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

Cointegration is a fundamentally different concept from correlation, and understanding the distinction is crucial for both risk management and trading.

Correlation vs. Cointegration:

What cointegration means:

Two non-stationary time series (e.g., stock prices that drift over time) are cointegrated if there exists a linear combination that IS stationary. In other words, even though each series wanders randomly, they wander together — the spread between them is mean-reverting.

Formal definition: If Xt and Yt are both I(1) (non-stationary, integrated of order 1), and there exists a β such that:

Zt = Yt - βXt is I(0) (stationary)

Then X and Y are cointegrated.

Testing for cointegration:

1. Engle-Granger two-step:

• Step 1: Regress Y on X: Yt = α + βXt + εt
• Step 2: Test if the residuals (εt) are stationary using the ADF test
• If residuals are stationary → cointegration exists

1. Johansen test: More powerful, handles multiple variables simultaneously

Pairs trading application:

If two stocks are cointegrated, the spread between them (adjusted by the cointegration coefficient) is mean-reverting. This creates a trading opportunity:

Example: Meridian Energy and Summit Power are both large utility stocks. Analysis shows they are cointegrated with β = 0.85.

Spread = Price(Meridian) - 0.85 × Price(Summit)

• Historical mean spread: $2.50
• Current spread: $5.80 (2.2 standard deviations above mean)

Trade:

• Short Meridian (overpriced relative to Summit)
• Long 0.85 shares of Summit for each share of Meridian shorted
• Wait for spread to revert toward $2.50
• Close both positions for profit

Risk management implications:

1. Hedge ratio stability: Correlation-based hedges can break down; cointegration-based hedges are more robust
2. Pairs trading risk: The spread CAN diverge further before reverting — need stop-losses
3. Regime changes: Cointegration can break if the fundamental relationship changes (merger, regulation, business model shift)
4. Lookback period: Using too much historical data may include periods where the relationship didn't exist

Exam tip: FRM tests the distinction between correlation and cointegration, the Engle-Granger procedure, and why cointegration is important for long-term hedging and trading strategies.

Learn more time series analysis on AcadiFi's FRM course.