The risk-free rate is 3.1 percent and the expected return on the market is 11 percent. Stock A has a beta of 1.34. For a given year, Stock A returned 16.7 percent while the market returned 12.2 percent. The systematic portion of Stock A's unexpected return was _____ percent and the unsystematic portion was _____ percent.
A) 1.41; 1.61
B) 1.61; 1.41
C) 1.61; 3.01
D) 1.41; 1.20
E) 4.62; 1.41

Question

Quizplus · Accepted Answer

First, we need to calculate the expected return of Stock A using the CAPM:
Expected Return = Risk-free rate + Beta*(Expected market return - Risk-free rate)
Expected Return = 3.1% + 1.34*(11% - 3.1%)
Expected Return = 12.892%

Next, we can calculate the unexpected return of Stock A:
Unexpected Return = Actual Return - Expected Return
Unexpected Return = 16.7% - 12.892%
Unexpected Return = 3.808%

To find the systematic portion of the unexpected return, we use:
Systematic Portion = Beta * (Actual market return - Expected market return)
Systematic Portion = 1.34 * (12.2% - 11%)
Systematic Portion = 1.61%

Finally, we can calculate the unsystematic portion:
Unsystematic Portion = Unexpected Return - Systematic Portion
Unsystematic Portion = 3.808% - 1.61%
Unsystematic Portion = 2.198%

Therefore, the answer is B) 1.61; 1.41.

The Risk-Free Rate Is 3