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

A risk manager uses basic historical simulation with 500 daily P&L observations to estimate 1-day 99% VaR for a trading portfolio. Which statement best describes how the VaR is obtained?

Historical simulation sorts observed P&L outcomes and reads the loss at the chosen quantile. With 500 observations at 99% confidence, VaR sits near the fifth-worst loss. No distribution is assumed, and averaging tail losses would instead give expected shortfall.

  1. AFit a normal distribution to the 500 P&L values and multiply the standard deviation by 2.33
  2. BSort the 500 P&L values and read the loss at the 1% quantile, which lies near the fifth-worst lossCorrect
  3. CRun 10,000 Monte Carlo paths from a calibrated stochastic process and take the 99th percentile
  4. DAverage the five worst losses in the sample to obtain the 99% loss

Explanation

Basic historical simulation is non-parametric: it ranks historical P&L and picks the quantile. With 500 observations, 1% corresponds to 5 observations in the tail, so VaR is around the fifth-worst loss. Averaging the tail losses gives expected shortfall, not VaR.

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