FRM Exam Part II · Capital Regulation Before the Global Financial Crisis

Basel II Credit Risk Approaches: Standardized and IRB

Updated 11 October 2026 · Fact-checked

Basel II sets credit risk capital as 8% of risk-weighted assets. The standardized approach assigns risk weights from external ratings. The IRB approaches use the bank's own models. Foundation IRB estimates only PD, while advanced IRB also estimates LGD, EAD and maturity. IRB capital covers unexpected loss at a 99.9% one-year confidence level.

Understand Basel II Credit Risk Approaches: Standardized and IRB

Basel II asks a bank to hold capital equal to at least 8% of risk-weighted assets (RWA) for credit risk. The only real question is how to measure RWA. Basel II gives banks three routes: the standardized approach, the foundation IRB approach and the advanced IRB approach.

In the standardized approach, each exposure gets a fixed risk weight set by the regulator. The weight depends on the type of borrower (sovereign, bank, corporate, retail, residential mortgage) and, for most borrowers, on an external credit rating. A highly rated corporate gets 20%. An unrated corporate gets 100%. A weak, low-rated corporate gets 150%. Simple, but it is not very risk-sensitive and depends on rating agencies.

The internal ratings-based (IRB) approaches let a bank, with supervisory approval, use its own risk estimates. The four inputs are PD (probability of default over one year), LGD (loss given default), EAD (exposure at default) and M (effective maturity). These go into a supervisory formula that gives the capital requirement K per unit of exposure.

The difference between the two IRB approaches is who supplies the inputs. In foundation IRB, the bank estimates PD. The supervisor sets LGD (45% for senior unsecured claims, 75% for subordinated claims), EAD and a fixed maturity of 2.5 years. In advanced IRB, the bank estimates PD, LGD, EAD and maturity, subject to supervisory standards.

The IRB formula comes from the Vasicek single-factor model. It measures the loss in a bad year (99.9% confidence, one-year horizon) minus the expected loss. So IRB capital covers unexpected loss only. Expected loss (PD × LGD × EAD) is meant to be covered by provisions and pricing. The asset correlation ρ falls as PD rises, from 24% at very low PD to 12% at very high PD, for corporate exposures.

Key formulas to remember

Minimum capital: Capital = 8% × RWA; Applies to total credit risk RWA under all three approaches.
Standardized RWA: RWA = Σ (Exposure × Risk weight); Corporate: AAA to AA- 20%; A+ to A- 50%; BBB+ to BB- 100%; below BB- 150%; unrated 100%.
Other standardized weights: Sovereign: AAA to AA- 0%, A+ to A- 20%, BBB+ to BBB- 50%, BB+ to B- 100%, below B- 150%, unrated 100%. Retail 75%. Residential mortgage 35%.; Banks have two options (based on sovereign rating or on the bank's own rating). Check which one the question uses.
Expected loss: EL = PD × LGD × EAD; Not covered by IRB capital K. It is handled through provisions.
IRB capital per unit of EAD (corporate): K = [LGD × N((N⁻¹(PD) + √ρ × N⁻¹(0.999)) ÷ √(1 − ρ)) − PD × LGD] × (1 + (M − 2.5) × b) ÷ (1 − 1.5 × b); N is the standard normal CDF, N⁻¹ its inverse. The first bracket is the 99.9% worst-case loss minus expected loss.
Asset correlation: ρ = 0.12 × (1 − e^(−50×PD)) ÷ (1 − e^(−50)) + 0.24 × [1 − (1 − e^(−50×PD)) ÷ (1 − e^(−50))]; Ranges between 12% (high PD) and 24% (low PD) for corporates.
Maturity adjustment factor b: b = (0.11852 − 0.05478 × ln(PD))²; Used in the maturity term. M is floored at 1 year and capped at 5 years.
IRB RWA: RWA = K × 12.5 × EAD; The 12.5 is 1 ÷ 8%. Capital = K × EAD.
Foundation IRB supervisory inputs: LGD = 45% (senior unsecured), 75% (subordinated); M = 2.5 years; Bank supplies PD only. Advanced IRB: bank supplies PD, LGD, EAD and M.

How to solve Basel II Credit Risk Approaches: Standardized and IRB questions

Use the same short routine for any Basel II credit risk question. It keeps you from mixing up approaches.

1Identify the approach: standardized, foundation IRB or advanced IRB. Look for words like external rating, own estimates, supervisory LGD.
2Identify the asset class: sovereign, bank, corporate or retail. The risk-weight table depends on it.
3For standardized, match each exposure to its rating bucket and read off the risk weight. Treat unrated corporates as 100%.
4For IRB, list which inputs the bank supplies (PD, LGD, EAD, M) and which the supervisor fixes. Foundation: only PD is the bank's.
5Compute RWA: standardized is exposure × weight. IRB is K × 12.5 × EAD. Add up across exposures.
6Convert to capital: multiply RWA by 8%. If the question gives K, capital is simply K × EAD.
7Check the interpretation: IRB capital covers unexpected loss at 99.9% over one year, and expected loss is separate.

Quickest way: Fast route: rating bucket, then RWA × 8%

When to use it: Use this for numerical standardized questions and for IRB questions where K or the risk weight is given. Under time pressure you will almost never need to compute the full IRB formula.

Standardized: write each exposure with its weight, multiply, add, then take 8%.
IRB with K given: capital = K × EAD, RWA = capital × 12.5.
For foundation versus advanced questions, ask who supplies LGD, EAD and M. If the supervisor does, it is foundation.
For direction questions, remember: higher PD, LGD or EAD raises capital. Longer maturity raises capital. Higher PD lowers asset correlation, which partly offsets.

Common mistakes in Basel II Credit Risk Approaches: Standardized and IRB

Forgetting the 12.5 multiplier, or using it the wrong way round.
Students remember K as a capital number and then treat it as a risk weight.
Fix: K is capital per unit of EAD. RWA = K × 12.5 × EAD. Capital = 8% × RWA gives back K × EAD.
Applying the 45% LGD to every exposure under foundation IRB.
45% is the figure most students remember.
Fix: 45% is for senior unsecured claims. Subordinated claims get 75%. Collateral can lower it under the supervisory rules.
Using the corporate rating table for sovereigns or banks.
The tables look alike, but the weights differ. A AAA to AA- sovereign gets 0%, not 20%.
Fix: Identify the borrower type first, then read the table for that type.
Saying IRB capital covers both expected and unexpected loss.
Students link capital to total credit loss.
Fix: The IRB capital function subtracts PD × LGD. It is unexpected loss only. Expected loss goes through provisions.
Treating maturity as a bank input in foundation IRB.
Maturity is easy to assume as always a bank estimate.
Fix: Foundation uses a fixed 2.5 years. In advanced IRB the bank estimates M, floored at 1 year and capped at 5 years.
Assuming a BBB- corporate gets 50%.
Mixing up the sovereign and corporate tables.
Fix: For corporates, BBB+ to BB- is 100%. Only A+ to A- is 50%.

Worked examples

Example 1

A bank uses the Basel II standardized approach. Its corporate exposures are: USD 10 million rated AA, USD 8 million rated A, USD 5 million unrated and USD 4 million rated B+. Find the RWA and the minimum capital.

Show the solution

AA corporate falls in AAA to AA-: weight 20%. RWA = 10 × 0.20 = 2.0 million.
A corporate falls in A+ to A-: weight 50%. RWA = 8 × 0.50 = 4.0 million.
Unrated corporate: weight 100%. RWA = 5 × 1.00 = 5.0 million.
B+ is below BB-: weight 150%. RWA = 4 × 1.50 = 6.0 million.
Total RWA = 2.0 + 4.0 + 5.0 + 6.0 = 17.0 million.
Minimum capital = 8% × 17.0 = 1.36 million.

Answer: RWA is USD 17.0 million and minimum capital is USD 1.36 million.

Example 2

Under advanced IRB, a corporate loan has EAD of USD 20 million, PD of 1% and effective maturity of 4 years. Before the maturity adjustment, the capital requirement is 3.0% of EAD. Using the supervisory maturity adjustment, find the capital and RWA.

Show the solution

Compute b = (0.11852 − 0.05478 × ln(0.01))². ln(0.01) = −4.60517, so b = (0.11852 + 0.25227)² = (0.37079)² ≈ 0.13748.
Maturity adjustment = (1 + (4 − 2.5) × b) ÷ (1 − 1.5 × b) = (1 + 0.20622) ÷ (1 − 0.20622) = 1.20622 ÷ 0.79378 ≈ 1.52.
Adjusted K = 3.0% × 1.52 = 4.56% of EAD.
Capital = 4.56% × 20 million = USD 0.912 million.
RWA = K × 12.5 × EAD = 0.0456 × 12.5 × 20 = USD 11.4 million.
Check: 8% × 11.4 = 0.912 million, which matches.

Answer: Adjusted K is about 4.56% of EAD, so capital is about USD 0.912 million and RWA is about USD 11.4 million.

Exam tips

Know the foundation versus advanced split cold: who supplies PD, LGD, EAD and M. This is the most common conceptual question.
Memorize the corporate and sovereign weights separately, plus 75% retail and 35% residential mortgage.
Expect interpretation questions: IRB uses a 99.9% one-year confidence level and the capital charge excludes expected loss.
For direction questions, reason before calculating. Higher PD, LGD or EAD, or longer maturity, raises capital.
Questions usually give K or the weights. Do not waste time deriving N⁻¹ values unless they are supplied.

Practice questions from Capital Regulation Before the Global Financial Crisis

Basel II Credit Risk Approaches: Standardized and IRB: frequently asked questions

What is the difference between foundation and advanced IRB?

In foundation IRB, the bank estimates PD only. The supervisor sets LGD, EAD and maturity. In advanced IRB, the bank estimates PD, LGD, EAD and maturity under supervisory standards, so capital is more sensitive to the bank's own data.

Why is the IRB capital charge multiplied by 12.5?

Minimum capital is 8% of RWA, so RWA equals capital divided by 8%, which is capital × 12.5. The IRB formula gives capital K per unit of exposure, so RWA = K × 12.5 × EAD.

Does IRB capital cover expected loss?

No. The formula takes the loss at the 99.9% level and subtracts PD × LGD. So it covers unexpected loss. Expected loss is covered by provisions and loan pricing.

What risk weight does an unrated corporate get under the Basel II standardized approach?

100%. Corporates rated below BB- get 150%, so an unrated borrower is not automatically treated as the riskiest. Weights for sovereigns and banks follow different tables.