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Statistical Arbitrage

Difficulty intermediate

Overview

Statistical arbitrage (stat arb) uses quantitative models to identify and exploit pricing inefficiencies across multiple securities simultaneously. Unlike pairs trading (2 assets), stat arb typically involves portfolios of 20-100+ securities.

Core Methodology

Mean-Reverting Portfolios

Find a portfolio of assets whose combined value is mean-reverting:

Portfolio Value = Σ wᵢ × Assetᵢ

Find weights w that minimize variance of portfolio returns
while maintaining market neutrality

where: wᵢ weight on asset i (long positive, short negative) · Assetᵢ price or return of asset i · Σ sum over the basket. does: constructs a synthetic mean-reverting spread from many assets. Constrained optimization: minimize portfolio variance subject to net-beta = 0 — the foundation of multi-asset stat arb.

Cointegration-Based Portfolios

Johansen Test

Tests for multiple cointegrating relationships across a basket of assets — an extension of the two-variable Engle-Granger procedure to N variables.

  • Estimates the number of independent linear combinations of the basket that are stationary (the cointegration rank r).
  • Trace and max-eigenvalue statistics are compared to critical values to choose r.
  • Each cointegrating vector defines a mean-reverting spread; the portfolio weights for trading are read directly from those eigenvectors.
  • Requires sufficient history (typically 250+ trading days) and ongoing re-estimation as relationships drift.

Risk Management

Risk Mitigation
Model breakdown Monitor cointegration, have stops
Liquidity Trade liquid names only
Execution cost Use VWAP/TWAP, minimize market impact
Crowding Many funds run similar strategies
Regime change Adaptive models, regime detection

Performance Expectations

Metric Typical Range
Sharpe Ratio 1.5-3.0
Max Drawdown 3-10%
Win Rate 55-65%
Annualized Return 8-15%
Market Beta Near zero

Practical Guidelines

  1. Transaction Costs Kill — Stat arb margins are thin
  2. Execution Matters — Slippage can eliminate edge
  3. Monitor Continuously — Relationships break down
  4. Diversify — Many uncorrelated stat arb strategies
  5. Capacity Limits — Strategy degrades with more capital
  6. Infrastructure Required — Needs sophisticated systems

Next Steps