Exact Reconciliation with Narrative Preservation

Executive overview

Attribution effects that explain each period well do not add up to the compounded cumulative active return. Existing linkers smooth the effects or spread the residual by a fixed rule. This paper reframes linking as a controlled optimization: reconciliation is non-negotiable, and the attribution narrative is preserved as much as the math allows.

LD7S and LD8S are convex quadratic programs that start from the raw cumulative effects and solve directly for a linked vector that reconciles exactly. Distortion is measured relative to each effect’s size, and sign, dominant-driver and top-band preservation enter as governed soft penalties.

Findings, in order

1. Linking is residual allocation. The gap q = D − ΣG is distributed across buckets by a convex QP instead of a fixed formula.
2. Distortion is measured relative to size. Weights of 1/(|G|+ε)² stop small effects from being overwhelmed by adjustments that are trivial for large ones.
3. LD7S protects the dominant driver. A soft penalty discourages any outcome in which the largest raw contributor is displaced.
4. LD8S protects the top band. Pairwise penalties extend preservation to the leading group of contributors.
5. A reproducible worked example. Three periods and five effects show raw effects of 90.0000 bps against a compounded target of 90.2865 bps, compared with Cariño, Frongello, Menchero, modified Frongello and reverse Frongello.
6. Validated for production. Monte Carlo, adversarial, out-of-distribution, metamorphic, numerical-conditioning and production-control suites, with a governed fallback from LD8S to LD7S at high bucket counts.

Novelty