Monte Carlo simulation: in how many of 10,000 paths would your money have lasted?

A calculation that plays through not one but many possible paths. Paperball builds 10,000 paths from real monthly returns and evaluates them — for example: “In 94% of the simulated paths, the money would have lasted.” That is neither a probability nor a forecast, but an analysis of the past.

A backtest looks back: it uses real prices to work out what would have become of your money — exactly as things turned out at the time. That gives a single path. The Monte Carlo simulation asks one question more: what if the good and the bad years had come in a different order? To find out, it cuts the real price history into pieces of twelve months each and puts them back together 10,000 times. That shows you how differently things could have gone — for example, in how many of these paths your withdrawals would have lasted to the end. In short: the backtest shows what happened; Monte Carlo shows the range. Neither is a forecast.

From the real price history: from the calculation of a saved portfolio, from the backtest of a portfolio in the Community-Backtests or from total return index series, i.e. including distributions. Draws are made in twelve-month blocks so that market phases stay together — crisis years such as 2008 or 2022 remain intact.

At least five years. For an asset mix, what counts is the period in which all building blocks have data — the calculation never uses a series that did not exist yet at the time. A fixed interest rate does not count here, as it has no history.

A backtest needs at least one year, a Monte Carlo simulation at least five years in which all selected securities have prices. If that is not enough, there are two possible reasons. First: the security is simply still young. If an ETF was launched three years ago, there are only three years of prices — nobody can extend them. For the calculation you can then use an older security with similar holdings, for example another ETF on the same index. Second: the security is older, but our data provider does not deliver its prices far enough back. Then you add the missing prices yourself: on the “Watchlist” page, upload a price file (CSV) for the security — this is available on every plan. Tip: you can find free prices at onvista.de and investing.com. With a free account you can download the historical prices there as a CSV file, and Paperball reads both formats directly.

If you sort all paths by their result, the median is the path exactly in between: one half ends above it, the other below. 5 % of paths lie below the lower bound, the same share above the upper bound, and 90 % between the two. So the lower bound is not a worst case — there are weaker paths below it.

The same paths, except that the first years of withdrawals are exactly the months of a real crisis in their real order — such as the financial crisis or the high inflation of the 1970s. This shows you what a weak sequence right at the start would have meant. Paperball calculates every crisis that lies entirely within the price history of the basis, plus the weakest ten years of that history.

Yes, if you want. For a saved portfolio, Monte Carlo uses the tax settings of its backtest, which you can change; for asset mixes and portfolios from the Community-Backtests you switch taxes on. Every withdrawal is sold so that your amount arrives after tax on the gain share; each year, the tax on buffer interest, a wealth tax and the advance lump sum are added. A portfolio's costs and its tax on rebalancing are already part of its return series; an asset mix is calculated without costs. Approximated are the reduced rate after a holding period and the tax on distributions, which only applies on sale.

No. Paperball is a calculation tool and does not provide investment advice or investment recommendations. Monte Carlo recombines past price history into possible paths. That is not a forecast. You make decisions about your investments yourself.

No. The Monte Carlo simulation and the portfolio backtester belong to the same account, and you need no subscription for either. Every simulation costs credits, whatever it is based on; with the starter credits your first ones are free, after that you buy more credits or take a subscription — see all prices.