Riemannian Covariance Estimation and Regime Detection for Portfolio Management: Benchmark Results

Key Points

• The study aims to evaluate Riemannian geometric methods for improving portfolio covariance estimation and regime detection.
• Conducted 615+ tests across 5 independent Monte Carlo universes.
• Compared Riemannian methods against traditional Euclidean covariance estimates.
• Assessed positive-definiteness and conditioning of covariance estimates using geodesic shrinkage.
• Analyzed correlation structure shifts through geodesic distance.
• 63% of Euclidean covariance estimates failed positive-definiteness, while Riemannian methods showed 0% failure (p<0.0001).
• Geodesic shrinkage significantly improved the quality of covariance estimates.
• Portfolio performance metrics (Sharpe, drawdown) were not statistically significant across tested universes.