Suppose we have the following returns for large-company stocks and Treasury bill
ID: 2653100 • 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. (Round your answers 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 and round your final answers 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 and round your final answer 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 and round your final answer 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
Year Large Company (%) US Treasury Bill (%) 1 3.96 6.56 2 14.46 4.4 3 19.15 4.27 4 -14.53 7.31 5 -32.02 5.2 6 37.41 6.37 A. Arithmetic Return for Large Company stock = (sum of returns in each year)/No. of years Arithmetic Return for Large Company stock = (3.96 + 14.46+19.15-14.53-32.02+37.41)/6 Arithmetic Return for Large Company stock = 4.738% Arithmetic Return for US Treasury Bill = (sum of returns in each year)/No. of years Arithmetic Return for US Treasury Bill = (6.56+4.4+4.27+7.31+5.2+6.37)/6 Arithmetic Return for US Treasury Bill = 5.685% B. Standard Deviation (SD) of Large company stocks (entire population is assumed) SD = ((Sum of the square of difference in return and mean return)/n)^(1/2) X = 4.738% SD =( ((x1-X)^2 + (x2-X)^2 +(x3-X)^2 +(x4-X)^2 +(x5-X)^2 +(x6-X)^2 )/6)^(1/2) SD= (((3.96 - 4.738)^2 + (14.46-4.738)^2 + (19.15 - 4.738)^2 + (-14.53 - 4.738)^2 + (-32.02 - 4.738)^2+ (37.41 - 4.738)^2)/6)^(1/2) SD = 22.70% Standard Deviation (SD) of Large US Treasury bills (entire population is assumed) SD = ((Sum of the square of difference in return and mean return)/n)^(1/2) X = 5.685% SD =( ((x1-X)^2 + (x2-X)^2 +(x3-X)^2 +(x4-X)^2 +(x5-X)^2 +(x6-X)^2 )/6)^(1/2) SD = (( (6.56-5.685)^2 +(4.4-5.685)^2 +(4.27-5.685)^2 +(7.31-5.685)^2 +(5.2-5.685)^2 +(6.37-5.685)^2 ) /6)^(1/2) SD = 1.137% C1 Year Large Company (%) US Treasury Bill (%) Observed Risk Premium (%) = Return on large stock - T-bills return 1 3.96 6.56 -2.60 2 14.46 4.4 10.06 3 19.15 4.27 14.88 4 -14.53 7.31 -21.84 5 -32.02 5.2 -37.22 6 37.41 6.37 31.04 Arithmetic Average of observed risk premium = (Sum of risk premium of each year)/no. of years Arithmetic Average of observed risk premium = (-2.6 + 10.06+14.88-21.84-37.22+31.04)/6 Arithmetic Average of observed risk premium = -.95% approx. C2 X = -.95 SD = ((Sum of the square of difference in return and mean return)/n)^(1/2) SD =( ((x1-X)^2 + (x2-X)^2 +(x3-X)^2 +(x4-X)^2 +(x5-X)^2 +(x6-X)^2 )/6)^(1/2) SD = (((-2.60 - .95)^2 + (10.06 - .95)^2 + (14.88 - .95)^2 + (-21.84 - .95)^2 + (-37.22 - .95)^2 + (31.04 - .95)^2 )/6)^(1/2) SD = 22.99% approx.