In order to fund her retirement, Karen needs her portfolio to have an expected return of 13.5 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 Karen to achieve her investment requirement? (Round answer to 1 decimal place, e. g. 17.5%.)

The return of stock C should be 25% for Karen to achieve her target.

Explanation:

The expected return on a portfolio is the weighted average of the individual stocks' returns that form up the portfolio. To calculate the expected return on the portfolio we use the following formula,

Portfolio return = wA * rA  +  wB * rB  +  ...  +  wN * rN

Where,

Let return of Stock C be x.

0.135 = 0.25 * 0.09  +  0.5 * 0.1  +  0.25 * x

0.135 = 0.0225  +  0.05  +  0.25x

0.135 - 0.0225 - 0.05 = 0.25x

0.0625 = 0.25x

x = 0.0625 / 0.25

x = 0.25 or 25%

The return of stock C should be 25% for Karen to achieve her target.

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