Methodology

The complete methodology for the RiskModels hierarchical factor model is published and maintained on riskmodels.org, its canonical home.

That page is the full derivation: the L1/L2/L3 regression cascade, orthogonalization and link betas, Huber–Vasicek beta estimation, hedge-ratio construction, variance decomposition, the geometric return bridge, and the L* selection rule. It is kept in one place so it stays citable and downloadable as a PDF for model governance and allocator files, rather than drifting between two sites.

What stays in these docs

The methodology page explains why the numbers are what they are. For how to retrieve them and build with them, stay here:

• ERM3 Engine Design — the implementation assumptions: time-safe construction, Security Master discipline, and why the hedge outputs remain executable with raw ETFs.
• API Reference — the live decomposition and metrics endpoints, with wire field names and response schemas.
• API Docs — coverage, the endpoint map, pricing, and the main research workflow.

L* selection in the API

The L* selection rule from the methodology page lands on three concrete API surfaces:

• GET /api/lstar — per-ticker daily series of the dispatched level, hedge ratios, and residual return; supports a custom ?threshold= override.
• lstar_rr — the Lstar-dispatched residual return in MetricsV3 (GET /api/metrics/{ticker}, POST /api/batch/analyze, V3 history fetches), materialized by the engine’s canonical selector, including the cost-aware walk-forward GBM.
• lstar_level — the level the cascade picked: 1 (L1, market only) / 2 (L2, market + sector) / 3 (L3, market + sector + subsector) / null (no recommendation — both L2 and L3 ER missing).

Prefer lstar_rr over a fixed-depth l3_rr for "best residual" queries — fixed-L3 subtracts a subsector layer even when the model would not have prescribed it, so it overstates residual cleanness on names where lstar_level is 1 or 2. The full derivation of the 1% threshold and the marginal-ER cascade rule is on the methodology page.

For the math behind the numbers those endpoints return, read the methodology on riskmodels.org.

Canonical requests omit threshold. Supplying it explicitly requests the legacy marginal-ER rule, even when its value is 0.01. The selected level dispatches its complete hedge vector: L1 uses L1 market HR; L2 uses L2 market and sector HRs; L3 uses L3 market, sector, and subsector HRs. The market/SPY ratio changes with depth; do not truncate an L3 vector to construct L2.

recommended_hedge_level additionally applies the existing user-segment economic gates and can differ from canonical LSTAR. /hedge-basket/{ticker} returns legs for this final recommendation. The legacy threshold_used response field remains the configured fallback/override threshold; it does not mean a canonical materialized GBM choice was derived from a 1% rule.