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Monte Carlo: many market histories

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.
  • 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. 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. A home's value varies by 14.7% a year.
  • 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.
  • 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.
  • 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.
  • 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.

Connected to

  • 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.
  • 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.
  • 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.

Sources