Therefore, your visual intuition proves math is incorrect then? If people are going to try to argue from a quantitative perspective, they should understand it in context. To make a statement that high correlation is a requirement for co-integration, assumes that the correlation is measured mathematically. As you've observed, however, sometimes math is not enough to draw a conclusion. That doesn't mean you abandon it, however. You find out why and where it may fail in practice.
No. Allow me to try again. Your correlation calculation is correct for what it is. However, it is incomplete, and doesn't catch the fact that the proposed spread trade is implicitly dependent on a correlation that exists at a longer time frame. THAT correlation will most certainly show up in the "correlation math" at that longer timeframe - if you choose to look for it. The mistake is not in the math itself - it's in the choice of math. That's the blind spot.
That's a very good retort. And I agree with you here. The fact of the matter, though, is that people and algorithms draw conclusions (by necessity) from a much smaller window. And as you astutely pointed out, they often (wrongly) rely on mathematical models to make that inference. In the case that the algorithm looked at this example, it might reject the series based on low correlation. No one knows that the underlying model will continue out to infinity, they can only make inferences based upon what they have. My goal was to demonstrate that the idea that a sampled series must have high correlation to pass co-integration is just not always true. Good to know there are some sharp thinkers here.
What do you mean??? I was just trying to give the simplest example of cointegration with zero correlation I could think of. So what do you think the correlation is if not 0? I was trying to keep it concise but here's the logic: if B's expected return is positive when A is up - positive correlation. if B's expected return is negative when A is up - negative correlation. If B's expected return is 0 - no correlation. If one of the stocks has a 0 expected return in every period the correlation should be zero.