Answer to Question #182783 in Financial Math for Niroshan

Question

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.

Answer 1

Firstly, we can calculate the return per unit of risk for first asset as follows:

$Return\space per\space unit \space of\space risk=\frac{Return}{ Standard\space deviation}$

$=\frac{10}{0.14}=71.4285714285$

Now, we can calculate return per unit of risk for second asset as follows:

$=\frac{20}{0.2}=100$

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

$\frac{15}{Standard\space deviation} <100$

$Standard\space deviation>\frac{15}{100}$

$Standard\space deviation>0.15$

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.