A portfolio consists of one risky asset and one risk-free asset. The risky asset has an expected return of 13.2 percent and a beta of 1.43. The risk-free asset has an expected return of 3.8 percent. How much of the portfolio is invested in the risk-free asset if the portfolio beta is 1.06?
A) 26 percent
B) 34 percent
C) 42 percent
D) 65 percent
E) 74 percent

Question

Quizplus · Accepted Answer

The portfolio beta is a weighted average of the betas of the assets. Let x be the proportion invested in the risky asset. Then, 1.43x + 0(1-x) = 1.06. Solving for x gives x = 1.06 / 1.43 = 0.7413. Therefore, the proportion invested in the risk-free asset is 1 - 0.7413 = 0.2587, or approximately 26 percent.

A Portfolio Consists of One Risky Asset and One Risk-Free