CHAPTER 3
Hedging Strategies Using Futures
Practice Questions
Problem 3.8.
In the Chicago Board of Trade?s 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 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
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
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 3.4 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 $8. It closes out its position on November 10. The spot price and futures price at this time are $95 and $92. The gain on the futures position is
(92 ? 88)×16,000 = $64,000
The effective cost of the oil is therefore
20,000×95 ? 64,000 = $1,836,000
or $91.80 per barrel. (This compares with $91.00 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.\statement true? Explain your answer.
The statement is not true. The minimum variance hedge ratio is
?S ?FIt is 1.0 when ??0?5 and ?S?2?F. Since ??1?0 the hedge is clearly not perfect.
?
Problem 3.14.
“If there is no basis risk, the minimum variance hedge ratio is always 1.0.\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 F1?b2. Since both F1 and b2 are known this has a variance of zero and must be the best hedge.
Problem 3.15
“For an asset where futures prices are usually less than spot prices, long hedges are likely to be particularly attractive.\
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. An illustration is provided by Example 3.2.
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
1?20?7??0?6
1?4The beef producer requires a long position in 200000?0?6?120?000 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 use futures contracts 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
50?000?301?3??26
50?1?500contracts is required. It will be profitable if the stock outperforms the market in the sense that its return is greater than that predicted by the capital asset pricing model.
Problem 3.19.
Suppose that in Table 3.5 the company decides to use a hedge ratio of 1.5. How does the decision affect the way the hedge is implemented and the result?
If the company uses a hedge ratio of 1.5 in Table 3.5 it would at each stage short 150 contracts. The gain from the futures contracts would be
1.50?1.70?$2.55
per barrel and the company would be $0.85 per barrel better off.
Problem 3.20.
A futures contract is used for hedging. Explain why the daily settlement of the contract can give rise to cash flow problems.
Suppose that you enter into a short futures contract to hedge the sale of an asset in six months. If the price of the asset rises sharply during the six months, the futures price will also rise and you may get margin calls. The margin calls will lead to cash outflows. Eventually the cash outflows will be offset by the extra amount you get when you sell the asset, but there is a mismatch in the timing of the cash outflows and inflows. Your cash outflows occur earlier than your cash inflows. A similar situation could arise if you used a long position in a futures contract to hedge the purchase of an asset and the asset’s price fell sharply. An extreme example of what we are talking about here is provided by Metallgesellschaft (see Business Snapshot 3.2).
Problem 3.21.
The expected return on the S&P 500 is 12% and the risk-free rate is 5%. What is the expected return on the investment with a beta of (a) 0.2, (b) 0.5, and (c) 1.4?
a) 0?05?0?2?(0?12?0?05)?0?064 or 6.4% b) 0?05?0?5?(0?12?0?05)?0?085 or 8.5% c) 0?05?1?4?(0?12?0?05)?0?148 or 14.8%
Further Questions
Problem 3.22
It is now June. A company knows that it will sell 5,000 barrels of crude oil in September. It uses the October CME Group futures contract to hedge the price it will receive. Each
contract is on 1,000 barrels of ??light sweet crude.?? What position should it take? What price risks is it still exposed to after taking the position?
It should short five contracts. It has basis risk. It is exposed to the difference between the October futures price and the spot price of light sweet crude at the time it closes out its
position in September. It is also possibly exposed to the difference between the spot price of light sweet crude and the spot price of the type of oil it is selling.
Problem 3.23
Sixty futures contracts are used to hedge an exposure to the price of silver. Each futures contract is on 5,000 ounces of silver. At the time the hedge is closed out, the basis is $0.20 per ounce. What is the effect of the basis on the hedger?s financial position if (a) the trader is hedging the purchase of silver and (b) the trader is hedging the sale of silver?
The excess of the spot over the futures at the time the hedge is closed out is $0.20 per ounce. If the trader is hedging the purchase of silver, the price paid is the futures price plus the basis.
The trader therefore loses 60×5,000×$0.20=$60,000. If the trader is hedging the sales of silver, the price received is the futures price plus the basis. The trader therefore gains $60,000.
Problem 3.24
A trader owns 55,000 units of a particular asset and decides to hedge the value of her position with futures contracts on another related asset. Each futures contract is on 5,000 units. The spot price of the asset that is owned is $28 and the standard deviation of the change in this price over the life of the hedge is estimated to be $0.43. The futures price of the related asset is $27 and the standard deviation of the change in this over the life of the hedge is $0.40. The coefficient of correlation between the spot price change and futures price change is 0.95.
(a) What is the minimum variance hedge ratio?
(b) Should the hedger take a long or short futures position?
(c) What is the optimal number of futures contracts with no tailing of the hedge? (d) What is the optimal number of futures contracts with tailing of the hedge?
(a) The minimum variance hedge ratio is 0.95×0.43/0.40=1.02125. (b) The hedger should take a short position.
(c) The optimal number of contracts with no tailing is 1.02125×55,000/5,000=11.23 (or 11 when rounded to the nearest whole number) (d) The optimal number of contracts with tailing is 1.012125×(55,000×28)/(5,000×27)=11.65 (or 12 when rounded to the nearest whole number).
Problem 3.25
A company wishes to hedge its exposure to a new fuel whose price changes have a 0.6
correlation with gasoline futures price changes. The company will lose $1 million for each 1 cent increase in the price per gallon of the new fuel over the next three months. The new fuel's price change has a standard deviation that is 50% greater than price changes in gasoline futures prices. If gasoline futures are used to hedge the exposure what should the hedge ratio be? What is the company's exposure measured in gallons of the new fuel? What position measured in gallons should the company take in gasoline futures? How many gasoline futures contracts should be traded?
The hedge ratio should be 0.6 × 1.5 = 0.9. The company has an exposure to the price of 100 million gallons of the new fuel. It should therefore take a position of 90 million gallons in gasoline futures. Each futures contract is on 42,000 gallons. The number of contracts required is therefore
90,000,000?2142.9
42,000or, rounding to the nearest whole number, 2143.
Problem 3.26
A portfolio manager has maintained an actively managed portfolio with a beta of 0.2. During the last year the risk-free rate was 5% and equities performed very badly providing a return of ?30%. The portfolio manage produced a return of ?10% and claims that in the circumstances it was good. Discuss this claim.