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Answer: 0.85
## Explanation Using the Capital Asset Pricing Model (CAPM) formula: \[E(R_i) = R_f + \beta_i[E(R_M) - R_f]\] Where: - \(E(R_i)\) = Expected return of the fund = 7.1% - \(R_f\) = Risk-free rate = 3.2% - \(E(R_M)\) = Expected return of the market (Russell 2000 Index) = 7.8% - \(\beta_i\) = Beta of the fund (what we're solving for) Rearranging the formula to solve for beta: \[\beta_i = \frac{E(R_i) - R_f}{E(R_M) - R_f}\] \[\beta_i = \frac{7.1\% - 3.2\%}{7.8\% - 3.2\%} = \frac{3.9\%}{4.6\%} = 0.8478 \approx 0.85\] **Key Points:** - The volatility information (7.9% for the fund and 9.8% for the index) is not needed for this calculation since we're using CAPM - Beta represents the fund's sensitivity to market movements - A beta of 0.85 means the fund is less volatile than the market (defensive)
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An endowment fund manager is estimating the market risk of Alpha Industrial Fund. The fund has an expected annual return of 7.1% and volatility of 7.9% and is benchmarked against the Russell 2000 Index. The manager assumes that the expected annual return of the Russell 2000 Index is 7.8% with an annual volatility of 9.8%. According to the CAPM, if the risk-free rate is 3.2% per year, what is the beta of Alpha Industrial Fund?
A
0.85
B
0.95
C
1.13
D
1.23
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