Hierarchical Reconciliation with Narrative Preservation

Executive overview

Real attribution reports are hierarchies: total, asset class, region or sector, and security. A linked report is defensible only if every parent equals the sum of its children and the top equals cumulative active return. Linking each level independently routinely breaks that, because the adjustments disagree between levels.

HLD parametrizes the linked report by its bottom level, so coherence holds by construction. Top-level reconciliation is a hard constraint, distortion is controlled at every node, and narrative penalties apply level by level. The base formulation is a weighted projection of the raw tree onto the coherent, reconciled set.

Findings, in order

1. Per-level linking does not compose. Independent optimization at each level violated coherence in 99.6% of 500 coherent Monte Carlo scenarios.
2. Coherence becomes structural. Solving for the bottom level through a summing matrix guarantees that parents equal the sum of their children.
3. Base-HLD is a weighted projection. This ties attribution linking to the hierarchical forecast reconciliation literature (Hyndman et al.; Wickramasuriya et al.).
4. Strong comparative results. Under reconciliation- and coherence-gated loss, HLD8S won or tied in 69.4% of scenarios and HLD7S in 65.8%.
5. Multi-system inputs expose leaf-only methods. When levels come from different systems, leaf-only methods fail reconciliation itself.
6. Hardened at production scale. 1,500 mixed-depth and ragged hierarchies, 3,000 production solves and 400 independent objective-oracle comparisons.

Novelty