Question

Year	Stock X	Stock Y
1	12.00%	10.00%
2	4.00%	18.00%
3	15.00%	2.00%
4	1.00%	8.00%

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

Please round to 6 decimal places, the answer should be negative. Thanks

Answer 1

Year	Stock X	Stock Y
1	12%	10%
2	4%	18%
3	15%	2%
4	1%	8%

Expected Return

Expected Return of Stock X = E[X] = (12%+4%+15%+1%)/4 = 32%/4 = 8%

Expected Return of Stock Y = E[Y] = (10%+18%+2%+8%)/4 = 38%/4 = 9.5%

Covariance for a sample size of n is calculated using the below formula:

Cov(X,Y) = [(R_X1-E[X])(R_Y1-E[Y])+(R_X2-E[X])(R_Y2-E[Y])+(R_X3-E[X])(R_Y3-E[Y])+(R_X4-E[X])(R_Y4-E[Y])]/(n-1)

Sample size = n = 4

n-1 = 3

Covariance between X and Y = Cov(X,Y) = [(12%-8%)*(10%-9.5%)+(4%-8%)*(18%-9.5%)+(15%-8%)*(2%-9.5%)+(1%-8%)*(8%-9.5%)]/3 = [0.0002+(-0.0034)+(-0.00525)+0.00105]/3 = -0.0074/3 = -0.002466666666

Covariance of the returns of Stock X and Stock Y = Cov(X,Y) = -0.002467 (Rounded to 6 decimal places)

Answer -> -0.002467

Method 2: Using Excel

We can also calculate the Covariance using the COVARIANCE.S functin in Excel as shown below:

=COVARIANCE.S(B2:B5,C2:C5) = -0.002467

Answer -> -0.002467