The drunk man his dog and the difference between correlation and cointegration

 

If you are looking at cross-market trades, you must think through the difference between correlation, cointegration, and causality. There is a good analogy associated with a drunk man and his dog to discuss the difference. 

The drunk leaves the bar to go home and his dog starts to follow him. He is wandering. There is correlation between their movements but not a strong connection. They may be moving in the same direction, but it is not a tight relationship as the owner wanders the street. At some point the drunk man may attach the dog to his leash, the connection means there is a limit to how far the drunk and dog can move apart. The alternative is that the drunk will call out to his dog which may limit the difference between the two. The two can now be said to be cointegrated. The dog can only go so far away from his master. Finally, as the two get close to the house, the dog may pull his master to the doorstep. Here we have causality.  See the original piece by Michael P Murray. 

Correlation is defined for stationary variables such as return, cointegration focuses on the relationship of two non-stationary variables, say the difference in two prices which is the basis for pairs trades. Correlation across prices may not have strong meaning. The correlation across returns will have value but may not be useful for trading because the two variables can have strong dispersion. If the two variables have a common trend, the adjusted difference may be stationary and mean-reverting, this information is very useful if the relationship is well-behaved. Two variables cointegrated can have mean-reversion that can be exploited because there is a long-run relationship between the two variables. 

When thinking about trading two variables that may not be stationary, a difference can be taken (volatility adjusted or a regression) to test if the difference is stationary. If the difference is stationary or cointegrated, there is a better opportunity for profitable trading between the two. The stationary relationship can allow management of a pairs trade. If there is no stationarity, the cross-market trade cannot be exploited.