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Question 5 : Commodity Futures ( 2 1 0 ) Table 1 shows the hypothetical daily closing prices for one unit of corn, and the

Question 5: Commodity Futures (210) Table 1 shows the hypothetical daily closing prices for one unit of corn, and the daily prices for the corn futures contract with maturity date Jan 4. The futures contract size is 100 units of corn.
The initial margin required for the futures contract is $10,000 per contract. The maintenance margin is $7,000 per contract. The risk free rate is 2%(annual, continuously compounded). Assume this is the rate you earn on your margin account.
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(1) Suppose you take a long position in 10 futures contracts on Jan 1. What is your profit/loss on Jan 2 and Jan 3? What is the balance in your margin account at the end of Jan 2 and Jan 3? Do you face any margin calls?
(2) Following (1), at the end of Jan 4, you will pay 390 per unit to purchase the corn, and your margin account is returned to you. What is your total profit/loss from Jan 1 to Jan 4, both including interest and excluding interest? (Hint: when excluding interest, total payoff should be the same as the formula N0(ST-F0,T).)
(3) Repeat part (1) for a short position of 5 futures contracts.
(4) Suppose there is a lease market for corn. Using the Jan 1 corn price and futures price, what is the implied equilibrium lease rate (annual, continuously compounded) on corn?
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