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

A analyst applies the basic i.i.d. bootstrap to 500 daily returns of an asset whose returns show strong volatility clustering and positive autocorrelation, in order to estimate the standard error of the 10-day average return. Which is the most accurate assessment?

The i.i.d. bootstrap likely understates the standard error. Resampling single observations destroys autocorrelation and volatility clustering, which would otherwise increase the variability of multi-day averages. A block bootstrap, which resamples consecutive blocks, preserves the dependence and is more appropriate.

  1. AThe method likely understates the standard error because resampling individual observations destroys the serial dependence, so a block bootstrap would be more appropriateCorrect
  2. BThe method likely overstates the standard error because resampling with replacement adds extra noise that a block bootstrap would remove
  3. CThe method is unbiased because the bootstrap never requires independence of observations
  4. DThe method is valid only if the number of resamples equals the sample size of 500

Explanation

The i.i.d. bootstrap assumes observations are independent. With positive autocorrelation, the variance of multi-day averages is larger than under independence, and random resampling breaks that dependence, so the standard error is understated. Block bootstrap resamples consecutive blocks to retain dependence. The number of resamples is unrelated to validity.

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