Question

The past five monthly returns for ug company are 3.25%, -1.25%, 4.25%, 5.36% and – 2.29%. what is the standard deviation of the returns?

Answer 1

The standard deviation is a measure of the dispersion of returns. Calculated by finding the mean, determining deviations, squaring them, calculating variance, and finally taking the square root. Result: 3.02%.

1. Calculate the Mean:

Find the average of the monthly returns by adding them up and dividing by the number of returns.

`\[\text{Mean} = (3.25 - 1.25 + 4.25 + 5.36 - 2.29) / 5 = 1.68%\]`

2. Calculate Deviations:

Subtract the mean from each monthly return to get the deviations.

`\[\text{Deviations} = [3.25 - 1.68, -1.25 - 1.68, 4.25 - 1.68, 5.36 - 1.68, -2.29 - 1.68]\]`

3. Square Deviations:

Square each deviation.

`\[\text{Squared Deviations} = [3.1044, 9.1024, 7.0564, 14.6496, 14.6129]\]`

4. Calculate Variance:

Find the average of the squared deviations.

`\[\text{Variance} = (3.1044 + 9.1024 + 7.0564 + 14.6496 + 14.6129) / 5 = 9.1054\]`

5. Calculate Standard Deviation:

Take the square root of the variance to get the standard deviation.

`\[\text{Standard Deviation} = √(9.1054) \approx 3.02%\]`