Cross-Exchange Arbitrage Metrics: Understanding the 16 Statistical Indicators

Cross-exchange perpetual futures arbitrage involves going long on one exchange and short on another, profiting from funding rate differentials and spread convergence. If you're new to the concept, see our complete guide to crypto arbitrage first. But how do you know whether a particular opportunity is genuinely attractive or a trap?

We assume you're comfortable with perpetual futures, funding rates, and the idea of being long on one venue and short on another. If not, read our funding arbitrage guide first. This article focuses on how we evaluate opportunities, not on the strategy itself.

Our Arbitrage Analysis dashboard computes 16 statistical metrics organized into four layers. This guide explains each metric: what it measures, why it matters, the formula behind it, and how to read the traffic-light indicator.

Who this is for: You're already tracking cross-exchange funding or spot-perp opportunities and want to prioritize which pairs and entries are worth taking. We don't explain what arbitrage or funding rates are - we explain how the dashboard's 16 indicators work so you can use them with confidence. If you're still learning the basics, start with our funding arbitrage guide or what is crypto arbitrage.

Reading time: 14 minutes

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The Four Layers

The overall score is a weighted average of layer scores: green = 2, yellow = 1, red = 0. An overall score above 1.5 is green, above 0.8 is yellow, below is red.

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Key Terms (What We're Measuring)

A few terms appear in many metrics. Defining them once here keeps the rest of the guide readable.

• Index price - The reference price an exchange uses for its perpetual contract. It is usually a spot or composite price (e.g. from several spot markets). The perpetual (perp) price trades around this; funding rates are designed to pull the perp price toward the index.
• Basis - The percentage difference between the perpetual mid price and the index price on the same exchange: $(\text{perpMid}-\text{indexPrice})/\text{indexPrice}$. Positive basis means the perp trades at a premium; funding (from longs to shorts) is meant to push it back toward the index. Basis is central to Metrics 4, 5, and 11.
• Spread (between exchanges) - Here, the percentage difference between the two exchanges' perpetual prices (or mids), e.g. $({\text{price}}_{\text{short}}-{\text{price}}_{\text{long}})/{\text{price}}_{\text{long}}$. We care whether this spread is wide enough to enter and whether it reverts over time.
• Half-life - In our context, the time (e.g. in hours) for about half of a deviation (e.g. spread or basis) to decay back toward its average. Short half-life = fast reversion; long half-life = slow or unreliable reversion.
• Z-score - How many standard deviations the current value is from its recent average. |Z| > 2 means "unusually far from normal" and often marks an extended spread (potential entry).

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Layer 1: Structural Safety

These metrics act as a gate check. If they fail, the trade entry and carry metrics become unreliable because the two exchanges may not be pricing the same underlying reality.

Metric 1 - Index Return Correlation

What it measures: How closely the two exchanges' index prices move together over time (using log returns).

Formula:

Pearson correlation of log-return series:

Interpretation:

• Green (≥ 0.99): Excellent - the exchanges see virtually the same price.
• Yellow (≥ 0.95): Acceptable, but some divergence exists.
• Red (< 0.95): Dangerous - the index prices are not tracking each other well.

Why it matters: If the index prices diverge, the futures prices on each exchange can drift apart structurally, not just temporarily. No arbitrage force pulls them back together.

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Metric 2 - Index Spread Stats

What it measures: Statistical properties of the spread between the two index prices over time.

Computed values:

• Mean - average spread level
• Standard deviation - typical spread fluctuation
• Maximum deviation - worst observed divergence
• Half-life - how quickly the spread reverts to its mean, using a simple autoregressive model (today's spread depends on yesterday's). Informally: the time for roughly half of a typical deviation to disappear; short half-life means the two index prices snap back together quickly.

Half-life formula:

Traffic light: Based on half-life - green if short (reverts quickly), red if long.

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Metric 3 - Cointegration (Engle-Granger)

What it measures: Whether the two index prices maintain a stable long-run equilibrium, even if they diverge temporarily. If they're cointegrated, the spread between them tends to mean-revert; if not, the spread can drift without bound.

Procedure:

1. Regress one index price on the other: index_short = α + β × index_long + ε
2. Test the residuals ε for stationarity (ADF test): stationarity means the gap between the two prices doesn't grow without bound

Interpretation:

• Green (p < 0.05): Cointegrated - prices have a stable long-run relationship.
• Yellow (p < 0.10): Marginal evidence.
• Red (p ≥ 0.10): No evidence of cointegration - spread may drift without bound.

Why it matters: Correlation tells you returns move together. Cointegration tells you price levels maintain a stable relationship. Two prices can be correlated in returns but still drift apart in levels.

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Layer 2: Per-Exchange Efficiency

These metrics check whether each exchange's funding rate mechanism works as economic theory predicts.

Metric 4 - Basis → Funding R²

What it measures: How predictable the funding rate is from the basis - the percentage by which the perpetual trades above or below the index on that exchange. In theory, funding is set to pull the perp toward the index, so basis should help predict the next funding rate. This metric checks whether that relationship holds on each exchange.

Formula:

We run this regression and report R² (the coefficient of determination): the fraction of the variance in the next funding rate explained by avgBasis (0–1). TWAP is time-weighted average of basis over the interval. Higher R² means funding is more predictable from basis.

Computed separately for each exchange.

Interpretation:

• Green (R² > 0.5): Funding strongly tracks basis - the mechanism works.
• Yellow (R² > 0.2): Moderate predictability.
• Red (R² ≤ 0.2): Funding is disconnected from basis - unreliable.

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Metric 4.5 - Coefficient Asymmetry (Funding Flip Risk)

What it measures: The difference between the β coefficients (slopes) from the two exchanges' basis-funding regressions. Even when both exchanges show high R² values (strong predictability), a large difference in β means the exchanges respond to basis changes with different intensities - creating funding flip risk.

Why it matters: High R² tells you funding is predictable from basis on each exchange individually. But if one exchange has β ≈ 1.0 (basis translates almost 1:1 into funding) while the other has β ≈ 0.1 (basis barely affects funding), then when market sentiment shifts and both bases move in the same direction, your net funding can flip from positive to negative (or vice versa).

Example scenario:

• Kucoin (Long): β = 1.0061 → basis changes translate fully into funding
• Bitget (Short): β = 0.1249 → basis changes barely affect funding
• Initial state: Both negative basis → you receive net funding
• Market turns bullish: Both bases swing positive → Kucoin funding swings violently while Bitget stays stable → you now pay net funding

Formula:

Where β values come from the regressions in Metric 4.

Interpretation:

• Green (< 0.3): Similar response - funding mechanisms are balanced.
• Yellow (< 0.6): Moderate asymmetry - monitor funding stability.
• Red (≥ 0.6): Dangerous asymmetry - high risk of funding flipping against you on sentiment shifts.

Critical insight: This metric catches what R² alone misses. Two exchanges can both have R² > 0.99 (excellent predictability) but still be dangerous to pair if their β coefficients are mismatched.

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Metric 5 - Basis Half-Life

What it measures: How quickly the basis on each exchange reverts toward zero - i.e. how fast the perpetual price is pulled back toward the index. Fast reversion suggests the exchange's funding mechanism is doing its job.

Formula: AR(1) regression on the basis time series, same half-life formula as Metric 2.

Interpretation:

• Green (< 4h): Fast reversion - the exchange efficiently arbitrages its own basis.
• Yellow (< 12h): Moderate.
• Red (≥ 12h): Slow - the basis can persist, making funding less predictable.

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Metric 6 - Funding Volatility

What it measures: Rolling standard deviation of funding rates over the selected time window.

Traffic light: Based on coefficient of variation (std/mean). Low CV = stable regime (green), high CV = erratic (red).

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Layer 3: Trade Entry

These are the core trade-timing metrics.

Metric 7 - Executable Spread

What it measures: The actual spread you capture using executable prices.

Formula:

Positive means you sell higher than you buy.

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Metric 8 - Mid Spread Z-Score

What it measures: How extreme the current spread between the two exchanges is relative to its recent history. The Z-score is how many standard deviations the current spread is from its recent mean (current value minus average, divided by standard deviation). |Z| > 2 means the spread is unusually wide (or narrow) and may be a candidate for entry.

Formula:

Where $\mu$ and $\sigma$ are the rolling mean and standard deviation of the spread over the selected window.

Interpretation:

• Green (Z > 2): Spread is significantly extended - good entry.
• Yellow (1.5 < Z ≤ 2): Moderately extended.
• Red (Z ≤ 1.5): Spread is within normal range or compressed - no edge. Negative Z means the spread is tighter than average (bad entry timing).

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Metric 9 - Futures Spread Half-Life (THE Key Metric)

What it measures: How long you should expect to wait for the spread between the two exchanges' futures prices to revert to its mean.

Formula: AR(1) on the mid-spread time series.

Interpretation:

• Green (< 8h): Fast convergence - you can hold for just 1–2 funding intervals.
• Yellow (< 24h): Moderate - plan for a multi-day hold.
• Red (≥ 24h): Slow - the spread may take days to converge; you're more exposed to spread risk and timing.

This is the single most important metric. If the half-life is long, you're more exposed to spread risk and convergence timing - closer to a convergence bet than to tight arbitrage. You can still profit from funding, but the spread may stay wide or widen for a long time before reverting.

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Metric 10 - Maximum Adverse Excursion (MAE)

What it measures: Historically, when you enter at elevated Z-scores, how much worse does the spread get before it reverts?

Computed at two thresholds:

• Z > 2: More common entries
• Z > 3: Rare, extreme entries

Interpretation:

• Green (< 1%): Minimal adverse movement before reversion.
• Yellow (< 3%): Manageable but requires margin buffer.
• Red (≥ 3%): Significant risk of drawdown.

Why it matters: This directly sizes your margin requirement. If MAE is 2%, you need at least 2% margin buffer per side to avoid liquidation before the spread converges.

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Metric 11 - Spread Decomposition

What it measures: Whether the spread between the two exchanges' perp prices comes mainly from basis divergence (each exchange's perp vs its own index - a funding/sentiment gap that tends to revert) or index divergence (the two exchanges' index prices differ - a structural issue that may not mean-revert). Basis-driven spread is the kind arbitrage can exploit; index-driven spread is riskier.

Formula:

Where $\text{basis}=(\text{perpMid}-\text{indexPrice})/\text{indexPrice}$ per exchange.

Displayed as: Current snapshot values plus a time series chart showing both components.

Interpretation:

• Green: Index component is small (< 30% of total spread) - spread is basis-driven.
• Red: Index component dominates (> 60%) - structural divergence, dangerous.

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Metric 12 - Break-Even Intervals

What it measures: How many funding intervals you need to hold (assuming spread stays flat) to earn back the round-trip trading fees.

Formula:

Entry spread here is the spread you capture at entry (e.g. selling the short exchange's bid and buying the long exchange's ask). If that captured spread exceeds round-trip fees, you're ahead from the spread alone before any funding or spread move - no assumption about exit spread.

Interpretation:

• Green (≤ 3 intervals): Breaks even quickly.
• Yellow (≤ 10): Multi-day hold needed.
• Red (> 10): Too long - funding must remain favorable for extended period.

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Layer 4: Carry Quality

These metrics evaluate whether the funding income (carry) is reliable.

Metric 13 - Funding Differential Stats

What it measures: The statistical properties of the net funding you receive (short rate − long rate, normalized to a common 8h interval).

Displayed values: Mean, standard deviation, current value, and current percentile rank vs. history.

Traffic light: Based on percentile rank - green if current differential is above the 75th percentile historically.

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Metric 14 - Autocorrelation + Sign Persistence

What it measures: Two complementary views of funding stability:

1. Lag-1 autocorrelation: Is today's funding differential predictive of tomorrow's? High autocorrelation means the regime persists.
2. Sign persistence: What percentage of the last 30 funding payments had the same sign (positive/negative) as the current one?

Interpretation:

• Green: Autocorrelation > 0.5 AND sign persistence > 80% - stable carry regime.
• Yellow: Either metric is moderate.
• Red: Both are low - carry is unreliable and may flip against you.

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Metric 15 - Historical PnL Simulation

What it measures: The actual profit distribution if you had entered this trade at every historical point and held for 1, 2, or 3 funding intervals.

Formula:

For each historical entry point, simulated over different holding periods.

Displayed values: Mean PnL, median PnL, 5th percentile (worst case), 95th percentile (best case) for each holding period.

Interpretation:

• Green: Median PnL is positive even for a 1-interval hold.
• Yellow: Only profitable at 3-interval hold.
• Red: Negative median PnL - historically unprofitable.

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Reading the Traffic Lights

Each metric has its own traffic light. The layer lights show the worst metric in that layer. The overall score uses a weighted average where structural safety has the highest weight (3x).

A green overall score means the trade passes all safety checks and has favorable entry timing and carry characteristics. A yellow score means caution is warranted - check which specific metrics are yellow or red. A red score means at least one critical metric is concerning.

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Important Disclaimers

1. Past performance does not guarantee future results. All metrics are computed from historical data. Market conditions can change.
2. Metrics are only as good as the data. If price or funding data has gaps or errors, metric values may be unreliable.
3. Not financial advice. These metrics are analytical tools. You are responsible for your own trading decisions.
4. Execution risk. These metrics do not account for slippage, order book depth, withdrawal times, or exchange-specific risks.
5. Margin and liquidation risk. Even if metrics are favorable, insufficient margin on either exchange can lead to forced liquidation and loss. See our risk management guide for position sizing and safety practices.

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Key Takeaways

• 16 metrics in four layers: Structural Safety (gate check), Per-Exchange Efficiency, Trade Entry, and Carry Quality - each answers a specific question about the opportunity.
• Formulas are interpretable: Log-return correlation, half-life, Z-score, coefficient asymmetry, MAE, spread decomposition, and PnL simulation all have clear formulas and traffic-light thresholds.
• Structural safety first: If index correlation or cointegration fails, treat the pair with caution regardless of entry metrics.
• Coefficient asymmetry reveals hidden risk: High R² doesn't guarantee safety - mismatched β coefficients can cause funding to flip against you.
• Spread half-life is the key entry metric: Short half-life means true arbitrage; long half-life means you are betting on convergence.
• Use the dashboard: The Funding Arbitrage dashboard computes all 16 metrics in real time so you can compare pairs and time entries.

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Next Steps

Put these metrics into practice:

1. Try the Funding Arbitrage dashboard to see the 16 indicators for live pairs.
2. Read the funding rate arbitrage guide for strategy context.
3. Compare supported exchanges for fees and data quality.
4. Use the arbitrage calculator to size positions and break-even.

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Summary