Skip to content

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

Two simulation designs estimate the same expected value with the same 10,000 draws. Design A uses plain independent draws, whose payoff variance is 64. Design B uses a variance reduction technique that lowers the payoff variance to 16 with the same number of draws and no extra cost. What is the ratio of Design B's standard error to Design A's?

The ratio is 0.50. Design A's standard error is 8 divided by 100, or 0.08, and Design B's is 4 divided by 100, or 0.04. Standard error depends on the square root of variance, so a fourfold variance cut only halves it.

  1. A0.25
  2. B0.50Correct
  3. C4.00
  4. D0.0625

Explanation

Standard error = sqrt(variance/N). A: sqrt(64/10,000) = 0.08. B: sqrt(16/10,000) = 0.04. Ratio = 0.04/0.08 = 0.50. The option 0.25 is the variance ratio, mistakenly used as the standard error ratio.

Did you get it right without looking?

One question tells you little. A timed set on Simulation and Bootstrapping shows your real accuracy, how long you take and where you lose marks.

Practise Simulation and BootstrappingFree diagnostic mock

More Simulation and Bootstrapping questions