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: Year Treasury Bills Inflation 1 8.11% 9.83% 2 8.92 13.36 3 6.74 7.87 4 5.88 5.61 5 6.32 7.63 6 8.57 10.01 7 11.55 14.32 8 13.21 13.77 a. Calculate the average return for Treasury bills and the average annual inflation rate for this period. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Treasury bills 8.66 % Inflation 10.30 % b. Calculate the standard deviation of Treasury bill returns and inflation over this period. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Treasury bills 2.57 % Inflation 3.23 % c. What was the average real return for Treasury bills over this period? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Average real return % ReferenceseBook & Resources

Explanation / Answer

a.The average Returns for T-bills andInflation rates are as follows

b. Calculation of  the standard deviation of Treasury bill returns and inflation over this period.

T- bill Variance= 1/7( (8.11%-8.66%)2+(8.92%-8.66%)2+(6.74%-8.66%)2+(5.88%-8.66%)2+(6.32%-8.66%)2+(8.57%-8.66%)2+(11.55%-8.66%)2+(13.21%-8.66%)2)

= 6.62

Standard Deviation T- bill =( 6.62)^0.5 = 2.57%

Inflation Variance= 1/7((9.83%-10.3%)2+ (13.36%-10.3%)2+ (7.87%-10.3%)2+ (5.61%-10.3%)2+ (7.63%-10.3%)2+ (10.01%-10.3%)2+ (14.32%-10.3%)2+ (13.77%-10.3%)2

= 10.41

Inflation Standard Deviation =( 10.41)^0.5 = 3.23%

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

To find average real return we will use fisher's equation

r = ((1+R)/(1+h)) -1

Year Treasury bill returns % Inflation Rates % 1 8.11 9.83 2 8.92 13.36 3 6.74 7.87 4 5.88 5.61 5 6.32 7.63 6 8.57 10.01 7 11.55 14.32 8 13.21 13.77 Total 69.3 82.4 Average Return        8.66%      10.30% (69.3/8) (82.4/8)

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