Question

Portfolio Beta

You have a $2 million portfolio consisting of a $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.2. You are considering selling $100,000 worth of one stock with a beta of 1.1 and using the proceeds to purchase another stock with a beta of 1.4. What will the portfolio's new beta be after these transactions? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Solution :

As per the information given in the question we have

Beta of the portfolio = 1.2

Value of the portfolio = $ 2 million = $ 2,000,000   ;

The portfolio has $ 100,000 investment in each of 20 different stocks.

Thus the weight of each stock investment = $ 100,000 / $ 2,000,000 = 0.05

A stock worth $ 100,000 with a beta of 1.1 is sold and the proceeds are used to purchase another stock with a beta of 1.4.

We know that the weighted of each stock is = 0.05

Thus the weight of the stock sold = weight of stock purchased = 0.05

Thus the portfolio’s new beta = Old Portfolio beta – weighted beta of the stock sold + weighted beta of the stock purchased

= 1.2 – ( weight of the stock sold * beta of the stock sold) + ( weight of the stock purchased * beta of the stock purchased )

= 1.2 – ( 0.05 * 1.1 ) + ( 0.05 * 1.4 )

= 1.2 – 0.055 + 0.070

= 1.215

= 1.22 ( when rounded off to two decimal places )

Thus the portfolio’s new beta = 1.22