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

9 %    

20 %    

2

27        

41        

3

16        

-14        

4

-17        

-28        

5

18        

49        

Requirement 1:

(a)

Calculate the arithmetic average return for X.

13.25

8.59

10.60

11.98

12.93

(b) Calculate the arithmetic average return for Y. 13.60% 17% 16.59% 15.37% 11.02%

Requirement 2:

(a) Calculate the variance for X. (Do not round intermediate calculations.)

0.034912

0.027655

0.027930

0.022623

0.034568

(b)	Calculate the variance for Y. (Do not round intermediate calculations.)

0.113430

0.141787

0.124358

0.099486

0.091878

3.

(a)	Calculate the standard deviation for X. (Do not round intermediate calculations.)

18.59%

13.54%

16.53%

16.71%

20.89%

(b) Calculate the standard deviation for Y. (Do not round intermediate calculations.) 42.10% 33.68% 31.54% 27.28% 35.26%

Answer 1

a) arithmetic average return for X = (9+27+16-17+18)/5 = 10.6%

b) arithmetic average return for Y = (20+41-14-28+49)/5 = 13.6%

c) variance for X = [(0.09-0.106)² + (0.27-0.106)² + (0.16-0.106)² + (-0.17-0.106)² + (0.18-0.106)²]/(5-1)

= 0.027930

d) variance for Y = [(0.2-0.136)² + (0.41-0.136)² + (-0.14-0.136)² + (-0.28-0.136)² + (0.49-0.106)²]/(5-1)

= 0.113430

e) standard deviation for X = sqrt(0.027930) = 16.71%

f)  standard deviation for Y = sqrt(0.113430) = 33.68%