Use the following returns for X and Y. Returns Year X Y 1 22.5 % 28.5 % 2 – 17.5
ID: 2651059 • Letter: U
Question
Use the following returns for X and Y.
Returns
Year
X
Y
1
22.5
%
28.5
%
2
–
17.5
–
4.5
3
10.5
30.5
4
21.0
–
16.0
5
5.5
34.5
Requirement 1:
Calculate the average returns for X and Y. (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)
Average returns
X
8.4 %
Y
14.6 %
Requirement 2:
Calculate the variances for X and Y. (Do not round intermediate calculations. Round your answers to 6 decimal places (e.g., 32.161616).)
Variances
X
Y
Requirement 3:
Calculate the standard deviations for X and Y. (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)
Standard deviations
X
16.13 %
Y
23.14 %
Use the following returns for X and Y.
Explanation / Answer
Answer:
Calculation of the average returns for X and Y
Returns
Year
X
Y
1
22.50%
28.50%
2
-17.50%
-4.50%
3
10.50%
30.50%
4
21.00%
-16.00%
5
5.50%
34.50%
Total
42.00%
73.00%
Average Return = Total /5
8.40%
14.60%
Calculation of the variances and Standard Deviation for X
Year
Return
Average Return
Deviation
Deviation ^2
A
B
C =A-B
C^2
1
22.50%
8.40%
14.10%
1.99%
2
-17.50%
8.40%
-25.90%
6.71%
3
10.50%
8.40%
2.10%
0.04%
4
21.00%
8.40%
12.60%
1.59%
5
5.50%
8.40%
-2.90%
0.08%
Sum of Deviation ^2
10.41%
Variance = Sum of Deviation ^2 /(5-1)
2.60%
Standard Deviation = Variance ^(1/2)
16.13%
Calculation of the variances and Standard Deviation for Y
Year
Return
Average Return
Deviation
Deviation ^2
A
B
C =A-B
C^2
1
28.50%
14.60%
13.90%
1.93%
2
-4.50%
14.60%
-19.10%
3.65%
3
30.50%
14.60%
15.90%
2.53%
4
-16.00%
14.60%
-30.60%
9.36%
5
34.50%
14.60%
19.90%
3.96%
Sum of Deviation ^2
21.43%
Variance = Sum of Deviation ^2 /(5-1)
5.36%
Standard Deviation = Variance ^(1/2)
23.15%
Calculation of the average returns for X and Y
Returns
Year
X
Y
1
22.50%
28.50%
2
-17.50%
-4.50%
3
10.50%
30.50%
4
21.00%
-16.00%
5
5.50%
34.50%
Total
42.00%
73.00%
Average Return = Total /5
8.40%
14.60%
Calculation of the variances and Standard Deviation for X
Year
Return
Average Return
Deviation
Deviation ^2
A
B
C =A-B
C^2
1
22.50%
8.40%
14.10%
1.99%
2
-17.50%
8.40%
-25.90%
6.71%
3
10.50%
8.40%
2.10%
0.04%
4
21.00%
8.40%
12.60%
1.59%
5
5.50%
8.40%
-2.90%
0.08%
Sum of Deviation ^2
10.41%
Variance = Sum of Deviation ^2 /(5-1)
2.60%
Standard Deviation = Variance ^(1/2)
16.13%
Calculation of the variances and Standard Deviation for Y
Year
Return
Average Return
Deviation
Deviation ^2
A
B
C =A-B
C^2
1
28.50%
14.60%
13.90%
1.93%
2
-4.50%
14.60%
-19.10%
3.65%
3
30.50%
14.60%
15.90%
2.53%
4
-16.00%
14.60%
-30.60%
9.36%
5
34.50%
14.60%
19.90%
3.96%
Sum of Deviation ^2
21.43%
Variance = Sum of Deviation ^2 /(5-1)
5.36%
Standard Deviation = Variance ^(1/2)
23.15%
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