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In order to fund her retirement, Linda needs her portfolio to have an expected return of 12
In order to fund her retirement, Linda needs her portfolio to have an expected return of 12.3 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 Linda to achieve her investment requirement? (Round answer to 1 decimal place, eg. 17.5%) Expected annual return %
Expert Solution
Given
Required return = 12.3%
We know that Expected return on the portfolio is the sum of weight average return of individual stocks
Computation of Expected return on portfolio
| Stock | Weight | Return( % ) | Weighted Average return ( Weight * Return ) |
| 1 | 0.25 | 9 | 2.25 |
| 2 | 0.5 | 10 | 5 |
| 3 | 0.25 | x | 0.25x |
| Total | 7.25% + 0.25x |
Let the return on third stock be x%
We know that Expected return on the portfolio is the sum of weight average return of individual stocks
However the expected return or the required return on portfolio is equal to 12.3%
7.25% + 0.25x = 12.3%
0.25x = 12.3% -7.25%
0.25x = 5.05%
x = 5.05% / 0.25
x = 20.2%
Hence the minimum return on the 3rd stock must be 20.2%
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