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

A risk manager runs a Monte Carlo simulation to estimate the expected value of a portfolio payoff. The standard error of the estimate with 10,000 independent draws is 0.50 (in USD millions). Ignoring other effects, how many independent draws are required to reduce the standard error to 0.10?

250,000 draws are needed. Monte Carlo standard error falls with the square root of the number of draws, so cutting it from 0.50 to 0.10 (a factor of five) requires 25 times as many draws, which is 10,000 multiplied by 25, or 250,000.

  1. A50,000
  2. B100,000
  3. C250,000Correct
  4. D20,000

Explanation

Standard error is proportional to 1/sqrt(N). Reducing it by a factor of 5 (0.50 to 0.10) requires N to increase by 5^2 = 25 times: 10,000 x 25 = 250,000. Choosing 50,000 wrongly scales linearly by 5.

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