FRM Exam Part II · Fundamental Review of the Trading Book

FRTB Modellability, P&L Attribution and Backtesting Explained

Updated 11 October 2026 · Fact-checked

Under FRTB, a bank keeps internal model approval only desk by desk. Each desk must pass the P&L attribution test and desk-level backtesting. Risk factors that fail the risk factor eligibility test are non-modellable and get a stress scenario capital charge instead of being in Expected Shortfall. Bank-level backtesting sets the capital multiplier.

Understand Modellability, P&L Attribution and Backtesting

FRTB lets a bank use its internal models approach (IMA) only if the model is proven reliable. The proof is done at trading desk level, not for the whole bank. A desk that fails goes back to the standardized approach. This is the answer to how banks lose internal model approval.

There are three checks. First, modellability: is each risk factor backed by enough real price data? Second, P&L attribution: does the risk model's hypothetical P&L track what the front office actually calculates? Third, backtesting: do actual losses exceed VaR too often?

A risk factor is modellable if it passes the risk factor eligibility test (RFET). This needs enough real, observable prices, either from the bank's own trades or from committed quotes or external data. A factor that fails is a non-modellable risk factor (NMRF). NMRFs are kept out of the Expected Shortfall model. Each gets a stress scenario capital charge (SES), calibrated to a loss at least as large as the ES calibration (97.5%) over the stress period, with a liquidity horizon of at least 20 days. Idiosyncratic credit spread NMRFs and other NMRFs are treated differently in aggregation.

The P&L attribution (PLA) test compares hypothetical P&L (HPL), from the front office pricing models, with risk-theoretical P&L (RTPL), from the risk model using only its risk factors. Two metrics are used: the Spearman correlation and the Kolmogorov-Smirnov (KS) distance. Each gives a green, amber or red zone, and the desk zone is the worse of the two. A red desk cannot use IMA. An amber desk can, but pays a capital surcharge.

For backtesting, the bank counts exceptions at the desk level against 99% and 97.5% one-day VaR over the last 250 days. A desk with more than 12 exceptions at 99%, or more than 30 at 97.5%, is not allowed on IMA. Bank-wide 99% VaR exceptions set a multiplier on the capital charge, as in the Basel traffic light approach.

Key formulas to remember

Risk factor eligibility test (RFET): Modellable if: at least 24 real price observations in the last 12 months, with no 90-day period holding fewer than 4, OR at least 100 observations in the last 12 months; Observations must be real prices, and an observation counts at most once per day. The 24-observation route also needs at least 4 observations in every 90-day period. The 100-observation route has no 90-day condition. Fail both routes and the factor is an NMRF.
NMRF capital charge: SES is calibrated to a loss at least as large as the ES calibration (97.5%) over the stress period, with a liquidity horizon of at least 20 days, or the factor's own horizon if longer; NMRFs are charged outside the ES model. Aggregation depends on the factor type and the assumed correlations.
Hypothetical vs risk-theoretical P&L: PLA compares HPL (front office) with RTPL (risk model) using Spearman correlation and KS distance; HPL and RTPL are compared daily over the same 250 days, with RTPL using only the risk factors in the model.
PLA zones: Spearman correlation: Green: ρ > 0.80 | Amber: 0.70 ≤ ρ ≤ 0.80 | Red: ρ < 0.70; Higher correlation is better.
PLA zones: KS distance: Green: KS < 0.09 | Amber: 0.09 ≤ KS ≤ 0.12 | Red: KS > 0.12; Lower distance is better. Desk zone is the worse of the two metrics.
Desk-level backtesting limit: Desk fails if exceptions over last 250 days: > 12 at 99% VaR or > 30 at 97.5% VaR; Uses both actual and hypothetical P&L for exception counting.
Bank-level capital multiplier (99% VaR exceptions in 250 days): Green: 0–4 exceptions, multiplier add-on 0 | Amber: 5–9, add-on 0.20 to 0.42 | Red: 10 or more, add-on 0.50; Under FRTB the base multiplier is 1.5, so the total ranges from 1.50 (green) to 2.00 (red). Amber add-ons by count: 5 = 0.20, 6 = 0.26, 7 = 0.33, 8 = 0.38, 9 = 0.42. Do not mix this with the older Basel market risk traffic light scale, which has a base of 3.0, add-ons from 0.40 to 1.00 and a total range of 3.0 to 4.0. Check which framework the question uses.

How to solve Modellability, P&L Attribution and Backtesting questions

Most questions give you data for one desk or one risk factor and ask what happens. Work through the tests in order and separate the desk-level tests from the bank-level multiplier.

1Identify the level: risk factor, desk, or bank. Modellability is per risk factor, PLA and desk backtesting are per desk, the multiplier is per bank.
2For a risk factor, count real price observations over 12 months and check both the 24-with-gap rule and the 100-observation rule.
3If the factor fails, label it an NMRF. It leaves the ES model and gets a stress scenario capital charge.
4For PLA, compare each metric with its thresholds, then take the worse zone as the desk result.
5Map the result: green means IMA with no add-on, amber means IMA with a capital surcharge, red means standardized approach.
6For backtesting, count exceptions over the last 250 days and compare with the desk limits and the bank-level traffic light zone.
7State the consequence in plain words: capital multiplier, surcharge, or fall back to the standardized approach.

Quickest way: Zone-then-consequence shortcut

When to use it: Use this when the question gives a correlation, KS distance or exception count and asks for the outcome.

Write the thresholds once on scratch paper: Spearman 0.80 / 0.70, KS 0.09 / 0.12, exceptions 4 / 9.
Place each number in a zone without calculating anything.
For PLA, the worse zone wins.
Link zone to consequence: red PLA means standardized approach, amber means surcharge, green means no add-on.
Eliminate options that mix levels, for example a desk test used to set the bank multiplier.

Common mistakes in Modellability, P&L Attribution and Backtesting

Taking the better of the two PLA metrics as the desk result.
Students assume one passing metric is enough.
Fix: The desk takes the worse zone of Spearman and KS.
Adding NMRFs into the Expected Shortfall model.
It seems natural to include every risk factor in the model.
Fix: NMRFs are excluded from ES and charged separately under the stress scenario capital charge.
Confusing the desk exception limits with the bank multiplier zones.
Both use 250-day exception counts, so they look alike.
Fix: Desk limits (12 at 99%, 30 at 97.5%) decide IMA eligibility. The 0 to 4, 5 to 9 and 10 or more zones at bank level set the multiplier.
Treating hypothetical P&L and risk-theoretical P&L as the same.
Both are model-based daily P&L figures.
Fix: HPL is from front office valuation models. RTPL is from the risk model using only its risk factors. PLA tests the gap between them.
Counting any price quote as an observation for the RFET.
Students overlook the word real.
Fix: Only real price observations count, such as actual trades or committed quotes. Indicative or modelled prices do not.

Worked examples

Example 1

A bank's risk factor has 30 real price observations over the past 12 months, but in one 90-day period it has only 3 observations. Is it modellable?

Show the solution

Check the 24-observation route: 30 is at least 24, but the 90-day period has only 3, which is fewer than 4. This route fails.
Check the 100-observation route: 30 is less than 100. This route fails.
Both routes fail, so the factor is not eligible.

Answer: The factor is an NMRF. It is excluded from the ES model and receives a stress scenario capital charge.

Example 2

A desk has a Spearman correlation of 0.76 and a KS distance of 0.08 in its PLA test. What is its PLA zone and consequence?

Show the solution

Spearman 0.76 lies between 0.70 and 0.80, so it is amber.
KS 0.08 is below 0.09, so it is green.
The desk takes the worse zone, which is amber.
Amber means the desk may stay on IMA but must hold a capital surcharge.

Answer: Amber zone. The desk stays on IMA with a capital surcharge.

Exam tips

Memorise the six PLA thresholds: 0.80 and 0.70, 0.09 and 0.12, and remember lower KS is better.
Read whether the question is about a risk factor, a desk or the bank before choosing a test.
Look for real price wording in RFET questions. It is often the trap.
When a desk fails, the answer is a move to the standardized approach, not a zero capital charge.
Check the reading's exact table for amber multiplier add-ons if asked for a number.

Practice questions from Fundamental Review of the Trading Book

Modellability, P&L Attribution and Backtesting: frequently asked questions

What is a non-modellable risk factor in FRTB?

It is a risk factor that fails the risk factor eligibility test because it lacks enough real price observations. It is taken out of the Expected Shortfall model. Capital for it comes from a stress scenario charge instead.

How do banks lose internal model approval under FRTB?

Approval is held desk by desk. A desk loses it if it falls in the red PLA zone or breaches the desk-level backtesting exception limits. It then uses the standardized approach.

What does the FRTB P&L attribution test compare?

It compares hypothetical P&L from front office models with risk-theoretical P&L from the risk model. It uses Spearman correlation and the KS distance. The worse zone of the two sets the desk result.

How is the FRTB backtesting multiplier different from desk-level backtesting?

Desk-level backtesting decides whether a desk can stay on IMA. Bank-level 99% VaR exceptions fall into green, amber or red zones and set the capital multiplier. Do not mix the two.