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FRM Part I · FRM Exam Part I · Measures of Financial Risk

A risk analyst has 500 daily P&L observations and uses historical simulation to estimate 99% one-day VaR. Ordering losses from largest to smallest, the 5th largest loss is USD 2.40 million and the 6th largest loss is USD 2.10 million. Using the convention that VaR is the loss at which exactly 1% of observations lie in the tail (i.e., 5 observations lie at or beyond the VaR), which estimate of 99% VaR is most consistent with a simple order-statistic approach that places the quantile between the 5th and 6th largest losses?

The 99% VaR is USD 2.25 million. Five of 500 observations make up 1% of the tail, so the quantile lies between the 5th and 6th largest losses. Taking their midpoint, (2.40 + 2.10)/2, gives the estimate, rather than choosing either single observation.

  1. AUSD 2.25 millionCorrect
  2. BUSD 2.40 million
  3. CUSD 2.10 million
  4. DUSD 4.50 million

Explanation

With 500 observations, 1% equals 5 observations. The quantile falls between the 5th and 6th largest losses, so the midpoint is (2.40 + 2.10)/2 = USD 2.25 million. Using only the 5th loss ignores that the boundary lies between two points. Summing is meaningless for a quantile.

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