Quantitative research project studying mean-reversion of the E-mini S&P 500 (ES) calendar spread against its cost-of-carry fair value during quarterly roll windows. Covers four roll periods from September 2024 through June 2025, with full signal development, regime gate engineering, and in-sample / out-of-sample backtest evaluation.
Alpha source: The observed calendar spread (ES_back − ES_front) persistently deviates from its theoretical fair value:
FV = S × (r_f − q) × ΔT
where r_f = SOFR (via FRED), q = S&P 500 trailing dividend yield (~1.30%), and ΔT = time between expiries from Databento definition schema.
Signal: Enter when the z-score of (spread − FV) crosses ±2.5σ on a 10-minute rolling window (edge-triggered; fill executes at T+1). Exit uses a standard two-layer TP/SL: 90% of position at +0.50 pt (SL moves to breakeven) and 10% at +0.75 pt. Low-z overlay: entries with |entry_z| < 2.0 at fill time use a single layer at +0.25 pt instead. Position sizing is 10 lots per signal.
HC add-on: When |z_fill| > 3.0 at the T+1 fill bar, an unconditional 10-lot add-on executes at T+2, doubling the position to 20 lots with a blended entry price. The add-on is gated only by the same FOMC exclusion as the primary signal. Across all 4 windows: n=117 HC trades, WR=76.1%, avg net/lot=+$2.86. Conditional on window volatility: W1/W2/W4 positive (WR 72–80%), W3 marginal (one gap trade −$4,312 at 2× lots on 2025-03-14). Fixed-point SL does not scale with window sigma.
Session decomposition: Three session types analyzed — European (07:00–12:29 UTC), US RTH (13:30–20:15 UTC), Post-close — with European session identified as the primary alpha source.
Transaction costs: $8.04/lot round-trip (exchange fees + NFA + broker); fill model uses synthetic midprice (zero slippage assumption).
Monoyios, M. & Sarno, L. (2002). "Mean Reversion in Stock Index Futures Markets: A Nonlinear Analysis." Journal of Futures Markets, 22(4), 285–314. DOI: 10.1002/fut.10008
The paper models futures basis nonlinear mean reversion using an ESTAR (Exponential Smooth-Transition Autoregressive) signal:
Phi(gamma; z) = 1 − exp(−gamma^2 · z^2)
Phi → 0 near equilibrium (unit-root regime); Phi → 1 far from equilibrium (fast mean-reversion). Implemented in scripts/ms_baseline.py.
ESTAR baseline results (gamma=0.5, mean-reversion exit at |z|<0.25, SL=0.50pt):
| Pool | n | avg_net/lot | p-value | 95% CI | Sharpe |
|---|---|---|---|---|---|
| IS (W1+W2) | 3,000 | −$4.36 | <0.001*** | [−$4.58, −$4.15] | −0.71 |
| OOS (W3+W4) | 1,782 | −$4.00 | <0.001*** | [−$4.27, −$3.74] | −0.70 |
The naive ESTAR parameterisation fails on 1-second intraday bars: the mean-reversion exit (|z| < 0.25) fires at the first tick-back, producing hold times of ~0 minutes and 4,782 trades across 4 windows. The $8.04/lot TC destroys all gross edge.
The same z-score signal with no regime gate (regime_gate='none').
| Split | n | avg_net/lot | p-value |
|---|---|---|---|
| IS (W1+W2) | 308 | +$1.09 | 0.365 |
| OOS (W3+W4) | 371 | +$1.64 | 0.264 |
V1 (blue) vs Z-Score Ungated (gray). The large W4 drawdown in Ungated is absorbed by V1's drift gate. IS/OOS split at the dashed line.
V1 consistently reduces losses in the weaker IS window (W2) and outperforms Ungated in both OOS windows (W3, W4). Faded bars = IS; solid = OOS.
ESTAR exits at the first tick-back on 1-second bars (hold_med = 0 min), turning all gross edge into TC loss. Ungated and V1 achieve positive per-lot returns; V1 widens the margin in OOS (+$2.47 vs +$1.64/lot).
V1 adds a drift_4h regime gate (symmetric: block entries in the direction of sustained intraday drift, ±0.10 pt threshold, 4-hour lookback) over the ungated signal.
V1 (strategy):
| Split | n | Avg Net/Lot | p-value | 95% CI |
|---|---|---|---|---|
| IS (W1+W2) | 246 | +$1.26 | 0.361 | [−$1.45, +$3.96] |
| OOS (W3+W4) | 299 | +$2.47 | 0.006*** | [+$0.70, +$4.25] |
| OOS European | 90 | +$3.90 | 0.013** | [+$0.85, +$6.96] |
Ungated (benchmark):
| Split | n | Avg Net/Lot | p-value | 95% CI |
|---|---|---|---|---|
| IS (W1+W2) | 308 | +$1.09 | 0.365 | [−$1.28, +$3.46] |
| OOS (W3+W4) | 371 | +$1.64 | 0.264 | [−$1.24, +$4.52] |
| OOS European | 100 | +$6.28 | <0.001*** | [+$3.48, +$9.08] |
V1 vs Z-score Ungated:
| Metric | Z-score Ungated | V1 |
|---|---|---|
| Net P&L (10-lot) | +$9,452 | +$10,488 |
| Max Drawdown | −$6,659 | −$3,115 |
| Recovery Factor | 1.42 | 3.37 |
| OOS per-trade Sharpe | +0.058 | +0.159 |
| Annualized Sharpe (OOS) | — | +3.88 (90% CI: [+1.38, +6.63]) |
Verdict: Marginal positive edge; not yet deployable. V1 achieves statistically significant OOS edge overall (p=0.006***) and in the European session (p=0.013**). Ungated OOS is not significant (p=0.264), confirming the drift gate carries the edge. Evaluation is underpowered (4 roll windows); proper OOS requires ≥10 periods. IS→OOS rank correlation (Spearman) ρ=0.771.
Roll windows:
| Window | Contracts | Roll Date | Role |
|---|---|---|---|
| W1 | ESU4 → ESZ4 | Sep 16, 2024 | In-sample |
| W2 | ESZ4 → ESH5 | Dec 16, 2024 | In-sample |
| W3 | ESH5 → ESM5 | Mar 17, 2025 | Out-of-sample |
| W4 | ESM5 → ESU5 | Jun 16, 2025 | Out-of-sample |
Per-window results (all sessions combined, V1):
| Window | n | WR | Net P&L ×10 | p |
|---|---|---|---|---|
| W1 ESU4→ESZ4 (IS) | 120 | 85.0% | +$3,933 | 0.078 |
| W2 ESZ4→ESH5 (IS) | 126 | 75.4% | −$843 | 0.740 |
| W3 ESH5→ESM5 (OOS) | 197 | 87.3% | +$4,736 | 0.015* |
| W4 ESM5→ESU5 (OOS) | 102 | 84.3% | +$2,662 | 0.160 |
src/
strategy.py # Core backtest engine: gate system, simulate(), compute_stats()
scripts/
ms_baseline.py # M&S (2002) ESTAR external baseline
run_sessions.py # Multi-window, multi-session backtest runner
run_backtest.py # Single-window backtest entrypoint
result_summary.py # IS/OOS performance report with bootstrap CIs
databento_cost_estimate.py # Phase 2a: cost estimation before data pull
databento_datapull.py # Phase 2b: tick data pull (idempotent)
notebooks/
01_eda.ipynb # W1 exploratory data analysis
02_signal_analysis.ipynb # Five-signal evaluation (FV z-score, lead-lag, OBI, TFI, FOMC)
03_zscore_simulation.py # Z-score parameter sweep
04_threshold_analysis.py # Entry/exit threshold optimisation
05_robustness_globex.py # Globex session robustness check
07_tearsheet.py # W1 performance tearsheet
08_fomc_trend.py # FOMC event-day analysis
09-13_... # Additional window and signal analyses
results_dashboard.ipynb # Portfolio equity curves and MDD visualisation
supplementary/ # 36 publication-quality analysis notebooks
config.py # Shared paths and window definitions
generate_notebooks.py # Script to regenerate all supplementary notebooks
A1-A5 # Performance & equity curves
B1-B4 # FV deviation analysis
C1-C3 # OU process & z-score dynamics
D1-D5 # Trade analytics
E1-E9 # Bid-ask spread dynamics
F1-F4 # Spike events
G1-G3 # Volume migration
H1-H3 # Pre-roll context
es_roll_analysis_workflow.md # Full pipeline design specification
data/,results/, andreports/are gitignored. Tick data lives on external storage (~25–35 GB per roll window formbp-10).
# Python 3.14 venv
source .venv/bin/activate
pip install -r requirements.txtSet your Databento API key in the environment:
export DATABENTO_API_KEY="your_key_here"Data files are expected at /Volumes/SEAGATE/Databento_Futures/. Update paths in notebooks/supplementary/config.py if your storage location differs.
# Estimate data costs before pulling (review output before proceeding)
python scripts/databento_cost_estimate.py
# Pull tick data (idempotent — skips existing parquet files)
python scripts/databento_datapull.py
# Run M&S ESTAR external baseline
python scripts/ms_baseline.py
# Run full session backtest (Z-score Ungated + V1 gate variants)
python scripts/run_sessions.py
# Generate IS/OOS performance report with bootstrap CIs
python scripts/result_summary.py
# Regenerate all 36 supplementary notebooks
python notebooks/supplementary/generate_notebooks.pyFive alpha signals were evaluated across W1 and W2:
- FV Deviation Z-Score — selected; only signal with consistent positive edge
- Lead-Lag (front → back) — rejected; peak cross-correlation at lag=0s (contemporaneous, not predictive)
- Order Book Imbalance (OBI) — rejected; r ≈ +0.001 to −0.006 across windows (near-zero)
- Trade Flow Imbalance (TFI) — rejected; reverses sign across windows
- FOMC event-driven jump — implemented as full-day exclusion filter only
Eight regime gates were evaluated; two were accepted into V1:
- drift_4h gate — symmetric gate: blocks entries in the direction of sustained intraday drift (4-hour lookback, ±0.10 pt threshold); short-blocking arm saved +$134 IS; long-blocking arm empirically inactive across all 4 windows (spread has structural upward intraday drift during ES roll periods)
- low-z two-layer exit — modified exit for |z| < 2.0 bucket; saved +$58 IS
This repository contains research code and results for educational and analytical purposes. Nothing here constitutes financial advice or a recommendation to trade. Past backtest performance does not guarantee future results. ES futures carry substantial risk of loss.