Strategy #0000000019 · Statistical arbitrage and relative value
Pairs trading and spread mean reversion
Define a hedged spread and pre-commit to entry, exit and failure conditions.
Pairs trading selects economically or statistically linked assets, estimates a hedged spread and trades a pre-defined deviation with explicit exit rules.
Historical relationships can break; define exits, stops and time limits before entry.
Three ways in
Understand the story. Then inspect the risk.
Start with a familiar situation, check the payoff, then test how the numbers change.
The idea · in two minutes
Rose does not assume two lines will always meet because they once moved together
Rose selects two firms and estimates their hedge relationship using a formation sample. She trades only when the spread crosses a pre-set entry threshold and keeps pair selection separate from the evaluation period to avoid look-ahead.
If entry is at z=+2 and the spread later returns to +0.5, with an assumed $4 per spread standard deviation, a short spread earns (2−0.5)×$4=$6 gross per unit before costs. This only describes the model while the estimated relationship remains tradable.
Jack asks what happens after a merger, product change or funding shock. Rose sets a maximum holding period, stop and model-review rule. If stationarity breaks, she does not treat a new mean as a guaranteed target. Legging, borrow recalls and gaps can expand losses.
- 進場 Z=+2.0At entry, z=+2 represents a spread above its formation-period mean.
- 退出 Z=+0.5Assuming a reversion to z=+0.5, the move is 1.5 spread standard deviations.
- 扣除成本At $4 per standard deviation, gross P&L is $6; less assumed $0.50 cost is $5.50 per unit.
Illustrative research examples only. They are not live signals or a recommendation.
The mechanics · payoff and exposure
Select a pair and hedge ratio in a training sample, then apply pre-defined entry, exit and failure rules to a standardised spread.
β is estimated using formation data; μ and σ are the formation spread mean and standard deviation; z_in is the entry threshold. A tradable rule also fixes exits, maximum holding time, stop, share conversion, rebalance timing and costs.
Greeks: the directional intuition
- Hedge ratio
- Measures sensitivity to implied volatility.
- Spread stationarity
- Measures sensitivity to implied volatility.
- Half-life
- Measures sensitivity to implied volatility.
- Legging / borrow
- Measures sensitivity to implied volatility.
Select a pair and hedge ratio in a training sample, then apply pre-defined entry, exit and failure rules to a standardised spread.
Practical context · published observations
Short positive spread: read the record with its caveats.
The chart uses the published figures or explicitly labelled study inputs below. A historical index or model replay is not the same as an investor’s realised account return.
價格、β、均值、標準差與交易成本皆是假設，沒有真實配對資料或回測；模型關係斷裂時結果可能完全不同。 Source ↗ · Methodology ↗
Change assumptions and inspect the scenario
Inputs illustrate the strategy mechanics; they are not live quotes, forecasts or investment advice.
Variants · same family, different risk levers
Pair selection and mean-reversion models use different estimators.
Distance, cointegration, OU processes and machine learning are distinct models, not interchangeable labels for one backtest.
| Related strategy | Relationship | What changes | New cost or risk |
|---|---|---|---|
| Distance method | Historical price distance | Selects similar standardised price paths over a formation window. | Scale, formation length and corporate actions matter; similarity is not stationarity. |
| Cointegration pairs | Long-run equilibrium | Tests whether a linear combination of prices is stationary. | The cointegrating vector is estimated with error and can change structurally. |
| Partial cointegration | Partial mean reversion | Allows the spread to contain stationary and non-stationary components. | More complex estimation does not eliminate parameter drift. |
| Ornstein–Uhlenbeck entry/exit | Continuous-time model | Estimates mean, reversion speed and cost-aware trading boundaries. | The process assumptions may not fit jumps or changing regimes. |
| Multiple-cluster mean reversion | Group neutralisation | De-means returns against an industry or cluster average. | A poor grouping can mistake shared fundamentals for a tradable spread. |
| Copula pairs | Dependence structure | Models nonlinear tail dependence to set pair trading thresholds. | Tail estimates require data and can shift across regimes. |
| Sparse mean-reverting basket | Multi-asset portfolio | Uses sparse weights to construct a mean-reverting basket. | Selection, regularisation and capacity constraints can overfit. |
| Deep-RL pairs thresholds | Learned exits | Uses reinforcement learning to choose dynamic entry and exit thresholds. | Reward design, simulated costs and state shifts create large out-of-sample risk. |
If the spread is no longer stationary, its historical mean and volatility are no longer reliable trading targets.
Read beyond the summary
References
Primary sources and research used to describe the strategy and its limits.
- 01Gatev, Goetzmann & Rouwenhorst (2006), Pairs Trading: Performance of a Relative-Value Arbitrage Rule.research
- 02Engle & Granger (1987), Co-Integration and Error Correction: Representation, Estimation, and Testing.research
- 03Rad, Low & Faff (2016), The Profitability of Pairs Trading Strategies: Distance, Cointegration and Copula Methods.research
- 04Leung & Li (2015), Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit.research
- 05Kakushadze & Serur (2018), 151 Trading Strategies, §§3.8–3.10.source