Financial Risk Manager Part 1
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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:
- Covariance = 0.027
- Variance of the stock = 12%
- Risk-free rate of return = 6%
- Expected market return = 13%
- Actual stock's return = 14.5%
- Beta = 1.1
Determine the correct alpha of UUA's stock and its appropriate interpretation.
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TTanishq
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.
Explanation:
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._
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