What is Pairs Trading?

Basic Concept of Pairs Trading

Pairs Trading is a market-neutral investment strategy introduced in the mid-1980s by a quantitative analysis team led by Nunzio Tartaglia, a quantitative trader at the renowned Wall Street investment bank Morgan Stanley. Also known as statistical arbitrage or market-neutral strategy, it’s a trading approach that aims to profit from price differentials between two correlated assets. It’s commonly used in financial markets, particularly stocks, futures, forex, or cryptocurrency. The key idea behind pairs trading is to select two highly correlated assets and profit from temporary price divergences by buying the undervalued asset and selling the overvalued one. Traders typically view these divergences as short-term phenomena, expecting prices to revert to their historical normal relationship eventually.

Classical Statistical Arbitrage Method Under Market-Neutral Premise

The core of the pairs trading strategy lies in capitalizing on short-term price divergences between two correlated assets, using hedging to generate additional returns (i.e., Alpha returns). This strategy is based on a fundamental assumption: The price difference between paired assets will revert to the mean over time. This means that the reversion phenomenon is closely related to the irrational behaviors of traders in the market.

When many traders generally believe that certain assets will move in a particular direction, prices often show momentum in rising. This increase usually lacks fundamental support and thus quickly falls back after reaching a certain high point. Similarly, assets with falling prices also exhibit downward momentum. When rational market behavior dominates, prices typically return to their original levels. By adopting a pairs trading strategy, traders can profit from the divergence in prices of these two types of assets.

In practical operation, the process of pairs trading can be summarized as follows: Investors first select a pair of correlated assets. When the price difference between the two widens, traders buy the lower-priced asset while simultaneously short-selling the higher-priced asset. When the price difference narrows, traders close the position on the undervalued asset, ending the trade.

How to Implement Pairs Trading?

Cointegration and Correlation Testing

In pairs trading, finding cointegrated asset pairs is key to success. These asset pairs are characterized by relatively stable price differences over the long term rather than relying solely on short-term correlations. For example, suppose an investor chooses stocks from two tech companies - Company A and Company B. While short-term market sentiment and news events may cause price fluctuations in these two stocks, their price difference tends to fluctuate around an average value over the long term.

In practical operation, the first step is to clean the data and then use correlation analysis to screen for asset pairs with highly correlated price trends. The Pearson correlation coefficient is typically used to measure the correlation between the prices of two assets, selecting pairs with high correlation coefficients as candidates. Next, these assets must undergo cointegration testing to ensure a stable long-term relationship between their prices. Common cointegration test methods include the Engle-Granger two-step method and Johansen test, which can help confirm whether the price difference exhibits mean-reverting characteristics.

Additionally, conducting stationarity tests on the price difference of asset pairs is crucial, typically using the Augmented Dickey-Fuller (ADF) test to determine if the price difference fluctuates around a mean. If the price difference series is stationary, these asset pairs are suitable for pairs trading. Finally, mean reversion tests, such as autocorrelation function analysis, are needed to confirm whether the price difference tends to revert to the mean. Investors can better identify asset pairs with long-term arbitrage potential through this series of steps.

In pairs trading, finding cointegrated asset pairs is crucial for success. The characteristic of these asset pairs is that their price difference tends to be stable over the long term rather than relying solely on short-term correlations. For instance, if an investor chooses stocks from two tech companies - Company A and Company B. Although the prices of these two stocks may fluctuate in the short term due to market sentiment and news events, their price difference typically fluctuates around a mean value over the long term.

Risk Control and Stop-Loss

Although the pairs trading strategy aims to capture price difference regression, market trends don’t always develop as expected. When the price difference shows excessive deviation, it’s necessary to implement a timely stop-loss to prevent further losses. When the price difference returns to the mean, profits should be decisively locked in. At the same time, position size should be managed reasonably based on the account’s capital size and personal risk tolerance, avoiding risks brought by over-concentrated investments. The strategy must be dynamically adjusted according to market changes and historical backtesting results to improve its adaptability and profitability.

In addition, traders should closely monitor market news and major events, use correlation coefficients to assess the correlation of asset pairs, and combine technical indicators to judge market trends and evaluate risks, ensuring a full grasp of potential risks.

Application of Pair Trading in Cryptocurrencies

In the cryptocurrency market, pair trading is a flexible and strategic arbitrage method that can help investors find stable profit opportunities in a volatile market. Investors must choose a pair of highly correlated crypto assets, such as Bitcoin (BTC) and Ethereum (ETH), ensuring they have similar market fluctuations and technical characteristics. Next, by calculating the yield and price difference, focus on the signals generated when the price difference exceeds a specific threshold. Once such an opportunity is captured, investors can flexibly apply trading strategies: buying the lower-priced asset while short-selling the higher-priced asset to achieve arbitrage.

Potential Trading Pairs in Cryptocurrencies

In the crypto market, various asset pairs may exhibit cointegration relationships suitable for pair trading. Mainstream coin pairs like Bitcoin (BTC) and Ethereum (ETH) are among the most popular pairings due to their market performance and trends influencing each other. Bitcoin (BTC) and Bitcoin Cash (BCH) also often show cointegration relationships because of their similar origins and technical backgrounds. In DeFi projects, Uniswap (UNI) and SushiSwap (SUSHI), as well as Aave (AAVE) and Compound (COMP), frequently have token prices driven by similar market forces, as they are major competitors in decentralized trading platforms and lending protocols, respectively. Additionally, mainstream stablecoin pairs such as Tether (USDT) and USD Coin (USDC) typically maintain relatively stable prices. However, their price differences may fluctuate within a small range under extreme market conditions.

Bitcoin (BTC) and Ethereum (ETH)

As the two main cryptocurrencies in the crypto market, BTC is viewed as “digital gold,” while ETH is the native token of the Ethereum network. Due to their high market share, BTC and ETH serve as market “indicators” and usually show high synchronicity in most market cycles. Changes in market sentiment, especially views on the entire cryptocurrency industry, are often simultaneously reflected in the prices of BTC and ETH. Although their technologies and application scenarios differ, their price fluctuations are often similar as they are both core assets in the market.

An important indicator often referenced by traders is the BTC/ETH ratio. When Bitcoin performs strongly relative to Ethereum, it usually reflects a more conservative market sentiment, with investors tending to choose Bitcoin, which has a larger market cap and lower volatility, as a safe-haven asset. Conversely, if Ethereum performs stronger, it implies a more aggressive market sentiment, with investors focusing more on the potential of the Ethereum ecosystem, especially in decentralized applications (dApps), decentralized finance (DeFi), and NFTs.

When the correlation between BTC and ETH is high, it indicates consistent market sentiment and concentrated risk. When the correlation decreases, market expectations for the prospects of these two assets begin to diverge, potentially providing traders with differentiated investment opportunities. Traders can manage risk and hedge operations based on changes in correlation. If the correlation is low, they may use pair trading to arbitrage from the price difference fluctuations between the two. In cases of high correlation, traders would reduce the double-risk exposure to both in their portfolios.

Furthermore, when the BTC/ETH ratio deviates from its historical average or shows abnormal fluctuations, it usually indicates an imbalance in the price relationship between the two. At this time, traders can use mean reversion strategies, conducting reverse trades when the ratio is too high or too low and waiting for it to return to normal levels, thereby obtaining stable returns.

In addition to BTC and ETH, other public chain tokens also show varying degrees of correlation.

Bitcoin (BTC) and Bitcoin Cash (BCH)

Bitcoin Cash is a hard fork of Bitcoin aimed at improving transaction speed and reducing fees. Due to their shared technical foundation—with BCH being an “improved version” of Bitcoin—its price often follows Bitcoin’s trends. When the Bitcoin network becomes congested or transaction fees rise, BCH typically gains attention as an alternative. The technical similarities between BTC and BCH allow investors to arbitrage using their price fluctuations, especially when discussions about scaling and transaction fees intensify in the market. In the past month, the correlation between BTC and BCH reached 0.84, somewhat related to BTC’s high market dominance.

Uniswap (UNI) and SushiSwap (SUSHI)

These two major decentralized exchanges in the DeFi space have high similarities in market demand, user base, and functionality. Overall market views on the DeFi sector usually affect the prices of both tokens simultaneously, especially during liquidity mining or platform competition. When liquidity incentives or new features are introduced, UNI and SUSHI prices may show fluctuation differences, providing arbitrage opportunities for investors. UNI and SUSHI maintained a correlation level of 0.83 over the past seven days (as of 10/22), while the correlation coefficient for the past year was 0.64.

Aave (AAVE) and Compound (COMP)

Aave and Compound are two major decentralized lending platforms, with their tokens AAVE and COMP providing platform governance and incentives. The health of the DeFi industry directly affects the prices of these two tokens, and when the market is bullish on decentralized lending, AAVE and COMP often rise together. The correlation coefficient between AAVE and COMP reached 0.93 in the past 30 days, while the correlation coefficient for the past year was 0.03, which can be ignored. This serves as a typical reminder that correlation test results should be analyzed based on different time windows for specific issues.

Stablecoin Pairs

Stablecoins are pegged to the US dollar. As stablecoins, their goal is to maintain a 1:1 peg with the dollar, so price fluctuations are usually minimal. However, under extreme market conditions, when liquidity is tight, or regulations change, temporary price differences may occur. When extreme market situations arise, short-term price differences between USDT and USDC provide opportunities for low-risk arbitrage.

Example of Pair Trading in Cryptocurrencies: BTC and ETH

Import required libraries
import yfinance as yf
import pandas as pd
import numpy as np
import statsmodels.api as sm
from statsmodels.tsa.stattools import coint, adfuller

1.Get historical data for BTC and ETH
def get_crypto_data(tickers, start, end):
data = yf.download(tickers, start=start, end=end)[‘Adj Close’]
return data

Download BTC and ETH data
start_date = ‘2020-01-01’
end_date = ‘2024-01-01’
tickers = [‘BTC-USD’, ‘ETH-USD’]
data = get_crypto_data(tickers, start_date, end_date)

Cointegration test
Engle-Granger cointegration test

def engle_granger_coint_test(y, x):

# Regress y on x
x = sm.add_constant(x)
model = sm.OLS(y, x).fit()
residuals = model.resid
# Perform ADF unit root test on regression residuals
result = adfuller(residuals)
p_value = result[1]
return p_value

Perform cointegration test
p_value = engle_granger_coint_test(data[‘BTC-USD’], data[‘ETH-USD’])
print(f”协整检验的p值: {p_value:.4f}”)

Interpret test results
if p_value < 0.05:
print(“BTC and ETH are cointegrated”)

else:
print(“BTC and ETH are not cointegrated”)

It’s worth noting that the correlation between different cryptocurrencies varies significantly across different periods. Taking BTC and ETH as an example, during periods of high correlation when the overall market is rising or falling, the prices of BTC and ETH often fluctuate in sync, with correlation coefficients typically ranging from 0.6 to 0.9. This makes them a common asset pair in pair trading, as their price movements have a high degree of synchronicity, facilitating arbitrage based on price differences. However, during periods of low correlation, such as specific events or extreme market volatility, when one cryptocurrency might fluctuate independently due to technical upgrades or significant news, the correlation may temporarily weaken.

Key considerations for Cryptocurrency Pair Trading

Pair trading, a classic statistical arbitrage strategy, presents unique advantages and challenges when applied to cryptocurrency. Unlike traditional markets, crypto’s higher volatility can cause rapid price fluctuations, potentially impacting the strategy’s effectiveness. Limited liquidity in some crypto assets may affect trade entry, exit timing, and costs. Data acquisition and analysis difficulties can lead to unreliable correlation and cointegration test results. Additionally, regulatory uncertainties and policy shifts may disrupt market behavior, influencing trading strategies. The crypto market also faces heightened technical risks, such as exchange vulnerabilities and network attacks, which could result in investment losses. Consequently, implementing pair trading in the crypto market demands more cautious and adaptable strategic approaches.