Letters to the editor

Just Because I Didn't Answer His Question

Rob Bennett followed up with this letter.

I much appreciate the material you provided in response to my question. It is most helpful.

Is it possible to provide the worst-case scenario result in addition to the "Calculated Rate" result? My thought is that many people view the 7 percent number as a worst-case scenario result. They are thinking "I might do a whole lot better than 7 percent real, but I am guaranteed AT LEAST 7 percent real if I just hold on to my stocks long enough."

I believe that that is a technically correct statement. So the only way to argue against it is to point out how long it might take to get there. I presume that it would take longer to get to 7 percent in a worst-case scenario than it would take to get there under a "Calculated Rate" calculation. I would like to be able to cite to people how long it would take them to get to 7 percent in a worst-case scenario, for purchases made today, for purchases made in January 2000, and for purchases made at moderate valuations. I think it would also be helpful to know the number that applies at extremely low valuations (since that provides a contrast with how long it takes starting from the January 2000 valuation levels).

Thanks for any further help you can provide.

Rob

I finally realized that I could give Rob something meaningful.

Quick and dirty, INEXACT statistics

So long as you are willing to back away from claims of precision, you can get into the statistical ballpark of an answer. This does NOT actually answer Rob's question, but it is meaningful nonetheless.

Refer to the regression equations and add a couple of COARSE APPROXIMATIONS based upon Gaussian (i.e., normal, bell curve) statistics.

APPROXIMATION 1: The eyeball-derived confidence limits correspond to a (two-sided) confidence level in the neighborhood of 90% (and one-sided confidence levels of 95%). Under no circumstance am I willing to assign a greater level of confidence. On the other hand, I would strongly resist any assertion that the actual confidence level is worse than 80% or 85%. (The standard Gaussian approximation usually does an excellent job until you get into unlikely events, that is, into the tails.)

APPROXIMATION 2: One-half of the wide (90% two-sided) outer confidence limits correspond (roughly) to 60% (two-sided) inside confidence limits. That is, there is a 20% chance that an outcome will be below the lower inside confidence limit. There is a 20% chance that an outcome will be above the upper inside confidence limit.

Now look at the S&P500 Regression Equations. Divide the confidence limits in half. Using the 1921-1962 equations, the inner confidence limits are plus 1.9% and minus 2.0% at 20 years. The inner confidence limits are plus and minus 1.1% (which is one-half of 2.2%) at 30 years. They are plus and minus 0.7% (which is one-half of 1.4%) at 40 years.

Now let's apply these confidence limits.

With today's valuations, the lower confidence limit, lower inner confidence limit, calculated returns, the upper inner confidence limit and the upper confidence limit:

100E10/P = 3.5%
20-year returns: 0.8% 2.8% 4.78% 6.7% 8.6%
30-year returns: 3.6% 4.7% 5.81% 6.9% 8.0%
40-year returns: 4.2% 4.9% 5.62% 6.3% 7.0%

With January 2000 valuations, the lower confidence limit, the lower inner confidence limit, calculated returns, the upper inner confidence limit and the upper confidence limit:

P/E10 = 43.77
20-year returns: 0.2% 2.2% 4.15% 6.0% 8.0%
30-year returns: 3.3% 4.4% 5.49% 6.6% 7.7%
40-year returns: 3.9% 4.6% 5.27% 6.0% 6.7%

At typical valuations, the lower inner confidence limit, calculatedreturns and the upper inner confidence limit:
P/E10 = 14
20-year returns: 2.7% 4.7% 6.68% 8.6% 10.5%
30-year returns: 4.6% 5.7% 6.77% 7.9% 9.0%
40-year returns: 5.3% 6.0% 6.67% 7.4% 8.1%

At a bargain valuation, the lower inner confidence limit, calculated returns and the upper inner confidence limit:
P/E10 = 8
20-year returns: 5.5% 7.5% 9.47% 11.4% 13.3%
30-year returns: 6.0% 7.1% 8.17% 9.3% 10.4%
40-year returns: 6.8% 7.5% 8.22% 8.9% 9.6%

At today's valuations, a 7% return is above the upper inner confidence limit in all three cases. The chance that the real, annualized, total return of the stock market (S&P500) equals or exceeds 7% is less than 20% at 20, 30 and 40 years from now. (Stated differently, there is an 80% chance that the total return will be below 7%.) In fact, the odds are about 5% that the return will equal or exceed 7% when it is 40 years from today.

Very close to the peak of the bubble, at the January 2000 valuations, a 7% return was well above the upper inner confidence limit in all three cases. In fact, it is above the upper confidence limit at 40 years. The odds are less than 5% that the real, annualized, total return of the S&P500 will be as high a 7% in January 2040.

The story would have been much different if we were at typical valuations. The odds of exceeding 7% would have been close to (but slightly under) 50%-50% at 20, 30 and 40 years.

P/E10 = 8 is a bargain level, but it is a level that we can reasonably expect to revisit within the next two decades. For someone starting at P/E10 = 8, the odds better than 80% that his returns will exceed 7%.

I still did not answer Rob's question

It is possible to answer Rob's question. It would require additional statistical approximations.

Rob asked about how long you would have to wait. I showed what is likely AT years 20, 30 and 40, but not in between.

There is a problem with presenting historical data. What should I do about early successes? For example, suppose that the return in the first year is 14%. Am I supposed to tell Rob that he will meet his threshold in year one? NO! Rob is more interested in knowing what will happen AFTER a specified delay, which could be 20 years or more.

My solution is to present tables that show the FIRST YEAR INSIDE OF A DECADE that returns 7% annualized during that decade. I do the same for each decade up to the sixth (years 51-60).

Many times, there has been a gap. The total return never reached 7% in a sequence during a particular decade. In fact, many times the total return never climbed back to 7% (annualized) after 30 or 40 years.

Tables of the FIRST YEAR within a DECADE to return 7%, 6%, 5% and 4%.

I have listed the FIRST YEAR within a DECADE to reach 7%, 6%, 5% and 4% in the tables the link below. These tables cover sequences starting in 1871-2000.
S&P500 FIRST YEAR within a DECADE with returns above 7%, 6%, 5% and 4%.

I have listed the FIRST YEAR within a DECADE to reach 7% in the years 1921-2000 below. I list the year at the start of the sequence and the first year with a return of 7% or more in years 1-10, 11-20, 21-30, 31-40, 41-50 and 51-60. Entries of "n" and “nn” mean that there were NO years exceeding 7% within that decade. The data end in 2002.


1921   1   11   21   31   41   51 
1922 1 11 21 31 41 51
1923 2 11 21 31 41 51
1924 1 11 21 31 41 52
1925 1 11 21 31 41 nn
1926 1 11 27 31 41 nn
1927 1 12 28 31 41 nn
1928 1 nn 28 31 41 nn
1929 n nn nn 36 nn nn
1930 n nn 29 31 nn nn
1931 6 nn 24 31 41 nn
1932 2 12 21 31 44 55
1933 1 11 21 31 43 54
1934 2 12 21 31 nn nn
1935 1 11 21 31 nn nn
1936 n 19 21 31 nn nn
1937 n 19 22 31 nn nn
1938 1 17 21 31 nn 59
1939 7 16 21 31 nn 58
1940 6 15 21 31 nn 57
1941 5 11 21 31 nn 55
1942 1 11 21 31 45 51
1943 1 11 21 31 44 51
1944 1 11 21 nn 43 52
1945 1 11 21 nn nn 51
1946 9 11 21 nn nn 51
1947 3 11 21 40 43 51
1948 1 11 21 38 41 51
1949 1 11 21 37 41 51
1950 1 11 21 37 45 51
1951 1 11 21 nn 45 51
1952 1 11 21 nn 45
1953 2 11 nn nn 44
1954 1 11 nn nn 44
1955 1 11 nn nn 43
1956 3 11 nn nn 43
1957 2 11 nn nn 42
1958 1 11 nn nn 41
1959 3 nn nn nn 41
1960 2 nn nn 40 nn
1961 1 nn nn 39 nn
1962 3 nn nn nn
1963 1 nn nn 36
1964 1 nn nn nn
1965 1 nn nn nn
1966 n nn nn nn
1967 1 nn nn nn
1968 n nn nn nn
1969 n nn nn nn
1970 3 nn 29 31
1971 1 nn 27 nn
1972 1 nn 26
1973 n nn 26
1974 n nn 23
1975 1 11 21
1976 n 11 21
1977 10 13 21
1978 8 11 21
1979 7 11 21
1980 1 11 21
1981 5 11 21
1982 1 11
1983 1 11
1984 2 11
1985 1 11
1986 1 11
1987 3 11
1988 1 11
1989 1 11
1990 2 11
1991 1 11
1992 4
1993 1
1994 2
1995 1
1996 1
1997 1
1998 1
1999 1
2000 n

Coming Letters to the Editor

I have received a letter from Greg asking whether I-Bonds can make a good alternative to TIPS in a retirement portfolio. The short answer is YES. The longer answer is coming soon. There are many special details, many unique to an individual's circumstance.

I have received a question about when Gummy's numbers suggest buying an annuity. I want to look into it carefully. In the meantime, visit Gummy's site. Read what he says about annuities. Read about how SMART his wife turned out to be in spite of what everybody else was saying at the time!

I have received a compliment of Rob Bennett's article (which I originally received as a letter) about Subject: Using SWR Analysis to Compare Asset Classes: Edited.

AND ROB DIDN'T WRITE IT!

Mike wrote the compliment. He said, "Good point by Rob about examining assumptions. He has a knack for making me think about things in different ways."

Earlier Letters

Rob Bennett's October 6, 2005 Request

This is what Rob asked for in the first place. I provided information, but I did not answer his question.
Rob Bennett's October 6, 2005 Request

Glossary for Beginners

I am amenable to writing a Glossary for Beginners.
Glossary for Beginners

From a Novice in Investing

Read this letter and use its links to earlier letters.
From a Novice in Investing

Have fun.

John Walter Russell
October 8, 2005