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Money

Monte Carlo simulation

Running a plan thousands of times with randomly generated returns (and sometimes inflation) to see the range of possible outcomes.

Explanation

A straight-line projection that assumes, say, 6% every year shows one possible future, and not a very realistic one. Markets do not deliver averages smoothly, and as sequence-of-returns risk shows, the order of returns matters once you are withdrawing.

Monte Carlo simulation addresses this by:

  1. Generating a random sequence of yearly returns for each asset class, using expected returns, volatilities and correlations (some models also randomize inflation).
  2. Running your full plan through that sequence: contributions, withdrawals, taxes, loan interest, rebalancing.
  3. Repeating thousands of times (each run is a “trial” or “path”).
  4. Summarizing the results, for example the share of trials that never ran out of money and the 10th, 50th and 90th percentile balances each year.

Limitations to keep in mind:

  • Results are only as good as the assumptions. Optimistic return inputs produce optimistic results.
  • Many models draw returns from a bell curve, which understates extreme events, and treat each year as independent, which ignores how markets sometimes trend or revert.
  • Simulations usually assume you keep following the same plan, while real people adjust.
  • A precise-looking number like “87.3%” carries more uncertainty than it implies.

An alternative is historical simulation, which replays actual past sequences. It uses real market behavior but has far fewer independent periods to test.

In scenarios, Monte Carlo mode runs your plan many times, shows a fan chart of percentile bands, a success rate, and (for leveraged plans) how often a margin call occurred.

Example

You simulate a 30-year retirement 10,000 times. Each year’s stock return is drawn at random from a distribution with a 7% average and 15% volatility.

One year of one trial: the random draw is 1.2 standard deviations below average, so the return is 7% − 1.2 × 15% = −11%. A $1,000,000 balance, after a $40,000 withdrawal, becomes $960,000 × 0.89 = $854,400.

After all trials, 8,700 never ran out of money: a success rate of 8,700 ÷ 10,000 = 87%. Sorting the 10,000 ending balances, the 5,000th-ranked value is the median outcome.

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