A stock has a beta of 1.30 and an expected return of 16 percent. The risk-free rate is 5 percent. If a portfolio of the two assets has a beta of 0.85, what is the weight of the stock?
A) 34.62%
B) 48.71%
C) 59.87%
D) 65.38%
E) 54.21%

Question

Quizplus · Accepted Answer

Using the Capital Asset Pricing Model (CAPM):

Expected Return = Risk-free rate + Beta * (Market Return - Risk-free rate)

16% = 5% + 1.30 * (Market Return - 5%)

Market Return = 19.23%

Using the formula for portfolio beta:

Portfolio Beta = (Weight of Stock * Beta of Stock) + (Weight of Risk-Free Asset * Beta of Risk-Free Asset)

0.85 = (Weight of Stock * 1.30) + (1 - Weight of Stock) * 0

0.85 = (Weight of Stock * 1.30)

Weight of Stock = 65.38%

A Stock Has a Beta of 1