Stock XYZ has a beta of 1.2 and an expected return of 14%; the risk-free asset (T-bills) currentlyearns 4%. If the portfolio of the two assets has a beta of 0.8, what are the portfolio weights?
A) risk-free asset = 67%, stock XYZ = 33%
B) risk-free asset = 33%, stock XYZ = 67%
C) risk-free asset = 3%, stock XYZ = 97%
D) risk-free asset = 50%, stock XYZ = 50%

Question

Quizplus · Accepted Answer

To determine the portfolio weights, we can use the formula:
Beta of portfolio = (Weight of asset A x Beta of asset A) + (Weight of asset B x Beta of asset B)
0.8 = (w x 1.2) + ((1-w) x 0)
0.8 = 1.2w
W = 0.67 or 67% for stock XYZ
The remaining weight for the risk-free asset would be:
1 - 0.67 = 0.33 or 33%
Therefore, choice B is the correct answer.

Stock XYZ Has a Beta of 1