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FRM Exam Part II · Backtesting VaR

Basel Traffic Light Approach to VaR Backtesting

Updated 11 October 2026 · Fact-checked

The Basel traffic light approach counts VaR exceptions over the last 250 trading days at 99% confidence. Zero to four exceptions is green, five to nine is yellow, ten or more is red. The multiplier is 3.00 in green, rises from 3.40 to 3.85 in yellow, and is 4.00 in red.

Understand Basel Traffic Light Approach

A bank's internal VaR model sets its market risk capital under the older Basel internal models approach. Regulators need a simple way to check that the model is not understating risk. They use backtesting: compare the daily 99% one-day VaR with the next day's trading P&L and count each day the loss is larger than VaR. That day is an exception.

If the model is correct, the chance of an exception each day is 1%. Over 250 days you expect about 2.5 exceptions. The number of exceptions follows a binomial distribution with n = 250 and p = 0.01. Some exceptions are just bad luck, so regulators do not punish every deviation from 2.5.

The traffic light approach turns the count into three zones. Green zone: 0 to 4 exceptions. The model is accepted. Yellow zone: 5 to 9 exceptions. The result is suspicious but could be chance, so the bank is penalised gradually. Red zone: 10 or more exceptions. The model is presumed to be inaccurate and is almost automatically rejected.

The penalty is a plus factor added to the base multiplier of 3. Market risk capital is the higher of the previous day's 10-day 99% VaR and the multiplier times the average 10-day 99% VaR over the last 60 days, plus any specific risk charge. A larger multiplier means more capital. In the green zone the plus factor is 0, so the multiplier is 3.00. In the yellow zone it rises with each exception. In the red zone it is 1, so the multiplier is 4.00.

The design balances two errors. Rejecting a good model is a Type I error. Accepting a bad model is a Type II error. The yellow zone exists because the exception count cannot cleanly separate good and bad models, so the penalty is graded rather than all-or-nothing.

Key formulas to remember

Backtesting setup
Exception when daily loss > 1-day 99% VaR; window = last 250 trading days
Expected exceptions = 250 × 1% = 2.5.
Zones
Green: 0-4; Yellow: 5-9; Red: 10 or more exceptions
Boundaries are fixed by Basel; learn them exactly.
Plus factors in the yellow zone
5 → 0.40; 6 → 0.50; 7 → 0.65; 8 → 0.75; 9 → 0.85
Green plus factor is 0; red plus factor is 1.00.
Multiplier
Multiplier = 3 + plus factor
Gives 3.00 (green), 3.40 to 3.85 (yellow), 4.00 (red).
Capital charge (simplified)
Capital = max(VaR(t-1), multiplier × average 10-day 99% VaR over the last 60 days) + specific risk charge
VaR(t-1) is the previous day's 10-day 99% VaR. The specific risk charge is added after the higher-of comparison. Exam questions often give one VaR figure, so you then compute multiplier × VaR.
Binomial exceptions
X ~ Binomial(250, 0.01); mean = 2.5; standard deviation = √(250 × 0.01 × 0.99) ≈ 1.57
Useful for judging how unusual a count is.

How to solve Basel Traffic Light Approach questions

Use this method for any traffic light question, whether it asks for the zone, the multiplier or the capital.

  1. 1Confirm the VaR is 1-day at 99% confidence and the window is 250 trading days.
  2. 2Count exceptions: days where the loss exceeded that day's VaR. Gains and losses smaller than VaR do not count.
  3. 3Assign the zone: 0-4 green, 5-9 yellow, 10 or more red.
  4. 4Find the plus factor: 0 in green, from the yellow table, or 1.00 in red. Add it to 3 for the multiplier.
  5. 5If capital is asked, multiply the multiplier by the 10-day 99% VaR (scale 1-day VaR by √10 if only that is given).
  6. 6Interpret: state whether the model is accepted, penalised, or presumed flawed, and whether a Type I or Type II error concern applies.

Quickest way: Zone-and-table shortcut

When to use it: Use when the question gives an exception count and asks for zone, multiplier or capital change.

  1. Memorise 4 / 9 as the cut-offs: up to 4 green, up to 9 yellow.
  2. Memorise yellow multipliers: 3.40, 3.50, 3.65, 3.75, 3.85 for 5 to 9 exceptions.
  3. Multiplier ratio gives the capital change directly: new multiplier ÷ old multiplier − 1.
  4. Eliminate options that put the multiplier below 3 or above 4.

Common mistakes in Basel Traffic Light Approach

  • Putting 5 exceptions in the green zone, or 10 in the yellow zone.

    Students recall the cut-offs as 'under 5' and 'under 10' and shift them by one.

    Fix: Green is 0-4, yellow is 5-9, red is 10 or more. Check the boundary counts first.

  • Reporting the plus factor as the multiplier.

    The tables list plus factors such as 0.40, and students stop there.

    Fix: Always add the plus factor to 3. Five exceptions gives 3.40, not 0.40.

  • Treating the red-zone multiplier as discretionary.

    Confusion with the yellow zone, where supervisors have discretion.

    Fix: In the red zone the plus factor of 1.00 is applied automatically, and the model is presumed flawed. Supervisory discretion applies in the yellow zone.

  • Counting days with any loss as exceptions.

    Mixing up a loss with a loss exceeding VaR.

    Fix: Compare each day's loss with that day's VaR. Only losses larger than VaR count.

  • Using 95% VaR or a 10-day VaR for the exception count.

    The capital uses 10-day VaR, so students assume backtesting does too.

    Fix: Backtest one-day 99% VaR against daily P&L. Use 10-day VaR only in the capital calculation.

Worked examples

Example 1

A bank backtests its 1-day 99% VaR over 250 days and records 7 exceptions. (a) Which zone is this? (b) What is the multiplier? (c) The 10-day 99% VaR is $20 million. What is the capital charge on this basis, and how much more than at the green-zone multiplier?

Show the solution
  1. Seven exceptions lies in 5-9, so the zone is yellow.
  2. The plus factor for 7 exceptions is 0.65, so the multiplier is 3 + 0.65 = 3.65.
  3. Capital = 3.65 × $20 million = $73 million.
  4. At the green multiplier: 3 × $20 million = $60 million.
  5. Extra capital = $73 million − $60 million = $13 million.

Answer: Yellow zone; multiplier 3.65; capital $73 million, which is $13 million more than at 3.00.

Example 2

A bank's 1-day 99% VaR is $4 million. Over 250 days it had 11 exceptions. Find the multiplier and the capital charge using 10-day VaR scaled by the square root of time, and give the percentage increase over the base multiplier of 3.

Show the solution
  1. Eleven exceptions is 10 or more, so the zone is red.
  2. Plus factor is 1.00, so multiplier = 4.00.
  3. 10-day VaR = $4 million × √10 = $4 million × 3.1623 = $12.65 million.
  4. Capital = 4.00 × $12.65 million = $50.6 million.
  5. Capital at the base multiplier of 3.00 = 3 × $12.65 million = $37.95 million.
  6. Increase = $50.6 million − $37.95 million = $12.65 million, which is $12.65 million ÷ $37.95 million = 33.3%.

Answer: Red zone; multiplier 4.00; capital rises from $37.95 million to $50.6 million, an increase of 33.3%.

Exam tips

  • Memorise the zone cut-offs and all five yellow multipliers; questions often test them directly.
  • Check whether the question gives 1-day or 10-day VaR before computing capital.
  • If asked why the yellow zone exists, link it to Type I and Type II errors: a good model can show 5-9 exceptions by chance.
  • Expect scenario questions asking what supervisors should do: yellow means investigate causes, red means presume the model is flawed.
  • Expected exceptions is 2.5, so be ready to say how unusual a given count is.

Practice questions from Backtesting VaR

Basel Traffic Light Approach in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Basel Traffic Light Approach: frequently asked questions

What are the Basel traffic light zones?

With 250 days of 99% VaR backtesting, 0-4 exceptions is green, 5-9 is yellow and 10 or more is red. Green keeps the multiplier at 3.00. Yellow raises it gradually and red sets it at 4.00.

How does the Basel multiplier change with VaR exceptions?

The multiplier is 3 plus a plus factor. Plus factors are 0.40, 0.50, 0.65, 0.75 and 0.85 for 5, 6, 7, 8 and 9 exceptions. At 10 or more exceptions the plus factor is 1.00.

Why does the yellow zone exist?

Exception counts are noisy, so a correct model can sometimes show five to nine exceptions. Regulators avoid rejecting such models outright. They apply a graded penalty instead, and supervisors look at the cause of the exceptions.

Do I need to know the plus factors for the FRM exam?

Yes, it is safest to know them. Questions may ask for the multiplier or the capital impact of a given exception count.