Forex Maths & Physics

Correlation vs Cointegration — Don't Get Fooled

Two of the most confused ideas in trading are correlation and cointegration. They sound similar, but mistaking one for the other is how pairs traders lose money. The difference is the difference between a coincidence and a relationship.

Correlation is fragile

Correlation measures whether two series move together *right now*. The trouble is that it is unstable and often spurious — a statistical accident. Ice-cream sales and shark attacks are correlated, but only because both rise in summer; neither causes the other. Markets are full of these mirages: two pairs that "always move together" for a year and then go their separate ways.

Cointegration is structural

Two series are cointegrated if, although each one individually wanders like a random walk, a particular combination of them stays bounded — it mean-reverts. Formally, there is a coefficient β such that the spread

is stationary: it has a stable mean and keeps returning to it. That spread Z_t — not either price alone — is the thing you actually trade. When it stretches too far from its mean, you bet on it snapping back, exactly the Ornstein–Uhlenbeck mean-reversion dynamic from our earlier piece.

Why the distinction is everything

• Correlation can be high while the spread runs away forever — you would be adding to a losing position with no anchor.
• Cointegration gives you a fair value to revert to — a principled reason the trade should work and a way to size and stop it.
• Correlation answers "do they wiggle together?"; cointegration answers "is there a tether between them?". Only the tether is tradeable.

Doing it properly

• Test for cointegration (e.g. Engle–Granger or Johansen), don't eyeball a correlation.
• Estimate the half-life of the spread to set your holding period.
• Watch for breaks. A structural change — a central-bank regime shift, a changed peg — can sever the tether. Cointegration that held for years can end, and that is where the large losses hide.

Correlation is a snapshot; cointegration is a relationship with a memory. Trade the spread, confirm the tether, and respect the day it breaks.

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