Answer:
Year Treasury Bills Inflation Real return
1 7.82 9.42 -1.48
2 8.6 13.04 -3.93
3 6.44 7.55 -1.03
4 5.6 5.35 0.24
5 6.02 7.31 -1.20
6 8.25 9.67 -1.29
7 11.23 13.98 -2.41
8 12.85 13.37 -0.46
a. Average return for Treasury bill = (7.82 + 8.6 + 6.44 + 5.6 + 6.02 + 8.25 + 11.23 + 12.85) / 8
Average return for Treasury bill = 66.81 / 8
Average return for Treasury bill = 8.35125
Average return for Treasury bill = 8.35
Average annual inflation rate = (9.42 + 13.04 + 7.55 + 5.35 + 7.31 + 9.67 + 13.98 + 13.37) / 8
Average annual inflation rate = 79.69 / 8
Average annual inflation rate = 9.96125
Average annual inflation rate = 9.96
b. X bar = Average
Standard Deviation = (x-X)^2
For year 1 = (7.82 - 8.35)^2 = 0.2809. Hence, the Standard deviation of other years will be calculated and summed-up to give the Standard deviation of Treasury bill return and of Inflation over this period respectively.
Standard deviation of Treasury bill returns = 2.55
Standard deviation of inflation over this period = 3.20
c. Real return for Treasury bills = ((1+nominal return)/(1+inflation rate)-1)*100
For Year 1, Real return = (1 + 7.82%) / (1 + 9.42%) - 1) * 100
Real return = 1 + 0.078 / (1 + 0.0942) - 1 * 100
Real return = (1.078 / 1.0942) -1 * 100
Real return = 0.98519 - 1 * 100
Real return = -0.01480 * 100
Real return = -1.48
Hence, the average real return for Treasury bills over this period = (-1.48 + -3.93 + -1.03 + 0.24 + -1.20 + -1.29 + -2.41 + -0.46) / 8
Average real return for Treasury bills = -11.56 / 8
Average real return for Treasury bills = -1.445