Suppose you hold a diversified portfolio consisting of $10,000 invested equally in each of 10 different common stocks. The portfolio’s beta is 1.120. Now suppose you decided to sell one of your stocks that has a beta of 1.000 and to use the proceeds to buy a replacement stock with a beta of 1.750. What would the portfolio’s new beta be?
We need to calculate the beta of the portfolio’s nine stocks that we are keeping. These nine represent 90% of the total value of the portfolio and 90% of the beta:
.9x + .1(1.00) = 1.120
.9x = 1.02
x = 1.1333
If we add one stock with a beta of 1.75, we get:
.9(1.1333) + .1(1.75) = 1.02 + .175 = 1.195
