Cointegration and Pair Trading

An informative guide on the concepts of cointegration and pair trading, exemplified through a case study of Coca-Cola and PepsiCo.

TL; DR

• Cointegration is a statistical concept where two or more time series variables move together in a way that their linear combination is stationary.

• Pair trading is a market-neutral strategy that exploits the cointegration between two stocks, such as Coca-Cola and PepsiCo, to generate profits from temporary price deviations.

• The guide includes steps to implement pair trading and strategies for diversifying with general cointegrated pairs across different sectors.

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Understanding Cointegration and Pair Trading

Pair trading is a market-neutral trading strategy that involves matching a long position with a short position in two stocks with a high correlation. The strategy is based on the idea that if the stocks have moved together historically, they will continue to do so in the future, and any divergence will be temporary.

What is Cointegration?

Cointegration is a statistical property of a collection of time series variables which indicates that a linear combination of them has a stable mean and variance over time. In simpler terms, it means that the series can wander around but will have a tendency to move back towards a common mean, thus maintaining a certain equilibrium.

Mathematical Definition of Cointegration

Cointegration can be formally defined as follows:

• Let $X_t$ and $Y_t$ be two non-stationary time series.

• If a linear combination $aX_t + bY_t$ is stationary, then $X_t$ and $Y_t$ are said to be cointegrated.

Stationarity and Non-Stationarity

A time series is stationary if its statistical properties such as mean, variance, and autocorrelation are all constant over time. Non-stationary series, on the other hand, have statistical properties that change over time.

Pair Trading with Coca-Cola and PepsiCo

Let's consider a practical example of pair trading with two leading companies in the beverage industry: Coca-Cola (KO) and PepsiCo (PEP). These companies are major competitors in their market and their stock prices are often influenced by similar factors, such as consumer preferences, sugar prices, and global economic conditions.

Steps to Implement Pair Trading

1. Identify the Pair: Choose two stocks that are historically correlated. For our example, we choose Coca-Cola and PepsiCo.

2. Test for Cointegration: Use statistical tests such as the Augmented Dickey-Fuller (ADF) test to check if the pair is cointegrated.

3. Determine the Spread: Calculate the spread by finding the appropriate hedge ratio and then creating the spread series.

   $$\text{Spread}_t = \text{Price}_{\text{Coca-Cola},t} - \beta \times \text{Price}_{\text{PepsiCo},t}$$

   Where $\beta$ is the hedge ratio.

4. Define Entry and Exit Points: Establish when the spread has deviated sufficiently from its mean to enter a trade and when to exit based on a reversion to the mean.

5. Execute Trades: Go long on the stock that is undervalued and short on the stock that is overvalued based on the spread.

Calculating the Hedge Ratio

The hedge ratio can be calculated using a statistical method called Ordinary Least Squares (OLS) regression, which finds the best-fitting line through the data points of the two stock prices.

Diversifying with General Cointegrated Pairs

While Coca-Cola and PepsiCo provide a classic example of a cointegrated pair, traders often seek to diversify their strategies by identifying multiple pairs across different sectors.

Finding Cointegrated Pairs

1. Select a Universe of Stocks: Choose a set of stocks from various industries.

2. Calculate Price Ratios: For each pair of stocks, calculate the price ratio over a historical period.

3. Test for Stationarity: Use the ADF test to check if the price ratios are stationary.

4. Rank Pairs: Rank the pairs based on their p-values from the ADF test, with lower p-values indicating stronger evidence of cointegration.

Building a Portfolio of Pairs

• Diversify Across Sectors: Include pairs from different sectors to reduce sector-specific risk.

• Monitor Correlations: Regularly check the correlations and cointegration status as market conditions change.

• Risk Management: Allocate capital appropriately and set stop-loss orders to manage risk.

By following these steps, traders can create a diversified portfolio of cointegrated pairs, potentially reducing risk and increasing the opportunity for profit through pair trading strategies.