Corr & Cov

[higaurav]

Hi David,

We said that "zero covariance will mean zero correlation but converse not necessarily true". I am little confused when I look at the formula..because Corr (AB) = Cov (A,B)/ SD A * SD B

Now in this if Corr (AB) = 0, it will always lead to zero covariance. I am sure that I am missing some point that you are trying to bring by that statement. Pls suggest.

 

[David Harper CFA FRM]

OM -

I may have been imprecise. I meant to parrot Gujarati's correlation coefficient property (3.4, property 5) where the point is that correlation coefficient is linear but "dependencies" are often non-linear. Such that:

if independent, then covariance = 0, and if covariance =0, then correlation = 0
However, if correlation = 0, then covariance = 0 but variables may not be independent; i.e., the dependence may be non-linear

or to further paraphrase this property 5:

independence implies correlation = 0, but
correlation = 0 does not imply independence

(i think when i said this i was incorrectly thinking about correlation/covariance and, really, you are right about the formula of course, and the point here is not between correlation/covariance but rather between covariance and independence/dependence)

David

 

[higaurav]

David, this makes sense.. Now I get your point. Thanks once again