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Monte Carlo simulation

Running thousands of randomised return paths to estimate the distribution of outcomes for a portfolio or withdrawal plan rather than a single average.

An average is a poor planning tool. A plan that works at a 7% average return may fail in a third of paths that average 7% but arrive in an unhelpful order. Simulation makes that spread visible.

Typical output: run 10,000 paths for a $1,000,000 portfolio withdrawing $40,000 a year for 30 years, and report that 86% of paths end with money remaining. The 14% failure rate is the number worth acting on, not the median ending balance.

The results are only as good as the assumptions. Drawing returns independently from a normal distribution understates crashes and ignores the way bad years cluster. Bootstrapping from actual historical blocks, and stress-testing with a deliberately poor first decade, gives a more honest picture. See sequence-of-returns-risk and risk-of-ruin.

Related: sequence-of-returns-risk, safe-withdrawal-rate, risk-of-ruin, backtesting, mean-variance-optimization

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

Risk of ruin against risk per tradeA curve climbing steeply as the share of the account risked on each trade grows, even though every trade carries a small positive edge.CHANCE OF LOSING THE ACCOUNT0%20%40%60%80%05%10%15%20%25%RISK PER TRADE (% OF ACCOUNT)2% → 1.8%5% → 20%10% → 45%20% → 67%assumes a 52% win rate at 1:1, ruin = account goneruin chance = (0.48 ÷ 0.52) ^ (100 ÷ risk %)
Risk of ruin. The chance of losing the whole account, plotted against the share of it staked on each trade, for a method that wins 52% of the time at even money. The edge is the same all along the curve; only the bet size changes.

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