Suppose we have the following returns for large-company stocks and Treasury bill
ID: 2730625 • Letter: S
Question
Suppose we have the following returns for large-company stocks and Treasury bills over a six year period:
Year Large Company US Treasury Bill
1 3.96 6.56
2 14.46 4.40
3 19.15 4.27
4 –14.53 7.31
5 –32.02 5.20
6 -37.41 6.37
a. 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.)
Average returns
Large company stocks 4.74 %
T-bills 5.69 %
b. 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.)
Standard deviation
Large company stocks 24.87 %
T-bills 1.246 %
c-1 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.)
Average risk premium -0.95 %
c-2 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.)
Standard deviation ?%
Just cannot figure out the standard deviation of the risk premium I have tried everything!
It is not 22.98 or 22.69
Explanation / Answer
Finding the std deviation of the risk premium Year Largr Co US treasury Bill Risk Premium=Rp Average Risk Premium=Rm (Rp-Rm)^2 1 3.96% 6.56% -2.60% -0.95% 0.00027 2 14.46% 4.40% 10.06% -0.95% 0.01211 3 19.15% 4.27% 14.88% -0.95% 0.02505 4 -14.53% 7.31% -21.84% -0.95% 0.04365 5 -32.02% 5.20% -37.22% -0.95% 0.13158 6 37.41% 6.37% 31.04% -0.95% 0.10231 Total 0.314980 Population Variance=Total/6 0.05250 Sample Variance =Total/5 0.06300 Population Sample Variance 0.05250 0.06300 Standard Deviation =Squaret root of variance 22.91% 25.10% So Popoulation std deviation of Risk premium= 22.91% Sample Std Deviation of Risk premium= 25.10%