A sharp order-three obstruction to the aggregation of conditional price-of-risk attribution

Battle Count: 64

Directly relevant to quantitative trading through: (1) the squared Sharpe ratio as a central performance metric, (2) causal decomposition of conditional price-of-risk attribution for factor/strategy evaluation, (3) admissibility screening of information structures used in portfolio construction, (4) the order-three obstruction as a concrete failure mode in multi-strategy books where pairwise diagnostics pass but pooled attribution is invalid, and (5) the permutation-calibrated screening protocol as an operational tool for risk managers. The paper bridges the Hansen-Richard conditioning-information literature with modern causal inference, providing actionable diagnostics for attribution systems.

High complexity due to: (1) deep filtration-theoretic machinery (immersion, H-hypothesis, initial/progressive enlargement, Girsanov), (2) L2 Hilbert space projection geometry with Pythagorean decomposition, (3) causal back-door adjustment requiring DAG specification and regular conditional kernels, (4) the explicit order-three construction with Rademacher variables and Brownian increments, (5) the masking hypergraph encoding for maximal admissible sub-books, and (6) the permutation-calibrated screening protocol requiring out-of-sample R2 estimation. The theoretical framework requires graduate-level stochastic analysis and causal inference expertise. The screening protocol is more operationally accessible.

All experiments are synthetic, seeded with numpy.random.default_rng, and fully specified in Appendix A. Code is archived on Zenodo (doi:10.5281/zenodo.20843643) and available on GitHub. Every figure is exactly reproducible from the supplementary scripts. No proprietary data is used.