So I am still studying for CFA level one, and it has been years since I took a statistics course. Anyway, the formula is Correlation=Covariance(x,y)/(standard deviation of x times the standard deviation of y) It is easy enough to calculate...but where did the formula come from? As in, how was it derived? Also, how do we know it always stays between -1 and +1? I am just curious, because although variance, standard deviation and covariance are all intuitive to me, and although the concept of correlation is very easy to grasp, for some reason the formula is not making intuitive sense to me. Thanks in advance.