4.9.5 Failure Modes & Real-World Practice

Basic Prerequisites: 03 · Market Risk & FRTB and 04 · Credit & Operational Risk.

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1. Intuition & Practical Objective

The capital framework is a model of risk written into law, and every model has failure modes. This page names the three that matter most for practitioners, ties each to first principles, and quantifies each so the failure is a number, not a slogan:

1. Regulatory arbitrage - because capital scales with risk weight, not risk, a bank can raise its ratio by re-labelling the same economic exposure (securitisation, guarantees, model approval). The firm’s reported safety improves; the system’s does not.
2. Procyclicality - risk weights, PDs, and volatilities all rise in a downturn, so required capital increases exactly when banks can least raise it, amplifying the cycle the rules were meant to dampen.
3. Model approval & measurement error - the internal approaches (IRB, IMA) let a bank supply its own parameters. If validation is weak, the bank’s capital becomes a number it controls against itself, and the supervisor’s sign-off becomes the only real check.

The objective is not cynicism. It is the discipline of knowing which lever a ratio can be moved with, so that a reported improvement can be interrogated: did the bank reduce risk, or reduce the weight?

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2. Mathematical Ground Truth & Derivations

Arbitrage in one identity. The ratio is $E/{\sum }_i{E}_{i}r{w}_i$. Holding capital $E$ and exposure $E_i$ fixed, any reduction in $r{w}_i$ raises the ratio:

$$\frac{\partial }{\partial r{w}_i}\left(\frac{E}{\mathrm{RWA}}\right)=-\frac{E{E}_i}{{\mathrm{RWA}}^2}<0.$$

So the cheapest way to “improve” capital is never to de-risk - it is to find the lowest $r{w}_i$ for the same cash-flow. The reform countermeasure is to reduce the scope for $rw$ differences: the output floor ($\mathrm{RWA}\ge 72.5\%{\mathrm{RWA}}_{\text{SA}}$, §06) caps how far internal models may cut RWA below the standardised measure.

Procyclicality as a function of ratings/vol. RWA moves with $rw(\text{rating})$, and PD moves with the cycle, so

$$\frac{\partial \mathrm{RWA}}{\partial \text{downturn}}>0⟹\frac{\partial (\text{capital ratio})}{\partial \text{downturn}}<0.$$

The framework’s attempted antidotes: the countercyclical buffer (build CET1 in good times, release in bad), through-the-cycle PD calibration, and the output floor. None fully removes the feedback.

Measurement error compounds through the ratio. If a bank’s IRB/IMA parameters understate true risk, both the numerator (via how capital is computed) and the denominator (RWA) are affected; a systematic underestimation of loss given default, say, cuts capital more than proportionally because it also lowers the conditional-loss term $N^{-1}(\mathrm{PD})+\sqrt{R}{N}^{-1}(0.999)$.

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3. Computational Implementation - the three failures in numbers

Stdlib only. Each block is a concrete, exploitable or dangerous effect.

Failure 1 - regulatory arbitrage via securitisation.

Failure 2 - procyclicality: a book-wide rating migration.

Failure 3 - the model gap: identical risk, different RWA.

What the numbers say. (i) Re-wrapping a $100 corporate loan as a AAA securitisation tranche cuts its capital requirement by 80% with no change in the underlying cash flows - the arbitrage is a classification trade. (ii) A two-notch downgrade of an entire book lifts RWA 50% and pushes the CET1 ratio from 10.00% to 6.67% - a solvency-threatening fall caused entirely by the rating of unchanged positions. (iii) Two banks with the same economic risk can report 10.00% and 11.76% purely because one uses IRB - the denominator is not comparable, which is why the output floor exists. All three failures live in the denominator, not the numerator.

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4. Failure Modes & First-Principles Breakdowns (numbered)

1. Arbitrage → the ratio decouples from risk. Because $E/\mathrm{RWA}$ falls in $rw$, the cheapest ratio improvement is re-labelling, not de-risking. Remedies: the output floor, leverage ratio (which ignores $rw$ entirely), and disclosure.
2. Procyclicality → capital rises when it can least be raised. Ratings, PDs, and volatilities are all cycle-dependent, so RWA is highest in the bust. The countercyclical buffer and through-the-cycle calibration reduce, but do not remove, the feedback (Brunnermeier-style amplification, Liquidity Risk & Funding).
3. Model approval → the sign-off is the only real check. IRB/IMA parameters are the bank’s own; a mis-validated PD or LGD understates capital and, because it is multiplicative, does so non-linearly. The AMA’s abolition (§04) is the concrete case of a model route withdrawn after losses revealed the error.
4. The leverage/RWA split means two liabilities to manage. A bank can be comfortable on one ratio and thin on the other: low-RWA books pass the risk-based test but blow the 3% leverage test; low-leverage books pass leverage but can still be RWA-fragile. Practitioners must track both (06).
5. Liquidity is not in the capital ratio. A bank can be well-capitalised and still die of a run - the reason the LCR/NSFR exist as separate, hard constraints (§06). Capital is a solvency buffer; liquidity is a survival buffer; they are not substitutes.

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5. References

• BCBS - Basel III: Finalising Post-Crisis Reforms (2017, d424). The policy responses to these exact failures: constrained IRB use, the revised output floor, and the leverage backstop. Read from the corpus PDF.
• BCBS - Basel III: A Global Regulatory Framework (2010, d189). Introduces the capital conservation and countercyclical buffers explicitly to fight procyclicality. Read from the corpus PDF.
• Brunnermeier, Markus K. - Deciphering the Liquidity and Credit Crunch 2007–2008, J. Economic Perspectives 23(1):77–100 (2
• Hull, John C. - Risk Management and Financial Institutions (5
• Hull, John C. - Options, Futures, and Other Derivatives (11th ed.)

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6. Connected Graph Bridges

• Back: 03 · Market Risk & FRTB · 04 · Credit & Operational Risk · Index Hub
• Forward: 06 · Advanced Extensions (LCR, NSFR, Leverage, Output Floor)
• Sibling: Liquidity Risk & Funding · Stress Testing & Scenario Analysis (Pillar 2)