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FRM Part II · FRM Exam Part II · Estimating Market Risk Measures: An Introduction and Overview

A risk analyst uses 500 daily P&L observations to estimate 1-day 95% historical simulation VaR. Which statement best describes how the estimate is obtained?

Historical simulation VaR is the empirical quantile of ranked past P&L, with no distribution assumed. With 500 observations at 95%, it is about the 25th worst loss. Averaging the worst 25 losses would instead give expected shortfall.

  1. AFit a normal distribution to the P&L and multiply the standard deviation by 1.645
  2. BRank the P&L observations and read off the loss level exceeded by about 5% of observations, roughly the 25th worst lossCorrect
  3. CAverage the 25 worst losses to obtain the loss that is exceeded in the tail
  4. DScale the largest observed loss by the square root of the confidence level

Explanation

Historical simulation is non-parametric: it sorts historical P&L and takes the empirical quantile. At 95% with 500 observations, 5% is 25 observations, so VaR is around the 25th worst loss. Averaging the tail losses gives expected shortfall, not VaR.

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