Question

"

Year	Stock X	Stock Y
1	9.00%	-6.00%
2	-8.00%	11.00%
3	18.00%	2.00%
4	3.00%	5.00%

What is the covariance of the returns of Stock X with the returns of Stock Y?"

Round to 6 decimal places please.

Answer 1

Covariance =

Cov(x,y) = Σ ((x_i – x) * (y_i – y)) / N

here xj= return of stock x

x = mean of return of stockx in jth interval

yj = return of stock y

y = mean of return of stock y in jth interval

N = number of intervals , i.e. 4

Step1 : finding mean

mean = sum of stock returns/number of intervals

mean of x = (0.09-0.08+0.18+.03)/4 = 0.055

mean of y = (-0.06+0.11+0.02+0.05)/4 = 0.03

Step2 : Finding difference between each value and mean price

Year (A)	Stock X (B)	return of X ( C)	x - mean x (D)	Stock Y ( E)	return of Y (F)	y - mean y (G)	(D)*(G)
1	9.00%	0.09	0.035	-6.00%	-0.06	-0.09	-0.00315
2	-8.00%	-0.08	-0.135	11.00%	0.11	0.08	-0.0108
3	18.00%	0.18	0.125	2.00%	0.02	-0.01	-0.00125
4	3.00%	0.03	-0.025	5.00%	0.05	0.02	-0.0005
	mean x	0.055		mean y	0.03		sum = -0.0157

= -0.0157

Step3: Dividing by N

Covariance = -0.0157/4

= -0.003925 ( rounded to 6 decimal places)