Basket Trading Improvement using Bayesian Optimization

Statistical Arbitrage · Johansen Cointegration · Bayesian Portfolio Optimization · Walk-Forward Validation

This project implements a complete, research-grade basket trading strategy that improves upon the classical Johansen cointegration baseline using Bayesian Optimization (BO) to find superior portfolio weights that maximize a risk-adjusted objective.

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📐 Architecture

Data Collection (yfinance)
       ↓
Cointegration Analysis (Johansen Test)
       ↓
Spread Construction & Verification (ADF + Half-life)
       ↓
Baseline Trading Strategy (Z-Score Mean Reversion)
       ↓
Bayesian Optimization (scikit-optimize GP)
       ↓
Rolling Walk-Forward Backtest (Out-of-Sample)
       ↓
Evaluation & Reporting

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🗂️ Project Structure

BasketBO/
├── data/                     # Downloaded price CSVs (gitignored)
├── results/                  # Output plots and metrics (gitignored)
├── notebooks/                # Jupyter notebooks for exploration
├── src/
│   ├── __init__.py
│   ├── data_loader.py        # yfinance downloader + config loader
│   ├── cointegration.py      # Johansen test & baseline weights
│   ├── spread.py             # ADF test, half-life estimation
│   ├── strategy.py           # Z-score, signal generation
│   ├── backtester.py         # Vectorized PnL backtester
│   ├── metrics.py            # Sharpe, CAGR, max drawdown, win rate
│   ├── optimizer.py          # Bayesian Optimization (BO) engine
│   ├── rolling_window.py     # Walk-forward optimization framework
│   └── visualization.py      # Equity curves, spread, weight plots
├── configs/
│   └── config.yaml           # All parameters in one place
├── main.py                   # Pipeline entry point (all 7 phases)
├── requirements.txt
└── README.md

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🚀 Getting Started

1. Install Dependencies

pip install -r requirements.txt

2. Configure

Edit configs/config.yaml to set your universe, strategy parameters, and BO settings:

data:
  tickers: [AAPL, MSFT, NVDA, ORCL, CSCO]
  start_date: '2015-01-01'

strategy:
  rolling_window: 30
  entry_z: -2.0
  exit_z: 0.5

optimizer:
  init_points: 15
  n_iter: 35

3. Run the Full Pipeline

python main.py

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📊 Output

Results are saved to results/:

File	Description
in_sample_equity.png	Equity curves (in-sample, Johansen vs BO)
out_of_sample_equity.png	Walk-forward equity curves
johansen_spread.png	Spread with entry/exit signals
bo_spread.png	BO-optimized spread with signals
johansen_weights.png	Weight evolution per window (Johansen)
bo_weights.png	Weight evolution per window (BO)
evaluation_metrics.csv	Metrics comparison table

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🧪 Methodology

Phase 1 — Data Collection

Downloads adjusted close prices for 5 technology stocks using yfinance.

Phase 2 & 3 — Cointegration & Spread

• Runs the Johansen cointegration test to find the first cointegrating vector.
• Constructs the basket spread S_t = wᵀ · Pₜ.
• Validates mean reversion via Augmented Dickey-Fuller (ADF) test.
• Estimates half-life of mean reversion using an Ornstein-Uhlenbeck model.

Phase 4 — Baseline Strategy

• Computes a rolling z-score of the spread.
• Enters long when z < −2, short when z > +2, exits when |z| < 0.5.
• Tracks Sharpe, CAGR, max drawdown, win rate, profit factor.

Phase 5 — Bayesian Optimization

• Uses Gaussian Process-based BO (scikit-optimize) to search for weights w ∈ [−1, 1]⁵.
• Objective: maximize Sharpe − 0.5 × |MaxDrawdown| subject to a stationarity penalty (ADF p-value).
• Normalizes weights to Σ|wᵢ| = 1.

Phase 6 — Rolling Walk-Forward Backtest

• Train window: 2 years. Test window: 3 months (quarterly).
• Each window independently runs Johansen and BO, then trades out-of-sample.
• Provides an honest, leak-free evaluation over the full history.

Phase 7 — Evaluation

• Compares Johansen vs BO across all rolling windows.
• Saves plots and a metrics CSV.

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📈 Key Metrics Tracked

Metric	Description
Sharpe Ratio	Annualized risk-adjusted return
CAGR	Compound Annual Growth Rate
Max Drawdown	Largest peak-to-trough decline
Win Rate	% of profitable trading days
Profit Factor	Gross profits / gross losses
Half-life	Mean reversion speed (days)

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🔬 Advanced Extensions

• Deep Kernel Learning BO (replace GP with DKL for non-stationary objectives)
• Regime Detection (separate BO for bull/bear markets via HMM)
• Multi-Objective BO (Pareto frontier: Sharpe vs Drawdown via Optuna/BoTorch)
• Dynamic Threshold Optimization (add entry_z and exit_z to BO search space)
• Transaction Cost Modeling (commission + bid-ask + slippage)

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🛠️ Tech Stack

Tool	Purpose
yfinance	Market data
statsmodels	Johansen test, ADF test
scikit-optimize	Gaussian Process Bayesian Optimization
pandas / numpy	Data manipulation
matplotlib	Visualization
sklearn	OU half-life regression

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📝 References

1. Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors. Econometrica.
2. Avellaneda, M. & Lee, J.H. (2010). Statistical Arbitrage in the US Equities Market. Quantitative Finance.
3. Mockus, J. (1975). On Bayesian Methods for Seeking the Extremum. IFIP Technical Conference.