On this page
Use historical resampling when the observed record is a credible set of scenarios and you want to retain its empirical shape. Use Monte Carlo when you need scenarios drawn from an explicitly specified probability model, including outcomes beyond those observed. Neither output is a forecast: the historical method depends on the sample being relevant, while Monte Carlo depends on the model and its parameters.
The choice is about the source of each draw
In historical resampling, a draw is selected from returns already in the dataset, usually with replacement. The method does not require a named distribution, but it cannot draw a return outside that dataset. A short or unusually calm sample therefore leaves important possibilities unseen. Bootstrapping observed data and Monte Carlo analysis are both listed in CFA Institute’s Simulation Methods learning outcomes; its candidate body of knowledge places simulation and scenario analysis within Quantitative Methods.
In Monte Carlo, the analyst supplies a distribution, parameters and a rule for translating draws into values. It can generate a loss larger than any in the sample if the chosen model permits one. That range is conditional on the specification; a thin-tailed model can still understate severe losses. The exam decision is to identify the input assumption before comparing the outputs.
An illustrative pair of paths
Suppose an invented position begins at £100 and the only observed annual returns are a fall of 10%, no change and a rise of 10%. For a two-year historical bootstrap, select the fall followed by the rise, replacing the first draw before the second. The path ends at £99: £100 becomes £90, then £90 rises by 10% to £99. The method could also select the same return twice because draws are with replacement.
For a separate illustrative Monte Carlo run, assume annual returns are independently drawn from a normal distribution with mean zero and standard deviation 10%. Suppose its two random draws are a fall of 15% and a rise of 5%. Applying the same compounding rule gives £100, then £85, then £89.25. These are supplied example draws, not estimated market data or a likely path. Their purpose is to show that the assumed model can produce a return absent from the three historical observations.
What candidates tend to overclaim
- Historical does not mean future-proof. Resampling preserves only what is in the selected record; it cannot demonstrate that an unobserved tail is impossible.
- Modelled does not mean more accurate. Monte Carlo adds flexibility, but the distribution, dependence assumptions and valuation rule can all be wrong.
- One path is not a risk estimate. To estimate a distribution, repeat the drawing rule many times and summarise the resulting outcomes; the two paths above only expose the mechanics.
For revision, state the draw source, then the limitation, before interpreting any simulated percentile. The CFA programme page gives the wider exam context, while the Omni methodology explains the study approach.
Sources
- Simulation Methods | CFA Institute · cfainstitute.org · Retrieved
- Candidate Body of Knowledge (CBOK) | CFA Institute · cfainstitute.org · Retrieved
