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	15 %	22 %
2	33	43
3	22	-9
4	-23	-23
5	24	51

Calculate the arithmetic average return for X.

   

Calculate the arithmetic average return for Y.

  

Calculate the variance for X.

   

Calculate the variance for Y.

  

Calculate the standard deviation for X.

   

Calculate the standard deviation for Y.

Answer 1

Arthematic Average Return of X
Year	Returns X
1	15%
2	33%
3	22%
4	-23%
5	24%
Sum of Returns	71%
Arthematic Average Return = Sum /n	14.2%
Arthematic Average Return of Y
Year	Returns Y
1	22%
2	43%
3	-9%
4	-23%
5	51%
Sum of Returns	84%
Arthematic Average Return = Sum /n	16.8%

Varaince & Standard Deviation of X
Year	Returns X	X-Avg X	(X-Avg X)^2
1	15%	0.8000%	0.000064
2	33%	18.8000%	0.035344
3	22%	7.8000%	0.006084
4	-23%	-37.2000%	0.138384
5	24%	9.8000%	0.009604
Sum of (X-Avg X)^2	0.189480
Vairiance = [ sum(X-Avg X)^2] / n	0.037896	i.e., 3.79%
Standard devaiation = Sqrt of Variance	0.19466895	i.e., 19.47%
Varaince & Standard Deviation of Y
Year	Returns Y	Y-Avg Y	(Y-Avg Y)^2
1	22%	5.2000%	0.002704
2	43%	26.2000%	0.068644
3	-9%	-25.8000%	0.066564
4	-23%	-39.8000%	0.158404
5	51%	34.2000%	0.116964
Sum of (Y-Avg Y)^2	0.413280
Vairiance = [ sum(Y-Avg Y)^2] / n	0.082656	i.e., 8.27%
Standard devaiation = Sqrt of Variance	0.28749957	i.e., 28.75%

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