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 p erfect 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.
示例和范例
Give three reasons why the treasurer of a company might not hedge the company’s exposure to a particular risk.
(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  065080642081
..⨯=.. This means that the s ize 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 a stock index 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  20000000128891080250
,,.⨯=.⨯ 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
(a) July
(b)September
(c)March
保持理智英文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哪里能下载免费的access
1.Estimate the company’s future cash flows in Japanese yen and U.S. dollars
2.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 J
une 8 when the futures price is $88.00. It closes out its position on November 10. The spot price and futures price at this time are $90.00 and $89.10. The gain on the futures position is
(89.10 − 88.00) × 16,000 = 17,600
The effective cost of the oil is therefore
20,000 × 90 – 17,600 = 1,782, 400
or $89.12 per barrel. (This compares with $88.90 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  S F
σρσ It is 1.0 when 05=.ρ and 2S F =σσ. Since 10<.ρ the hedge is clearly not perfect.
Problem 3.14.
“If there is no basis risk, the minimum variance hedge ratio is always 1.0." Is this statement true? Explain your answer.
The statement is true. Using the notation in the text, if the hedge ratio is 1.0, the hedger locks in a price of 12F b +. Since both 1F  and 2b  are known this has a variance of zero and must be the best hedge.
Problem 3.15
动漫特效“For an asset where futures prices for contracts on the asset are usually less than spot prices, long hedges are likely to be particularly attractive." Explain this statement.
A company that knows it will purchase a commodity in the future is able to lock in a price close to the futures price. This is likely to be particularly attractive when the futures price is less than the spot price.
Problem 3.16.
The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound)
1.2. The standard deviation of monthly changes in the futures price of live cattle for the closest
contract is 1.4. The correlation between the futures price changes and the spot price changes is 0.7. It is now October 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15. The producer wants to use the December live-cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle. What strategy should the beef producer follow?
The optimal hedge ratio is  12070614
..⨯=.. The beef producer requires a long position in 20000006120000⨯.=, lbs of cattle. The beef producer should therefore take a long position in 3 December contracts closing out the position on November 15.
超文本标记语言是什么意思Problem 3.17.
position of the dayA corn farmer argues “I do not use futures co ntracts for hedging. My real risk is not the price of corn. It is that my whole crop gets wiped out by the weather.”Discuss this viewpoint. Should the farmer estimate his or her expected production of corn and hedge to try to lock in a price for expected production?
If weather creates a significant uncertainty about the volume of corn that will be harvested, the farmer should not enter into short forward contracts to hedge the price risk on his or her expected production. The reason is as follows. Suppose that the weather is bad and the farmer’s
production is lower than expected. Other farmers are likely to have been affected similarly. Corn production overall will be low and as a consequence the price of corn will be relatively high. The farmer’s problems  arising from the bad harvest will be made worse by losses on the short futures position. This problem emphasizes the importance of looking at the big picture when hedging. The farmer is correct to question whether hedging price risk while ignoring other risks is a good strategy.
Problem 3.18.
On July 1, an investor holds 50,000 shares of a certain stock. The market price is $30 per share. The investor is interested in hedging against movements in the market over the next month and decides to use the September Mini S&P 500 futures contract. The index is currently 1,500 and one contract is for delivery of $50 times the index. The beta of the stock is 1.3. What strategy should the investor follow? Under what circumstances will it be profitable?
A short position in  50000301326501500,⨯.⨯=⨯,

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