An expectation need not be a possible outcome
€10,000Starting money
50% chance → 20% gain€12,000
50% chance → 10% loss€9,000
A probability-weighted average of the two branches. Neither branch pays this amount.
Expected return weights possible outcomes by their estimated probabilities. An average supplies no promised payment or known personal result.
Calculate the average without inventing a third outcome
0.5 × 20% + 0.5 × (−10%) = 5%; the two balances average €10,500. This restricted model still has only its two outcomes.
Real investments have many possibilities and uncertain probabilities. A sensible estimate cannot identify your outcome, and risk creates no obligation to reward you. Consider potential return alongside losses you could sustain.
Keep evidence within its observed limits
A longer history broadens evidence without ensuring future conditions or every risk are represented. A quiet record does not rule out severe losses. Simulating unchanged assumptions more often does not fix a missing risk.
Separate history, backtests and model projections
A backtest applies rules to past data, without necessarily recording anyone following them then. Costs, information available at the time and choices made after seeing the results can affect it. Past performance, targets and projections differ; none is a contractual return for an investor starting today.
Vanguard’s appendix warns that historical patterns may differ from future returns and that projections may understate extreme adverse scenarios absent from the estimation period. The source supports this evidence limitation, not adoption of its outlook or portfolio forecasts. A forecast later succeeding does not remove the limitation.
Time may allow flexibility, not guarantee recovery, business survival or freedom from earlier spending needs. Even without a reliable personal probability, an unlikely event deserves attention if it blocks an essential payment or creates unaffordable debt.
Check the target inside the model
Inside one set of assumptions
Success criterion: reach the model’s target balance at its target date.
90 / 100simulated paths reach that target · 10 do not
Outside this count: risks omitted from the assumptions. These are model results, not observed future lives and not a guarantee of a 90% real-world chance.
A target-date balance may miss an earlier bill, future prices or interrupted earnings. Repeating the simulation cannot add risks its assumptions leave out.
Separate known terms from chosen assumptions
On 22 October 2026, a hypothetical statement shows €12,000 assigned to a fixed €13,000 bill due on 22 October 2027. These are nominal euros; a separately assigned reserve is outside this capital. The bill and starting balance are given conditions. A budget estimates a €1,000 contribution at the end of the year; future earnings could change it.
For this exercise, choose 0%, +5% and −15% investment returns after investment expenses, before personal taxes. These are stress scenarios, not predictions or a complete list of risks: deliberate inputs with no historical estimate or probability attached. Keep the contribution at the end, so it earns none of that year’s return.
€12,000 now → investment change → contribution at the deadline
| Path: return / end contribution | Before → after contribution | Against payment |
|---|---|---|
| 1. 0% / €1,000 | €12,000 → €13,000 | Exactly funded |
| 2. +5% / €1,000 | €12,600 → €13,600 | €600 surplus |
| 3. −15% / €500 | €10,200 → €10,700 | €2,300 gap |
Holding the €1,000 contribution constant, changing 0% to +5% adds €600. That is sensitivity to one input. In path 3, investments fall and the contribution shrinks together: €12,000 × 0.85 + €500 = €10,700, leaving €2,300 missing. The joint stress changes two assumptions; it cannot tell you which one caused the whole gap.
Record the basis of each input: statement for capital, bill terms for amount and deadline, budget for contributions, explicitly chosen conditions for returns. A historical sample or projection would require dates, market, currency, income and cost scope, as well as an explanation of why it informs this goal. More simulations cannot supply that evidence.
What could resolve the shortfall?
Check whether the payment really is fixed, when contributions become available, and how lower income affects essentials and the separately assigned reserve. Do not add that reserve without reconciling its other jobs. Additional funding, a smaller expense or a later date changes a real input when the terms permit it. Raising an assumed return changes no available money.
The three paths do not exhaust possible outcomes. An earlier bill, higher expense or delayed access could break a goal that reaches its modelled year-end target.
Make a scenario record with new conditions
A second hypothetical statement dated 22 October 2026 gives €9,000 now and a fixed €10,000 nominal-euro payment on 22 October 2027. A contribution arrives only at the end. Use these three chosen combinations: +4% / €1,200 contribution; 0% / €1,200; −20% / €300. Returns include investment expenses; personal taxes are omitted. No reserve is included.
Calculate the three ending amounts and gaps. Mark the fixed conditions, estimated contributions and chosen return assumptions with their basis. Propose a feasible funding, expense or date change and name an unknown that needs verification.
Compare the scenarios and review criteria
€9,000 now → investment change → contribution at the deadline
| Path: return / end contribution | Before → after contribution | Against payment |
|---|---|---|
| 1. +4% / €1,200 | €9,360 → €10,560 | €560 surplus |
| 2. 0% / €1,200 | €9,000 → €10,200 | €200 surplus |
| 3. −20% / €300 | €7,200 → €7,500 | €2,500 gap |
The ending balances are €10,560, €10,200 and €7,500. The joint stress leaves €2,500 missing. These are conditions, not chances of success or worst possible losses.
For example, investigate whether other genuinely available funding can cover €2,500, or whether the payment can be reduced or moved under its actual terms. Check the budget and bill before treating either change as possible. A larger assumed return alone is not a repair.
Check that the same nominal-euro deadline is used throughout, the contribution earns no return before arrival, and facts remain separate from assumptions. Different proposed changes are acceptable when their funding and conditions are explicit. Keep the record for the next chapter: which inputs could deteriorate together?