Using the following returns calculate the arithmetic average

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)

Solution

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%