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 1.39. 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 1.10. What would your portfolio's new beta be? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

The portfolio beta is a weighted avrege of the betas of the stocksi n the portfolio.

Weight of the stock that was replaced = 1/20 since the investments in all stocks is equal

Hence 1.39= 1*1/20 + sum of weighted average of the other stocks

1.39 = 0.05+ sum of weighted average of the other stocks

sum of weighted average of the other stocks= 1.39- 0.05 = 1.34

Since the stock with beta of 1 is replaced

New Beta of portfolio = 1.1* 1/20 + sum of weighted average of the other stocks

= 1.1*1/20 + 1.34

= 1.396

rounded off to

1.4