Methodology of the free calculators: Vorabpauschale, savings plan, withdrawal and leveraged ETF

In depth8 min read · updated 28 October 2026 · 6 sources

Portfolio Lab's free calculators need neither an account nor price data: you enter numbers, and the computational core applies open formulas to them. This page describes what the code actually computes: the Vorabpauschale (advance lump-sum taxation) calculator under § 18 InvStG (Investment Tax Act), the savings plan with compound interest and costs, the withdrawal plan with optional Monte Carlo simulation and the leveraged ETF with volatility drag, each with its defaults, assumptions and limitations. Tax figures apply to private investors with a brokerage account in Germany under current law; the pages are not investment or tax advice.

Overview: four calculators, open formulas

All four calculators live in a single file of the computational core; the pages only display what the API returns. Inputs have fixed limits, such as a term of 1 to 60 years for the savings plan or leverage of 0.1 to 5. Anything outside these limits is rejected by the calculator with a message instead of producing nonsense.

• Vorabpauschale: for one fund and one calendar year, the basic income, the Vorabpauschale, the taxable portion after partial exemption (Teilfreistellung) and saver's allowance (Sparer-Pauschbetrag), the tax and the timing of the deduction.
• Savings plan and compound interest: initial amount, monthly contribution with annual increase, return, running costs and, if you wish, taxes up to the sale.
• Withdrawal: how long a sum of capital lasts, which withdrawal it supports exactly to the end and, with Monte Carlo, how safe that is when returns fluctuate.
• Leveraged ETF: mean return versus median, volatility drag, financing costs and a simulated distribution compared with L × index return.

The simulations use a fixed seed and 5,000 paths: the same inputs give the same figures. The remaining Monte Carlo error of a success probability p is √(p (1 − p) / 5,000), i.e. just over 0.7 percentage points at p = 50%.

Vorabpauschale under § 18 InvStG

The calculator follows the law InvStG (2016) and uses the same base rate as the backtest's tax engine (3.20% for 2026 according to BMF (2026)). The basic income is 70% of the base rate applied to the value at the start of the year, but at most the increase in value plus distributions; the Vorabpauschale is the part of the basic income that the distributions do not cover.

The taxable amount is the Vorabpauschale after partial exemption (equity funds 30%, mixed funds 15%, real estate funds 60% or 80%, other funds 0%) and after whatever saver's allowance is still available. The tax is the flat-rate withholding tax (Abgeltungsteuer) under EStG (2009) plus a 5.5% solidarity surcharge; with church tax at rate k, the flat-rate tax amounts to e / (4 + k) of the tax base e, plus the solidarity surcharge and church tax at rate k on that amount.

The bank already taxes distributions when they are paid; the calculator only deducts them from the basic income and does not include their own tax. On a later sale, the Vorabpauschalen already applied reduce the gain (§ 19 InvStG), so they are not taxed twice. If the base rate was not positive (2021 and 2022), no Vorabpauschale arises.

Savings plan: monthly, with costs in the fund price

The savings plan calculates in months. The contribution goes into the account at the start of each month (annuity due), the initial amount on the first day. The return p.a. is the same every year and is converted into a monthly return; the calculator deducts the running costs from the fund assets every month, using the same conversion as the backtest. The annual increase raises the contribution after every twelve months.

With taxes, the calculator keeps the same tax ledger as the backtest: each purchase as a separate lot, the Vorabpauschale every year with a fixed assumed base rate (default: the value for 2026), and the tax on it paid from the settlement account, not from the portfolio. At the end of the term, everything is sold; the gain after deducting the Vorabpauschalen is taxed after partial exemption. The saver's allowance applies per calendar year, and the ledger offsets a year's losses against the income of the same year.

Withdrawal: duration, sustainable withdrawal, Monte Carlo

The withdrawal (payout plan) is likewise deducted at the start of the month, and the remainder grows at the monthly return. If the withdrawal is inflation-adjusted, it rises by the inflation rate after every twelve months. The calculator tracks the capital for up to 100 years: if there is no longer quite enough for a withdrawal, it shows the number of full months and the remainder as a final partial withdrawal.

The Monte Carlo simulation draws monthly returns from a lognormal distribution with ln(1 + R) ~ N(ln(1 + r) / 12; σ² / 12). The return you enter is therefore the median, not the mean. This keeps the median path close to the calculation without fluctuations. Success means that all withdrawals over the term are paid in full. That just over half of the paths fail, even though the calculation without fluctuations just about works out, illustrates sequence risk: bad years at the start can hardly be made up later. Bengen (1994) used historical US data to test which inflation-adjusted initial withdrawal would have survived every period; the simulation asks the same question with random rather than historical returns.

Leveraged ETF: mean, median and volatility drag

A leveraged ETF resets its leverage L every trading day. The calculator uses the same daily formula as the leverage in the backtest: L times the index return, the financed part L − 1 costs the money market rate plus a spread, below L = 1 the remainder earns the money market rate, and running costs come on top. If the index follows a geometric Brownian motion, continuous-time calculation yields closed-form formulas, as derived for leveraged ETFs and tested on real funds by Avellaneda and Zhang (2010).

The simulation runs 5,000 paths with 252 trading days per year and lognormal daily returns; the index without costs runs alongside on the same random numbers. If a day falls to −100% or worse, the leveraged ETF is worthless. The page shows the median and mean, percentiles of the final value, the probability of doing worse than the index or than L × index return, and the distribution up to the 99th percentile. Why daily rebalancing makes the outcome path-dependent is also described by Cheng and Madhavan (2009).

Limitations and assumptions

• Constant rates: return, inflation, interest and costs apply over the entire term. Real markets move in phases; lognormal, independent returns underestimate crashes and fat tails, especially for leveraged ETFs.
• Base rate for future years: it is unknown. The savings plan assumes a fixed value, by default the value for 2026.
• Simplified taxes: no other investment income, no most-favourable assessment (Günstigerprüfung), allowance only for this savings plan or fund; distributing funds only via the distributions in the Vorabpauschale calculator. The withdrawal and leveraged ETF calculators work without taxes.
• No trading costs: no front-end load, order fees or spreads; leveraged ETFs without tracking differences.
• No advice: the calculators show what the formulas make of the inputs. Whether a savings plan, a withdrawal or a leveraged ETF suits you depends on more than these figures.

This page describes how Portfolio Lab calculates; past results are not a forecast. All terms in the glossary.