Consider the following table for a period of six years. Calculate the arithmetic
ID: 2651771 • Letter: C
Question
Consider the following table for a period of six years.
Calculate the arithmetic average returns for large-company stocks and T-bills over this time period. (Do not round intermediate calculations. Enter your answers as a percentage 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 time period. (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)
What was the arithmetic 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 percentage rounded to 2 decimal places (e.g., 32.16).)
What was the standard deviation of the risk premium over this period? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
Returns Year Large-Company Stocks U.S.Treasury Bills Year 1 – 16.49 % 7.65 % Year 2 – 27.01 8.17 Year 3 37.59 6.23 Year 4 24.29 6.87 Year 5 – 7.88 5.63 Year 6 6.93 8.18
Explanation / Answer
Answer:
1
Calculation of the arithmetic average returns
Year
Large-Company Stocks
U.S. Treasury Bills
Year 1
-16.49%
7.65%
Year 2
-27.01%
8.17%
Year 3
37.59%
6.23%
Year 4
24.29%
6.87%
Year 5
-7.88%
5.63%
Year 6
6.93%
8.18%
Total
17.43%
42.73%
Arithmetic average returns
2.91%
7.12%
(Total /6)
2
Calculation of the standard deviation of the returns
Large-Company Stocks
Year
Return
Average Return
Deviation
Deviation Square
A
B
C
D = B-C
D*D
Year 1
-16.49%
2.91%
-19.40%
3.76%
Year 2
-27.01%
2.91%
-29.92%
8.95%
Year 3
37.59%
2.91%
34.69%
12.03%
Year 4
24.29%
2.91%
21.39%
4.57%
Year 5
-7.88%
2.91%
-10.79%
1.16%
Year 6
6.93%
2.91%
4.03%
0.16%
Sum of Deviation square
30.64%
Standard deviation = (Sum of D square /5)^(1/2)
24.75%
U.S. Treasury Bills
Year
Return
Average Return
Deviation
Deviation Square
A
B
C
D = B-C
D*D
Year 1
7.65%
7.12%
0.53%
0.00%
Year 2
8.17%
7.12%
1.05%
0.01%
Year 3
6.23%
7.12%
-0.89%
0.01%
Year 4
6.87%
7.12%
-0.25%
0.00%
Year 5
5.63%
7.12%
-1.49%
0.02%
Year 6
8.18%
7.12%
1.06%
0.01%
Sum of Deviation square
0.06%
Standard deviation = (Sum of D square /5)^(1/2)
1.06%
3
Calculation of the observed risk premium and Arithmetic Average
Year
Large-Company Stocks
U.S. Treasury Bills
Risk Premium
A
B
A-B
Year 1
-16.49%
7.65%
-24.14%
Year 2
-27.01%
8.17%
-35.18%
Year 3
37.59%
6.23%
31.36%
Year 4
24.29%
6.87%
17.42%
Year 5
-7.88%
5.63%
-13.51%
Year 6
6.93%
8.18%
-1.25%
Total
-25.30%
Arithmetic average returns
-4.22%
(Total /6)
4
Calculation of standard deviation of the risk premium
Year
Premium
Average Premium
Deviation
Deviation Square
A
B
C
D = B-C
D*D
Year 1
-24.14%
-4.22%
-19.92%
3.97%
Year 2
-35.18%
-4.22%
-30.96%
9.59%
Year 3
31.36%
-4.22%
35.58%
12.66%
Year 4
17.42%
-4.22%
21.64%
4.68%
Year 5
-13.51%
-4.22%
-9.29%
0.86%
Year 6
-1.25%
-4.22%
2.97%
0.09%
Sum of Deviation square
31.85%
Standard deviation = (Sum of D square /5)^(1/2)
25.24%
1
Calculation of the arithmetic average returns
Year
Large-Company Stocks
U.S. Treasury Bills
Year 1
-16.49%
7.65%
Year 2
-27.01%
8.17%
Year 3
37.59%
6.23%
Year 4
24.29%
6.87%
Year 5
-7.88%
5.63%
Year 6
6.93%
8.18%
Total
17.43%
42.73%
Arithmetic average returns
2.91%
7.12%
(Total /6)
2
Calculation of the standard deviation of the returns
Large-Company Stocks
Year
Return
Average Return
Deviation
Deviation Square
A
B
C
D = B-C
D*D
Year 1
-16.49%
2.91%
-19.40%
3.76%
Year 2
-27.01%
2.91%
-29.92%
8.95%
Year 3
37.59%
2.91%
34.69%
12.03%
Year 4
24.29%
2.91%
21.39%
4.57%
Year 5
-7.88%
2.91%
-10.79%
1.16%
Year 6
6.93%
2.91%
4.03%
0.16%
Sum of Deviation square
30.64%
Standard deviation = (Sum of D square /5)^(1/2)
24.75%
U.S. Treasury Bills
Year
Return
Average Return
Deviation
Deviation Square
A
B
C
D = B-C
D*D
Year 1
7.65%
7.12%
0.53%
0.00%
Year 2
8.17%
7.12%
1.05%
0.01%
Year 3
6.23%
7.12%
-0.89%
0.01%
Year 4
6.87%
7.12%
-0.25%
0.00%
Year 5
5.63%
7.12%
-1.49%
0.02%
Year 6
8.18%
7.12%
1.06%
0.01%
Sum of Deviation square
0.06%
Standard deviation = (Sum of D square /5)^(1/2)
1.06%
3
Calculation of the observed risk premium and Arithmetic Average
Year
Large-Company Stocks
U.S. Treasury Bills
Risk Premium
A
B
A-B
Year 1
-16.49%
7.65%
-24.14%
Year 2
-27.01%
8.17%
-35.18%
Year 3
37.59%
6.23%
31.36%
Year 4
24.29%
6.87%
17.42%
Year 5
-7.88%
5.63%
-13.51%
Year 6
6.93%
8.18%
-1.25%
Total
-25.30%
Arithmetic average returns
-4.22%
(Total /6)
4
Calculation of standard deviation of the risk premium
Year
Premium
Average Premium
Deviation
Deviation Square
A
B
C
D = B-C
D*D
Year 1
-24.14%
-4.22%
-19.92%
3.97%
Year 2
-35.18%
-4.22%
-30.96%
9.59%
Year 3
31.36%
-4.22%
35.58%
12.66%
Year 4
17.42%
-4.22%
21.64%
4.68%
Year 5
-13.51%
-4.22%
-9.29%
0.86%
Year 6
-1.25%
-4.22%
2.97%
0.09%
Sum of Deviation square
31.85%
Standard deviation = (Sum of D square /5)^(1/2)
25.24%