Monte Carlo Portfolio Calculator

What the Monte Carlo portfolio calculator does

The Monte Carlo portfolio calculator shows how an investment portfolio might grow when returns are uncertain. It simulates 2,000 market histories, each with its own mix of good and bad years, and reports where those paths end: a median outcome, a low outcome at the 10th percentile and a high outcome at the 90th percentile.

You enter a starting amount, a monthly contribution, an expected annual return, the volatility of that return and how many years you plan to stay invested. Alongside the three percentiles, the tool shows what a constant return every year would give, how much you pay in over the whole period, and the share of simulated paths that end below that total. The chart draws the 10th, 50th and 90th percentile year by year.

Why a range is more useful than a single number

Most simple growth calculators assume the same return every year, which gives one tidy figure and hides the uncertainty. Two portfolios with the same average return can end far apart if one took a smooth path and the other swung up and down.

With a 10th percentile outcome next to the median, you can check whether you would still reach your objective if returns disappoint. A goal that only works when everything goes right is fragile.

How the simulation works

For every year of every path, the calculator draws a return from a normal distribution whose mean is your expected return and whose standard deviation is your volatility. One path might earn 19% in its first year, lose 8% in its second and earn 4% in its third, while the next meets a completely different sequence.

Within each year the balance compounds monthly at that year's return, and your contribution is added at the end of every month. With volatility set to zero every path earns exactly the expected return, and the calculator reproduces the classic future-value formula to the cent, which confirms that the simulation adds uncertainty around the familiar result.

The random numbers come from a pseudo-random generator with a fixed seed, so the same inputs always replay the same 2,000 paths. The paths come in mirrored pairs: every random shock is used once as drawn and once with its sign flipped, a standard technique that keeps the simulation from leaning towards lucky or unlucky draws. When you change an input, all paths are recalculated with the same underlying shocks, so the difference you see comes from your change.

The 2,000 ending balances are then ranked. The median is the balance in the middle, the 10th percentile is the balance that one path in ten fails to reach, and the 90th percentile is the balance only one path in ten exceeds.

The inputs

• The initial investment has the full term to compound, so it does a large share of the work, especially over long horizons.
• Each monthly contribution compounds for the remaining months, and over decades contributions often outgrow the initial amount.
• The expected annual return is the average each simulated year is drawn around. Every path shifts with it, so a realistic long-run figure matters more than an optimistic one.
• Volatility sets how far yearly returns scatter around the average. Raising it pushes the 10th and 90th percentiles apart and raises the chance of ending below what you paid in.
• A longer term lifts every percentile through compounding and gives the paths more time to drift apart.

Reading the results

Half of the simulated paths end above the median and half below. It can sit slightly above or below the constant-return figure, and the gap between the two shows how much the ups and downs change the typical result.

The 10th percentile is the figure to plan around. Nine paths in ten end higher, so if your goal still works at this level, your plan is resilient. If it only works at the median or above, a cushion, a longer horizon or a higher contribution would strengthen it. The chance of ending below what you paid in puts a number on the risk of losing money over the whole period.

The 90th percentile shows the upside, but do not build commitments around it.

Comparing scenarios

• Increase your monthly contribution and watch the whole range lift. A sustainable increase usually beats an aggressive one you cannot maintain.
• Raise the volatility to see how much wider the range becomes and how the chance of a shortfall grows.
• Extend the term by several years to see the effect of compounding, even as the range widens.
• Lower the expected return to a conservative figure to test your plan against a cautious outlook.

Assumptions and limits

Each simulated year is independent of the one before and follows a normal distribution, so there are no fat tails, no crashes more severe than a bell curve allows and no replay of real market history. Real returns come in clusters, and extreme years happen more often than a normal distribution suggests.

The average return and volatility stay constant for the whole period, and the model ignores taxes, fees and inflation. The 2,000 paths are a sample, so each percentile carries a small sampling error, usually well under 1% for the median and 1 to 2.5% for the 10th and 90th percentiles. The lines in the chart are percentiles taken year by year, not individual paths. Use the projection to understand the shape of uncertainty and to build a plan that can absorb a weak stretch, not as a forecast of an exact balance.

This article is general information only and is not financial advice.

About This Monte Carlo Portfolio Calculator

Use this Monte Carlo portfolio calculator to get an instant estimate based on the figures you enter. Adjust the inputs above to match your situation, or browse all our calculators to plan your next step.