Last Updated: 2026-01-27
The Capital Formula
This file defines how the major risk components combine into a single required capital number. Each component’s calibration details live in its own module.
For any Prime's portfolio, total capital requirement is:
Total Capital = Σ Position Capital
+ Category Cap Penalties
Per-position calculation:
For each position with stressed pull-to-par (SPTP):
Duration Capacity = Cumulative liability amount in buckets ≥ required bucket
Matched Portion = min(Position Size, Available Duration Capacity)
Unmatched Portion = Position Size - Matched Portion
Matched Capital = Matched Portion × Risk Weight
Unmatched Capital = Unmatched Portion × max(Risk Weight, FRTB Drawdown)
Position Capital = Matched Capital + Unmatched Capital
For liquid, tradable positions without pull-to-par (e.g., perpetual spot exposures):
Position Capital = Position Size × max(Risk Weight, FRTB Drawdown)
For collateralized lending positions (gap risk / liquidation shortfall):
Position Capital = Position Size × max(Risk Weight, Gap Risk CRR)
Implementation note: if the risk weight and forced-loss terms use different exposure bases (e.g., notional vs market value vs EAD), compute both in dollars first and apply max(...) to the dollar capital amounts.
Where Each Component Is Defined
- Duration + matching:
duration-model.md,matching.md - Fundamental risk weight:
asset-classification.md(risk weight primitive) +asset-type-treatment.md(how it applies) - Market risk / FRTB drawdown:
market-risk-frtb.md - Collateralized lending gap risk:
collateralized-lending-risk.md - Category caps (concentration limits):
correlation-framework.md
Duration capacity consumption:
- Positions consume duration capacity in order of matching
- Once capacity at a bucket is consumed, additional positions requiring that bucket are unmatched
- Capacity at longer buckets can match shorter-duration assets (bucket 48 can match an asset with 360-day SPTP)
Category caps enforce concentration limits via 100% CRR on excess (see correlation-framework.md).
Term Halo (NFAT) positions: For positions held via Term Halo books, CRR varies by book phase — Filling (low), Deploying (high, reflecting information opacity during obfuscated deployment), At Rest (medium, based on attested risk characteristics), with CRR increasing if re-attestation is missed. See smart-contracts/nfats.md for the qualitative book-phase CRR incentive structure. Numeric CRR calibration values for NFAT book-phases are pending and will be published in the risk-framework when available.
Capital funding: This formula outputs Total Required Risk Capital (TRRC). For how TRRC is funded across JRC/SRC tiers with ingression-adjusted recognition, see accounting/risk-capital-ingression.md.