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FRM Exam Part II · Credit Risk

Credit Risk Capital and the Basel Framework

Updated 11 October 2026 · Fact-checked

Credit risk capital is the minimum capital a bank must hold against loan losses. You compute risk-weighted assets (RWA) as exposure × risk weight, then capital = RWA × the required ratio. The standardized approach uses fixed regulatory weights. The IRB approach uses the bank's own PD, and in advanced IRB also LGD, EAD and maturity, in a supervisory formula.

Understand Credit Risk Capital and Basel Framework

Banks lend money, and some borrowers do not repay. Regulators force banks to hold capital to absorb unexpected losses. Basel rules set how much. The idea is simple: riskier assets need more capital, so each asset is scaled by a risk weight to give risk-weighted assets (RWA).

Under the standardized approach, the regulator sets the risk weights. They depend on the borrower type and, in many cases, an external rating. For example, Basel II gave a 100% weight to unrated corporates and 0% to highly rated sovereigns. It is simple and comparable across banks, but not very risk-sensitive.

Under the internal ratings-based (IRB) approach, the bank estimates risk parameters and a regulatory formula turns them into capital. In foundation IRB, the bank estimates PD (probability of default) and the supervisor sets LGD, EAD and others. In advanced IRB, the bank estimates PD, LGD (loss given default), EAD (exposure at default) and maturity, subject to supervisory approval.

The IRB formula is built on the Vasicek single-factor model. It gives a conditional PD in a stress scenario (the 99.9th percentile of the systematic factor). Capital covers unexpected loss only: stressed loss minus expected loss. Expected loss is covered by provisions and pricing.

Basel III finalization keeps both approaches but adds an output floor, so that IRB-based RWA cannot fall below a set percentage of standardized RWA, and restricts IRB use for some exposures. Capital ratios are then applied to RWA, for example a minimum total capital ratio of 8% before buffers.

Key formulas to remember

Risk-weighted assets
RWA = Exposure × Risk weight
Exposure is EAD after any permitted credit risk mitigation. Sum across all exposures.
Minimum capital
Capital = RWA × capital ratio
Basel minimum total capital is 8% of RWA, before buffers. Common Equity Tier 1 minimum is 4.5%.
Expected loss
EL = PD × LGD × EAD
Covered by provisions, not by IRB capital.
IRB conditional PD (Vasicek)
WCDR = N[ (N⁻¹(PD) + √ρ × N⁻¹(0.999)) ÷ √(1 − ρ) ]
N is the standard normal CDF, ρ the asset correlation. 0.999 is the confidence level.
IRB capital requirement (before maturity adjustment)
K = LGD × (WCDR − PD)
Unexpected loss per unit of EAD. Wholesale exposures also get a maturity adjustment.
IRB RWA
RWA = K × 12.5 × EAD
12.5 is 1 ÷ 8%. Older Basel text also applied a scaling factor of 1.06.
Capital to RWA conversion
RWA = Capital requirement × 12.5
Use when a problem gives a capital charge and asks for RWA.

How to solve Credit Risk Capital and Basel Framework questions

Use this order for any credit risk capital question.

  1. 1Identify the approach: standardized, foundation IRB or advanced IRB. This decides who supplies the inputs.
  2. 2List the exposure type and EAD. Convert off-balance-sheet items with a credit conversion factor if given.
  3. 3For standardized, apply the risk weight for the borrower type or rating. Adjust for collateral or guarantees only as the question allows.
  4. 4For IRB, collect PD, LGD, EAD and correlation. Compute K = LGD × (WCDR − PD), or use the given K.
  5. 5Convert to RWA: standardized RWA = EAD × weight; IRB RWA = K × 12.5 × EAD.
  6. 6Apply the capital ratio (for example 8%) to get the capital requirement.
  7. 7Interpret: compare approaches, check the output floor, and note that IRB capital covers unexpected, not expected, loss.

Quickest way: Quick RWA and capital check

When to use it: Use when the question gives exposures and weights, or a capital charge, and you only need RWA or capital.

  1. Multiply EAD by risk weight for each exposure and add them to get RWA.
  2. Multiply RWA by 8% (or the stated ratio) for capital.
  3. If given capital K per unit, multiply by 12.5 to convert to a risk weight (K = 0.04 means 50%).
  4. Eliminate answer options that confuse RWA with capital, or that include EL in IRB capital.

Common mistakes in Credit Risk Capital and Basel Framework

  • Reporting RWA when asked for capital, or the reverse.

    Both numbers appear in the same calculation and the last step is easy to skip.

    Fix: Underline what is asked. Capital = RWA × 8% (or the stated ratio).

  • Including expected loss in IRB capital.

    Students remember EL = PD × LGD × EAD and add it in.

    Fix: IRB capital K = LGD × (WCDR − PD). The subtraction of PD removes expected loss.

  • Using the bank's own LGD and EAD under foundation IRB.

    The two IRB variants are blurred together.

    Fix: Foundation: bank supplies PD only. Advanced: bank supplies PD, LGD, EAD and maturity.

  • Forgetting the 12.5 multiplier.

    K looks like a risk weight already.

    Fix: K is a capital ratio on EAD. RWA = K × 12.5 × EAD.

  • Saying IRB always gives lower capital than standardized.

    IRB is marketed as more risk-sensitive.

    Fix: IRB can be higher or lower. The Basel III output floor limits how far IRB RWA can fall below standardized RWA.

Worked examples

Example 1

A bank has a ₹200 crore corporate loan risk-weighted at 100% and a ₹300 crore residential mortgage risk-weighted at 35%. Compute RWA and the minimum capital at 8%.

Show the solution
  1. Corporate RWA = 200 × 100% = ₹200 crore.
  2. Mortgage RWA = 300 × 35% = ₹105 crore.
  3. Total RWA = 200 + 105 = ₹305 crore.
  4. Capital = 305 × 8% = ₹24.4 crore.

Answer: RWA is ₹305 crore and the minimum capital is ₹24.4 crore.

Example 2

Under IRB, a USD 50 million exposure has an IRB capital requirement K of 4.8% of EAD (maturity adjustment already included). Find RWA, the implied average risk weight and the capital at 8%.

Show the solution
  1. RWA = K × 12.5 × EAD = 0.048 × 12.5 × 50 million.
  2. 0.048 × 12.5 = 0.60, so the risk weight is 60%.
  3. RWA = 0.60 × 50 million = USD 30 million.
  4. Capital = 8% × 30 million = USD 2.4 million, which equals K × EAD = 0.048 × 50 million.

Answer: RWA is USD 30 million, the implied risk weight is 60%, and the capital is USD 2.4 million.

Exam tips

  • Read whether the question gives capital or RWA, and which one it wants. Examiners test this switch often.
  • Know exactly which inputs the bank supplies in foundation and advanced IRB.
  • Remember IRB covers unexpected loss at 99.9% confidence; expected loss goes to provisions.
  • For Basel III finalization, link the output floor to limiting the benefit of internal models.
  • If options differ by a factor of 12.5 or 8%, check that step first.

Practice questions from Credit Risk

Credit Risk Capital and Basel Framework in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Credit Risk Capital and Basel Framework: frequently asked questions

What is the difference between standardized and IRB approaches?

The standardized approach uses regulator-set risk weights based on exposure class and external ratings. The IRB approach uses the bank's internal estimates of PD, and in advanced IRB also LGD, EAD and maturity, in a supervisory formula. IRB needs supervisory approval.

How do you calculate credit risk RWA?

For standardized, multiply EAD by the risk weight. For IRB, compute K = LGD × (WCDR − PD), then RWA = K × 12.5 × EAD. Capital is then RWA times the required ratio.

Why is the 12.5 multiplier used?

It is the reciprocal of the 8% minimum capital ratio. Multiplying a capital charge by 12.5 converts it to RWA, so applying 8% brings you back to the capital charge.

What confidence level does the IRB formula use?

It uses 99.9% over a one-year horizon, applied to the systematic factor in the Vasicek single-factor model.