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

A risk manager bootstraps daily returns of an equity portfolio by drawing individual days at random with replacement from five years of data. The returns display strong volatility clustering. What is the main consequence of using the iid bootstrap here?

The iid bootstrap shuffles days independently, which removes the ordering that creates volatility clustering. Consequently, simulated multi-day paths lack persistent high-volatility episodes, and risk measures over longer horizons are likely understated. Block bootstrap methods are used to preserve some of this dependence.

  1. AThe bootstrapped distribution will have a mean that is biased to zero
  2. BThe resampled series destroys the time-dependence in volatility, so multi-day risk estimates will tend to understate the clustering effectCorrect
  3. CThe estimated standard errors will be exactly zero
  4. DThe method will produce negative variances in some replications

Explanation

Random daily draws break the serial dependence in squared returns, so volatility clustering is lost. Multi-day horizon losses from bursts of high volatility are then understated. The mean is not forced to zero, standard errors are not zero, and variances cannot be negative.

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