The Decision Geometry of Covariance Estimation for the Global Minimum-Variance Portfolio under Heavy Tails

Battle Count: 59

Highly relevant to quantitative trading and portfolio management. The paper provides exact theoretical guidance on how covariance estimation error translates into portfolio suboptimality, identifies which error directions matter for the GMVP, quantifies the amplification from portfolio concentration and covariance conditioning, and establishes convergence rates under heavy tails. Practical implications include: scoring estimators by realised portfolio variance rather than matrix-norm accuracy, concentrating estimation effort on assets the portfolio actually weights, and monitoring concentration and conditioning as live risk diagnostics. The results directly inform minimum-variance and risk-parity allocator design.

The theoretical results (exact identity, bound, geometry) are analytical and require no implementation beyond standard linear algebra. The simulation verification involves generating skew-t/t-copula returns, computing centred sample covariances, and fitting log-log slopes, which is straightforward. The main complexity lies in correctly implementing the centring (Remark 3), the closed-form covariance of the skew-t model, and the pre-registered analysis protocol. No ML training or complex optimization is required.

The paper features a pre-registered analysis plan with committed statistical analysis, seeded generators for bit-for-bit reproducibility, supplementary code (dfc_thm1_verify.py, lemma_core.py, closed_form_sigma_true_verify.py, battery3_centered_results, battery3b_cond5_results, resolve_k35_cond5), and all covariance estimates are centred. The design, sample-size ladder, per-claim pass criteria, and summary statistics were fixed in writing before the confirmation run. Repository URL to be inserted on acceptance.