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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
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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