Pair trading is a strategy designed to exploit short-term price discrepancies between two highly related financial assets. Pioneered at Morgan Stanley in the 1980s, this strategy falls under the umbrella of statistical arbitrage, allowing traders to profit from the relative performance of two assets rather than the absolute direction of the stock market.
Key Takeaways
- Involves pairing one long position with one short position to isolate relative performance.
- Relies heavily on correlation, cointegration, and Z-scores to identify mispricing.
- Assumes that historical price spreads will eventually return to their long-term average.
- Uses hedge ratios to balance the capital allocation between the two legs of the trade.
- Requires clear entry and exit rules, as relationships can occasionally break down permanently.
How Does Pair Trading Work?
The first step in pair trading is to identify two stocks with a strong relationship. They could be in the same industry, have similar customers, or face similar economic conditions.
Suppose that Stock A and Stock B tend to move similarly. If Stock A suddenly goes up a lot more than Stock B, the spread between the two is wider than normal.
A trader may then consider Stock A relatively expensive and Stock B relatively cheap. The trader could:
- Buy Stock B, the relatively weaker stock.
- Short-sell Stock A, the relatively stronger stock.
- Monitor the difference between the two stocks.
- Close both positions if the relationship moves back towards its normal level.
So, the trader is not simply wagering on one stock going up or down. The focus is mainly on the performance of the two stocks against each other.
For example, if two banking stocks usually move together, but one stock drops on company-specific news, a trader might expect the spread to tighten once the event’s impact wears off.
Correlation vs Cointegration
|
Comparison Feature |
Correlation |
Cointegration |
|
Core Definition |
Measures how closely two stocks have moved in relation to each other in the past. |
Examines whether the structural relationship between two stocks remains stable over time. |
|
Value Range |
Measured on a scale from -1 to +1 (+1 for identical movement, 0 for no relationship, -1 for inverse movement). |
Evaluated using statistical tests for stationarity rather than a fixed coefficient scale. |
|
Spread Behavior |
Two assets can maintain a high correlation while their absolute price spread continues to diverge indefinitely. |
The price spread between the two assets is mean-reverting, fluctuating around a predictable long-term average. |
|
Utility in Pair Trading |
Useful for initially screening assets that move in tandem, though insufficient on its own. |
Essential for execution, as the strategy depends on the price spread returning to its normal historical level. |
Spread, Hedge Ratio and Z-Score
Traders can use several measures to study the relationship between two stocks.
Spread
The spread represents the relative difference between the two stocks. A simple form of the calculation is:
Spread = Price of Stock A − (Hedge Ratio × Price of Stock B)
The spread helps traders see whether the relationship between the two stocks is close to its normal level or has moved unusually far away.
Hedge Ratio
The hedge ratio helps determine how much of one stock to buy or short-sell relative to the other.
For example, a trader may find that buying 1 share of Stock A and short-selling 1.5 shares of Stock B yields a more balanced position given their historical relationship.
The hedge ratio can be estimated using methods such as linear regression. It also helps account for differences in the prices and movements of the two stocks.
Z-Score
The Z-score shows how far the current spread is from its historical average.
A simple formula is:
Z-score = (Current Spread − Average Spread) / Standard Deviation
A high positive Z-score indicates the spread is unusually wide relative to its normal level. A large negative Z-score means the spread is unusually narrow.
Traders can use these readings to identify when the difference between the two stocks may be large enough to consider a pair trade.
Complete Z-Score Example
Suppose a pairs trader is trading Stock A and Stock B. After calculating the appropriate hedge ratio, the trader creates a spread between the two positions and tracks its historical behaviour.
Assume the spread has:
- Historical average (mean) spread: ₹20
- Standard deviation of the spread: ₹5
- Current spread: ₹30
The Z-score measures how far the current spread is from its historical average in terms of standard deviations:
Z-score = (Current Spread − Mean Spread) ÷ Standard Deviation
Z-score = (₹30 − ₹20) ÷ ₹5 = 2
A Z-score of +2 means that the current spread is two standard deviations above its historical average. If the trader expects the spread to revert towards its mean, they may consider a pairs trade that benefits if the spread narrows. For example, they could short the relatively overperforming side and buy the relatively underperforming side, using the hedge ratio to determine the appropriate position sizes.
If the spread subsequently falls from ₹30 back towards its historical mean of ₹20, the trade may generate a profit. However, a high or low Z-score does not guarantee mean reversion, as the spread can continue moving further away from its historical average.
How to Choose a Pair?
Choosing the right pair is one of the most important parts of pair trading. Stocks should not be selected simply because they belong to the same industry.
Step 1: Fundamental and Business Model Screening
Filter for companies operating within the same sector (such as private sector banking or IT services) that share comparable business models, target customers, and risk profiles.
Step 2: Economic Exposure Alignment
Verify that both candidate assets respond similarly to macroeconomic drivers, regulatory changes, and broader market cycles.
Step 3: Preliminary Correlation Filtering
Calculate historical price correlation over a defined lookback period (e.g., 12 to 24 months) to isolate pairs exhibiting a strong positive relationship.
Step 4: Cointegration Testing
Apply statistical stationarity tests (such as the Engle-Granger or Johansen test) to the price spread to ensure the relationship is mean-reverting rather than prone to indefinite divergence.
Step 5: Spread Stability and Backtesting
Analyse historical spread charts to confirm that fluctuations occur reliably around a stable long-term mean with no erratic structural breaks, ensuring viability for pair trading execution.
Entry and Exit
Once a suitable pair has been identified, traders need clear rules for entering and leaving the trade.
Entry
An entry may be considered when the spread moves significantly away from its normal level. Traders can use the Z-score to help measure this move.
For example, a trader may set a predefined threshold such as:
- Z-score below -2: Consider buying the relatively weaker stock and short-selling the other.
- Z-score above +2: Consider short-selling the relatively stronger stock and buying the other.
The exact level depends on the trading strategy and the historical behaviour of the pair.
Exit
The trade can be closed when the spread moves back towards its normal level.
For example, if the spread returns to the mean and the Z-score is close to zero, the trader may exit both positions.
If the relationship does not act as expected, traders can also use a stop-loss or time-based exit. This can help to limit losses if the pair continues to diverge. It is worth noting that Z-score thresholds vary between strategies.
Advantages of Pair Trading
Pair trading has the advantage of focusing on relative price movements rather than just betting on the market going up or down.
The strategy can offset some of the exposure to broad market moves by buying one stock and shorting the other. This is why pair trading is often described as a market-neutral strategy.
The two positions are still in different stocks, so the strategy is not completely free from market risk.
Another benefit is that pair trading provides a structured way to look for temporary differences between related stocks. Measures such as correlation, cointegration, and Z-score can help to make a decision.
Risks of Pair Trading
Pair trading is not a guaranteed profit strategy. One of its biggest risks is that the relationship between two stocks may break down permanently.
For example, a significant change in a company's business, management, financial condition, or industry could cause the stock to behave differently from its prior pattern.
Indian Market Execution Considerations for Pair Trading
- Regulatory constraints on short selling: Indian regulations explicitly prohibit naked short selling. Traders executing the short leg of a pair must ensure timely delivery obligations are met, typically utilizing the Securities Lending and Borrowing (SLB) platform or squaring off intraday positions if operating strictly within an intraday framework.
- Liquidity and derivative availability: Robust pair execution requires selecting stocks with deep market depth and active derivative segments (stock futures and options) to minimize execution slippage and accommodate leverage.
- Cost structures and STT: Transaction expenses in the Indian market including brokerage, Exchange Transaction Charges, Goods and Services Tax (GST), SEBI turnover fees, and the Securities Transaction Tax (STT) apply to both legs of the trade independently, directly impacting net convergence margins.
- Corporate action adjustments: Dividend payouts, stock splits, rights issues, and mergers can trigger sudden artificial jumps in price spreads. Positions must be monitored or squared off ahead of major corporate announcements to prevent structural distortion of the cointegration model.
Other risks include:
- False signals: A spread may appear unusually wide but continue moving further away.
- Changing relationships: Stocks that once moved together may stop doing so.
- Short-selling costs: Borrowing costs and other charges can reduce returns.
- Transaction costs: Buying and selling two positions creates additional trading costs.
- Slippage: The difference between the price you expect to execute a trade and the actual price at which the trade is executed.
- Model risk: Statistical associations derived from historical data may not hold for future market conditions.
This is why investors need clear entry and exit rules and should periodically verify that the relationship between the two stocks remains valid.
Conclusion
Pair trading can be useful for those who want to focus on the difference between two related stocks rather than trying to predict whether the market will go up or down. This strategy may not always work, as the correlation between the two stocks can change over time. So, traders should have clear trading rules, monitor their positions, and keep potential losses in check.
