need it within 3 hours
CHAPTER 3
Hedging Strategies Using Futures
Practice Questions
Problem 3.1.
Under what circumstances are (a) a short hedge and (b) a long hedge appropriate?
A short hedge is appropriate when a company owns an asset and expects to sell that asset in the future. It can also be used when the company does not currently own the asset but expects to do so at some time in the future. A long hedge is appropriate when a company knows it will have to purchase an asset in the future. It can also be used to offset the risk from an existing short position.
Problem 3.2.
Explain what is meant by basis risk when futures contracts are used for hedging.
Basis risk arises from the hedger’s uncertainty as to the difference between the spot price and futures price at the expiration of the hedge.
Problem 3.3.
Explain what is meant by a perfect hedge. Does a perfect hedge always lead to a better outcome than an imperfect hedge? Explain your answer.
A perfect hedge is one that completely eliminates the hedger’s risk. A perfect hedge does not always lead to a better outcome than an imperfect hedge. It just leads to a more certain outcome.
Consider a company that hedges its exposure to the price of an asset. Suppose the asset’s price movements prove to be favorable to the company. A perfect hedge totally neutralizes the company’s gain from these favorable price movements. An imperfect hedge, which only partially neutralizes the gains, might well give a better outcome.
Problem 3.4.
Under what circumstances does a minimum-variance hedge portfolio lead to no hedging at all?
A minimum variance hedge leads to no hedging when the coefficient of correlation between the futures price changes and changes in the price of the asset being hedged is zero.
Problem 3.5.
Give three reasons why the treasurer of a company might not hedge the company’s exposure to a particular risk. Explain your answer.
(a) If the company’s competitors are not hedging, the treasurer might feel that the company will experience less risk if it does not hedge. (See Table 3.1.) (b) The shareholders might not want the company to hedge because the risks are hedged within their portfolios. (c) If there is a loss on the hedge and a gain from the company’s exposure to the underlying asset, the treasurer might feel that he or she will have difficulty justifying the hedging to other executives within the organization.
Problem 3.6.
Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean?
The optimal hedge ratio is
This means that the size of the futures position should be 64.2% of the size of the company’s exposure in a three-month hedge.
Problem 3.7.
A company has a $20 million portfolio with a beta of 1.2. It would like to use futures contracts on the S&P 500 to hedge its risk. The index futures is currently standing at 1080, and each contract is for delivery of $250 times the index. What is the hedge that minimizes risk? What should the company do if it wants to reduce the beta of the portfolio to 0.6?
The formula for the number of contracts that should be shorted gives
Rounding to the nearest whole number, 89 contracts should be shorted. To reduce the beta to 0.6, half of this position, or a short position in 44 contracts, is required.
Problem 3.8.
In the corn futures contract, the following delivery months are available: March, May, July, September, and December. State the contract that should be used for hedging when the expiration of the hedge is in a) June, b) July, and c) January
A good rule of thumb is to choose a futures contract that has a delivery month as close as possible to, but later than, the month containing the expiration of the hedge. The contracts that should be used are therefore
July
September
March
Problem 3.9.
Does a perfect hedge always succeed in locking in the current spot price of an asset for a future transaction? Explain your answer.
No. Consider, for example, the use of a forward contract to hedge a known cash inflow in a foreign currency. The forward contract locks in the forward exchange rate — which is in general different from the spot exchange rate.
Problem 3.10.
Explain why a short hedger’s position improves when the basis strengthens unexpectedly and worsens when the basis weakens unexpectedly.
The basis is the amount by which the spot price exceeds the futures price. A short hedger is long the asset and short futures contracts. The value of his or her position therefore improves as the basis increases. Similarly, it worsens as the basis decreases.
Problem 3.11.
Imagine you are the treasurer of a Japanese company exporting electronic equipment to the United States. Discuss how you would design a foreign exchange hedging strategy and the arguments you would use to sell the strategy to your fellow executives.
The simple answer to this question is that the treasurer should
Estimate the company’s future cash flows in Japanese yen and U.S. dollars
Enter into forward and futures contracts to lock in the exchange rate for the U.S. dollar cash flows.
However, this is not the whole story. As the gold jewelry example in Table 3.1 shows, the company should examine whether the magnitudes of the foreign cash flows depend on the exchange rate. For example, will the company be able to raise the price of its product in U.S. dollars if the yen appreciates? If the company can do so, its foreign exchange exposure may be quite low. The key estimates required are those showing the overall effect on the company’s profitability of changes in the exchange rate at various times in the future. Once these estimates have been produced the company can choose between using futures and options to hedge its risk. The results of the analysis should be presented carefully to other executives. It should be explained that a hedge does not ensure that profits will be higher. It means that profit will be more certain. When futures/forwards are used both the downside and upside are eliminated. With options a premium is paid to eliminate only the downside.
Problem 3.12.
Suppose that in Example 3.2 of Section 3.3 the company decides to use a hedge ratio of 0.8. How does the decision affect the way in which the hedge is implemented and the result?
If the hedge ratio is 0.8, the company takes a long position in 16 December oil futures contracts on June 8 when the futures price is $68.00. It closes out its position on November 10. The spot price and futures price at this time are $70.00 and $69.10. The gain on the futures position is
The effective cost of the oil is therefore
or $69.12 per barrel. (This compares with $68.90 per barrel when the company is fully hedged.)
Problem 3.13.
“If the minimum-variance hedge ratio is calculated as 1.0, the hedge must be perfect." Is this statement true? Explain your answer.
The statement is not true. The minimum variance hedge ratio is
It is 1.0 when 
and
. Since