The Monte Carlo Simulation
Wrapped in a Pack to guide you through uncertainty
A Monte Carlo simulation is a computer-based model that uses random sampling to predict the outcomes of an event. It’s particularly useful for understanding complex systems with many variables that are difficult to predict like inflation and the evolution of the financial markets.
Planning for retirement based on a single market prediction is like trying to guess your commute time based on one drive you made on a quiet Sunday. It doesn’t account for rush hour, bad weather, or road work. A Monte Carlo simulation is more like driving that route hundreds of times, at all hours and in all conditions. It gives you a much better picture: “Most days, it’ll take me 30–40 minutes, but there’s a 10% chance it could take an hour.” It does the same for your portfolio, testing it against thousands of potential economic climates to show you the range of likely outcomes.
This is the core of the Monte Carlo simulation, which you can run for yourself using the Coda Pack discussed in this article. You can get it here.
This video explains what a Monte Carlo Simulation is.
Why Averages Lie and Probabilities Tell the Truth
Let’s be honest: planning your financial future with a single “average” return is tempting. You plug in 7% growth, and the spreadsheet shows a beautiful, straight line going up. The problem? Your financial journey will never be a straight line.
Real life is bumpy. Some years the market soars, other years it drops. The order in which those good and bad years happen — what experts call the “sequence of returns risk” — is what makes or breaks a financial plan. A major downturn in the first two years of your retirement is far more dangerous than one 20 years later.
So, how do we model those bumps?
This is where we need to think in terms of probabilities, not certainties. We need a way to measure the potential bumpiness of our investments. In finance, that measure is called Standard Deviation.
Think of it as a “range of likelihood.” A low standard deviation means the returns are likely to be close to the average (a smooth road). A high standard deviation means the returns can swing wildly (a road full of potholes and peaks).
The image above shows this perfectly:
- The peak in the middle is the average return you expect (e.g., 7%).
- The width of the curve represents the standard deviation. A narrow curve (low standard deviation) means most of your yearly returns will be very close to that 7%. A wide curve (high standard deviation) means you could easily have a year at +25% or -15%.
By adding standard deviation to our model, we stop asking, “What will my final number be?” and start asking the much more powerful question:
“Out of 10,000 possible futures, what percentage of them are successful?”
This is the core of the Monte Carlo simulation. It runs thousands of different “stories” for your money, each with a unique sequence of returns based on the average and the “bumpiness” (standard deviation) you defined. This is how you move from a single, fragile guess to a robust, confidence-based plan.
The Levers of Your Financial Plan
To get started, think of your financial plan as a long road trip. Your goal is to reach your destination without running out of fuel (money). The levers you can pull in this simulation are the key forces that will shape this journey.
First, we need to define the basic parameters of your trip. This begins with your Initial Capital, which is the amount of fuel in your tank at the start, and your Monthly Allowance, which is your planned rate of fuel consumption. The relationship between these two creates your withdrawal rate — a key indicator of your plan’s sustainability. For example, starting with €1,000,000 and spending €40,000 annually gives you a 4% withdrawal rate, a common benchmark. The final basic input is the Simulation Years, which is simply the length of your road trip. A 30-year journey from age 65 to 95 naturally carries more uncertainty than a 20-year one.
In addition to your main portfolio, you can add other sources of fuel for your journey. The Pack allows you to model steady income streams like a Monthly Pension or Monthly Additional Income (from a rental property, for example). These levers are powerful because they reduce the pressure on your main tank, often dramatically improving your plan’s success rate.
The Four Forces Shaping Your Journey
With the basics set, we now get to the four dynamic forces that make each simulated journey unique. Think of them as the performance of your vehicle and the weather you’ll face.
The first major force is your portfolio’s performance, which is determined by both its speed and the road it’s on. Your Average Return is the average speed of your car. An aggressive portfolio is like a sports car aiming for an 8–10% average return, while a more conservative one is a steady sedan averaging around 4%. But average speed is only half the story. The Return Standard Deviation represents the condition of the road. Is it a smooth highway (low volatility of 8%) or a bumpy mountain pass with wild swings (high volatility of 20% or more)? This models the critical “sequence of returns risk” — the danger of hitting a giant pothole, like a market crash, early in your trip, from which you might never recover.
The second force is inflation, which acts like the weather. Average Inflation is a constant headwind pushing against you, silently eroding your spending power and forcing your engine to work harder. A long-term average might be 2.5%, but we all know the wind isn’t constant. That’s where Inflation Standard Deviation comes in. It represents the unpredictable gusts. Some years the headwind is a gentle breeze, but in others, a powerful gust — a sudden spike in inflation — can hit you broadside, forcing you to burn through your fuel (capital) much faster than planned.
By defining these forces, you’re not just creating one plan; you’re setting the stage for thousands of possible journeys.
Max 20,000 scenarios
You might wonder why the Pack allows a maximum of 20,000 scenarios and not, say, a million. The reason is all about finding the perfect balance between statistical accuracy and practical performance. While more simulations can sound better, you quickly hit a point of diminishing returns. The difference in the final success rate between 20,000 and 100,000 simulations is often hundredths of a percentage point — a tiny refinement that doesn’t change your decision. 20,000 runs are more than enough to achieve a stable and trustworthy result. Beyond that, the real cost is performance. Each simulation is a complex calculation, and running hundreds of thousands would make the tool slow and likely hit ’s execution time limits. The 20,000 cap is the sweet spot: it delivers maximum confidence in the outcome while ensuring the tool remains fast, responsive, and reliable.
The output
After running your road trip thousands of times with different road conditions and weather patterns, the simulation doesn’t give you a single, certain answer. Instead, it provides a set of probabilities that paints a rich, detailed picture of your plan’s resilience. Here’s how to make sense of it.
The headline number is the Success Rate. This is simply the percentage of the simulated futures where you did not run out of money. An 85% success rate means that in 8,500 of the 10,000 possible journeys, you reached your destination with fuel still in the tank. For retirement planning, a rate above 85% is often considered robust, giving you strong confidence in your strategy.
Beyond that simple pass/fail metric, the results give you a sense of the range of possible outcomes. The Median End Capital shows you the middle-of-the-road result among all the successful scenarios. Half the successful trips ended with more than this amount, and half ended with less, making it a far more realistic expectation than a simple average. To understand your risk, you’ll want to look at the 10th Percentile. This is your plan’s stress test; it tells you the final capital in the worst 10% of successful cases. If this number is still an amount you’re comfortable with, it provides a powerful sense of security. On the flip side, the 90th Percentile shows you the potential upside — in the best 10% of successful futures, you ended up with at least this much money.
Finally, for the scenarios that did fail, the Average Years to Failure tells you, on average, when the money ran out. This helps you understand the fragility of your plan. A plan that tends to fail in year 28 is very different from one that fails in year 12. Together, these numbers move you beyond a simple guess, offering a complete view of your financial plan’s strengths and weaknesses.
Diving Deeper: The Year-by-Year Story
While the main results table gives you the big picture, sometimes you want to see how one of those “stories” plays out. That’s where the MonteCarloYearlyBreakdown table comes in. For any scenario you've created, you can use this second table to generate a detailed, year-by-year projection of a single, random simulation. It shows you the market returns, inflation, and capital changes for each year, giving you a tangible feel for the "sequence of returns risk" and how your journey might unfold.
From Simulation to Strategy
You now understand the forces shaping your financial road trip and how to read the dashboard of probabilities. The real power of this tool, however, isn’t just in running the numbers once; it’s in asking “what if?” This Pack is your personal financial sandbox, allowing you to explore trade-offs and see their impact instantly.
Is your success rate a bit lower than you’d like? See what happens if you reduce your monthly spending by €200 or plan to work just one year longer. Are you curious about the impact of risk? Compare a conservative portfolio against an aggressive one and pay close attention to how the 10th and 90th percentile outcomes change. The goal isn’t to find a single “perfect” number but to discover a strategy you have genuine confidence in — a plan that you’ve already stress-tested against thousands of possible futures.
Ultimately, this tool doesn’t predict the future. Nothing can. But it replaces a single, fragile guess with a robust understanding of possibilities. It gives you the clarity to prepare for uncertainty and make informed decisions. So go ahead, start pulling the levers, explore your scenarios, and build a financial plan you can truly trust.
With this Pack, you can move from theory to a personalized, robust financial strategy. If you found this guide helpful, you can get the Pack here: [Link to Coda Pack Gallery]. On a personal note, creating these in-depth posts takes a lot of time and effort. While I love sharing my knowledge, a little support goes a long way. If you found this helpful, what about a donation and sharing this post with your fellow Coda enthusiasts? Every bit of encouragement helps!
My name is Christiaan, and I regularly blog about Coda. While this article is free, my professional services (including consultations) are not, but I’m always happy to chat and explore potential solutions. You can find my free contributions in the Coda Community and on X. The Coda Community is a fantastic resource for free insights, especially when you share a sample doc.
