What is a Monte Carlo projection?

It runs your investment many times — here, 1,000 simulated paths — drawing each year's return at random from a distribution around your expected return, instead of assuming the same return every year. The output is a spread of possible after-tax balances (a 10th-to-90th-percentile fan) rather than a single line, which reflects that real returns vary year to year. It is an illustrative model of uncertainty, not a forecast of what any ETF will do.

How does it handle NZ tax?

Tax is applied each year using the method you select — PIE @ PIR, FIF @ FDR, or FIF @ CV — with the same mechanics as the after-tax calculator. FIF @ FDR taxes 5% of opening market value at your marginal rate regardless of the actual return that year; PIE @ PIR and FIF @ CV depend on the realised gain. Because returns are randomised, the tax differs path to path under PIE and CV, while FDR tax tracks the (also-random) account balance.

What return and volatility should I enter?

Use a long-run average return and a volatility (standard deviation) that match the ETF's exposure. As an illustrative guide, a broad diversified equity index ETF has historically sat around 13–17% annual volatility; single-country, single-sector, or thematic ETFs are typically higher. These are assumptions you choose, not promises — higher expected return generally comes with a wider fan of outcomes.

Why do the numbers change slightly each time?

Each set of 1,000 paths uses fresh random returns, so the percentile figures shift a little run to run. That variability is inherent to a Monte Carlo model. The shape — a median outcome with a widening range around it — is stable; the exact dollar figures are indicative, not precise.

Can a real outcome be worse than the lower (P10) figure?

Yes. The model draws returns from a normal distribution, but real markets have fat tails — crashes happen more often and more severely than a normal curve implies — and return-sequencing risk matters near the end of the horizon. A genuine worst case can be worse than the 10th-percentile figure shown. Treat the lower band as a rough poor-returns scenario, not a floor.

Tool · Updated 2026-09-05

Monte Carlo projection: the range of after-tax outcomes

A single average-return line hides the thing that actually matters: returns vary year to year, and the order they arrive in changes where you land. This tool runs your ETF investment 1,000 times with randomised returns and shows the full after-tax spread — under your chosen NZ tax wrapper — plus how often it reaches your goal.

Your assumptions

Principal invested (NZD)$50,000Time horizon (years)1–30 yearsExpected average return7.0% per year (illustrative; not a forecast)Return volatility (std dev)15% per year — broad-index ETF ≈ 13–17%; single-sector / thematic higherTax methodCompare all three methods side by side →Savings goal (optional, NZD)$150,000Your PIR (for PIE @ PIR)Your marginal rate (for FIF FDR / CV)

Median outcome (P50)

$96,675

half above, half below · PIE @ PIR · year 15

Lower outcome (P10)

$57,208

1 in 10 paths below — poor-returns scenario

Upper outcome (P90)

$163,094

1 in 10 paths above — strong-returns scenario

Reached goal

14%

141 of 1,000 paths reached $150,000

Range of outcomes by year

Each bar spans the 10th–90th percentile of 1,000 simulated after-tax balances (PIE @ PIR); the notch marks the median (P50). The fan widens because uncertainty compounds over time.

$52,403

$54,736

$57,047

$59,843

$62,070

$64,185

$67,787

$70,608

$74,560

Y10

$78,079

Y11

$81,559

Y12

$84,229

Y13

$89,062

Y14

$92,876

Y15

$96,675

P10–P90 range

Median (P50)

Caveats

This is a stochastic model, not a forecast. It shows a spread of hypothetical outcomes under your assumptions — it does not predict what any ETF will actually do.
Returns are drawn from a normal distribution. Real markets have fat tails (crashes are more frequent and severe than a normal curve implies) and return-sequencing risk, so genuine worst cases can be worse than the P10 shown here.
Past performance is not a reliable indicator of future returns. Your expected-return and volatility inputs are assumptions, not promises.
Tax is applied annually using the selected method's current mechanics. FIF @ FDR uses the 5% deemed rate on opening value regardless of actual return; PIE and FIF @ CV depend on the realised gain. Real-world tax has further detail (e.g. the FDR/CV annual election) — see the after-tax calculator and your tax adviser.
The spread between the P10, P50 and P90 bands is the point of a Monte Carlo model — it is uncertainty, not a range of forecasts. Changing any assumption re-draws the paths; returning to the same assumptions reproduces the same figures, so a number you were shown can be checked.
General information only, not personalised financial advice. For advice see a licensed financial adviser.

Monte Carlo projection: the range of after-tax outcomes

Caveats

Continue with

After-tax calculator

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FDR vs Comparative Value method

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