Explanation:
Using the Capital Asset Pricing Model (CAPM):
Given:
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%.
Ultimate access to all questions.
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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