High-level Summary of Basel III Reforms: formula sheet

Key formulas

Risk-based capital ratio

Capital ratio = Regulatory capital ÷ Risk-weighted assets

The finalisation reforms change the denominator, not the definition of capital.

Leverage ratio

Leverage ratio = Tier 1 capital ÷ Total exposure measure

Non-risk-based backstop, which does not use RWAs.

Output floor

Total RWA = max(RWA from internal models, floor % × RWA from standardised approaches)

The floor is 72.5% under the finalised Basel III framework. It applies to total RWAs, not each risk type separately.

Risk-weighted assets

RWA = Exposure (after CCF and credit risk mitigation) × Risk weight

Minimum capital = capital ratio × RWA. For example, 8% of RWA is the total capital minimum before buffers.

Loan-to-value ratio

LTV = Loan amount ÷ Property value

Property value must be prudently assessed and not raised except for modifications that improve the property. Higher LTV gives a higher risk weight.

Whole-loan residential weights (not materially dependent on property cash flows)

LTV ≤ 50%: 20%; 50–60%: 25%; 60–80%: 30%; 80–90%: 40%; 90–100%: 50%; > 100%: 70%

Whole-loan approach applies the weight to the entire loan. Weights are for general residential exposures. Check your reading for the variants.

Other key corporate and retail weights

Unrated corporate: 100%; unrated corporate SME: 85%; regulatory retail: 75%; ADC: 150%

Rated corporates use rating-based weights, such as 20% for AAA to AA-, 50% for A, 75% for BBB, 100% for BB, and 150% below BB-.

Due diligence rule

Risk weight after due diligence ≥ risk weight from external rating

Due diligence can only raise the weight, never lower it.

Output floor (aggregate)

Floored RWA = max[ RWA(internal models) ; 72.5% × RWA(standardised approaches) ]

Applied to total RWA across credit, market and operational risk, not exposure by exposure.

Maximum capital benefit from models

Maximum reduction = 1 − 72.5% = 27.5% of standardised RWA

Models can never cut total RWA below 72.5% of the standardised total.

Impact of the floor

Add-on RWA = max[ 0 ; 72.5% × Standardised RWA − Internal-model RWA ]

The floor binds only when the add-on is positive.

Capital ratio after floor

CET1 ratio = CET1 capital ÷ Floored RWA

Use floored RWA as the denominator when the floor binds.

Input floor reminder

PD floor = 0.05% for corporate and bank exposures

Input floors are minimums on PD, LGD and EAD inputs. Floored inputs raise RWA from the model.

Business Indicator (BI)

BI = ILDC + SC + FC (each a three-year average)

BI is measured in euros in the Basel text. It is an average of the last three years, not a single year.

Interest, leases and dividend component

ILDC = min[ |Interest income − Interest expense| , 2.25% × Interest-earning assets ] + Dividend income

The 2.25% cap limits the net interest part. Dividend income is added after the cap.

Services component

SC = max(Other operating income, Other operating expense) + max(Fee income, Fee expense)

Take the larger of each pair. Income and expense do not net off.

Financial component

FC = |Net P&L trading book| + |Net P&L banking book|

Use absolute values. A trading loss still adds to BI.

BIC, bucket 1

BI ≤ €1bn: BIC = 12% × BI

ILM is set to 1 for banks in this bucket.

BIC, bucket 2

€1bn < BI ≤ €30bn: BIC = €120m + 15% × (BI − €1bn)

The €120m is 12% of the first €1bn. Marginal rates apply only to the slice above each threshold.

BIC, bucket 3

BI > €30bn: BIC = €4,470m + 18% × (BI − €30bn)

€4,470m = €120m + 15% × €29bn.

Loss Component

LC = 15 × average annual operational losses over the previous 10 years

Losses are those above the data thresholds the bank applies.

Internal Loss Multiplier

ILM = ln[ e − 1 + (LC ÷ BIC)^0.8 ]

e ≈ 2.71828, so e − 1 ≈ 1.71828. If LC = BIC, ILM = 1.

Operational risk capital and RWA

Capital = BIC × ILM; RWA = 12.5 × Capital

The 12.5 is the reciprocal of the 8% minimum capital ratio.

CVA (concept)

CVA ≈ LGD × Σ EE(tᵢ) × PD(tᵢ₋₁, tᵢ) × discount factor

Unilateral CVA is the discounted expected loss from counterparty default. Higher exposure, spread or LGD raises it.

BA-CVA reduced version

K_reduced = √[(ρ × Σ SCVA_c)² + (1 − ρ²) × Σ SCVA_c²], with ρ = 50%; SCVA_c = (1/α) × RW_c × Σ_NS (M_NS × EAD_NS × DF_NS), with α = 1.4

SCVA_c is the stand-alone CVA of counterparty c. The counterparty risk weight RW_c sits outside the sum. The sum runs over the netting sets NS of that counterparty, using the effective maturity M_NS, the exposure EAD_NS and the supervisory discount factor DF_NS for each. The 1/α scaling (α = 1.4) is already inside SCVA_c. Do not confuse DF with the 0.65 scalar, which is applied later. ρ = 50% is the supervisory correlation of systematic parts.

BA-CVA with hedges

K_full = β × K_reduced + (1 − β) × K_hedged, with β = 0.25

Hedging recognition is limited. Eligible hedges are single-name CDS, single-name contingent CDS and index CDS used to hedge counterparty credit spread risk. K_hedged also includes an indirect hedge component and a hedge-misalignment component.

BA-CVA capital charge in the capital stack

Capital requirement = DS_BA-CVA × K, with DS_BA-CVA = 0.65

The discount scalar of 0.65 applies to the BA-CVA charge. It is separate from the supervisory discount factor DF inside SCVA.

SA-CVA structure

Charge = Delta + Vega risk across risk classes (IR, FX, counterparty credit spread, reference credit spread, equity, commodity), scaled by the CVA multiplier m_CVA = 1 by default

No default risk charge or curvature charge in SA-CVA. The charge is scaled by the CVA multiplier m_CVA, which is 1 by default; supervisors may require a higher value. It is aggregated like the FRTB sensitivities-based method.

Simplified option

CVA capital = 100% × counterparty credit risk capital

A bank may choose this option if its aggregate notional of non-centrally cleared derivatives is ≤ €100 billion. The supervisor keeps discretion to require a CVA calculation instead.

Basel III leverage ratio

Leverage ratio = Tier 1 capital ÷ Total exposure measure

No risk weights. Minimum is 3%.

G-SIB leverage ratio buffer

Leverage buffer = 50% × G-SIB higher-loss-absorbency (HLA) risk-based buffer

Met with Tier 1 capital. Applies only to G-SIBs.

G-SIB minimum leverage requirement

Requirement = 3% + 50% × HLA buffer

Example: HLA of 2.5% gives 3% + 1.25% = 4.25%.

Exposure measure components

Exposure = On-balance-sheet + Derivatives + SFT + Off-balance-sheet (after CCFs)

Off-balance-sheet items use CCFs, with a 10% floor for unconditionally cancellable commitments.

Risk-based ratio (for contrast)

Capital ratio = Capital ÷ Risk-weighted assets

Sensitive to risk weights. The leverage ratio is not.

Output floor test

RWA = max(RWA under internal models; floor % × RWA under standardised approaches)

Applied to total RWA, not to each risk type separately.

Output floor phase-in schedule

2023: 50% | 2024: 55% | 2025: 60% | 2026: 65% | 2027: 70% | 2028: 72.5%

Rises by 5 percentage points a year, then a final 2.5 points in 2028.

Key dates (revised timetable)

Finalised standards: 1 January 2023 | Output floor fully phased in: 1 January 2028

Both were deferred one year in March 2020 (from 2022 and 2027).

Transitional cap on floor impact

Increase in RWA from the floor ≤ 25% × RWA before the floor

Optional supervisory cap during the phase-in years (2023-2027). It falls away when the floor reaches 72.5% on 1 January 2028.

Quick revision

• The 2017 reforms aim to cut RWA variability and restore credibility in internal models.
• Output floor: total RWA must be at least 72.5% of RWA computed using the standardised approaches.
• The 2017 package began the output floor phase-in at 50% in 2022 and reached 72.5% in 2027. In 2020 the Committee deferred implementation by one year to 1 January 2023, with the 72.5% floor fully applying from 1 January 2028.
• The revised standardised approach for credit risk is more risk-sensitive and reduces mechanical reliance on external ratings.
• Real estate exposures in the standardised approach are risk-weighted by loan-to-value ratio.
• IRB: advanced IRB is no longer allowed for large corporates (consolidated revenues above €500 million) and for banks and other financial institutions, and the equity IRB approach is removed.
• IRB input floors limit how low model estimates can go. For example, the PD floor is 0.05% for corporate and bank exposures, with different floors for other exposure classes.
• The final framework is formally the revised operational risk standardised approach, commonly called the SMA. It replaces the basic indicator, standardised and advanced measurement approaches for operational risk.
• SMA capital = Business Indicator Component × Internal Loss Multiplier; marginal coefficients are 12%, 15% and 18% by BI band. For banks in the lowest bucket (BI up to €1 billion), the ILM is set to 1, so capital equals the BIC.
• Business Indicator bands: up to €1 billion, €1 billion to €30 billion, and above €30 billion.
• The revised CVA framework removes the internal model approach and uses SA-CVA or BA-CVA.
• The leverage ratio (Tier 1 capital ÷ exposure measure) must be at least 3%; the G-SIB leverage buffer is 50% of the G-SIB risk-weighted buffer.

Common mistakes

• Saying the finalisation reforms raised the definition or quality of capital. Fix: Remember the split: first package built capital, buffers, leverage and liquidity; the finalisation fixes RWA measurement.
• Claiming internal models are eliminated. Fix: Internal models remain for many exposures but face restrictions, input floors and the output floor.
• Assuming due diligence can lower a risk weight below the rating-based weight. Fix: Remember it is a one-way override. It can only increase the weight.
• Saying the revised approach removes external ratings entirely. Fix: Ratings remain in use where permitted. The change is that ratings are not used mechanically and non-rated alternatives exist.
• Applying the 72.5% floor to each exposure separately. Fix: The output floor applies to total RWA in aggregate. Compare two totals.
• Calculating the floor as 27.5% of standardised RWA instead of 72.5%. Fix: The floor level is 72.5%. The 27.5% is only the maximum benefit.
• Applying a single rate to the whole BI, for example 15% × BI for a €5bn bank. Fix: Apply 12% to the first €1bn, 15% to the next slice up to €30bn, and 18% above that. Use the €120m and €4,470m anchors.
• Netting income and expense in the services component, or using the net figure instead of the larger one. Fix: Take max(other operating income, other operating expense) plus max(fee income, fee expense). No netting.
• Saying CVA capital covers losses from counterparty default. Fix: Remember default losses sit in the counterparty credit risk charge. CVA capital covers mark-to-market losses from spread and exposure changes.
• Thinking the internal model approach is still available to banks with approval. Fix: The revised framework removed it. Choose between BA-CVA and SA-CVA.

Exam tips

• Know the two stated goals: credibility of RWAs and comparability of ratios.
• Be able to list the key elements: revised standardised credit approach, revised IRB, new operational risk approach, revised CVA, output floor and leverage ratio changes.
• Expect output floor calculations; always compare against the standardised total.
• Watch for absolute words like 'eliminates' or 'replaces'; they usually signal a wrong option.
• Memorise the anchor weights: unrated corporate 100%, SME 85%, retail 75%, ADC 150%.
• When the stem mentions due diligence, the answer is a weight at least as high as the rating-based one.
• In real estate questions, compute LTV first and check whether repayment depends on property cash flows.
• Link SA-CR to the output floor: internal model RWA is floored against standardised RWA, so SA-CR matters beyond standardised banks.