Frequently Asked Questions

CorrGrid.com is a tool designed to evaluate hidden relationships between financial instruments.

It utilizes various metrics, such as correlation and cointegration, alongside methods that analyze behavior free from external factors (excluding broad-market or sector-specific influences). This approach reveals the instruments’ individual, small-group, pairwise, and hidden trends (see the concept of DarkTrend). By leveraging these metrics, CorrGrid identifies the most promising pairs, triplets, or quadruplets for pair trading, correlation trading, mean-reversion strategies, and statistical arbitrage.

Additionally, CorrGrid identifies complex interdependencies and structural relationships between instruments using graph visualizations called Market Topology. It leverages minimal spanning trees (MSTs) to highlight the most significant connections among assets.

Raw correlations are calculated using the mid-price, which is the average of the Best Bid and Best Ask prices at the opening and closing of regular trading sessions. Based on these mid-prices, overnight and overday returns (semi-daily returns) are computed for the past 100 days, resulting in 199 return values. For all selected pairs of financial instruments (approximately 3,500 × 3,500 pairs), robust Kendall’s Tau correlations are calculated and then transformed into the Pearson correlations scale for interpretability.

Kendall’s Tau (a type of correlation) is preferred over Pearson’s correlation because it handles heteroskedasticity (uneven variability in the data) and is more robust against outliers (extreme data points), which are common in financial data.

Pearson’s correlation sensitivity to outliers and heteroskedasticity can cause spurious correlations (inflated correlation values where no true relationship exists). Conversely, since Pearson’s correlation only measures linear relationships, it can underestimate or miss non-linear correlations or those obscured by noise and outliers.

To facilitate interpretation, CorrGrid transforms Kendall’s Tau into the Pearson’s correlation scale using the mathematical relationship: r=sin( πτ / 2).

This formula is based on Greiner’s equality, which establishes a mathematical connection between Kendall’s Tau and Pearson’s correlation under specific conditions.

CorrGrid uses the mid-price (best bid + best ask / 2), rather than the last price or trade prices, to avoid several common issues associated with transaction-based data.

The mid-price eliminates the effects of bid-ask bounce, a phenomenon where rapid alternations between bid and ask prices can distort return calculations, and avoids issues caused by delayed or infrequent trades, which can introduce noise or inaccuracies, especially in less liquid instruments.

Variants of correlation and cointegration calculations on CorrGrid are based on the concept of DarkTrend:

• ex-SPY refers to correlations and cointegrations calculated using prices or returns with the influence of broad market movements removed, using SPY (an ETF tracking the S&P 500) as a proxy.
• ex-ETF refers to correlations and cointegrations calculated using prices or returns with sector- or industry-specific influences removed, using the most relevant and liquid sector ETFs as proxies.

The Anchor ETF used for ex-ETF calculations is selected from a predefined pool of liquid, sector-defining ETFs. Kendall’s correlation is calculated using high-frequency trading (HFT) data, specifically one-hour overlapping returns with a 5-second step, over a rolling 1-month window.

Using HFT data allows for a more accurate identification of an instrument’s association with a sector or industry ETF, as it captures fine-grained, short-term price dynamics that better reflect the market’s preferences for aligning the instrument with a particular ETF or sector.

To ensure consistency in sequential selection (day-to-day), a slight hysteresis is applied to prevent frequent switching between ETFs with similar correlations.

ex-ETF and ex-SPY returns are calculated using a linear regression-based approach to remove the external influences of sectoral or broad market movements, focusing on the intrinsic dynamics of an instrument. For more details, see the concept of DarkTrend here.

The process includes the following key elements:

1. Calculation of High-Frequency Beta Coefficients (HFT Betas):
   • HFT Betas are derived from raw HFT overlapping returns (one-hour overlapping midquote returns with a 5-second step). Since overlapping returns introduce autocorrelation, GLS regression is used, as it effectively handles overlapping data.
   • Betas represent a linear coefficient that quantifies an instrument’s sensitivity to external influences, serving as a measure of how external factors drive the instrument’s returns.
   • BetaSPY is calculated against SPY, which serves as the proxy for the broad market.
   • BetaETF is calculated against the Anchor ETF selected via the largest Kendall’s correlation (see “How is the ETF selected”).
2. Calculation of ex-Returns:
   • ex-Returns are computed by removing the external linear component, as determined by the HFT Beta coefficients:
     ex-Return = Raw Return − 𝛽 × Proxy Return (SPY or ETF)

Market Topology is a network structure formed by identifying the strongest and most significant connections between financial instruments. It represents the underlying relationships and interdependencies within the market, providing a visual and analytical framework to understand how instruments are connected and influence one another.

CorrGrid constructs Market Topology using the Minimum Spanning Tree (MST) method, implemented with Kruskal’s algorithm. The structure is based on pairwise correlations and cointegrations, with values less than 0.1, including negative correlations, being ignored.

For measuring distances between instruments, Euclidean distance is used. This ensures that closer distances represent stronger positive relationships, emphasizing the most meaningful connections in the market.

While cointegration is typically treated as a binary property (either present or absent), CorrGrid uses Johansen’s eigenvalue method to calculate the strength of cointegration. This method identifies stable long-term relationships by analyzing the eigenvalues of a system of time-series equations.

CorrGrid takes the largest eigenvalue from Johansen’s test as the measure of cointegration strength. If the test’s significance level does not meet a 99% confidence threshold, the cointegration is considered absent and assigned a value of zero. This approach allows for a more detailed assessment, enabling users to evaluate not only the presence of cointegration but also its relative intensity across different pairs of instruments.

Correlation is a statistical measure that quantifies the relationship between two financial instruments, indicating how closely they move together.

Pairs with a high but not perfect correlation (less than 1.0, ensuring variability for trading opportunities) can be used for correlation / mean-reversion / pair trading, and statistical arbitrage. High correlation also helps identify substitutes within the same segment or sector, enabling traders to work with lagging assets when a preferred ETF or stock is unavailable, less liquid, or for reasons related to taxes or commissions.

Negative correlations, on the other hand, are ideal for finding instruments suitable for hedging positions, as they tend to move in the opposite direction of the hedged asset, offsetting potential losses.

Cointegration refers to a long-term statistical relationship between two or more instruments, where their prices move together over time, even if they deviate in the short term. CorrGrid calculates cointegration strength using Johansen’s eigenvalue method, identifying instruments with consistent relationships. This is particularly useful for statistical arbitrage and mean-reversion strategies, as deviations from equilibrium can highlight actionable opportunities.

The Hurst exponent (H), a value between 0 and 1, measures whether a price series tends to persist in its previous direction or revert to its average:

• H > 0.5: Indicates persistence (also called “momentum” or “MOMO”). Prices are more likely to continue moving in the same direction they have been.
• H < 0.5: Indicates mean-reversion (“meanrev” or “MR”). Prices are more likely to reverse direction and move back towards their average.

A simple rule applies: strategies such as statistical arbitrage, mean-reversion trading, and pair trading are only effective for instruments (individual assets or asset combinations like pairs, triplets, etc.) with H < 0.5. The lower the H, the higher the potential performance of these strategies.

However, extremely low H values may indicate non-tradable instruments. Such values often result from market effects like bid-ask bounce, which reflect low liquidity. These conditions are typically exploited by major market makers as a profit source.

Therefore, when selecting instruments with low H, it is essential to consider tradability. A viable selection should ensure that the Range to Bid-Ask Spread ratio is significantly greater than 10 (»10). This balance helps avoid liquidity traps while maintaining strategy effectiveness.

Hurst Boost (HB) is a proprietary CorrGrid metric that evaluates how effectively a multi-asset combination enhances mean-reversion or momentum properties (measured by the Hurst Exponent) compared to the single “best” asset in that combination.

For a pair of assets (A, B), Hurst Boost is defined as:

          HB = HPair − min( HA, HB )

Example:

• Asset A:   HA = 0.5
• Asset B:   HB = 0.45
• Pair: A − 0.33* × B,     HPair = 0.4.

^* - for illustration purposes

Hurst Boost (HB) = 0.4 − min( 0.5, 0.45 ) = -0.05

A negative Hurst Boost indicates the combination enhances mean-reversion more than the best individual asset (lower Hurst exponent = stronger mean-reverting behavior).

Key Rule:

• The more negative the Hurst Boost (HB), the better the pair/portfolio is for mean-reversion strategies (e.g., statistical arbitrage, pairs trading).
• Use Hurst Boost (HB) to rank combinations: prioritize those with the most negative values for mean-reversion based strategies.

Half Life (HL) quantifies the expected time (in days) for a price series or spread to revert halfway to its mean after a deviation. It is a critical metric for mean-reversion strategies, as it helps traders estimate the duration of potential trades and optimize entry/exit points. HL is derived from the Ornstein-Uhlenbeck (OU) process, which models mean-reverting behavior.

Range to Bid-Ask Spread (RS) is CorrGrid’s proprietary liquidity metric that quantifies how many average bid-ask spreads fit within the typical daily price variability of a trading position, which could be a single asset, a pair, or a multi-legged structure (collectively referred to as a composite position). It evaluates the tradability of an asset—or any composite position—by comparing its volatility to the transaction costs imposed by the bid-ask spread.

Technically, RS is calculated by dividing the standard deviation of daily returns over 100 trading days by the 100-day average of the median daily bid-ask spreads.

The importance of this metric becomes particularly clear when considering two-legged (and more complex) composite positions. By offsetting systematic risks through hedging strategies (such as long-short strategies), multi-legged composite positions can significantly reduce their overall volatility. However, in real market conditions—where transaction costs such as bid-ask spreads are unavoidable—this lower volatility can make a synthetic instrument (or composite position) challenging to trade (e.g., when opening, closing, or rebalancing positions), even if it appears attractive in theory.

Therefore, when selecting pairs, triplets, or quadruplets for statistical arbitrage, pair trading, or mean-reversion strategies, it is essential to consider not only their trading quality metrics (e.g., Hurst Exponent, Cointegration) but also their tradability—specifically, whether their overall volatility is sufficient to offset transaction costs. This is where the Range to Bid-Ask Spread metric truly stands out, thanks to its practical simplicity and clear interpretability.

Key Rule:

• RS > 10

The Hedge Ratio (HR) is essentially a weighting coefficient that determines the proportion of the second asset in a multileg position. Originally, it was defined as the ratio of dollar values between two assets, ensuring that the exposure of one instrument offsets the systematic risks of the other. However, in the context of CorrGrid, HR represents the proportion of the second asset that needs to be bought (long) or sold (short) to achieve specific characteristics in a synthetic instrument (multileg position).

Methods of Calculation

There are multiple ways to calculate HR, depending on the strategy and underlying statistical assumptions. The most common approaches include:

1. Johansen Cointegration-Based HR: Derived directly from the Johansen test for cointegration, ensuring that the constructed synthetic spread (multileg position) remains stationary over time.
2. Beta Coefficient from Regression: HR can also be estimated as the Beta coefficient from a regression model, representing the sensitivity of one asset’s returns to another.

Yes, CorrGrid includes delisted instruments in its calculations to ensure they are bias-free. All metrics, such as correlations and cointegrations, are computed using data available as of the specific historical date being analyzed. Delisted instruments are considered under their tickers as they existed at the time, eliminating survivorship bias and providing a complete and accurate representation of historical market relationships.

CorrGrid includes stocks and ETFs that are sufficiently liquid. Instruments are selected based on how many bid-ask spreads fit within the daily price range (Range to Spread), averaged over the last 100 trading days. Only instruments with a score consistently greater than 5 are included, ensuring they meet the liquidity threshold for meaningful analysis and practical use.

A slight hysteresis is applied to avoid frequent changes in the selection of instruments, ensuring stability over time. Approximately 3,500 instruments meet these criteria and form the basis for CorrGrid’s analyses (>10,000,000 pairs per day, per metric, per scope).

Stocks↔ETFs refers to the scope that includes all pairwise correlations or cointegrations calculated between individual stocks and ETFs. It excludes relationships between stocks themselves or between ETFs. This option allows for a targeted analysis of the interactions between the ETF market and the underlying stock market.