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Calculating returns and Variability: Using the following returns, calculate the average returns, the variances and the standard deviations for X and Y

Business Sep 26, 2020

Calculating returns and Variability: Using the following returns, calculate the average returns, the variances and the standard deviations for X and Y.
Returns
Year X Y
1 16% 34%
2 18% -7%
3 -9% -12%
4 21% 41%
5 2% 10%

Expert Solution

Please see the attached file. For X X= X 2 = 16% 0.0256 18% 0.0324 -9% 0.0081 21% 0.0441 2% 0.0004 Total= 48% 0.1106 n=no of observations= 5 Mean= 9.60% =48.%/5 variance={?X 2 - n(Mean) 2 }/(n-1)= 0.01613 =(0.1106-5*0.096^2)/(5-1) standard deviation =?Variance= 12.70% =?0.01613 Answer: Average return= 9.60% Variance= 0.01613 Standard deviation= 12.70% For Y Y= Y 2 = 34% 0.1156 -7% 0.0049 -12% 0.0144 41% 0.1681 10% 0.01 Total= 66% 0.313 n=no of observations= 5 Mean= 13.20% =66.%/5 variance={?Y 2 - n(Mean) 2 }/(n-1)= 0.05647 =(0.313-5*0.132^2)/(5-1) standard deviation =?Variance= 23.76% =?0.05647 Answer: Average return= 13.20% Variance= 0.05647 Standard deviation= 23.76%
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