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# Forwards, Futures and Options

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1. A farmer anticipates having 50,000 bushels of wheat ready for harvest in September. What would be the implications of hedging by (a) selling 8 contracts (b) selling 10 contracts, and (c) selling 12 contracts of September wheat?

2. The crude oil futures contract on the NYMEX covers 1,000 barrels of crude oil and is quoted in dollars and cents per barrel. The minimum price change is \$0.01. The initial margin requirement is \$3,375 and the maintenance requirement is \$2,500. Suppose you purchased the contract at \$27.42 putting up the initial margin. At what price would you receive a margin call?

3. The over-the-counter forward price of commodity is currently \$45 and expires in one year. The risk-free interest rate is 10 percent. Suppose that six months later the spot price of the commodity is \$52. What is the forward contract worth at that time?

4. You observe a futures contract with a value of \$102. Call options with a strike price of \$100 and 3 months to expiration on the same contract are selling for \$4. Put options with the same strike and time to expiration are selling for \$1.75. If the risk-free interest rate is 10 percent verify that put-call parity holds.

5. Suppose the September S&P 500 stock index futures was priced at 960.50. At the same time The S&P 500 index was 956.49. The contract expires 73 days later. Assuming continuous compounding, is the contract correctly priced if the risk-free rate is 5.96 percent and the dividend yield on the index is 2.75 percent?
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Directions: Type your answer to each question where indicated. Use more space if needed. At least 6 lines.

#### Solution Preview

1. A farmer anticipates having 50,000 bushels of wheat ready for harvest in September. What would be the implications of hedging by (a) selling 8 contracts (b) selling 10 contracts, and (c) selling 12 contracts of September wheat?

Size of contracts (CBOT)
1 contract= 5,000 bushels

For 50,000 bushels, number of contracts required for hedging= 10 =50,000 / 5,000

(a) selling 8 contracts
With 8 contracts 40,000 bushels are hedged =5,000 x 8
Remaining 10,000 bushels are not hedged
Therefore, there is a speculative cash postion for 10,000 bushels
Thus there is under-hedging

(b) selling 10 contracts

With 10 contracts 50,000 bushels are hedged =5,000 x 10
Since, the cash position is for 50,000 bushels
The entire cash position is hedged

(c) selling 12 contracts

With 12 contracts 60,000 bushels are accounted for =5,000 x 12
Since, the cash position is for 50,000 bushels
There is overhedging
Therefore, there is a speculative future postion ...

#### Solution Summary

Answers questions on hedging, margin call, put call parity, future price etc.

\$2.19