Geometric Observables for Financial Regime Detection

By Will Hammond

Rating

1325
Battle Count: 63

Relevance

8/10
Highly relevant for risk management and regime detection in quantitative trading. Berry Phase Rate achieves walk-forward OOS d=0.72 with ~67% fewer false alarms than Random Forest (1.2 vs 3.6/yr) and requires no crisis labels. SPY de-risking experiment cuts maximum drawdown by ~51% (from -55% to -27%) with improved Sharpe (0.70 vs 0.61). Geometric channels are largely uncorrelated with classical methods (mean |ρ|≈0.22), suggesting orthogonal risk signals for composite overlays. However, observables respond to stress rather than predicting it (reverse Granger causality), limiting predictive utility. Label-free operation is valuable for unprecedented crises where supervised methods fail.

Implementation Complexity

7/10
Moderate-to-high complexity. Requires understanding of Hilbert space formalism, Hermitian operators, Fubini-Study metric, Berry curvature via plaquette/Wilson loop computation, and quantum Fisher information. However, all computation runs on classical hardware with O(n³) eigensolve per step. At n=16, representative timings are ~1-2s per observable for T=3,447 on single CPU. The QCML framework is well-defined but requires careful implementation of gauge-invariant formulas, expanding-window z-scoring, and nested walk-forward HPO. Operator construction (random vs PCA-inspired) adds a design choice. No quantum hardware needed despite 'quantum' terminology.

Reproducibility

5/5
All code available at GitHub (https://github.com/willhammondhimself/qcml-geometric-sde). Market data from Yahoo Finance via open-source yfinance library (v0.2.x), freely available. Seed 42 used for all stochastic elements. Full hyperparameter configurations, crisis definitions, and canonical result JSON files provided. WRDS CRSP alternative loader included. All results reproducible without paid subscription.

About this paper

Methodology: QCML Geometric Regime Detection. Problem types: Anomaly Detection, Risk Management, Dimensionality Reduction, Classification, Online Learning, Semi-supervised Learning, Unsupervised Learning.

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