FRM Part I · FRM Exam Part I · Calculating and Applying VaR
A Monte Carlo VaR estimate at 95% confidence for a portfolio is USD 2.00 million using 5,000 trials. The analyst wants to cut the standard error of the VaR estimate (due to sampling) roughly in half, holding everything else constant. Approximately how many trials are needed?
About 20,000 trials are needed. Monte Carlo sampling error shrinks in proportion to one over the square root of the number of trials, so halving the error requires four times as many trials, which is 5,000 multiplied by 4.
- A10,000
- B20,000Correct
- C25,000
- D7,500
Explanation
Sampling error of a quantile estimate falls with the square root of the number of trials. Halving the error requires multiplying trials by 4: 5,000 × 4 = 20,000. Doubling to 10,000 would only reduce error by a factor of about 1.41.
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