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	12 %	21 %
2	30	42
3	19	-8
4	-20	-22
5	21	50

   

Requirement 1:
(a)	Calculate the arithmetic average return for X.
	(Click to select)10.04%12.40%15.13%14.01%15.50%

   

(b)	Calculate the arithmetic average return for Y.
	(Click to select)16.60%20.75%13.45%20.25%18.76%

  

Requirement 2:
(a)	Calculate the variance for X. (Do not round intermediate calculations.)
	(Click to select)0.0461630.0369300.0368120.0460140.029913

   

(b)	Calculate the variance for Y. (Do not round intermediate calculations.)
	(Click to select)0.1211000.0784730.0905290.0968800.113161

  

Requirement 3:
(a)	Calculate the standard deviation for X. (Do not round intermediate calculations.)
	(Click to select)24.02%19.09%19.22%15.57%21.45%

   

(b)	Calculate the standard deviation for Y. (Do not round intermediate calculations.)
	(Click to select)25.21%31.13%38.91%33.64%30.09%

Answer 1

Based on below table

1. (a)Arithmetic average return for X. = 12.40%
(b) Arithmetic average return for Y = 16.60%

2. (a) the variance for X =0.03693
(b) The variance for Y =0.09688

3. ( a) the standard deviation for X = 19.22%
(b) ( a) the standard deviation for Y = 31.13%

	A	B	C	D	E	F	G	H	I
	Returns
	Year	X	Y	Average Returns of X	Average Returns OF Y	Variance Yearly (Return of X - Average of X)^2	Variance Yearly(Return of Y - Average of Y)^2	Standard Deviation of X	Standard Deviation of Y
1	1	12%	21%	12.40%	16.60%	0.000016	0.001936	19.22%	31.13%
2	2	30%	42%	Average(B1:B5)	Average(C1:C5)	0.030976	0.064516	(Standard Deviation = Variance^0.5	(Standard Deviation = Variance^0.6
3	3	19%	-8%	Excel Function	Excel Function	0.004356	0.060516
4	4	-20%	-22%			0.104976	0.148996
5	5	21%	50%			0.007396	0.111556
						0.03693	0.09688
						Total Variance = Sum of Individual Varinace/(n-1)	Total Variance =Sum of Individual Varinace/(n-1)

Best of Luck. God Bless