The problem with point estimates
Ask a risk team "when will we breach our liquidity threshold?" and you'll typically get a single number: "approximately 45 days." This answer is precise and almost certainly wrong.
The real answer is a distribution. Under baseline conditions, the breach might occur anywhere between 30 and 90 days. Under stressed conditions, the range shifts to 10-50 days. The tail — those scenarios beyond the 95th percentile — is where institutions are most vulnerable and least prepared.
Monte Carlo simulation makes this distribution visible.
How it works
The method is conceptually simple:
- Define the variables that affect your resilience metric (interest rates, credit spreads, vendor dependencies, regulatory actions)
- Assign probability distributions to each variable based on historical data and expert judgment
- Run thousands of randomised scenarios, sampling from each distribution
- Aggregate the results to see the full probability distribution of outcomes
Each simulation run produces a single outcome. A thousand runs produce a histogram. Ten thousand runs produce a reliable probability distribution with well-defined percentiles.
From distribution to decision
The value isn't in the simulation itself — it's in what the distribution reveals.
P5 (5th percentile): The optimistic scenario. Only 5% of simulations produce a better outcome than this. Useful for best-case planning but dangerous as a target.
P50 (median): The central tendency. Half of scenarios are better, half are worse. This is your most likely outcome, but it tells you nothing about the tails.
P95 (95th percentile): The stress scenario. Only 5% of simulations produce a worse outcome. This is where resilience planning lives — if you can survive the P95 scenario, you can survive most of what reality throws at you.
The gap between P5 and P95 is your uncertainty range. A narrow gap means high confidence in the outcome. A wide gap means significant uncertainty — and significant uncertainty means you need contingency plans.
Stressed vs. baseline scenarios
Running Monte Carlo under two regimes reveals how sensitive your resilience is to adverse conditions:
- Baseline: Current economic conditions, normal operational environment
- Stressed: Adverse rate movements, vendor failures, regulatory enforcement actions
The shift between baseline and stressed distributions quantifies the impact of adverse conditions. If your P50 shifts from 45 days to 25 days under stress, your resilience buffer is thinner than a point estimate would suggest.
Practical considerations
Sample size matters. A hundred simulations give you a rough shape. A thousand give you reliable percentiles. Ten thousand give you stable tail estimates. Beyond that, you're paying computation cost for diminishing precision.
Input distributions matter more than simulation count. The quality of your Monte Carlo output is bounded by the quality of your input distributions. Garbage distributions in, garbage distributions out — just with more decimal places.
Correlation structure matters. Variables aren't independent. Interest rate hikes correlate with credit spread widening. Regulatory enforcement actions cluster. Ignoring correlations produces unrealistically narrow distributions.
Integration with scenario intelligence
Monte Carlo becomes most powerful when combined with causal models. Rather than treating each variable as independent, map the causal relationships: a geopolitical event triggers supply chain disruption, which triggers vendor failure, which triggers operational risk.
This is the approach behind Roach Resilience — combining causal graph propagation with Monte Carlo simulation to produce probability-weighted assessments that respect the cascading nature of real-world risk.