Retirement Time Machine

retire in January of withdraw each year, % of the starting sum (real) in stocks (the rest in bonds), rebalanced monthly for how many years

this retirement

the same years, reversed

same returns, opposite order

its safe maximum

the most that lasted, this start

history at this rate

ever running out, closed form

P(ν, 2w/σ²), forever

this mix, a year (real)

μ and σ, 1871–2026

This retirement, in multiples of the starting sum (real) · in order · the same years reversed

The safe maximum of every start year · your withdrawal · ● your start

Robert Shiller's monthly real total returns of the S&P Composite and of 10-year Treasuries, 1871–2026. Each January the retiree takes the same real amount; a retirement runs out when a withdrawal finds less than that. The closed form treats the mix as a geometric Brownian motion with the μ and σ of its January-to-January returns and asks whether the money ever runs out (Dufresne, 1990).