Question

Given the following historical returns, calculate the average return and the standard deviation

Year	Return
1	12%
2	7%
3	10%
4	9%

Answer 1

Average Return(mean) =Sum of returns/Number of returns

Year 1=12% year 2=7% Year 3=10% year 4=9%

Average Return (mean)=12%+7%+10%+9%/4 =9.5%

Standard deviation is the square root of variance

Variance=Sigma(return -mean)^2/N

=Sigma(12-9.5)^2+(7-9.5)^2+(10-9.5)^2+(9-9.5)^2/4

we get 13/4 =3.25

Standard deviation is the squareroot of variance so standard deviation =Squareroot of 3.25=1.80

I have computed this on excel too and I'm attaching a screenshot.VAR.P is the function used for variance and SQRT for squareroot .Average function is used for obtaining Average returns.