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

A firm simulates portfolio losses with a Monte Carlo model that draws asset returns from a multivariate normal distribution calibrated to calm-period data. During a crisis, actual losses far exceed the simulated 99.9% quantile. Which is the best diagnosis based on known simulation limitations?

This is model risk. The simulation assumed normal returns and calm-period correlations, which understate fat tails and crisis co-movement. More trials only reduce sampling error, not the error from a wrong model or inputs, so the high quantile loss was badly underestimated.

  1. AThe number of trials was too large, producing excessive sampling error
  2. BMonte Carlo output cannot be used for quantiles above 99%
  3. CModel risk: the assumed distribution and calibrated correlations did not reflect crisis dynamics, and more trials cannot fix thisCorrect
  4. DThe random number generator was truly random, so results are unreliable

Explanation

Simulation output is only as good as its assumed model and inputs. Normality and calm-period correlations understate fat tails and crisis correlation. Increasing trials reduces sampling error but not model error. Large trial counts reduce, not increase, sampling error, and Monte Carlo can estimate high quantiles.

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