Question

Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. ReturnsYear X Y1 15% 21%2 26 36 3 7 13 4 â13 â26 5 11 15

Answer 1

Answer:

A) X = 9.2%, Y = 11.8%

B) VARX = 204.2, VARY = 527.7

C) SD.X = 14.29, SD.Y = 22.97

Explanation:

Given that;

                           Returns

year                     X                  Y

1                           15%               21%

2                          26                 26

3                          7                    13

4                         -13                 -26

5                          11                   15

a) arithmetic average returns (mean)

Mean = ∑x / n

Mean X = [15 + 26 + 7 - 13 + 11] / 5 = 46 / 5 = 9.2%

MeanY = [21 + 36 + 13 - 26 + 15] / 5 = 59 / 5 = 11.8 %

b) the variances

VAR =  ∑(x-mean)² / n-1

VARX = [(15 - 9.2)² + (26 - 9.2)² + (7 - 9.2)³ + (-13 - 9.2)² + (11 - 9.2)²] / (5 - 1)

= [33.64 + 282.24 + 4.84 + 492.84 + 3.24] / 4 = 816.8 / 4 = 204.2

VARY = [(21 - 11.8)² + (36 - 11.8)² + (13 - 11.8)² + (-26 - 11.8)² + (15 - 11.8)²] / (5 - 1)

= [84.64 + 585.64 + 1.44 + 1,428.84 + 10.24] / 4 = 2,110.8 / 4 = 527.7

c) the standard deviations

SD = √ Variance

SD.X = √204.2 = 14.29%

SD.Y = √527.7 = 22.97%