Question

You hold a diversified portfolio consisting of many different common stocks with a total market value of $100,000. The portfolio beta is equal to 1.15. You have decided to sell one of your stocks, a lead mining stock whose beta is equal to 0.5 , for $10,000 net and to use the proceeds to buy $10,000 of stock in a steel company whose beta is equal to 1.3 . What will be the new beta of the portfolio? (Round to two digit decimal places, e.g., 1.15)

Answer 1

Old Portfolio Beta = 1.15
Value of Portfolio = $100,000
Value of Stock sold = $10,000
Beta of Stock sold = 0.50
Value of Stock purchased = $10,000
Beta of Stock purchased = 1.3

Weight of Stock sold = $10,000 / $100,000
Weight of Stock sold = 0.10

Weight of Stock purchased = $10,000 / $100,000
Weight of Stock purchased = 0.10

New Portfolio Beta = Old Portfolio Beta - Weight of Stock sold * Beta of Stock sold + Weight of Stock purchased * Beta of Stock purchased
New Portfolio Beta = 1.15 - 0.10 * 0.50 + 0.10 * 1.30
New Portfolio Beta = 1.23

So, beta of new portfolio is 1.23