Question

Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio's beta is 0.75. 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 1.90. What would your portfolio's new beta be?

Answer 1

Note for each share the investment is same

Given portfolio's initial beta = 0.75

So initial summation of beta of all 20 stocks (given investment amount is same for each stock is) 0.75 * 20 = 15

Now when a stock with beta 1 is sold and another with beta 1.90 is bought then the summation of portfolio beta of all stocks will be = 15 - 1+1.90 = 15.90

Thus portfolio's new beta will be = 15.90 / 20 =0.795