You have a $9,000 portfolio which is invested in stocks A, B, and a risk-free asset. $4,000 is invested in stock A. Stock A has a beta of 1.84 and stock B has a beta of 0.68. How much needs to be invested in stock B if you want a portfolio beta of.95?
A) $0
B) $1,750
C) $3,279
D) $5,000

Question

Quizplus · Accepted Answer

To achieve a portfolio beta of 0.95, you can use the formula for the weighted average of the betas of the individual investments. Let $x$ be the amount invested in stock B. The total amount invested in stocks A and B is $9000 - (9000 - 4000 - x)$, where $9000 - 4000 - x$ is the amount invested in the risk-free asset, which has a beta of 0. The equation to solve is:$$1.84(4000) + 0.68(x) = 0.95(4000 + x)$$Solving for $x$ gives the amount that needs to be invested in stock B to achieve the desired portfolio beta. When you solve the equation, you find that $x = 1750$, meaning $1,750 needs to be invested in stock B.

You Have a $9,000 Portfolio Which Is Invested in Stocks