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Answer: The market is concerned that a possible shortage (i.e., lack of supply) in wheat might occur and this is reflected in a convenience yield of about 4.0% per annum as a proportion of the spot price
### Analysis For a commodity futures contract, the cost-of-carry relationship is: \[ F_0 = S_0 e^{(r + u - y)T} \] where: - \(S_0 = 5.00\) - \(r = 3\%\) - \(u = 12\%\) storage cost - \(T = 0.75\) years - \(y\) = convenience yield If we ignore convenience yield, the theoretical futures price would be: \[ F_0 = 5.00 \times e^{(0.03 + 0.12)(0.75)} \approx 5.594 \] The observed futures price is **5.430**, which is lower than this. That suggests a **positive convenience yield**. Solving for the convenience yield gives approximately: \[ y \approx 4\%\text{ per annum} \] ### Correct answer **D) The market is concerned that a possible shortage in wheat might occur and this is reflected in a convenience yield of about 4.0% per annum as a proportion of the spot price**
Author: Manit Arora
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Q-716.3. The spot price of wheat is $5.00 per bushel while the risk free-rate is 3.0% per annum with continuous compounding. The cost to store wheat is 12.00% per annum as a proportion of the spot price. The traded (observed) price of a nine-month wheat futures contract, F(0, 0.75), is $5.430. Among the following choices, which of the following scenarios is the most likely?
A
Arbitragers will immediately compel the futures contract price to increase by $0.165
B
Arbitragers will immediately compel the futures contract price to increase by $1.370
C
We can currently conduct a cash-and-carry arbitrage, borrowing to buy the asset at the current spot price, for a future profit of about $0.316 per bushel
D
The market is concerned that a possible shortage (i.e., lack of supply) in wheat might occur and this is reflected in a convenience yield of about 4.0% per annum as a proportion of the spot price
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