Futures Statistical Arb

Regular trading bets on one instrument going up or down. Stat arb trades two instruments against each other, profiting from their relationship normalizing. It's market neutral - less affected by overall market direction.

This is 'spread divergence' risk. Use stop-losses (e.g., exit if Z-score > 3.5). The relationship you modeled may be temporarily or permanently broken. Never assume infinite mean reversion.

Look for instruments with: (1) Fundamental link (same sector, related products), (2) High historical correlation (> 0.7), (3) Cointegration (statistically proven relationship). Test before trading.

Standard is ±2.0 (captures ~5% of extreme observations). More aggressive: ±1.5 (more trades, more false signals). More conservative: ±2.5 (fewer trades, higher conviction).

Basic stat arb can be done with spreadsheets and charting software. Advanced stat arb benefits greatly from programming (Python, R) for testing cointegration, calculating rolling statistics, and backtesting.

Most common: OLS regression. Regress Instrument A prices on Instrument B prices. The slope (beta) is your hedge ratio. For 1 unit of A, trade (hedge ratio) units of B. Update periodically.

Dollar-neutral: Equal dollar amounts each leg. Beta-neutral: Adjusted for market sensitivity. If A has beta 1.2 and B has beta 0.8, beta-neutral requires different sizing to neutralize market risk.

Common approaches: (1) Fixed window (recalculate every N days), (2) Rolling window (continuous update), (3) Kalman filter (dynamic estimation). For most, weekly or bi-weekly updates work well.

Half-life is time for spread to revert halfway to mean. Short half-life (< 5 days) = Quick reversion, shorter trades. Long half-life (> 20 days) = Slow reversion, longer holding. Affects position sizing and time stops.

Engle-Granger test: (1) Regress A on B, (2) Test residuals with ADF test. If p-value < 0.05, cointegrated. Alternatively, use Johansen test for multiple series. Many stats packages have built-in functions.

Kalman Filter treats hedge ratio as dynamic state variable, updating it optimally with each new observation. This captures changing relationships in real-time, unlike static historical regression.

PCA extracts principal components from return series. PC1 typically represents market factor. After removing common factors, residuals (alpha) are traded. More sophisticated than simple pairs; handles multiple assets.

Options: (1) Hidden Markov Models to detect regimes, (2) Rolling cointegration tests, (3) Correlation monitoring with alerts, (4) Adaptive parameters. Key: Have exit rules for relationship breakdown.

Balance between: capturing mean reversion quickly vs. market impact costs. Factors: spread volatility, half-life, liquidity. Almgren-Chriss framework can be adapted. Generally, trade into position over multiple fills.

Diversify across multiple pairs with low correlation between spreads. Use portfolio optimization (mean-variance on spread returns). Set concentration limits. Monitor aggregate risk (VaR, correlation among pairs).