Fundamentalsoffuturesandoptionsmarkets

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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 2013. 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 2013 to December 2014.

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 2014 and October 2014, the price received

for this production can be hedged by shorting a total of 30 October 2014 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.

-5

20 30 40 50 60 70

Profit

Stock Price

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.

It may well be true that there is just as much chance that the price of oil in the future will be

above the futures price as that it will be below the futures price. This means that the use of a

futures contract for speculation would be like betting on whether a coin comes up heads or

tails. But it might make sense for the airline to use futures for hedging rather than speculation.

The futures contract then has the effect of reducing risks. It can be argued that an airline

should not expose its shareholders to risks associated with the future price of oil when there

are contracts available to hedge the risks.

Problem 1.19.

“Options and futures are zero-sum games.” What do you think is meant by this statement?

The statement means that the gain (loss) to the party with the short position is equal to the

loss (gain) to the party with the long position. In total, the gain to all parties is zero.

Problem 1.20.

A trader enters into a short forward contract on 100 million yen. The forward exchange rate

is $0.0080 per yen. How much does the trader gain or lose if the exchange rate at the end of

the contract is (a) $0.0074 per yen; (b) $0.0091 per yen?

a) The trader sells 100 million yen for $0.0080 per yen when the exchange rate is $0.0074

per yen. The gain is

100 0 0006

×.

millions of dollars or $60,000.

b) The trader sells 100 million yen for $0.0080 per yen when the exchange rate is $0.0091

per yen. The loss is

100 0 0011×.

millions of dollars or $110,000.

Problem 1.21.

A trader enters into a short cotton futures contract when the futures price is 50 cents per

pound. The contract is for the delivery of 50,000 pounds. How much does the trader gain or

lose if the cotton price at the end of the contract is (a) 48.20 cents per pound; (b) 51.30 cents

per pound?

a) The trader sells for 50 cents per pound something that is worth 48.20 cents per pound.

Gain = ($0.5000 − $0.4820) × 50,000 = $900.

b) The trader sells for 50 cents per pound something that is worth 51.30 cents per pound.

Loss = ($0.5130 − $0.5000) × 50,000 = $650.

Problem 1.22.

A company knows that it is due to receive a certain amount of a foreign currency in four

months. What type of option contract is appropriate for hedging?

A long position in a four-month put option can provide insurance against the exchange rate

falling below the strike price. It ensures that the foreign currency can be sold for at least the

strike price.

Problem 1.23.

A United States company expects to have to pay 1 million Canadian dollars in six months.

Explain how the exchange rate risk can be hedged using (a) a forward contract; (b) an option.

The company could enter into a long forward contract to buy 1 million Canadian dollars in

six months. This would have the effect of locking in an exchange rate equal to the current

forward exchange rate. Alternatively the company could buy a call option giving it the right

(but not the obligation) to purchase 1 million Canadian dollars at a certain exchange rate in

six months. This would provide insurance against a strong Canadian dollar in six months

while still allowing the company to benefit from a weak Canadian dollar at that time.

Problem 1.24

A trader buys a call option with a strike price of $30 for $3. Does the trader ever exercise the

option and lose money on the trade. Explain.

Yes, the trader will exercise if the asset price is greater than $30, but will cover the cost of the

call option only if the price is greater than $33. The trader exercises and loses money if the

price is between $30 and $33.

Problem 1.25

A trader sells a put option with a strike price of $40 for $5. What is the trader’s maximum

gain and maximum loss? How does your answer change if it is a call option?

The trader’s maximum gain from the put option is $5. The maximum loss is $35,

corresponding to the situation where the option is exercised and the asset price is zero. If the

option were a call, the trader’s maximum gain would still be $5, but there would be no bound

to the loss as there is in theory no limit to how high the asset price could rise.

Problem 1.26

‘‘Buying a stock and a put option on the stock is a form of insurance.’’ Explain this

statement.

If the stock price declines below the strike price of the put option, the stock can be sold for

the strike price.

Further Questions

Problem 1.27 (Excel file)

Trader A enters into a forward contract to buy an asset for $1000 an ounce in one year.

Trader B buys a call option to buy the asset for $1000 in one year. The cost of the option is

$100. What is the difference between the positions of the traders? Show the profit as a

function of the price of the asset in one year for the two traders.

Trader A makes a profit of S

 1000 and Trader B makes a profit of max(S

 1000,

0) –100 where S

is the price of the asset in one year. Trader A does better if S

is above

$900 as indicated in the diagram below

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