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CFA Level I Exam · Simulation of Financial Asset Prices and Returns

Limitations of Monte Carlo Simulation and Bootstrap Resampling

Updated 7 October 2026 · Fact-checked

Monte Carlo simulation draws random values from an assumed distribution, so its results are only as good as its assumptions. It gives answers, not analytic insight. Historical simulation uses actual past data (changes in the variable) and makes no distributional assumption. Bootstrap resamples observed data with replacement.

Understand Limitations and Bootstrap Resampling

Simulation is a statistical tool. You build a model, feed it random inputs, run it thousands of times and study the spread of outputs. It is useful when no neat formula exists, for example pricing a path-dependent option or testing a portfolio under many scenarios.

Its main limitation is dependence on assumptions. In Monte Carlo simulation, you choose the distribution (such as normal or lognormal), its parameters (mean, volatility) and the correlations between variables. If these are wrong, the output is wrong, however many trials you run. More trials reduce sampling error, not model error. This is the "garbage in, garbage out" problem.

A second limitation is that simulation gives answers, not insight. It is not an analytic method. An analytic formula such as Black-Scholes-Merton shows how value changes with each input. A simulation gives one set of numbers for one set of inputs. To see sensitivity, you must re-run it. It can also be complex, slow and costly, and it provides only statistical estimates, not exact values.

Historical simulation uses actual past changes in the variable, for example past daily returns. It makes no assumption about the distribution. But it assumes the future will look like the past, so it cannot capture events that did not occur in the sample period. It also only uses the one path history gave you.

Bootstrap resampling repeatedly draws observations from the observed sample with replacement, so each draw is from the same data. Each resample is the same size as the original. You compute the statistic (mean, median, standard deviation) on each resample and study the resulting distribution. It needs no assumption about the population distribution and works for statistics with no known formula. Its limit: it is only as good as the sample. If the sample is small or unrepresentative, the bootstrap is too. Monte Carlo, by contrast, draws from a specified distribution.

Key formulas to remember

Bootstrap resample size
Resample size = original sample size n; draws made with replacement
Each observation can appear more than once, or not at all, in a resample.
Bootstrap standard error of a statistic
SE = standard deviation of the statistic across the B resamples
Compute the statistic on each resample, then take the standard deviation of those B values.
Monte Carlo vs historical vs bootstrap source of random draws
Monte Carlo: assumed distribution | Historical simulation: actual past data | Bootstrap: observed sample, with replacement
Use this to classify any exam description quickly.

How to solve Limitations and Bootstrap Resampling questions

Use this approach for any conceptual question comparing simulation methods or asking about their limits.

  1. 1Identify the method named or described: Monte Carlo, historical simulation or bootstrap.
  2. 2Ask where the random inputs come from: an assumed distribution, actual past data, or the sample drawn with replacement.
  3. 3Check what the question asks: a strength, a limitation, or a difference.
  4. 4For limitations, link to the source: assumed distribution and parameters for Monte Carlo; past repeating itself for historical simulation; sample quality for bootstrap.
  5. 5Remember that simulation gives statistical estimates, not analytic insight or exact answers.
  6. 6Eliminate options that claim more trials fix wrong assumptions, or that bootstrap draws without replacement.
  7. 7For calculations, compute the statistic for each resample, then summarise across resamples.

Quickest way: Source-of-draws test

When to use it: Use when you have about 90 seconds and the question compares or classifies simulation methods.

  1. Ask: where do the draws come from?
  2. Assumed distribution means Monte Carlo, so the weakness is assumptions.
  3. Actual history means historical simulation, so the weakness is the past may not repeat.
  4. Sample with replacement means bootstrap, so the weakness is sample quality.
  5. Pick the option matching that link and drop the other two.

Common mistakes in Limitations and Bootstrap Resampling

  • Believing more Monte Carlo trials fix a wrong model.

    Large trial counts feel like accuracy.

    Fix: More trials cut sampling error only. Wrong distribution or parameters still produce wrong output.

  • Saying bootstrap samples without replacement.

    Confusion with ordinary sampling from a population.

    Fix: Bootstrap always draws with replacement, and each resample matches the original sample size.

  • Saying historical simulation assumes a normal distribution.

    Mixing it up with Monte Carlo or parametric methods.

    Fix: Historical simulation uses actual past observations, so it needs no distributional assumption.

  • Treating simulation as giving analytic insight.

    Simulations produce precise-looking numbers.

    Fix: It gives statistical estimates for given inputs. Analytic formulas show how outputs depend on inputs.

  • Thinking bootstrap can recover information not in the sample.

    Resampling seems to create new data.

    Fix: Bootstrap only reuses the observed data. A biased or tiny sample gives a biased or unreliable result.

Worked examples

Example 1

An analyst estimates portfolio risk by drawing 100,000 random returns from a normal distribution with parameters set from judgment. Which is the most significant limitation of this approach? A) The results cannot be computed quickly. B) The results depend on the assumed distribution and parameters. C) The results use actual historical returns only.

Show the solution
  1. The draws come from an assumed distribution, so this is Monte Carlo simulation.
  2. Monte Carlo output is driven by the chosen distribution and inputs.
  3. Option A is not the key limitation; option C describes historical simulation, not this method.
  4. Option B matches the main limitation.

Answer: B

Example 2

A sample has 5 observed returns: 2%, 4%, 6%, 8%, 10%. A bootstrap resample is drawn with replacement: 4%, 4%, 10%, 8%, 2%. What is the mean of this resample? A) 5.0% B) 5.6% C) 6.0%

Show the solution
  1. The resample has 5 draws, the same size as the original. The repeated 4% is allowed because bootstrap uses replacement.
  2. Sum: 4 + 4 + 10 + 8 + 2 = 28.
  3. Mean: 28 ÷ 5 = 5.6%.
  4. Option A (5.0%) is below the result and option C (6.0%) is the original sample mean, a trap. The answer is B.

Answer: B (5.6%)

Exam tips

  • Match each limitation to its method: assumptions for Monte Carlo, past-repeats for historical, sample quality for bootstrap.
  • Watch for the phrase with replacement. It signals bootstrap.
  • Reject any option saying simulation yields exact or analytic results.
  • If calculating a resample statistic, check the resample size equals the original size first.

Practice questions from Simulation of Financial Asset Prices and Returns

Limitations and Bootstrap Resampling: frequently asked questions

What are the limitations of Monte Carlo simulation?

Results depend on the assumed distribution, parameters and correlations. It gives statistical estimates, not analytic insight into how inputs drive outputs. It can also be complex and computationally costly.

What is the difference between Monte Carlo and historical simulation?

Monte Carlo draws from an assumed probability distribution. Historical simulation uses actual past observations and so needs no distribution assumption. Its weakness is that the future may differ from the past.

What is bootstrap resampling in finance?

Bootstrap repeatedly draws observations with replacement from your observed sample, each resample matching the original size. You compute a statistic on each resample to estimate its distribution and standard error, without assuming a population distribution.

Does bootstrap need a normal distribution?

No. It relies only on the observed sample. That makes it useful for statistics with no known formula, though a poor sample gives poor results.