Question

Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. Returns Year Х 10 % 19 % 28 40 17 -12 -18 19 48 Requirement 1: (a) Calculate the arithmetic average return for X. (Click to select) (b) Calculate the arithmetic average return for Y. (Click to select) A Requirement 2: (a) Calculate the variance for X. (Do not round intermediate calculations.) (Click to select) (b) Calculate the variance for Y. (Do not round intermediate calculations.) (Click to select) Requirement 3: (a) Calculate the standard deviation for X. (Do not round intermediate calculations.) (Click to select) (b) Calculate the standard deviation for Y. (Do not round intermediate calculations.) (Click to select)

Answer 1

Solution:
1.	Average return
a.	11.20%	For X
b.	13.80%	For Y
2	Variance
a.	307.70    %^2 or    0.03077      in decimal	For X
b.	1033.20 %^2   or   0.1033.20    in decimal	For Y
3.	Standard deviation
a.	17.54%	For X
b.	32.14%	For Y
Working Notes:
For X
	a	b = a - 11.2%	b^2
Year	Annual total return (%) R	(R-r)	(R-r)^2
1	10	-1.20	1.440
2	28	16.80	282.240
3	17	5.80	33.640
4	-18	-29.20	852.640
5	19	7.80	60.840
Sum of annual return	56.00	Sum of (R-r)^2	1230.80
	Mean (r) = sum of returns / no of returns
	Mean (r) = 56%/5
	Mean (r) =11.20%
	Where n = no of return considered = 5
	Variance = Sum of (R-r)^2 /(n-1)
	Variance = 1230.80 %^2 /(5-1)
	Variance = 1230.80 %^2 /4
	Variance = 307.70 %^2
	OR
	Variance = 0.03077
	standard deviation (s.d.) = Square root of (Sum of (R-r)^2 /(n-1))
	standard deviation (s.d.) = Square root of (1230.80 %^2 /(5-1))
	standard deviation (s.d.) = Square root of (1230.80 %^2 /4)
	standard deviation (s.d.) = Square root of (307.70 %^2)
	standard deviation (s.d.) = (307.70 %^2)^(1/2)
	standard deviation (s.d.) = 17.5413796%
	standard deviation (s.d.) = 17.54%
For Y
	a	b = a - 13.80%	b^2
Year	Annual total return (%) R	(R-r)	(R-r)^2
1	19	5.20	27.040
2	40	26.20	686.440
3	-12	-25.80	665.640
4	-26	-39.80	1584.040
5	48	34.20	1169.640
Sum of annual return	69.00	Sum of (R-r)^2	4132.80
	Mean (r) = sum of returns / no of returns
	Mean (r) = 69%/5
	Mean (r) =13.80%
	Where n = no of return considered = 5
	Variance = Sum of (R-r)^2 /(n-1)
	Variance = 4132.80 %^2 /(5-1)
	Variance = 4132.80 %^2 /4
	Variance = 1033.20 %^2
	OR
	Variance = 0.10332
	standard deviation (s.d.) = Square root of (Sum of (R-r)^2 /(n-1))
	standard deviation (s.d.) = Square root of (4132.80 %^2 /(5-1))
	standard deviation (s.d.) = Square root of (4132.80 %^2 /4)
	standard deviation (s.d.) = Square root of (1033.20 %^2)
	standard deviation (s.d.) = (1033.20 %^2)^(1/2)
	standard deviation (s.d.) = 32.143428%
	standard deviation (s.d.) = 32.14%
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