Question

Your portfolio has a beta of 1.17. The portfolio consists of 14 percent U.S. Treasury bills, 31 percent in stock A, and 55 percent in stock B. Stock A has a risk-level equivalent to that of the overall market. What is the beta of stock B?

Answer 1

Portfolio beta= (Proportion of stock A * Beta of stock A) + (Proportion of stock B * Beta of stock B) + (Proportion of T-Bills * Beta of T-Bills)
Proportion of stock A=31%
Proportion of stock B=55%
Proportion of stock T-Bills=14%
Given that, the risk level of stock A is equivalent to that of the overall market, so beta of stock A will be equal to 1.
Beta of T-bills=0
Beta of stock B=?
Portfolio beta=1.17
Portfolio beta=31%*1+55%*Beta of stock B + 14%*0
=>1.17=0.31+55%*Beta of stock B + 0
=>1.17-0.31=55%*Beta of stock B
=>0.86=55%*Beta of stock B
=>Beta of stock B=0.86/55%=1.563636364 or 1.56 (Rounded to two decimal places)