Question

1. Your stock investments return 8%, 12%, and -4% in consecutive years. What is the variance?

A)0.0069

B)0.0096

D)0.0036

D)0.0049

E)0.0089

2. What would be the standard deviation of the returns 8%, 12%, and -4% in consecutive years?

A) 4.33%

B) 5.35%

C) 6.33%

D) 3.65%

E) 8.31%

Answer 1

Part 1:
The mean of these values is calculated as the sum of observations divided by the number of observations.
=(0.08+0.12-0.04)/3=0.053333333
Now,
(0.08-0.053333333)^2=0.000711111
(0.12-0.053333333)^2=0.004444444
(-0.04-0.053333333)^2=0.008711111
The sum of the values is:
0.000711111+0.004444444+0.008711111=0.013866666
Here, variance of a sample=0.013866666/(Number of observations -1)
=0.013866666/(3-1)=0.013866666/2
=0.006933333 or 0.0069 (Rounded to 2 decimal places)

Answer: Hence, the variance is 0.0069

Part 2:
Standard deviation of the sample is calculated as the square root of variance.
As we have the same values as part 1, we only need to take a square root of the variance to get the value for standard deviation.
Standard deviation= (0.0069)^(1/2)
=0.083066239 or 8.31% (Rounded to 2 decimal places)

Answer: Hence, the standard deviation is 8.31%