FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
A simulation of a portfolio's one-day loss uses 10,000 independent draws and estimates the mean loss as 2.0 million with sample standard deviation 6.0 million. The team wants to cut the standard error of the estimated mean to one-third of its current level, using plain Monte Carlo with the same dispersion. Approximately how many draws are required?
About 90,000 draws are needed. Standard error falls with the square root of N, so cutting it to one-third requires nine times as many draws: from 10,000 to 90,000. Merely tripling the draws would reduce error by only about 42 percent.
- A30,000
- B90,000Correct
- C100,000
- D270,000
Explanation
Standard error = s/sqrt(N). Current SE = 6/100 = 0.06 million. Target SE = 0.02 million, so sqrt(N) = 6/0.02 = 300 and N = 90,000. Tripling the draws to 30,000 only reduces SE by a factor of about 1.73.
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