Question

Consider the following table for an eight-year period:

Year	T-bill return		Inflation
1	7.31	%	8.69	%
2	8.14		12.32
3	5.89		6.92
4	5.17		4.88
5	5.47		6.68
6	7.74		9.00
7	10.58		13.27
8	12.20		12.50

Calculate the 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 for Treasury bills	%
Average annual inflation rate	%

Calculate the standard deviation of Treasury bill returns and inflation over this time period. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation of Treasury bills	%
Standard deviation of inflation	%

(a)Calculate the real return for each year. (A negative answer should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Year	Real return
1	%
2	%
3	%
4	%
5	%
6	%
7	%
8	%

(c)What is the average real return for Treasury bills? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Average real return for Treasury bills             %

Answer 1

Since it is not mentioned whether arithmatic or geometric average is required, I have calculated the geometric averages:

T-Bill average return '=(1.0731*1.0814*1.0589*1.0517*1.0547*1.0774*1.1058*1.122)^(1/8)-1 = 7.79%

Inlation average rate =(1.0869*1.1232*1.0692*1.0488*1.0668*1.09*1.1327*1.125)^(1/8) - 1 = 9.24%

2) Calculation of Standard deviation

Standard Deviation : T-Bills
Year	T-bill return (X)	Mean (x?)	( x-x? )	( x-x? )^2
1.00	7.31%	7.79%	-0.48%	0.00%
2.00	8.14%	7.79%	0.35%	0.00%
3.00	5.89%	7.79%	-1.90%	0.04%
4.00	5.17%	7.79%	-2.62%	0.07%
5.00	5.47%	7.79%	-2.32%	0.05%
6.00	7.74%	7.79%	-0.05%	0.00%
7.00	10.58%	7.79%	2.79%	0.08%
8.00	12.20%	7.79%	4.41%	0.19%
Sum of (( x-x? )^2)				0.43%

Standard Deviation = (Sum of (( x-x? )^2)/(n-1))^(1/2)= (0.43%/(8-1))^(1/2) = 2.48%

Standard Deviation : Inflation
Year	Inflation (y)	Mean (?)	( y-? )	( y-? )^2
1.00	8.69%	9.24%	-0.55%	0.00%
2.00	12.32%	9.24%	3.08%	0.09%
3.00	6.92%	9.24%	-2.32%	0.05%
4.00	4.88%	9.24%	-4.36%	0.19%
5.00	6.68%	9.24%	-2.56%	0.07%
6.00	9.00%	9.24%	-0.24%	0.00%
7.00	13.27%	9.24%	4.03%	0.16%
8.00	12.50%	9.24%	3.26%	0.11%
Sum of (( y-? )^2)				0.68%

Standard Deviation = (Sum of (( y-? )^2)/(n-1))^(1/2)= (0.68%/(8-1))^(1/2) = 3.12%

3) Calcualtion of real rates for each year and average real rate

Real return = ((1+T-bill return)/(1+inflation)) -1

Year	Real return
1.00	=(1+0.0731)/(1+0.0869) = -0.0127
2.00	=(1+0.0814)/(1+0.1232) = -0.0372
3.00	=(1+0.0589)/(1+0.0692) = -0.0096
4.00	=(1+0.0517)/(1+0.0488) = 0.0028
5.00	=(1+0.0547)/(1+0.0668) = -0.0113
6.00	=(1+0.0774)/(1+0.09) = -0.0116
7.00	=(1+0.1058)/(1+0.1327) = -0.0237
8.00	=(1+0.122)/(1+0.125) = -0.0027

Average real return =(0.9873*0.9628*0.9904*1.0028*0.9887*0.9884*0.9763*0.9973)^(1/8) - 1 = -1.33%

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