Answer-first summary for fast verification
Answer: 1.28%
If the investor is indifferent between holding physical gold and holding it synthetically via futures, the futures price must reflect the full cost of carry. Using continuous compounding and assuming no convenience yield is given: \[ F = S e^{(r+s)T} \] where \(s\) is the storage cost. Solve for \(s\): \[ s = \ln(F/S) - r \] \[ s = \ln(1860/1800) - 0.02 \approx 0.03279 - 0.02 = 0.01279 \] So the storage cost is approximately **1.28% per annum**.
Author: Manit Arora
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Question 188.2.
The spot price of gold is $1,800/oz and the one-year forward price is $1,860/oz. The (nominal one year) risk free rate is 2.0% per annum with continuous compounding. An investor evaluates two options: either buy, store and hold physical gold (without lending the stored gold) or hold gold synthetically by taking a long position in gold futures. The investor determines she is exactly indifferent to hold physical or synthetic gold. What must be the storage cost of gold per annum?
A
Negative storage cost
B
0.72%
C
1.28%
D
1.64%
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