A $36,000 portfolio is invested in a risk-free security and two stocks. The beta of stock A is 1.29 while the beta of stock B is 0.90. One-half of the portfolio is invested in the risk-free security. How much is invested in stock A if the beta of the portfolio is 0.58?
A) $6,000
B) $9,000
C) $12,000
D) $15,000
E) $18,000

Question

Quizplus · Accepted Answer

First, we need to use the formula for the beta of a portfolio:
βp = wAβA + wBβB + wFβF
where wA, wB, and wF are the proportions of the portfolio invested in stock A, stock B, and the risk-free security, respectively. We know that wF = 0.5, so we can plug in the other values and solve for wA:
0.58 = wA(1.29) + (1 - wA - 0.5)(0.9)
0.58 = 1.29wA + 0.45 - 0.9wA - 0.45
0.13 = 0.39wA
wA = 0.33
So 33% of the portfolio is invested in stock A, which is $12,000:
$36,000 * 0.33 = $12,000

A $36,000 Portfolio Is Invested in a Risk-Free Security and Two