Suppose you hold a diversified portfolio consisting of a $10,000 investment in each of 12 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 use the proceeds to buy a replacement stock with a beta of 1.34. What would the portfolio's new beta be?
A) 1.15
B) 1.21
C) 1.28
D) 1.34

Question

Quizplus · Accepted Answer

The first step is to calculate the current total value of the portfolio:

Total investment = $10,000 x 12 = $120,000

Next, we need to determine the current beta of the portfolio:

Beta = 1.25

If we sell one of the stocks with a beta of 1.00, we need to subtract the beta of that stock from the portfolio's total beta:

New portfolio beta = (Total investment - Amount sold x Beta of stock sold) / Total investment

New portfolio beta = ($120,000 - $10,000 x 1.00) / $120,000

New portfolio beta = 1.17

Then, we need to add the beta of the replacement stock:

New portfolio beta = (Total investment - Amount sold x Beta of stock sold + Amount bought x Beta of stock bought) / Total investment

New portfolio beta = ($120,000 - $10,000 x 1.00 + $10,000 x 1.34) / $120,000

New portfolio beta = 1.28

Therefore, the answer is C) 1.28.

Suppose You Hold a Diversified Portfolio Consisting of a $10,000