Let's discuss academic research on mean-reverting trading strategies...

Bottom line is you will not get cointegration unless there is correlation between either the underlyings or some combination of the derivatives of the underlyings.

Cointegration is not the same as correlation, it is however a very close cousin and suffers from the same genetic defects and has qualitatively similar upsides.
 
Here's a simple way to visualize it.

You've established through whatever means that A and B are cointegrated. Suddenly A moves quickly in one direction and does NOT come back.

The only way for cointegration to not break is if B also moves up in a strong manner. It doesn't have to happen right away or in one jump (as it would with correlation), but it will happen relatively soon or the cointegration has gone to shit.

Therefore, when it matters most, ie when directional volatility is increasing, it is fair to say that cointegration implies correlation.
 
Quote from Random.Capital:

Here's a simple way to visualize it.

You've established through whatever means that A and B are cointegrated. Suddenly A moves quickly in one direction and does NOT come back.

The only way for cointegration to not break is if B also moves up in a strong manner. It doesn't have to happen right away or in one jump (as it would with correlation), but it will happen relatively soon or the cointegration has gone to shit.

Therefore, when it matters most, ie when directional volatility is increasing, it is fair to say that cointegration implies correlation.
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And the correlation has gone to shit, too?
 
Quote from MGB:

And the correlation has gone to shit, too?
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Well that's where it gets tricky.:)

If the starting point was one where there was little net directional movement, it is possible that the traditional correlation measures are telling you the two underlyings are NOT correlated while the cointegration measuring is saying YEAH BABY. So it looks like there is no correlation to break.

Yet if you step back to the qualitative perspective, they clearly were correlated, since neither one was moving away from the other over any of the longer timeframes.

IMO it is very dangerous to draw conclusions from either correlation or cointegration when the underlyings are jello, for the same reasons in both cases. By "dangerous" I don't mean "don't do it!", I mean "it's trickier than it looks, make sure you know what you're doing".
 
This stuff is much clearer with concrete examples. Here is a simple example of cointegration w/o correlation:

Stock A and B only trade on alternate days. Stock A's return is random on days it trades, its price follows a random walk. Stock B's return is the same as yesterday's Stock A return.

There is perfect price cointegration (awesome pair to trade). But zero comtemporaneous correlation - when one stock's return is always 0 there can be no correlation.

Cointegration does not imply correlation. At least not contemporaneous correlation which is what most people mean.
 
Quote from marine:

People who pairs trade trade co-integration! They do not trade correllation!

In general if you find a pair that is co-integrated, then most likely it will be correlated but this is not always true and in fact you do not want it to be true.

The best pair to trade is one that is co-integrated (i.e. stationary) but is negatively correllated.
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Statement #1 is correct.

Statement #2 is extremely misleading...
Because cointegration will result in high correlation...
Over any medium term period...
For example, > 0.80 over 3 months.
If correlation is lower than that... you will take too many losses to succeed.

Statement #3 is false...
Because positive or negative cointegration is equally advantageous for stat arbitrage...
But you will find many more opportunities for hedging positive pairs or baskets.
 
Quote from black diamond:

But zero comtemporaneous correlation - when one stock's return is always 0 there can be no correlation.
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This is like arguing 1 + 1 does NOT equal 2, because when I add one drop of water to another, I only end up with one drop.
 
Anyone following along should heed Equalizer's advice, when he suggests to actually play with some of these concepts in excel to validate the concepts with your own eyes.

Below are two series that are co-integrated.
You may extend the series out to infinity and there are no gaps in continuity.
Being that they are models, the relationships (i.e. corr/coint) will also continue out to infinity. As you can see, the spread (bottom) would be a very nice pair to trade, would it not?

The correlation between these series?
It is very low... .31.

I.e. you do not (theoretically) need to have a high correlation to have a co-integrated pair that is very trade friendly. Conversly, you can have a very highly correlated pair that is not co-integrated.

Does that mean this is a very practical case? No, because as some have asserted, there is no guarantee for the relationship to continue in reality.
However, understanding the basic concepts is helpful.
 

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Quote from dtrader98:

The correlation between these series?
It is very low... .31.
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Anyone with a lick of sense can look at the top chart and see the two series are highly correlated, by strictly visual inspection alone. The fact that your correlation measure is giving a low value does not mean the correlation is low - it means you are measuring the wrong thing.

This kind of math is exactly why so many "quant" strategies get into trouble.
 
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