Question

Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. Returns Year X Y 1 11 % 20 % 2 29 41 3 18 -12 4 -19 -26 5 20 49 Requirement 1: (a) Calculate the arithmetic average return for X. (b) Calculate the arithmetic average return for Y. Requirement 2: (a) Calculate the variance for X. (Do not round intermediate calculations.) (b) Calculate the variance for Y. (Do not round intermediate calculations.) Requirement 3: (a) Calculate the standard deviation for X. (Do not round intermediate calculations.) (b) Calculate the standard deviation for Y. (Do not round intermediate calculation

Answer 1

Requirement 1:

(a) Arithmetic average return for X

Year	return(%)
1	11
2	29
3	18
4	-19
5	20
	59
Arithimetic average = 59 / 5 = 11.8%

(b) Arithmetic average return for Y

Year	return(%)
1	20
2	41
3	-12
4	-26
5	49
	72
Arithimetic average = 72 / 5 = 14.4%

Requirement 2:

(a) Variance for X

Year	GR(%)	AR(%)	(GR-AR)	(GR-AR)^2
1	11	11.8	-0.8	0.64
2	29	11.8	17.2	295.84
3	18	11.8	6.2	38.44
4	-19	11.8	-30.8	948.64
5	20	11.8	8.2	67.24
			TOTAL	1350.8
	Variance = 1350.8 / 5 = 270.16

(b)  Variance for Y

Year	GR(%)	AR(%)	(GR-AR)	(GR-AR)^2
1	20	14.4	5.6	31.36
2	41	14.4	26.6	707.56
3	-12	14.4	-26.4	696.96
4	-26	14.4	-40.4	1632.16
5	49	14.4	34.6	1197.16
			TOTAL	4265.2
	Variance = 4265.2 / 5 = 853.04

Requirement 3:

(a) standard deviation for X = square root of variance of X = 16.4365446%

(a) standard deviation for Y = square root of variance of Y = 29.2068485%