CFAI Sample 5 - Ques 15 Correlation

CFA Level I
#1

Hi all, theres a question 15 on correlation. If A goes up by 1 unit, B always goes up by 0.5 unit and C goes down by 0.5 unit. And the answer says that A and B are perfectly correlated whie A and C are negatively correlated. Anyone has a clue? Thanks

#2

It’s been discussed before, but the idea is that they are still lines…

#3

can someone explain this??? i have a hard time understandin why +1…

#4

Correlation is the strength of the relationship, not the magnitude. In this case, A=2B, and A=-2C WITH NO ERROR. If you know A, you know B and C. So they are perfectly correlated - A,B positively, A,C negatively, and B,C negatively.

#5

But it will be true for any one observation. The relationship will always be linear. Can someone please give an example of non-linear relationship using only one observation ? If A increases by “x” , B increases by “y”, it will also be linear to me – that every change in A brings “y/x” change in B. Am I missing something?

#6

Exactly. Those would all produce a perfectly linear relationship. The alternative would be something like “A increases by 1 from a value of 1 to a value of 2, and B increases by 1. A increases by 1 from a value of 2 to a value of 3, and B increases by 2.” Because a change in A does not lead to a constant change in B, the relationship is not linear, and so they are not perfectly positively correlated. Still positively correlated, but r would not be 1.

#7

thanks. Thats what I thought after getting it incorrect on the sample exam…

#8

I feel in this trap of selecting (0.5, -0.5) as the answer too :-))