# Solution of Week6

Last Updated: 28 Jan 2021
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## Problem 1. 7.

Suppose that you write a put contract with a strike price of \$40 and an expiration date in three months. The current stock price is \$41 and the contract is on 100 shares. What have you committed yourself to? How much could you gain or lose? You have sold a put option. You have agreed to buy 100 shares for \$40 per share if the party on the other side of the contract chooses to exercise the right to sell for this price. The option will be exercised only when the price of stock is below \$40. Suppose, for example, that the option is exercised when the price is \$30.

You have to buy at \$40 shares that are worth \$30; you lose \$10 per share, or \$1,000 in total. If the option is exercised when the price is \$20, you lose \$20 per share, or \$2,000 in total. The worst that can happen is that the price of the stock declines to almost zero during the three-month period. This highly unlikely event would cost you \$4,000. In return for the possible future losses, you receive the price of the option from the purchaser.

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## Problem 1. 21.

“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 aggregate, the net gain to all parties is zero.

## Problem 1. 30

The price of gold is currently \$1,000 per ounce. The forward price for delivery in one year is \$1,200. An arbitrageur can borrow money at 10% per annum. What should the arbitrageur do? Assume that the cost of storing gold is zero and that gold provides no income. The arbitrageur should borrow money to buy a certain number of ounces of gold today and short forward contracts on the same number of ounces of gold for delivery in one year.

This means that gold is purchased for \$1000 per ounce and sold for \$1200 per ounce. Assuming the cost of borrowed funds is less than 20% per annum this generates a riskless profit.

## Problem 2. 3.

Suppose that you enter into a short futures contract to sell July silver for \$17. 20 per ounce. The size of the contract is 5,000 ounces. The initial margin is \$4,000, and the maintenance margin is \$3,000. What change in the futures price will lead to a margin call? What happens if you do not meet the margin call? There will be a margin call when \$1,000 has been lost from the margin account.

This will occur when the price of silver increases by 1,000/5,000 ? \$0. 20. The price of silver must therefore rise to \$17. 40 per ounce for there to be a margin call. If the margin call is not met, your broker closes out your position.

## Problem 2. 10.

Explain how margins protect investors against the possibility of default. A margin is a sum of money deposited by an investor with his or her broker. It acts as a guarantee that the investor can cover any losses on the futures contract. The balance in the margin account is adjusted daily to reflect gains and losses on the futures contract.

If losses are above a certain level, the investor is required to deposit a further margin. This system makes it unlikely that the investor will default. A similar system of margins makes it unlikely that the investor’s broker will default on the contract it has with the clearing house member and unlikely that the clearing house member will default with the clearing house.

## Problem 2. 11.

A trader buys two July futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is \$6,000 per contract, and the maintenance margin is \$4,500 per contract.

What price change would lead to a margin call? Under what circumstances could \$2,000 be withdrawn from the margin account? There is a margin call if more than \$1,500 is lost on one contract. This happens if the futures price of frozen orange juice falls by more than 10 cents to below 150 cents per pound. \$2,000 can be withdrawn from the margin account if there is a gain on one contract of \$1,000. This will happen if the futures price rises by 6. 67 cents to 166. 67 cents per pound.

## Problem 2. 21.

What do you think would happen if an exchange started trading a contract in which the quality of the underlying asset was incompletely specified?

The contract would not be a success. Parties with short positions would hold their contracts until delivery and then deliver the cheapest form of the asset. This might well be viewed by the party with the long position as garbage! Once news of the quality problem became widely known no one would be prepared to buy the contract. This shows that futures contracts are feasible only when there are rigorous standards within an industry for defining the quality of the asset. Many futures contracts have in practice failed because of the problem of defining quality.

## Problem 2. 6

Trader A enters into futures contracts to buy 1 million euros for 1. 4 million dollars in three months. Trader B enters in a forward contract to do the same thing. The exchange (dollars per euro) declines sharply during the first two months and then increases for the third month to close at 1. 4300. Ignoring daily settlement, what is the total profit of each trader? When the impact of daily settlement is taken into account, which trader does better? The total profit of each trader in dollars is 0. 03? 1,000,000 = 30,000. Trader B’s profit is realized at the end of the three months.

Trader A’s profit is realized day-by-day during the three months. Substantial losses are made during the first two months and profits are made during the final month. It is likely that Trader B has done better because Trader A had to finance its losses during the first two months.

## Problem 2. 29

A company enters into a short futures contract to sell 5,000 bushels of wheat for 450 cents per bushel. The initial margin is \$3,000 and the maintenance margin is \$2,000. What price change would lead to a margin call? Under what circumstances could \$1,500 be withdrawn from the margin account?

There is a margin call if \$1000 is lost on the contract. This will happen if the price of wheat futures rises by 20 cents from 450 cents to 470 cents per bushel. \$1500 can be withdrawn if the futures price falls by 30 cents to 420 cents per bushel. Problem 2. 30. Suppose that there are no storage costs for crude oil and the interest rate for borrowing or lending is 5% per annum. How could you make money on May 26, 2010 by trading July 2010 and December 2010 contracts on crude oil? Use Table 2. 2. The July 2010 settlement price for oil is \$71. 51 per barrel. The December 2010 settlement price for oil is \$75. 3 per barrel. You could go long one July 2010 oil contract and short one December 2010 contract. In July 2010 you take delivery of the oil borrowing \$71. 51 per barrel at 5% to meet cash outflows. The interest accumulated in five months is about 71. 51? 0. 05? 5/12 or \$1. 49. In December the oil is sold for \$75. 23 per barrel which is more than the amount that has to be repaid on the loan. The strategy therefore leads to a profit. Note that this profit is independent of the actual price of oil in June 2010 or December 2010. It will be slightly affected by the daily settlement procedures.

## 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. 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. 5

Give three reasons why the treasurer of a company might not hedge the company’s exposure to a particular risk. Explain your answer.  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. ) The shareholders might not want the company to hedge because the risks are hedged within their portfolios.  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. 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.