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Top Cointegrated Assets on the Topology Screen

11:30 AM    /       /    6 min read    /       /   
manual

This section describes the Top Cointegrated Assets list displayed on the Market Topology screen.

Before proceeding, it is crucial to read and understand the Top/Bottom Correlations documentation, as this section builds upon the concepts explained there.

Overview

This list displays the top 100 most cointegrated assets (pairs, triplets and quadruplets), relative to the selected instrument (if exists).

Unlike the correlation-based analysis, which focuses on short-term relationships, cointegration identifies long-term equilibrium relationships between assets. If two or more assets are cointegrated, it suggests a tendency for the assets to revert to a common mean over time, making them suitable for pairs trading and mean reversion strategies.

We use quantified cointegration, that is why we speak of the strength of cointegration.

Cointegration Metric

Instead of correlation, this functionality utilizes the Johansen test statistic. The Johansen test is a statistical procedure for testing cointegration between assets. Under specific conditions, the test procedure allows us to compare the strength of cointegrating relationships, enabling us to rank and select the “best” candidates for pairs trading. For details, see here.

One of the indicators of the strength of cointegration (specifically, the maximum eigenvalue) provides a numerical value between 0 and 1, representing the strength of the cointegrating relationship.

In practice, we consider a value of 0.05 or higher as an indication of significant cointegration along with other mandatory conditions (a positive ADF test and a 95% p-value for the Johansen test itself).

Please familiarize yourself with “Top/Bottom Correlations on the Topology Screen” before reading further.

Modes: Raw, ex/SPY, and ex/ETF

The three modes familiar from the correlations analysis – Raw, ex/SPY, and ex/ETF – are also available for cointegration analysis:

  • Raw mode: Identifies assets that are directly cointegrated with the selected instrument, without any adjustments.
  • ex/SPY mode: Removes the influence of the broad market (approximated by SPY) from all instruments before calculating the Johansen test statistic and Hedge Ratios. This helps uncover cointegrating relationships that might be masked by overall market movements.
  • ex/ETF mode: Similar to ex/SPY, but removes the influence of sector-specific movements using anchor ETFs before assessing cointegration and Hedge Ratios. This reveals even finer, more specific cointegrating relationships.

The method for removing the influence of SPY and sector ETFs is identical to that described in the correlations documentation. The key difference lies in the metric used to assess the relationship between the (potentially adjusted) legs.

Hedge Ratios

While Beta coefficients, estimated to minimize volatility in the correlation approach, were used as hedge ratios, in the cointegration approach, we obtain Hedge Ratios derived directly from the Johansen test procedure.

Key Differences and Usage

It’s important to note following:

  • Because significant cointegrating relationships are statistically less frequent than significant correlations, many instruments may not have any identified cointegrated partners.
  • This tool is designed to identify the most strongly cointegrated pairs for the selected asset.



Short Long Mode Description
Coi Cointegration Raw Cointegration is a long-term relationship where asset prices tend to move together, returning to a stable Hedge Ratio despite individual price drifts. The strength of cointegration is quantified using the Johansen test’s maximum eigenvalue, a value between 0 and 1. Cointegration is confirmed only when all of the following conditions are met: the Johansen test’s maximum eigenvalue is 0.05 or higher, the ADF test p-value is 0.05 or less, and the Johansen test is statistically significant (99% confidence level).
ex/SPY Same as Raw mode, but cointegration is calculated using “purified” prices, which are obtained by removing the influence of the overall market (using SPY) from the original price changes and then converting these “purified” changes back into a “purified” price series. This allows to identify cointegration relationships that might be hidden by general market movements. In the ex/SPY mode, the Hedging Formula typically consists of three legs.
ex/ETF Same as ex/SPY mode, but instead of removing the influence of the overall market using SPY, the influence of the relevant sector is removed using anchor ETFs, chosen individually for each asset based on the strongest affinity, quantified by robust correlation. Anchor ETFs are large, highly liquid exchange-traded funds that closely track specific sectors or industries, selected using a small hysteresis to prevent frequent day-to-day changes (jitter) in the selection. This allows for the discovery of even finer and more specific cointegrating relationships. The Hedging Formula here may consist of up to four legs.
Corr Correlation Raw Measures how simultaneously the price changes of two or more assets move together. A value of +1 means the price changes are perfectly matched – when one goes up, the other goes up by a proportional amount. -1 means they are perfectly inversely matched – when one goes up, the other goes down by a proportional amount. 0 means they move independently. Calculated from the price changes (returns) of the assets using the robust Kendall Tau rank correlation, which is then converted to a Pearson correlation coefficient using Greiner’s equality formula. Kendall Tau is robust to outliers, less sensitive to extreme values, and can capture non-linear relationships.
ex/SPY Same as Raw mode, but measures how simultaneously “purified” price changes move, excluding the influence of the overall market (using SPY). This helps you see how assets are related to each other independently of general market fluctuations, potentially revealing hidden relationships.
ex/ETF Same as ex/SPY mode, but excluding the influence of the specific sector (using sector ETFs, chosen individually for each asset based on the strongest affinity, quantified by robust correlation). These anchor ETFs are large, highly liquid exchange-traded funds, selected using a small hysteresis to prevent frequent day-to-day changes (jitter) in the selection. This reveals the relationships between assets that are due only to their individual characteristics, not to broader market or sector trends, potentially revealing hidden relationships even deeper than the sector level (e.g., sub-sector clusters).
R2 R2 Raw Measures how much the price swings (volatility) are reduced when you use a hedging asset. 100% means the price swings are completely eliminated. 0% means the hedge has no effect. The higher the value, the better the hedge.
ex/SPY Measures how much the price swings are reduced after removing the effect of the overall market (using SPY) and the pairing asset. It tells you how well your hedge eliminates the influence of general market movements and common risks shared by the paired assets.
ex/ETF Measures how much the price swings are reduced after removing the effect of the relevant sector (using anchor ETFs) and the pairing asset. It tells you how well your hedge eliminates the influence of sector-specific movements and common risks shared by the paired assets.
cointegration market topology johansen test top cointegrated help tutorial trading tools pairs trading statistical arbitrage
February 20, 2025   4.6
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