Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio's beta is 0.65. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 1.0 for $7,500 and use the proceeds to buy another stock with a beta of 1.50. What would your portfolio's new beta be

0.68

Explanation:

A portfolio consists of an investment of $7,500

The amount of common stock is 20

The portfolio beta is 0.65

Suppose one of the stock in the portfolio is sold with a beta of 1.0 for $7,500

The proceeds realized is then used to purchase another stock with a beta of 1.50

The first step is the to calculate the change in beta

Change in beta = 1.50-1

= 0.5

The next step is to divide the change in beta by the number of common stock

= 0.5/20

= 0.025

Therefore, the new beta can be calculated as follows

= 0.65+0.025

= 0.68

Hence the new portfolio's beta is 0.68