Quick answer: the Fundamental Review of the Trading Book (FRTB) changes the question from “what is a high quantile of recent trading loss?” to a richer regulatory calculation that tries to capture tail severity, market illiquidity, data scarcity and model reliability. Under the internal-models approach, the core market-risk measure is Expected Shortfall rather than Value at Risk; risk factors are assigned liquidity horizons; only sufficiently observable risk factors are treated as modellable; non-modellable risk factors receive a separate stress treatment; and model permission is tested at trading-desk level using backtesting and P&L-attribution evidence. The standardised approach provides a separate sensitivities-based route.

FRTB is not one formula. It is a chain of tests asking whether a trading-risk number is sufficiently tail-sensitive, liquidity-aware, data-supported and empirically connected to the desk’s actual P&L.

Page role: what this article owns

The existing Bukit Timah Tutor article How Banks Measure Market Risk explains VaR, Expected Shortfall, backtesting and stress scenarios as general risk mathematics. The Basel Output Floor article owns the cross-risk constraint between standardised and internal-model RWAs.

This page owns the narrower regulatory-computational question: how does FRTB turn a trading book into a market-risk capital number, and what evidence must an internal model survive before a desk can use it?

1. Why replace VaR as the central internal-model risk measure?

Value at Risk at confidence level α reports a quantile of the loss distribution. If the 99% one-day VaR is S$10 million, the model says that 99% of modelled days have losses no worse than S$10 million. But VaR says little about the average severity of the remaining 1%.

Expected Shortfall answers a different question:

ES_α = E[L | L is in the tail beyond the α-quantile]

In plain English: once losses are already unusually bad, how bad are they on average?

The Basel Committee’s revised market-risk framework shifted the internal-model approach from VaR to a 97.5% Expected Shortfall measure calibrated to stress and explicitly incorporated varying liquidity horizons. See the Basel Committee’s revised market-risk framework and the current Basel market-risk model requirements.

2. A counterexample: two portfolios can have the same VaR and different tail risk

Imagine two simplified loss distributions. Both have a 99th-percentile loss of S$10 million. Portfolio A’s extreme losses cluster around S$11–12 million. Portfolio B occasionally loses S$40–50 million.

The two portfolios can report similar VaR while having dramatically different Expected Shortfall. That is a falsifier for the claim that “same VaR means same tail risk.”

This does not make ES perfect. ES still depends on the loss model, scenario set, data history and risk-factor representation. It simply asks a more informative tail question.

3. Liquidity horizon: a position cannot be assumed to disappear instantly

Trading-risk models often start from short-horizon price changes, but different risk factors cannot necessarily be neutralised equally quickly under stress. A major-currency interest-rate exposure may be much easier to hedge than an illiquid structured-credit exposure.

FRTB therefore assigns prescribed liquidity horizons to broad risk-factor categories. The internal-model Expected Shortfall is built from a 10-business-day base and scaled/aggregated to reflect longer liquidity horizons where required.

The conceptual transformation is:

short-horizon shock distribution → liquidity-horizon-adjusted tail loss.

This matters because a security can look statistically low-volatility in ordinary data while becoming difficult to exit in stress. FRTB treats market liquidity as part of capital rather than an afterthought.

4. Modellability is an evidence test, not a model-complexity test

A risk factor is not “modellable” merely because a bank can write an equation for it. FRTB asks whether there are enough verifiable real-price observations to support its use in the internal model.

The Basel Risk Factor Eligibility Test (RFET) contains detailed observation criteria. One route requires at least 24 real-price observations over the relevant annual calibration period, with no more than one observation per day counted. The detailed framework also contains spacing requirements and rules for what qualifies as a real price.

This creates a useful epistemic rule:

model sophistication cannot substitute for missing market evidence.

A complex stochastic process fitted to sparse, stale or unverifiable quotes can be mathematically elegant and still fail the regulatory evidence test.

5. Non-modellable risk factors are separated rather than quietly extrapolated

If a risk factor does not satisfy the modellability criteria, FRTB does not simply allow the internal ES engine to interpolate it as though the data existed. It becomes a non-modellable risk factor (NMRF) and receives a separate stress-scenario capital treatment.

This is important for public understanding because “no data” and “low risk” are not the same statement. Sparse observations can mean the market is illiquid, new, bespoke or inactive. The NMRF framework treats evidence scarcity as a reason for caution.

6. The standardised approach is a sensitivity engine

The FRTB standardised approach is not a historical-simulation ES model. Its primary component is a sensitivities-based method. Positions are mapped into prescribed risk classes and risk factors; delta, vega and curvature sensitivities are weighted and aggregated using regulatory correlation structures. Separate components capture default risk and residual risks.

At a high level:

Capital_SA = sensitivity-based risk + default risk charge + residual-risk add-on

where the sensitivity-based block itself combines multiple risk classes and correlation scenarios.

The standardised approach trades some model specificity for comparability and supervisory consistency. That makes it both a capital route and a useful benchmark against internal-model outputs.

7. The internal-models approach is desk-specific

Under FRTB, internal-model approval is attached to eligible trading desks rather than automatically granted to the bank as one indivisible block. A large bank can therefore have some desks on the internal-models approach and others on the standardised approach.

This creates a computational governance problem. The bank must maintain desk definitions, risk-factor mappings, model permissions and evidence trails so that the capital engine knows which methodology applies to which positions.

8. P&L attribution asks whether the risk model explains the desk

A market-risk model can backtest well and still fail to describe the economics of the trading desk if the model omits material pricing factors or uses representations inconsistent with front-office valuation.

P&L attribution compares two constructed profit-and-loss series, broadly separating the effects captured by the risk model from the desk’s theoretical P&L under controlled definitions. The exact Basel tests use prescribed statistical measures and thresholds.

The deeper logic is:

If the risk model says it represents the desk, changes in the modelled risk factors should explain a sufficiently similar pattern of P&L.

A poor attribution result is evidence of a representation gap: missing risk factors, inconsistent market data, valuation differences, unexplained residuals or other mapping weaknesses.

9. Backtesting asks whether realised outcomes are consistent with the model

Backtesting compares modelled risk forecasts with subsequent P&L outcomes. Too many exceedances indicate that the risk measure is understating actual variation or that the desk/model mapping is unstable.

Backtesting does not prove a model is correct. Passing can occur by chance, through conservatism, or because the evaluation window misses the next regime. It is one falsification channel among several.

10. Default risk receives a separate charge

Spread volatility and jump-to-default are not the same risk. A corporate bond can move because its credit spread widens without defaulting, or it can experience a discrete default event. FRTB therefore includes a default-risk charge alongside market-risk components.

This separation prevents continuous-price models from being asked to carry the entire burden of discontinuous credit events.

11. A compact FRTB computational pipeline

Classify positions into trading-book scope and trading desks.
Map positions to risk factors such as rates, credit spreads, FX, equity and commodity variables.
Choose the applicable route: standardised approach or an approved internal-model route for the desk.
For SA, compute prescribed sensitivities and aggregate delta, vega and curvature risk.
Add default-risk and residual-risk components where required.
For IMA, construct stress-calibrated Expected Shortfall for modellable factors.
Apply liquidity-horizon treatment so less liquid factors contribute over longer horizons.
Run the RFET and separate non-modellable risk factors.
Calculate NMRF stress-scenario charges.
Run desk-level backtesting.
Run P&L-attribution tests.
Aggregate permitted desk capital under the applicable framework.
Reconcile against the standardised calculation and wider capital constraints.

12. Inputs and outputs

Typical inputs: positions, desk assignments, valuation-market data, sensitivities, historical/stress risk-factor data, real-price observations, liquidity-horizon categories, default exposures, P&L series and regulatory parameters.

Typical outputs: standardised capital, internal-model ES, NMRF charge, default-risk charge, P&L-attribution status, backtesting status, desk eligibility, and total market-risk RWA/capital after the applicable aggregation rules.

13. Assumptions and weak links

Historical representativeness: stress data must be relevant to the portfolio’s current risks.
Risk-factor mapping: positions must be represented by the factors that truly move their value.
Liquidity classification: prescribed horizons simplify real market depth and may not match every episode.
Price-observation quality: apparent observations must be genuine, representative and verifiable.
Desk stability: organisational changes can change the object being backtested.
Valuation consistency: front-office and risk-model P&L definitions must be reconcilable.
Correlation stability: aggregation benefits can weaken in stress.

14. Failure modes and counterexamples

Tail blindness: two portfolios share the same VaR but have very different extreme-loss severity.
False liquidity: a factor is treated as quickly hedgeable because normal-day turnover is high, but stress depth disappears.
Data-count gaming: many observations exist but come from economically repetitive or non-representative sources.
Risk-factor omission: P&L attribution fails because a desk’s pricing model contains material factors absent from the risk model.
Backtest complacency: a desk passes because recent conditions were benign.
Model migration: a desk changes products faster than the model or modellability evidence updates.
Methodology fragmentation: positions move between desks or approaches without clean ownership and reconciliation.

15. Diagnostics and falsifiers

Which risk factors generate the largest Expected Shortfall contribution?
How much capital comes from liquidity-horizon scaling rather than raw 10-day volatility?
Which factors fail modellability and why?
Do NMRF charges cluster in genuinely illiquid products or reveal a data-governance weakness?
Which trading desks have the largest gap between risk-theoretical and hypothetical P&L?
Are backtesting exceptions concentrated in one market regime?
Does the standardised capital rise when internal-model risk also rises, or are the two measures telling different stories?
What position would produce a large loss under a risk factor absent from the model?

A useful falsifier for “our internal model captures the desk” is a repeated P&L pattern that the model cannot reproduce even though the front-office valuation explains it with known market factors. That points to a representation gap rather than mere random noise.

16. Alternatives and limits

No regulatory framework is a complete economic-risk model. FRTB capital can be supplemented internally by stress testing, scenario analysis, concentration metrics, liquidity analytics and position-level limits. The standardised approach can be more comparable but less tailored. Internal models can be more risk-sensitive but depend more heavily on data, mapping and validation.

Expected Shortfall itself does not say why a tail loss occurs. Scenario decomposition, sensitivities and stress narratives are still needed to make the number actionable.

17. Verification and update triggers

recheck trading-book and desk mappings after organisational/product changes;
re-run modellability tests as real-price observations roll through time;
review stress calibration when portfolio composition changes materially;
investigate clustered backtesting exceptions rather than treating them as isolated misses;
reconcile front-office pricing factors with risk-model factors after valuation-model changes;
track the share of capital coming from NMRFs;
verify current local implementation rules because Basel standards and jurisdictional effective dates can differ.

18. Current implementation caution

The Basel Framework is the global standard, but implementation timing differs by jurisdiction and has changed over time. For example, the Bank of England has separately communicated UK Basel 3.1 market-risk implementation arrangements. A public educational article should therefore distinguish the Basel algorithmic architecture from the local date on which a particular bank becomes legally subject to it.

See the Bank of England market-risk implementation material.

Connections across the Bukit Timah Tutor finance-algorithms lane

Market-risk measurement — the mathematical foundation below FRTB.
Market-making algorithms — the trading decisions whose positions feed the capital engine.
Basel output floor — a separate cross-risk capital constraint.
Model validation — the broader discipline surrounding internal-model permission and monitoring.

Research anchors

The deeper lesson

FRTB is useful to study because it shows what happens when a mathematical risk measure is forced to meet the world. Tail loss is not enough; the framework asks how long risk might take to exit. A formula is not enough; the framework asks whether real prices support the factor. Backtesting is not enough; the framework asks whether modelled factors actually explain desk P&L. The result is a chain from position → factor → sensitivity/distribution → liquidity → evidence → validation → capital. Every weak link can change the answer.

Educational boundary: This article explains public market-risk mathematics and Basel concepts. It is not regulatory advice, trading advice, investment advice or a capital calculation for any specific bank.

Small Group Tutorials

How FRTB Market-Risk Algorithms Turn Trading Positions into Capital: Expected Shortfall, Liquidity Horizons, Modellability, P&L Attribution and Backtesting