4.9.6 Advanced Extensions

Basic Prerequisites: 02 · Capital & RWA and Liquidity Risk & Funding.

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1. Intuition & Practical Objective

The risk-based capital ratio is necessary but not sufficient. Basel III bolts three more constraints onto it, each closing a hole the 2008 crisis exposed:

• Liquidity Coverage Ratio (LCR) - a 30-day survival test: enough high-quality liquid assets to cover stressed net cash outflows for a month. Capital says “you can absorb the loss”; the LCR says “you can pay while you absorb it.”
• Net Stable Funding Ratio (NSFR) - a one-year structural funding test: stable funding must cover illiquid assets. It stops a bank from funding long-dated assets with overnight money.
• Leverage ratio - a non-risk-based backstop: Tier 1 over total exposure, ignoring risk weights entirely, so that a bank cannot inflate its risk-based ratio by loading up on zero-weighted assets.
• Output floor - a denominator floor: internal-model RWA may not fall below $72.5\%$ of the standardised-approach RWA, capping the model gap (05).

Together with the risk-based ratio these form four constraints a bank must satisfy simultaneously, and in practice a different one binds for different banks. Knowing which binds is the practitioner’s craft.

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2. Mathematical Ground Truth & Derivations

Liquidity (BCBS 2013, d238; 2014, d295).

$$\boxed{\mathrm{LCR}=\frac{\text{Stock of HQLA}}{\text{Net cash outflows over 30 calendar days}}\ge 100\%}\boxed{\mathrm{NSFR}=\frac{\text{Available stable funding (ASF)}}{\text{Required stable funding (RSF)}}\ge 100\%}$$

HQLA is tiered (Level 1: cash/central-bank reserves/high-grade sovereigns, no haircut; Level 2A ~15%; Level 2B 25–50%), and stressed inflows are capped at $75\%$ of stressed outflows so a bank cannot net its way to a healthy ratio. ASF/RSF weight funding and assets by stability (retail deposits stable; wholesale short-term unstable; loans illiquid; HQLA liquid).

Leverage ratio (BCBS 2010, d189).

$$\boxed{\text{Leverage ratio}=\frac{\text{Tier 1 capital}}{\text{Total exposure measure}}\ge 3\%}$$

This is the ratio that ignores risk weights. It exists because a bank can hold a huge book of low/zero-weighted assets (sovereigns, cash) with a fat risk-based ratio and yet be terrifyingly levered.

Output floor (BCBS 2017, d424).

$$\boxed{{\mathrm{RWA}}_{\text{used}}=\max ({\mathrm{RWA}}_{\text{internal}},72.5\%\times {\mathrm{RWA}}_{\text{SA}})}$$

phased in from $50\%$ (2022) to $72.5\%$ (1 January 2027). It is the direct legislative countermeasure to the model gap: however clever the internal model, at least $72.5\%$ of the standardised RWA counts.

Why four, not one. Risk-based capital answers “is the book risky?”; leverage answers “is the book big?”; LCR answers “can you survive a month of stress?”; NSFR answers “is your funding structurally sound?” Each is blind to what the others see.

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3. Computational Implementation - the four constraints + the floor

Standard library. Computes all four constraints and shows the floor biting.

What the numbers say. (i) All four constraints are met in the base case, but each has a different bank for which it binds first: the sovereign-heavy bank reports a 40% risk-based ratio and still fails leverage at 2.00% - the exact hole the backstop fills. (ii) The output floor cuts a bank’s apparent CET1 ratio from 12.00% to 10.34% by adding RWA, not by removing capital: $1.7$ points of reported strength that existed only because of the model. (iii) The binding constraint is an empirical fact about each bank, not a fixed rule - the practitioner’s job is to know which.

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4. Failure Modes & First-Principles Breakdowns

1. Optimising one ratio, failing another. A desk maximising return on risk-weighted assets will pile into low-$rw$, high-exposure assets (sovereign carry, repo) and blow the leverage ratio and the LCR. The constraints must be optimised jointly.
2. LCR window-dressing. The LCR is a point-in-time ratio; banks can flatter it around reporting dates by shortening funding or hoarding HQLA, then re-lever. Monitoring tools (maturity-mismatch metrics) exist precisely because a single ratio can be gamed.
3. NSFR penalises the wrong business at the margin. Very stable long-term assets (e.g. high-quality mortgages) still attract RSF, so the NSFR can push banks away from durable lending - a real design tension between stability and the supply of credit.
4. The output floor is a blunt instrument. It reduces RWA comparability problems but also penalises good internal models (that correctly measure low risk) alongside bad ones, and it bites hardest on low-risk, model-heavy books (e.g. mortgages). It is a backstop, not a risk measure.
5. Four constraints ≠ one coherent objective. They can conflict (liquidity hoarding vs lending; leverage vs low-risk assets). Regulatory “capital” is a multi-constraint feasibility problem, not a single number - the deepest practical lesson of the post-crisis framework.

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5. References

• BCBS - Basel III: The Liquidity Coverage Ratio and Liquidity Risk Monitoring Tools (January 2013, BIS d238). $\mathrm{LCR}=\mathrm{HQLA}/\text{30-day net outflows}\ge 100\%$, HQLA tiers, the inflow cap. Read from the corpus PDF.
• BCBS - Basel III: The Net Stable Funding Ratio (October 2014, BIS d295). $\mathrm{NSFR}=\mathrm{ASF}/\mathrm{RSF}\ge 100\%$, one-year horizon, ASF/RSF weights. Read from the corpus PDF.
• BCBS - Basel III: A Global Regulatory Framework (2010, d189). The $3\%$ Tier 1 leverage ratio (parallel-run specification) and its rationale. Read from the corpus PDF.
• BCBS - Basel III: Finalising Post-Crisis Reforms (2017, d424). The revised leverage exposure measure and the output floor with its $50\%\to 72.5\%$ phase-in. Read from the corpus PDF.
• Brunnermeier & Pedersen - Market Liquidity and Funding Liquidity, RFS 22(6):2201–2238 (2
• Hull, John C. - Risk Management and Financial Institutions (5

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6. Connected Graph Bridges

• Back: 05 · Failure Modes · Index Hub
• In-folder: 01 · From Zero · 02 · Capital & RWA · 03 · Market Risk & FRTB · 04 · Credit & Operational Risk
• Sibling: Liquidity Risk & Funding · Counterparty Risk & xVA · Stress Testing & Scenario Analysis
• Forward: Portfolio Risk Constraints & Mean–Variance (capital as an optimisation constraint)