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%?
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It only takes a minute to sign up.Sign up to join this community
Does this mean that correlation is 40%? No.
Very simple example (in R). Let A and B be stocks with returns
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)
> mean(stockA)  0.05 > mean(stockB)  0.02 > cor(stockA, stockB)  0 > > stockA = c(0.04, 0.05, 0.05, 0.06) > stockB = c(0.01, 0.02, 0.02, 0.03) > mean(stockA)  0.05 > mean(stockB)  0.02 > cor(stockA, stockB)  1
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]