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FRM Part II · FRM Exam Part II · Non-parametric Approaches

A risk analyst computes 1-day 95% VaR using basic historical simulation on 500 daily P&L observations of a portfolio. Losses are expressed as positive numbers. Which statement correctly describes how the VaR estimate is obtained?

Basic historical simulation sorts the observed P&L and reads the empirical 5th percentile loss, which with 500 observations is about the 25th worst outcome. It makes no distributional assumption. Averaging the tail losses would produce expected shortfall rather than VaR.

  1. AFit a normal distribution to the P&L and multiply the standard deviation by 1.645
  2. BSort the P&L observations and read off the loss that is exceeded by 5% of observations, about the 25th worst lossCorrect
  3. CAverage the 25 worst losses in the sample
  4. DWeight the most recent observations more heavily and then pick the 5th percentile

Explanation

Basic historical simulation is non-parametric: it ranks historical P&L and takes the empirical quantile. With 500 observations, 5% is 25 observations in the tail, so VaR is at about the 25th worst loss. Averaging the 25 worst losses gives expected shortfall, not VaR.

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