Who this is for — Anyone who wants to see how much a metric or drawdown may change when the path changes, without mistaking a cloud of simulations for a forecast of the future.
Monte Carlo denotes a family of methods that generates many realisations from a probabilistic model. The bootstrap resamples the available observations to approximate the distribution of a statistic. In trading, they are used to explore uncertainty in return, drawdown, loss sequence, parameters and scenarios.
Every simulation is conditional on a generative mechanism: distribution, dependence, stationarity, blocks, parameters and costs. It cannot repair data leakage, survivorship bias, selection among thousands of models or unrealistic fills. Nor can it credibly invent a regime, crisis or operational constraint absent from the input unless an explicit model introduces it. Neither method forecasts future outcomes.
Different methods, different questions
| Method | What it generates | Properties preserved | Main risk |
|---|---|---|---|
| Order permutation | reorders the same outcomes once | set of outcomes and total P&L before compounding | destroys dependence and does not estimate new outcomes |
| IID bootstrap | draws observations with replacement | empirical marginal distribution | treats units as independent and identically distributed |
| Block bootstrap | resamples contiguous blocks | part of local dependence | result is sensitive to block choice and stationarity conditions |
| Stationary bootstrap | uses blocks of random length | weak dependence under assumptions | length parameter and regime changes |
| Parametric Monte Carlo | simulates from an estimated distribution or process | structure specified by the model | model risk and unrepresented tails |
| Scenario simulation | imposes shocks or narratively coherent states | risks selected by the designer | incomplete coverage and unidentified probabilities |
“Monte Carlo” does not automatically mean that the model is parametric; “bootstrap” does not automatically mean that dependence is preserved. A serious description names the algorithm, resampled unit, block size, number of replications, seed, parameter-estimation method and aggregation procedure.
What is being resampled?
A trade is often an ambiguous unit. Several trades may depend on the same signal or market episode; overlapping positions share returns; cross-sectional strategies produce many trades at the same rebalance. An IID bootstrap of individual trades treats them as independent trials and may understate uncertainty.
Possible units include:
- portfolio returns by period;
- cross-sectional vectors at the same timestamp;
- time blocks of returns and states;
- trading episodes or campaigns defined before the outcome;
- residuals from a model, while keeping the systematic component separate;
- estimated parameters and innovations simulated from a specified process.
The choice must preserve the dependence relevant to the question. When studying portfolio drawdown, resampling every leg separately can erase the correlations that matter most during critical episodes.
Order, compounding and drawdown
Without compounding and path-dependent constraints, reordering the same P&L does not change the final sum; it does change the sequence and therefore the maximum drawdown. With percentage sizing, margin, liquidation, volatility targeting or limits, order may also change final capital and future positions.
Statistics calculated for each simulated path may include:
- maximum drawdown and recovery duration;
- cumulative or compounded return;
- conditional probability of crossing a defined limit;
- turnover and margin requirements;
- distribution of Sharpe, expectancy or other estimators;
- sensitivity of the suspension criterion.
The resulting quantile is not an objective probability of what will happen. It is the probability within the simulated model, given the input and assumptions.
Block bootstrap and dependence
The block bootstrap draws contiguous sequences to preserve part of the autocorrelation, volatility clustering and co-movement. Block length creates a trade-off: blocks that are too short lose dependence; blocks that are too long reduce the number of units that can effectively be recombined.
The stationary bootstrap of Politis and Romano uses random lengths, producing a resampled series that is stationary in the theoretical design. This method also requires conditions and a choice of expected length. If the process changes regime structurally, treating all blocks as exchangeable may be misleading.
It is useful to compare several motivated specifications, not to search for the one producing the most favourable interval. Sensitivity to the method is itself a result.
Parametric simulation and scenarios
A parametric model can represent dynamics unavailable through simple resampling, but it introduces further assumptions. Normality, independence, volatility process, correlations and regime transitions must be stated and diagnosed. Estimating parameters from the same small sample and then simulating them as certain understates estimation uncertainty.
Scenarios can add shocks that are absent or infrequent: gaps, wider spreads, adverse correlations, higher borrow costs, delays and margin calls. They need not be assigned a precise probability to serve as vulnerability tests. It is, however, incorrect to mix deterministic scenarios and probabilistic quantiles as though they had the same meaning.
Illustrative example
A strategy has daily returns with volatility clustering. The IID bootstrap produces a narrow fan; a block bootstrap produces more concentrated loss sequences and a wider range of drawdowns. It does not follow that the second method is automatically “true”: the comparison reveals that the conclusion depends on temporal dependence.
The analyst documents both specifications, justifies the range of block lengths and adds a separate scenario with higher costs and wider spreads. The analyst neither selects the most convenient number nor presents a quantile as a guarantee.
Reproducible protocol
- Define the question and statistic before simulation.
- Identify the unit and dependence that the method must preserve.
- State the model, parameters, blocks, replications and seed.
- Include compounding, sizing, costs and constraints when they change the path.
- Propagate estimation uncertainty when materially relevant.
- Compare motivated specifications and show sensitivity.
- Separate probabilistic quantiles from scenarios without assigned probabilities.
- Preserve code, inputs and outputs for reproducibility.
Simulation is a lens on conditional uncertainty. It is most useful when it makes visible what the single historical path conceals and least useful when it adds thousands of decimal places to a weak model.
Sources
- Bradley Efron, Bootstrap Methods: Another Look at the Jackknife — foundational paper on bootstrap resampling and estimation.
- Dimitris N. Politis and Joseph P. Romano, The Stationary Bootstrap — random-length block bootstrap for weakly dependent, stationary data.
- Andrew W. Lo, The Statistics of Sharpe Ratios — the effect of temporal dependence on the distribution and annualisation of the Sharpe ratio.
- Joseph Simonian, CFA Institute Research Foundation, Investment Model Validation: A Guide for Practitioners — the role of Monte Carlo, bootstrap and stress testing in investment-model validation.