Why isn't it appropriate to use correlation between prices in a pairs trade strategy?

I've already seen this question and read through all the answers, but I'm still confused about why you shouldn't use price correlation in a pairs trade strategy.

For example, if I'm looking at the price ratio between two stocks, and I find the current price ratio deviates from the norm, doesn't a high price correlation tell me that the two prices are bound to converge to the same movements and so I have an opportunity to sell high and buy low?

You could, and it doesn't hurt for you to test this yourself. Some of my best work has come from drawing the opposite conclusion to conventional wisdom or stylized "facts" in publications.

That said, it's trivial to construct an example where you won't be able to spread a correlated pair. Suppose the underlying data generation process is $$y_t = x_t^2$$, you will find very high correlation between the two but obviously $$x_t \in \mathbb{o}\left(y_t\right)$$ and the two will diverge.

If you are correlating prices that would imply that you are sizing positions based on the number of shares in each position. This can result in a book that is very biased in terms of dollars invested. This is not conventional and actually, makes little sense--most of the time.

Most pair trading strategies weight positions by dollar value which is why normally, percentage changes would be used to correlate.

• Correlation is insensitive to scale; $\text{corr}(x,y)=\text{corr}(1000x,y)$, i.e. you can multiply one of the series by 1000 (or any number except for a zero) and you will still get the same correlation. Thus your answer is wrong. – Richard Hardy Jun 24 '17 at 9:36
• The real reasons are rather mathematical and are nicely explained here and here. – Richard Hardy Jun 24 '17 at 9:45
• Interesting take. Any reference to back up your answer? – AK88 Jun 24 '17 at 10:49

Whatever correlations appear during a bull direction market (the slow upward grind with rare down days and pallid implied relativity), these correlations undergo deposition to near zero when the market does correct. Their is your price extreme indicator, but often the cost to carry associated with the prolonged time it takes for market correction is too much to bear for most people. It is much like going long volatility in those market conditions (Valid concept, difficult and expensive in reality).