Monte Carlo Simulation

Definition

A Monte Carlo simulation is a way of testing a financial plan against uncertainty. Instead of projecting your portfolio forward along one path built on average returns, the computer simulates thousands of possible futures — each one a different randomized sequence of good and bad years — and then reports the *distribution* of outcomes across all of them.

The name comes from the casino district of Monaco, because the method is built on randomness: each simulated year, the computer draws a return at random from a statistical model of how markets behave (typically defined by an expected return and a level of volatility). String 30 of those random draws together and you get one plausible 30-year retirement. Repeat that 10,000 times and you get 10,000 plausible retirements — some where the market cooperates, some where a brutal bear market lands in year one.

The output is not a single number like "your portfolio will grow to $2.1 million." It is a set of probabilities: *In 93% of simulated futures the money lasted 30 years. In the median future you ended with $1.4 million. In the worst 10% of futures you ended with under $200,000.* That shift — from one predicted path to a range of outcomes with odds attached — is the entire point.

Core idea: an average-return projection tells you what happens in a world that does not exist — one where the market returns the same number every year. A Monte Carlo simulation tells you what happens across thousands of worlds that *could* exist, including the ugly ones.

Why It Matters

The single-path projection most people start with — "assume 7% a year, subtract withdrawals, see where you land" — has a fatal blind spot: averages hide the order of returns. Two retirees can earn the identical average return over 30 years and end up in opposite places, because one absorbed the bad years early while withdrawing and the other got them late. That is sequence of returns risk, and no straight-line projection can see it. A Monte Carlo simulation is built to see it: every simulated path is a different *ordering* of returns, so the paths where a crash lands in year one show up in the results as depleted portfolios — exactly as they would in real life.

Monte Carlo analysis is also where the most familiar retirement statistics come from. When you read that "the 4% rule works about 95% of the time," that percentage *is* a success rate from simulation or historical-path testing: someone ran a withdrawal plan across thousands of scenarios and counted how many survived. Without simulation, a claim like that has no meaning — a single projected path either works or it does not, with no "percent of the time" attached.

For income investors, this matters because the questions that keep you up at night are probability questions, not average questions. *Will my money last if I retire into a bad decade? How much cushion do I really have? What happens to my plan if I withdraw 5% instead of 4%?* Simulation is the standard tool for answering all of them, and it is the engine behind most professional planning software — including DividendVision's own forecast tool, which runs Monte Carlo projections on your actual portfolio rather than a hypothetical one.

How a Simulation Works

You do not need to run the math yourself to use the results well, but knowing the moving parts helps you judge them. Every Monte Carlo retirement simulation has the same skeleton:

1. Inputs. You (or the tool) specify an expected return and volatility for each asset class — say, higher return and higher swings for a stock fund like VOO or SCHD, lower for a bond fund like BND — plus the correlations between them (how much they move together). Then you add your plan: starting balance, contributions or withdrawals, and the time horizon.
2. One trial. For each simulated year, the computer draws a random return for each asset from the statistical model, applies it to the balance, then applies that year's withdrawal or contribution. Repeat for every year of the horizon. That is one complete "future."
3. Thousands of trials. The process repeats — commonly 1,000 to 10,000 times — each trial using a fresh random sequence. The randomness is what generates the variety: some trials front- load the good years, some front-load the disasters.
4. Read the distribution. The trials are then sorted and summarized. The two headline outputs are the success rate — the percentage of trials in which the portfolio never hit zero before the horizon ended — and the percentile outcomes, often drawn as a "fan chart" that widens over time: the 90th percentile (a great outcome), the median (the middle path), and the 10th percentile (a bad-luck outcome).

Success rate  =  trials that never ran out of money  /  total trials

  Example: 9,300 of 10,000 simulated retirements still had money
  at year 30  ->  93% success rate

One subtlety worth knowing: the whole exercise is only as good as those inputs. Feed the simulator an optimistic expected return or an understated volatility and it will confidently produce optimistic nonsense — simulation multiplies your assumptions; it does not check them.

Reading the Results

The most common mistake with Monte Carlo output is staring at the median. The median path is the *coin-flip* outcome — half the simulated futures did better, half did worse. You do not plan a retirement around a coin flip. The information you actually paid for lives in the bad tail:

• Obsess over the 10th–25th percentile, not the median. These are the "unlucky but entirely plausible" futures — the ones where you retire into a weak decade. If your plan still works at the 10th or 25th percentile, it is robust. If it only works at the median, you are betting your retirement on at-least-average luck.
• Treat the success rate as a dial, not a verdict. Most planners consider roughly 85% to 95% a sensible target zone for a retirement plan. Below about 80%, the failure risk is material and worth acting on. Chasing 100%, on the other hand, usually means underspending for decades to eliminate scenarios that were already rare — and a plan can always be adjusted mid-flight, which the simulation's rigid assumptions ignore.
• Look at *when* failures happen and *how deep* the dips get. A plan that fails in year 29 is a very different problem from one that fails in year 12. Likewise, the fan chart shows how low the balance sinks along the way — a path can "succeed" while spending a decade uncomfortably close to zero.

Rule of thumb: the median tells you what to hope for; the 10th–25th percentile tells you what to plan for.

Example

Here is what typical Monte Carlo output looks like for one plan tested at two withdrawal rates. The setup: a $1,000,000 portfolio split between stock and bond index funds, a 30-year horizon, 10,000 trials, and a first-year withdrawal that then rises with inflation — the classic structure of the 4% rule. Every number below is illustrative, generated from assumed returns and volatility to show the *shape* of the output, not a forecast of any real portfolio:

Read the table the way a planner would. At a 4% withdrawal, the plan succeeded in 9,300 of the 10,000 trials, and even the unlucky 10th-percentile retiree finished with money left. The median retiree ended with *more* than they started with — a reminder that the 4% rate was calibrated to survive bad sequences, so in ordinary sequences it leaves a surplus.

Now look at what one extra percentage point of spending did. At 5%, the success rate dropped from 93% to 78% — roughly 2,200 of the 10,000 simulated futures ran out of money. The 10th percentile now reads $0: since more than 10% of trials failed, the 10th-percentile "outcome" is a depleted portfolio, and even the 25th percentile finished with only about $150,000. The median tells a gentler story ($800,000 remaining), which is exactly why the median misleads: the extra spending felt affordable in the *middle* futures while quietly breaking the *bottom quarter* of them.

This is the kind of trade-off a single average projection cannot show — and the kind DividendVision's forecast tool lets you test against your own holdings, withdrawal plan, and time horizon rather than a textbook portfolio.

Common Mistakes

• Trusting the output more than the inputs deserve. The simulation is only a machine for compounding your assumptions. If the assumed expected return is 1% too high, every success rate and percentile in the report inherits that optimism. Garbage in, confident-looking garbage out. Rerun any plan with more conservative return assumptions before you rely on it.
• Forgetting that normal-distribution models understate extremes. Many simulators draw returns from a bell curve, but real markets produce crashes larger and more frequent than a bell curve predicts — the fat tails discussed in tail risk and measured by tools like value at risk. A simulator built on normal returns will quietly undercount the very disasters you are running it to prepare for.
• Assuming correlations hold in a crisis. Simulations use historical correlations between assets, but in severe selloffs, correlations tend to spike — things that usually offset each other fall together. Diversification benefits baked into the model can overstate the protection you will actually get in the worst trials.
• Planning to the median. Half of all futures are worse than the median path. A plan judged only by its middle outcome has not been stress-tested at all — the 10th–25th percentile is where the test happens.
• Treating the success rate as a promise. "93% success" is not a guarantee with a 7% asterisk. It is a statement about a *model* of the future, built from assumptions that are themselves uncertain — a probability sketch for comparing plans and spotting fragility, not a contract with the market.
• Running it once and filing it away. A simulation is a snapshot of your plan under today's balance and assumptions. It earns its keep when you re-run it after big life or market changes and adjust course early.

FAQ

What is a Monte Carlo simulation in retirement planning?

It is a computer test that runs your retirement plan — starting balance, withdrawals, contributions, time horizon — through thousands of randomized market scenarios instead of one average-return projection. Each scenario draws a different random sequence of yearly returns, so the results capture bad-luck orderings (like a crash right after you retire) that a straight-line average hides. The output is a distribution: a success rate, a median outcome, and the range of percentile outcomes.

What success rate should I aim for?

Most planners treat roughly 85% to 95% as a sensible zone for a retirement plan. Materially below 80% means failure is a realistic outcome worth fixing — by spending less, working longer, or adjusting the portfolio. Pushing for 100% is usually counterproductive: it forces decades of underspending to eliminate already-rare scenarios, and it ignores that real retirees adapt — trimming withdrawals in bad markets — while the simulation assumes they rigidly never do.

How accurate are Monte Carlo simulations?

They are as accurate as their assumptions, and no more. The expected returns, volatility, and correlations you feed in drive everything that comes out; small changes in those inputs can swing a success rate by ten points or more. Standard simulators also tend to understate extreme events, because bell-curve models produce fewer severe crashes than real markets do — see tail risk. Use the results to compare plans and find fragile spots, not as a precise prediction of your future balance.

How is a Monte Carlo simulation different from a historical backtest?

A backtest replays the actual past — for example, testing a withdrawal plan against every real 30-year period on record, which is how the 4% rule was originally derived. A Monte Carlo simulation instead generates *new* randomized scenarios from statistical assumptions, so it can produce sequences worse (or better) than anything in the historical record. Backtests are limited to one realized history; simulations explore futures that have not happened yet, at the cost of depending on modeled assumptions.

How many simulation trials are enough?

Most tools run 1,000 to 10,000 trials; beyond a few thousand the headline numbers barely move between runs. More trials smooth out the randomness of the simulation itself, but they do nothing to fix bad inputs. If the answer looks too good, question the return assumptions, not the trial count.

Does a Monte Carlo simulation account for sequence of returns risk?

Yes — that is arguably its main job. Because every trial is a different random *ordering* of returns, the simulation naturally includes futures where the worst years land immediately after retirement, while withdrawals are largest relative to the balance. Those bad-sequence trials are the ones that fail and drag the success rate down, which is exactly the danger described in sequence of returns risk. A single average-return projection, by contrast, contains no sequence at all — every year is identical, so the risk is invisible.