FRM Part II · FRM Exam Part II · Factor Theory
Using a single-factor model, a portfolio manager estimates that Stock Z has a beta of 1.4 to the market factor. The risk-free rate is 3%, and the market factor risk premium is 5%. Stock Z has returned an average of 11% per year. What is Stock Z's alpha under the model?
Alpha is +1.0%. The model-implied expected return is the 3% risk-free rate plus beta of 1.4 times the 5% market premium, which equals 10%. Stock Z actually returned 11%, so the unexplained return, its alpha, is 1.0 percentage point.
- A+1.0%Correct
- B-1.0%
- C+3.0%
- D+8.0%
Explanation
Expected return = 3% + 1.4 x 5% = 10%. Alpha = 11% - 10% = +1.0%. Choosing +8% results from using excess return without subtracting beta times premium, and +3% from omitting the risk-free rate in the expected return.
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