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Answer: No expected gain/loss
Compute the expected return on corn using CAPM: \[ k = r_f + \beta(E[R_m]-r_f) = 4\% + 0.40(9\%-4\%) = 4\% + 2\% = 6\% \] With a 2% annual storage cost and a 6-month horizon, the forward price from cost of carry is: \[ F(0,0.5) = 7.00 \times e^{(0.04+0.02)\times 0.5} = 7.00e^{0.03} \approx 7.212 \] The expected future spot price, using the expected return of 6%, is: \[ E[S(0.5)] = 7.00 \times e^{0.06\times 0.5} = 7.00e^{0.03} \approx 7.212 \] Expected gain on a **short** futures position is approximately: \[ F(0,0.5) - E[S(0.5)] \approx 0 \] So there is **no expected gain/loss**. Correct answer: **C**.
Author: Manit Arora
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Question-167.4. The spot price of corn is $7.00 per bushel. Corn has a market beta of 0.40 and a storage cost of 2.0% per annum (continuous). The market return is 9.0% and the riskfree rate is 4.0% per annum. A corn farmer plans to sell corn in six months and therefore hedges with a short position in corn futures. What is the expected future gain per bushel on the corn futures contract?
A
Loss of $0.07 per bushel
B
Loss of $0.02
C
No expected gain/loss
D
Gain of $0.05
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