
Answer-first summary for fast verification
Answer: 13.2%
**Explanation:** The correct answer is **B (13.2%)**. 1. **Calculate the beta (β) of the security:** The beta is calculated using the formula: \[ \beta = \frac{\rho_{i,m} \times \sigma_i}{\sigma_m} \] Where: - \(\rho_{i,m}\) is the correlation between the security and the market (0.8). - \(\sigma_i\) is the standard deviation of the security (35%). - \(\sigma_m\) is the standard deviation of the market portfolio (20%). Substituting the values: \[ \beta = \frac{0.8 \times 35\%}{20\%} = 1.4 \] 2. **Calculate the expected return using CAPM:** The CAPM formula is: \[ E(R_i) = R_f + \beta \times [E(R_m) - R_f] \] Where: - \(R_f\) is the risk-free rate (2%). - \(E(R_m)\) is the expected return of the market (10%). Substituting the values: \[ E(R_i) = 2\% + 1.4 \times (10\% - 2\%) = 2\% + 1.4 \times 8\% = 2\% + 11.2\% = 13.2\% \] **Why not A or C?** - **Option A (5.7%)** is incorrect because it miscalculates the beta by reversing the standard deviations of the security and the market portfolio. - **Option C (16.0%)** is incorrect because it excludes the risk-free rate from the calculation of the market risk premium.
Author: LeetQuiz Editorial Team
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An analyst gathers the following information:
According to the Capital Asset Pricing Model (CAPM), the expected return of the security is closest to:
A
5.7%
B
13.2%
C
16.0%
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