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: | Zone | Exceptions (out of 250) | Multiplier Add-on | Interpretation | |---|---|---|---| | **Green** | 0 – 4 | None (k = 3.0) | Model is performing adequately | | **Yellow** | 5 – 9 | +0.40 to +0.85 | Possible model issues — supervisory review required | | **Red** | 10+ | +1.0 (k = 4.0) | Serious model deficiency — automatic penalty | **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.