Answer: 12.2%

The expected return of the new fund designed to replicate the directional moves of the China Shanghai Composite Stock Market Index (SHANGHAI) with twice the volatility can be calculated using the Capital Asset Pricing Model (CAPM). The CAPM formula is given by: \[ R_i = R_f + \beta_i \times (R_m - R_f) \] 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 its volatility relative to the market. - \( R_m \) is the expected return on the market index. Given: - \( R_f = 3.0\% \) (risk-free rate) - \( R_m = 7.6\% \) (expected annual return of SHANGHAI) - The fund has twice the volatility of the index, so \( \sigma_i = 2 \times \sigma_m = 2 \times 14.0\% = 28.0\% \) - The correlation between the fund's returns and the index is 1.0, which implies a perfect positive relationship. The beta (\( \beta_i \)) can be calculated using the formula: \[ \beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^2} = \frac{\text{Corr}(R_i, R_m) \times \sigma_i}{\sigma_m} \] Since the correlation is 1.0 and the fund has twice the volatility of the index: \[ \beta_i = \frac{1.0 \times 28.0\%}{14.0\%} = 2 \] Now, applying the CAPM formula: \[ R_i = 0.03 + 2 \times (0.076 - 0.03) = 0.03 + 2 \times 0.046 = 0.03 + 0.092 = 0.122 \text{ or } 12.2\% \] Thus, the expected return of the fund using the CAPM is 12.2%, which corresponds to option A.

Author: LeetQuiz Editorial Team