4.9 Basel & Regulation

Basic Prerequisites: VaR & Expected Shortfall (the risk measures whose capital charges this folder turns into rules) and Credit Risk & the Merton Model (the default machinery behind the credit-risk formulas). (these are the folder-level prerequisites for pages 02–06; page 01 states its own, smaller, entry requirements)

1. Intuition & Practical Objective

Regulation is the other half of quantitative risk: not “how do we measure the tail?” but “how much loss-absorbing capital must a bank hold against it, and who checks?” The Basel accords are the international answer, and they are the reason a bank’s risk numbers are not academic - a firm that mis-measures a tail does not merely report a wrong number, it either hoards too much capital (losing to competitors) or too little (failing the next crisis).

The architecture is three-legged:

• Pillar 1 - minimum capital. A ratio of capital to risk-weighted assets (RWA), floored at 8% of RWA (Basel III adds a 4.5% CET1 minimum and a 6% Tier 1 minimum plus buffers). RWA converts every exposure into an equivalent quantum of risk: credit, market, and operational.
• Pillar 2 - supervisory review (ICAAP/SREP). The supervisor judges risks the formula missed (concentration, model risk, interest-rate risk in the banking book).
• Pillar 3 - disclosure. Market discipline through public reporting.

This folder is a hub: it (a) gives the fast capital-ratio and RWA lookup below (job #1 of the sub-topic), and (b) routes you through six sub-pages that walk from raw intuition about why banks are regulated, through capital and RWA arithmetic, the market-risk FRTB regime (SA vs IMA), credit and operational risk, the failure modes, and the liquidity/leverage/output-floor extensions.

The one-sentence essence. “Capital is a buffer against unexpected loss, and the entire Basel edifice is one long argument about how to convert a portfolio of heterogeneous risks into a single number - RWA - that a ratio can divide into.”

2. Mathematical Ground Truth & Derivations

Quick-Reference Lookup (job #1). Every ratio below is transcribed from the primary BCBS documents (Fisher-verified against the corpus PDFs; the numbers in the check column were re-executed and reproduced exactly - see §3).

Notation: $E_i$ = exposure of asset $i$, $r{w}_i$ = its regulatory risk weight, $\mathrm{RWA}={\sum }_i{E}_{i}r{w}_i$; $CET1,T1,T2$ = Common Equity Tier 1, Tier 1, Tier 2 capital; $T1=CET1+AT1$; $k$ = multiplier.

Buffer stack above the 4.5% CET1 minimum (Basel III): capital conservation buffer $+2.5\%$; countercyclical buffer $+0$–$2.5\%$; G-SIB surcharge $+1$–$3.5\%$. The MDA (maximum distributable amount) restricts dividends and buybacks as a bank eats into these buffers - the teeth of the regime.

The two regulators you must not conflate. The risk-based ratio (capital/RWA) answers “how risky is the book?”; the leverage ratio (capital/exposure) answers “how big is the book?” They fail in opposite directions: RWA can be gamed down, exposure cannot; leverage ignores risk entirely. Basel III applies both because each catches what the other misses (§05).

3. Computational Implementation - the ratio engine

This runs on the standard library only and reproduces every verified number above. It builds a small bank balance sheet, computes credit/market/operational RWA, then every headline ratio.

4. Failure Modes & First-Principles Breakdowns

Hub signposts - the folder’s failure-mode analysis lives in 05 · Failure Modes & Practice. In one line each:

1. Regulatory arbitrage. Because capital scales with risk weight, not risk, a bank can raise its ratio without reducing risk by shifting the same economic exposure into a lower-weighted wrapper (securitisation, guaranteed structures). Risk weights are a model of risk, and models can be gamed (§05).
2. Procyclicality. Risk weights are calibrated to ratings and volatility, both of which are lower in booms and higher in busts - so required capital falls exactly when the economy is fragile and rises exactly when banks cannot raise it. The output floor and buffers are the attempted antidotes (§05, §06).
3. Model approval & measurement error. The internal-models approach (IMA) and IRB use the bank’s own parameters. Supervisory approval is a gate, but a mis-calibrated PD or an ES model that passes backtesting yet misses a stressed regime turns capital into a number the bank controls against itself (§03, §05).

5. References

• BCBS - Minimum Capital Requirements for Market Risk (January 2019, BIS d457; the FRTB). Replaces 99% VaR with 97.5% Expected Shortfall, splits into a sensitivities-based standardised approach (SA) and an internal-models approach (IMA). The single most important current market-risk regulation; read in full from the corpus PDF.
• BCBS - Basel III: Finalising Post-Crisis Reforms (December 2017, BIS d424). The “endgame”: revised credit/operational/CVA capital, the leverage ratio, and the output floor ($72.5\%$ from 2027). Read from the corpus PDF.
• BCBS - Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems (December 2010, BIS d189). Defines the CET1/Tier 1/total minima, the capital conservation buffer, and the 3% leverage ratio test. Read from the corpus PDF.
• BCBS - Amendment to the Capital Accord to Incorporate Market Risks (1996, BIS). Origin of the internal-models (VaR) approach: 99%/10-day VaR, multiplier $\ge 3$. Read from the corpus PDF.
• BCBS - Basel II: International Convergence of Capital Measurement and Capital Standards (2
• Hull, John C. - Risk Management and Financial Institutions (5th ed., 2018, Wiley). Ch on Basel I/II/III, Solvency II, and post-crisis reform
• Hull, John C. - Options, Futures, and Other Derivatives (11th ed.)

6. Connected Graph Bridges

• Foundational base: VaR & Expected Shortfall · Credit Risk & the Merton Model
• Sub-pages (in-folder): 01 From Zero · 02 Capital & RWA · 03 Market Risk & FRTB · 04 Credit & Operational Risk · 05 Failure Modes · 06 Advanced Extensions
• Sibling topics: Counterparty Risk & xVA (the CVA capital charge) · Liquidity Risk & Funding (source of the LCR/NSFR) · Stress Testing & Scenario Analysis (Pillar 2)
• Forward: Portfolio Risk Constraints & Mean–Variance (capital as a constraint)

Beginner: start at 01 · Practitioner: start at 05