IRB risk weight formula, step by step

A risk weight answers one question: of every 100 units of exposure, how much counts as risky for capital purposes? Under the internal ratings-based approach the answer comes from three inputs, not from a supervisor's table.

• PD, probability of default over one year, as a percentage.
• LGD, the share of the exposure expected to be lost if default happens.
• M, effective maturity in years, and only for corporate exposures.

Exposure at default (EAD) does not change the risk weight; it only scales the result. Multiply the two to get risk-weighted assets, and take 8% of that for the capital requirement.

For a corporate exposure, the capital requirement per unit of exposure is:

K = LGD × Φ[(Φ⁻¹(PD) + √R × Φ⁻¹(0.999)) / √(1 − R)] − PD × LGD

with a maturity adjustment:

K = K × (1 + (M − 2.5) × b) / (1 − 1.5 × b), b = (0.11852 − 0.05478 × ln PD)²

The risk weight is that number scaled to a percentage:

RW = K × 12.5 × 100

Φ is the standard normal distribution and Φ⁻¹(0.999) is its 99.9% quantile, about 3.09. The 99.9% is the supervisory confidence level: the formula asks how much loss the portfolio would take in a very bad year.

R measures how much borrowers tend to default together. For corporates:

R = 0.12 × (1 − e^(−50 × PD)) / (1 − e^(−50)) + 0.24 × [1 − (1 − e^(−50 × PD)) / (1 − e^(−50))]

At very low PD the correlation approaches 0.24; at high PD it falls towards 0.12. Retail classes use fixed correlations: 0.15 for residential mortgages, 0.04 for qualifying revolving, and a PD-dependent value for other retail. Corporate SME applies the firm-size adjustment, which subtracts up to 0.04 from R as consolidated annual sales fall below EUR 50 million.

Corporate exposure, CRR3, PD 1%, LGD 40%, maturity 2.5 years:

• Correlation R = 19.3%
• Capital requirement K = 6.56%
• Risk weight = 82.06%
• EAD of EUR 10,000,000 → RWA of EUR 8,205,940
• Capital requirement at 8% → EUR 656,475

The same exposure under CRR, which applies a 1.06 scaling factor, gives 87.0%. Open the calculator with these inputs to see the numbers and the risk weight curve.

Corporate, LGD 40%, maturity 2.5 years. CRR3 is the default; CRR includes the 1.06 factor.

The two columns cross at very low PD. Under CRR the 0.03% floor meets the 1.06 factor; CRR3 raises the corporate PD floor to 0.05%, which lifts the risk weight at the bottom of the range.

Retail formulas drop the maturity adjustment and use class-specific correlations and floors. Under CRR3 the calculator applies input floors for LGD: 5% for residential mortgages, 50% for qualifying revolving exposures and 30% for other retail. Secured and unsecured retail carry different correlations, which is why the same PD and LGD produce different risk weights across those classes.

• Entering PD as a decimal where a percentage is expected, which moves the result by two orders of magnitude.
• Forgetting the maturity adjustment for corporates, or assuming it applies to retail.
• Applying the SME firm-size adjustment without consolidated annual sales in EUR.
• Treating the risk weight as the capital requirement. Capital is 8% of RWA, so a 100% risk weight consumes 8% of exposure in capital, not 100%.
• Reading the result as a regulatory number. It is indicative: approved models, supervisory floors and add-ons sit outside this page.

• IRB risk weight calculator: the formula above, applied to your inputs.
• Standardised approach calculator: risk weights without internal models.
• Scope and limits: what the calculator does not cover.