Question

Suppose we have the following Treasury bill returns and inflation rates over an eight year period:Year Treasury Bills (%) Inflation (9%)1 7.82 9.422 8.6 13.043 6.44 7.554 5.6 5.355 6.02 7.316 8.25 9.677 11.23 13.988 12.85 13.37a. Calculate the average return for Treasury bills and the average annual inflation rate for this period.b. Calculate the standard deviation of Treasury bill returns and inflation over this period.c. What was the average real return for Treasury bills over this period?

Answer 1

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