Eigenvalue Factor Model

Eigenvalue-based equity factor model applying Random Matrix Theory to extract idiosyncratic alpha signals from S&P 500 return data.

Methodology directly derived from PhD work on signal extraction in high-noise high-dimensional datasets.

Structure

factor_model/
├── src/
│   ├── data.py        # price download, cleaning, return computation
│   ├── covariance.py  # Ledoit-Wolf shrinkage, condition number analysis
│   ├── factors.py     # eigendecomposition, Marchenko-Pastur RMT
│   ├── portfolio.py   # signal construction, long-short portfolio, backtester
│   └── evaluate.py    # Sharpe, IC decay, performance plots
├── data/              # cached price parquet (auto-created)
├── plots/             # output charts (auto-created)
├── main.py            # full pipeline
└── requirements.txt

Setup

pip install -r requirements.txt
python main.py

First run downloads ~500 tickers from Yahoo Finance and caches to data/prices.parquet. Subsequent runs load from cache.

Key Methodology

Step	Method	Analogy to PhD
Covariance estimation	Ledoit-Wolf shrinkage	Regularised least-squares, avoids ill-conditioned matrix inversion
Factor count selection	Marchenko-Pastur RMT	Signal vs noise threshold from random matrix theory
Factor decomposition	Eigenvalue decomposition	fPCA on time-series, energy concentration in leading eigencomponents
Signal extraction	Idiosyncratic return z-score	Residual after projecting out systematic components
Validation	Walk-forward OOS	Out-of-sample testing across multiple configurations

Output

plots/beta_diagnostics.png — Beta distribution, vol reduction, SPY corr

plots/eigenvalue_spectrum.png — RMT factor count (market-neutral covariance)

plots/ic_decay_mean_reversion.png — MR signal IC by horizon

plots/momentum_diagnostics.png — 6-panel momentum dashboard: IC decay (short+long horizons),Daily IC time series, Top/bottom decile spread, Signal autocorrelation, Cross-sectional dispersion, Rolling ICIR

plots/signal_comparison_ic.png — MR vs Momentum vs Combined IC

plots/is_performance.png — In-sample 4-panel dashboard

plots/oos_performance.png — Out-of-sample 4-panel dashboard

plots/walk_forward_performance.png— Walk-forward OOS dashboard

plots/beta_neutrality.png — Portfolio beta scatter and rolling beta

Requirements

Python 3.9+