Question

Problem 7.31 (Solution Video) In order to fund her retirement, Barbara needs her portfolio to have an expected return of 10.5 percent per year over the next 30 years. She has decided to invest in Stocks 1, 2, and 3, with 25 percent in Stock 1, 50 percent in Stock 2, and 25 percent in Stock 3. If Stocks 1 and 2 have expected returns of 9 percent and 10 percent per year, respectively, then what is the minimum expected annual return for Stock 3 that is likely to enable Barbara to achieve her investment requirement? (Round answer to 1 decimal place, e.g. 17.5%) Expected annual return % Click if you would like to Show Work for this question: Open Show Work

Answer 1

The Correct Answer is 13.0 %

Expected Return of Portfolio = Weighted Average returns from Stock

Weight of Stock A = 25% or 0.25

Weight of Stock B = 50% or 0.50

Weight of Stock C = 25% or 0.25

Return from Stock A = 9%

Return from Stock B = 10%

Let the Return from Stock C be X

Therefore Expected Return of Portfolio = Weight of Stock A * Return from Stock A + Weight of Stock B * Return from Stock B + Weight of Stock C * Return from Stock C

10.50 = 0.25 * 9 + 0.50 * 10 + 0.25 * X

10.50 = 2.25 + 5 + 0.25 X

10.50 = 7.25 + 0.25 X

3.25 = 0.25 X

X = 3.25 / 0.25

X = 13.0 %

Therefore minimum expected return from Stock 3 should be 13.0% so as to enable Barbara to achieve her investment target of 10.5 %.