Monte Carlo simulation

A plain projection applies one expected return to every year and draws one line. A Monte Carlo simulation repeats the projection over many randomly generated sequences of returns, so a run can have a bad decade early, a good one late, or anything in between. Run the plan many times and the result is a set of paths rather than one.

The paths are summarized two ways. At a given age, ranking the balances gives percentiles: the 10th percentile is the balance that one path in ten falls below. At the plan's end, counting the paths that still hold money gives the success rate.

A success rate is not the chance that a real retirement works out. It is a count of simulated paths, and the paths come from the assumptions put into the simulation: the expected return, how widely the returns vary, the spending and the length of the plan. Change an assumption and the rate is recomputed from the new one.

A plan is simulated 500 times. The runs start from the same balance and take out the same planned spending; only the yearly returns differ. At the plan's end age, 440 of the 500 paths still hold money and 60 have reached zero.

The success rate is 440 out of 500, or 88%. The figure does not say how early the other 60 paths ran out, or how much money the 440 had left.

Paths simulated

500

Paths at zero before the end

− 60

Paths still funded at the end

440

Success rate, 440 ÷ 500

88%

A single projection at an average return shows where the plan lands if every year earns that average. A simulation shows how far the balance can land from that line when the returns vary, and in how many runs it reaches zero.

The success rate counts paths and nothing else. A path that ran out a year before the end and one that ran out twenty years before it count the same.

The Taiga Finance Retirement savings planner simulates every plan it solves. Its “Chance money lasts” figure is the share of simulated return sequences in which the money lasted to the plan's end. Opened, it lists the “Real return” and the “Return spread” the paths drew from, the number of “Simulated return sequences” and the “Sequences that never ran out”.

On the balance chart, the band between the 10th and 90th percentiles of simulated paths is the “Simulated range”, shown or hidden by a chip in the chart header. The expected real return is set under “Assumptions”; the spread is fixed at 12 points around it, and each path re-runs the plan under its own randomized yearly returns.