Suppose we have the following returns for large-company stocks and Treasury bill
ID: 2766865 • 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 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 answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Suppose we have the following returns for large-company stocks and Treasury bills over a six year period:
Explanation / Answer
Answer
Answer : (a), (b), c(1) & c(2)
Figures in $
Year
Large company
(X-mean)
(X-mean)2
X
1
3.96
-0.6267
0.39
2
14.12
9.5333
90.88
3
19.01
14.4233
208.03
4
-14.67
-19.2567
370.82
5
-32.16
-36.7467
1350.32
6
37.26
32.6733
1067.55
Total
27.52
N
6
Average (mean) = (Total/N)
4.5867
SUM of (X-mean)2
3087.99
N-1
5
SUM of (X-mean)2 / N-1
617.60
Standard deviation =Square root of [SUM of (X-mean)2 / N-1]
24.85
Figures in $
Year
US Tresary bill
(X-mean)
(X-mean)2
X
1
4.5
-0.6933
0.48
2
4.88
-0.3133
0.10
3
3.8
-1.3933
1.94
4
6.96
1.7667
3.12
5
4.88
-0.3133
0.10
6
6.14
0.9467
0.90
Total
31.16
N
6
Average (mean) = (Total/N)
5.1933
SUM of (X-mean)2
6.64
N-1
5
SUM of (X-mean)2 / N-1
1.33
Standard deviation =Square root of [SUM of (X-mean)2 / N-1]
1.15
Year
Large company
US Tresary bill
Risk premium
A
B
A-B
1
3.96
4.5
-0.54
2
14.12
4.88
9.24
3
19.01
3.8
15.21
4
-14.67
6.96
-21.63
5
-32.16
4.88
-37.04
6
37.26
6.14
31.12
Figures in $
Year
Risk premium as per above table
(X-mean)
(X-mean)2
X
1
-0.54
0.0667
0.00
2
9.24
9.8467
96.96
3
15.21
15.8167
250.17
4
-21.63
-21.0233
441.98
5
-37.04
-36.4333
1327.39
6
31.12
31.7267
1006.58
Total
-3.64
N
6
Average (mean) = (Total/N)
-0.6067
SUM of (X-mean)2
3123.08
N-1
5
SUM of (X-mean)2 / N-1
624.62
Standard deviation =Square root of [SUM of (X-mean)2 / N-1]
24.99
Figures in $
Year
Large company
(X-mean)
(X-mean)2
X
1
3.96
-0.6267
0.39
2
14.12
9.5333
90.88
3
19.01
14.4233
208.03
4
-14.67
-19.2567
370.82
5
-32.16
-36.7467
1350.32
6
37.26
32.6733
1067.55
Total
27.52
N
6
Average (mean) = (Total/N)
4.5867
SUM of (X-mean)2
3087.99
N-1
5
SUM of (X-mean)2 / N-1
617.60
Standard deviation =Square root of [SUM of (X-mean)2 / N-1]
24.85