This article by the Mad Fientist goes into a safe withdrawal rate prediction as a function of CAPE. There is also a calculator on the website that currently lists SWR at 3.5% due to a Shiller CAPE ratio of 32. This does assume a 80/20 asset allocation.
For what it’s worth.
https://www.madfientist.com/safe-withdrawal-rate/
The calculator is based on Kitces' 0.77 correlation between earnings yield (inverse of CAPE 10) and forward 10-year returns. It's been 25+ years since I knew anything about statistics, but I think I remember that to calculate a valid correlation coefficient, you need independent data samples. It seems very likely that there is quite a bit of autocorrelation between all of the data points within one business cycle. Someone who remembers statistics better than I do can correct me if I'm wrong, but if Kitces used a time interval that is any shorter than a complete business cycle, I'm thinking the 0.77 number is suspect.
The Kitces graph in the mad Fientist article only covers somewhere between four and six business cycles, depending on how you count the peaks, thus it is based on a pretty small sample size. And the article doesn't address all the questions that have been raised about whether CAPE still works the same way it did 30+ years ago. There is no denying a relationship between CAPE earnings yield and SWR, at least up through the 1980s, but it has been pretty loose at times, it's based on fairly scant data (from a statistical point of view), and by predicting the future we are extrapolating beyond the data set that was used to construct the model. So I would be inclined to take the calculator results with a grain of salt.
I totally understand the desire of early FIREees to have some sort of calculated assurance that their plan is likely to succeed. But these exercises often end up giving the impression of much greater precision and accuracy than is really warranted by the data available. Within the modern history of US financial markets, there have been four secular bull markets (1920s, 1940s-1960s, 1980s-1990s, 2009-?) and three secular bear markets (1930s, 1970s, and 2000s). While these cycles share some broad common themes, they have many substantial differences also (e.g., high inflation was the hallmark of the 1970s secular bear, whereas the 2000's featured low inflation and the Great Depression actually had deflation). I don't think we can take this data set and say "CAPE is 32, therefore your SWR should be 3.5." What I think we can say is something like: "Markets have been going up for a while, we've been making new highs for the last few years, and valuations are lofty by historical standards, therefore you probably should build in a few safety buffers. You'll have to decide for yourself how big that buffer should be, and you won't know whether it was enough (or too much) for at least a decade. Sorry, but that's the best we can do."
My personal safety buffer is: if you're retiring when the market is making new highs, your SWR should produce a 100% historical success rate. That way you at least know that it would take something worse than the worst that history has ever served up to sink your plan. If you end up with too much, I'm sure there are many worthy charities that could benefit from your mistake.
