BAFI1026 Tutorial 6 Solution PDF

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Tutorial 6 – Futures and Forward Contracts Problem 6 The party with a short position in a futures contract sometimes has options as to the precise asset that will be delivered, where delivery will take place, when delivery will take place, and so on. Do these options increase or decrease the futures...

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Tutorial 6 – Futures and Forward Contracts Problem 6.1 The party with a short position in a futures contract sometimes has options as to the precise asset that will be delivered, where delivery will take place, when delivery will take place, and so on. Do these options increase or decrease the futures price? Explain your reasoning. These options make the contract less attractive to the party with the long position and more attractive to the party with the short position. They therefore tend to reduce the futures price.

Problem 6.2 What are the most important aspects of the design of a new futures contract? The most important aspects of the design of a new futures contract are the specification of the underlying asset, the size of the contract, the delivery arrangements, and the delivery months.

Problem 6.3 Explain how margin protect investors against the possibility of default.

Margin is 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 further margin. This system makes it unlikely that the investor will default. A similar system of margin accounts 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 6.4 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 Under what circumstances could $2,000 be withdrawn from the margin account?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 lb. $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 lb.

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Problem 6.5 Show that, if the futures price of a commodity is greater than the spot price during the delivery period, then there is an arbitrage opportunity. Does an arbitrage opportunity exist if the futures price is less than the spot price? Explain your answer. If the futures price is greater than the spot price during the delivery period, an arbitrageur buys the asset, shorts a futures contract, and makes delivery for an immediate profit. If the futures price is less than the spot price during the delivery period, there is no similar perfect arbitrage strategy. An arbitrageur can take a long futures position but cannot force immediate delivery of the asset. The decision on when delivery will be made is made by the party with the short position. Nevertheless companies interested in acquiring the asset will find it attractive to enter into a long futures contract and wait for delivery to be made. Problem 6.6 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 6.7 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 6.8 “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

 2 F It is 1.0 when  0 5 and S . Since   10 the hedge is clearly not perfect.

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Problem 6.9 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2 0 7  0 6 14 200000 06 120 000 lbs of cattle. The beef The beef producer requires a long position in producer should therefore take a long position in 3 December contracts closing out the position on November 15.

Problem 6.10 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). BAFI1026 Tut 6 S1 2018

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Problem 6.11 A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding.

a) What are the forward price and the initial value of the forward contract? b) Six months later, the price of the stock is $45 and the risk-free interest rate is still 10%. What are the forward price and the value of the forward contract? a) The forward price,

F0

, is given by equation (5.1) as: F0 40e 0 11 44 21

or $44.21. The initial value of the forward contract is zero.

b) The delivery price K in the contract is $44.21. The value of the contract, f, after six months is given by equation (5.5) as: f  45  4421e  010 5

295 i.e., it is $2.95. The forward price is:

45e0 10 5  47 31 or $47.31.

Problem 6.12 The risk-free rate of interest is 7% per annum with continuous compounding, and the dividend yield on a stock index is 3.2% per annum. The current value of the index is 150. What is the six-month futures price? Using equation (5.3) the six month futures price is

150e (007 0032)05 15288 or $152.88.

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