Question

Your colleague in a financial institution says that she has been tracking the movements
of the monthly returns of IBM and Yahoo stock returns. Using data on these returns over the last
10 years, she says that she has computed the COVARIANCE between these two returns series and
found that it is 0.00038. Since this COVARIANCE is so low and close to zero, she says that there
does not seem to be any linear association between the two return series.
You tell her that (choose one of the following)

(i) her reasoning is faulty because….. (must give reason)
(ii) her reasoning is correct because....(must give reason)

Answer 1

(i) her reasoning is faulty because in order to determine if the variables are linearly associated, one must look at the correlation coefficient but not covariance because the value of the covariance is not a standardized value and covariance only shows the direction of the relationship, not the strength of the relationship.

Only sign of the covariance is important. Positive sign indicates that the variables move in the same direction while the negative sign indicates that the variables move in the opposite direction. On the other hand, the correlation coefficient a standardized value that ranges from -1 to +1 and the sign of the correlation coefficient is same as that of covariance. So, the correlation coefficient indicates the direction (by it's sign) and the strength of the linear relationship (by it's magnitude). If correlation coefficient is away from 0 (or close to 1 or -1), the variables have strong linear relationship. If correlation coefficient is 0, then the two variables are not linearly related.

For example, let us say, the standard deviation of IBM returns =0.02 and the standard deviation of Yahoo returns =0.02

Correlation =Covariance/Product of std.deviations =0.00038/(0.02*0.02) =0.00038/0.0004 =0.95 which is close to 1 indicating that the linear relationship between the two variables is strong.

So, we need to find out the correlation coefficient by using std.deviations.