Pairs Trading: A Deep Dive into this Market Neutral Strategy

In the financial world, “pairs trading” is a market concept that involves
identifying two related securities that move in harmony.

The selection of securities is akin to choosing dance partners who move well
together. To make the best selections, traders delve into historical
relationships and perform correlation analysis. However, the market, much
like life, is unpredictable. Even the best pairs can fall out of sync.

This article explains how pairs trading works, with a focus on how the spread is calculated, how to manage risk and exit a trade, and the analytical tools traders use. So, let’s
get started.

Table of Contents

• Foundations in Pairs Trading
• Statistical Arbitrage Trading Strategy
• How to Implement Pairs Trading
• How Do You Calculate the Spread for Pairs Trading?
• Quantitative Trading Strategies
• High-Frequency Cointegration-Based Pairs Trading Model Using Historical Equity Data
• Using Bookmap for Pairs Trading
• Cointegration Model or Simple Correlation-Based Strategy: Which Should You Build?
• Conclusion
• FAQ

Foundations in Pairs Trading

Pairs trading is firmly grounded in the principles of

statistical arbitrage

and mean reversion. It’s a market strategy that involves:

• Methodical identification of two closely related securities, often
  two stocks operating within the same sector.

• Creating a pair to trade based on the historical relationship
  between their prices.

Let’s understand the rationale.

The Rationale Behind the Strategy

Pairs trading doesn’t focus on the individual performance of each stock but
rather on the relative performance between the two stocks. The ultimate goal
is to comprehend the consistent distance or relationship.

For instance, if two stocks were racing cars, pairs trading wouldn’t bet on
who wins, but on the distance between them staying consistent.

The Basis of Pairs Trading

Pairs trading as a strategy is based on these two foundational concepts:

 

How Correlation Drives Pairs Trading

In the context of pairs trading,

correlation

can be likened to two synchronized swimmers. Just as these swimmers move in
harmony, correlated stocks move together and show a similar directional
movement in their prices. When graphing the correlation between stock pairs
over time, you would typically see a line or chart showing the degree of
correlation.

In ideal circumstances, this trend should:

– Stay consistently high and stable over time

Such a trend signifies a robust positive correlation, indicating that the
prices of the paired stocks move harmoniously in the same direction.

 

Is Stock Correlation Foolproof?

No, it is not. Despite the apparent synchrony in correlated pairs, there
have been instances where even highly correlated stocks have deviated from
their expected behavior. Let’s explore the various factors contributing to
these deviations:

i. Unforeseen Events: Sudden market shocks, economic crises, regulatory
changes, or unexpected news can disrupt the customary correlation between
related stocks.

 

ii. Company-Specific News: Events such as earnings reports, management
changes, or product success or failure can prompt one stock within a
correlated pair to diverge from the other.

 

iii. Changes in Investor Sentiment: Shifting market trends, alterations in
investor sentiment, or changes in macroeconomic conditions can also lead to
temporary interruptions in the correlation between paired stocks.

 

Statistical Arbitrage Trading Strategy

Statistical arbitrage is the family of strategies that trade temporary price gaps between related securities using statistical models. Pairs trading is its simplest form: two securities and one spread. Larger versions trade baskets of dozens or hundreds of stocks, hedge against sector and factor exposure, and manage everything as one portfolio.

The word “arbitrage” can mislead. A classic arbitrage locks in a profit with no risk. Statistical arbitrage does not. It makes many bets that each have a positive expected value, and any single bet can lose.

The best-known academic test of pairs trading was published in 2006 by Gatev, Goetzmann and Rouwenhorst. They matched stocks over a 12-month formation period, traded the pairs for the next six months, and opened a position when prices diverged by more than two standard deviations. Using daily data from 1962 to 2002, they found average annualized excess returns of up to 11% for portfolios of top pairs, and profits that typically exceeded conservative cost estimates. Later research found that the profits have declined over time as the strategy became widely known. For the broader idea, see Bookmap’s guide to arbitrage trading.

Cointegrated Stock Pair Trading

Correlation measures whether two stocks’ returns move together from day to day. Cointegration asks something different: does the distance between their prices keep returning to an average? Two stocks can have highly correlated returns and still drift apart for years, which is a problem for a pairs trade, because the spread never comes back. A cointegrated pair cannot drift apart permanently. A common picture is a dog on a long leash: the dog and its owner can wander, but not far from each other.

A standard check is the Engle-Granger test. First, regress one price on the other to get a hedge ratio. Then test whether the leftover, the spread, is stationary, meaning it fluctuates around a stable average, for example with an augmented Dickey-Fuller test. A low p-value suggests that the spread mean-reverts.

Two cautions apply:

• A result in one window is not a promise. Relationships break, so the test has to be repeated and the pair checked on data it was not selected on.

• Scanning creates false positives. Testing 1,000 stocks means 499,500 pairs. Even if no real relationships existed, a 5% significance level would flag about 24,975 of them by chance. Pairs found by scanning should be confirmed out of sample, and ideally have an economic reason to move together, such as the same industry, the same business or two share classes of one company.

For the correlation side, see Bookmap’s guide to market correlations.

What Are the Main Risks of Statistical Arbitrage?

Statistical arbitrage has several risks that a simple pairs example hides:

• The relationship breaks. A merger, an earnings shock, a regulatory change or a bankruptcy can end the link between two stocks, and the spread may never revert.

• False discoveries and overfitting. Scanning many pairs and tuning parameters to a backtest can produce a strategy that only works on the past.

• Costs on four trades. Entering and exiting two legs means four trades, each with a spread, commissions and slippage, plus borrow fees on the short leg. Bookmap’s guide to slippage covers the calculation.

• Short selling limits. Shares must be borrowed, borrow can be expensive or unavailable, and a lender can recall the shares. In the US, a short sale price test can also apply after a stock falls sharply in one day.

• Legging risk. One leg fills and the other does not, leaving a directional position. Bookmap’s guide to TWAP and VWAP covers ways to work orders.

• Leverage. Margin calls can force a trader to close at the worst moment.

• Crowding. In the week of August 6, 2007, a number of quantitative long/short equity hedge funds suffered unprecedented losses. Researchers Khandani and Lo hypothesized that it started with the rapid unwind of one or more large quantitative market-neutral portfolios, and spread through stop-loss and de-leveraging policies.

• Decay. Strategies lose their edge as more traders use them.

How to Implement Pairs Trading

Choosing the appropriate pair is the cornerstone of successful pairs
trading. Usually, this decision is based on historical co-movement between
two stocks. Let’s explore this process in greater detail.

Selecting the Right Pair

Selecting a stock pair for pairs trading can be likened to selecting dance
partners. Just like good dancers move in sync, a successful pair in trading should show a strong historical relationship in their prices, and ideally a spread that keeps returning to its average. Statisticians test for this with cointegration, covered below.

Let’s understand it better through a hypothetical case.

• There are two tech companies, say A and B.

• Both have shown a consistent historical relationship in their stock
  prices.

• Over a span of six months, both stocks have consistently moved in
  tandem.

This correlation can be observed through:

• Rigorous statistical analysis

• Comprehensive charting

• Thorough research into their historical price movements.

How Choosing the Wrong Pair Hurts Traders

Traders can suffer substantial losses if:

• The selected pair doesn’t exhibit a strong historical correlation

• Unforeseen factors disrupt the typical relationship between the
  chosen assets

This unfortunate outcome occurs when poorly matched correlated assets
deviate from their usual pattern, moving apart rather than converging. It
underscores the critical importance of careful pair selection in pairs
trading.

How Can Traders Choose Optimal Pairs?

 

Calculating the Spread and Entry Points

The “spread” is like the lead in the dance for pairs trading. It represents
the difference in prices between the two paired securities. Just as a lead
dancer guides the movements, the spread guides the trade decisions in pairs
trading.

Let’s have a closer look at its calculation through a hypothetical scenario.

• Consider a pair of stocks, Company X and Company Y.

• Their prices are $50 and $45 respectively.

• To calculate the spread, subtract the price of one stock from the
  other:

  • Spread: Stock X price ($50) – Stock Y price ($45) = $5

Suppose that over the past year the spread has averaged $5, with a typical swing of about $1 (its standard deviation). A spread of $5 is then right at its average.

How to Spot Entry Points Via Spread Analysis?

In pairs trading, an entry point occurs when one stock stumbles (such as
experiencing a price decline) while the other doesn’t. Let’s assume in the
above example, Stock X stumbles, dropping to $48, but Stock Y remains steady
at $45. This fluctuation causes the spread to narrow below its average. The revised spread
would be calculated as follows: Stock X price ($48) – Stock Y price ($45) =
$3. A spread of $3 is $2 below its average, or two standard deviations, which some traders treat as a potential entry point.

Trading Opportunity

This deviation of the spread from its average indicates a possible opportunity for pairs traders.
Their primary aim is to profit from the expected reversion of the spread
back to its historical average. In such a case, most traders would resort to
the following strategy:

 

Managing Risk and Exit Strategies

You can think of the market as a tempestuous sea, subject to constant
changes and unpredictability. Even the most robust pairs in pairs trading
can fall out of sync due to unforeseen events or shifts in market dynamics.
This falling out creates the need for concrete risk management strategies,
such as:

• Setting Stop-Loss Orders:

  • Implementing stop-loss orders helps in limiting potential trade
    losses.

  • In pairs trading, the stop usually applies to the spread, not to one stock. Most stock brokers do not offer a stop order on a spread, so traders monitor the spread or its z-score and close both legs together when it reaches a set level.

  • For instance, a trader can decide in advance to close both legs if the spread moves a set number of standard deviations beyond the entry level.

• Position Sizing:

  • Managing the size of positions taken in each stock within the
    pair is essential.

  • By allocating an appropriate portion of the overall portfolio to
    each trade, traders can control risk exposure.

Let’s highlight the importance of risk management and forming appropriate
exit strategies through some hypothetical stories of trades gone south:

The Event

• Consider a pair of stocks, Company A and Company B.

• Both maintain a historically strong correlation.

• A trader enters a pairs trade when the spread widens due to
  unexpected market volatility.

• Committed to risk management, the trader sets an exit level for the spread.

The Break

• Instead of reverting as anticipated, the stocks continue to move
  further apart.

• The trader sensed a break in their usual correlation.

The Saving Exit Strategy

• As the spread moves beyond the predetermined threshold, the trader closes both legs.

• The position gets closed to limit further losses.

The Result

While the trade ultimately results in a loss, owing to the unforeseen
divergence between the paired stocks, the trader’s unwavering adherence to a
disciplined exit strategy serves as a safeguard against more substantial
losses. This narrative underscores the paramount importance of risk
management and the implementation of well-considered exit strategies in
pairs trading.

How Do You Calculate the Spread for Pairs Trading?

The earlier example uses a simple price difference, which works only if one share of X offsets one share of Y. There are three common ways to define the spread:

The hedge ratio, beta, is usually the slope of a regression of X on Y over a formation window. Here is the earlier example with a beta of 1.10. The starting spread is 50 – 1.10 x 45 = 0.50. Suppose that over the past year the average spread was 0.50, with a standard deviation of 1.00. When X falls to $48 and Y stays at $45, the spread becomes 48 – 49.50 = -1.50, and the z-score is:

z = (spread – average spread) / standard deviation = (-1.50 – 0.50) / 1.00 = -2.0

That means X is cheap relative to Y by two standard deviations, so the trade is long X and short Y. The hedge ratio also sets the share counts: long 1,000 shares of X ($48,000) and short 1,100 shares of Y ($49,500) is roughly dollar neutral.

A z-score says how unusual the spread is. It does not say the spread must return. Use a window long enough to give a stable average and standard deviation, and re-estimate the hedge ratio from time to time. One naming point: this “spread” is not the bid-ask spread. For that, see Bookmap’s guide to spreads in financial markets.

Quantitative Trading Strategies

Pairs trading is one of several quantitative strategies: strategies that use rules and statistics tested on data instead of case-by-case judgment. Common families include mean reversion (pairs trading and statistical arbitrage), momentum and trend following, factor strategies such as value and quality, and market making and execution algorithms.

They share a process:

1. A hypothesis. Why should the edge exist? For pairs, related stocks are priced by similar forces, so their spread reverts.

2. Clean data. Prices adjusted for splits and dividends, with aligned timestamps.

3. A signal. For pairs, the z-score of the spread.

4. A backtest with costs. Spread, commissions, slippage and borrow fees.

5. An out-of-sample test. Data the model was not built on.

6. Risk and sizing rules. The hedge ratio, exposure limits and exit levels.

7. Execution and monitoring. Live trading rarely matches the backtest, so track the difference.

For the planning and risk side, see Bookmap’s guides to creating a trading plan and risk management.

Market Neutral Investing

Market neutral means a portfolio is built to have little exposure to the overall market, so returns come from the relative performance of its positions. There are three levels:

• Dollar neutral. The long and short sides have equal dollar value.

• Beta neutral. The long and short sides have equal market exposure after adjusting for each stock’s beta.

• Factor and sector neutral. Exposures to sectors, size, value and other factors are balanced as well.

A dollar-neutral pair is not automatically beta neutral. Take the earlier example: $48,000 long in X with a market beta of 1.2 is $57,600 of beta-adjusted exposure, and $49,500 short in Y with a beta of 1.0 is -$49,500. The net is +$8,100, so a 5% market drop would cost about $405 on that exposure alone, even though the dollars look balanced.

Market neutral does not mean risk free. Sector and factor exposure, borrow costs, short squeezes, crowded positions and a broken relationship all remain.

High-Frequency Cointegration-Based Pairs Trading Model Using Historical Equity Data

This section builds a simple cointegration-based pairs model on price data. “High frequency” here means intraday bars, such as one-minute prices. It does not mean microsecond trading, which needs exchange co-location and infrastructure that most traders do not have.

The steps:

1. Prepare the data. Adjust for splits and dividends, align timestamps, remove bad prints and use one price type (last trade or mid price) consistently.

2. Split the data. Use a formation window to build the model and a later trading window to test it. In the example, the first 500 one-minute bars form the model.

3. Test for cointegration. Run an Engle-Granger test on the formation window.

4. Estimate the hedge ratio. Use a regression on the formation window.

5. Build the spread and a rolling z-score.

6. Set rules. Entry, exit and stop levels.

7. Backtest with costs and test out of sample.

Costs decide whether intraday pairs work. Suppose the spread’s standard deviation is $0.05 per share-pair. A trade entered at two standard deviations and closed at the average captures about $0.10. Entering and exiting two legs means four half-spreads. With a 1 cent bid-ask spread on each stock, that is about $0.02, and with $0.01 of fees the trade nets about $0.07. If spreads widen to 3 cents, costs rise to about $0.06 plus $0.01 in fees, and the net falls to about $0.03. At intraday frequencies, bid-ask bounce can also make a spread look more mean-reverting than you can trade, so test with realistic fills. Bookmap’s guides to market microstructure and tick size cover why.

Mean Reversion Pairs Trading Strategy With Dynamic Z-Score Entry Thresholds

A fixed entry at plus or minus 2 treats every market condition the same. Dynamic thresholds adapt in three ways:

• A rolling window. The z-score uses the recent average and standard deviation of the spread, here the last 120 bars, so it reflects current conditions.

• A threshold that scales with recent behavior. In the script, the entry level never drops below 2.0 and rises to the rolling 90th percentile of the absolute z-score when the spread has been volatile.

• A re-estimated hedge ratio. Some traders re-estimate beta periodically, or use a Kalman filter, so the model follows a slowly changing relationship.

The script exits when the z-score returns inside 0.5, and stops out when it moves beyond 1.5 times the entry threshold. A time stop, closing a trade that has not reverted within a set number of bars, is another common rule.

Relate the windows to the spread’s speed of reversion. If a spread mean-reverts with an autoregressive coefficient of 0.95 per bar, its half-life is about 13.5 bars, so a 120-bar window covers many cycles and a 10-bar window does not. A shorter window reacts faster but is noisier, and every extra parameter increases the chance of overfitting.

Using Bookmap for Pairs Trading

The usage of modern tools, like Bookmap, helps traders to:

• Gain a deeper understanding of correlations

• Add liquidity and order flow context to entries and exits

Bookmap offers features such as the Correlation Tracker, Market Pulse, heatmaps and volume dots that add liquidity and order flow context when trading pairs. These add-ons do not calculate a hedge ratio or run cointegration tests, so many traders use a spreadsheet or Python for that part.
Let’s understand it further.

Leveraging Bookmap for Pairs Trading Analysis

 

The Role of Algorithmic and Automated Trading

Back in the day, trading floors were filled with traders shouting orders and
frantically gesturing. Trading was human-driven and characterized by high
emotion and energy. In stark contrast, the present trading is silent. The
buzz of human activity has been completely replaced by the quiet efficiency
of algorithm-driven trading.

How Important are Algorithms?

Algorithms function as the unsung heroes of modern trading. They tirelessly
work in the background and:

• Analyze vast amounts of data

• Scan numerous stock pairs

• Quickly identify potential opportunities based on predefined
  parameters.

Algorithms can execute trades in milliseconds, far faster than a human, and apply their rules consistently.

Manual vs. Automated Trading for Pairs Trading

There’s an ongoing debate regarding manual versus automated trading for
pairs trading strategies. Let’s shed some light on it:

 

The Synergy of Manual and Automated Approaches

The debate between manual and automated trading for pairs trading doesn’t
necessarily need to be an “either/or” scenario. There’s a growing trend
toward a hybrid approach, in which traders combine the strengths of both
methods.

Traders often use automated tools for data analysis, pattern recognition,
and trade execution. At the same time, they apply their human expertise to
oversee and interpret the broader market context.

Cointegration Model or Simple Correlation-Based Strategy: Which Should You Build?

The two approaches answer different questions:

A sensible workflow uses both: correlation to screen a large list down to candidates, then cointegration to test whether a spread is tradable, then an out-of-sample check and a reason the pair should be linked. If you cannot test cointegration, a correlation-based pair is better treated as a hypothesis than as a strategy.

Trading Equities, ETFs or Crypto Assets: Which Market Fits?

The same strategy meets different frictions in each market:

For stocks, see Bookmap’s guide to evaluating stock liquidity. For crypto, see liquidation cascades in crypto and Bookmap for crypto.

Conclusion

Pairs trading represents a trading strategy in which two correlated assets
are identified. Emphasis is laid upon historical data to establish the
correlation. However, this strategy isn’t foolproof and can fail due to
unforeseen events or changes in investor sentiments.

This vulnerability creates the need for a robust exit strategy.
Additionally, tools like Bookmap’s Correlation Tracker let traders overlay the paired instruments and see the liquidity around each leg.

Pairing these tools with a solid grounding in the statistics helps traders manage the risks of pairs trading. Looking to deepen your
understanding of market dynamics?

Dive into the intricate world of market correlations, their significance,
and their direct influence on trading decisions.

Discover how market correlations impact your trading journey with our
in-depth guide!

 

FAQ

What is pairs trading?

Pairs trading buys one security and sells short a related one, based on the idea that the spread between them will return to its average.

What is statistical arbitrage?

It is a family of strategies that trade temporary price gaps between related securities using statistical models. Unlike classic arbitrage, it is not risk-free.

How do you calculate the spread for pairs trading?

Define the spread as X minus beta times Y, where beta is the hedge ratio from a regression. Then compute the z-score: the spread minus its average, divided by its standard deviation.

What is the difference between correlation and cointegration?

Correlation measures whether returns move together. Cointegration measures whether the price spread keeps returning to an average. A pair can be highly correlated and still drift apart.

What are the main risks of statistical arbitrage?

The relationship breaking, overfitting, costs on four trades, short selling limits, legging risk, leverage, crowded positions and declining profits.

Is pairs trading market neutral?

It aims to be, but dollar neutral does not mean beta neutral, and sector exposure, borrow costs and crowding remain. Market neutral does not mean risk free.

What z-score should I use to enter a pairs trade?

There is no universal level. A well-known academic study used two standard deviations. Test the level on your own data, and consider thresholds that adapt to recent volatility.

Can you do pairs trading with ETFs or crypto?

Yes. ETFs are often easier to borrow but have small spreads, so costs matter. In crypto, perpetual futures allow shorting without borrowing, but funding payments and shifting relationships add risk.

Does pairs trading still work?

A well-known study found profits from 1962 to 2002, but later research found that profits have generally declined over time. Costs, crowding and correct pair selection decide the result.

What data do I need for a cointegration model?

Clean historical prices for both securities, adjusted for splits and dividends, with aligned timestamps, and enough history for a formation window and a separate test window.