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

A risk manager uses Monte Carlo to estimate the 99% one-day VaR of a portfolio using 1,000 simulated losses. She wants to compare this with an estimate based on 10,000 trials. Which statement is most accurate?

The 99% VaR sits at about the 10th largest loss in 1,000 trials and the 100th largest in 10,000 trials. The larger simulation has many more tail observations, so its quantile estimate has smaller sampling error, though both target the same true VaR.

  1. AThe 1,000-trial VaR is the 10th largest loss, and the 10,000-trial VaR is the 100th largest loss; the larger run has less sampling error in the tail estimate.Correct
  2. BThe 1,000-trial VaR is the 99th largest loss, so the estimate is unbiased regardless of the sample size.
  3. CBoth estimates have identical sampling error because the confidence level is the same.
  4. DThe 10,000-trial VaR must be larger because more trials always produce more extreme losses on average, which biases VaR upward.

Explanation

At 99% confidence, 1% of trials lie in the tail: 10 of 1,000 and 100 of 10,000 (roughly; the quantile sits at about the 10th/100th largest loss). Quantile estimation error shrinks as the number of tail observations grows, so the larger run is more precise. The other options misstate the rank or the dependence on sample size.

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