SOLUTIONS MANUAL
FUNDAMENTALS OF FUTURES AND OPTIONS MARKETS
9TH EDITION
CHAPTER 1: INTRODUCTION
PRACTICE QUESTIONS
Problem 1.8.
Suppose you own 5,000 shares that are worth $25 each. How can put options be used to
provide you with insurance against a decline in the value of your holding over the next four
months?
You should buy 50 put option contracts (each on 100 shares) with a strike price of $25 and an
expiration date in four months. If at the end of four months the stock price proves to be less
than $25, you can exercise the options and sell the shares for $25 each.
Problem 1.9.
A stock when it is first issued provides funds for a company. Is the same true of an exchange-
traded stock option? Discuss.
An exchange-traded stock option provides no funds for the company. It is a security sold by
one investor to another. The company is not involved. By contrast, a stock when it is first
issued is sold by the company to investors and does provide funds for the company.
Problem 1.10.
Explain why a futures contract can be used for either speculation or hedging.
If an investor has an exposure to the price of an asset, he or she can hedge with futures
contracts. If the investor will gain when the price decreases and lose when the price increases,
a long futures position will hedge the risk. If the investor will lose when the price decreases
and gain when the price increases, a short futures position will hedge the risk. Thus either a
long or a short futures position can be entered into for hedging purposes.
If the investor has no exposure to the price of the underlying asset, entering into a futures
,contract is speculation. If the investor takes a long position, he or she gains when the asset’s
price increases and loses when it decreases. If the investor takes a short position, he or she
loses when the asset’s price increases and gains when it decreases.
Problem 1.11.
A cattle farmer expects to have 120,000 pounds of live cattle to sell in three months. The live-
cattle futures contract on the Chicago Mercantile Exchange is for the delivery of 40,000
pounds of cattle. How can the farmer use the contract for hedging? From the farmer’s
viewpoint, what are the pros and cons of hedging?
The farmer can short 3 contracts that have 3 months to maturity. If the price of cattle falls, the
gain on the futures contract will offset the loss on the sale of the cattle. If the price of cattle
rises, the gain on the sale of the cattle will be offset by the loss on the futures contract. Using
futures contracts to hedge has the advantage that it can at no cost reduce risk to almost zero.
Its disadvantage is that the farmer no longer gains from favorable movements in cattle prices.
Problem 1.12.
It is July 2016. A mining company has just discovered a small deposit of gold. It will take six
months to construct the mine. The gold will then be extracted on a more or less continuous
basis for one year. Futures contracts on gold are available on the New York Mercantile
Exchange. There are delivery months every two months from August 2016 to December 2017.
Each contract is for the delivery of 100 ounces. Discuss how the mining company might use
futures markets for hedging.
The mining company can estimate its production on a month by month basis. It can then short
futures contracts to lock in the price received for the gold. For example, if a total of 3,000
ounces are expected to be produced in September 2017 and October 2017, the price received
for this production can be hedged by shorting a total of 30 October 2017 contracts.
Problem 1.13.
Suppose that a March call option on a stock with a strike price of $50 costs $2.50 and is held
until March. Under what circumstances will the holder of the option make a gain? Under
what circumstances will the option be exercised? Draw a diagram showing how the profit on
a long position in the option depends on the stock price at the maturity of the option.
,The holder of the option will gain if the price of the stock is above $52.50 in March. (This
ignores the time value of money.) The option will be exercised if the price of the stock is
above $50.00 in March. The profit as a function of the stock price is shown in Figure S1.1.
20
Profit
15
10
5
Stock Price
0
20 30 40 50 60 70
-5
Figure S1.1 Profit from long position in Problem 1.13
Problem 1.14.
Suppose that a June put option on a stock with a strike price of $60 costs $4 and is held until
June. Under what circumstances will the holder of the option make a gain? Under what
circumstances will the option be exercised? Draw a diagram showing how the profit on a
short position in the option depends on the stock price at the maturity of the option.
The seller of the option will lose if the price of the stock is below $56.00 in June. (This
ignores the time value of money.) The option will be exercised if the price of the stock is
below $60.00 in June. The profit as a function of the stock price is shown in Figure S1.2.
, 60
Profit
50
40
30
20
10
Stock Price
0
0 20 40 60 80 100 120
-10
Figure S1.2 Profit from short position in Problem 1.14
Problem 1.15.
It is May and a trader writes a September call option with a strike price of $20. The stock
price is $18, and the option price is $2. Describe the investor’s cash flows if the option is
held until September and the stock price is $25 at this time.
The trader has an inflow of $2 in May and an outflow of $5 in September. The $2 is the cash
received from the sale of the option. The $5 is the result of the option being exercised. The
investor has to buy the stock for $25 in September and sell it to the purchaser of the option
for $20.
Problem 1.16.
An investor writes a December put option with a strike price of $30. The price of the option is
$4. Under what circumstances does the investor make a gain?
The investor makes a gain if the price of the stock is above $26 at the time of exercise. (This
ignores the time value of money.)
Problem 1.17.
The CME Group offers a futures contract on long-term Treasury bonds. Characterize the
investors likely to use this contract.
FUNDAMENTALS OF FUTURES AND OPTIONS MARKETS
9TH EDITION
CHAPTER 1: INTRODUCTION
PRACTICE QUESTIONS
Problem 1.8.
Suppose you own 5,000 shares that are worth $25 each. How can put options be used to
provide you with insurance against a decline in the value of your holding over the next four
months?
You should buy 50 put option contracts (each on 100 shares) with a strike price of $25 and an
expiration date in four months. If at the end of four months the stock price proves to be less
than $25, you can exercise the options and sell the shares for $25 each.
Problem 1.9.
A stock when it is first issued provides funds for a company. Is the same true of an exchange-
traded stock option? Discuss.
An exchange-traded stock option provides no funds for the company. It is a security sold by
one investor to another. The company is not involved. By contrast, a stock when it is first
issued is sold by the company to investors and does provide funds for the company.
Problem 1.10.
Explain why a futures contract can be used for either speculation or hedging.
If an investor has an exposure to the price of an asset, he or she can hedge with futures
contracts. If the investor will gain when the price decreases and lose when the price increases,
a long futures position will hedge the risk. If the investor will lose when the price decreases
and gain when the price increases, a short futures position will hedge the risk. Thus either a
long or a short futures position can be entered into for hedging purposes.
If the investor has no exposure to the price of the underlying asset, entering into a futures
,contract is speculation. If the investor takes a long position, he or she gains when the asset’s
price increases and loses when it decreases. If the investor takes a short position, he or she
loses when the asset’s price increases and gains when it decreases.
Problem 1.11.
A cattle farmer expects to have 120,000 pounds of live cattle to sell in three months. The live-
cattle futures contract on the Chicago Mercantile Exchange is for the delivery of 40,000
pounds of cattle. How can the farmer use the contract for hedging? From the farmer’s
viewpoint, what are the pros and cons of hedging?
The farmer can short 3 contracts that have 3 months to maturity. If the price of cattle falls, the
gain on the futures contract will offset the loss on the sale of the cattle. If the price of cattle
rises, the gain on the sale of the cattle will be offset by the loss on the futures contract. Using
futures contracts to hedge has the advantage that it can at no cost reduce risk to almost zero.
Its disadvantage is that the farmer no longer gains from favorable movements in cattle prices.
Problem 1.12.
It is July 2016. A mining company has just discovered a small deposit of gold. It will take six
months to construct the mine. The gold will then be extracted on a more or less continuous
basis for one year. Futures contracts on gold are available on the New York Mercantile
Exchange. There are delivery months every two months from August 2016 to December 2017.
Each contract is for the delivery of 100 ounces. Discuss how the mining company might use
futures markets for hedging.
The mining company can estimate its production on a month by month basis. It can then short
futures contracts to lock in the price received for the gold. For example, if a total of 3,000
ounces are expected to be produced in September 2017 and October 2017, the price received
for this production can be hedged by shorting a total of 30 October 2017 contracts.
Problem 1.13.
Suppose that a March call option on a stock with a strike price of $50 costs $2.50 and is held
until March. Under what circumstances will the holder of the option make a gain? Under
what circumstances will the option be exercised? Draw a diagram showing how the profit on
a long position in the option depends on the stock price at the maturity of the option.
,The holder of the option will gain if the price of the stock is above $52.50 in March. (This
ignores the time value of money.) The option will be exercised if the price of the stock is
above $50.00 in March. The profit as a function of the stock price is shown in Figure S1.1.
20
Profit
15
10
5
Stock Price
0
20 30 40 50 60 70
-5
Figure S1.1 Profit from long position in Problem 1.13
Problem 1.14.
Suppose that a June put option on a stock with a strike price of $60 costs $4 and is held until
June. Under what circumstances will the holder of the option make a gain? Under what
circumstances will the option be exercised? Draw a diagram showing how the profit on a
short position in the option depends on the stock price at the maturity of the option.
The seller of the option will lose if the price of the stock is below $56.00 in June. (This
ignores the time value of money.) The option will be exercised if the price of the stock is
below $60.00 in June. The profit as a function of the stock price is shown in Figure S1.2.
, 60
Profit
50
40
30
20
10
Stock Price
0
0 20 40 60 80 100 120
-10
Figure S1.2 Profit from short position in Problem 1.14
Problem 1.15.
It is May and a trader writes a September call option with a strike price of $20. The stock
price is $18, and the option price is $2. Describe the investor’s cash flows if the option is
held until September and the stock price is $25 at this time.
The trader has an inflow of $2 in May and an outflow of $5 in September. The $2 is the cash
received from the sale of the option. The $5 is the result of the option being exercised. The
investor has to buy the stock for $25 in September and sell it to the purchaser of the option
for $20.
Problem 1.16.
An investor writes a December put option with a strike price of $30. The price of the option is
$4. Under what circumstances does the investor make a gain?
The investor makes a gain if the price of the stock is above $26 at the time of exercise. (This
ignores the time value of money.)
Problem 1.17.
The CME Group offers a futures contract on long-term Treasury bonds. Characterize the
investors likely to use this contract.
