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Answer: 18.5%
## Explanation Using the Capital Asset Pricing Model (CAPM): **Given:** - Market return (Sensex) = 12.3% - Risk-free rate = 2.5% - Market volatility = 19.0% - Fund volatility = 2 × Market volatility = 38.0% - Correlation between fund and market = 1 **Step 1: Calculate the fund's beta (β)** Beta formula: β = (Correlation × Fund volatility) / Market volatility β = (1 × 38.0%) / 19.0% = 2.0 **Step 2: Apply CAPM formula** CAPM: Expected return = Risk-free rate + β × (Market return - Risk-free rate) Expected return = 2.5% + 2.0 × (12.3% - 2.5%) Expected return = 2.5% + 2.0 × 9.8% Expected return = 2.5% + 19.6% Expected return = 22.1% Wait, this gives 22.1%, but the provided answer is 18.5%. Let me recalculate: Actually, when correlation is 1 and volatility is twice the market, the beta should be exactly 2.0. Let me verify: β = (ρ × σ_fund) / σ_market = (1 × 38%) / 19% = 2.0 Then: E(R) = Rf + β × (Rm - Rf) = 2.5% + 2.0 × (12.3% - 2.5%) = 2.5% + 2.0 × 9.8% = 2.5% + 19.6% = 22.1% However, the provided answer is 18.5%. This suggests there might be an error in the question or answer key. Given the parameters and CAPM formula, the correct expected return should be 22.1%, not 18.5%.
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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 BSE Sensex Index but with twice the volatility of the index. The Sensex has an expected annual return of 12.3% and volatility of 19.0%, and the risk-free rate is 2.5% per year. Assuming the correlation between the fund's returns and that of the index is 1, what is the expected return of the fund using the capital asset pricing model?
A
18.5%
B
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