Cointegration is a statistical property of two or more non-stationary time series that share a common stochastic trend, so a fixed linear combination of them is stationary — meaning they cannot drift arbitrarily far apart and revert toward a long-run equilibrium relationship.
How it works
Two integrated-of-order-one (I(1)) series x and y are cointegrated if there exists a vector β such that y − βx is stationary (I(0)). The deviation from equilibrium is mean-reverting, formalised in the error-correction model where short-run dynamics are pulled back toward the long-run anchor. Engle-Granger and Johansen procedures test for and estimate the cointegrating vector.
Why it matters now
In asset-pricing theory, cointegration of finitely-valued endowment streams is the technical lever that bounds the aggregate endowment and rules out explosive bubble paths; in markets it underpins pairs trades, term-structure spreads, and breakeven-versus-nominal relationships that desks expect to revert in the 2025-2026 regime.
Example
Classic case: spot and one-month forward FX rates. Both are individually non-stationary random walks, but covered interest parity ties them together — the basis (forward minus spot adjusted for the rate differential) is stationary and mean-reverting. A trader observing a 2-standard-deviation widening in a cointegrated 2s10s or breakeven spread sizes a convergence position expecting reversion to the long-run cointegrating equilibrium rather than betting on either leg's level.
Frequently asked
- What does it mean for two assets to be cointegrated?
- Two assets are cointegrated when, despite each price wandering as a non-stationary random walk, a fixed linear combination of them is stationary and mean-reverting. The pair shares a common stochastic trend, so the spread between them cannot drift apart indefinitely — it is pulled back toward a long-run equilibrium, formalised by the Engle-Granger 1987 framework.
- How is cointegration different from correlation?
- Cointegration concerns long-run equilibrium between levels of non-stationary series, while correlation measures short-run co-movement of returns. Two series can be highly correlated day-to-day yet diverge permanently, or weakly correlated yet cointegrated — bound by a stationary spread. Correlation is unstable and regime-dependent; a genuine cointegrating relationship implies error-correction back toward equilibrium.
- Why does cointegration matter in asset-pricing theory?
- Cointegration of finitely-valued endowment streams bounds the aggregate endowment and rules out explosive, non-stationary bubble paths in equilibrium models. Because cointegrated assets share a common trend rather than diverging, their present values stay finite, a technical condition that underpins existence proofs in heterogeneous-agent and incomplete-markets asset-pricing frameworks.
- How do traders use cointegration?
- Traders use cointegration to build convergence trades: identify two cointegrated instruments, measure the stationary spread, and position for reversion when it widens beyond its historical band. Pairs trading, term-structure spreads like 2s10s
Glossary · 2s10s
2s10s is the spread between the 2-year and 10-year US Treasury yields, the most-watched gauge of yield-curve slope. A positive (steeper) reading reflects normal upward-sloping curves; a negative (inverted) reading — long yields below short yields — has historically preceded US recessions.
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