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Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio’s beta is 1.12. Now suppose you decide to sell one of the stocks in your portfolio with a beta of 1.0 for $7,500 and to use these proceeds to buy another stock with a beta of 1.75. What would your portfolio’s new beta be?
Expert Answer
You have the Portfolio of $7,500 investment in each of 20different common stocks.
Current Portfolio beta = 1.12
You decide to sell one of the stocks in your portfolio with abeta of 1.0 for $7,500
Buy new stock with a beta of 1.75
Selling stock’s beta = 1.0
Current Portfolio beta = 1.12
1.12 = (1/20) (1.0) + (19/20)B
1.12 = 0.05 (1.0) + (19/20)B
1.12-0.05 = (19/20)B
1.07 = (19/20)B
New Stock’s Beta = 1.75
Total New Beta of the Current Stock = 1.07 + (1/20)(1.75)
= 1.07 + 0.0875
= 1.1575
Current Portfolio’s New Beta = 1.1575
