I have
finally figured out how William Bernstein came up with his numbers. (Reference: the Four Pillars of Investing by William Bernstein.) He relies entirely on the
Gordon Equation and
Monte Carlo simulations. He validates his Monte Carlo simulations by using the results from the Trinity Study and other studies that use the historical sequence methodology.
He causes a whole lot of confusion because he likes to come up with plausible rules of thumb. He throws around percentages all over the place. There are some logical errors hidden within the details behind these plausibility arguments.
Now let us take advantage of some quotes that
hocus has extracted.
Page 56: "Going forward, it looks like stock and bond returns should be in the 6 percent range, not the 10 percent historical reward. Don't shoot me, I'm only the messenger. [Comment: This translates into an SWR of 2 percent]....
"On an intellectual level, most investors have no trouble understanding the notion that high past returns result in high prices, which, in turn, result in lower future returns. But at the same time, most investors find this almost impossible to accept on an emotional level.....
Page 57: "At the end of the day, the Fisher DDM method of discounting interest streams is the only proper way to estimate the value of stocks and bonds. Future long-term returns are quite accurately predicted by the Gordon Equation....
What Bernstein has done is this: He used the Gordon Model to estimate the long-term growth rate of stocks at recent valuations. His estimate was 3.5% real growth. Then he used his Monte Carlo simulation and calculated a Safe Withdrawal Rate. The answer was 2%.
raddr makes similar calculations assuming 3.5%. I suspect that his Monte Carlo simulator is much more accurate than William Bernstein's.
I (
JWR1945) believe that there needs to be an adjustment to the Gordon Equation/Dividend Discount Model. It is because payout ratios are much lower now than they were previously. See the following thread (by
JWR1945) dated Tue Feb 11, 2003 at 10:27 pm CST about
stock market return projections.
http://nofeeboards.com/boards/viewtopic.php?t=494
With the help of
BenSolar and others, my final numbers are in the neighborhood of 4.7% for the real return of the stock market for the next decade or two.
We now have three numbers. The lowest is 3.5% and it is favored by William Bernstein and possibly
raddr. The intermediate projection is 4.7% that I favor and possibly
BenSolar. The long-term historical real rate of return is 6.5% to 7%.
If I were to use Bernstein's approach, I would have come up with a larger estimate of the Safe Withdrawal Rate for 2000 than he did. If would have been lower than that of the historical sequence method because I would have projected lower real stock market returns. I actually used a different approach. (I scaled the answer back into the historical range of valuations.) My estimate was 2.3%.
Have fun.
John R.