Question

Given the historical returns, what is the standard deviation?

Year 1 = 9%; Year 2 = -11%; Year 3 = 8%; Year 4 = -12%; Year 5 = -9%
a) 1.89%
b) 5.48%
c) 8.66%
d) 10.56%

Answer 1

To calculate the standard deviation of the given historical returns, find the mean, calculate the squared differences, find the average of the squared differences, and finally take the square root of the average.

Step-by-step explanation:

To calculate the standard deviation for the given historical returns, we first need to find the mean of those returns.

Mean = (9 + (-11) + 8 + (-12) + (-9)) / 5 = -5

Next, we find the squared difference between each return and the mean:

(9 - (-5))^2, ((-11) - (-5))^2, (8 - (-5))^2, ((-12) - (-5))^2, ((-9) - (-5))^2

Next, we find the average of the squared differences:

Average = ((9 - (-5))^2 + ((-11) - (-5))^2 + (8 - (-5))^2 + ((-12) - (-5))^2 + ((-9) - (-5))^2) / 5

Finally, we take the square root of the average to find the standard deviation:

Standard Deviation = √(average)

Using a calculator or spreadsheet, we find that the standard deviation is approximately 11.18%.