Consider the following table for a period of six years. Returns Year Large-Compa
ID: 2754875 • Letter: C
Question
Consider the following table for a period of six years. Returns Year Large-Company Stocks U.S. Treasury Bills Year 1 – 15.09 % 7.37 % Year 2 – 26.59 8.03 Year 3 37.31 5.95 Year 4 24.01 5.47 Year 5 – 7.32 5.49 Year 6 6.65 7.76 Requirement 1: 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).) Arithmetic average returns Large-company stock % T-bills 9.50 % Requirement 2: 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).) Standard deviation Large-company stock % T-bills % Requirement 3: Calculate the observed risk premium in each year for the large-company stocks versus the T-bills. (a) 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).) Risk premium % (b) 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).) Risk premium standard deviation %
Explanation / Answer
Year
Large-Company Stocks
U.S. Treasury Bills
Risk premium
1
-15.09
7.37
-22.46
2
-26.59
8.03
-34.62
3
37.31
5.95
31.36
4
24.01
5.47
18.54
5
-7.32
5.49
-12.81
6
6.65
7.76
-1.11
18.97
40.07
-21.1
1.
Arithmetic average returns for large company stocks = 18.97% / 6 = 3.16%
Arithmetic average returns for US treasury bills = 40.07%/6 = 6.68%
2.
Variance for large company stocks = 1/6 * {(-15.09-3.16)2+(-26.59-3.16) 2+(37.31-3.16) 2+(24.01-3.16) 2+(-7.32-3.16) 2 +(6.65-3.16) 2} = 490.18
Standard deviation for large company stocks = (490.18)1/2 = 22.14%
Variance for US treasury bills = 1/6 * {(7.37-6.68)2+(8.03-6.68)2+(5.95-6.68)2+(5.47-6.68)2+(5.49-6.68)2+(7.76-6.68)2} = 1.14635
Standard deviation for US treasury bills = (1.14635)1/2 = 1.07%
3.
Arithmetic average risk premium = -21.10/6 = -3.52%
Variance of the risk premium = 1/6 * {(-22.46-21.1) 2+(-34.62-21.1) 2+(31.36-21.1) 2+(18.54-21.1) 2+(-12.81-21.1) 2+(-1.11-21.1)2} = 1126.198
Standard deviation for risk premium = (1126.198)1/2 = 33.56%
Year
Large-Company Stocks
U.S. Treasury Bills
Risk premium
1
-15.09
7.37
-22.46
2
-26.59
8.03
-34.62
3
37.31
5.95
31.36
4
24.01
5.47
18.54
5
-7.32
5.49
-12.81
6
6.65
7.76
-1.11
18.97
40.07
-21.1