28.03.2023 - 07:25

Suppose we have the following Treasury bill returns and inflation rates over an eight year period: || Year || Treasury Bills || Inflation 19.4711.32 210.3514.9338.089.284

Suppose we have the following Treasury bill returns and inflation rates over an eight year period:

Year Treasury Bills Inflation
1 9.47 11.32
2 10.35 14.93
3 8.08 9.28
4 7.15 6.81
5 7.66 9.04
6 9.98 11.49
7 12.83 15.67
8 14.63 15.53

a. Calculate the average return for Treasury bills and the average inflation rate ?

b. Calculate the standard deviation of Treasury bills and the average annual inflation rate?

c. What was the average real return for Treasury bills over this period?

Answers (1)
  • DJMaxwell
    April 2, 2023 в 13:54

    a. To calculate the average return for Treasury bills and the average inflation rate, we simply need to add up all the values and divide by the total number of years:

    Average return for Treasury bills = (9.47 + 10.35 + 8.08 + 7.15 + 7.66 + 9.98 + 12.83 + 14.63) / 8 = 10.15%

    Average inflation rate = (11.32 + 14.93 + 9.28 + 6.81 + 9.04 + 11.49 + 15.67 + 15.53) / 8 = 11.42%

    Therefore, the average return for Treasury bills over this period was 10.15% and the average inflation rate was 11.42%.

    b. To calculate the standard deviation of Treasury bills and the average annual inflation rate, we can use the following formula:

    Standard deviation = sqrt(sum of (x - mean)^2 / n)

    where x is each individual value, mean is the average value, and n is the total number of values.

    For Treasury bills:

    mean = 10.15%

    n = 8

    Using a spreadsheet or calculator, we get:

    Standard deviation for Treasury bills = 3.02%

    For inflation:

    mean = 11.42%

    n = 8

    Using a spreadsheet or calculator, we get:

    Standard deviation for inflation = 3.22%

    Therefore, the standard deviation of Treasury bills over this period was 3.02% and the standard deviation of inflation was 3.22%.

    c. The real return for Treasury bills is the return adjusted for inflation. We can calculate the average real return for Treasury bills over this period using the following formula:

    Average real return = (1 + average return for Treasury bills) / (1 + average inflation rate) - 1

    Substituting the values we calculated earlier, we get:

    Average real return = (1 + 0.1015) / (1 + 0.1142) - 1 = -0.0115 or -1.15%

    Therefore, the average real return for Treasury bills over this period was -1.15%. This means that, on average, the return on Treasury bills did not keep up with inflation over this period.

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