Financial goal planning: Monte Carlo & 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 useful question is this: given the plan you have, how likely are you to get there? Monte Carlo simulation answers 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 monthly returns. It explores how much the outcome can swing if the future doesn't repeat the past exactly. Every path starts from the same initial capital and applies a return each month, drawn from a distribution calibrated on expected compound return 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 expected compound return and volatility 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 year-by-year chart of capital: 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 finishes around $207,000; the pessimistic 5th percentile stays near $95,000, below the goal. Overall success probability, the share of paths reaching $200,000 or more, is about 53%.

These figures come from a site simulation with these parameters; with different inputs or another random draw, they change.

Assumptions and limits worth knowing

The model generates monthly lognormal returns, calibrated on expected compound return and volatility you set, or taken from historical monthly returns if you run the analysis after a backtest. The portfolio is treated as a single whole: after a backtest its returns reflect the rebalancing chosen there. 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 leaves out transaction costs, tax on realized gains, and an unplanned withdrawal.

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.

On a backtest you get it with Plus and Pro, applied to your portfolio, using the historical mean and volatility just calculated. To see it in action, the 60/40 Demo on the Backtest page already shows the result. The standalone version, without a backtest first, is in the Planner on Plus and Pro.

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. That share is how often the plan finished below the goal under the conditions tested. The pessimistic scenario belongs in the same reading as 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, and the choice is read off that number.