Answer-first summary for fast verification
Answer: 2.70%
## 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)
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A risk analyst at an asset management company is assessing the past performance of an internally managed equity fund. The analyst obtains the following information on the market and the fund over the last year:
Based on the information above, what is the Jensen's alpha for the equity fund over the same period?
A
2.40%
B
2.70%
C
3.69%
D
4.15%
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