What is cointegration and how is it used in pairs trading?

Question

AcadiFi · Accepted Answer

Cointegration occurs when two or more non-stationary series (each I(1)) share a long-run equilibrium: some linear combination of them is stationary. The series wander individually, but their spread oscillates around a constant mean. This is the statistical foundation of pairs trading. Formally, if x_t and y_t are both I(1) but z_t equals y_t minus beta times x_t is I(0), then x and y are cointegrated with cointegrating vector (1, negative beta). Example: statistical arbitrage analyst Ingrid Voss at Höhenland Capital finds that Calderbury Energy and Westmoor Power, two UK utilities, are cointegrated. Log prices are individually random walks, but the spread log P_C minus 0.92 times log P_W is mean-reverting with half-life of 12 trading days. Trading strategy: when the spread exceeds two standard deviations above its mean, short Calderbury and long 0.92 shares of Westmoor per share of Calderbury, betting on reversion. Close when spread returns to mean. ```mermaid flowchart LR A[Price A
I 1] --> S[Spread] B[Price B
I 1] --> S S --> M{Stationary?} M -->|Yes| C[Cointegrated
pairs trade] M -->|No| N[Not cointegrated] ``` Test for cointegration using the Engle-Granger two-step method: (1) regress y on x, (2) apply ADF to the residuals. If residuals are stationary, cointegration exists. The Johansen test generalizes to multiple series and multiple cointegrating vectors.

What is cointegration and how is it used in pairs trading?

Master Level II with our CFA Course

Related Questions

Practice Questions