Question

Stock A has a beta of 1.2 and an expected return of 10%. The risk-free asset currently earns 4%. If a portfolio of the two assets has an expected return of 6%, what is the beta of the portfolio? A) 0.3 B) 0.4 C) 0.5 D) 0.6 E) 0.7

Answer 1

Let weight of Stock A = w

therefore, weight of Stock B = 1 - w

Now,

Portfolio Return = Return of Stock A * Weight of Stock A + Return of Stock B * Weight of Stock B

0.06 = (0.10 * w) + (0.04 * (1 - w))

0.06 = 0.10w + 0.04 - 0.04w

0.06 - 0.04 = 0.06w

0.02 = 0.06w

w = 0.33

Stock A's Weight = 33.33%

Stock B's Weight = 66.67%

Now,

Portfolio Beta = Stock A's Beta * Weight + Stock B's Beta * Weight

= 1.2 * 0.3333 + 0 * 0.6667 (Because Risk free Asset Beta = 0)

Portfolio Beta = 0.4

Option B is correct