[Russell91]

fwiw, correlation actually is transitive if strong enough. This is obvious if corr(x,y) = 1 and corr(y,z) = 1, then corr(x,z) = 1. More generally, you can get this constraint by looking at the minimal value a for which the matrix [[1, corr(x,y), a], [corr(x,y), 1, corr(y, z)], [a, corr(y,z), 1]] remains positive semidefinite to find the minimal correlation of x and z given that of (x,y) and (y,z). I mention this because in this case the correlations may be strong enough so that the minimal a is positive, and because it's important to understand exactly when our intuition about transitivity of correlation breaks down.

For example, when x,y and y,z are perfectly correlated, we can see that corr(x,z) must be greater than 0.9 from: http://www.wolframalpha.com/input/?i=%5B%5B1%2C1%2C0.9%5D%2C...