Dynamic Causal Portfolio Choice: Hedging the Rotation of the Common-Driver Manifold

Battle Count: 96

The paper is directly relevant to quantitative trading and portfolio management. It provides a rigorous dynamic portfolio theory that: (1) reduces the intertemporal problem to driver dimension m rather than asset dimension n, enabling scalable computation for large portfolios; (2) identifies a first-order hedging demand against the rotation of the information geometry, with quantified certainty-equivalent gains of ~1-2.5%; (3) establishes that separator switches create irreducible unhedgeable risk in continuous-asset markets; (4) provides a geometric turnover decomposition showing that part of rebalancing is purely geometric and unavoidable; (5) offers a practical decision rule for refining the driver set based on expected partial Sharpe ratio. The companion applied papers report out-of-sample outperformance on real markets. The framework is implementable via the two-stage O(nk²) structure.

The theoretical framework is mathematically sophisticated, requiring: (1) solving semilinear parabolic PDEs (HJB equations) with quadratic-gradient nonlinearities via implicit IMEX schemes; (2) computing state-dependent projectors MC(z) and pullback metrics G(z); (3) implementing the transport connection with strain correction on Grassmannian bundles; (4) online regime detection with streaming covariance estimation; (5) handling viscosity solutions for verification in the state-dependent sensitivity case. However, the computational structure is favorable: the dynamic problem lives in driver dimension m (not asset dimension n), the two-stage assembly is O(nk²) via Woodbury, and the Riccati system for affine-Gaussian cases is tractable. The main practical challenge is accurate estimation of the geometry B(z), as the hedge degrades rapidly with estimation error.

The paper provides a complete reproducibility package on GitHub and Zenodo (doi.org/10.5281/zenodo.21226184). All experiments use fixed seeds in a pinned environment (Python 3.12, numpy 2.4.4, scipy 1.17.1, matplotlib 3.10.8). Synthetic data-generating processes are fully specified. Theoretical proofs are self-contained with appendix. Multi-seed validation is reported (8 seeds for hedging, 400-500 economies for monotonicity). Convergence studies are included for the PDE solver.