Planning a financial goal with Monte Carlo and DCA

You want to reach a specific amount within a specific number of years: a down payment on a house, a retirement cushion, a rainy-day fund. The question that actually matters isn't "how much will the market return", nobody knows that in advance, it's "given the plan I have, how likely am I to get there?". Monte Carlo simulation answers exactly that question, not with a single number but with a distribution of possible outcomes.

What this analysis does

The analysis generates thousands of future paths for your portfolio, each with a different sequence of annual returns. It isn't a prediction of what the market will do: it's a way to explore how much the outcome can swing if the future doesn't repeat the past exactly. Every path starts from the same initial capital and adds a return each year, drawn from a distribution calibrated on the expected mean and volatility. At the end, the share of paths that clear the goal becomes the success probability.

The number of simulations is adjustable: ten thousand is the default trade-off between estimate precision and calculation speed, and it's the value most users will never need to touch.

Where the simulated returns come from

In the Planner, you set the mean and volatility of annual returns yourself, in the section's parameters. That's the assumption the entire cone rests on: raise or lower them and every percentile shifts, not just the median. If instead you run the analysis right after a backtest, the portfolio derives those two numbers from its own historical monthly returns, no need to estimate them by hand, but the result also inherits the strengths and quirks of that particular historical period.

The difference matters more than it sounds like it should. An optimistic expected return set in the Planner, or a backtest run over a decade of unusually favorable markets, produce the same effect: a cone shifted higher than what real markets are likely to deliver in the years ahead.

DCA and inflation: what changes in the math

If you've set up DCA, each period's contribution gets added before the return applies, what finance calls an annuity due: your money starts working from the first day of the period, not the last. You choose the contribution frequency yourself, monthly, quarterly, semi-annual or annual.

With inflation switched on, the goal stops being a fixed number and becomes a moving target in real terms. A concrete example: at 2% inflation a year, $100,000 ten years from now is worth roughly $82,000 in today's purchasing power. It's that adjusted figure, not the nominal $100,000, that the portfolio actually has to clear to count as a success.

The cone chart: how to read it

The main result is a chart showing how the capital could evolve year by year, not as a forecast but as a map of plausible scenarios. It has four elements to read together.

The inner band covers the 25th and 75th percentiles, the middle half of the simulated paths. The outer band reaches the 5th and 95th, 90% of cases. The narrower the bands, the more predictable the outcome; the more they widen over time, the more the sequence of returns matters beyond just their average.

The center line is the median, the 50th percentile: half the simulations finish above it, half below. A separate line tracks contributions only, initial capital plus every DCA payment made, with no return at all: it's the theoretical floor if the market returned exactly zero for the whole period, and it's useful for seeing how much of the final result comes from contributions versus growth. The dashed red line marks the goal: if the cone clears it comfortably, the probability is high; if most of the bands sit below it, the probability is low.

A numbers example

Starting capital of $20,000, monthly DCA of $300, a 20-year horizon, expected return of 6% a year with 15% volatility, a $200,000 goal, inflation switched off. Across ten thousand simulated paths, the median might land around $220,000, comfortably above target; but the pessimistic band at the 5th percentile, the one with the worst return sequences, might sit closer to $140,000, below the mark. Overall success probability, the share of paths reaching $200,000 or more, might come out around 75%: a plan with good odds, not a certainty.

These numbers are a constructed example meant to show how to read the output, not the result of an actual simulation: the real probability depends on the parameters you enter and varies from case to case.

Assumptions and limits worth knowing

The model assumes annual returns follow a lognormal distribution, with mean and volatility you set yourself, or derived from historical monthly returns if you run the analysis after a backtest. The portfolio is treated as rebalanced every year back to its original weights, and the returns used are gross of tax.

The most important limit concerns the lognormal assumption itself: it tends to underestimate fat tails, meaning extreme events, and it doesn't capture correlated systemic crises like 2008, where multiple assets fall together in ways the statistical model doesn't anticipate. When the mean and volatility parameters come from a backtest, a particularly favorable or unfavorable historical stretch skews the projections in one direction or the other. The analysis also leaves out transaction costs, tax on realized gains, and unplanned liquidity needs, an emergency that forces you to pull capital outside the plan.

When the success probability doesn't convince you, there's also a reverse path: instead of estimating probability from the plan, you start from the probability you want and work out what needs to change to get there. There are three levers, and they can be combined: the time horizon, how many years to add; the DCA amount, how much more to contribute to close the gap; and, only in the flow tied to a backtest, portfolio allocation along the efficient frontier calculated on the same historical data. In the Planner you can move the first two, the allocation lever requires an efficient frontier already calculated, available only after a backtest.

In BacktestFolio

Financial Goal Analysis generates the Growth projection (Ibbotson cone) chart and, below it, six panels showing the portfolio value at the horizon for each scenario: pessimistic at the 5th percentile, only one simulation in twenty finishes worse; cautious at the 25th; median at the 50th; favorable at the 75th; optimistic at the 95th. Each panel also shows the scenario's implied CAGR, the annual compound return that would produce that result, useful for comparing against your own return targets without redoing the math by hand.

You can try it free right after running a backtest, on the same page, using the mean and volatility just calculated from your history. The standalone version, without needing to run a backtest first, is in the Planner for Plus subscribers.

Frequently asked questions

Does a 75% success probability mean I still have a problem in 25% of cases?

It means that among the thousands of simulated return sequences consistent with the parameters you entered, one in four finishes below the goal. It isn't a prediction of what will happen, it's the rate at which the plan fell short under the conditions tested: one more reason to look at the pessimistic scenario too, not just the median.

Is it better to raise the DCA or extend the horizon when probability is low?

It depends on which of the two levers you can actually move. A higher DCA works immediately, a longer horizon gives compounding more time but pushes the goal further out. Inverse goal planning calculates exactly how much each lever requires, turning the choice into a number to compare rather than a hunch.

Financial goal planning: Monte Carlo & DCA