Question

Consider the following table for a period of six years:

	Returns
Year	Large-Company Stocks					U.S. Treasury Bills
1		–	15.89	%		7.53	%
2		–	26.83			8.11
3			37.47			6.11
4			24.17			6.27
5		–	7.64			5.57
6			6.81			8.00

a-1.	Calculate the arithmetic average returns for large-company stocks and T-bills 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.)
a-2.	Calculate the standard deviation of the returns for large-company stocks and T-bills 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.)

Calculate the observed risk premium in each year for the large-company stocks versus the T-bills.
b-1.	What was the arithmetic average risk premium 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.)
b-2.	What was the standard deviation of the risk premium over this period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a 1)The arithmatic avg for stock is 3.01 and for T bill is 6.93

	X
	-15.89
	-26.83
	37.47
	24.17
	-7.64
	6.81
Average of stock returns	3.015

	Y
	7.53
	8.11
	6.11
	6.27
	5.57
	8
Average of T-bill returns	6.931667

a2) The standard dev for Stock is 24.53 and for T bill is 1.08  

Note: we have considered sample mean, so we have divided the sum by 5

	X	X- X avg	(X- X avg)^2	Std dev
	-15.89	-18.905	357.399025
	-26.83	-29.845	890.724025
	37.47	34.455	1187.147025
	24.17	21.155	447.534025
	-7.64	-10.655	113.529025
	6.81	3.795	14.402025
Sample Average of stock returns	3.015		Sample Mean= 602.14	sqrt mean= 24.53

	Y	Y-Y avg	( Y-Y avg)^2	Std dev
	7.53	0.6	0.36
	8.11	1.18	1.3924
	6.11	-0.82	0.6724
	6.27	-0.66	0.4356
	5.57	-1.36	1.8496
	8	1.07	1.1449
Average of T-bill returns	6.93		Sample mean=1.17098	sqrt mean= 1.08

B1) The arithmatic average of Risk premium is -3.9166 or -3.92

	X	Y	X- Y
	-15.89	7.53	-23.42
	-26.83	8.11	-34.94
	37.47	6.11	31.36
	24.17	6.27	17.9
	-7.64	5.57	-13.21
	6.81	8	-1.19
Average of Risk Premium			-3.916666667

B2) The standard dev of Risk premium is 25.12

	Z	Z-Z avg	(Z-Z avg)^2	Std dev
	-23.42	-19.5033	380.3798811
	-34.94	-31.0233	962.4470043
	31.36	35.27667	1244.443446
	17.9	21.81667	475.9670899
	-13.21	-9.29333	86.36598249
	-1.19	2.72667	7.434729289
Average of Risk prem	-3.91667		Sample mean=631.40	sqrt mean=25.12

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