Question

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

Year	Treasury Bills	Inflation
1	7.37%	8.79%
2	8.07	12.42
3	5.95	7.02
4	5.15	4.94
5	5.53	6.78
6	7.72	9.10
7	10.64	13.37
8	12.18	12.60

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.)

Answer 1

Standard Deviation of Treasury Bills

Possible Returns(xi) Deviation(xi-mean of xi) Deviation squared

7.37 -0.46 0.21

8.07 0.24 0.06

5.95 -1.88 3.52

5.15 -2.68 7.16

5.53 -2.30 5.27

7.72 -0.11 0.01

10.64 2.81 7.92

12.18 4.35 18.96

43.11

Mean of xi Sum/Number

62.61/8

7.83

Standard Deviation Mean of Deviation Squared

43.11/8

5.39

Standard Deviation of Inflation

Possible Returns(xi) Deviation(xi-mean of xi) Deviation squared

8.79 -0.59 0.35

12.42 3.04 9.26

7.02 -2.36 5.56

4.94 -4.44 19.69

6.78 -2.60 6.75

9.1 -0.28 0.08

13.37 3.99 15.94

12.6 3.22 10.38

68.00

Mean of xi Sum/Number

75.02/8

9.38

Standard Deviation Mean of Deviation Squared

68/8

8.50

Average Real rate of return

Real Rate of Return {(1+nominal rate)/(1+inflation rate)}-1

Year Calculation Calculation Real Rate of return

1 {(1+0.0737)/(1+0.0879)}-1 0.9869 -0.0131

2 {(1+0.0807)/(1+0.1242)}-1 0.9613 -0.0387

3 {(1+0.0595)/(1+0.0702)}-1 0.9900 -0.0100

4 {(1+0.0515)/(1+0.0494)}-1 1.0020 0.0020

5 {(1+0.0553)/(1+0.0678)}-1 0.9883 -0.0117

6 {(1+0.0772)/(1+0.0910)}-1 0.9874 -0.0126

7 {(1+0.1064)/(1+0.1337)}-1 0.9759 -0.0241

8 {(1+0.1218)/(1+0.1260)}-1 0.9963 -0.0037

-0.1119

Average Real rate of Return Total/Number

-0.014

-1.40%