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Answer: 12.2%
## Explanation Using the Capital Asset Pricing Model (CAPM): $$ R_i = R_f + \beta_i \times (R_m - R_f) $$ Where: - $R_i$ = expected return on the fund - $R_f$ = risk-free rate = 3.0% = 0.03 - $R_m$ = expected return on the index = 7.6% = 0.076 - $\beta_i$ = beta of the fund ### Calculating Beta ($\beta_i$) The beta formula is: $$ \beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^2} = \frac{\text{Corr}(R_i, R_m) \times \sigma_i \times \sigma_m}{\sigma_m^2} = \frac{\text{Corr}(R_i, R_m) \times \sigma_i}{\sigma_m} $$ Given: - Correlation $\text{Corr}(R_i, R_m)$ = 1.0 - Fund volatility $\sigma_i$ = 2 × index volatility = 2 × 14.0% = 28.0% - Index volatility $\sigma_m$ = 14.0% $$ \beta_i = \frac{1.0 \times 2 \times \sigma_m}{\sigma_m} = 1.0 \times 2.0 = 2.0 $$ ### Calculating Expected Return $$ R_i = 0.03 + 2.0 \times (0.076 - 0.03) $$ $$ R_i = 0.03 + 2.0 \times 0.046 $$ $$ R_i = 0.03 + 0.092 $$ $$ R_i = 0.122 = 12.2\% $$ Therefore, the expected return of the fund using CAPM is **12.2%**.
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An investment advisor is analyzing the range of potential expected returns of a new fund designed to replicate the directional moves of the China Shanghai Composite Stock Market Index (SHANGHAI) but with twice the volatility of the index. SHANGHAI has an expected annual return of 7.6% and a volatility of 14.0%, and the risk-free rate is 3.0% per year. Assuming the correlation between the fund's returns and that of the index is 1.0, what is the expected return of the fund using the CAPM?
A
12.2%
B
19.0%
C
22.1%
D
24.6%