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

A risk manager uses the iid bootstrap on 500 daily P&L observations to estimate 99% VaR. Volatility is known to cluster strongly, with large losses following large losses. Which is the most important limitation of the plain iid bootstrap here?

The main limitation is that the iid bootstrap treats observations as independent and shuffles them, which destroys volatility clustering and other serial dependence. Resampled series therefore misrepresent the dynamics of the data. Block bootstrap methods are used to preserve some dependence.

  1. AIt resamples observations as independent, destroying the serial dependence in volatility, so the resampled data do not reflect clusteringCorrect
  2. BIt requires the returns to be normally distributed to be valid
  3. CIt cannot be used to estimate quantiles, only means
  4. DIt always overstates VaR because resampling with replacement duplicates the worst loss

Explanation

The iid bootstrap assumes observations are independent, so random resampling breaks time-ordering and volatility clustering. Approaches such as block bootstrap address this. The bootstrap does not require normality and can estimate quantiles; it does not systematically overstate VaR.

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