Adaptive market-neutral statistical arbitrage using graph diffusion, multi-layer regime detection, and Riemannian correlation geometry.
| Metric | Value |
|---|---|
| Annual Return | 42.50% |
| Sharpe Ratio | 1.99 |
| Max Drawdown | -13.74% |
| Win Rate | 56.0% |
| Best Quarter | Q2: +34.75% (Sharpe 7.02) |
Validation on Unseen Data (Apr-Nov 2025): 1.11% return with positive Sharpe
Watch how the stock correlation landscape shifts through time. Peaks represent stocks deviating from normal correlations - these are the trading opportunities. Notice the sustained high peaks in Q2 2025 (when the strategy returned +34.75%) versus the flat terrain in Q1 (when it lost -10.95%).
See all visualizations in visualizations/ and detailed analysis in docs/RESULTS.md.
- CAPM Decomposition: Remove market beta to isolate idiosyncratic returns
- Correlation Graph: Build correlation matrix of residuals
- Graph Laplacian Diffusion: Separate systematic sector moves from idiosyncratic alpha
- Rough Signal: Extract mean-reversion opportunities (the actual trading signal)
- Universe: Top 80 stocks by liquidity (daily point-in-time filtering)
- Long: 10 stocks with most negative idiosyncratic residuals (reverting down)
- Short: 10 stocks with most positive idiosyncratic residuals (reverting up)
- Rebalancing: Daily
- Sizing: Equal-weighted within each leg
3-layer regime detection prevents trading during structural breaks:
- Market Trend (SPY vs 200-day SMA)
- Correlation Regime (0.40-0.65 sweet spot detection)
- Riemannian Manifold Drift (SPD matrix geodesic distance)
# Clone repository
git clone https://github.com/yourusername/topological-arbitrage
cd topological-arbitrage
# Create virtual environment
python -m venv venv
source venv/Scripts/activate # On Windows: venv\Scripts\activate
# Install dependencies
pip install -r requirements.txt# Full year 2025 backtest
python backtest.py
# Custom date range
python backtest.py --start 2025-01-01 --end 2025-12-31
# With visualizations
python backtest.py --visualize# Initialize new portfolio
python live_paper_trading.py --init --capital 100000
# Run daily update
python live_paper_trading.py
# View status
python live_paper_trading.py --status
# Launch web dashboard
python live_dashboard.py # Open http://localhost:5000topological-arbitrage/
├── README.md # This file
├── RESULTS.md # Performance results & quarterly breakdown
├── LICENSE # MIT License
├── requirements.txt # Python dependencies
├── .gitignore
│
├── Core Strategy
├── paper_trading_main.py # Backtesting orchestrator
├── paper_trading_engine.py # Portfolio management & execution
├── paper_trading_monitor.py # Performance tracking
├── paper_trading_config.py # Configuration & parameters
│
├── Signal Generation
├── graph_diffusion.py # Laplacian decomposition
├── capm.py # CAPM residual calculation
├── data_loader.py # Market data fetching
│
├── Regime Detection (3-Layer)
├── market_trend_filter.py # Layer 1: SPY trend
├── correlation_regime.py # Layer 2: Correlation sweet-spot
├── riemannian_regime.py # Layer 3: Manifold drift
├── riemannian_geometry.py # SPD manifold operations
│
├── Live Trading System
├── live_paper_trading.py # Real-time daily execution
├── live_dashboard.py # Web monitoring interface
├── schedule_live_trading.py # Task scheduler integration
│
├── Data & Configuration
├── our_stocks.csv # 80-stock universe
├── fundamentals.csv # Stock metadata
├── paper_trading_config.py # All strategy parameters
│
├── Results & Documentation
├── RESULTS.md # Performance analysis
├── docs/
│ ├── METHODOLOGY.md # Mathematical foundations
│ ├── REGIME_DETECTION.md # 3-layer detection system
│ └── ARCHITECTURE.md # Code architecture guide
│
├── examples/
│ ├── basic_backtest.py # Simple example
│ └── custom_parameters.py # Parameter configuration
│
├── publication_results/ # 2025 validation data
├── validation_results/ # OOS validation (Apr-Nov 2025)
├── q1_2026_results/ # Q1 2026 results
│
└── data_cache/ # Cached market data
- Graph Laplacian diffusion signal generation
- 3-layer adaptive regime detection
- Point-in-time stock universe selection (no lookahead bias)
- Daily rebalancing with transaction costs
- Persistent live trading system with state management
- Web dashboard for monitoring
- Complete audit trail of all trades and decisions
- Backtested 2018-2024 (in-sample)
- Walk-forward validation 2025 (unseen data)
- Out-of-sample validation Apr-Nov 2025 (positive Sharpe)
- Live paper trading since Mar 3, 2026 (daily decision logs)
from paper_trading_main import run_backtest
results = run_backtest(
start_date='2025-01-02',
end_date='2025-12-31',
initial_capital=100000
)
print(f"Return: {results['total_return']:.2%}")
print(f"Sharpe: {results['sharpe_ratio']:.2f}")
print(f"Max DD: {results['max_drawdown']:.2%}")from paper_trading_config import STRATEGY_PARAMS
# Modify strategy parameters
STRATEGY_PARAMS['n_longs'] = 15
STRATEGY_PARAMS['n_shorts'] = 15
STRATEGY_PARAMS['window_size'] = 90
# Run with new config
results = run_backtest(strategy_params=STRATEGY_PARAMS)from live_paper_trading import LivePaperTradingEngine
# Initialize
engine = LivePaperTradingEngine(initial_capital=100000)
# Daily update
signals = engine.update()
print(f"Combined exposure: {signals['combined_long_exposure']:.1%}")- Favorable Regime (corr 0.40-0.65): Sharpe 2.5-3.5, full exposure
- Neutral Regime (transitional): Sharpe 1.0-2.0, 50% exposure
- Hostile Regime (structure breakdown): No positions, 100% cash
See RESULTS.md for regime-stratified performance breakdown.
All strategy parameters in paper_trading_config.py:
STRATEGY_PARAMS = {
'n_longs': 10, # Number of long positions
'n_shorts': 10, # Number of short positions
'rebalance_interval': 1, # Days between rebalances
'universe_size': 80, # Total stocks in universe
'window_size': 60, # Days for correlation window
'laplacian_alpha': 0.8, # Diffusion parameter
'transaction_cost_bps': 20, # 0.20% per trade
}
REGIME_CONFIG = {
'market_trend_enabled': True,
'correlation_regime_enabled': True,
'riemannian_regime_enabled': True,
'correlation_sweet_spot': (0.40, 0.65), # Favorable range
}The strategy is based on spectral graph theory and geometric statistics:
- Graph Laplacian Diffusion: Separate smooth (sector) from rough (idiosyncratic) signals
- Riemannian Geometry: Model correlation matrices on SPD manifold with correct geodesic distances
- CAPM: Remove systematic market factor before analysis
- Mean Reversion: Bet that deviations from peer correlations revert
See docs/METHODOLOGY.md for mathematical details and equations.
- Source:
our_stocks.csv(80 stocks, point-in-time selection) - Liquidity Filter: Top 80 by 120-day average volume
- Sectors: Broad market coverage (tech, healthcare, finance, energy, etc.)
- Source: yfinance
- Frequency: Daily OHLCV
- Lookback: 120+ days for initialization
- Update: Daily after market close
- Return: 42.50%
- Sharpe: 1.99
- Max DD: -13.74%
- Win Rate: 56%
| Quarter | Return | Sharpe | Max DD |
|---|---|---|---|
| Q1 2025 | -10.95% | -2.61 | -13.39% |
| Q2 2025 | +34.75% | 7.02 | -2.58% |
| Q3 2025 | +6.46% | 1.49 | -4.92% |
| Q4 2025 | +10.63% | 2.15 | -3.98% |
Key Insight: Strategy performs best when stocks deviate from normal correlations (volatile periods) - the exact conditions where alternative risk management fails.
See RESULTS.md for:
- Full historical breakdown (2018-2025)
- Quarterly visualizations
- Regime-stratified performance
- Risk metrics by period
Web dashboard tracks:
- Portfolio value & daily returns
- Regime detection status (market, correlation, Riemannian)
- Current positions and weights
- Trade activity and rebalance timing
- Performance metrics
python live_dashboard.py
# Open http://localhost:5000- Execution: Perfect fills at closing prices
- Costs: 20 bps per trade (realistic institutional)
- Shorting: Unlimited short availability (conservative)
- Slippage: Not modeled (would reduce returns ~50-100 bps/year)
- Data: Survivorship bias limited by point-in-time universe selection
- Correlation Breakdown: When correlations approach 0 or 1
- Regime Transitions: Rapid shifts in market structure
- Sector Concentration: Strategy may cluster in certain sectors
- Liquidity: Performance may degrade with less liquid stocks
- METHODOLOGY.md - Mathematical foundations
- REGIME_DETECTION.md - 3-layer detection system
- ARCHITECTURE.md - Code organization
- agents.md - Original development notes
MIT License - See LICENSE file for details.
If you use this code in research, please cite:
@software{topological_arbitrage_2025,
title = {Topological Long-Short Arbitrage Strategy},
author = {Your Name},
year = {2025},
url = {https://github.com/yourusername/topological-arbitrage}
}Issues, pull requests, and improvements welcome! Please ensure:
- Code follows existing style (numpy docstrings, type hints)
- All backtests reproduce historical results
- New features include performance validation
- Issues: GitHub issues for bugs and feature requests
- Questions: See documentation in
docs/directory - Live Results: Check web dashboard for current performance
Last Updated: March 3, 2026 Status: Active live trading + daily backtesting validation