Problem 10-8 Risk Premiums [LO 2] Calculate the arithmetic average returns for l
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Question
Problem 10-8 Risk Premiums [LO 2]
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).)
Consider the following table for a period of six years.Explanation / Answer
Requirement 1
Arithmetic average returns = sum of return/ no. of years
Large company stocks = 17.32%/ 6
= 2.87%
US treasury bills = 42.92%/6
= 7.15%
Requirement 2
Standard Deviation = (sum of (R- AR)^2 /(n-1))^0.50
Large company stock
year
R
R- AR
(R-AR)^2
1
-16.59%
-20.05%
0.04022
2
-27.04%
-30.50%
0.09305
3
37.61%
34.15%
0.11659
4
24.31%
20.85%
0.04346
5
-7.92%
-11.38%
0.01296
6
6.95%
3.49%
0.00122
0.30749
Standard Deviation = (0.30749 / (6-1))^0.50
= 24.80%
US treasury bills
year
R
R- AR
(R-AR)^2
1
7.67%
0.52%
0.00003
2
8.18%
1.03%
0.00011
3
6.25%
-0.90%
0.00008
4
6.97%
-0.18%
0.00000
5
5.64%
-1.51%
0.00023
6
8.21%
1.06%
0.00011
0.00056
Standard Deviation = (0.00056 / (6-1))^0.50
= 1.06%
Requirement 3
a)
Risk premium = return of large company stock return on US T bill
Year
LC
TB
Risk premium
1
-16.59%
7.67%
-24.26%
2
-27.04%
8.18%
-35.22%
3
37.61%
6.25%
31.36%
4
24.31%
6.97%
17.34%
5
-7.92%
5.64%
-13.56%
6
6.95%
8.21%
-1.26%
17.32%
42.92%
-25.60%
Part b)
Average Risk premium = -25.60%/ 6
=-4.27%
year
R
R- AR
(R-AR)^2
1
-24.26%
-19.99%
0.03997
2
-35.22%
-30.95%
0.09581
3
31.36%
35.63%
0.12693
4
17.34%
21.61%
0.04668
5
-13.56%
-9.29%
0.00864
6
-1.26%
3.01%
0.00090
0.31894
Standard Deviation = (0.31894)^0.50
= 56.47%
year
R
R- AR
(R-AR)^2
1
-16.59%
-20.05%
0.04022
2
-27.04%
-30.50%
0.09305
3
37.61%
34.15%
0.11659
4
24.31%
20.85%
0.04346
5
-7.92%
-11.38%
0.01296
6
6.95%
3.49%
0.00122
0.30749
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