correlation vs cointegration

Cointegration is the foundation upon which pair trading (“statistical arbitrage”) is built. If two stocks simply move in a correlated manner, there may never be any widening of the spread. Without a temporary widening of the spread in either direction, there is no opportunity to short (or buy) the spread, and no reason to expect the spread to revert to the mean either.

What is the difference between correlation and cointegration? If  A and B were really correlated, when A goes up one day, B would likely go up also on the same day, and vice versa. Their daily (or weekly, or monthly) returns would have risen or fallen in synchrony. But that’s not what my analysis was about. I claim that A and B are cointegrated, meaning that the two price series cannot wander off in opposite directions for very long without coming back to a mean distance eventually. But it doesn’t mean that on a daily basis the two prices have to move in synchrony at all

Now consider stock A and stock C.

Stock C clearly doesn’t move in any correlated fashion with stock A: some days they move in same direction, other days opposite. Most days stock C doesn’t move at all! But notice that the spread in stock prices between C and A always return to about $1 after a while. This is a manifestation of cointegration between A and C. In this instance, a profitable trade would be to buy A and short C at around day 10, then exit both positions at around day 19. Another profitable trade would be to buy C and short A at around day 31, then closing out the positions around day 40.

Theoretically, cointegration is time-scale independent. So we cannot say a pair of stocks are cointegrated on a time scale of years, but not minutes. However, it is meaningful to ask what the average mean-reversion time is.