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

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

  

Returns
Year X Y
1 13 %     25 %    
2 31         46        
3 20         -13        
4 -21         -27        
5 22         54        

   

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.
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Answer #1

for X

Year return (x) (x-mean)^2
1 13.00% 0
2 31.00% 0.0324
3 20.00% 0.0049
4 -21.00% 0.1156
5 22.00% 0.0081
Sum 65.00% 0.161
Average return 13.00%
variance 0.04025
standard deviation 20.06%

for Y

Year return (x) (x-mean)^2
1 25.00% 0.0064
2 46.00% 0.0841
3 -13.00% 0.09
4 -27.00% 0.1936
5 54.00% 0.1369
Sum 85.00% 0.511
Average return 17.00%
variance 0.12775
standard deviation 35.74%

variance = sum of (x-mean)^2/n-1

standard deviation = sqrt(variance)

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