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FRM Part I · FRM Exam Part I · Simulation and Bootstrapping

A bank estimates the 99% VaR of a portfolio by Monte Carlo simulation. Which statement about sampling error in this estimate is most accurate compared with estimating the simulated mean using the same number of trials?

Tail quantile estimates such as 99% VaR typically have larger sampling error than the simulated mean. The quantile relies on few observations in the sparse tail rather than an average of all draws, so results vary more between simulation runs and need more trials for the same accuracy.

  1. AThe VaR estimate has the same sampling error because both are averages of the same draws
  2. BThe VaR estimate typically has larger sampling error because it depends on few observations in the tailCorrect
  3. CThe VaR estimate has no sampling error because the quantile is deterministic given the model
  4. DThe VaR estimate has smaller sampling error because extreme outcomes are averaged out

Explanation

A 99% quantile is determined by observations in the sparse tail, so with N trials only about 1% of draws inform it, making it noisier than the mean. It is not an average of all draws, and it is still random across simulation runs. Sampling error does not vanish simply because the model is fixed.

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