The original trinity study and the modern studies that have replicated and expanded on its results used 30 year intervals, not 20 year intervals. That's an important distinction because making 25 years of living expenses (the retirement stash suggested by the 4% rule) last 20 years would mean you could afford to actually lose money on your investments and make it to the end. A 30 year interval requires you at least earn a positive return.

Actually, the original study and the 2009 update both report results based on 15, 20, 25, and 30-yr time horizons.

You also have mentioned in multiple threads about the trinity study being nearly 20 years old. That'd be a valid point if it was one paper that was never replicated or iterated upon. Instead, you'll see that there are dozens if not hundreds of follow up studies that have tested different sets of assumptions and investment strategies and spending strategies.

So why aren't we referencing them as well?

Finally with regards to using historical data to test the success of investment strategies you say: "However, they don't account for the possibility that the market starts out very expensive and that subsequent years could perform poorly." Is it your position that there are no historical time points where the stock market started out extremely overvalued and performed poorly for years?

No, my position is that if retirement begins with stocks overvalued, it is faulty to assume that future 15-30 yr investment returns will follow historical experience. This position to supported not only by the CAPE link but also in Ben Stein's interesting book "Yes You Can Time the Market".

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Those are the predicted average returns, but what is the variance around those estimates? Within the range of historical returns on investment, variance and sequence of return has a much bigger impact on sustainable withdrawal rates than the overall CAGR of the time frame.

Yes, the returns are predicted based on a formula, but based on a structire with intuitive appeal. Although variance numbers are not provided, they do provide minimum, 25th percentile, 75th percentile, and maximum returns.

A CAPE of 15-20 can be expected to generate an 8.7% return, with a 25th %ile of +7 and a 75th %ile of +12 over the next 10-15 years

A CAPE of 30+ can be expected to generate a +0.5% return with a 25th %ile of -1 and a 75th %ile of +3 over the next 10-15 years

If you wanted to try mixing both studies, in this CAPE 30 environment, you might try simulating a portfolio which experiences a 0.5% return for 10 years and then returns to normal and see how that might change the simulation.

Also, you're falling into a bit of a fallacy by trying to correlate the comparative recentness or antiquity of an idea with accuracy.

In this case, I don't see any fallacy. I think the study remains useful and insightful but can be very much improved upon when the assumptions regarding investment returns are updated with modern information. I have done actuarial work and spreadsheets since 1996. Even though there was innovation going on in 1996, the world did not implement credit scoring to insurance, decided it had a better model, and stopped improving it. There have been been many more changes in first 20 years of my career, and I am reluctant to take 20-yr research at face value without considering how much better than study could look today.

But if you buy into the idea that the older an idea is the less accurate it is, I'll point out that the idea of looking of CAPE dates back also 30 years to this 1988 paper by Shiller & Campbell (sorry for the PDF link):

http://scholar.harvard.edu/files/campbell/files/campbellshiller_jf1988.pdf

Star Research took the idea of CAPE (assuming that 1988 article actually refers to CAPE) and was able to show that there is a relationship between CAPE and future investment returns across the globe, giving further credence to an idea that was good in the first place.