Assume that we have three assets.
The first one has expected return μ1 = 10% and standard deviation of return equal to σ1 = 0.14. The second has expected return μ2 = 20% and standard deviation of return equal to σ2 = 0.2. The third asset has expected return μ3 = 15%.
We would like to determine the range of the standard deviation of the third asset so that non of the asset dominates another.
This range is an interval with a lower bound a and an upper bound b.
What equals the lower bound a of the interval? Please insert your result with two decimals.
Firstly, we can calculate the return per unit of risk for first asset as follows:
Now, we can calculate return per unit of risk for second asset as follows:
Now, we can see that return per unit of risk is more for second asset as compared to first asset. In such a case second asset will dominate first asset.
So, lower bound of standard deviation for third asset can be calculated as follows:
Risk per unit of third asset should be less than 100
So, lower bound will be 0.15 for standard deviation of third asset because in this case, third asset and second asset will not be able to dominate each other.
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