Pairs Trading Explained: Hedge Ratios, Z-Scores and Cointegration Risk
Pairs trading seeks to express a relative-price view between two related securities rather than an outright prediction of the broad market. A typical position buys one asset and sells another, using a defined hedge ratio. Its apparent neutrality can be deceptive: the spread may stop reverting, both legs can be costly to transact, and the short position may create borrow or financing requirements.
Key takeaways
- A long-short pair expresses a relative-price thesis rather than a guaranteed market-neutral hedge.
- The hedge ratio must be specified from the economics of the exposure or a point-in-time statistical model.
- A z-score measures deviation from an estimated distribution; it is not a probability that prices must revert.
- Cointegration is distinct from simple historical correlation, and the estimated relationship can fail.
What makes a pairs trade different?
A long-only investor might buy a share because company earnings look attractive. A pairs trader could instead buy company A and sell company B because A appears undervalued relative to B under a specified valuation or statistical model. The objective is to gain when their relative pricing relationship moves in the intended direction.
The gross exposure can be substantial even if the net notional is small. Two legs also create two execution prices and different borrow, financing and corporate-action risks. A pair should be assessed as one integrated exposure without assuming that it eliminates market volatility.
Choosing related securities
Common research candidates include businesses in the same industry, different share classes, closely related ETFs or assets linked by production economics. The economic relationship matters because a purely statistical historical connection may disappear after a business acquisition, regulation change or alteration in sector profitability.
The securities should have comparable trading hours, reliable price data and sufficient liquidity. If the short leg is difficult to borrow, a backtest that assumes unlimited borrow at a trivial fee will be misleading. Even close industry peers may have very different balance sheets and sensitivity to commodity or currency moves.
What is the hedge ratio?
A hedge ratio determines how much of each leg is held. Dollar neutrality means the gross value of the long position equals the absolute gross value of the short position at inception. Beta neutrality instead targets approximately offsetting market betas, while regression-based ratios are often based on historical price or log-price relationships.
These choices do not produce the same trade. A £10,000 long and £10,000 short pair is initially dollar neutral, but if the long stock has a beta of 1.5 and the short one 0.8, meaningful market sensitivity remains. Select and document the exposure intended to be hedged.
How a spread and z-score are constructed
A simple statistical spread can be defined as price A minus h times price B, where h is a hedge ratio estimated from an eligible historical window. For log prices or nonstationary series, choose a formulation consistent with the statistical model and the instruments. Do not interchange dollar-price regressions and return regressions without explaining the difference.
A z-score is the current spread minus its estimated historical mean, divided by its estimated standard deviation. A value of +2 indicates a spread two estimated standard deviations above that reference mean. It does not mean the next move has a fixed probability of being negative, especially if the spread distribution or mean has changed.
Correlation is not cointegration
Two share prices can be highly correlated over a period and still drift farther apart over time. Cointegration is a stronger statistical idea concerning a stationary linear combination of nonstationary series under suitable assumptions. Researchers may test the estimated residual for stationarity, but formal inference requires appropriate critical values and careful attention to model selection.
Even a historically cointegrated pair may break down because of changing company economics or a structural regime shift. A result found after trying hundreds of pairs may reflect data snooping. Out-of-sample testing, transaction costs and an economic rationale remain necessary.
A worked long-short outcome
Suppose the trader buys £10,000 of A and shorts £10,000 of B in a simplified fully funded economic comparison. A gains 5% and B gains 2%. The long leg gains £500 and the short leg loses £200, giving £300 profit before stock-borrow costs, dividends, commissions and financing.
If instead A falls 8% while B rises 4%, the long leg loses £800 and the short leg loses £400, producing a £1,200 loss. The ‘hedged’ label has not prevented a substantial adverse relative move. A real trade can face larger losses if the short must be recalled or if the positions are financed with leverage.
Designing entries and exits
A research design may consider spread deviation thresholds, confirmation that the economic relationship remains intact, a maximum holding time and a loss or structural-break exit. It should specify precisely how the spread is calculated and when a signal becomes tradeable after market data arrive.
The rule must be evaluated net of costs on both legs and with realistic stock borrowing. It is not sufficient to record that spread deviations often revert if the opportunity cannot be executed at prices assumed by the backtest. Threshold tuning on the complete sample is another form of overfitting.
A professional evaluation checklist
Record each security’s corporate actions, tradability, historical membership, model estimation window, hedge ratio updates, entry and exit conventions and margin. Stress beta mismatch, borrow fee changes, spread widening and simultaneous illiquidity. Evaluate whether the pair’s returns depend on a small number of exceptional observations.
Run the model through different market regimes and track how long the spread remained away from its assumed mean. Avoid expressing any entry z-score as a dependable opportunity without estimating the chance and cost of structural failure.
Worked comparison table
| Hypothetical outcome | £10,000 long A | £10,000 short B | Combined P&L |
|---|---|---|---|
| A +5%, B +2% | +£500 | −£200 | +£300 before costs |
| A −8%, B +4% | −£800 | −£400 | −£1,200 before costs |
| Borrow fee and trading costs | Applies | Applies plus stock borrow | Reduces net outcome |
Hypothetical calculations and rounded examples are for educational purposes, not forecasts or trade recommendations.
Frequently asked questions
Does pairs trading always remove market risk?
No. Dollar, beta and statistical neutrality are different and can each leave important residual exposures.
Does a z-score of 2 guarantee mean reversion?
No. It measures deviation under an estimated model; distributions and relationships can change.
Is correlation the same as cointegration?
No. Cointegration concerns a particular stationary relationship between nonstationary price series.
Why are short borrowing costs important?
A stock can be expensive or unavailable to borrow, and recalls can force adverse exits.
Sources and further reading
Related education: Mean reversion trading and How to measure trading slippage.
Traders MBA provides general financial education, not personal financial advice or trading signals. Market and leveraged-instrument losses can exceed expectations.