Explanation

The correct answer is B (2.70%).

To calculate Jensen's alpha, we use the relationship between the Treynor performance index (TPI) and Jensen's alpha (α):

$\text{TPI} = \frac{\alpha}{\text{beta}} + (R_m - R_f)$

Where:

• TPI = 8.00% = 0.08
• Beta = 0.65
• R_m = Market return = 5.60% = 0.056
• R_f = Risk-free rate = 1.75% = 0.0175

Substituting the values:

$`$0.08` = \frac{\alpha}{0.65} + (0.056 - 0.0175)$$

$`$0.08` = \frac{\alpha}{0.65} + 0.0385$$

$\frac{\alpha}{0.65} = 0.08 - 0.0385 = 0.0415$

$\alpha = 0.0415 \times 0.65 = 0.026975 \approx 2.70\%$

Why other options are incorrect:

• A (2.40%): This results from simply subtracting market return from TPI (0.08 - 0.056 = 0.024)
• C (3.69%): This results from dividing (TPI - market return) by beta ((0.08 - 0.056)/0.65 = 0.0369)
• D (4.15%): This results from adding risk-free rate to the difference between TPI and market return (0.0175 + 0.024 = 0.0415)