 # Easy CFAI test question

A very basic correlation question from one of the CFAI online exams: If variable A increased by 1 unit, variable B increased by 0.5 units and variable C decreased by 0.5 units. What is the correlation between: A and B: 0.5 or 1.0 A and C: -05 or -1.0 The given answer is 1 and -1 but this doesn’t seem right to me. Am I losing my mind after 400hrs of study??

I think this question has already been discussed. One way to think about it is two stocks of the same value that move identically together. Their correlation is 1. Then one stock gets split. As a result, an increase of \$1 in the non-split stock only results in a \$0.50 increase in the split stock. But the correlation is still 1 – they move together exactly and you can predict with certainty the movement of one based on the movement of the other. The correlation doesn’t change simply because of a change in the magnitude of one of the stocks.

Thanks chebychev! You’re right this has been discussed. So much for me paying attention!

great explanation. thank you. i fell victim to this question also.

i quickly put in the numbers in the data function of my calculator A 1 2 3 B 1 1.5 2 C 2 1.5 1 and i got the right answers… back up plan i guess!

I still don’t get it. Lets say the original correation was .5. Isn’t it possible that If variable A increased by 1 unit, variable B increased by 0.5 units, assuming there was no stock split? How can you determine that the correlation is 1 just from the information given?

I got stumped on this one too. Question doesn’t tell anything about splits. Why do we need to make this assumption? In a non-split scenario, this doesn’t hold true.

I answered 0.5 and -0.5 too. Would be good to know why there is an assumption of perfect prior correlation, if it isn’t stated… thanks