Suppose you hold a diversified portfolio consisting of a $10,000 investment in each of 12 different common stocks. The portfolio's beta is 1.25. Now suppose you decided to sell one of your stocks that has a beta of 1.00 and to use the proceeds to buy a replacement stock with a beta of 1.34. What would the portfolio's new beta be?
A) 1.15
B) 1.21
C) 1.28
D) 1.34

Question

Quizplus · Accepted Answer

First, we need to calculate the initial beta of the portfolio:
Portfolio Beta = (Weight of Stock 1 x Beta of Stock 1) + (Weight of Stock 2 x Beta of Stock 2) + ... + (Weight of Stock 12 x Beta of Stock 12)

Since we have equal investments in each stock, the weight of each stock is 1/12, so:
Portfolio Beta = (1/12 x 1.00) + (1/12 x 1.00) + ... + (1/12 x 1.00)  (12 terms)
Portfolio Beta = 1.00

Next, we need to calculate the new beta after selling one stock and buying another:
New Portfolio Beta = (Weight of Stock 1 x Beta of Stock 1) + (Weight of Stock 2 x Beta of Stock 2) + ... + (Weight of Stock 11 x Beta of Stock 11) + (Weight of Stock 12 x Beta of Stock 12)

Since we still have equal investments in each stock except for the one we sold and bought a replacement for, the weight is still 1/12 for each stock except for the replacement stock which has a weight of 1/12 as well.
New Portfolio Beta = (1/12 x 1.00) + (1/12 x 1.00) + ... + (1/12 x 1.34)  (11 terms) + (1/12 x 1.34)
New Portfolio Beta = 1.28

Therefore, the portfolio's new beta would be 1.28, so the best choice is C.

Suppose You Hold a Diversified Portfolio Consisting of a $10,000