Answer to Question #115165 in Financial Math for katia

Question

Suppose you held a diversified portfolio consisting of 10 different common stocks, investing $500 in each stock. The portfolio’s beta is 1.9. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 0.8 for $500 and use the proceeds to buy another stock with a beta of 1.25. What would your portfolio’s new beta be?

Answer 1

The beta of a portfolio is defined as the sum of the beta of its constituent stocks multipled by the weight of each stock.

B-beta

1.9=0.1*sumB₁

sumB₁=1.9*10=19

sumB₂=19-0.8+1.25=19.45

newB=sumB*0.1=19.45*0.1=1.945