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 0.6, for $10,000 net and to use the proceeds to buy $10,000 of stock in a steel company whose beta is equal to 1.5. What will be the new beta of the portfolio? (Round to two digit decimal places, e.g., 1.15)

Answer 1

Solution:

Portfolio beta = 1.15

Total market value = $1,00,000

Weight of sold stock = 10000/100000= 0.1

Weight of purchased stock = 10000/100000= 0.1

Beta of sold stock = 0.6

Beta of purchase stock = 1.5

New beta of the portfolio = 1.15 - ( 0.6*0.1) + ( 1.5*0.1)

New beta of the portfolio = 1.15-0.06 + 0.15= 1.24