Christopher Schildt

Every projection — accumulation, drawdown, or a historical replay — runs the same recursion, once per month, from your current age to 100:

This is also the exact calculation the AI Coach runs whenever you ask it about your future finances — it never does the math itself, it calls this same code every time. More on why, in the AI Usage Policy.

Everything below describes how r(n) and C(n) get their values.

What’s included — and what isn’t

Other Assets stay off this curve deliberately. Wealthspan asks one specific question — will your liquid capital cover your spending? — and an asset you can’t readily draw down to pay a bill doesn’t answer it.

Debt

Debt is modelled as cash flow, not as a balance-sheet offset. Each debt’s monthly payment reduces your spending total, which reduces your surplus, which reduces what compounds. Once a debt is paid off, its payment drops out and your surplus rises accordingly. The model never subtracts your outstanding debt balance from your portfolio value — Wealthspan tracks what you’re building, not your net worth.

Tax

Income is taxed by type, not by age or retirement status:

Pension contributions come out of earned income before tax — the way they actually work — then get added back untaxed to your monthly total, since they’re going into your investments rather than your spending.

Monthly surplus and shortfall

Withdrawing £1,000 net from a portfolio doesn’t cost the portfolio £1,000 — it costs however much needs to be sold to net £1,000 after tax. The model accounts for that at every age, so working an extra year never looks artificially better or worse than reality.

Rate of return

You choose one of three allocation tiers, each a fixed real (inflation-adjusted) annual rate, converted to a monthly rate: Conservative (3%), Balanced (5%), Growth (7%). Where we hold your actual portfolio allocation, we pre-select the tier that matches it.

That headline rate is then discounted by the share of your portfolio currently held in cash — cash isn’t earning the same return as cash invested, so it’s excluded from the growth calculation, not double-counted. One honest limitation worth stating: this cash percentage is a snapshot, taken once from your current holdings, not something the model re-checks month by month. A 50-year projection therefore assumes your cash allocation today stays constant for the rest of your life. It’s a simplification, not a forecast of your future rebalancing decisions.

Inflation

The model runs in real terms throughout. Anything you enter is treated as today’s money and stays level in real terms unless marked as inflation-linked, in which case it grows at an assumed 2.5% a year. This keeps the projection in comparable, today’s-money terms rather than mixing inflated future numbers with current ones.

Historical backtesting

Rather than assuming one fixed return every year, the same equation runs again — 95 separate times — using real historical returns instead of a flat rate: 152 years of US stock market data (1871–2022) and 98 years of US bond data (1928–2025), from two established academic datasets. For blended stock/bond scenarios, the model uses the 95 years both datasets share (1928–2022), starting your exact plan from every one of those years — so you can see how it would have held up starting in the Depression, the 1970s, or 2008, not just an “average” year.

The stock series is adjusted down by 2.3 percentage points a year, reflecting that US markets have historically outperformed the rest of the world’s by roughly that margin — so the projection doesn’t quietly assume uniquely strong US returns forever.

This modelling is currently based on US market history.

The core method

Every survival curve in the product — whether the interactive chart in the Healthspan widget or the single headline number on your Home tab — starts from the same actuarial transformation:

In plain terms: S_adjusted(x) is the number the whole equation is solving for — your own adjusted chance of surviving to a given age x, once one specific habit has been factored in. It’s what actually gets plotted on the curve, at every age from where you are now to 100.

The right side says how to get there: take the population baseline, S(x), and raise it to the power of HR. Raising a number to a power isn’t multiplication — it’s a stronger kind of scaling, and here it works like a dial. An HR below 1 (say, 0.5 — half the population’s risk) pushes your adjusted survival curve above the baseline. An HR above 1 (say, 1.5 — 50% higher risk) pushes it below the baseline. An HR of exactly 1 leaves the baseline exactly where it is.

This is the standard method actuaries and epidemiologists use to adjust a baseline survival curve for a single risk factor. Every curve you see is this same equation, run against your own current habits.

Why we only show one variable at a time

Multiplying several hazard ratios together — say, your VO2 max hazard ratio times your sleep hazard ratio — technically produces a number. But doing that assumes the two risk factors act entirely independently of each other, with no interaction at all. That assumption isn’t something the research actually supports with enough precision to model responsibly. Real risk factors interact in ways the literature hasn’t fully quantified.

So rather than combine everything into one falsely precise “your total adjusted lifespan,” the interactive chart shows one variable’s effect at a time, clearly labelled, against the population baseline. It’s a deliberate trade-off: less impressive-looking at first glance, considerably more honest about what the evidence can actually support.

How this becomes your Home tab’s Lifespan Outlook

The Lifespan Outlook figure on your Home tab runs the identical equation across every health variable we can measure or reasonably estimate for you, and surfaces the single one currently furthest from the population average — for better or worse — as a signed number of years, alongside a plain sentence naming what’s driving it (“Your consistent strength training is associated with a longer-than-average lifespan,” for example). It’s the same evidence, the same maths, and the same population baseline as the full interactive chart — just collapsed to the one number and one sentence that’s most useful at a glance, rather than the full picture the widget itself gives you.

What none of this is

Not a diagnosis. Not a personal life-expectancy prediction. It’s population-level evidence, applied honestly to your own tracked and self-reported data — a way to see where your habits sit relative to people like you, not a forecast of your actual future.

Every health domain is built on named, peer-reviewed sources — not wellness-blog consensus. A sample, grouped by module: