Suppose we have the following Treasury bill returns and inflation rates over an
ID: 2766858 • Letter: S
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 for this period. (Do not round intermediate calculations. Enter your answers as a percent rounded 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. Enter your answers as a percent rounded 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. Do not round intermediate calculations. Enter your answer as a percent rounded 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
Year
Treasury Bill
Inflation Rate
Real Return
1
7.37%
8.79%
-1.42%
2
8.07%
12.42%
-4.35%
3
5.95%
7.02%
-1.07%
4
5.15%
4.94%
0.21%
5
5.53%
6.78%
-1.25%
6
7.72%
9.10%
-1.38%
7
10.64%
13.37%
-2.73%
8
12.18%
12.60%
-0.42%
Total
62.61%
75.02%
-12.41%
Average return for Treasury bill = 62.61%/8 = 7.82625%
Average return for inflation rate = 75.02%/8 = 9.3775%
Average real return for Treasury bill = -12.41%/8 = -1.55125%
To find out standard deviation, we first need to calculate variance. Using the equation for variance, we find the variance for treasury bill for this period was:
Variance for Treasury Bills = 1/5*[(.0737 – .0782625)2 + (.0807 – .0782625)2 + (.0595 – .0782625)2 + (.0515 – .0782625)2 + (0.0553 – .0782625)2 + (0.0772 – .0782625)2 + (0.1064 – .0782625)2 + (0.1218 – .0782625)2]
Variance = 0.000862132
Standard Deviation for Treasury Bills = Variance1/2 = 0.0008621321/2 = 0.02936208
Variance for Inflation Ratio = 1/5*[(.0879 – .093775)2 + (.1242 – .093775)2 + (.0702 – .093775)2 + (.0494 – .093775)2 + (0.0678 – .093775)2 + (0.0910 – .093775)2 + (0.1337 – .093775)2 + (0.1260 – .093775)2]
Variance = 0.001359995
Standard Deviation for Inflation rate = Variance1/2 = 0.001359995 1/2 = 0.03687811
Year
Treasury Bill
Inflation Rate
Real Return
1
7.37%
8.79%
-1.42%
2
8.07%
12.42%
-4.35%
3
5.95%
7.02%
-1.07%
4
5.15%
4.94%
0.21%
5
5.53%
6.78%
-1.25%
6
7.72%
9.10%
-1.38%
7
10.64%
13.37%
-2.73%
8
12.18%
12.60%
-0.42%
Total
62.61%
75.02%
-12.41%
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