Abel's Calculators

If you've used a retirement calculator recently, you've probably seen a "Monte Carlo simulation" button or a "probability of success" number. These tools are genuinely useful — far more useful than simple average-return projections — but most people who use them don't actually understand what's happening under the hood.

That matters, because understanding the mechanism helps you interpret the results correctly. A "92% probability of success" means something specific, and if you misread it you'll make different decisions than you should.

Here's how it works, from the ground up.

The Problem with Average Returns

The standard way to project an investment portfolio is to assume a fixed annual return — say, 7% — and compound it forward. Put in $500,000 today, withdraw $25,000 per year, and at 7% you run out of money in... year 47. Simple.

The problem is that markets don't return 7% every year. They return +28% one year, −18% the next, +14% the year after. The average might be 7%, but the path matters — especially when you're withdrawing money.

Here's a stark illustration. Imagine two investors who both earn an average of 5% per year over 10 years:

What a Monte Carlo Simulator Actually Does

The name comes from the Monte Carlo casino in Monaco — a nod to randomness and probability. The technique was developed in the 1940s by physicists working on the Manhattan Project who needed to model neutron behavior using random sampling. It migrated into finance decades later for the same reason: some systems are too complex to solve with a formula, but easy to simulate.

In financial planning, the process looks like this:

That's the whole mechanism. Random returns, applied year by year, repeated thousands of times, with the results tallied. No black box, no magic.

How to Read the Results

The output of a Monte Carlo simulation is a probability distribution, not a prediction. Understanding this distinction is important.

Probability of success

This is the percentage of simulations where the portfolio didn't run out of money. It's not a guarantee. An 87% success rate means that in 13% of the 10,000 simulated market sequences — roughly 1,300 of them — the portfolio was depleted before the end of the planned retirement.

What counts as "good enough" is a personal question. Many financial planners target 85–90% as a reasonable range. Going for 99% usually means withdrawing so little that you'll almost certainly leave a large unspent estate. Going for 70% means accepting meaningful ruin risk.

The percentile fan

Most simulators also show a range of outcomes at each future year — the 10th, 50th, and 90th percentile portfolio values. This is more useful than success rate alone, because it shows you how bad failure looks and how good success looks.

In this example, the median retiree ends up with nearly double their starting portfolio — the plan is conservative for most futures. But the 10th percentile result is zero, meaning about 10% of simulations resulted in portfolio depletion. That's the risk number to focus on.

What Monte Carlo Gets Wrong

Monte Carlo simulation is a significant improvement over average-return projections, but it's not perfect. A few limitations worth knowing:

Returns aren't normally distributed

Most Monte Carlo simulators model annual returns as a normal distribution (bell curve). Real markets have "fat tails" — extreme crashes happen more often than a normal distribution predicts. The 2008 financial crisis, the 2020 COVID crash, and the 1987 Black Monday were all statistically "impossible" events under a normal distribution model. This means Monte Carlo can underestimate true tail risk.

Returns aren't independent year-to-year

The simulator treats each year's return as a fresh random draw, independent of the previous year. In reality, markets have momentum, mean reversion, and correlation to economic cycles. A standard Monte Carlo model doesn't capture the fact that a terrible year is sometimes followed by a bounce, or that valuations matter for forward returns.

It's only as good as its assumptions

The expected return and volatility figures that feed the simulation are typically drawn from historical averages. If the future has lower returns than the past — which some analysts argue is likely given current market valuations — the simulation will be too optimistic. Changing the expected return assumption by just 1–2% can move the probability of success by 10+ percentage points.

It ignores spending flexibility

Standard simulations model rigid withdrawals: the same inflation-adjusted amount every year, no matter what the market does. Real retirees adapt — they spend less during downturns, delay big purchases, or pick up part-time income. A plan that looks like it has an 80% success rate under rigid withdrawal assumptions might have a 95% success rate if you'd realistically cut spending by 15% in a bad year. Some advanced simulators model this flexibility; many don't.

Historical Simulation vs Monte Carlo

There's a related but different approach called historical (backtesting) simulation, which uses actual historical return sequences instead of randomly generated ones. The Trinity Study used this method — it tested every rolling 30-year period in US market history and asked "did the portfolio survive?"

The advantage of historical simulation is that it uses real market sequences, including real crashes and recoveries. The disadvantage is that there are only so many non-overlapping 30-year periods in history — the sample size is small. Monte Carlo generates thousands of scenarios, giving you much more statistical coverage, but at the cost of the real-sequence fidelity.

Neither is strictly better. They're different tools with different trade-offs. A good retirement plan uses both.

What to Actually Do With This

Monte Carlo simulation is most useful not as a single number to optimize, but as a tool for testing your plan under stress.

Instead of asking "Is my plan safe?", ask:

• "What happens if I delay Social Security by 3 years?" Run both versions and compare the probability of success.
• "How much does a 10% spending cut in down years improve my odds?" Most simulations let you model spending flexibility.
• "What's my break-even asset allocation?" More stocks increases expected return but also volatility. Where's the sweet spot for your specific plan?
• "How does my plan change if expected returns are 1% lower than historical averages?" This sensitivity test tells you how dependent your plan is on optimistic assumptions.

The number itself — "87% probability of success" — is less important than the direction it moves when you change your inputs. That's where the insight lives.