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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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    $\begingroup$ 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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