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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

A trading desk has a 99% one-day VaR of USD 10 million. Over the past 250 days, it recorded 2 exceptions. A regulator notes that both exceptions occurred on consecutive days during a market shock, with losses of USD 25 million and USD 30 million. Which conclusion is best supported?

The model passes the simple count test, but the clustering of the two exceptions and their large size relative to VaR indicate weaknesses. Backtesting by count ignores independence and tail severity, so VaR may be understating risk during stress, which suggests expected shortfall or stress tests should supplement it.

  1. AThe model passes unconditional coverage, but the clustering of exceptions and their size suggest VaR is understating tail risk and independence may failCorrect
  2. BThe model is rejected because 2 exceptions is below the expected 2.5, indicating overly conservative VaR
  3. CThe model is fully validated because the number of exceptions is within the green zone, so the size of losses is irrelevant
  4. DThe model should be rejected because VaR always fails to detect clustering by construction

Explanation

Two exceptions against 2.5 expected is acceptable for unconditional coverage (green zone). However, consecutive exceptions violate independence (conditional coverage), and losses of 2.5-3 times VaR show VaR gives no information about tail severity. Being below expectation does not by itself reject a model, and size matters for risk assessment even though backtests count only frequency.

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