All the Numbers

Monte Carlo: many market histories

From the All the Numbers wiki · The plan itself

A plain projection grows every account at one fixed rate, which no market does. Monte Carlo runs the same plan many times, each time with different yearly returns, and reports how the results are spread. It describes a range of outcomes under the plan's assumptions. It is not a forecast, and it is not a probability that the plan succeeds in the real world.

The rules

  • 500 runs, called paths. The random draws are seeded, so the same plan gives the same result each time.[1]
  • Returns vary each year. A year's gross return is lognormal, centred so that the middle path grows at exactly the plan's rate. The plan's own projection is therefore the middle of the spread.[2] See expected returns.
  • Volatility is the yearly standard deviation. It is read from PWL Capital's table by the account's expected return: 11.02% at the default 6.35%, up to 13.03% at 6.92% and down to 5.41% at 3.58%, and held at those ends beyond them.[3] A home's value varies by 14.7% a year.[4] See home prices.
  • One market for every investment account. They rise and fall together. Each home moves on its own, independent of the market and of other homes.
  • Years are independent. A bad year does not make the next one better or worse.

What the engine does

  • Runs each path through the ordinary plan, so tax, withdrawals, borrowing and benefits respond to the path as they would to a real year.
  • Keeps inflation, pay, tax rules, savings interest and mortgage rates as the plan has them. Only investment returns and home prices are random: cash and savings accounts earn their set rate in every run.[1]
  • Shows the bands: at each year-end the 10th, 25th, 50th, 75th and 90th percentile of net worth, in the chart as a light band for the middle 80% of paths, a darker one for the middle half, and a line for the median. Figures can be shown in today's dollars. See net worth for what is counted.
  • Sorts each path into three outcomes: finished without borrowing, finished owing on a line of credit (or borrowed and repaid), or ran out.
  • "Ran out" means the plan could not pay a month's bills even after drawing on its accounts in order and borrowing to the lenders' limit. That path stops, and its line ends where the money did. Its later years are left out of the bands rather than counted as zero, and the share of paths still running is reported each year.[1] Late in a plan where many runs stop, the bands describe the runs that are left, which are the luckier ones.
  • Gives each outcome rate with a 95% margin for the error from using 500 paths.

What it deliberately does not

  • It does not randomize inflation, pay, interest or mortgage rates. For one bad event on top of the plan, see stress tests and scenarios.
  • It does not model extreme years more severe than the normal curve, runs of bad years, or recovery after a fall. Each year is a separate draw.
  • It does not link home prices to the market.
  • It does not change the mix of investments as a person ages, or vary how long they live. The horizon is the plan's; see the plan horizon.

See also

  • Events outside the plan's horizon · An event, purchase or sale dated before the plan starts or after it ends is ignored rather than clamped into range, and the plan says which one it dropped.
  • Expected returns and fees · The default return is 6.35% a year, nominal and net of fees, for an 80/20 stock and bond portfolio. It is an expected long-run average, not a forecast, and an account's own rate replaces it.
  • Home prices over time · A home's value is projected by growing it at one assumed rate, 3.5% a year by default, which is PWL Capital's 1% real return on a house plus 2.5% inflation. It is an editable assumption, not a forecast, and the Simulation view shows how widely a real home's value varies around it. A home added to a plan starts at $600,000 with 20% down until you enter its own figures.
  • Inflation and today's dollars · The default inflation rate is 2.5% a year. A future dollar amount can be shown as is, or divided by (1 + inflation) for each year to show what it would buy today.
  • Net worth, as the plan counts it · Net worth is everything the plan holds (cash, investment and registered accounts, homes at market value) minus mortgages, credit lines, debts and tax owing. It is not reduced for selling costs or for tax on money still in an RRSP.
  • Scenarios and life events · The Scenarios page lets you drop dated events onto a copy of your plan, such as a job loss, a market drop or a rate jump, and see where net worth ends up. Each event is a change to the plan run through the ordinary projection, not a separate calculator.
  • Stress tests · A stress test reruns the whole plan with one thing made worse, such as a higher mortgage rate at renewal or a year of lost income, and reports how far final net worth moves and whether the plan still pays its bills. It carries no probabilities.
  • When the plan runs short of cash · When a month needs more money than the plan has, it draws savings in a set order, then borrows on a home equity line at 5.13% and an unsecured line at 8.38%, as far as a lender would lend. When no lender would lend more, the projection stops.
  • Which assumption matters most · The sensitivity chart moves one assumption at a time, down and up by a fixed step, and ranks them by how much the final net worth in today's dollars changes. Inflation is often the largest bar because it moves much more than one number.

References

  1. ↑PWL Capital — Financial Planning Assumptions, Tables 2 and 8 (volatilities); our convention. The stopped paths and the unrandomized savings rate are our reading: PWL gives volatilities for invested portfolios only, and a path with no money left has no net worth to rank · Monte Carlo runs the plan many times with each year's investment return and home appreciation drawn at random — lognormal, centred so the middle path is the plan, with PWL's volatilities; all investment accounts move together, each home on its own; inflation, pay, tax rules and interest rates stay as the plan has them. It reports how often the plan finishes without borrowing, finishes owing, or stops, each with its sampling error, and the spread of net worth year by year. A path that runs out of money and credit stops, and each year's spread is taken over the paths still running that year; cash and savings accounts earn their set rate on every path. · effective 2026-10-01
  2. ↑PWL Capital — Financial Planning Assumptions (Market Capitalization Weighted Portfolio), mid-year 2026 data update, Table 8 (Portfolio Expected Returns) · Default expected return on an investment account a year, nominal and net of fees, for an 80/20 equity/bond market-cap portfolio (PWL Capital, Financial Planning Assumptions, Table 8) · 6.35% · effective 2026-08-17
  3. ↑PWL Capital — Financial Planning Assumptions (Market Capitalization Weighted Portfolio), mid-year 2026 data update, Table 8 (Portfolio Expected Returns) · Yearly volatility (standard deviation) of a diversified portfolio by its expected return: 13.03% at 6.92% (100/0), 11.02% at 6.35% (80/20), 9.12% at 5.73% (60/40), 7.42% at 5.06% (40/60), 5.41% at 3.58% (0/100) (PWL Capital, Financial Planning Assumptions, Table 8) · See the source · effective 2026-08-17
  4. ↑PWL Capital — Financial Planning Assumptions (Market Capitalization Weighted Portfolio), mid-year 2026 data update, §3 Primary Residence, Table 2 · Yearly volatility of an individual Canadian home's value: market plus idiosyncratic (PWL Capital, Financial Planning Assumptions, §3 and Table 2) · 14.7% · effective 2026-08-17