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Answer: 12.2%
The expected return of the new fund using the Capital Asset Pricing Model (CAPM) can be calculated with the formula: \[ R_i = R_f + \beta_i * (R_m - R_f) \] Where: - \( R_i \) is the expected return on the fund. - \( R_f \) is the risk-free rate. - \( \beta_i \) is the beta of the fund, which measures the fund's volatility in relation to the market index. - \( R_m \) is the expected return on the market index. Given: - The risk-free rate \( R_f \) is 3.0% per year. - The expected annual return of the Shanghai Composite Stock Market Index (SHANGHAI), \( R_m \), is 7.6%. - The new fund has twice the volatility of the index, so its beta \( \beta_i \) is calculated as: \[ \beta_i = \frac{\text{Volatility of the fund}}{\text{Volatility of the index}} = \frac{2 \times \text{Volatility of the index}}{\text{Volatility of the index}} = 2 \] Plugging the values into the CAPM formula: \[ R_i = 0.03 + 2.0 \times (0.076 - 0.03) \] \[ R_i = 0.03 + 2.0 \times 0.046 \] \[ R_i = 0.03 + 0.092 \] \[ R_i = 0.122 \] \[ R_i = 12.2\% \] Therefore, the expected return of the fund is 12.2%, which corresponds to option A.
Author: LeetQuiz Editorial Team
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A financial consultant is evaluating the potential expected returns of a new investment vehicle designed to replicate the market trends of the China Shanghai Composite Stock Market Index (SHANGHAI) but with twice the index's volatility. For context, the SHANGHAI has an estimated annual return of 7.6% and an annual volatility of 14.0%. Additionally, the annual risk-free rate is currently 3.0%. Given that the correlation between the investment's returns and the SHANGHAI index's performance is 1.0, calculate the expected return of the investment using the Capital Asset Pricing Model (CAPM).
A
12.2%
B
19.0%
C
22.1%
D
24.6%
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