Question

You are managing a portfolio of 10 stocks which are held in equal amounts. The current beta of the portfolio is 1.64, and the beta of Stock A is 2.0. If Stock A is sold, what would the beta of the replacement stock have to be to produce a new portfolio beta of 1.55?"

Group of answer choices

1.1

1

0.9

0.75

0.5

Answer 1

Stock B = Other stocks

Portfolio Beta = Stock A's Beta * 0.1 + Stock B's Beta * 0.9

1.64 = 2 * 0.1 + Stock B's Beta * 0.9

1.64 = 0.2 + Stock B's Beta * 0.9

1.64 - 0.2 = Stock B's Beta * 0.9

Stock B's Beta = 1.44 / 0.9

Stock B's Beta = 1.6

Now,

Stock A is replaced with another Stock. Let say Stock C. So,

Portfolio Beta = Stock B's Beta * 0.9 + Stock C's Beta * 0.1

1.55 = 1.6 * 0.9 + Stock C's Beta * 0.10

1.55 = 1.44 + Stock C's Beta * 0.1

1.55 - 1.44 = Stock C's Beta * 0.1

Stock C's Beta = 0.11 / 0.1

Stock C's Beta = 1.1

Therefore, Beta of replacement Stock is 1.1

Option A is correct