Suppose we have the following returns for large-company stocks and Treasury bill
ID: 2724944 • Letter: S
Question
Suppose we have the following returns for large-company stocks and Treasury bills over a six year period Calculate the arithmetic average returns for large-company stocks and T-bills over this period. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16) calculate the standard deviation of the returns for the large-company stocks and T-bills over this period. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16) Calculate the observed risk premium in each year for the large-company stocks versus the T-bills. What was the average risk premium over this period? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16) Calculate the observed risk premium in each year for the large-company stocks versus the t-bills. What was the standard deviation of the risk premium over this period? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16)Explanation / Answer
1
Calculation of Arithmatic Average for Large Co. Stocks:
Year
Return
1
3.66
2
14.44
3
19.03
4
-14.65
5
-32.14
6
37.27
Total
27.61
Arithmatic Average = Total / 6 =
4.60
2
Calculation of Arithmatic Average for Treasury Bills:
Year
Return
1
4.66
2
2.33
3
4.12
4
5.88
5
4.9
6
6.33
Total
28.22
Arithmatic Average = Total / 6 =
4.70
3
Calculation of Standard Deviation for Large Co. Stocks:
Year
Return
Avg. Return
Deviation
Deviation ^2
A
B
C = A-B
D = C*C
1
3.66
4.60
(0.94)
0.886736111
2
14.44
4.60
9.84
96.79280278
3
19.03
4.60
14.43
208.1768028
4
-14.65
4.60
(19.25)
370.6266694
5
-32.14
4.60
(36.74)
1349.950069
6
37.27
4.60
32.67
1067.220003
Sum of Deviation ^2 =
3093.653083
Standard Deviation = (Sum of Deviation ^2 / (N-1))^(1/2)
= (3093.653 / (6-1))^(1/2) =
24.87
%
4
Calculation of Standard Deviation for Treasury Bills:
Year
Return
Avg. Return
Deviation
Deviation ^2
A
B
C = A-B
D = C*C
1
4.66
4.70
(0.04)
0.001878
2
2.33
4.70
(2.37)
5.632711
3
4.12
4.70
(0.58)
0.340278
4
5.88
4.70
1.18
1.384544
5
4.9
4.70
0.20
0.038678
6
6.33
4.70
1.63
2.646044
Sum of Deviation ^2 =
10.044133
Standard Deviation = (Sum of Deviation ^2 / (N-1))^(1/2)
= (10.044133 / (6-1))^(1/2) =
1.42
%
1
Calculation of Arithmatic Average for Large Co. Stocks:
Year
Return
1
3.66
2
14.44
3
19.03
4
-14.65
5
-32.14
6
37.27
Total
27.61
Arithmatic Average = Total / 6 =
4.60
2
Calculation of Arithmatic Average for Treasury Bills:
Year
Return
1
4.66
2
2.33
3
4.12
4
5.88
5
4.9
6
6.33
Total
28.22
Arithmatic Average = Total / 6 =
4.70
3
Calculation of Standard Deviation for Large Co. Stocks:
Year
Return
Avg. Return
Deviation
Deviation ^2
A
B
C = A-B
D = C*C
1
3.66
4.60
(0.94)
0.886736111
2
14.44
4.60
9.84
96.79280278
3
19.03
4.60
14.43
208.1768028
4
-14.65
4.60
(19.25)
370.6266694
5
-32.14
4.60
(36.74)
1349.950069
6
37.27
4.60
32.67
1067.220003
Sum of Deviation ^2 =
3093.653083
Standard Deviation = (Sum of Deviation ^2 / (N-1))^(1/2)
= (3093.653 / (6-1))^(1/2) =
24.87
%
4
Calculation of Standard Deviation for Treasury Bills:
Year
Return
Avg. Return
Deviation
Deviation ^2
A
B
C = A-B
D = C*C
1
4.66
4.70
(0.04)
0.001878
2
2.33
4.70
(2.37)
5.632711
3
4.12
4.70
(0.58)
0.340278
4
5.88
4.70
1.18
1.384544
5
4.9
4.70
0.20
0.038678
6
6.33
4.70
1.63
2.646044
Sum of Deviation ^2 =
10.044133
Standard Deviation = (Sum of Deviation ^2 / (N-1))^(1/2)
= (10.044133 / (6-1))^(1/2) =
1.42
%
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