Suppose you hold a portfolio consisting of a $10,000 investment in each of 8 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 1.05.What would the portfolio's new beta be? Do not round your intermediate calculations.
A) 1.11
B) 1.26
C) 1.14
D) 1.24
E) 1.41

Question

Quizplus · Accepted Answer

The original portfolio beta is 1.25, calculated as the weighted average of the betas of the individual stocks. When you sell a stock with a beta of 1.00 and buy a stock with a beta of 1.05, the overall portfolio beta increases slightly. The calculation involves removing the impact of the stock with a beta of 1.00 and adding the impact of the stock with a beta of 1.05. The change in beta for the portfolio due to this transaction is (1.05 - 1.00) / 8 = 0.00625. Adding this to the original portfolio beta of 1.25 gives a new beta of 1.25625, which rounds to 1.26.

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