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Answer: The alpha of UUA is 0.8% and the stock has outperformed the market.
## Explanation To calculate Jensen's alpha (α), we use the formula: **α = Actual Return - Expected Return (CAPM)** Where the CAPM expected return is: **E(R) = R_f + β × (E(R_m) - R_f)** Given: - Actual stock return = 14.5% = 0.145 - Risk-free rate (R_f) = 6% = 0.06 - Expected market return (E(R_m)) = 13% = 0.13 - Beta (β) = 1.1 **Step 1: Calculate CAPM expected return** E(R) = 0.06 + 1.1 × (0.13 - 0.06) E(R) = 0.06 + 1.1 × 0.07 E(R) = 0.06 + 0.077 E(R) = 0.137 or 13.7% **Step 2: Calculate alpha** α = 0.145 - 0.137 α = 0.008 or 0.8% **Interpretation:** A positive alpha of 0.8% indicates that the stock has **outperformed** the market by 0.8% after adjusting for its systematic risk (beta). The stock generated higher returns than what would be expected given its risk level according to CAPM. **Note:** The covariance (0.027) and variance (12%) data are not needed for this calculation since beta is already provided. These would be used if we needed to calculate beta from first principles.
Author: Tanishq Prabhu
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Ross Linn is analyzing the performance of different stocks of a portfolio using the alpha measure of performance. Linn has compiled the following data regarding UUA:
Determine the correct alpha of UUA's stock and its appropriate interpretation.
A
The alpha of UUA is 0.8% and the stock has underperformed the market.
B
The alpha of UUA is 0.8% and the stock has outperformed the market.
C
The alpha of UUA is -4.625% and the stock has underperformed the market.
D
The alpha of UUA is -4.625% and the stock has outperformed the market.