Question

Given the following return information, what are the variance and standard deviation of stock A and return of the market index? Month Return of Stock A Return of Market 2 3 4 5 2.3 2.5 1.9 2.4 2.1 Index (%) 1.3 5.0 0.8 1.9 1.1 Using the table and your calculations from above, calculate the covariance and correlation of Stock A's returns and the return of the market index

Answer 1

The variance and standard deviation for return of Stock A can be calculated as follows:

Standard Deviation = $\sqrt{}$($\sum$x² / N)

x is the deviation of the observations from their mean value and x² is the square of those deviations. N is the total number of observations.

Mean = Sum of all observation / Total number of observations = 11.2 / 5 = 2.24

X	x = X - Mean	x2
2.3	0.06	0.0036
2.5	0.26	0.0676
1.9	-0.34	0.1156
2.4	0.16	0.0256
2.1	-0.14	0.0196
Total		0.232

Standard Deviation = $\sqrt{}$($\sum$x² / N) = $\sqrt{}$(0.232 / 5) = $\sqrt{}$0.0464 = 0.2154 is the answer

Variance is nothing but the square of standard deviation. So, variance is 0.0464 is the answer.

The variance and standard deviation for return of market index can be calculated as follows:

Standard Deviation = $\sqrt{}$($\sum$y² / N)

y is the deviation of the observations from their mean value and y² is the square of those deviations. N is the total number of observations.

Mean = Sum of all observation / Total number of observations = 10.1 / 5 = 2.02

Y	y = Y - Mean	y2
1.3	-0.72	0.5184
5.0	2.98	8.8804
0.8	-1.22	1.4884
1.9	-0.12	0.0144
1.1	-0.92	0.8464
Total		11.748

Standard Deviation = $\sqrt{}$($\sum$y² / N) = $\sqrt{}$(11.748 / 5) =  $\sqrt{}$2.3496 = 1.53 is the answer.

Variance is 2.3496 is the answer.