How is economic capital for credit risk calculated, and how does it differ from regulatory capital?
I understand that expected loss = PD x LGD x EAD, but economic capital seems to go beyond that. My FRM textbook mentions unexpected loss and the need for capital to absorb tail losses. Can someone explain the full framework?
Economic capital is the amount of capital a bank needs to absorb unexpected credit losses at a chosen confidence level. It goes beyond regulatory minimums to reflect the bank's own risk assessment.
The Loss Distribution Framework:
Credit losses over a horizon (typically 1 year) follow a skewed distribution:
- Expected Loss (EL) = PD x LGD x EAD = the average loss the bank expects. Covered by loan pricing (spread) and provisions.
- Unexpected Loss (UL) = the volatility of losses around EL. This is what capital must cover.
- Economic Capital = Loss at the chosen confidence level (e.g., 99.97%) minus EL
Calculating Unexpected Loss for a Single Exposure:
UL = EAD x sqrt[PD x sigma_LGD^2 + LGD^2 x PD x (1-PD)]
Where sigma_LGD is the standard deviation of LGD.
Example — Clearview Bank, single $10M loan:
- PD = 2%, LGD = 45% (sigma_LGD = 25%), EAD = $10M
- EL = 0.02 x 0.45 x $10M = $90,000
- UL = $10M x sqrt[0.02 x 0.0625 + 0.2025 x 0.02 x 0.98]
- UL = $10M x sqrt[0.00125 + 0.003969] = $10M x sqrt[0.005219] = $10M x 0.0722 = $722,000
Portfolio Economic Capital:
For a portfolio, you need the loss distribution at the target confidence level. Methods include:
- Vasicek/Basel formula: Assumes single-factor Gaussian copula. Economic capital scales with asset correlation and confidence level.
- CreditMetrics: Full simulation of rating migrations and defaults
- CreditRisk+: Actuarial model treating defaults as Poisson events
Economic Capital vs. Regulatory Capital:
| Feature | Economic Capital | Regulatory Capital |
|---|---|---|
| Confidence level | Bank's choice (99.95-99.99%) | Fixed (99.9% for Basel) |
| Correlation | Bank's estimate | Basel formula |
| LGD | PIT or custom | Downturn LGD |
| Horizon | Flexible | 1 year |
| Purpose | Internal risk management | Minimum regulatory requirement |
| Diversification | Fully recognized | Partially |
FRM Key Points:
- Economic capital is typically higher than regulatory capital for high-quality banks (they use higher confidence levels)
- Correlation is critical — high correlation concentrates losses in the tail
- RAROC (Risk-Adjusted Return on Capital) = (Revenue - EL - Expenses) / Economic Capital
- Banks use economic capital for business-line allocation, performance measurement, and strategic decisions
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