Question

Year	Stock X	Stock Y
1	12.00%	-6.00%
2	-9.00%	16.00%
3	14.00%	8.00%
4	4.00%	8.00%

What is the correlation of Stock X and Stock Y?

Answer 1

Calculation of Correlation of Stock X and Y

Correlation (X,Y) = Covariance (X,Y) [ S.D(X) * S.D(Y) ]

Year	Stock X	Stock Y	Given return - Average return	Given return - Average return	Square	Square
a	b	c	d= (b-avg return)	e= (c-avg return)	d2	e2
1	12	-6	6.75	-12.5	45.56	156.25
2	-9	16	-14.25	9.5	203.06	90.25
3	14	8	8.75	1.5	76.56	2.25
4	4	8	-1.25	1.5	1.56	2.25
Total (T)	21	26	0	0	326.75	251
Number of years (N)	4	4
Average return (T/N)	5.25	6.5

S.D =

S.D (X) =

= 9.038 %

S.D (Y) =

= 7.92%

Covariance (X,Y) = [ (Given return - Average Return) of X * (Given return - Average Return) of Y ] number of years

= -208 / 4

= -52

Correlation (x,y) = Covariance (X,Y) [S.D(X) * S.D(Y) ]

= - 52 / (9.038 * 7.92)

Correlation between security X and Y = - 0.726

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