How Monte Carlo retirement simulations work

The one-paragraph version

The simulator takes your plan — current pot, savings rate, retirement age, target spend, any guaranteed income — and replays it 5,000 times. Each replay rolls a different random sequence of yearly investment returns drawn from a probability distribution that matches the historical behaviour of global equities. At the end of each replay we check whether your money survived to your plan-to age. The percentage that survive is the probability of success. The percentile bands of pot values per year give the fan chart.

What we sample (the returns)

Annual real returns are sampled from a log-normal distribution with a default mean of 5% and standard deviation of 12%. "Real" means after inflation, so all figures stay in today's pounds and the maths doesn't drift over decades.

Log-normal is the standard choice for modelling investment returns because:

• It can't go below −100% — you can't lose more than your pot.
• It has positive skew — occasional big up years and rarer bigger up years, which matches reality.
• It's the standard distribution used in academic finance (Black-Scholes uses it; nearly every retirement simulator does too).

The 5% real / 12% volatility numbers match the long-run behaviour of globally diversified equity portfolios (Dimson, Marsh, Staunton, Credit Suisse Global Investment Returns Yearbook). UK-only equities have historically been slightly lower, US-only slightly higher; 5% is the global midpoint. For a 60/40 stock-bond portfolio the equivalent would be roughly 3.5% real with 8–9% volatility — adjust your expectations downward if your portfolio is more defensive.

growth_factor = exp( μ_log + σ × Z ), where Z ~ N(0,1)
μ_log = ln(1 + 0.05) − 0.5 × 0.12² ≈ 0.0419
annual_return = growth_factor − 1

What we apply (the year-by-year machinery)

For each year of each simulation:

1. Sample one annual real return from the log-normal distribution above.
2. Apply it to the pot multiplicatively: pot = pot × (1 + r).
3. If you're still pre-retirement, add this year's contribution.
4. If you're in retirement, work out what gross drawdown you need to meet your target net spend, after considering guaranteed income and tax. Subtract that gross drawdown from the pot.
5. If the pot hits zero, mark the simulation as failed and record the depletion age.

At the end of all 5,000 simulations we have, for every age between today and your plan-to age, a list of 5,000 pot values. Sorting that list gives the percentile bands shown in the fan chart.

The UK tax model

Drawdown tax is calculated each year using a simplified UK income-tax model:

• Personal Allowance: £12,570 (frozen until at least 2028 by current legislation).
• Basic rate band: 20% on income from £12,570 to £50,270.
• Higher rate band: 40% on income from £50,270 to £125,140.
• Additional rate (45%) and personal-allowance taper above £100,000 are not modelled — they affect a small minority of retirees.
• National Insurance is correctly not applied to retirement income (NI is on earned income only).

SIPP drawdown is split 25% tax-free (the Pension Commencement Lump Sum) and 75% taxable as earned income. ISA withdrawals are entirely tax-free. State Pension and DB pensions are fully taxable as earned income.

When a drawdown is needed, we iterate to find the gross drawdown that nets your target after tax. Three iterations is sufficient for £1 precision across all typical drawdown sizes.

How we treat guaranteed income

"Guaranteed income" in the simulator means streams that pay in from outside the invested pot — State Pension, defined-benefit (DB) pensions, annuities. These are subtracted from your target spend before computing the gross drawdown needed. They are taxed correctly (basic + higher-rate bands apply just as with the drawdown).

SIPP drawdown, ISA withdrawals and GIA income are not treated as guaranteed — they come from the invested pot, which the simulator is already modelling.

State Pension is £11,502 per year for 2026/27 (the new full State Pension, weekly rate £221.20), starting at age 67. The free tool assumes the full rate if you tick the box — set it differently in the full WealthR app if you have a partial NI record.

What we don't model

This is a planning aid, not an exhaustive simulation. The deliberate simplifications:

• Scottish income tax rates — the basic/higher bands differ. The full WealthR app handles this; the free tool uses rUK rates.
• Dividend allowance, savings allowance, capital gains — the free tool assumes all drawdown comes from a SIPP (75% taxable). GIA-heavy retirees will see slightly different real numbers.
• Variable spending — assumes the same real-£ spend every year. Most retirees actually spend more in early "go-go" years and less later. The Guyton-Klinger rule, "fun-money" floors and other dynamic withdrawal strategies are not modelled here.
• Sequence of contributions — pre-retirement contributions are modelled as constant in real terms. If you'll plausibly contribute more later (promotions, employer match changes), the result is conservative.
• Asset allocation glide-paths — uses one volatility figure across the full timeline. In reality most retirees de-risk into retirement (lower volatility post-65). Glide-paths can be modelled with custom assumptions in WealthR Pro.
• Healthcare shocks, divorce, late-life care costs — none of these are in the model. A retirement plan should have a buffer for one-off bad years separate from the Monte Carlo number.
• Inflation diverging from real-return baseline — modelling in real terms is equivalent to assuming the inflation rate is "baked in" to the 5% return. Periods of unusually high inflation (1970s, 2022–2023) would compress real returns and lower the success probability.

Why 5,000 simulations and not 10,000?

5,000 is the smallest number that gives stable probability-of-success figures (within about ±1pp on re-run). 10,000 doubles compute time for a barely-visible improvement in precision. The full WealthR Pro app can bump this to 10,000 or 25,000 if you want a higher-confidence number.

How accurate is "82%"?

The probability number is the output of a model. It is not a literal statement about your future. It assumes returns will continue to behave roughly as they have over the last century, which is a strong assumption (the last century included both world wars, the Great Depression and the global financial crisis, so it's not naively optimistic — but it could be wrong).

Treat the number as a comparative tool, not a prophecy. What it's good for: seeing how small changes (retire 2 years later, spend 10% less, save £200 more per month) move the probability. What it's not good for: deciding whether 82% is "high enough" or whether 78% means you'll be poor in retirement. Most planners target 80–95% confidence and adjust the plan if the number is outside that range.

What's different in the full WealthR app

The simulator inside the WealthR app uses the same engine but with significantly more inputs and accuracy:

• Pulls your actual ISA balance, every SIPP and DB pension, partner pensions, BTL income, property equity from your real tracked data.
• Applies the full UK tax model — Scottish rates, HICBC, Marriage Allowance, dividend and savings allowances, personal-allowance taper.
• Treats each pot separately for drawdown order optimisation (e.g. take ISA before SIPP, or vice versa depending on tax).
• Saves multiple named scenarios so you can compare side by side (Pro).
• Generates a PDF report you can share with an IFA (Pro).

Source code and audit

The simulation engine is a single client-side JavaScript file (/mc.js) loaded on both the free tool and inside the app. It runs entirely in your browser — your inputs never leave your device. The file is heavily commented; if you want to audit the maths, view source.

This is a planning aid, not regulated financial advice. For a definitive plan tailored to your circumstances, consult a UK financial adviser registered with the FCA.