Question

Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio's beta is 2.05. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 1.0 for $7,500 and use the proceeds to buy another stock with a beta of 0.75. What would your portfolio's new beta be? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Answer:

What would your portfolio's new beta be? 2,04

Explanation:

"To calculate the ending Beta by changing one stock it's necessary to find how much weigh the stock we are removing from the portfollio.

7.500 / 150.000 = 0,050 , now we have the participation of the stock in the portfolio, then we weigh the beta of the stock we want to remove by this number, 1,00 (Beta) x 0,050 (weight in the portfolio) = 0,050 (Beta), the number it's the same as the weight because the Beta is 1,00.

Now with this final number we can ponderate the new Beta in the Portfolio, so we multiply the 0,50 (weight) * 0,75 (New Beta) = 0,038 New Beta. We substitute the beta we remove for this one and we get the NEW BETA PORTFOLIO of 2,04. Please see details below:

Portfolio  #   Beta    NEW Beta   Weight  Old Beta   New Beta  

$ 7.500 1  1,00   0,75   0,05   0,05   0,04  

$ 7.500 2  2,05   2,05   0,05   0,10   0,10  

$ 7.500 3  2,05   2,05   0,05   0,10   0,10  

$ 7.500 4  2,05   2,05   0,05   0,10   0,10  

$ 7.500 5  2,05   2,05   0,05   0,10   0,10  

$ 7.500 6  2,05   2,05   0,05   0,10   0,10  

$ 7.500 7  2,05   2,05   0,05   0,10   0,10  

$ 7.500 8  2,05   2,05   0,05   0,10   0,10  

$ 7.500 9  2,05   2,05   0,05   0,10   0,10  

$ 7.500 10  2,05   2,05   0,05   0,10   0,10  

$ 7.500 11  2,05   2,05   0,05   0,10   0,10  

$ 7.500 12  2,05   2,05   0,05   0,10   0,10  

$ 7.500 13  2,05   2,05   0,05   0,10   0,10  

$ 7.500 14  2,05   2,05   0,05   0,10   0,10  

$ 7.500 15  2,05   2,05   0,05   0,10   0,10  

$ 7.500 16  2,05   2,05   0,05   0,10   0,10  

$ 7.500 17  2,05   2,05   0,05   0,10   0,10  

$ 7.500 18  2,05   2,05   0,05   0,10   0,10  

$ 7.500 19  2,05   2,05   0,05   0,10   0,10  

$ 7.500 20  3,10   3,10   0,05   0,15   0,15  

$ 150.000               1,000   2,05   2,04