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FRM Part II · FRM Exam Part II · Validating Bank Holding Companies' Value-at-Risk Models for Market Risk

A validator benchmarks a bank's 99% one-day VaR of USD 12.0 million against a vendor model giving USD 15.0 million. Over 250 days, the bank's model had 7 exceptions and the vendor model's VaR, applied to the same P&L, had 3. Which conclusion is best supported?

The bank's model likely understates risk. Expected exceptions are 2.5, yet it had 7, and its VaR is 20% below the benchmark. The vendor's 3 exceptions are near expectation. The consistent evidence warrants investigation of the bank's model.

  1. AThe bank's model is adequately calibrated because 7 is close to the expected 2.5
  2. BThe vendor model is overstated because it produced fewer exceptions than expected
  3. CThe bank's model likely understates risk; the benchmark gap and excess exceptions point the same way and warrant investigationCorrect
  4. DNo conclusion is possible because benchmark and backtest results cannot be combined

Explanation

Expected exceptions at 99% over 250 days are 2.5. Seven is well above that, and the bank VaR is 20% below the benchmark (12 vs 15), so both pieces of evidence indicate understatement. The vendor's 3 exceptions are close to 2.5, so it looks reasonable rather than overstated.

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