What is Pair Trading? Pair Trading Strategy with Python

Pair trading is a market-neutral trading strategy that involves buying and selling two highly correlated instruments simultaneously to exploit any divergence in their prices. In pair trading, the trader takes a long position in one security and a short position in another security that has a strong positive correlation with the first security.

The idea behind pair trading is that if the two securities have a strong positive correlation, they will tend to move together in the same direction. However, occasionally, due to market or industry-specific factors, there may be a divergence in their prices. The pair trader aims to capture this divergence by simultaneously buying and selling the two securities.

To do a pair trade in stocks, the trader must first identify two stocks that are highly correlated. This can be done by analyzing historical price data or using statistical measures such as correlation coefficients. Once two stocks are selected, the trader will take a long position in one stock and a short position in the other stock. The position sizes should be equal or adjusted based on the relative volatility of the two stocks.

The best strategy for pair trading for stocks involves careful selection of two highly correlated stocks, identifying a divergence in their prices, and taking advantage of the price difference by simultaneously buying and selling the two stocks. It is important to continuously monitor the pair trade to adjust the position sizes as the correlation between the two stocks may change over time. Additionally, risk management is critical as there may be unforeseen events that could cause a significant divergence in the prices of the two stocks.

Overall, pair trading can be a profitable strategy for traders who have a good understanding of market dynamics and the ability to identify and execute opportunities in a timely manner.

Pair Trading Strategy with Python

Now, let’s see how we can implement a basic pair trade strategy with Python:

import pandas as pd
import numpy as np
import statsmodels.api as sm

# Define two stocks to trade
stock1 = 'AAPL'
stock2 = 'MSFT'

# Load historical price data for the two stocks
data1 = pd.read_csv(f'{stock1}.csv', index_col='date')
data2 = pd.read_csv(f'{stock2}.csv', index_col='date')

# Calculate the spread between the two stocks
spread = data1['close'] - data2['close']

# Calculate the rolling mean and standard deviation of the spread
spread_mean = spread.rolling(window=30).mean()
spread_std = spread.rolling(window=30).std()

# Calculate the z-score of the spread
z_score = (spread - spread_mean) / spread_std

# Create a trading signal based on the z-score
signal = np.where(z_score > 2, -1, np.where(z_score < -2, 1, 0))

# Calculate the returns of the two stocks
stock1_returns = data1['close'].pct_change()
stock2_returns = data2['close'].pct_change()

# Calculate the returns of the pair trade
pair_trade_returns = signal[:-1] * stock1_returns[1:] - (1 - signal[:-1]) * stock2_returns[1:]

# Calculate the cumulative returns of the pair trade
cumulative_pair_trade_returns = pair_trade_returns.cumsum()

# Plot the cumulative returns of the pair trade
cumulative_pair_trade_returns.plot(figsize=(10, 5))

In this example, we first define two stocks to trade (AAPL and MSFT) and load their historical price data. We then calculate the spread between the two stocks and the rolling mean and standard deviation of the spread. We use these values to calculate the z-score of the spread, which we use to generate a trading signal. The trading signal is based on a threshold z-score of +/- 2. If the z-score is greater than 2, we short the first stock and go long the second stock. If the z-score is less than -2, we go long the first stock and short the second stock. Otherwise, we hold no position.

We then calculate the returns of the two stocks and use the trading signal to calculate the returns of the pair trade. Finally, we calculate the cumulative returns of the pair trade and plot them. Note that this is a very simple example and there are many ways to refine and improve this strategy. Additionally, risk management is critical when implementing any trading strategy.

What is z-score?

A z-score, also known as a standard score, is a statistical measure that indicates how many standard deviations a data point is from the mean of a dataset. It is calculated as the difference between a data point and the mean of the dataset, divided by the standard deviation of the dataset:

z = (x – μ) / σ

where z is the z-score, x is the data point, μ is the mean of the dataset, and σ is the standard deviation of the dataset.

The z-score can be positive or negative, depending on whether the data point is above or below the mean, respectively. A z-score of zero indicates that the data point is equal to the mean. A z-score of 1 indicates that the data point is one standard deviation above the mean, and a z-score of -1 indicates that the data point is one standard deviation below the mean.

The z-score is useful for comparing data points from different datasets that have different scales and distributions. By standardizing the data, we can compare data points in terms of their relative positions within their respective datasets. The z-score is also used in various statistical tests, such as hypothesis testing and confidence interval estimation.