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 .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 .58?
A)$6,000
B)$9,000
C)$12,000
D)$15,000
E)$18,000

Question

Quizplus · Accepted Answer

The portfolio beta is a weighted average of the betas of its components. With half the portfolio in a risk-free security (beta = 0), the remaining $18,000 is split between Stock A and Stock B. Let x be the amount in Stock A, then (18,000 - x) is in Stock B. The equation is: 0.5*0 + (x/36,000)*1.29 + ((18,000-x)/36,000)*0.90 = 0.58. Solving for x gives $12,000.

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