Question

Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.   

	Returns
Year	X	Y
1	11 %	20 %
2	29	41
3	18	-12
4	-19	-26
5	20	49

   

Requirement 1:
(a)	Calculate the arithmetic average return for X.

   

(b)	Calculate the arithmetic average return for Y.

  

Requirement 2:
(a)	Calculate the variance for X. (Do not round intermediate calculations.)

   

(b)	Calculate the variance for Y. (Do not round intermediate calculations.)

  

Requirement 3:
(a)	Calculate the standard deviation for X. (Do not round intermediate calculations.)

   

(b)	Calculate the standard deviation for Y. (Do not round intermediate calculations.)

Answer 1

I am calculating the variance and standard deviation for both sample and population data, please comment and let me know in general what you guys expect to be calculated?

Year	Return X	Return Y	(Return X - Average return of X)^2	(Return Y - Average return of Y)^2
1	11.00%	20.00%	0.00640%	0.31360%
2	29.00%	41.00%	2.95840%	7.07560%
3	18.00%	-12.00%	0.38440%	6.96960%
4	-19.00%	-26.00%	9.48640%	16.32160%
5	20.00%	49.00%	0.67240%	11.97160%
Total	59.00%	72.00%	13.50800%	42.65200%

n = 5 for population data

n = 4 for sample data

#	Particulars	For sample data	For population data
a	Average Return X = Total X /5 =	11.800000%	11.800000%
b	Average Return Y = Total Y /5 =	14.400000%	14.400000%
a	Variance X = Total of ((Return X - Average return of X)^2)/n =	3.377000%	2.701600%
b	Variance Y = Total of ((Return Y - Average return of Y)^2)/n =	10.663000%	8.530400%
a	Standard deviation X = Variance X^0.5 =	18.376616%	16.436545%
b	Standard deviation Y = Variance Y^0.5 =	32.654249%	29.206849%