Suppose Stan holds a portfolio consisting of a $10,000 investment in each of 8 different common stocks. The portfolio's beta is 1.25. Now suppose Stan decided to sell one of his stocks that has a beta of 1.00 and to use the proceeds to buy a replacement stock with a beta of 1.35. What would the portfolio's new beta be?
A) 1.17
B) 1.23
C) 1.29
D) 1.36

Question

Quizplus · Accepted Answer

The portfolio's initial beta is calculated as follows:

Portfolio beta = (weight of stock 1 x beta of stock 1) + (weight of stock 2 x beta of stock 2) + ... + (weight of stock 8 x beta of stock 8)
Portfolio beta = (8/8 x 1.25) = 1.25

After selling a stock with a beta of 1.00, the portfolio's beta will be adjusted based on the new weightings of the remaining stocks and the new stock with a beta of 1.35:

Portfolio beta = (weight of stock 1 x beta of stock 1) + (weight of stock 2 x beta of stock 2) + ... + (weight of stock 7 x beta of stock 7) + (weight of stock 8 x beta of stock 8)
Portfolio beta = (7/8 x 1.25) + (1/8 x 1.35) = 1.29

Therefore, the portfolio's new beta would be 1.29, which is closest to choice letter C (1.29).

Suppose Stan Holds a Portfolio Consisting of a $10,000 Investment