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

Which limitation is most characteristic of basic historical simulation VaR at a 99.9% confidence level using two years of daily data?

At 99.9% with about 500 observations, the tail holds roughly half a data point, so the VaR estimate is unstable and cannot exceed the worst observed loss. Historical simulation does not assume normality or need a covariance matrix, and it captures fat tails present in the sample.

  1. AIt requires the returns to be normally distributed
  2. BIt cannot incorporate fat tails or skewness that are in the data
  3. CFew or no observations lie in the extreme tail, making the estimate unstable and bounded by the worst observed lossCorrect
  4. DIt requires a covariance matrix of risk factors to be estimated

Explanation

Two years is about 500 observations, so the 0.1% tail contains roughly half an observation. The estimate depends on one or two extreme points and cannot exceed the worst historical loss. Historical simulation does capture fat tails and needs no covariance matrix or normality assumption.

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