Question

h A stock had returns of 19.06 percent, 22.79 percent, −16.25 percent, 9.47 percent, and 28.54 percent for the past five years. What is the standard deviation of the returns? 22.02% 3.10% 17.62% 31.04% 14.10%

Answer 1

Solution:
	Answer is 3rd option 17.62%
	The sample standard deviation of annual return (%) = 17.62%
Working Notes:
	a	b = a - 12.722%	b^2
Year	Annual total return (%) R	(R-r)	(R-r)^2
1	19.06	6.338	40.170244
2	22.79	10.068	101.364624
3	-16.25	-28.972	839.376784
4	9.47	-3.252	10.575504
5	28.54	15.818	250.209124
Sum of annual return	63.61	Sum of (R-r)^2	1241.69628
	Mean (r) = sum of returns / no of returns
	Mean (r) = 63.61%/5
	Mean (r) =12.722%
	Where n = no of return considered = 5
	standard deviation (s.d.) = Square root of (Sum of (R-r)^2 /(n-1))
	standard deviation (s.d.) = Square root of (1241.69628/(5-1))
	standard deviation (s.d.) = Square root of (1241.69628/4)
	standard deviation (s.d.) = Square root of (310.42407)
	standard deviation (s.d.) = (310.42407)^(1/2)
	standard deviation (s.d.) = 17.61885552
	standard deviation (s.d.) = 17.62%
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