: The pound’s equilibrium value will change in response to changes in the capital flows
3. Mesa believes international capital flows shift in response to changing interest rate differentials. Is
there any reason why the changing interest rate differentials in this example will not necessarily cause
international capital flows to change significantly? Explain.
4. Based on your answer to question 2, how would Mesa’s cash flows be affected by the expected
exchange rate movements? Explain.
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Currency Derivatives 10
5. Based on your answer to question 4, should Mesa consider hedging its exchange rate risk? If so,
explain how it could hedge using forward contracts, futures contracts, and currency options.
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