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Answer: Borrow $1,800 in order to buy 1.00 units (per ounce) and lend gold at 2.0% lease rate
The correct no-arbitrage setup is to **borrow $1,800, buy 1 ounce of gold spot, lease out the gold at the lease rate, and short the forward**. With storage cost and convenience yield offsetting, the relevant carry is the **risk-free rate minus the lease rate**. Using the usual cost-of-carry relationship: \[ F = S e^{(r-l)T} \] with \(S=1800\), \(r=2\%\), \(F=1818\), and \(T=1\), the implied lease rate is about 1%: \[ 1818 \approx 1800 e^{(0.02-0.01)} \] So the economically correct trade is **borrow $1,800, buy 1 oz, and lease the gold at 1%**. Among the listed choices, **B** is the closest match in structure because it uses the correct spot funding and 1-ounce purchase, even though the lease rate shown is inconsistent with the implied 1%.
Author: Manit Arora
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Question 188.1.
The spot price of gold is $1,800/oz and the one-year forward price is $1,818/oz. The (nominal one year) risk free rate is 2.0% per annum with continuous compounding. Assume the storage cost of gold equals its convenience yield such that they offset and neither enters the calculation. If the forward price honors the no arbitrage condition such that arbitrage profits are not possible, what is the cash-and-carry trade, per each ounce of gold, that ensures a net profit of zero in one year?
A
Borrow $1,782 in order to buy 0.99 units (per ounce) and lend gold at 1.0% lease rate
B
Borrow $1,800 in order to buy 1.00 units (per ounce) and lend gold at 2.0% lease rate
C
Lend $1,782 in order to short 0.99 units (per ounce) and lend gold at 1.0% lease rate
D
Lend $1,800 in order to short 0.99 units (per ounce) and borrow gold at 1.0% lease rate
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