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

An analyst estimates the expected payoff of a derivative by Monte Carlo simulation. The standard deviation of the simulated payoffs is 8.0 and the analyst uses 400 independent draws. What is the standard error of the estimated mean payoff?

The standard error is 0.40. It equals the standard deviation of the simulated payoffs, 8.0, divided by the square root of the number of draws, which is 20 for 400 draws. Dividing by N itself instead of its square root would wrongly give 0.02.

  1. A0.02
  2. B0.40Correct
  3. C2.00
  4. D0.20

Explanation

Standard error = sigma / sqrt(N) = 8.0 / sqrt(400) = 8.0 / 20 = 0.40. The option 0.20 comes from dividing by N=1600's root or mistakenly halving. The option 2.00 uses sigma/sqrt(16) style errors, and 0.02 divides sigma by N (400) rather than by its square root.

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