Answer-first summary for fast verification
Answer: $3,309.99
Use CAPM to estimate the index’s expected total return: \[ \mathbb{E}[R] = r_f + \beta (\mathbb{E}[R_m] - r_f) \] \[ \mathbb{E}[R] = 0.03 + 1.80(0.09 - 0.03) = 0.03 + 1.80(0.06) = 0.138 \] So the expected total return is 13.8% per annum. Because the index has a dividend yield of 2.0% per annum, the expected capital appreciation rate is: \[ 0.138 - 0.02 = 0.118 \] For 10 months, \(T = 10/12 \approx 0.833\). Therefore, \[ \mathbb{E}[S(T)] = S_0 e^{0.118T} \] \[ \mathbb{E}[S(0.833)] = 3000\, e^{0.118(0.833)} \approx 3000\, e^{0.0983} \approx 3309.99 \] So the nearest answer is **C**.
Author: Manit Arora
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Q-718.3. The current price of a technology index is 3,000 and its yield, q, is 2.0% per annum with continuous compounding; i.e., about 2.010% per annum with semi-annual compounding. The riskfree rate is 3.0% per annum with continuous compounding. The discount rate for the index can be determined by the capital asset pricing model (CAPM) where its beta is 1.80 and the market's expected return is 9.0%; i.e., the market's expected excess return is 6.0%. Which is nearest to the index’s expected future spot price in 10 months, ?
A
$3,025.10
B
$3,127.64
C
$3,309.99
D
$4,005.05
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