Assume these are the stock market and Treasury bill returns for a 5-year period
ID: 2616218 • Letter: A
Question
Assume these are the stock market and Treasury bill returns for a 5-year period Year Year 1 Year 2 Year 3 Year 4 Year 5 T-Bill Return 1.70 20 13 05 07 Stock Market Return -37.13 28.40 17.06 1.08 16.16 a. What was the risk premium on common stock in each year? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Year Year 1 Year 2 ear 3 Year 4 Year 5 Risk premiu b. What was the average risk premium? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Average risk premium c. What was the standard deviation of the risk premium? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Standard deviatioExplanation / Answer
a. Risk Premium = Expected Stock Market Return - T-Bill
Risk Premiums,
For Year 1 = -37.13% - 1.70% = -38.83%
For Year 2 = 28.40% - 0.20% = 28.20%
For Year 3 = 17.06% - 0.13% = 16.93%
For Year 4 = 1.08% - 0.05% = 1.03%
For Year 5 = 16.16% - 0.07% = 16.09%
b. Average Risk Premium = (-38.83% + 28.20% + 16.93% + 1.03% + 16.09%)/5 = 4.68% --> Answer
c. Standard deviation is mathematically given by:
Risk Premium
Squared Deviations from Mean
-38.83%
= (-0.3883 - 0.04684)^2 = 0.18935
28.20%
= (0.282 - 0.04684)^2 = 0.05530
16.93%
= (0.1693 - 0.04684)^2 = 0.01500
1.03%
= (0.0103 - 0.04684)^2 = 0.00134
16.09%
= (0.1609 - 0.04684)^2 = 0.01301
Standard devaition2 = Sum of all squared deviations/(n - 1) = 0.27399/4 = 0.068497
Standard deviation = 26.17% --> Answer
Risk Premium
Squared Deviations from Mean
-38.83%
= (-0.3883 - 0.04684)^2 = 0.18935
28.20%
= (0.282 - 0.04684)^2 = 0.05530
16.93%
= (0.1693 - 0.04684)^2 = 0.01500
1.03%
= (0.0103 - 0.04684)^2 = 0.00134
16.09%
= (0.1609 - 0.04684)^2 = 0.01301