Johnny's portfolio consists of $100,000 invested in a stock which has a beta = 0.9, $150,000...

Johnny's portfolio consists of $100,000 invested in a stock which has a beta = 0.9, $150,000 invested in a stock which has a beta = 1.2, and $50,000 invested in a stock which has a beta = 1.5. The risk-free rate is 4 percent. Last year this portfolio had a required rate of return of 13 percent. This year nothing has changed except for the fact that the market risk premium has decreased by 2 percent (This year market risk premium = Last year market risk premium - 2%). and risk free remains constant. What is the portfolio's current year required rate of return?

Expert Solution

Investment in Stock 1 = $100,000
Investment in Stock 2 = $150,000
Investment in Stock 3 = $50,000

Total Investment = Investment in Stock 1 + Investment in Stock 2 + Investment in Stock 3
Total Investment = $100,000 + $150,000 + $50,000
Total Investment = $300,000

Weight of Stock 1 = Investment in Stock 1 / Total Investment
Weight of Stock 1 = $100,000 / $300,000
Weight of Stock 1 = 0.33333

Weight of Stock 2 = Investment in Stock 1 / Total Investment
Weight of Stock 2 = $150,000 / $300,000
Weight of Stock 2 = 0.50000

Weight of Stock 3 = Investment in Stock 1 / Total Investment
Weight of Stock 3 = $50,000 / $300,000
Weight of Stock 3 = 0.16667

Portfolio Beta = Weight of Stock 1 * Beta of Stock 1 + Weight of Stock 2 * Beta of Stock 2 + Weight of Stock 3 * Beta of Stock 3
Portfolio Beta = 0.33333 * 0.90 + 0.50000 * 1.20 + 0.16667 * 1.50
Portfolio Beta = 1.15

Change in Market Risk Premium = -2.00%

New Portfolio Required Return = Old Portfolio Required Return + Change in Market Risk Premium * Portfolio Beta
New Portfolio Required Return = 13.00% - 2.00% * 1.15
New Portfolio Required Return = 13.00% - 2.30%
New Portfolio Required Return = 10.70%

jeff jeffy answered 1 year ago

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