Question

Suppose we have the following Treasury bill returns and inflation rates over an eight- year period: Year WN Treasury Bills 10.45% 11.36 9.06 8.34 8.88 11.23 14.11 15.97 Inflation 12.55% 16.00 10.29 7.97 10.29 12.77 16.98 16.90 00 O a. Calculate the arithmetic average return for Treasury bills and the average annual inflation rate (consumer price index) for this period. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Average return Treasury bills Inflation

Answer 1

Year	Treasury Bills	Inflation
1	10.45%	12.55%
2	11.36%	16.00%
3	9.06%	10.29%
4	8.34%	7.97%
5	8.88%	10.29%
6	11.23%	12.77%
7	14.11%	16.98%
8	15.97%	16.90%

[a] Arithmetic average for Treasury Bills would be sum of all the rates divided by number of years

Treasury average = 89.40/8

= 11.175%

Arithmetic average for Inflation would be sum of all the rates divided by number of years

Inflation average = 103.75/8

= 12.968%

[b] Standard Deviation Formula

2 \x – ī| 2 SD = 1 m

Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean), or expected value.

Year	Treasury Bills	Xi-(Avg of Xi) Squared	Inflation	Xi-(Avg of Xi) Squared
1	10.45%	0.01%	12.55%	0.00%
2	11.36%	0.00%	16.00%	0.09%
3	9.06%	0.04%	10.29%	0.07%
4	8.34%	0.08%	7.97%	0.25%
5	8.88%	0.05%	10.29%	0.07%
6	11.23%	0.00%	12.77%	0.00%
7	14.11%	0.09%	16.98%	0.16%
8	15.97%	0.23%	16.90%	0.15%
Average	11.18%		12.97%
	Sum of Deviations	0.50%		0.80%
	Sum of Deviations/n	0.06%		0.10%
	Square root	2.50%		3.17%

[C] Real Return = Treasury Return - Inflation

Year	Treasury Bills	Inflation	Real Return
1	10.45%	12.55%	-2.10%
2	11.36%	16.00%	-4.64%
3	9.06%	10.29%	-1.23%
4	8.34%	7.97%	0.37%
5	8.88%	10.29%	-1.41%
6	11.23%	12.77%	-1.54%
7	14.11%	16.98%	-2.87%
8	15.97%	16.90%	-0.93%
Average	11.18%	12.97%	-1.79%

Real Return = -1.79%