The calculator
Initial withdrawal rate3.1%1.5% + 0.5 / CAPE
First-year spending$30,625
Ending portfolio$1,630,914Horizon completed
CAPE 32.0 implies 3.1%, so $1,000,000 pays $30,625 in year one.
Success rate74%1000 seeded paths
10th percentile ending$0
Median ending$780,944
90th percentile ending$4,383,953
The formula
WR = 1.5% + ½ × (1 / CAPE). Earnings yield at CAPE 20 is 5%; half of that plus 1.5% is 4%. At CAPE 32 it is about 3.1%. After year one the dollar amount inflates like a fixed-real rule. That is the Early Retirement Now / valuation-based idea written as one equation, not a reproduction of any single paper's table.
Assumptions
One CAPE for the whole retirement. No fees, no taxes. Compare with a flat 4% and with guardrails that re-read the portfolio.