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 1.35.What would the portfolio's new beta be?
A)1.17
B)1.23
C)1.29
D)1.36
E)1.43

Question

Quizplus · Accepted Answer

The initial investment in each stock is $10,000, for a total portfolio value of $80,000 ($10,000 x 8 stocks). The beta of the portfolio is 1.25.

If a stock with a beta of 1.00 is sold, there will be a decrease in the portfolio's beta as this stock has a comparatively lower beta.

The amount received from selling the stock is not given, so let's assume it is also $10,000. If a replacement stock with a beta of 1.35 is bought, the portfolio's beta will increase.

To calculate the new beta, we can use the following formula:

New portfolio beta = (Total value of original portfolio - value of sold stock) x original portfolio beta + value of new stock x beta of new stock) / Total value of new portfolio

Plugging in the values, we get:

New portfolio beta = [(80,000 - 10,000) x 1.25 + 10,000 x 1.35] / 80,000 = 1.29

Therefore, the portfolio's new beta would be C) 1.29.

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