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Answer: $1,569$
First compute gold’s beta using \[ \beta = \rho \frac{\sigma_{gold}}{\sigma_{mkt}} = 0.80 \times \frac{0.30}{0.20} = 1.2 \] Then apply CAPM to infer gold’s expected return: \[ k = r_f + \beta(E[R_m]-r_f) = 3\% + 1.2(8\%-3\%) = 3\% + 6\% = 9\% \] With no lease rate, the expected future spot price in 6 months is: \[ E[S(0.5)] = 1500 \times e^{0.09\times 0.5} = 1500e^{0.045} \approx 1568.9 \approx 1569 \] So the correct answer is **C**.
Author: Manit Arora
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Question-167.2. The spot price of gold, , is $1,500 per ounce. The market return is 8.0% and the riskfree rate is 3.0% per annum with continuous compounding. The volatility of gold returns is 30% and the volatility of market returns is 20%. The correlation (rho) between gold and the market is +0.80. Assuming gold has no lease rate (i.e., no dividend yield or convenience yield), and that we can apply the capital asset pricing model (CAPM) to infer the discount rate () for gold, what is the expected future spot price of gold in six months, ?
A
$1,523$
B
$1,546$
C
$1,569$
D
$1,641$
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