Suppose you hold a portfolio consisting of a $50,000 investment in each of 8 different common stocks. The portfolio’s beta is 1.25. Now suppose you decided to sell one of your stocks that has a beta of 1.00 and to use the proceeds to buy a replacement stock with a beta of 1.55. What would the portfolio’s new beta be? 1.17 1.23 1.29 1.32 1.43
Answered on
To find the new beta of the portfolio after selling one stock and buying another, you can use the formula for the weighted average of betas:
New Portfolio Beta =
Old Total Beta - Beta of Sold Stock + Beta of New Stock
Number of Stocks
Given:
Initial number of stocks in the portfolio = 8
Old total beta of the portfolio = 8 × 1.25 = 10
Beta of the stock being sold = 1.00
Beta of the new stock bought = 1.55
Calculate the new portfolio beta:
New Portfolio Beta = 10 - 1.00 + 1.55 / 8
New Portfolio Beta = 10 + 0.55 / 8
New Portfolio Beta = 10.55 / 8
New Portfolio Beta = 1.31875
Rounded to two decimal places, the new portfolio beta would be approximately 1.32.
Answered on
To find the new beta of the portfolio after selling one stock and buying another, you can use the formula for the weighted average of betas:
New Portfolio Beta =
Old Total Beta - Beta of Sold Stock + Beta of New Stock
Number of Stocks
Given:
Initial number of stocks in the portfolio = 8
Old total beta of the portfolio = 8 × 1.25 = 10
Beta of the stock being sold = 1.00
Beta of the new stock bought = 1.55
Calculate the new portfolio beta:
New Portfolio Beta = 10 - 1.00 + 1.55 / 8
New Portfolio Beta = 10 + 0.55 / 8
New Portfolio Beta = 10.55 / 8
New Portfolio Beta = 1.31875
Rounded to two decimal places, the new portfolio beta would be approximately 1.32.