Answer: 0.3%

## Explanation M² (Modigliani-Modigliani) alpha measures the risk-adjusted performance of a portfolio relative to the market. The formula for M² alpha is: \[ M^2 \text{ alpha} = (R_p - R_f) \times \frac{\sigma_m}{\sigma_p} - (R_m - R_f) \] Where: - \(R_p\) = Portfolio return = 11% = 0.11 - \(R_f\) = Risk-free rate = 4% = 0.04 - \(R_m\) = Market return = 10% = 0.10 - \(\sigma_p\) = Portfolio standard deviation = 18% = 0.18 - \(\sigma_m\) = Market standard deviation = 20% = 0.20 **Step 1: Calculate the Sharpe ratio adjustment factor** \[ \frac{\sigma_m}{\sigma_p} = \frac{0.20}{0.18} = 1.1111 \] **Step 2: Calculate the adjusted portfolio excess return** \[ (R_p - R_f) \times \frac{\sigma_m}{\sigma_p} = (0.11 - 0.04) \times 1.1111 = 0.07 \times 1.1111 = 0.07778 \] **Step 3: Calculate the market excess return** \[ R_m - R_f = 0.10 - 0.04 = 0.06 \] **Step 4: Calculate M² alpha** \[ M^2 \text{ alpha} = 0.07778 - 0.06 = 0.01778 = 1.778\% \] **Step 5: Compare to options** - 1.778% is closest to 1.8% (Option C) Wait, let me recalculate carefully: Actually, the formula is: \[ M^2 = R_f + \left( \frac{R_p - R_f}{\sigma_p} \right) \sigma_m \] \[ M^2 \text{ alpha} = M^2 - R_m \] **Alternative calculation:** 1. Calculate Sharpe ratio of portfolio: \( \frac{0.11 - 0.04}{0.18} = \frac{0.07}{0.18} = 0.3889 \) 2. Calculate M²: \( 0.04 + 0.3889 \times 0.20 = 0.04 + 0.07778 = 0.11778 \) 3. Calculate M² alpha: \( 0.11778 - 0.10 = 0.01778 = 1.778\% \) This confirms that 1.778% is closest to 1.8%. **Therefore, the correct answer is C (1.8%).**

Author: LeetQuiz .