In order to fund her retirement Michele requires a portfolio

In order to fund her retirement, Michele requires a portfolio with an expected return of 0.11 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 0.09 and 0.10 per year, respectively, then what is the minimum expected annual return for Stock 3 that will enable Michele to achieve her investment requirement?

Solution

Expected return = return of stock 1*proportion invested in stock 1 + return of stock 2*proportion invested in stock 2 + return of stock 3*proportion invested in stock 3

0.11 = 0.09*0.25 + 0.10*0.50 + X*0.25

0.11 = 0.0225 + 0.05 + 0.25X

0.11 = 0.0725 + 0.25X

0.0375 = 0.25X

X = .15

Answer: 0.15