Using the following returns, calculate the arithmetic average returns, the varia

Question

Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y Returns Year 19% 40 27 16 -14 4 28 48 18 Requirement 1 (a) Calculate the arithmetic average return for X. 10.60% (b) Calculate the arithmetic average return for Y 13.00% Requirement 2 (a) Calculate the variance for X. (Do not round intermediate calculations.) (Click to select) (b) Calculate the variance for Y. (Do not round intermediate calculations.) Click to select) Requirement 3 (a) Calculate the standard deviation for X. (Do not round intermediate calculations.) Click to select) (b) Calculate the standard deviation for Y. (Do not round intermediate calculations.) (Click to select)

Explanation / Answer

Requirement 2:

a)

Variance of X = [( 0.09 - 0.1060)2 + ( 0.27 - 0.1060)2 + ( 0.16 - 0.1060)2 + ( -0.17 - 0.1060)2 + ( 0.18 - 0.1060)2] / 5 - 1

Variance of X = [ 0.000256 + 0.026896 + 0.002916 + 0.076176 + 0.005476] / 4

Variance of X = 0.11172 / 4

Variance of X = 0.02793

b)

Variance of Y = [( 0.19 - 0.13)2 + ( 0.4 - 0.13)2 + ( -0.14 - 0.13)2 + ( -0.28 - 0.13)2 + ( 0.48 - 0.13)2] / 5 - 1

Variance of Y = [ 0.0036 + 0.0729 + 0.0729 + 0.1681 + 0.1225] / 4

Variance of Y = 0.44

Variance of Y = 0.11

Requirement 3

a)

Standard deviation of X = ( 0.02793 ) 1/2

Standard deviation of X = 0.167123 or 16.7123%

b)

Standard deviation of Y = ( 0.11 ) 1/2

Standard deviation of Y = 0.331662 or 33.1662%

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