Question

A stock had returns of 5 percent, 9 percent, 11 percent, −8 percent, and 6 percent over the past five years. What is the standard deviation of these returns? Multiple Choice 11.14 percent 7.44 percent 8.44 percent 4.60 percent 5.97 percent

Answer 1

Solution:
	Answer is 2nd option 7.44 percent
Working Notes:
Notes:	Standard deviation we compute using formula standard deviation (s.d.) = Square root of (Sum of (R-r)^2 /(n-1)) where R is annual return , r is mean of returns and n is no of returns considered .
	a	b = (a - 4.6%)	b^2
		(return -mean)
Year	Returns ('R)	(R-r)	(R-r)^2
1	5	0.40	0.16
2	9	4.40	19.36
3	11	6.40	40.96
4	-8	-12.60	158.76
5	6	1.40	1.96
		Sum of (R-r)^2	221.20
	Mean (r) = sum of returns / no of returns
	Mean (r) = (5+9+11-8+6)/5
	Mean (r) =23/5
	Mean (r) =4.6%
	standard deviation (s.d.) = Square root of (Sum of (R-r)^2 /(n-1))
	Where n = no of return considered = 5
	standard deviation (s.d.) = Square root of (221.20/(5-1))
	standard deviation (s.d.) = Square root of (221.20/4)
	standard deviation (s.d.) = Square root of (55.30)
	standard deviation (s.d.) = (55.30)^(1/2)
	standard deviation (s.d.) = 7.436396977 %
	standard deviation (s.d.) = 7.44 %
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