Answer-first summary for fast verification
Answer: 3.21%
The implied convenience yield is solved from the cost-of-carry relationship: \[ F_0 = S_0 e^{(r + u - y)T} \] Given: - \(F_0 = 90\) - \(S_0 = 100\) - \(r = 4\%\) per annum continuously compounded - storage cost \(u = 2\%\) per month - \(T = 12\) months Using the per-month formulation shown in the source: \[ 90 = 100 \cdot e^{\left(\frac{4\%}{12} + 2\% - y\right)12} \] So: \[ \frac{90}{100} = e^{\left(\frac{4\%}{12} + 2\% - y\right)12} \] Taking natural logs and solving for \(y\): \[ y = \frac{4\%}{12} + 2\% - \frac{\ln(90/100)}{12} = 3.211\% \] Therefore, the implied convenience yield is **3.21% per month**.
Author: Manit Arora
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Question 165.4. The riskless rate is 4.0% per annum (continuous). Assume the spot price of oil is $100.00 and oil forward curve exhibits backwardation (inversion) such that the one-year futures price is $90.00. If the storage cost is 2.0% per month continuously compounded, what is the implied convenience yield of oil per month? Note: consistent with the assigned Hull, please assume in this case that the convenience yield can be precisely solved as the "plug variable" that reconciles the futures price with the spot price; in contrast to McDonald who takes a different approach as infers a no-arbitrage region from the convenience yield.
A. 1.12%
B. 1.68%
C. 2.21%
D. 3.21%
A
1.12%
B
1.68%
C
2.21%
D
3.21%
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