Question

Consider the following rates of return: US Large- Year Company Stocks 1 3.66 % 14.44 3 19.03 -14.65 -32.14 6 37.27 Treasury Bills 4.66 % 2.33 4.12 5.88 4.90 6.33 5 a. Calculate the arithmetic average returns for large-company stocks and T-bills over this period. (Do not round intermediate calculations and 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 and 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 arithmetic average risk premium over this period? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and 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 and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation

Answer 1

a). Arithmetic average = sum of all values/number of values

Arithmetic average for large-company stocks = (3.66% + 14.44% + 19.03% -14.65% -32.14% + 37.27%)/6 = 4.60%

Arithmetic average for Treasury bills = (4.66% + 2.33% + 4.12% + 5.88% + 4.90% + 6.33%)/6 = 4.70%

b). Variance = where n = number of returns; ri = return for period i; r = average return

Σ(ri – r)?

Standard deviation = variance^0.5

Standard deviation for large-company stocks = 22.71%

Standard deviation for Treasury bills = 1.29%

Calculations shown below:

Year (n) Large-company stocks (Rs) 3.66% 14.44% 19.03% -14.65% -32.14% 37.27% (Rs-R)^2 0.0001 0.0097 0.0208 0.0371 0.1350 0.1067 0.3094 0.0516 22.71% Total Return ('R) Standard deviation 4.60%

Year (n) 2 3 4 5 6 Total Return ('R) Standard deviation US Treasury bills (Rt) 4.66% 2 .33% 4.12% 5 .88% 4 .90% 6 .33% (Rt-R)^2 0.0000 0.0006 0.0000 0.0001 0.0000 0.0003 0.0010 0.0002 1.29% 4.70%

c-1). Average risk premium = -0.10%

c-2). Standard deviation of the risk period over this period = 22.81%

Calculations show below:

Year (n) Large-company stocks US Treasury Risk premium (Rs) bills (Rt) (Rp = Rs-Rt) 3.66% 4.66% -1.00% 14.44961 2.33%) 12.11% 19.03% 4.12% 14.91% -14.65% 5.88% -20.53% -32.14% 4.90% -37.04% 37.27% 6.33% 30.94% -0.61% -0.10% (Rp - R)^2 0.0001 0.0149 0.0225 0.0417 0.1364 0.0964 0.3121 0.0520 22.81% Total Return ('R) Standard deviation