BUSINFO 705 Chap.4 Monte Carlo Simulation for Risk
Monte Carlo Simulation for Risk
This chapter replaces a single forecast with repeated scenarios. It assigns distributions to uncertain inputs, generates a coherent set of draws for each trial and sends them through a verified spreadsheet relationship. The output distribution is then read through its mean, standard deviation, loss probability and intervals.
Particular care is given to the difference between a probability interval for individual outcomes and a confidence interval for an estimated mean. The workflow validates the deterministic model before randomness is introduced, inspects trial rows for support and dependency errors, and defines stability in decision-relevant units rather than relying on a large row count.
What this chapter covers
- 01
Input distributions and parameter evidence
- 02
Random draws in Excel
- 03
Coherent simulation trials
- 04
Output histograms and summary statistics
- 05
Loss probability at a threshold
- 06
Probability and confidence intervals
Worked example · free
Interpret a project risk simulation
- 1State the simulated mean profit of $82,000 under the current input model.
- 2Calculate loss probability as 150/2,000=7.5%.
- 2Interpret the central interval as a range for individual simulated outcomes, not confidence about the mean.
- 2Connect the risk-return profile to tolerance and identify the input most associated with adverse trials.
Key terms
- Simulation trial
- One coherent set of random input draws and the model output they produce.
- Input distribution
- A probability model representing uncertainty in one model parameter.
- Output distribution
- The collection of model results generated across repeated simulation trials.
- Loss probability
- The simulated proportion of outputs below the defined zero-profit threshold.
- Probability interval
- An interval summarising the central spread of individual simulated outputs.
- Monte Carlo error
- Sampling variation in a simulation estimate caused by using finitely many random trials.
Monte Carlo Simulation for Risk FAQ
Why use simulation instead of three scenarios?
Three scenarios show selected possibilities but not their relative likelihood. Simulation draws from input distributions many times and creates an output distribution, letting you estimate threshold probabilities, variability and intervals under the stated uncertainty model.
Does a large trial count validate the model?
No. More trials reduce random sampling noise in simulation estimates, but they do not make an implausible input distribution or incorrect spreadsheet relationship true. Validate formulas, supports, parameters and dependencies separately before trusting the output.
What is the difference between two interval types?
A probability interval describes where individual simulated outcomes tend to fall. A confidence interval for the mean describes uncertainty around the estimated average because the simulation uses a finite sample. They answer different questions and should be labelled explicitly.
What makes a simulation trial coherent?
One row should contain all uncertain draws for the same scenario and the single output generated from them. Combining demand from one row with cost or price from another breaks the intended joint scenario. Inspect several complete rows before copying formulas across thousands of trials.
How should I define simulation stability?
Choose a tolerance in decision units before rerunning, such as the largest acceptable change in loss probability or mean profit. Compare new runs against that tolerance. Stable estimates reduce finite-sample noise, but they do not establish that input distributions, dependencies or spreadsheet relationships are valid.
Assessment move
Verify the deterministic spreadsheet with a hand-calculated scenario before adding random functions. For each uncertain input, write its support, distribution, parameters and evidence source. Inspect several generated draws to ensure they stay within the intended support. Build one trial row with all inputs and one output, then copy it only after the row is correct.
Summarise the output with a histogram, mean, standard deviation and the probability of crossing the decision threshold. Practise explaining the difference between an outcome probability interval and a confidence interval for the mean. Rerun the model to judge whether the recommendation is stable to Monte Carlo sampling noise. Force low, central and high input values through the model before restoring random draws.
Inspect several extreme output rows and decide whether each is genuine tail behaviour or a formula fault. Check that all inputs in one row belong to the same trial and that copied references point to the intended parameters. Write down where independence is assumed, then invent a plausible dependency and predict how it could change the output tail.
Define a stability tolerance before increasing the trial count, such as a maximum acceptable change in loss probability. Compare two independent runs against that tolerance while keeping the difference between numerical stability and assumption sensitivity explicit. Preserve one set of trial values for audit and recompute a handful of outputs by hand.
Finish with a decision note that gives the relevant threshold probability, labels the interval type, names the most influential assumption and states the observation that should trigger a rerun.
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