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Monte Carlo simulation

How can monte carlo simulation support strategic choice or positioning?

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Contents

The Monte Carlo simulation is a mathematical problem-solving and risk a ssessment technique that approximates the probability of certain outcomes, and therefore the risk of certain outcomes, using computerised.

Monte Carlo simulation is a computational method for propagating uncertainty through a model. Instead of calculating one outcome from one set of assumptions, it repeatedly samples values from specified probability distributions and produces a distribution of possible outcomes. It can clarify risk, but it cannot make weak assumptions true.

When to use it

Use Monte Carlo simulation when several uncertain inputs interact and a decision depends on the range, likelihood or tail of resulting outcomes.

It is useful for product launches, investment appraisal, acquisition, project duration and cost, capacity, insurance and engineering. It helps answer:

Which launch has the most attractive risk-adjusted outcome?

What range of returns could an investment produce?

Which acquisition assumptions drive downside?

How long might a complex project take, and what budget contingency is justified?

Use simpler sensitivity analysis when only a few scenarios matter or reliable distributions cannot be estimated.

Origins

The modern method was developed at Los Alamos during and after the Second World War by researchers including Stanisław Ulam, John von Neumann, Nicholas Metropolis and Robert Richtmyer. Random sampling helped solve otherwise intractable physical calculations. The name refers to Monte Carlo’s association with games of chance, not to a claim that the method is gambling.

What it is

A simulation begins with a causal model. Uncertain inputs receive distributions that represent plausible values and their likelihoods. The computer samples a value for each input, calculates the outcome and repeats the process many times.

For a new plant, completion might plausibly occur in 12. months, 14 months, 16 months or 24 months, but those points alone do not define a distribution. Analysts must choose its shape, bounds and dependencies from evidence and expert elicitation.

The output can show expected results, percentiles, threshold probabilities and tail losses. It does not automatically show the “best case” and “worst case”: unbounded or poorly specified distributions can produce implausible extremes, while omitted risks never appear.

How to use it

Define the decision and model equations before choosing software. Identify uncertain drivers, gather relevant data and elicit expert judgement using a documented process. Select distributions that respect physical or commercial bounds.

Model correlations. Costs, delays, demand and prices rarely vary independently; ignoring dependence can materially understate or overstate risk. Separate parameter uncertainty from structural uncertainty and use scenarios for risks the model cannot represent.

Run enough iterations for the reported tail measures to stabilise. Validate code with known cases, inspect sampled values, compare outputs with historical experience and test sensitivity to distribution choices. Use reproducible random seeds for debugging, then confirm findings across seeds.

Excel or specialist tools can run simulations, but software convenience is not model validation. Record ownership, version, sources and review.

Practical example

A project has several sequential components. A fixed forecast says total completion will take 15 months, but each component is uncertain.

After modelling component durations and their dependencies, the simulation reports a 42 per cent chance of completion within 15 months and an 82 per cent chance within 18 months. Those estimates help plan contingency and stakeholder commitments. They are only credible if the input ranges, relationships and project logic are credible; the additional three months should be examined as an operational scenario rather than accepted mechanically.

Top practical tip

Show the distributions, correlations and assumptions that drive the result. Pair percentile outputs with sensitivity analysis so decision makers know what evidence deserves improvement.

Top pitfall

Thousands of iterations do not compensate for omitted variables, false independence or guessed distributions. Simulation quantifies the model you built, not reality itself.