CHAPTER 3满意度调查报告
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 ast and expects to ll that ast in the future. It can also be ud when the company does not currently own the ast but expects to do so at some time in the future. A long hedge is appropriate when a company knows it will have to purcha an ast in the future. It can also be ud to offt the risk from an existing short position.
Problem 3.2.
米筛Explain what is meant by basis risk when futures contracts are ud for hedging.
Basis risk aris 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 ast. Suppo the ast’s price movements prove to be favorable to the company. A perfect hedge totally neutralizes the company’s gain from the favorable price movements. An imperfect hedge, which only partially neutralizes the gains, might well give a better outcome.
Problem 3.4.
经典电影插曲
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 ast 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.
(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 becau 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 ast, the treasurer might feel that he or she will have difficulty justifying the hedging to other executives within the organization.
Problem 3.6.
烽火戏诸侯的故事
Suppo 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 u 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 ud for hedging when the expiration of the hedge is in a) June, b) July, and c) January
A good rule of thumb is to choo a futures contract that has a delivery month as clo as
possible to, but later than, the month containing the expiration of the hedge. The contracts that should be ud are therefore
(a) July
(b)September
(c)March
Problem 3.9.
Does a perfect hedge always succeed in locking in the current spot price of an ast for a future transaction? Explain your answer.我可以忍受
No. Consider, for example, the u 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 worns 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 ast and short futures contracts. The value of his or her position therefore improves as the basis increas. Similarly, it worns as the basis decreas.
Problem 3.11.
Imagine you are the treasurer of a Japane company exporting electronic equipment to the United States. Discuss how you would design a foreign exchange hedging strategy and the arguments you would u to ll the strategy to your fellow executives.
The simple answer to this question is that the treasurer should
1.Estimate the company’s future cash flows in Japane 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 rai 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 tho showing the overall effect on the company’s profitability of changes in the exchange rate at various times in the future. Once the estimates have been produced the company can choo between using futures and options to hedge its risk. The results of the analysis should be prented 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 ud both the downside and upside are eliminated. With options a premium is paid to eliminate only the downside.
Problem 3.12.
Suppo that in Example 3.2 of Section 3.3 the company decides to u 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 clos 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.)
刘咏尧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
“For an ast where futures prices for contracts on the ast are usually less than spot prices, long hedges are likely to be particularly attractive." Explain this statement.脚气的症状
A company that knows it will purcha a commodity in the future is able to lock in a price clo 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 clost
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 u 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
北京社平工资
..⨯=.. 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.
Problem 3.17.
A corn farmer argues “I do not u 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. Suppo 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 conquence the price of corn will be relatively high. The farmer’s problems arising from the bad harvest will be made wor by loss 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 u 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,⨯.⨯=⨯,
