Letters to the Editor

A New Take on the 7% Rule

I received this letter from Rob Bennett.
Rob Bennett's web site

I much appreciate the work you did preparing the tables re the "Buy-and-Hold" issue. I have a thought about a way that the message might be simplified for purposes of helping us to communicate it effectively....

I believe that many investors take comfort in the rule that I refer to as "the 7% Rule." The 7% Rule says that, so long as you are willing to hold stocks long enough, you will eventually obtain a 7 percent annualized real return on the investment. That sounds pretty darn good as a worst-case scenario to many people. I believe that the false confidence that many people place in the 7% Rule is responsible for much of the unwillingness we have seen to discuss what the historical data says in an honest and informed way.

The trouble is (as I now understand things)--the 7% Rule is in a technical sense correct. You really CAN count on a 7% annualized real return so long as you are willing to hold your stocks long enough....

Still, I don't believe that middle-class investors should take nearly as much comfort in the 7% Rule as many of them do. I believe that the comfort provided by the 7% Rule is largely a false comfort. I would like to be able to cite figures showing this to be so (presuming that it is in fact so, of course).

My sense of things is that the hole in the argument that stocks will provide a long-term annualized real return of 7 percent is that the phrase "long term" is generally ill-defined. My sense is that the number of years it will take to be sure of obtaining a 7 percent return VARIES for stock purchases made at different valuation levels. Is that so? If it is so, can we compile a table showing the difference in how long it takes to be sure of a 7 percent return from the various possible starting-point valuation levels?

There's are big differences between being sure of a 7 percent return in 10 years and being sure in 30 years and being sure in 50 years. If it is possible to compile a list of the possible wait-times for the coveted 7 percent return, I think that might demonstrate to a good number of people why valuation-informed investing is a good idea. My focus here is on the accumulation stage of investing rather than the distribution phase.

Rob

This is my response

I have collected and summarized relevant data.

I have added 40, 50 and 60 years to my list of S&P500 real, annualized returns.
S&P500 Returns

I have summarized these results. In one set of tables I show how many sequences had returns WITHIN a specified range. In another set of tables I show how many sequences had returns ABOVE a specified threshold.

I have separated results for sequences beginning in 1871 and in 1921. The 1871 sequences start with the years 1871, 1872, and so on up to the latest year that allows for a sequence of a specified length to be completed in 2002. That is, 10-year sequences start from the years of 1871-1992. Twenty-year sequences start from the years of 1871-1982 and so forth. Similarly, for the 1921 sequences. The 10-year sequences start from the years of 1921-1992. Twenty-year sequences start from the years 1821-1982 and so forth.
S&P500 Returns Statistics

Now look at the Number of Total Returns above threshold. From the 1871 sequences, all of the 10-year returns were above (3.99)%. All of the 20-year returns were above 0%. All of the 30-year returns were above 3%. All of the 40-year returns were above 3%. All of the 50-year returns were above 4%. All of the 60-year returns were above 5%.

Now look at the 1921 sequence data. All of the 10-year returns were above (3.99)%. All of the 20-year returns were above 0%. All of the 30-year returns were above 4%. All of the 40-year returns were above 5%. All of the 50-year returns were above 4%. All of the 60-year returns were above 5%.

All of these statistics disregard valuations. I have determined the regression equations for 20, 30 and 40-year time periods.
S&P500 Regression Equations

Here are the equations derived from 1921-1962 data. The value of x is the percentage earnings yield 100E10/P (or 100/[P/E10]) using Professor Roberts Shiller’s measure of valuation P/E10. The value of y is the calculated return (i.e., the real, annualized, total return).

1921-1962:

20 years:
y = 0.5209x + 2.9554
plus 3.8 and minus 4.0
R-squared = 0.2521

30 years:
y = 0.2624x + 4.8916
plus 2.2 and minus 2.2
R-squared = 0.2215

40 years:
y = 0.2896x + 4.6044
plus 1.4 and minus 1.4
R-squared = 0.5555

There is a lot of randomness. The confidence limits (eyeball estimates) using the 1921-1962 data are plus and minus 4% (approximately) at 20 years, 2.2% at 30 years and 1.4% at 40 years.

Today’s high prices reduce today’s likely 30 and 40-year S&P500 returns by 1%. Here are some numbers.

Calculated returns at today's valuations:
100E10/P = 3.5%
20-year return: 4.78%
30-year return: 5.81%
40-year return: 5.62%

Calculated returns for January 2000:
P/E10 = 43.77
20-year return: 4.15%
30-year return: 5.49%
40-year return: 5.27%

Calculated returns at typical valuations:
P/E10 = 14
20-year return: 6.68%
30-year return: 6.77%
40-year return: 6.67%

Earlier Letters

Glossary for Beginners

I would be happy to put together a glossary for beginners. Please let me know what I should include.
Glossary for Beginners

From a Novice in Investing

Refer to this September 18, 2005 letter and its links at the bottom of the page.
From a Novice in Investing

Have fun.

John Walter Russell
October 6, 2005