Question

Over the past 5 years, a stock has had total returns of 5.0%, 10.0%, -5.0%, 7.2% and 15.0%. What is the standard deviation of the stock’s return over the past 5 years?

6.63%

15.4%

7.4%

11.2%

Answer 1

Given about a stock's return for past 5 years.

Variance is calculated in the table below:

Mean u = (r1+r2+r3+r4+r5)/5

Mean - return = (u - x)

Variance = (sum of (x-u)^2)/n, here n = 5

So, variance = 0.00219/5 = 0.004389

So, standard deviation = Variance^(1/2) = (0.004389)^(1/2) = 0.0663 or 6.63%

year	Return(x)	(mean - return) = (u-x)	(x-u)^2
1	5.000%	1.440%	0.000207360
2	10.000%	-3.560%	0.001267360
3	-5.000%	11.440%	0.013087360
4	7.200%	-0.760%	0.000057760
5	15.000%	-8.560%	0.007327360
mean(u)	6.440%	Sum	0.0219

Option A is correct.