Monte Carlo Risk Simulation

Dashboard

Visual summary of simulation results with probability distributions, confidence intervals, and key risk metrics. Covers output distribution histograms, confidence interval display, key risk metrics at a glance and scenario probability breakdown.

Assumptions

Central parameter configuration for the simulation including iteration count, confidence levels, and random seed. Covers number of iterations, confidence level settings, random seed control and global model parameters.

Distributions

Define probability distributions for each uncertain input variable — normal, lognormal, triangular, uniform, and more. Covers multiple distribution types, parameter inputs (mean, std dev, min, max), distribution visualization and correlation matrix.

Simulation Engine

The core computation sheet that generates random samples and calculates outputs for each iteration. Covers random number generation, inverse distribution sampling, output calculation per iteration and iteration tracking.

Revenue Risk

Applies simulation to revenue forecasts, modeling uncertainty in volume, pricing, and market conditions. Covers revenue driver distributions, demand uncertainty modeling, price volatility scenarios and revenue-at-risk calculation.

Cost Risk

Models cost uncertainty including input prices, labor costs, and operational variability. Covers cost driver distributions, supply price volatility, operational efficiency variance and cost-at-risk metrics.

Portfolio VaR

Calculates Value at Risk for a portfolio of assets or exposures using simulation-based methodology. Covers portfolio var at multiple confidence levels, conditional var (cvar / expected shortfall), individual position contribution and diversification benefit.

Sensitivity

Identifies which input variables have the greatest impact on output uncertainty. Covers tornado diagram data, correlation analysis, rank-order sensitivity and key risk driver identification.

Scenario Analysis

Compares specific named scenarios (base, upside, downside, stress) against the simulated distribution. Covers named scenario definitions, probability of each scenario, scenario vs. distribution comparison and tail risk analysis.

Statistics

Comprehensive statistical summary of all simulation outputs. Covers mean, median, mode, standard deviation and variance, skewness and kurtosis and percentile table (1st through 99th).

Error Check

Validates simulation integrity and flags potential issues. Covers distribution parameter validation, convergence check, output range reasonableness and formula integrity.

Value at Risk (VaR)

VaR = μ − zα × σ

The maximum expected loss at a given confidence level over a specified time period. The simulation provides an empirical VaR from the output distribution.

Expected Shortfall (CVaR)

CVaR = E[Loss | Loss > VaR]

The average loss in the worst-case scenarios beyond VaR. A more conservative risk measure that captures tail risk.

Normal Inverse Sampling

X = μ + σ × NORM.INV(RAND())

Generates random samples from a normal distribution. The core technique used in Monte Carlo simulation.

Convergence Check

SE = σ / √n

Standard error decreases with more iterations. Used to verify that the simulation has run enough iterations for reliable results.

1.Define the Model Structure and Identify Uncertain Variables

Monte Carlo simulation starts with a deterministic model — a spreadsheet calculation where you change input assumptions to see how outputs change. The key step is identifying which inputs are uncertain and should be treated as random variables rather than fixed numbers. Common candidates include revenue growth rates, commodity prices, project timelines, default rates, and market returns. For each uncertain variable, determine whether it varies independently or is correlated with other variables — ignoring correlations can dramatically misrepresent the true risk.

2.Select Probability Distributions for Each Input

Assigning the right probability distribution to each uncertain variable is both the most important and most challenging step. Normal distributions work for many financial variables but understate tail risk. Lognormal distributions are appropriate for prices and ratios that cannot be negative. Triangular distributions are useful when you have minimum, most likely, and maximum estimates but limited historical data. Uniform distributions express complete uncertainty within a range. Use historical data to fit distributions where possible, and expert judgment calibrated against data where it isn't. The choice of distribution directly determines the shape of your output — get this wrong and your entire analysis is misleading.

3.Configure Correlations Between Variables

In reality, uncertain variables rarely move independently. Interest rates and default rates are correlated. Revenue and costs often move together. Commodity prices across related markets show strong co-movement. Model these relationships using a correlation matrix and a copula approach (Cholesky decomposition for the normal case). Failing to model correlations typically underestimates risk because it ignores the possibility that multiple adverse events occur simultaneously — which is exactly when portfolio diversification benefits break down and tail losses materialize.

4.Run the Simulation and Analyze Output Distributions

Execute thousands of iterations (10,000 is a common starting point), each time drawing random values for all uncertain inputs according to their specified distributions and correlations, then calculating the model outputs. The result is not a single answer but a full probability distribution of possible outcomes. Analyze this distribution using percentiles (P10, P50, P90), expected value, standard deviation, and tail metrics like Value at Risk (VaR) or Conditional VaR. Visualize the results with histograms and cumulative distribution functions. More iterations improve precision but yield diminishing returns — check convergence by monitoring how the output statistics stabilize.

5.Interpret Results and Drive Decision-Making

The power of Monte Carlo lies in transforming analysis from "what is the answer?" to "what is the range of possible answers and how likely is each?" Use the output distribution to answer practical questions: What is the probability of losing money? What is the worst-case outcome at a 95% confidence level? How much capital do we need to survive the 99th percentile scenario? Run sensitivity analysis to identify which uncertain inputs contribute most to output variability — this tells you where to focus risk mitigation efforts or where to invest in better data. A Monte Carlo simulation that doesn't change decisions is an academic exercise; one that reshapes risk management and capital allocation is invaluable.