Question

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

Year	Treasury Bills	Inflation
1	9.23%	11.07%
2	10.10	14.66
3	7.84	9.03
4	6.92	6.59
5	7.42	8.79
6	9.73	11.23
7	12.57	15.40
8	14.35	15.20

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	%
Inflation	%

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	%
Inflation	%

   

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

%

Answer 1

(a) Average = sum of all returns/no. of years

Year	T.E Return (%)	Inflation rate (%)
1	9.23	11.07
2	10.1	14.66
3	7.84	9.03
4	6.92	6.59
5	7.42	8.79
6	9.73	11.23
7	12.57	15.4
8	14.35	15.2
Avg	9.77	11.49

(b) Standard Deviation is the square root of Variance. We have calculated variance as under:-

Year	T.E Return	Deviation from mean 9.77	square of deviation
1	9.23	0.54	0.29
2	10.1	0.33	0.11
3	7.84	1.93	3.72
4	6.92	2.85	8.12
5	7.42	2.35	5.52
6	9.73	0.04	0.001
7	12.57	2.8	7.84
8	14.35	4.58	20.97
			46.571
		Variance	5.821375

So SD of TE. Return= (5.82)^1/2= 2.41

Inflation	Deviation from mean 11.49	square of deviation
11.07	0.42	0.17
14.66	3.17	10.05
9.03	2.46	6.05
6.59	4.9	24.01
8.79	2.7	7.29
11.23	0.26	0.07
15.4	3.91	15.29
15.2	3.71	13.76
		76.69
	Variance	9.58625

Standard Deviation of Inflation= (9.58)^1/2= 3.09 (c) Average resl return= sum(Return on T.E- Inflation)/8 Year T.E Return (%) Inflation rate (%) Real return (T.E Return- Inflation) 1 9.23 11.07 -1.84 2 10.1 14.66 -4.56 3 7.84 9.03 -1.19 4 6.92 6.59 0.33 5 7.42 8.79 -1.37 6 9.73 11.23 -1.5 7 12.57 15.4 -2.83 8 14.35 15.2 -0.85 Mean 9.77 11.49625 -1.72625 -1.94203125