Basel III: Finalising Post-crisis Reforms: formula sheet

Key formulas

Risk-based capital ratio

Capital ratio = Regulatory capital ÷ RWA

Variability in RWA directly changes the ratio. This is the core reason for the reforms.

Output floor rule

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

The 2017 package sets the floor at 72.5% of standardised RWA, calculated at total bank level, not per risk type.

Leverage ratio

Leverage ratio = Tier 1 capital ÷ Exposure measure

Non-risk-based backstop. The minimum is 3%, with a buffer for G-SIBs.

Implied floor binding test

Floor binds if 72.5% × standardised RWA > internal-model RWA

When it binds, the floored figure is used as the denominator.

Credit RWA

RWA = EAD × risk weight

EAD is the exposure net of specific provisions, and for off-balance-sheet items is the nominal amount × CCF.

Off-balance-sheet exposure

EAD = notional × CCF

Examples: unconditionally cancellable commitments 10%; other commitments 40%; transaction-related contingencies 50%; trade letters of credit 20%; direct credit substitutes 100%.

Loan-to-value

LTV = loan amount ÷ property value

For the bucket tables, the upper bound of each band is inclusive, so 80% falls in the 60–80% band.

Rated banks (ECRA)

AAA to AA-: 20%; A+ to A-: 30%; BBB+ to BBB-: 50%; BB+ to B-: 100%; below B-: 150%

Unrated banks use SCRA: Grade A 40%, Grade B 75%, Grade C 150%. Grade A banks meeting stated minimum CET1 and leverage levels can get 30%.

Rated corporates

AAA to AA-: 20%; A+ to A-: 50%; BBB+ to BBB-: 75%; BB+ to BB-: 100%; below BB-: 150%; unrated: 100%

Some jurisdictions allow 65% for unrated investment-grade corporates and 85% for unrated SMEs.

Residential real estate, not materially dependent on property cash flows (whole loan)

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

Jurisdictions may allow loan-splitting instead: the portion up to 55% of property value gets 20%, the rest gets the counterparty's weight.

Residential real estate, materially dependent on property cash flows

LTV ≤ 50%: 30%; 50–60%: 35%; 60–80%: 45%; 80–90%: 60%; 90–100%: 75%; > 100%: 105%

Income-producing property costs more capital than owner-occupied property.

Commercial real estate

Not cash-flow dependent: LTV ≤ 60%: lower of 60% and counterparty weight; LTV > 60%: counterparty weight. Cash-flow dependent: LTV ≤ 60%: 70%; 60–80%: 90%; > 80%: 110%

Land acquisition, development and construction (ADC) is 150%, with a lower weight allowed for some pre-sold residential projects.

Retail

Regulatory retail: 75%; transactors: 45%; other retail: 100%

Regulatory retail must meet orientation, product, granularity and low-value criteria.

A-IRB restriction

Corporate revenue > €500 million, or financial institution → F-IRB only (no A-IRB)

Equities: IRB not permitted; use standardised approach. Retail and corporates with revenue ≤ €500 million can still use A-IRB if approved.

PD floors

Corporate and bank: 0.05%. Retail mortgages: 0.05%. QRRE transactors: 0.05%. QRRE revolvers: 0.10%. Other retail: 0.05%

The corporate floor was previously 0.03%. Floor applies to the PD used in the formula.

LGD floors (unsecured)

Corporate: 25%. Retail mortgages: 5%. QRRE: 50%. Other retail: 30%

A-IRB banks apply these to own LGD estimates. Secured exposures have lower floors by collateral type.

LGD floors (secured, by collateral)

Financial collateral: 0%. Receivables: 10%. Commercial or residential real estate: 10%. Other physical collateral: 15%

Corporate and other retail secured exposures. Mortgages keep the 5% floor.

EAD floor

EAD ≥ drawn amount + 50% × (off-balance-sheet amount × standardised CCF)

Applies to A-IRB own EAD estimates. F-IRB CCFs are aligned with the standardised approach.

Supervisory LGD (F-IRB)

Senior unsecured corporate: 40%. Senior unsecured financial institution: 45%. Subordinated: 75%

Corporate figure was cut from 45% to 40%. Collateral reduces LGD.

Expected loss with floors

EL = max(PD, PD floor) × max(LGD, LGD floor) × max(EAD, EAD floor)

Use for exam arithmetic. The floors bind only when the model value is lower.

Business Indicator

BI = ILDC + SC + FC

Each component is a three-year average.

Interest, leases and dividend component

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

The cap of 2.25% of interest-earning assets limits the interest part.

Services component

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

Takes the larger side of each pair.

Financial component

FC = abs(Net P&L trading book) + abs(Net P&L banking book)

The absolute value of net P&L is taken separately for the trading book and the banking book, so a net gain or a net loss in each book increases BI.

BI buckets and marginal coefficients

Bucket 1: BI ≤ €1bn, 12%. Bucket 2: €1bn < BI ≤ €30bn, 15%. Bucket 3: BI > €30bn, 18%.

Coefficients are marginal: each applies only to the slice of BI inside the bucket.

BI Component

BIC = 12% × min(BI, 1bn) + 15% × [min(BI, 30bn) − 1bn]⁺ + 18% × (BI − 30bn)⁺

(x)⁺ means the larger of x and 0.

Loss Component

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

Losses are net of recoveries and above the loss data threshold. Banks subject to the ILM use 10 years of good-quality data; 5 years is acceptable on first implementation.

Internal Loss Multiplier

ILM = ln( e − 1 + (LC ÷ BIC)^0.8 )

Equals 1 when LC = BIC. Above 1 when LC > BIC; below 1 when LC < BIC. Set to 1 for bucket 1. National supervisors may require ILM = 1. If a bank lacks even 5 years of good-quality data, the supervisor decides and may require a lower threshold or ILM = 1.

Operational risk capital and RWA

Capital = BIC × ILM; RWA = 12.5 × Capital

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

Loss Component (LC)

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

Losses are net of recoveries and above the loss data threshold. The factor 15 is fixed.

Internal Loss Multiplier (ILM)

ILM = ln( e − 1 + (LC ÷ BIC)^0.8 )

If LC = BIC, ILM = 1. If LC > BIC, ILM > 1. If LC < BIC, ILM < 1. Floor at LC = 0 is about 0.54.

Operational risk capital

Capital = BIC × ILM

RWA = capital × 12.5.

BIC marginal coefficients

12% on BI up to €1bn; 15% on BI above €1bn up to €30bn; 18% above €30bn

Coefficients apply to each slice, not to the whole BI.

Loss data threshold

€20,000 standard; €100,000 may be allowed for bucket 2 banks at national discretion

Applies to inclusion of events in the loss data used for the loss component.

Data history required

10 years of data; minimum 5 years may be accepted at first implementation

With less than 5 years of good data, the bank uses BIC only (ILM = 1).

Standalone CVA capital per counterparty (BA-CVA)

SCVA_c = (1 ÷ α) × RW_c × Σ over netting sets (M_NS × EAD_NS × DF_NS)

α = 1.4. RW_c is the supervisory risk weight set by sector and credit quality (investment grade or high yield/unrated). DF_NS = 1 for banks using SA-CCR for EAD. For IMM banks, DF_NS = (1 − e^(−0.05 × M_NS)) ÷ (0.05 × M_NS).

Reduced BA-CVA aggregation

K_reduced = √[(ρ × Σ SCVA_c)² + (1 − ρ²) × Σ SCVA_c²]

ρ = 50%. The first term is the systematic part. The second is the idiosyncratic part. Sums run over all counterparties.

BA-CVA capital charge, reduced version

K_BA-CVA = DS × K_reduced, with DS = 0.65

DS is a supervisory scalar. Risk-weighted assets (RWA) = 12.5 × K.

Full BA-CVA

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

Then K_BA-CVA = DS × K_full. K_hedged reflects eligible hedges: single-name CDS, single-name contingent CDS and index CDS. Hedge recognition is limited and includes a hedge-misalignment penalty.

Small-book election

CVA capital = 100% × CCR capital requirement

Available only if aggregate notional of non-centrally cleared derivatives ≤ €100 billion and the supervisor permits it.

SA-CVA structure

K_SA-CVA = m_CVA × Σ over risk classes (delta and vega capital)

m_CVA is a multiplier set at 1 unless the supervisor raises it. Counterparty credit spread has delta only. Each risk class aggregates by buckets with prescribed risk weights and correlations.

Output floor

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

Applied to total RWA, in aggregate, not risk type by risk type.

Floor add-on

Add-on = max(0 ; 72.5% × RWA standardised − RWA internal models)

The extra RWA the floor creates when it binds.

Leverage ratio

Leverage ratio = Tier 1 capital ÷ Total exposure measure

Minimum 3%. Not risk-weighted.

G-SIB leverage buffer

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

Met with Tier 1 capital; added to the 3% minimum.

Phase-in path

50% → 55% → 60% → 65% → 70% → 72.5%

Steps of 5 percentage points, final step is 2.5 points.

Quick revision

• The finalisation aims to cut unwarranted RWA variability and restore trust in capital ratios.
• The revised standardised approach is more risk-sensitive than the earlier version.
• IRB use is restricted for some exposure classes, and input floors limit model parameters.
• Input floors apply to the PD, LGD and CCF/EAD parameters; they do not cap total RWA. Separately, EAD must be at least the on-balance-sheet exposure amount, which is a distinct measurement requirement and not an input floor.
• The output floor ties internal-model RWA to a share of standardised RWA.
• The revised standardised approach (BIC × ILM) replaces earlier operational risk approaches with one method. ILM is 1 for banks with a Business Indicator up to €1bn, and national authorities may set ILM to 1 for all banks in their jurisdiction, so loss data matters mainly for larger banks. The SMA was the 2016 proposal name.
• Loss data quality and governance support the operational risk standardised approach and are tested for process, not only numbers.
• The CVA framework revises capital for counterparty credit spread risk on derivatives. It removes the internal-model approach (IMA-CVA) and uses the standardised (SA-CVA) and basic (BA-CVA) approaches.
• The leverage ratio is a non-risk-based backstop to risk-weighted capital.
• Read each question for the approach named: standardised credit, IRB, operational risk standardised (BIC and ILM) or CVA.

Common mistakes

• Saying the main goal was to raise capital requirements sharply. Fix: The 2017 package targets RWA credibility and comparability. It was not designed for a significant overall capital increase.
• Thinking the output floor removes internal models. Fix: Internal models stay. The floor only limits how far model RWA can fall below standardised RWA.
• Using the old Basel II numbers, such as a flat 35% for residential mortgages or 100% for BBB corporates. Fix: Anchor on the revised tables: LTV-based mortgage weights and 75% for BBB corporates.
• Placing an LTV of exactly 80% in the 80–90% band. Fix: Bands are upper-bound inclusive. 80% belongs to 60–80%, which is 30% for whole-loan residential not dependent on property cash flows.
• Saying A-IRB is banned for all corporates. Fix: Only corporates with consolidated revenue above €500 million are barred from A-IRB. Smaller corporates can still use it.
• Saying IRB is barred for retail or specialised lending. Fix: Retail stays eligible for A-IRB. Specialised lending uses slotting where PD cannot be estimated. Equities are the class with no IRB at all.
• Applying one coefficient to the whole BI, such as 15% × BI for a €10 billion bank. Fix: Apply 12% to the first €1 billion, then 15% to the rest up to €30 billion, and so on.
• Using BI of a single year. Fix: BI components use a three-year average unless the question says otherwise.
• Using gross losses instead of net losses in the loss component Fix: The SMA uses losses net of recoveries. Subtract recoveries before averaging.
• Forgetting the factor 15 when computing LC Fix: LC = 15 × average annual loss. Always multiply before comparing with BIC.

Exam tips

• Always tie each reform back to RWA variability. Examiners reward that link.
• Memorise 72.5% and that it applies at total level to standardised RWA.
• Expect numerical floor questions: compute both RWAs, take the maximum.
• Watch for distractors claiming a big overall capital increase or a ban on internal models.
• Questions are often scenario-based. First state the exposure class, then the weight. Doing so quickly avoids picking an old Basel II weight.
• Expect LTV questions with numbers near band edges, such as exactly 60%, 80% or 90%. Remember that upper bounds are inclusive.
• Look for the 'old versus revised' contrast: more granular weights, less mechanical reliance on ratings, higher CCF on cancellable commitments, and LTV-based real estate.
• When a question mentions due diligence, the correct answer is usually that the bank must not rely solely on the external rating and must apply a higher weight if warranted.