Withdrawal plan calculator: would your portfolio have lasted?
Decide how much you want to withdraw — a fixed amount adjusted for inflation or a percentage of the portfolio. Paperball runs the plan through real prices, after costs and tax, and shows how long the money would have lasted.
In short
A withdrawal plan sets how much you take out of your portfolio every year. Whether it lasts depends on returns, inflation, tax and the order of the years. In the worked example below, 4 % of €500,000 — €20,000 in the first year, raised with inflation after that — would have lasted 30 years after German tax in 88 % of the 10,000 paths.
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- Backtest and Monte Carlo
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What you find out
Whether it would have lasted with real prices
The backtest plays your plan through the actual sequence of years: remaining wealth, lowest point, total withdrawn — and whether and when the portfolio would have run out.
In how many paths it would have lasted
The Monte Carlo simulation builds 10,000 possible sequences from real monthly returns and counts in how many your plan would have lasted to the end.
Which amount would have lasted
Paperball finds the highest withdrawal that would have lasted to the end in the backtest, and in Monte Carlo the highest that would have lasted in 90 % of paths.
Worked example: 4 % of €500,000 over 30 years
Say you have invested €500,000, 60% in German equities and 40% in German government bonds, and withdraw €20,000 in the first year, then more each year in line with inflation. This is how it would have turned out in 10,000 paths:
- Before tax92 %of paths would have lasted 30 years
- After German tax88 %of paths would have lasted 30 years
- Left at the end, median path€564,330in today's purchasing power, after tax
- Would have lasted in 9 out of 10 paths€19,424in the first year, that is 3.88 % of the starting wealth
The difference is the tax: every withdrawal is sold so that €20,000 arrives after tax. That means selling more, and that extra part is missing from the portfolio in the years that follow. In the median path, €332,450 in tax would have been due over 30 years, in euros of the respective years.
What would be left at the end varies widely: in the median path it would be €564,330 in today's purchasing power, at the lower bound €0 — only 5 % of paths would fall below — and at the upper bound €2,854,390.
With real starting years
With real starting years — one path per January from 1973 to 1996, in exactly the order in which the following years came — the money would have lasted in 24 of 24 starting years. It would have lasted in every one of these starting years.
When a crisis hits right at the start
The same paths, except that withdrawals begin with the months of a real crisis, in their real order:
| At the start of withdrawals | Would have lasted in | Median at the end, today's purchasing power |
|---|---|---|
| No particular crisis (all paths) | 88 % of paths | €564,330 |
| Financial crisis 2007–09 | 52 % of paths | €14,156 |
| Dot-com bubble 2000–03 | 34 % of paths | €0 |
| High inflation 1973–82 | 79 % of paths | €155,316 |
| The worst ten years in the price history | 66 % of paths | €70,839 |
The 4% rule: where it comes from and what changes in euros
The rule goes back to US financial planner William Bengen. In 1994 he used American prices to examine which first-year withdrawal — raised with inflation after that — would have lasted 30 years in every starting year he looked at. The Trinity study of 1998 counted, for various rates, allocations and periods, in how many periods the money would have lasted. Both calculated in dollars, without taxes and without costs.
For a portfolio in euros, three things change. The markets: German equities and government bonds have a different history from the US market. Inflation: the calculation uses Germany's. And tax: flat-rate withholding tax is due on the gain portion of every sale, plus the advance lump sum every year. In the worked example above, the rule would have lasted in 92 % of paths before tax and in 88 % after tax.
More in the guide to the 4% ruleWithdrawal calculator with a fixed return or Monte Carlo simulation?
Many withdrawal calculators use a fixed return: the same gain every year, the same inflation every year. Then there is exactly one answer — it lasts or it doesn't. The same plan as above, calculated once that way and once over 10,000 paths, both after tax:
| The same plan | Fixed return | Monte Carlo |
|---|---|---|
| Return | 8.0 % every year | real monthly returns in a new sequence, 8.0 % on average |
| Inflation | 2.7 % every year | that of the months drawn |
| Would have lasted 30 years | Yes | 88 % of paths |
| Left at the end, today's purchasing power | €596,616 | median €564,330, lower bound €0 |
| First-year withdrawal that would have lasted | €29,734 | €19,424 in 9 out of 10 paths |
The fixed return is the geometric mean of exactly the same price history — the same average, just without fluctuation and without order. What it lacks is the risk that weak years come right at the start of withdrawals. A capital drawdown calculator with a fixed return is fine for a first sense of scale; whether a plan would also have held up in weak sequences only the simulation shows.
What you can set
Withdrawals happen monthly, quarterly, half-yearly or yearly. You save a plan as a template and load it into any further calculation.
Fixed amount adjusted for inflation
An amount per month, quarter, half-year or year, raised by inflation every year if you like — that is also how you check the 4% rule.
Percentage of the current value
You withdraw a fixed share of the portfolio per year. The amount moves with the market, but the portfolio never runs empty.
Liquidity buffer for weak years
With a fixed amount, an interest-bearing pot next to the portfolio pays the withdrawal while the portfolio is well below its peak — and refills in good years.
Selling from overweight positions
In the backtest you sell proportionally or first what is above its target share — the withdrawal then pulls the portfolio back towards its allocation.
Pension and other income
In Monte Carlo you enter a pension, rent or part-time pay; the portfolio only covers what they do not.
Save first, then withdraw
If you like, a saving phase with a regular contribution runs before the withdrawals — in the backtest and in Monte Carlo, in one run.
Two views of the same plan
Both tools belong to the same account. Your plan says the most when you run it in both.
In the backtest: the path that happened
With real prices, order fees and tax. Each withdrawal is sold so that your amount arrives after costs and tax. You see exactly one path — the one from the past.
More about the portfolio backtesterIn Monte Carlo: many possible sequences
For withdrawals, the order of the years matters: a crash shortly after withdrawals begin weighs more than the same crash twenty years later. Monte Carlo draws the years in a new sequence and shows the range.
More about the Monte Carlo simulation
Sources
- William P. Bengen: “Determining Withdrawal Rates Using Historical Data”. Journal of Financial Planning, October 1994.
- Philip L. Cooley, Carl M. Hubbard, Daniel T. Walz: “Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable”. AAII Journal, February 1998 — the so-called Trinity study.
- Tax rules (German law): Section 32d EStG (flat-rate withholding tax), Section 20(9) EStG (saver's allowance), Section 18 InvStG (advance lump sum), Section 20 InvStG (partial exemption).
- Price history and consumer prices: a research series of German equities, German government bond yields from a central bank's yield curve and official consumer prices.
Questions about the withdrawal plan
What is a withdrawal plan?
A plan for how much you regularly withdraw from your portfolio, for example in retirement or during a sabbatical. Paperball runs it through historical prices and shows whether and how long your wealth would have carried the withdrawals.
What is the difference between a withdrawal plan and capital drawdown?
With capital drawdown, the withdrawal is sized so that the wealth is used up at a chosen point in time. A withdrawal plan can do that, but it doesn't have to: with a fixed amount you see whether the portfolio would have lasted to the end and what would have been left; with a percentage of the value it never runs completely empty.
Can I check the 4% rule?
Yes. The rule says: withdraw 4% of the starting wealth in the first year and raise that amount by inflation every year after. That is the fixed amount adjusted for inflation. Alternatively you withdraw 4% of the current value every year — then the amount moves with the portfolio. Where the rule comes from and which rates would have lasted over different lengths of time is explained in the guide to the 4% rule.
How is tax calculated on withdrawals?
Every withdrawal is sold so that your amount arrives after tax. Tax is only due on the gain portion of what is sold, after deducting the saver's allowance; for equity funds part of it is tax-free (partial exemption). On top of that comes the advance lump sum every year. In the backtest and in Monte Carlo you set the tax of your country.
What does a liquidity buffer do?
A pot next to the portfolio, sized in years of withdrawals and earning a fixed rate or the historical money market rate. When the portfolio is well below its peak, the buffer pays the withdrawal instead of selling at the low; in good years it refills. The buffer is available with a fixed amount.
Are a pension and other income taken into account?
In the Monte Carlo simulation, yes: you enter a pension, rent or part-time pay as a monthly amount from a year of your choice, rising with inflation if you like. They cover your needs first; only the rest comes from the portfolio. In the backtest the withdrawal comes from the portfolio alone.
Does the withdrawal plan cost extra?
No. The withdrawal plan is included in every plan, in the backtest and in Monte Carlo, also with your own securities and portfolios. A backtest or a Monte Carlo simulation costs as many credits with a withdrawal plan as without; you get starter credits when you sign up — see all prices.
Run the numbers on your own plan
Portfolio, withdrawal, buffer — enter your numbers and see how long they would have lasted with real prices.