VaR Backtest — Kupiec & Christoffersen

How to use it

1. Paste one row per day with date, P&L (negative for a loss) and the VaR forecast as a positive loss. A clustered-exceptions demo loads by default.
2. Pick the VaR confidence level: 95%, 97.5%, 99% or 99.5%.
3. Read the Kupiec p-value: whether the number of exceptions matches the confidence level.
4. Check the Christoffersen independence test (do exceptions cluster?) and the joint conditional-coverage test.
5. Read the Basel traffic-light zone from the exception count. The Basel rule is defined for 99% VaR over 250 days.

The method, step by step

Backtest a value-at-risk model by comparing realized losses to the VaR level over time and counting breaches, then running a Kupiec test to check the breach frequency matches the confidence level and a Christoffersen test to check breaches are independent rather than clustered. Clustered breaches are the dangerous failure: a model that is right on average but wrong in bunches will fail exactly when it matters.

1. Define the breach indicator

   For each period, mark a breach when the realized loss exceeds the VaR forecast for that period. This produces a sequence of zeros and ones, the breach indicator, which is the raw material for every VaR backtest. The VaR confidence level sets the expected breach rate: a 99 percent one-day VaR should be breached on about one percent of days. Everything downstream tests whether this sequence behaves the way the model claims.

   Use out-of-sample VaR forecasts. Backtesting a VaR model on the same data it was fit on overstates how well it works, just like any other backtest.

2. Run the Kupiec frequency test

   The Kupiec proportion-of-failures test checks whether the observed breach rate matches the expected rate implied by the confidence level. Too many breaches means the model understates risk; too few means it overstates risk and ties up capital needlessly. The test produces a statistic and a p-value for the null hypothesis that the breach frequency is correct. It is the first gate: a model that fails frequency is mis-scaled before you even look at timing.

   Too few breaches is a real failure too, not a free pass. An overly conservative VaR wastes capital and signals the model is not capturing the actual distribution.

3. Run the Christoffersen independence test

   Passing the frequency test is not enough, because breaches can occur at the right rate but bunch together in stressed periods. The Christoffersen test checks whether a breach today is independent of a breach yesterday. If breaches cluster, the model has the right average but the wrong dynamics: it underestimates risk precisely when volatility spikes. Independence is the property that tells you the model holds up in the conditions you most need it to.

   Clustered breaches mean your VaR is calm until it is suddenly very wrong, all at once. That is the failure mode that causes blowups.

4. Combine frequency and independence

   The Christoffersen conditional-coverage test combines both properties into one: correct breach frequency and independent breaches. A model must pass both to be trustworthy. Passing only frequency means the average is right but the timing is dangerous; passing only independence is meaningless if the rate is wrong. Read the combined test as the headline result, then use the individual tests to diagnose which property failed when it does.

   When the combined test fails, look at the components to localize the problem. Frequency failure is a scaling issue; independence failure is a dynamics issue, and they need different fixes.

5. Act on the diagnosis

   A frequency failure usually means recalibrating the VaR level or the distributional assumption. An independence failure usually means the model is not capturing volatility clustering, which calls for a model that updates its risk estimate as volatility changes rather than a static one. Either way, the backtest does not just pass or fail; it points at what to fix. Re-run the tests after the fix on fresh data to confirm the correction held.

   Independence failures point toward a volatility-aware model. A static VaR that ignores changing volatility will keep clustering breaches no matter how you rescale it.

Sources: Techniques for Verifying the Accuracy of Risk Measurement Models (Paul H. Kupiec, Federal Reserve (1995)) ; Evaluating Interval Forecasts (Peter F. Christoffersen, International Economic Review (1998))

Mistakes that undo the result

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Use it from code

The same calculation as a JavaScript module you can import. It runs where you import it, with no request, key or rate limit.

import { compute } from "https://aifinhub.io/engines/var-backtest-kupiec-christoffersen.js";

Input and output contract and the guide for agents.