Contrast historical simulation with Monte Carlo simulation and with bootstrap resampling
The idea
Three simulation methods differ in where their scenarios come from. Historical simulation replays actual past periods once each, in order. Bootstrap resampling draws observed returns at random with replacement, so it keeps the empirical distribution yet can build far more paths than history supplies. Monte Carlo simulation draws from probability distributions the analyst specifies, which allows outcomes more extreme than any observed and makes it easy to test alternative assumptions, but exposes the results to model risk if the distribution or its parameters are wrong. Running more Monte Carlo trials reduces sampling error, not model error. Both data-based methods assume the sample is representative of the future.
A practice question
Which simulation method builds scenarios by sampling observed returns at random with replacement?
- Bootstrap resampling — correct
- Historical simulationWhy not: Historical simulation replays each past period once, in order, rather than drawing at random.
- Monte Carlo simulationWhy not: Monte Carlo draws from an assumed probability distribution, not from the observed returns.
Bootstrapping treats the observed sample as the population and draws from it randomly with replacement, so it can build many more paths than the data contain.
A harder one
Which method can generate a single-period return more extreme than any in the historical record?
- Bootstrap resamplingWhy not: The bootstrap only reuses observed returns, so no single draw can exceed the historical extremes.
- Historical simulationWhy not: Historical simulation replays past moves, so its single-period outcomes are bounded by the sample.
- Monte Carlo simulation — correct
Because Monte Carlo draws from a specified distribution, it can produce values outside the observed range. Both historical methods are limited to returns that actually occurred.
The hardest tier
Which weakness do historical simulation and bootstrap resampling share?
- Both require a parametric distributionWhy not: Neither method specifies a distribution; that requirement belongs to Monte Carlo simulation.
- Both assume the sample represents the future — correct
- Both strip fat tails out of the dataWhy not: Both keep whatever fat tails the observed data contain, as they reuse actual returns.
Both methods draw only on observed data, so if the future differs from the sample period (a new regime or an unseen shock) the results will be misleading.
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