A retirement projection built on a single number — "assume 7% per year" — answers the wrong question. It tells you what happens on one perfectly smooth path that the market has never actually delivered. Real returns arrive jagged: a strong decade, a flat stretch, a crash three years before you plan to stop working. A Monte Carlo simulation replaces that single path with thousands of them, and the output stops being a number and becomes a distribution. This walks through building one in Python and, more importantly, understanding what it can and cannot tell you.
Why a Single Average Return Lies to You
The standard projection uses the deterministic compound-growth formula: start with a balance, multiply by (1 + r) every year, subtract withdrawals. It is easy to put in a spreadsheet and it produces a clean curve. The problem is that the clean curve corresponds to a sequence of identical annual returns, and no such sequence has ever occurred.
The full set of returns over 30 years does determine your ending balance if you never withdraw — multiplication is commutative. But the moment you take money out, the order of returns matters. A bad year early in retirement forces you to sell more shares to fund the same withdrawal, and those shares are gone before any recovery can compound them. Two retirees with the identical 30-year average can end up with wildly different outcomes depending on when the bad years landed. A single-average projection cannot see this. It computes one path and hides the distribution of paths around it.
