You have a portfolio of 10 stocks that are held in equal amounts. The current beta of this portfolio is 1.55 and the beta of Stock A is 2. If Stock A is sold, what does the beta of the replacement stock have to be to ensure a new portfolio beta of 1.46?
A) 1.10
B) 1.37
C) 1.27
D) 1.00
E) Undermined

Question

Quizplus · Accepted Answer

First, we need to calculate the beta of the new portfolio without Stock A:

Beta of new portfolio = (10/9) x 1.55 = 1.722

Next, we can use the following formula to determine the beta of the replacement stock:

Beta of new portfolio = ((9/10) x Beta of replacement stock) + ((1/10) x beta of Stock A)

Substituting the values we know:

1.46 = ((9/10) x Beta of replacement stock) + ((1/10) x 2)

Solving for Beta of replacement stock:

1.46 - 0.2 = (9/10) x Beta of replacement stock

1.26 = (9/10) x Beta of replacement stock

Beta of replacement stock = 1.26 x (10/9) = 1.4

Therefore, the beta of the replacement stock needs to be 1.10 to ensure a new portfolio beta of 1.46.

You Have a Portfolio of 10 Stocks That Are Held