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))

Year Treasury Bills Inflation 1 7.55            9.02            2 8.29            12.69            3 6.15            7.24            4 5.43            5.20            5 5.83            7.10            6 8.04            9.44            7 11.00            13.72            8 12.58            13.05           

Explanation / Answer

a. Average return for treasury bills = (7.55+8.29+6.15+5.43+5.83+8.04+11+12.58)/8 = 8.11%

Average inflation = (9.02+12.69+7.24+5.2+7.1+9.44+13.72+13.05)/8 = 9.68%

b. Variance of Treasury bill return = ((7.55-8.11)^2 + (8.29-8.11)^2 + ... + (12.58-8.11)^2)/8 = 5.61

Similarly, variance of inflation = ((9.02-9.68)^2 + ...+(13.05-9.68)^2)/8 = 8.74

Std deviation = square root of variance

Std deviation of Treasury bill return = 5.61^0.5 = 2.37%

Std deviation of inflation = 8.74^0.5 = 2.96%

c. Average real return = X

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

So (1+X)^8 * (1+9.68%)^8 = (1+8.11%)^8, so X = -1.43%

So real rate was negative, i.e. -1.43%

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