K-Means Clustering Algorithm For Pair Selection In Python – Part II


Visit: QuantInsti

In the first installment, Lamarcus explained K-Means Clustering. In today’s article, the author will try to implement statistical arbitrage without using K-Means first.

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. This means that 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? I mean 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
import pandas_datareader as pdr
#importing the Augmented Dickey Fuller Test to check for cointegration
from statsmodels.tsa.api import adfuller

In the next article, Lamarcus will work with the data and provide the sample code.

Disclosure: Interactive Brokers

Information posted on IBKR Traders’ Insight that is provided by third-parties and not by Interactive Brokers does NOT constitute a recommendation by Interactive Brokers that you should contract for the services of that third party. Third-party participants who contribute to IBKR Traders’ Insight are independent of Interactive Brokers and Interactive Brokers does not make any representations or warranties concerning the services offered, their past or future performance, or the accuracy of the information provided by the third party. Past performance is no guarantee of future results.

This material is from QuantInsti and is being posted with permission from QuantInsti. The views expressed in this material are solely those of the author and/or QuantInsti and IBKR is not endorsing or recommending any investment or trading discussed in the material. This material is not and should not be construed as an offer to sell or the solicitation of an offer to buy any security. To the extent that this material discusses general market activity, industry or sector trends or other broad based economic or political conditions, it should not be construed as research or investment advice. To the extent that it includes references to specific securities, commodities, currencies, or other instruments, those references do not constitute a recommendation to buy, sell or hold such security. This material does not and is not intended to take into account the particular financial conditions, investment objectives or requirements of individual customers. Before acting on this material, you should consider whether it is suitable for your particular circumstances and, as necessary, seek professional advice.

In accordance with EU regulation: The statements in this document shall not be considered as an objective or independent explanation of the matters. Please note that this document (a) has not been prepared in accordance with legal requirements designed to promote the independence of investment research, and (b) is not subject to any prohibition on dealing ahead of the dissemination or publication of investment research.

Any trading symbols displayed are for illustrative purposes only and are not intended to portray recommendations.