Question

PORTFOLIO BETA

Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio's beta is 1.55. 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 0.82. What would your portfolio's new beta be? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Final answer

New Beta = 1.54

Explanation

It was given that, $7500 was invested in each of the 20 different stocks. It means that investment is made in equal proportion and such proportion (or weight ) = 1/20

Even the new investment is also 7500, so in the new portfolio also, we have equal proportion for each stock.

So we deduct the weighted Beta of the stock sold and add the weighted Beta of the stock purchased to the current portfolio Beta.

New Beta = Old Beta - Weighted Beta of stock sold + Weighted Beta of stock purchased

= 1.55 - ( 1 * 1/20) + ( 0.82 * 1/20)

= 1.55 - 0.05 + 0.041

= 1.541 .................. ( or)............ 1.54