Answer-first summary for fast verification
Answer: 0.87
## Explanation Jensen's alpha is calculated using the formula: \[ \alpha = R_p - [R_f + \beta (R_m - R_f)] \] Where: - \( \alpha \) = Jensen's alpha = 4.75% = 0.0475 - \( R_p \) = Portfolio return = 14.2% = 0.142 - \( R_f \) = Risk-free rate = 4.25% = 0.0425 - \( R_m - R_f \) = Market risk premium = 6% = 0.06 Rearranging the formula to solve for beta: \[ \beta = \frac{R_p - R_f - \alpha}{R_m - R_f} \] Substituting the values: \[ \beta = \frac{0.142 - 0.0425 - 0.0475}{0.06} \] \[ \beta = \frac{0.052}{0.06} \] \[ \beta = 0.8667 \] The beta of 0.8667 is closest to **0.87**, which corresponds to option B.
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You are analyzing a portfolio that has a Jensen's alpha of 4.75% and an actual return of 14.2%. The risk-free rate is 4.25% and the market risk premium is 6%. Based on the information provided, the beta of the portfolio is closest to:
A
0.77
B
0.87
C
0.97
D
1.07
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