A quiz in Schewer QBank mentions - If Covariance is zero, it would not mean that there is no relationship. There can be a non linear relationship. But I also read in CFA book - Vol 1 Pg. 343 Jun 08 mentions- Covariance of returns is 0 if assets are unrelated. I am not able to understand, which is correct or both are correct but I have not understood it correctly?? Can someone please help me understand what a zero covariance would mean? Also when we say Linear relationship what is the main concept? Do the variables move together or what exactly? Thanks in advance.

Take treasury notes for example. The covariance with the returns of a stock is 0. change in treasury notes yield could influence the returns of a stock (or the market) but not directly.they could have a common cause for both securities return performance just a guess here

"If Covariance is zero, it would not mean that there is no relationship. There can be a non linear relationship. "

It seems to me now: 1.) covariance is never 0 for Linear relationships… 2.) covariance may or may not be 0 for Non-Linear relationship 3.) covariance is always zero, when assets are not related. (neither linear nor Non linear) 4.) If covariance is 0, we cannot deduce to a conclusion except that relation is not linear Is this correctly understood?

Yep - Good job.

sounds good to me, amitahuja…

good summary amit…