Concept · The RiskModels engine (ERM3)
Hierarchical cascade (L1/L2/L3)
L1 = market (SPY); L2 = sector ETF (e.g. XLK) fit on the L1 residual; L3 = subsector ETF (e.g. SOXX) fit on the L2 residual. Each level explains what the prior one left over.
In depth
L1 fits market (SPY); L2 fits the sector ETF on what L1 left over; L3 fits the subsector ETF on what L2 left over. Each level explains only its incremental risk, so the shares are additive.
Formula
r = β_m·r_m (L1) → β_s·r*_sector (L2) → β_u·r*_sub (L3) → ε
Compute it with the API
POST /api/decompose
# pip install riskmodels-py
client.decompose("NVDA")In the methodology
The three levels: L1, L2, L3 →Referenced by (1)
- Cascade Hedging and the Cost of Interpretability
Subsector ETF value, joint optimization, and executable hedge layers across 9,074 US mutual funds