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Blog main article:
Risk ≠ Variance - Why simulation is not a decision
Executive Summary
Monte Carlo is often considered the gold standard in board meetings and investment committees. Distributions, confidence intervals and scenario analyses create the impression of mathematical resilience. But here lies a structural misunderstanding: variance is not risk - and simulation is not a decision.
Variance measures dispersion. Risk, on the other hand, describes the danger of not achieving a defined goal. These two concepts are not mathematically identical. Anyone who simulates variance has not yet optimized a preference function, no constraints and no target function. They have merely evaluated probability spaces.
Monte Carlo answers the question: "What could happen?"
Decision optimization answers the question: "Which option maximizes goal achievement under restrictions?"
Simulation is an evaluation tool. Decision is an optimization problem.
The structural misunderstanding
Monte Carlo simulations generate thousands of random paths based on assumed distributions. The result is a probability distribution of possible outcomes. However, none of these simulations systematically searches the complete combination space of a portfolio.
In complex portfolios with n projects, there are 2ⁿ combinations. With 20 projects, that's over a million options. Simulation evaluates assumptions - it does not identify the global optimum.
Simulation vs. optimization
| Criterion | Simulation (Monte Carlo) | Optimization |
|---|---|---|
| Goal | Represent probabilities | Maximize/minimize target function |
| Logic | Random-based path generation | Systematic search in the decision space |
| Outcome | Distribution of possible outcomes | Mathematically optimal portfolio |
| Decision | Interpretation by management | Direct derivation from objective function |
Why variance is not a risk
High variance can mean high opportunities. Low variance can be systematically suboptimal. Risk does not arise from variance, but from missing the target relative to the strategic function of the portfolio.
A portfolio with low variance can nevertheless be significantly below its possible optimum. This is not a statistical problem - but a structural one.
The governance dimension
Simulation shifts responsibility back to the board. Results must be interpreted. Discussion replaces calculation. Opinion replaces mathematical selection.
Optimization, on the other hand, defines a target function ex ante and identifies the combination that generates the highest value under budget, risk and resource restrictions.
This is not a scenario. It is a property of the data.
Conclusion
Those who simulate understand uncertainty.
Those who optimize make decisions.
Risk management without optimization remains plausible locally - but potentially suboptimal globally.
FAQ
Is Monte Carlo useless?
No. Simulation is valuable for sensitivity analysis. However, it does not replace optimization logic.
Can simulation and optimization be combined?
Yes, simulation can model uncertainties, optimization selects the best combination among these uncertainties.
Why is scenario planning not enough?
Scenarios compare individual options. They do not systematically search the entire decision space.
What is the crucial difference?
Simulation describes possibilities. Optimization calculates the optimum.
Dr. Igor Kadoshchuk is a computer scientist, algorithm architect, and one of the leading minds behind mAInthink's optimization and decision-making algorithms. As scientific director of the StratePlan™ and DeepAnT platforms, he combines in-depth mathematical research with practical applications in project portfolio optimization, business, finance, and public administration.
He holds a PhD in computer science from the renowned Moscow Institute of Physics and Technology (MIPT), where he also taught as a professor of computer engineering and mathematics. He has decades of experience developing highly complex mathematical models for project portfolio optimization and financial systems, investment planning, and strategic decision-making. His professional career includes leading positions such as Head of IT at Gazprombank and Director of Project Management at TransTeleCom.
Dr. Kadoshchuk writes on the mAInthink AI Blog. Kadoshchuk on:
- Algorithmic strategy optimization
- New methods for calculating ROI and impact
- Project portfolio optimization beyond traditional tools
- The limits of human decision-making – and how AI overcomes them
His aim: to calculate strategy, not estimate it.
His contributions combine scientific precision with clear, understandable language – always with the goal of making complex decision-making spaces transparent, manageable, and measurable.