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Answer: $E[S(1.0)] = 1,367$ and $F(0, 1.0) = 1,326$
Using CAPM with \(\beta=1\): - Expected return on the index = risk-free rate + ERP = \(4\% + 3\% = 7\%\) - Dividend yield = \(2\%\) So the expected spot price in one year is \[ E[S(1)] = 1300 \times e^{(0.07-0.02)\times 1} = 1300e^{0.05} \approx 1366.7 \approx 1367 \] The one-year forward price uses the cost-of-carry model: \[ F(0,1) = 1300 \times e^{(0.04-0.02)\times 1} = 1300e^{0.02} \approx 1326.3 \approx 1326 \] Therefore, the correct answer is **A**.
Author: Manit Arora
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Question-167.1. Assume the current (spot) price of the S&P 500 Index is 1,300 and the dividend yield is 2.0% per annum. The overall market return is 7.0% and the risk-free rate is 4.0% per annum; i.e., the market risk premium (a.k.a., equity risk premium, ERP) is 3.0%. Assume all yields/rates are continuously compounded and that we can use the capital asset pricing model (CAPM) where the index has a beta of 1.0 to predict the expected return of the index. What are, respectively, the expected future spot price in one year, , and the one-year forward price, ?
A
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B
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