How do all the FRTB capital components aggregate into the total market risk capital requirement?

The total market risk capital under FRTB combines multiple components, with the specific formula depending on whether each desk uses the Internal Models Approach or the Standardized Approach. An output floor ensures that IMA capital doesn't fall too far below SA capital.\n\nIMA Capital Components:\n\n`mermaid\ngraph TD\n A[\"Total Market Risk Capital\"] --> B[\"IMA Desks\"]\n A --> C[\"SA Desks\"]\n B --> D[\"IMES
Internal Models ES\"]\n B --> E[\"NMRF Add-On
SES charges\"]\n B --> F[\"DRC
Default Risk Charge\"]\n B --> G[\"RRAO
Residual Risk Add-On\"]\n C --> H[\"SBM
Sensitivities-Based Method\"]\n C --> I[\"DRC_SA
SA Default Risk Charge\"]\n C --> J[\"RRAO
Residual Risk Add-On\"]\n D --> K[\"Multiplier: max(1, floor + penalty)\"]\n K --> L[\"Aggregate IMA Capital\"]\n E --> L\n F --> L\n G --> L\n H --> M[\"Aggregate SA Capital\"]\n I --> M\n J --> M\n L --> N[\"Total = IMA_total + SA_total\"]\n M --> N\n N --> O{\"Output Floor Test\"}\n O -->|\"Total < 72.5% x SA_all\"| P[\"Capital = 72.5% x SA_all\"]\n O -->|\"Total >= 72.5% x SA_all\"| Q[\"Capital = Total\"]\n`\n\nIMA Desk Capital Formula:\n\nC_IMA = max(IMES_{t-1}, m_c x IMES_avg) + SES + DRC + RRAO\n\nwhere:\n- IMES_{t-1} = most recent day's internal models ES\n- IMES_avg = 60-day average of IMES\n- m_c = multiplier (minimum 1.5, increased by backtesting failures)\n- SES = aggregate NMRF stressed scenario charges\n- DRC = default risk charge from simulation\n- RRAO = residual risk add-on for exotics\n\nSA Desk Capital Formula:\n\nC_SA = SBM + DRC_SA + RRAO\n\nwhere SBM = delta + vega + curvature charges aggregated across risk classes.\n\nThe Multiplier and Backtesting:\n\nThe multiplier m_c starts at 1.5 and increases based on the number of backtesting exceptions (days where actual loss exceeds the model's 99% VaR):\n\n| Exceptions (250 days) | Multiplier Addition |\n|---|---|\n| 0-4 (green zone) | +0.00 |\n| 5 | +0.40 |\n| 6 | +0.50 |\n| 7 | +0.65 |\n| 8 | +0.75 |\n| 9 | +0.85 |\n| 10+ (red zone) | +1.00 |\n\nWorked Example:\nPeninsula Bank has two IMA desks and one SA desk:\n\nIMA Desk 1 (Rates):\n- IMES: $38M, m_c = 1.5 (no exceptions), SES: $4M, DRC: $12M, RRAO: $0.1M\n- Capital: max($38M, 1.5 x $36M_avg) + $4M + $12M + $0.1M = $54M + $4M + $12M + $0.1M = $70.1M\n\nIMA Desk 2 (FX Options):\n- IMES: $22M, m_c = 1.65 (6 exceptions), SES: $1M, DRC: $3M, RRAO: $0.5M\n- Capital: max($22M, 1.65 x $20M_avg) + $1M + $3M + $0.5M = $33M + $1M + $3M + $0.5M = $37.5M\n\nSA Desk (Credit Exotics):\n- SBM: $42M, DRC_SA: $18M, RRAO: $0.8M\n- Capital: $60.8M\n\nPre-floor total: $70.1M + $37.5M + $60.8M = $168.4M\n\nOutput floor: If SA for entire trading book = $220M, then floor = 72.5% x $220M = $159.5M\n\nSince $168.4M > $159.5M, the floor is not binding. Final capital = $168.4M.\n\nMaster the complete FRTB framework in our FRM Part II course.