Suppose we have the following returns for large-company stocks and Treasury bill
ID: 2762478 • 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 3.92 5.90 2 14.18 2.53 3 19.37 3.76 4 –14.31 7.16 5 –31.80 5.42 6 37.08 6.24 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 % T-bills % 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 % T-bills % 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 % 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 %
Explanation / Answer
Solution:
Average Return = Sum of Returns / Number of years Year Company Stock US Treasury Bill 1 3.92% 5.90% 2 14.18% 2.53% 3 19.37% 3.76% 4 -14.31% 7.16% 5 -31.80% 5.42% 6 37.08% 6.24% Sum 28% 31% Number of years 6 6 Average Return = 4.74% 5.17% Variance = (Sum of square of difference between returns and average returns )/ Number of Year Company Stock Year Returns - Average returns Returns - Average returns * Returns - Average returns 1 -0.820% 0.01% 2 9.440% 0.89% 3 14.630% 2.14% 4 -19.050% 3.63% 5 -36.540% 13.35% 6 32.340% 10.46% Sum of square of difference between returns and average returns 30.48% Variance = Sum / Number of Year 5.08% Standard Deviation = Square root of Variance 22.54% US Treasury Bill Year Returns - Average returns Returns - Average returns * Returns - Average returns 1 0.732% 0.01% 2 -2.638% 0.07% 3 -1.408% 0.02% 4 1.992% 0.04% 5 0.252% 0.00% 6 1.072% 0.01% Sum of square of difference between returns and average returns 0.15% Variance = Sum / Number of Year 0.024% Standard Deviation = Square root of Variance 1.56%