# IBKR Quant Blog

### K-Means Clustering For Pair Selection In Python - Overview

In this series, we will cover what K-Means clustering is, how it can be used for solving the age-old problem of pair selection for Statistical Arbitrage, and the advantage of using K-Means for pair selection compared to using a brute force method. We will also create a Statistical Arbitrage strategy using K-Means for pair selection and implement the elbow technique to determine the value of K.

Let’s get started!

Part I – Life Without K-Means

To gain an understanding of why we may want to use K-Means to solve the problem of pair selection we will attempt to implement a Statistical Arbitrage as if there was no K-Means. That is, we will attempt to develop a brute force solution to our pair selection problem and then apply that solution within our Statistical Arbitrage strategy.

Let’s take a moment to think about why K-Means could be used for trading. What’s the benefit of using K-Means to form subgroups of possible pairs? Couldn’t we just come up with the pairs ourselves?

This is a great question and one undoubtedly you may have wondered about. To better understand the strength of using a technique like K-Means for Statistical Arbitrage, we’ll do a walk-through of trading a Statistical Arbitrage strategy if there was no K-Means. I’ll be your ghost of trading past so to speak.

First, let’s identify the key components of any Statistical Arbitrage trading strategy.

1. We must identify assets that have a tradable relationship
2. We must calculate the Z-Score of the spread of these assets, as well as the hedge ratio for position sizing
3. We generate buy and sell decisions when the Z-Score exceeds some upper or lower bound

To begin, we need some pairs to trade. But we can’t trade Statistical Arbitrage without knowing whether or not the pairs we select are cointegrated. Cointegration simply means that the statistical properties between our two assets are stable. Even if the two assets move randomly, we can count on the relationship between them to be constant, or at least most of the time.

Traditionally, when solving the problem of pair selection, in a world with no K-Means, we must find pairs by brute force or trial and error. This was usually done by grouping stocks together that were merely in the same sector or industry. The idea was that if these stocks were of companies in similar industries, thus having similarities in their operations, their stocks should move similarly as well. But, as we shall see, this is not necessarily the case.

The first step is to think of some pairs of stocks that should yield a trading relationship. We’ll use stocks in the S&P 500 but this process could be applied to any stocks within any index. Hmm, how about Walmart and Target. They both are retailers and direct competitors. Surely they should be cointegrated and thus would allow us to trade them in a Statistical Arbitrage Strategy.

Let’s begin by importing the necessary libraries as well as the data that we will need. We will use 2014-2016 as our analysis period.

#importing necessary libraries

#data analysis/manipulation

import numpy as np
import pandas as pd

#importing pandas datareader to get our data

#importing the Augmented Dickey Fuller Test to check for cointegration

Now that we have our libraries, let’s get our data.

#setting start and end dates
start='2014-01-01'
end='2916-01-01'
#importing Walmart and Target using pandas datareader
wmt=pdr.get_data_yahoo('WMT',start,end)
tgt=pdr.get_data_yahoo('TGT',start,end)

Before testing our two stocks for cointegration, let’s take a look at their performance over the period. We’ll create a plot of Walmart and Target.

#Creating a figure to plot on
plt.figure(figsize=(10,8))

#Creating WMT and TGT plots
plt.plot(wmt["Close"],label='Walmart')

plt.plot(tgt[‘Close'],label='Target')
plt.title('Walmart and Target Over 2014-2016')

plt.legend(loc=0)
plt.show()

In the above plot, we can see a slight correlation at the beginning of 2014. But this doesn’t really give us a clear idea of the relationship between Walmart and Target. To get a definitive idea of the relationship between the two stocks, we’ll create a correlation heat-map.

To begin creating our correlation heatmap, must first place Walmart* and Target* prices in the same dataframe. Let’s create a new dataframe for our stocks.

#initializing newDF as a pandas dataframe
newDF=pd.DataFrame()
#adding WMT closing prices as a column to the newDF
newDF['WMT']=wmt['Close']
#adding TGT closing prices as a column to the newDF
newDF['TGT']=tgt['Close']

Now that we have created a new dataframe to hold our Walmart* and Target* stock prices, let’s take a look at it.

We can see that we have the prices of both our stocks in one place.

In the next post, we will create a correlation heat map of stocks and run some ADF tests

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*Disclaimer: All investments and trading in the stock market involve risk. Any decisions to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.

If you want to learn more about K-Means Clustering for Pair Selection in Python, or to download the code, visit QuantInsti website and the educational offerings at their Executive Programme in Algorithmic Trading (EPAT™).

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