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Next filing · Form 10-Q · Q2 2026 · 54 daysFactor Research · Part 2 published: risk structure in 13F filings across five allocator stylesAPI Update · AOM portfolio chains — single snapshot call for multi-step analyze flowsAPI Update · POST /api/snapshot — canonical JSON portfolio snapshotPart 3 · The One Manager Skill That PersistsPart 1 · One Position, Four BetsNext filing · Form 10-Q · Q2 2026 · 54 daysFactor Research · Part 2 published: risk structure in 13F filings across five allocator stylesAPI Update · AOM portfolio chains — single snapshot call for multi-step analyze flowsAPI Update · POST /api/snapshot — canonical JSON portfolio snapshotPart 3 · The One Manager Skill That PersistsPart 1 · One Position, Four Bets
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Concept · The RiskModels engine (ERM3)

Geometric attribution bridge

Telescoping compound differences (market → sector → subsector → residual) so multi-period factor contributions sum exactly to the gross compound return — not the naive daily sum, which overstates by volatility drag.

In depth

Multi-period contributions compound, so a naive daily sum overstates by volatility drag. Telescoping compound differences make the four factor bars sum exactly to the gross compound return — an identity, not an approximation. Ordering (market→sector→subsector→residual) is required.

Formula

market=∏L1−1; sector=∏L2−∏L1; sub=∏L3−∏L2; residual=∏G−∏L3

Compute it with the API

GET /api/returns-decomposition

Full API docs ↗

In the methodology

Multi-period attribution: the geometric bridge →

Referenced by (0)

No working paper references this concept yet.

Related concepts

ERM3Hierarchical cascade (L1/L2/L3)Link beta (λ)Explained risk (ER)Replication equationRobust beta (Huber-M)Vasicek shrinkageL-star ruleResidual mean-reversion signal
← L-star ruleThe RiskModels engine (ERM3) · 9 / 10Residual mean-reversion signal →
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