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

A bank's 99% one-day VaR model produced 4 exceptions in 250 days, but all four occurred in the same week during a market sell-off. Which conclusion is most appropriate?

The count of four is statistically consistent with a 99% model, so frequency passes, but exceptions clustered in one week suggest dependence. Christoffersen's conditional coverage test, which checks independence along with coverage, is designed to detect this, and it signals the model adapts too slowly to volatility.

  1. AThe model passes both frequency and independence checks because 4 is below the expected 2.5 plus tolerance
  2. BThe unconditional coverage test is likely satisfied, but clustering suggests the independence property fails, which a conditional coverage (Christoffersen) test is designed to detectCorrect
  3. CThe model should be rejected under Kupiec's test because 4 exceeds 2.5
  4. DThe clustering is irrelevant to backtesting because only the total count matters

Explanation

Four exceptions against an expected 2.5 is well within Kupiec's acceptance range, so frequency looks fine. Exceptions bunched in one week violate independence, indicating the model reacts slowly to volatility changes. Christoffersen's conditional coverage test combines frequency and independence and can detect this.

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