Building Statistical Arbitrage Models

When To Use

• Designing a pairs trading or multi-leg market-neutral strategy from scratch
• Selecting cointegrated or correlated asset pairs from a candidate universe
• Generating entry/exit signals based on spread dynamics (z-score, Kalman filter, Ornstein-Uhlenbeck)
• Constructing a portfolio of stat arb positions with sector/beta neutrality constraints
• Backtesting and stress-testing an existing stat arb model before live deployment
• Migrating a discretionary relative-value approach into a systematic framework

Inputs To Gather

• Asset universe: equity tickers, ETFs, futures, or other instruments with sufficient liquidity and history (minimum 3–5 years daily data recommended)
• Pair selection criteria: cointegration test choice (Engle-Granger, Johansen), minimum half-life, correlation thresholds, sector/industry filters
• Signal parameters: lookback window, z-score entry/exit thresholds, regime-detection toggles
• Risk constraints: target gross/net exposure, maximum single-pair allocation, sector neutrality tolerance, beta-to-benchmark cap
• Cost assumptions: commission per share, estimated slippage model, borrow cost/availability for short legs [VERIFY against current prime broker schedule]
• Backtest parameters: in-sample vs. out-of-sample split, rebalance frequency, transaction cost treatment

Workflow

1. Universe Screening and Pair Formation

• Pull adjusted close prices for the candidate universe; verify for survivorship bias and corporate actions
• Compute pairwise cointegration tests across the universe; rank by test statistic significance
• Filter pairs: discard those with half-life outside target range (e.g., 5–60 trading days), insufficient cointegration p-value (< 0.05), or same-entity overlap
• Group surviving pairs by sector or factor exposure to ensure portfolio diversification

2. Spread Construction and Signal Design

• For each pair, estimate the hedge ratio via OLS, total least squares, or Kalman filter (dynamic hedge ratio preferred for non-stationary betas)
• Construct the spread series: spread_t = price_A_t − hedge_ratio × price_B_t
• Normalize spread to a z-score using a rolling lookback window; calibrate window length to the estimated half-life
• Define signal rules:
  • Entry long spread: z-score < −entry_threshold (e.g., −2.0)
  • Entry short spread: z-score > +entry_threshold
  • Exit: z-score reverts within ±exit_threshold (e.g., ±0.5) or stop-loss at ±stop_threshold (e.g., ±4.0)
• Optionally layer regime filters (e.g., suppress signals when realized spread volatility exceeds 2× its historical median)

3. Portfolio Construction Under Neutrality Constraints

• Allocate capital across active pairs using risk-parity, equal-dollar, or mean-variance weighting
• Enforce constraints:
  • Net dollar exposure ≤ target (e.g., ±5% of gross)
  • Net beta-to-index ≤ tolerance (e.g., ±0.10)
  • Single-pair concentration ≤ max allocation (e.g., 5% of gross)
  • Sector net exposure ≤ sector cap [VERIFY sector classification source: GICS, ICB, or custom]
• Rebalance at defined frequency; recalculate hedge ratios and re-run cointegration tests at each rebalance to retire degraded pairs

4. Backtest and Performance Attribution

• Run full backtest on the in-sample period with realistic transaction costs and borrow costs
• Compute key metrics: annualized return, Sharpe ratio, max drawdown, average holding period, win rate, profit factor
• Decompose PnL by pair, sector, and signal type to identify concentration risk
• Re-run on the out-of-sample period; flag any Sharpe degradation > 30% as potential overfit indicator
• Perform sensitivity analysis on entry/exit thresholds, lookback window, and hedge-ratio method

5. Risk and Stress Testing

• Simulate spread blow-ups: what happens if a pair's cointegration breaks permanently (structural break scenario)?
• Test under regime-specific stress periods (e.g., 2008 credit crisis, 2020 COVID dislocation, 2022 rate shock) [VERIFY data availability for chosen stress windows]
• Evaluate margin/liquidity impact: model margin calls under 3× normal spread volatility
• Check correlation of pair PnLs during stress — if pairwise correlation spikes, the portfolio loses diversification benefit

Output

Deliver a stat arb model package containing:

• Pair selection report: list of qualifying pairs with cointegration statistics, half-life, and sector labels
• Signal specification: entry/exit rules with parameterized thresholds and regime filters
• Portfolio allocation matrix: pair weights, gross/net exposure, beta exposure, and sector exposure
• Backtest results: equity curve, performance metrics (Sharpe, max drawdown, Calmar), in-sample vs. out-of-sample comparison
• Risk report: stress-test outcomes, break-even cost analysis, sensitivity tables for key parameters
• Implementation notes: rebalance schedule, hedge-ratio update cadence, pair retirement criteria, and data pipeline requirements

Quality Checks

• Confirm cointegration tests use the correct critical values for the number of pairs tested (Bonferroni or Holm correction for multiple comparisons)
• Verify hedge ratios are estimated on properly aligned, split/dividend-adjusted data
• Ensure backtest does not embed look-ahead bias (signals use only data available at signal time)
• Validate that transaction cost assumptions reflect current market conditions [VERIFY borrow costs for hard-to-borrow names]
• Check that portfolio-level neutrality constraints are satisfied at every rebalance point, not just on average
• Confirm out-of-sample period is truly held out and not used for any parameter tuning
• Flag any pair where the spread half-life drifts above the maximum threshold during the backtest as a candidate for early retirement