Suppose we have the following Treasury bill returns and inflation rates over an

Question

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

Calculate the average return for Treasury bills and the average annual inflation rate (consumer price index) for this period. (Round your answers to 2 decimal places. (e.g., 32.16))

Calculate the standard deviation of Treasury bill returns and inflation over this period. (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

What was the average real return for Treasury bills over this period? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places. (e.g., 32.16))

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

Explanation / Answer

a. Average return for treasury bills = (8.81+9.66+7.42+6.52+7.00+9.29+12.11+13.85)/8 = 9.33%

Average inflation = (10.60+14.18+8.59+6.21+8.35+10.77+14.92+14.60)/8 = 11.02%

b. Variance of Treasury bill return = ((8.81-9.33)^2 + (9.66-9.33)^2 + ... + (13.85-9.66)^2)/8 = 5.32

Similarly, variance of inflation = ((10.60-11.02)^2 + (14.18-11.02)^2 +(8.59-11.02)^2+(6.21-11.02)^2+(8.35-11.02)^2+(10.77-11.02)^2+ (14.92-11.02)^2+(14.60-11.02)^2)/8 = 9.30

Std deviation = square root of variance

Std deviation of Treasury bill return = 5.32^0.5 = 2.306%

Std deviation of inflation = 9.3^0.5 = 3.05%

c. Average real return = X

(1+X)^8 * (1+inflation)^8 = (1+nominal return)^8

So (1+X)^8 * (1+11.02%)^8 = (1+9.33%)^8,

(1+X)^8 = 0.8845

so X = -0.015%

So real rate was negative, i.e. -0.015%

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