You hold a diversified portfolio consisting of a R5,000 investment in each of 20 different ordinary shares.The portfolio beta is equal to 1.15.You have decided to sell one of your shares, a lead mining share whose ($\beta$). = 1.0, for R5,000 net and to use the proceeds to buy R5,000 of shares in a steel company whose ($\beta$). = 2.0.What will be the new beta of the portfolio?

Question

Quizplus · Accepted Answer

The beta of the lead mining share being sold is 1.0. The beta of the steel company being purchased is 2.0. 
The formula for calculating the new portfolio beta is:
[(current total value of shares in the portfolio) x (current portfolio beta) - (value of shares being sold x beta of shares being sold) + (value of shares being purchased x beta of shares being purchased)] / (current total value of shares in the portfolio)
Plugging in the values:
[(20 x R5,000) x 1.15 - (R5,000 x 1.0) + (R5,000 x 2.0)] / (20 x R5,000) = 1.20
Therefore, the new beta of the portfolio will be 1.20.

You Hold a Diversified Portfolio Consisting of a R5,000 Investment β\betaβ

You Hold a Diversified Portfolio Consisting of a R5,000 Investment $\beta$