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:
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.
Ultimate access to all questions.
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.
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