Question

# Suppose you held a diversified portfolio consisting of a \$7,500 investment in each of 20 different...

Suppose you held a diversified portfolio consisting of a \$7,500 investment in each of 20 different common stocks. The portfolio's beta is 2.12. 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 1.31. What would your portfolio's new beta be? Do not round intermediate calculations. Round your answer to two decimal places.

Beta of 19 stock * Weight of 19 Stocks + Beta of Sold Stock * Weight of Sold Stock = 2.12 (given)

Beta of 19 stock * (7500 * 19 / 7500* 20) + 1 * (7500 *1 / 7500* 20) = 2.12

Beta of 19 stock * 0.95 + 0.05 = 2.12

Beta of 19 stock = 2.12 - 0.05 / 0.95

Beta of 19 stock = 2.17894736842

New Beta of the portfolio = Beta of 19 stock * Weight of 19 Stocks + Beta of new Stock * Weight of new Stock

= 2.17894736842 * (7500 * 19 / 7500* 20) + 1.31 * (7500 *1 / 7500* 20)

= 2.07 + 0.0655

= 2.14

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