The formula
Risk-weighted assets answer a simple question: how much of the balance sheet should be treated as risky? Two numbers produce the answer.
RWA = EAD × RW
EAD is exposure at default, the amount owed if the borrower defaults. RW is the risk weight, the share of that exposure treated as risky. A 100% risk weight means the whole exposure counts. A 35% risk weight means a little more than a third counts.
The capital requirement follows from RWA, not from the exposure directly: capital = 8% × RWA. That is why a 100% risk weight costs 8 units of capital per 100 units of exposure, not 100.
Step 1: exposure at default
Start from the drawn balance and add the part of undrawn commitments expected to be drawn before default. For off-balance sheet items the conversion is done with a credit conversion factor: a 1,000,000 commitment with a 40% factor contributes 400,000 to EAD.
Use the exposure net of specific credit risk adjustments where the framework allows it, and keep collateral out of this step. Collateral affects LGD in the IRB approach and the risk weight in the standardised approach, not the exposure itself.
Step 2: risk weight
There are two ways to get the risk weight, and the choice belongs to the bank, not to the analyst.
- Standardised approach. The supervisor prescribes a weight per exposure class and, where relevant, external rating. An unrated corporate under CRR is 100%; a retail exposure is 75%; a residential mortgage has its own treatment. CRR3 amends several of these weights, especially for real estate.
- IRB approach. The weight comes from the formula using the bank's own PD and LGD estimates and, for corporates, maturity. At PD 1%, LGD 40% and maturity 2.5 years, the CRR3 weight is 82.06%.
This site implements both routes: the IRB calculator and the standardised approach calculator.
Step 3: capital
Multiply RWA by 8% for the Pillar 1 minimum. Of that 8%, at least 4.5% must be common equity tier 1, at least 6% tier 1, and the rest can be tier 2. Capital buffers sit on top and are set by the supervisor, so the effective requirement for a large bank is usually above 8%.
Worked example
Three exposures, two approaches, same arithmetic.
| Exposure | EAD | Risk weight | RWA | Capital at 8% |
|---|---|---|---|---|
| Corporate, IRB, PD 1%, LGD 40%, M 2.5 | 10,000,000 | 82.06% | 8,205,940 | 656,475 |
| Retail, standardised | 300,000 | 75% | 225,000 | 18,000 |
| Residential mortgage, standardised | 300,000 | 35% | 105,000 | 8,400 |
The corporate exposure consumes 78 times the capital of the mortgage for 33 times the exposure. Risk weight, not size, drives the difference.
Where the calculation goes wrong
- Multiplying exposure by capital instead of by risk weight.
- Using the drawn balance as EAD and ignoring undrawn commitments.
- Applying collateral twice: once by reducing EAD and again by reducing LGD.
- Mixing CRR and CRR3 weights in one portfolio. Pick a regime and keep it.
- Forgetting the SME supporting factor or the firm-size adjustment, whichever applies to the approach in use.
Questions
Is RWA the same as the capital requirement?
No. RWA is exposure times risk weight. The capital requirement is 8% of RWA.
Which risk weight applies to an unrated corporate?
Under the standardised approach and CRR it is 100%. CRR3 changes the treatment of certain unrated corporates, so the regime matters.
Does a 100% risk weight mean the exposure is lost?
No. It means the full exposure counts in RWA. At an 8% requirement, it consumes 8 units of capital per 100 units of exposure.