Bruce Niendorf holds the following portfolio: Bruce plans to sell Stock A and replace it with Stock E, which has a beta of 0.75. By how much will the portfolio beta change?
A) -0.190
B) -0.211
C) -0.234
D) -0.260
E) -0.286

Question

Bruce Niendorf holds the following portfolio:  Bruce plans to sell Stock A and replace it with Stock E, which has a beta of 0.75. By how much will the portfolio beta change?
A) -0.190 
B) -0.211 
C) -0.234 
D) -0.260 
E) -0.286

Quizplus · Accepted Answer

To calculate the change in the portfolio beta, we need to use the following formula:

Change in Beta = Weight of Old Stock * Beta of Old Stock - Weight of Old Stock * Beta of New Stock

First, we need to determine the weight of Stock A in the portfolio:

Weight of Stock A = Value of Stock A / Total Portfolio Value = $45,000 / $300,000 = 0.15

Next, we can use the given betas to calculate the change in beta:

Change in Beta = 0.15 * 1.20 - 0.15 * 0.75 = 0.18 - 0.1125 = -0.0675

Therefore, the portfolio beta will decrease by 0.0675, or 0.260 rounded to three decimal places (D).

Bruce Niendorf Holds the Following Portfolio: Bruce Plans to Sell