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Last Updated on 10 February, 2024 by Rejaul Karim

* Stock pair trading* offers genuine opportunities to achieve profits through simple and relatively low-risk positions. This simple yet profitable trading method proves that a trading strategy does not have to be complicated to be able to make money.

*is a popular short-term speculation strategy that has been around on Wall Street for a long time.*

**Pairs trading**Although profitable irrespective of the market direction, the concept of pairs trading is straightforward. In this post, we will examine research findings on this trading method and their explanations, but first, let’s explain what the strategy is about.

**What does pairs trading with stocks mean?**

Also known as statistical arbitrage, pair trading is a strategy that involves matching a long position with a short position in two highly correlated stocks. First introduced in the mid-1980s by a group of technical analyst researchers, the strategy is market-neutral, which means that the direction of the overall market does not affect its win or loss. Whether the market goes up, down, or sideways, the strategy can make money as long as the historical correlation would continue to exist.

The goal of this non-directional trading strategy is to match two stocks that historically have been highly correlated but are currently trading at a price relationship that is out of their historical trading range (divergence in price). So, the investor must have criteria for identifying the level of price divergence at which he makes the trades. For example, it could be when the pair’s price ratio diverges “x” number of standard deviations. The investor then buys the undervalued stock (the loser) and short-sells the overvalued stock (the winner), all while maintaining market neutrality.

The profits lie in the assumption that history would repeat itself, and if that happens, the prices will converge. When the prices converge, the investor makes profits. As you can see, the strategy is based on simple contrarian principles, or what we call the concept of mean reversion. Other principles at play are the correlation of stock prices and history repeating itself after a temporary disruption in the correlation — the strategy bets on convergence when the spread between stocks widens.

Now that we know what pair trading means, let’s take a look at some of the research findings and what academics have to say about why the strategy works and if it will continue working.

**Understanding why pairs trading with stocks works**

Pairs trading with stocks is a well-known strategy that investors have been using since the 1980s, but does it really work, and if it does, why? Let’s see examine some papers and see what academics have to say about it.

**Research findings**

In the paper titled, “Pairs Trading: Performance of a Relative Value Arbitrage Rule”, Gatev, Goetzmann, and Rouwenhorst backtested the strategy with daily data spanning over 1962-2002. They matched stocks into pairs with minimum distance between normalized historical prices and found that a simple trading rule yielded average annualized excess returns of up to 11 percent for self-financing portfolios of pairs. Interestingly, the profits typically exceeded conservative transaction costs estimates. Bootstrap results suggested that the pairs effect differs from previously documented reversal profits, while the robustness of the excess returns indicates that pairs trading profits from temporary mispricing of close substitutes. They, therefore, linked profitability to the presence of a common factor in the returns, which is different from conventional risk measures.

The strategy was also found to work in the European markets. In the paper titled, “European Equity Pairs Trading: The Effect of Data Frequency on Risk and Return”, Lucey and Walshe examined an equity pairs trading strategy using daily, weekly, and monthly European share price data over the period 1998-2007. They found that when stocks are matched into pairs with minimum distance between normalized historical prices, a simple trading rule based on volatility between these prices yielded annualized raw returns of up to 15% for the weekly data frequency. Bootstrap results suggested that returns from the strategy are attributable to skill rather than luck, while insignificant beta coefficients showed that this is a market-neutral strategy. The resistance of the strategy’s returns to reversal factors suggested that pairs trading is fundamentally different from previously documented reversal strategies based on mean reversion.

Bock and Mestel in the paper titled, “A Regime-Switching Relative Value Arbitrage Rule”, found that based on relative mispricing between a pair of stocks, pairs trading strategies create excess returns if the spread between two normally co-moving stocks is away from its equilibrium path and is assumed to be mean reverting. They noted the problem of differentiating between temporary and long-lasting deviation from the spread equilibrium, and to overcome this problem, the paper combined the literature on Markov regime-switching and the scientific work on statistical arbitrage.

Statistical arbitrage strategies have also been tested on other stock exchanges. For example, in the paper titled, “Selection of a Portfolio of Pairs Based on Cointegration: A Statistical Arbitrage Strategy”, Caldeira and Moura assessed the profitability of the strategy with data from the São Paulo stock exchange ranging from January 2005 to October 2012. The paper noted that statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads with a certain degree of predictability. The authors applied cointegration tests to identify stocks to be used in pairs trading strategies. In addition to estimating long-term equilibrium and modeling the resulting residuals, the authors selected stock pairs to compose a pairs trading portfolio based on an indicator of profitability evaluated in-sample. Their empirical analysis showed that the proposed strategy exhibited excess returns of 16.38% per year, Sharpe Ratio of 1.34, and low correlation with the market.

Similarly, Bowen and Hutchinson in “Pairs Trading in the UK Equity Market: Risk and Return” provided the first comprehensive UK evidence on the profitability of the pairs trading strategy. To evaluate the effect of market frictions on the strategy, they used several estimates of transaction costs. They presented evidence on the performance of the strategy in different economic and market states. Since evidence suggested that the strategy performs well in crisis periods, they controlled for both risk and liquidity to assess performance. Their results showed that pairs trading portfolios typically have little exposure to known equity risk factors, such as market, size, value, momentum, and reversal. However, a model controlling for risk and liquidity explained a far larger proportion of returns, but incorporating different assumptions about bid-ask spreads led to reductions in performance estimates. Also, allowing for time-varying risk exposures, conditioned on the contemporaneous equity market return, showed that risk-adjusted returns were generally not significantly different from zero.

Although the relative value arbitrage rule (“pairs trading”) is well-known on financial markets and dates back to the 1980s, more recent research shows that the positive returns of this strategy are slowly diminishing. For example, in the paper titled, “Empirical Investigation of an Equity Pairs Trading Strategy“, Chen, Chen, and Li showed that an equity pairs trading strategy generates large and significant abnormal returns when using past data. But in the end, they concluded that, in line with the adaptive market efficiency theory, the return to this simple pairs trading strategy has diminished over time.

However, the declining profitability has led academics to improve their strategy. For instance, in the paper, “Does simple pairs trading still work?”, Do and Faff re-examined evidence on ‘pairs trading’ documented in US markets by Gatev, Goeztmann, and Rouwenhorst (1999, 2006). Extending their original analysis to June 2008, they confirmed a declining trend in profitability. However, contrary to popular belief, they found that the rise in hedge fund activity was not a plausible explanation for the decline, but rather, that the underlying convergence properties are less reliable — that is, there is an increased probability that a pair of close substitutes over the past 12 months would no longer be close substitutes in the subsequent half year. By augmenting the original pair matching method to incorporate the time-series aspect of historical prices, and/or by focusing on industries with a high level of homogeneity, high profitability can be maintained.

**The explanations**

Many explanations have been thrown around as to the reason why the strategy provides an edge in the market. One popular explanation is that investors’ assumptions result in the high expected probability of future returns of the pairs trading portfolio. For instance, if prices of some stock pair were closely correlated in the past, there is a high probability that those two securities share common sources of fundamental return. So, a temporary shock could move one stock out of the common price band, thereby presenting a statistical arbitrage opportunity. Normally, traders continuously update the universe of pairs so as to make sure that pairs that no longer move in synchronicity are removed from trading. Thus, the portfolio includes only pairs with a high probability that their prices would be convergent. In other words, the trading pair behave the way they are expected to do.

However, Nunzio Tartaglia, the pioneer of this strategy, believes that the explanation of the pairs trading is psychological. According to him, “Human beings don’t like to trade against human nature, which wants to buy stocks after they go up not down.” In other words, pairs traders are disciplined enough to take advantage of the undisciplined over-reaction displayed by individual investors.

On the flip side, instead of providing an explanation for the pairs trading profits, some authors ruled out many explanations, including mean-reversion as previously documented in the literature, unrealized bankruptcy risk, and the inability of arbitrageurs to take advantage of the profits due to short-sale constraints. For example, examining the economic drivers of this strategy, Chen, Chen, and Li discovered that the return is not driven purely by the short-term reversal of returns. Secondly, they decomposed the pair-wise stock return correlations into those that can be explained by common factors (such as size, book-to-market, and accruals) and those that cannot, and they found that the pairs correlations explainable by common factors drive most of the pairs trading returns. Thirdly, they found that the value-weighted profits of pairs trading were higher in firms in a richer information environment — their trading strategy performed poorly in the recent liquidity crisis, suggesting that the pairs trading profits are not primarily driven by the delay in information diffusion and liquidity provision. And lastly, they found that the return to this simple pairs trading strategy has diminished over time, in line with the adaptive market efficiency theory.

However, as we have seen from the work of Do and Faff, by augmenting the original pair matching method to incorporate the time-series aspect of historical prices, and/or by focusing on industries with a high level of homogeneity, high profitability can be maintained.

**Factors that affect pairs trading with stocks **

Some of them include the following:

**Liquidity crisis**: When there is a liquidity crisis, the strategy tends to perform better, but that is not always the case as Chen, Chen, and Li found.**Volatility changes**: A change in volatility in one or both of the stocks in a pair can affect the profitability of the strategy, either positively or negatively.**Trading costs**: Of course, high trading fees can reduce profitability.

**Why take advantage of pair trading with stocks**

Pairs trading strategy may be helpful in hedging your stock portfolio during bear markets. Generally, the strategy is market neutral and so performs regardless of a bear market.

But interestingly, the strategy performs even better when there are market crises, as was shown by the work of Bowen and Hutchinson.

**How to implement pair trading**

Create an investment universe that consists of stocks from the various U.S exchanges, but make sure illiquid stocks are not part of the investment universe. Next, create the cumulative total return index for each stock (dividends included), but set the starting price during the formation period to $1 (price normalization).

Use a twelve-month formation period and six-month trading period to find the right pairs. You find the matching partner for each stock by looking for the security that minimizes the sum of squared deviations between two normalized price series. Pick top 20 pairs with the smallest historical distance measure. Open a long-short position when pair prices have diverged by two standard deviations — buy the loser and sell the winner — and close your positions when prices revert.

## FAQ

**How does pairs trading work?**

The goal of pairs trading is to identify two stocks that historically have been highly correlated but are currently trading at a price relationship outside their historical range. Traders use criteria like price divergence or statistical measures to identify trading opportunities. Profits are made by betting on the convergence of prices when the spread between the paired stocks widens.

**Why does pairs trading with stocks provide an edge in the market?**

Pairs trading profits are attributed to factors such as the statistical arbitrage opportunity presented by temporary shocks, mean reversion, and the ability to exploit over-reactions displayed by individual investors. Additionally, pairs trading portfolios are continually updated to ensure they include pairs with a high probability of price convergence.

**How can I implement pairs trading with stocks?**

To implement pairs trading, create an investment universe, normalize stock prices, use a formation period to identify pairs, and open a long-short position when pair prices have diverged by a specified measure (e.g., two standard deviations). Close positions when prices revert.