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

A risk manager bootstraps daily returns of an asset by drawing individual returns independently with replacement, but the returns show strong volatility clustering. What is the main problem with this approach?

An iid bootstrap shuffles returns independently, which destroys time dependence such as volatility clustering. Simulated paths then look unclustered and can misstate multi-day risk. Block bootstrapping, which resamples consecutive blocks, is a common remedy. The method does not impose normality or a zero mean.

  1. AIt increases the standard error because the sample size shrinks
  2. BIt destroys the time-series dependence in the data, so simulated paths do not display volatility clusteringCorrect
  3. CIt forces the mean of the simulated returns to equal zero
  4. DIt makes the simulated returns normally distributed

Explanation

The standard iid bootstrap assumes observations are independent. Drawing returns one at a time breaks the serial dependence in volatility, so simulated paths understate clustering and multi-day risk. Block bootstrap methods are a remedy. The sample size does not shrink, the mean is not forced to zero, and normality is not imposed.

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