Question

Suppose we have the following Treasury bill returns and inflation rates over an eight-year period: Year Treasury Bills Inflation 1 8.11%         9.83%         2 8.92            13.36            3 6.74            7.87            4 5.88            5.61            5 6.32            7.63            6 8.57            10.01            7 11.55            14.32            8 13.21            13.77            a. Calculate the average return for Treasury bills and the average annual inflation rate for this period. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. Calculate the standard deviation of Treasury bill returns and inflation over this period. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c. What was the average real return for Treasury bills over this period? (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.)

Answer 1

Year	Treasury Bills	Year	T	I	Dt= T-MeanT	Dt2	Di= I-MeanI	Di2
1	8.11	1	8.11	9.83	(0.55)	0.31	(0.47)	0.2
2	8.92	2	8.92	13.36	0.26	0.07	3.06	9.4
3	6.74	3	6.74	7.87	(1.92)	3.70	(2.43)	5.9
4	5.88	4	5.88	5.61	(2.78)	7.74	(4.69)	22.0
5	6.32	5	6.32	7.63	(2.34)	5.49	(2.67)	7.1
6	8.57	6	8.57	10.01	(0.09)	0.01	(0.29)	0.1
7	11.55	7	11.55	14.32	2.89	8.34	4.02	16.2
8	13.21	8	13.21	13.77	4.55	20.68	3.47	12.0
			69.30	82.40		46.32		72.90

(a)

Average Return (MeanA)= ∑A/n

Average Return (MeanT)= ∑T/n

= 69.3 / 8 = 8.66   

Average Return (MeanI) = ∑I/n

= 82.4 / 8 = 10.3

(b)

Standard Deviation A = √ ( da2/ n )

Standard Deviation T = √ ( dt2/ n )

= √ 46.32 / 8 = 2.406

Standard Deviation I = √ ( dI2/ n )

= √ (72.90/ 8) = 3.019

(c)Assuming the above returns of T-Bills include the inflation effect, we have to remove the effect of inflation from the T-Bills,

T	I	R= T- I (%)
8.11	9.83	7.31
8.92	13.36	7.73
6.74	7.87	6.21
5.88	5.61	5.55
6.32	7.63	5.84
8.57	10.01	7.71
11.55	14.32	9.90
13.21	13.77	11.39
		61.64

Average Real Return (MeanT)= ∑R / n

= 61.64 / 8 = 7.705