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

A risk manager compares the 99% 1-day VaR from historical simulation using 1,000 days of data against a parametric normal VaR. Which statement about historical simulation is most accurate?

Historical simulation can capture fat tails and nonlinear dependence present in actual data without distributional assumptions, but it is limited by the sample: if few extreme events occurred in the window, the 99% estimate rests on very few tail observations and may understate future risk.

  1. AIt requires an assumption about the distribution of returns but not about their correlations
  2. BIt can capture fat tails and nonlinearity in the empirical data, but is limited by the historical sample's coverage of extreme eventsCorrect
  3. CIt always gives a higher VaR than the parametric approach
  4. DIt eliminates estimation error because it uses actual data

Explanation

Historical simulation is non-parametric and uses actual joint behavior, so it captures fat tails and correlations present in the sample. However, if the sample has few extreme events, the 99% quantile is based on only about 10 observations and may miss future shocks. It does not always exceed parametric VaR, and it still has sampling error.

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