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%).