How does VaR backtesting work under Basel, and what is the traffic light system?

VaR backtesting is where risk models meet regulatory reality — and it's heavily tested on FRM Part II. Let me walk through the framework.

What Is VaR Backtesting?

Backtesting compares your model's daily VaR predictions against actual trading P&L. If your 99% VaR says 'we shouldn't lose more than $X on any given day with 99% confidence,' then over 250 trading days you'd expect about 2.5 exceptions (days where actual loss exceeds VaR).

An exception (or breach) occurs whenever the actual loss > predicted VaR.

The Basel Traffic Light System:

Basel uses a 250-day backtesting window and classifies banks into three zones:

How the Multiplier Works:

Under Basel, the market risk capital charge is:

$$\text{Capital} = \max\left(\text{VaR}_{t-1},\; k \times \frac{1}{60}\sum_{i=1}^{60}\text{VaR}_i\right) + \max\left(\text{sVaR}_{t-1},\; k \times \frac{1}{60}\sum_{i=1}^{60}\text{sVaR}_i\right)$$

The base multiplier k = 3.0. If you land in the yellow zone with 7 exceptions, k increases to 3.65, directly increasing your capital requirement by ~22%. In the red zone, k = 4.0 (a 33% increase).

Practical Example:

Atlas Global Trading runs a 99% 1-day VaR model. Over the past 250 trading days:

• VaR predicted an average daily max loss of $4.8M
• Actual losses exceeded VaR on 6 occasions (yellow zone)

The regulator now requires Atlas to explain those 6 exceptions. Acceptable reasons might include:

• An unexpected geopolitical event (e.g., sudden sanctions)
• A liquidity gap in an illiquid market
• Known model limitation being addressed

Unacceptable: 'We don't know why.' That pushes the conversation toward red-zone treatment.

Where Stressed VaR (sVaR) Fits In:

After 2008, Basel 2.5 introduced stressed VaR — the same VaR calculation but using a 12-month historical window from a period of significant market stress (e.g., 2007–2008, March 2020). This ensures capital charges don't collapse during calm markets.

The total capital charge is regular VaR plus stressed VaR, each with its own multiplier. This effectively doubles the capital floor compared to pre-crisis rules.

Exam Tips:

1. Know the exception count boundaries: Green ≤ 4, Yellow 5–9, Red ≥ 10.
2. The Kupiec test is the formal statistical test for whether the exception rate is consistent with the model's confidence level.
3. Stressed VaR uses a fixed stress window, not the most recent data — the window is chosen to be relevant to the bank's current portfolio.

AcadiFi's FRM Part II Market Risk module includes a full backtesting simulation exercise where you classify results under the traffic light system. Highly recommended for exam prep.