# Pairs Trading with Stocks

The practice often shows that profitable trading strategies do not have to be complicated, a good example is a well known Pairs Trading with Stocks. The Pairs Trading is a popular short-term speculation strategy with a long history on Wall Street. However, as it was previously mentioned, the concept of pairs trading is really simple. A potential investor has to find two stocks whose prices have moved together historically. Nextly, when the spread between them widens, short the winner and buy the loser. The profits lie in assumption that the history would repeat. If history repeats itself, prices will converge and the arbitrageur will profit. To sum it up, this strategy is based solely on simple contrarian principles and past stock prices. Simply said, the strategy bets on convergence when the spread between stocks widens.

Additionally, same pattern was found in the european markets. Lucey and Walshe in the "European Equity Pairs Trading: The Effect of Data Frequency on Risk and Return" examined an equity pairs trading strategy using daily, weekly and monthly European share price data over the period 1998-2007. The authors shows that when stocks are matched into pairs with minimum distance between normalised historical prices, a simple trading rule based on volatility between these prices yields annualised raw returns of up to 15% for the weekly data frequency.

On a less positive note, more recent reasearch states that the positive returns of this strategy are slowly diminishing. For example, Chen, Chen and Li in the "Empirical Investigation of an Equity Pairs Trading Strategy", have also showed while using past data that an equity pairs trading strategy generates large and significant abnormal returns. However, at the end they said that consistent with the adaptive market efficiency theory, the return to this simple pairs trading strategy has diminished over time. Eroding profits have led academics to improve the strategy. As example, we would like to mention the paper "Does simple pairs trading still work?" written by Do and Faff (the paper can be found in the "Other Papers" section).

## Fundamental reason

Pioneer of this strategy Nunzio Tartaglia states that the explanation of the pairs trading is psychological. He claims, that "Human beings don't like to trade against human nature, which wants to buy stocks after they go up not down." This means that pairs traders are the disciplined investors taking advantage of the undisciplined over-reaction displayed by individual investors.

The profits could be also explained by some logical assumptions that result in the high expected probability of future returns of the Pairs Trading portfolio. If prices of some stock pair in past were closely cointegrated, there is a high probability that those two securities share common sources of fundamental return correlations. However, a temporary shock could move one stock out of the common price band which presents a statistical arbitrage opportunity. Additionally, the universe of pairs is continuously updated and this ensures that pairs which no longer move in synchronicity are removed from trading. Therefore, the portfolio includes only pairs with high probability that their prices would be convergent. Moreover, the authors ruled out several explanations for the pairs trading profits, 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.

Chen, Chen and Li in the "Empirical Investigation of an Equity Pairs Trading Strategy" have examined the economic drivers of this strategy. First, they have found that this return is not driven purely by the short-term reversal of returns. Secondly, they have 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. Quoting the authors: "We find that the pairs correlations explainable by common factors drive most of the pairs trading returns. Third, the value-weighted profits of pairs trading are higher in firms in a richer information environment, and our trading strategy performs 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. Finally, consistent with the adaptive market efficiency theory, the return to this simple pairs trading strategy has diminished over time." The last only underlines the need for the enhanced Pair Trading strategy - for example the work of Do and Faff.

### Keywords:

## pairs trading, equity long short, arbitrage

## Simple trading strategy

Illiquid stocks are removed from the investment universe. Cumulative total return index is then created for each stock (dividends included) and starting price during formation period is set to $1 (price normalization). Pairs are formed over a twelve-month period (formation period) and are then traded in next six-month period (trading period). The matching partner for each stock is found by looking for the security that minimizes the sum of squared deviations between two normalized price series. Top 20 pairs with the smallest historical distance measure are then traded and long-short position is opened when pair prices have diverged by two standard deviations and the position is closed when prices revert back.

## Source Paper

Gatev, Goetzmann, Rouwenhorst: Pairs Trading: Performance of a Relative Value Arbitrage Rule

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=141615

Abstract:

We test a Wall Street investment strategy, pairs trading, with daily data over 1962-2002. Stocks are matched into pairs with minimum distance between normalized historical prices. A simple trading rule yields average annualized excess returns of up to 11 percent for selffinancing portfolios of pairs. The profits typically exceed conservative transaction costs estimates. Bootstrap results suggest that the pairs effect differs from previously-documented reversal profits. Robustness of the excess returns indicates that pairs trading profits from temporary mis-pricing of close substitutes. We link the profitability to the presence of a common factor in the returns, different from conventional risk measures.

## Other Papers

Do, Faff: Does simple pairs trading still work?

http://www.fma.org/Turin/Papers/LOPpairstrading.pdf:

Abstract:

We re-examine and enhance evidence on ‘pairs trading’ most prominently documented in US markets by Gatev, Goeztmann and Rouwenhorst (1999, 2006). Extending their original analysis to June 2008, we confirm a continuation of the declining trend in profitability. However, contrary to popular belief, we find that the rise in hedge fund activity is not a plausible explanation for the decline. Instead, we observe that the underlying convergence properties are less reliable - there is an increased probability that a pair of close substitutes over the past 12 months are no longer close substitutes in the subsequent half year. This fragility in the Law of One Price dynamics reflects increased fundamental risks, or uncertainty in market perception of relative values of the paired securities. Nevertheless, we still find more than half the selected pairs are either profitable or very profitable. Moreover, we demonstrate some success in identifying these successful cases 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.

Jacobs, Weber: Losing Sight of the Trees for the Forest? Pairs Trading and Attention Shifts

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2023539

Abstract:

This paper tests asset pricing implications of the investor attention shift hypothesis proposed in recent theoretical work. Our objective is to directly assess how the dynamics of investor inattention affect the relative pricing efficiency of linked assets. We create a novel proxy for investor distraction in the time series and explore its impact in a promising and so far widely neglected setup: Stock pairs trading (Gatev(2006)), a popular proprietary relative value arbitrage approach. Relying on almost 50 years of daily data for the US stock market as well as on evidence from eight major international stock markets, we provide broad and robust evidence for substantial distraction effects. For instance, the average one-month return on long-short US stock pairs that open on high distraction days is about twice as high as the return on pairs that open on low distraction days. A number of conceptually quite diverse tests further lend support to the idea of time-varying investor attention being an important source of friction in financial markets.

Chen, Chen, Li: Empirical Investigation of an Equity Pairs Trading Strategy

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1361293

Abstract:

We show that an equity pairs trading strategy generates large and significant abnormal returns. We then examine the economic drivers of this strategy. First, we find that this return is not driven purely by the short-term reversal of returns. Second, we decompose 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. We find that the pairs correlations explainable by common factors drive most of the pairs trading returns. Third, the value-weighted profits of pairs trading are higher in firms in a richer information environment, and our trading strategy performs 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. Finally, consistent with the adaptive market efficiency theory, the return to this simple pairs trading strategy has diminished over time.

Lucey, Walshe: European Equity Pairs Trading: The Effect of Data Frequency on Risk and Return

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2150217

Abstract:

This article examines an equity pairs trading strategy using daily, weekly and monthly European share price data over the period 1998-2007. The authors shows that when stocks are matched into pairs with minimum distance between normalised historical prices, a simple trading rule based on volatility between these prices yields annualised raw returns of up to 15% for the weekly data frequency. Bootstrap results suggest returns from the strategy are attributable to skill rather than luck, while insignificant beta coefficients provide evidence that this is a market neutral strategy. Resistance of the strategy’s returns to reversal factors suggest pairs trading is fundamentally different to previously documented reversal strategies based on concepts such as mean reversion.

Bock, Mestel: A Regime-Switching Relative Value Arbitrage Rule

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1213802

Abstract:

The relative value arbitrage rule ("pairs trading") is a well-established speculative investment strategy on financial markets, dating back to the 1980s. Based on relative mispricing between a pair of stocks, pairs trading strategies create excess returns if the spread between two normally comoving stocks is away from its equilibrium path and is assumed to be mean reverting. To overcome the problem of detecting temporary in contrast to longer lasting deviations from spread equilibrium, this paper bridges the literature on Markov regime-switching and the scientific work on statistical arbitrage.

Caldeira, Moura: Selection of a Portfolio of Pairs Based on Cointegration: A Statistical Arbitrage Strategy

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2196391

Abstract:

Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean- reverting spreads with a certain degree of predictability. This paper applies cointegration tests to identify stocks to be used in pairs trading strategies. In addition to estimating long-term equilibrium and to model the resulting residuals, we select stock pairs to compose a pairs trading portfolio based on an indicator of profitability evaluated in-sample. The profitability of the strategy is assessed with data from the São Paulo stock exchange ranging from January 2005 to October 2012. Empirical analysis shows that the proposed strategy exhibit excess returns of 16.38% per year, Sharpe Ratio of 1.34 and low correlation with the market.

Bowen, Hutchinson: Pairs Trading in the UK Equity Market: Risk and Return

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2350113

Abstract:

In this paper we provide the first comprehensive UK evidence on the profitability of the pairs trading strategy. Evidence suggests that the strategy performs well in crisis periods, so we control for both risk and liquidity to assess performance. To evaluate the effect of market frictions on the strategy we use several estimates of transaction costs. We also present evidence on the performance of the strategy in different economic and market states. Our results show 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 explains a far larger proportion of returns. Incorporating different assumptions about bid ask spreads leads to reductions in performance estimates. When we allow for time-varying risk exposures, conditioned on the contemporaneous equity market return, risk adjusted returns are generally not significantly different from zero.

Clegg: On the Persistence of Cointegration in Pairs Trading

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2491201

Abstract:

An exploratory study is conducted to assess the persistence of cointegration among U.S. equities. In other words, if a pair of equities is found to be cointegrated in one period, is it likely that it will be found to be cointegrated in the subsequent period? An examination is performed of pairs formed from constituents of the S&P 500 during each of the calendar years 2002-2012, comprising over 860,000 pairs in total. The evidence does not support the hypothesis that cointegration is a persistent property.

Jacobs, Weber: On the Determinants of Pairs Trading Profitability

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2545440

Abstract:

We perform a large-scale empirical analysis of pairs trading, a popular relative-value arbitrage approach. We start with a cross-country study of 34 international stock markets and uncover that abnormal returns are a persistent phenomenon. We then construct a comprehensive U.S. data set to explore the sources behind the puzzling profitability in more depth. Our findings indicate that the type of news leading to pair divergence, the dynamics of investor attention as well as the dynamics of limits to arbitrage are important drivers of the strategy's time-varying performance.

Leung, Li: Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2222196

Abstract:

Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. An optimal double stopping problem is formulated to analyze the timing to start and subsequently liquidate the position subject to transaction costs. Modeling the price spread by an Ornstein-Uhlenbeck process, we apply a probabilistic methodology and rigorously derive the optimal price intervals for market entry and exit. As an extension, we incorporate a stop-loss constraint to limit the maximum loss. We show that the entry region is characterized by a bounded price interval that lies strictly above the stop-loss level. As for the exit timing, a higher stop-loss level always implies a lower optimal take-profit level. Both analytical and numerical results are provided to illustrate the dependence of timing strategies on model parameters such as transaction cost and stop-loss level.

Xie, Liew, Wu, Zou: Pairs Trading with Copulas

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2383185

Abstract:

Pairs trading is a well-acknowledged speculative investment strategy that is widely used in the financial markets, and distance method is the most commonly implemented pairs trading strategy by traders and hedge funds. However, this approach, which can be seen as a standard linear correlation analysis, is only able to fully describe the dependency structure between stocks under the assumption of multivariate normal returns. To overcome this limitation, we propose a new pairs trading strategy using copula modeling technique. Copula allows separate estimation of the marginal distributions of stock returns as well as their joint dependency structure. Thus, the proposed new strategy, which is based on the estimated optimal dependency structure and marginal distributions, can identify relative undervalued or overvalued positions with more accuracy and confidence. Hence, it is deemed to generate more trading opportunities and profits. A simple one-pair-one-cycle example is used to illustrate the advantages of the proposed method. Besides, a large sample analysis using the utility industry data is provided as well. The overall empirical results have verified that the proposed strategy can generate higher profits compared with the conventional distance method. We argue that the proposed trading strategy can be considered as a generalization of the conventional pairs trading strategy.

Almeida: Improving Pairs Trading

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2432061

Abstract:

This paper tests the Pairs Trading strategy as proposed by Gatev, Goetzmann and Rouwenhorts (2006). It investigates if the profitability of pairs opening after an above average volume day in one of the assets are distinct in returns characteristics and if the introduction of a limit on the days the pair is open can improve the strategy returns. Results suggest that indeed pairs opening after a single sided shock are less profitable and that a limitation on the numbers of days a pair is open can significantly improve the profitability by as much as 30 basis points per month.

Rad, Yew Low, Faff: The Profitability of Pairs Trading Strategies: Distance, Cointegration, and Copula Methods

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2614233

Abstract:

We examine and compare the performance of three different pairs trading strategies - the distance cointegration, and copula methods - on the US equity market from 1962 to 2014 using a time-varying series of trading costs. Using various performance measures, we conclude that cointegration strategy performs as well as the distance method. However, the copula method shows relatively poor performance. Particularly, the distance, cointegration, and copula methods show a mean monthly excess return of 36, 33, and 5 bps after transaction costs and 88, 83, and 43 bps before transaction costs. In recent years, the distance and cointegration methods have presented less trading opportunities whereas this frequency remains stable for the copula method. While liquidity factor is negatively correlated to all strategies' returns, we find no evidence of their correlation to market excess returns. All strategies show positive and significant alphas after accounting for various risk-factors.

Goncu, Akyildirim: Statistical Arbitrage with Pairs Trading

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2610064

Abstract:

We analyse statistical arbitrage with pairs trading assuming that the spread of two assets follows a mean-reverting Ornstein-Uhlenbeck process around a long-term equilibrium level. Within this framework, we prove the existence of statistical arbitrage and derive optimality conditions for trading the spread portfolio. In the existence of uncertainty in the long-term mean and volatility of the spread, statistical arbitrage is no longer guaranteed. However, the asymptotic probability of loss can be bounded as a function of the standard error of the model parameters. The proposed framework provides a new filtering technique for identifying best pairs in the market. Empirical examples are provided for three pairs of stocks from the NYSE.

Cartea, Jaimungal: Algorithmic Trading of Co-Integrated Assets

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2637883

Abstract:

We assume that the drift in the returns of asset prices consists of an idiosyncratic component and a common component given by a co-integration factor. We analyze the optimal investment strategy for an agent who maximizes expected utility of wealth by dynamically trading in these assets. The optimal solution is constructed explicitly in closed-form and is shown to be affine in the co-integration factor. We calibrate the model to three assets traded on the Nasdaq exchange (Google, Facebook, and Amazon) and employ simulations to showcase the strategy's performance.

Riedinger: Demystifying Pairs Trading: The Role of Volatility and Correlation

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2774063

Abstract:

This paper investigates how the two technical drivers, volatility and correlation, influence the algorithm of the investment strategy pairs trading. We model and empirically prove the connection between the rule-based pair selection, the trading algorithm, and the total return. Our insights explain why pairs trading profitability varies across markets, industries, macroeconomic circumstances, and firm characteristics. Furthermore, we critically evaluate the power of the traditionally applied pair selection procedure. In the US market, we find risk-adjusted monthly returns of up to 76bp for portfolios, which are double sorted on volatility and correlation between 1990 and 2014. Our findings are robust to liquidity issues, bid-ask spread, and limits of arbitrage.

Mazo, Lafuente, Gimeno: Pairs Trading Strategy and Idiosyncratic Risk. Evidence in Spain and Europe.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2807956

Abstract:

Pairs trading strategy’s return depends on the divergence/convergence movements of a selected pair of stocks’ prices. However, if the stable long term relationship of the stocks changes, price will not converge and the trade opened after divergence will close with losses. We propose a new model that, including companies’ fundamental variables that measure idiosyncratic factors, anticipates the changes in this relationship and rejects those trades triggered by a divergence produced by fundamental changes in one of the companies. The model is tested on European stocks and the results obtained outperform those of the base distance model.

Do, Faff: Cointegration and Relative Value Arbitrage

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2826190

Abstract:

We examine a new method for identifying close economic substitutes in the context of relative value arbitrage. We show that close economic substitutes correspond to a special case of cointegration whereby individual prices have approximately the same exposure to a common nonstationary factor. A metric of closeness constructed from the cointegrating relation strongly predicts both convergence probability and profitability in cointegration-based pairs trading. From 1962 to 2013, a strategy of trading cointegrated pairs of near-parity generates 58 bps per month after trading costs, experiences a 71% convergence probability and outperforms a strategy of pairs selected by minimized price distances.

Donninger: Is Daily Pairs Trading of ETF-Stocks Profitable?

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2816288

Abstract:

Pairs trading is a venerable trading strategy. There is agreement that it worked fine in the far past. But it is less clear if it still profitable today. In this working paper the universe of eligible pairs is defined by the holdings of a given ETF. It is shown that the stocks must be from ETFs which select high-quality, low-volatility stocks. The usual closeness measure presented in the literature performs poor. The paper presents a simple and clearly superior alternative based on zero-crossings. The strategy performs with the correct universe and the improved pairs selection rule before trading costs quite fine. It depends on the assumed trading costs if this is also in real-trading life the case.

Figuerolla-Ferretti, Serrano, Tang, Vaello-Sebastia: Supercointegrated

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3005358

Abstract:

This paper uses S&P100 data to examine the performance of pairs trading portfolios that are sorted by the significance level of cointegration between their constituents. We find that portfolios that are formed with highly cointegrated pairs, named as "supercointegrated", yield the best performance reflecting a positive relationship between the level of cointegration and pairs trading profitability. The supercointegrated portfolio also shows superior out-of-sample performance to the simple buy-and-hold investments on the market portfolio in terms of Sharpe ratio. We link the time-varying risk of the pairs trading strategy to aggregated market volatility. Moreover we report a positive risk-return relationship between the strategy and market volatility, which is enhanced during the bear market. Our results remain valid when applying the strategy to European index data.

da Silva, Ziegelman, Caldeira: Pairs Trading: Optimizing via Mixed Copula versus Distance Method for S&P 500 Assets

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3070950

Abstract:

We carry out a study to evaluate and compare the relative performance of the distance and mixed copula pairs trading strategies. Using data from the S&P 500 stocks from 1990 to 2015, we find that the mixed copula strategy is able to generate a higher mean excess return than the traditional distance method under different weighting structures when the number of tradeable signals is equiparable. Particularly, the mixed copula and distance methods show a mean annualized value-weighted excess returns after costs on committed and fully invested capital as high as 3.98% and 3.14% and 12.73% and 6.07%, respectively, with annual Sharpe ratios up to 0.88. The mixed copula strategy shows positive and significant alphas during the sample period after accounting for various risk-factors. We also provide some evidence on the performance of the strategies over different market states.

Psaradellis, Laws, Pantelous, Sermpinis: Pairs Trading, Technical Analysis and Data Snooping: Mean Reversion vs Momentum

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3128788

Abstract:

We examine the technical trading rules performance on the statistical arbitrage investment strategy using daily data from 1990 to 2016 for 15 commodity, equity and currency pairs. Adopting the false discovery rate method to control for data snooping bias and exercising 18,412 technical trading rules, we find evidence of significant predictability and excess profitability, especially for commodity spreads, in which the best performing strategy generates an annualized mean excess return of 17.6%. In addition, we perform an out-of-sample analysis to cross-validate our results in different subperiods. We find that whilst the profitability of rules based on technical analysis exhibits a downward trend over the sample, the opportunities for pairs trading returns have been increased in certain cases.

## Hypothetical future performance

## Real-time implementation by QuantConnect

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