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4.9.1 Basel & Regulation from Zero

Basic Prerequisites: VaR & Expected Shortfall (what “risk” means before it becomes a rule).

1. Intuition & Practical Objective

This page builds the why of bank regulation with no prior regulatory knowledge needed. The objective is one idea: a bank is a leveraged, systemically important, partly-subsidised institution, and “capital” is the loss-absorbing buffer that makes its failure (a) less likely and (b) survivable without a taxpayer bailout.

Start with the dumbest question: why can’t a bank just take any risk it likes with depositors’ money? Because four things break the ordinary discipline of the market:

  1. Leverage. A bank funds itself mostly with debt (deposits, wholesale borrowing) and only a sliver of equity. At an 8% capital ratio a bank holds roughly 12.5 dollars of assets per dollar of equity - so a 1% loss on assets is a ~12.5% hit to equity. Leverage magnifies both return and ruin.
  2. Deposit insurance and the lender of last resort. Once deposits are insured and the central bank stands ready to lend, depositors stop policing the bank’s risk - and the bank gains an incentive to take more risk, since the upside is private and the downside is social. This is moral hazard.
  3. Contagion / externalities. A bank’s failure is not a private event: it freezes interbank funding and payment systems, hurting solvent bystanders. The private cost of failure is far below the social cost.
  4. Opacity. Outsiders cannot easily see how risky a bank’s book is, so market discipline is weak and slow.

Regulation is the response: force the bank’s owners to hold a minimum equity cushion so that losses fall on them first, and standardise how much cushion each type of risk demands. That is capital regulation, and its skeleton is one number - the ratio of capital to risk-weighted assets.

Three “aha”s:

  1. Capital ≠ cash. In regulation, “capital” means equity and equity-like funding (CET1), not the vault. It is the part of the funding that absorbs losses without triggering default, because it ranks last in a liquidation.
  2. Risk weighting is the whole game. A dollar of cash and a dollar of unrated corporate loan are not equally risky; the framework scales each by a risk weight before summing. The dispute over how to weight is where most of Basel’s complexity lives.
  3. A ratio is a shock absorber, and the arithmetic is shockingly blunt. If a bank has an capital ratio against fully-weighted assets, a loss of of those assets wipes it out. An 8% ratio buys an 8% loss budget - thin, which is why the post-2008 reforms added buffers on top.

2. Mathematical Ground Truth & Derivations

The buffer identity. Let be assets, equity, and suppose for the moment all assets carry weight 100%, so . The capital ratio is

A proportional loss of (dollars) on the assets leaves equity , hence

Setting gives the maximum absorbable loss - i.e. the capital ratio is the loss budget (when risk weights are 100%):

More generally, inserting risk weights decouples the two sides: the ratio is but the loss falls on , so a lower average risk weight raises the ratio without changing or - the seed of regulatory arbitrage (05 · Failure Modes).

The three pillars (Basel II onward).

  • Pillar 1: minimum capital for credit + market + operational risk.
  • Pillar 2: supervisory review (ICAAP/SREP) for risks Pillar 1 misses.
  • Pillar 3: public disclosure to restore market discipline.

The history in one line each. Basel I (1988): a crude risk-weight grid, total capital. Basel II (2004): three pillars, and internal models (IRB, AMA) allowed for credit and operational risk. Basel III (2010–2017): after the crisis, higher and better-quality capital (CET1 minima, buffers), a leverage backstop, liquidity ratios (LCR/NSFR), and the output floor that limits how far internal models can drive RWA down.

3. Computational Implementation - the shock absorber in numbers

The single most convincing way to see why capital matters: take a bank, hit it with losses, watch the ratio. Stdlib only.

Read the table. At an 8% ratio the bank survives a 5% asset loss but is wiped out by an 8% loss - and a 12% loss leaves equity negative, meaning creditors and the deposit insurer take the hit. The entire reform agenda (higher CET1 minima, buffers, the leverage backstop) exists because 8% was too thin when losses came in correlated waves in 2008.

4. Failure Modes & First-Principles Breakdowns

  1. The “capital = money in the vault” trap. Regulatory capital is funding structure, not liquidity. A bank can hold plenty of cash and still be under-capitalised; conversely “well-capitalised” says nothing about whether it can meet a run (that is the LCR’s job, §06).
  2. Leverage makes small errors fatal. Because , the same percentage asset loss produces a –times larger equity hit. Risk controls calibrated on asset returns systematically understate the equity (solvency) impact.
  3. Moral hazard is structural, not a behavioural quirk. Deposit insurance and LOLR remove depositor discipline; capital rules are the substitute discipline, which is why they must bind even when a bank would prefer them not to.
  4. Risk weights are a model of risk. The buffer is only as good as . Under-weight a real risk and the “shock absorber” is fiction - this is precisely the regulatory-arbitrage and procyclicality failures developed in 05 · Failure Modes.

5. References

  • Hull, John C. - Risk Management and Financial Institutions (5
  • BCBS - Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems (2010, BIS d189). The minimum ratios and buffer stack, in the regulators’ own words. Read from the corpus PDF.
  • BCBS - Basel II: International Convergence of Capital Measurement and Capital Standards (2
  • Hull, John C. - Options, Futures, and Other Derivatives (11th ed.)

6. Connected Graph Bridges

Graph View

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