What does the Kupiec proportion-of-failures test check in VaR backtesting?

Question

AcadiFi · Accepted Answer

The Kupiec proportion-of-failures test checks whether the observed exception rate is consistent with the VaR confidence level. For a 99 percent one-day VaR, exceptions should occur about 1 percent of the time over a sufficiently long sample. The test does not care where exceptions occur in time. It focuses on whether the total count is too high or too low relative to expectation.

Suppose Meridian Bank runs a 99 percent VaR model for 250 trading days and observes 9 exceptions. If the model were well calibrated, the expected count would be about 2.5 exceptions. Nine exceptions may indicate that the VaR model is underestimating risk. If there were zero exceptions, the model might be overly conservative, although context matters.

```mermaid
flowchart TD
  A[VaR forecasts] --> B[Compare next-day P/L]
  B --> C[Count exceptions]
  C --> D[Compare observed rate to expected rate]
```

FRM candidates should also remember what the test does not check. It does not test exception independence or clustering. A model with the right total number of breaches can still fail if exceptions arrive in clusters. On the exam, also state the horizon, confidence level, data source, modeling assumption, and validation step, because those choices usually explain why two reasonable VaR answers differ materially. Practice more in our FRM question bank.

What does the Kupiec proportion-of-failures test check in VaR backtesting?

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