Question

Using the following returns, calculate the average return, the variances, and the standard deviations for X and Y:

Returns

Year X Y

1 9% 12%

2 21 27

3 -27 -32

4 15 14

5 23 36

Answer 1

Average return = sum of return / no of years

Variance = sum of ( x -m) / n

where m = average return , n is the no of years

Standard deviation = variance ^0.5

Years	Return (x)	x-m	(x-m)^2
1	9	0.8	0.64
2	21	12.8	163.84
3	-27	-35.2	1239.04
4	15	6.8	46.24
5	23	14.8	219.04
Total	41		1668.80

Average return of X = 41 / 5 = 8.20%

Variance of X = 1668.80 / 5 = 333.76%

Standard deviation of X= 333.76^0.5 = 18.27%

Years	Return (x)	x-m	(x-m)^2
1	12	0.6	0.36
2	27	15.6	243.36
3	-32	-43.4	1883.56
4	14	2.6	6.76
5	36	24.6	605.16
Total	57		2739.20

Average return of X = 57 / 5 = 11.40%

Variance of X = 2739.20/5 = 547.84%

Standard deviation of X = 547.84^0.5 = 23.41%