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If Stock A returns 5% on average in year Y And Stock B returns 2% on average in year Y

Does this mean that correlation is 40%?

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closed as unclear what you're asking by Gordon, chollida, noob2, olaker May 12 '16 at 18:18

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Do you know what does correlation mean? I am voting to close this question as it lacks context. $\endgroup$ – Gordon May 12 '16 at 13:37
  • $\begingroup$ Yes, I know the formula. But this was asked in an interview and the problem was I started thinking that within the data we have it can be concluded that when a stocks returns 5% the other returns 2% in a broader way. It's meaningless though. That's where I was confused. $\endgroup$ – Dark Knight May 12 '16 at 13:42
  • $\begingroup$ You can add more background to your question to make it more meaningful. $\endgroup$ – Gordon May 12 '16 at 13:45
  • $\begingroup$ There is no background. Except that price of stock A is 5 times price of stock B. But the thing I now realised is, what if stock A went up and down ( for simplicity ) and stock B went down and up in the same period, then correlation would look negative but how do I answer the question? $\endgroup$ – Dark Knight May 12 '16 at 13:49
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Does this mean that correlation is 40%? No.

Very simple example (in R). Let A and B be stocks with returns stockA and stockB. Consider following example:

stockA = c(0.05, 0.04, 0.05, 0.06)
stockB = c(0.01, 0.02, 0.03, 0.02)
mean(stockA)
mean(stockB)
cor(stockA, stockB)

stockA = c(0.04, 0.05, 0.05, 0.06)
stockB = c(0.01, 0.02, 0.02, 0.03)
mean(stockA)
mean(stockB)
cor(stockA, stockB)

giving

> mean(stockA)
[1] 0.05
> mean(stockB)
[1] 0.02
> cor(stockA, stockB)
[1] 0
> 
> stockA = c(0.04, 0.05, 0.05, 0.06)
> stockB = c(0.01, 0.02, 0.02, 0.03)
> mean(stockA)
[1] 0.05
> mean(stockB)
[1] 0.02
> cor(stockA, stockB)
[1] 1
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The answer is no. First, the question is ambiguous about what year Y is. Is year Y actually 2015? Knowing those returns in one year says nothing about correlation. Second, if it means that if Stock A goes up 5% then Stock B will go up by 2%, then that also says nothing. What if Stock A goes down. Does stock B go up or down? Additionally, look at the averages. Create a series of every year Stock A goes up by exactly 2%. Then one can create any correlation you want, positive or negative, by playing with the Stock B returns. For example lots of small negative returns, and one large positive gets a negative correlation at the same time as a 2% average. [for example, in time series terms, A is up 2% exactly each time, but B goes from 1 to .9, .8, .7, .6, and then up to .95. The return is about 2% but the correlation would be negative 0.4 rather than positive 0.4]

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