Current Research
Previous Investigations:
Current Research A: Fundamental Breakthroughs associated with TIPS. Latest update: June 16, 2005.
Current Research A: Fundamental Breakthroughs associated with TIPS
Current Research B: Keeping In Tune with the Human Element. Updated August 21, 2005.
Current Research B: Keeping In Tune with the Human Element
Current Research C: True Buy-and-Hold Investing. Dated: September 12, 2005.
Current Research C: True Buy-and-Hold Investing
Current Research D: Expanded Switching Algorithms. Dated: October 23, 2005
Current Research D: Expanded Switching Algorithms
Current Research E: Managing Downside Risk in Financial Markets. Updated: January 1, 2006.
Current Research E: Managing Downside Risk in Financial Markets.
Current Research F: Intermediate-Term Returns
Dated: January 8, 2006.
I have written an Executive Summary for those with limited time.
Current Research F: Executive Summary
Unsatisfactory Conclusion
Our Current Research E investigations into Managing Downside Risk in Financial Markets ended in an unsatisfactory state.
Even though authors Frank Sortino and Stephen Satchell presented a far better analysis approach than Mean-Variance Optimization, I was unable to construct a satisfactory tool from the Forsey-Sortino Model that came with the book. I was seeking a tool that provides stable statistical estimates in the intermediate-term of 10 to 20 years. The model is built upon monthly returns.
I was able to show that using monthly returns is generally unsatisfactory. It strips away almost all of the predictive effects of valuations beyond a few months. This weakness invalidates a large portion of stock market research.
I have built a series of calculators based upon my Deluxe Calculator V1.1A08a, which I built by modifying the Retire Early Safe Withdrawal Calculator. The original calculator includes monthly selection of stock prices and dividends, but not P/E10 and CPI. It uses January values for each year. Each new calculator has the correct P/E10 and CPI values for its own month.
You can read about the Updated Calculator in the Notes Section. You can read the Calculator Description in the SWR Calculators Section.
Intermediate-Term Statistics
I am interested in the main portion of the stock market probability distribution. I am satisfied to work in the area in which the normal (Gaussian, bell shaped) distribution applies. I actually assume that percentage returns are normal. That is, I assume that the real, annualized, total returns (dividends reinvested) are normal. In terms of dollar gains and losses, I am assuming that the distribution is lognormal.
I am unwilling to assign to any finding a confidence level greater than 90% (two-sided, 95% one-sided).
The stock market is known to have a distinctively non-normal distribution. Ed Easterling of Crestmont Research has shown that you can approximate single-year stock market returns by using two separate lognormal distributions: one during secular (long lasting) bull markets and another during secular bear markets. Visit his web site. Look at his section on stocks. Read everything. It is well worth your time. Be sure to read about Significant Swings.
Crestmont Research
Visit my Books Section. I wrote about Ed Easterling’s book Unexpected Returns.
My interests differ from those of Nassim Taleb and Benoit Mandelbrot. They focus upon the infrequent events that make up the tails of the probability distribution function. You can read my comments about their books when you visit my Book Section.
Initial Investigation
I collected a complete set of tables with real, annualized, total returns (with zero expenses) for years 1871-1999. The tables show what happened in each series from Year One through Year 60.
I extracted data with real, annualized, total returns (with zero expenses) at Years 10, 20 and 30 for sequences beginning in 1921-1980. I included P/E10 and the percentage earnings yield 100E10/P (that is, 100/[P/E10]).
I made graphs of the real, annualized, total returns (with zero expenses) at Years 10 and 20 versus the percentage earnings yield 100E10/P for each month in the years 1923-1980. In addition, I made a graph with data from all twelve months and all years in 1923-1980.
I took advantage of Excel’s plotting capability to make linear curve fits (i.e., I determined regression equations) and to report R-squared. R-squared is the square of the correlation. It tells us the percentage of the variance that can be explained by the line. It does not tell us about the variance itself.
I have made eyeball approximations for the confidence limits. This is a close-enough approximation because I am not claiming precision.
Equations for Year 10
y is the total return.
x is the percentage earnings yield.
Jan 1923-1980:
y = 1.3564x-3.8223 plus and minus 6%.
R-squared = 0.383.
Feb 1923-1980:
y = 1.3695x-3.8889 plus and minus 7%.
R-squared = 0.3917.
Mar 1923-1980:
y = 1.3722x-3.923 plus and minus 7%.
R-squared = 0.4068.
Apr 1923-1980:
y = 1.3096x-3.3712 plus and minus 7%.
R-squared = 0.4057.
May 1923-1980:
y = 1.2863x-3.1522 plus and minus 7%.
R-squared = 0.4024.
June 1923-1980:
y = 1.2605x-2.8384 plus and minus 7%.
R-squared = 0.4067.
July 1923-1980:
y = 1.2857x-3.0917 plus and minus 7%.
R-squared = 0.404.
Aug 1923-1980:
y = 1.4817x-4.7854 plus and minus 8%.
R-squared = 0.4272.
Sep 1923-1980:
y = 1.4847x-4.9039 plus and minus 7%.
R-squared = 0.4327.
Oct 1923-1980:
y = 1.3735x-4.0512 plus and minus 7%.
R-squared = 0.4004.
Nov 1923-1980:
y = 1.4053x-4.2699 plus and minus 7%.
R-squared = 0.4039.
Dec 1923-1980:
y = 1.3627x-3.8776 plus and minus 7%.
R-squared = 0.395.
All months 1923-1980:
Year 10:
y = 1.3568x-3.7928 plus and minus 7%.
R-squared = 0.4042.
Equations for Year 20
y is the total return.
x is the percentage earnings yield.
Jan 1923-1980:
y = 1.0946x-1.5004 plus and minus 4%.
R-squared = 0.5591.
Feb 1923-1980:
y = 1.1111x-1.5717 plus and minus 4%.
R-squared = 0.5833.
Mar 1923-1980:
y = 1.1207x-1.6292 plus and minus 4%.
R-squared = 0.6091.
Apr 1923-1980:
y = 1.0791x-1.287 plus and minus 4%.
R-squared = 0.6044.
May 1923-1980:
y = 1.0513x-1.0526 plus and minus 4%.
R-squared = 0.5899.
June 1923-1980:
y = 0.9666x-0.3739 plus and minus 4%.
R-squared = 0.5535.
July 1923-1980:
y = 0.9685x-0.4428 plus and minus 4%.
R-squared = 0.5428.
Aug 1923-1980:
y = 1.1216x-1.6635 plus and minus 4%.
R-squared = 0.5686.
Sep 1923-1980:
y = 1.1317x-1.782 plus and minus 4%.
R-squared = 0.5764.
Oct 1923-1980:
y = 1.08x-1.4202 plus and minus 4%.
R-squared = 0.561.
Nov 1923-1980:
y = 1.1409x-1.8498 plus and minus 4%.
R-squared = 0.587.
Dec 1923-1980:
y = 1.142x-1.8027 plus and minus 4%.
R-squared = 0.6026.
All months 1923-1980:
Year 20:
y = 1.0795x-1.332 plus and minus 4%.
R-squared = 0.5591.
Initial Observations
The equations are similar. The predictive relationship between returns and valuations is stable.
This brute force approach is satisfactory so far.
Individual Decades
This time I look at individual decades. The equations at years 10 and 20 vary considerably.
I noticed a bending (or saturation) of the curves. I thinned the data, including only conditions with percentage earnings yields less than 10% (and P/E10 greater than or equal to 10). This got rid of the effects of the curvature, but the data still behaved badly.
Finally, I sorted equations into secular bull and bear market intervals as defined by Ed Easterling of Crestmont Research. Ed Easterling discovered that it makes sense to treat stock market returns as two lognormal distributions: one during secular (long lasting) bull markets and a different one during secular bear markets. You can read the details in his book Unexpected Returns. Refer to the table on page 80 with the title: Secular Bull & Bear Markets Profile. Or you can visit the Stock section of his web site and click Secular Cycles. Or you can do both.
Crestmont Research
Crestmont Research Secular Cycles
The best approach is to sort the equations separately in secular bull and bear markets.
Equations at Year 10
Basic Approach:
All months 1923-1980:
Year 10:
y = 1.3568x-3.7928 plus and minus 7%.
R-squared = 0.4042.
Distinctly bimodal.
All months 1923-1930:
Year 10:
y = 0.9756x-0.833 plus and minus 5%.
R-squared = 0.648.
All months 1931-1940:
Year 10:
y = 0.6536x-0.6798 plus and minus 3%.
R-squared = 0.5363.
All months 1941-1950:
Year 10:
y = 0.815x+4.8525 plus and minus 4%.
R-squared = 0.1161.
Distinctly bimodal.
All months 1951-1960:
Year 10:
y = 2.3077x-5.7901 plus and minus 3%.
R-squared = 0.7645.
All months 1961-1970:
Year 10:
y = 1.4045x-6.685 plus and minus 4%.
R-squared = 0.105.
Distinctly bimodal.
All months 1971-1980:
Year 10:
y = 1.9875x-12.654 plus and minus 3%.
R-squared = 0.8727.
Thinned Data
All conditions with 100E10/P<10%.
All months 1923-1980, thinned:
Year 10:
y = 2.1659x-8.8103 plus and minus 7%.
R-squared = 0.5098.
Distinctly bimodal.
All months 1923-1930, thinned:
Year 10:
y = 1.8139x-5.1657 plus and minus 3%.
R-squared = 0.821.
All months 1931-1940, thinned:
Year 10:
y = 1.139x-3.8848 plus 3% and minus 2%.
R-squared = 0.5187.
All months 1941-1950, thinned:
Year 10:
y = 0.9792x+3.4151 plus and minus 4%.
R-squared = 0.1162.
Distinctly bimodal.
All months 1951-1960, no thinning needed:
Year 10:
y = 2.3077x-5.7901 plus and minus 3%.
R-squared = 0.7645.
All months 1961-1970, no thinning needed:
Year 10:
y = 1.4045x-6.685 plus and minus 4%.
R-squared = 0.105.
Distinctly bimodal.
All months 1971-1980, thinned:
Year 10:
y = 2.3721x-15.282 plus 2 and minus 4%.
R-squared = 0.839.
Sorting based on Ed Easterling's Research
All months 1921-1980:
Year 10:
y = 1.1124x-2.1393 plus and minus 8%.
R-squared = 0.3795.
Complex.
All months 1921-1928:
Year 10:
y = 0.5717x+2.8115 plus 4% and minus 5%.
R-squared = 0.4468.
All months 1929-1932:
Year 10:
y = 0.5607x-0.4638 plus and minus 2%.
R-squared = 0.8672.
All months 1933-1936:
Year 10:
y = 0.7556x-0.592 plus 2% and minus 3%.
R-squared = 0.5296.
All months 1937-1941:
Year 10:
y = 1.9447x-9.3319 plus 2% and minus 3%.
R-squared = 0.7269.
All months 1942-1965:
Year 10:
y = 2.1108x-5.9544 plus 4% and minus 5%.
R-squared = 0.6813.
Bimodal.
All months 1966-1980:
Year 10:
y = 1.824x-11.075 plus and minus 3%.
R-squared = 0.8981.
Year 10 Comparisons
These are the data spreads using the basic approach:
All months 1923-1980: plus and minus 7%.
All months 1923-1930: plus and minus 5%.
All months 1931-1940: plus and minus 3%.
All months 1941-1950: plus and minus 4%.
All months 1951-1960: plus and minus 3%.
All months 1961-1970: plus and minus 4%.
All months 1971-1980: plus and minus 3%.
These are the data spreads when you thin the data so that 100E10/P<10%.
All months 1923-1980, thinned: plus and minus 7%.
All months 1923-1930, thinned: plus and minus 3%.
All months 1931-1940, thinned: plus 3% and minus 2%.
All months 1941-1950, thinned: plus and minus 4%.
All months 1951-1960, no thinning needed: plus and minus 3%.
All months 1961-1970, no thinning needed: plus and minus 4%.
All months 1971-1980, thinned: plus 2 and minus 4%.
These are the data spreads when you sort the data based on Ed Easterling's Research.
All months 1921-1980: plus and minus 8%.
All months 1921-1928: plus 4% and minus 5%.
All months 1929-1932: plus and minus 2%.
All months 1933-1936: plus 2% and minus 3%.
All months 1937-1941: plus 2% and minus 3%.
All months 1942-1965: plus 4% and minus 5%.
All months 1966-1980: plus and minus 3%.
These are the values of R-squared using the basic approach:
All months 1923-1980: R-squared = 0.4042.
All months 1923-1930: R-squared = 0.648.
All months 1931-1940: R-squared = 0.5363.
All months 1941-1950: R-squared = 0.1161.
All months 1951-1960: R-squared = 0.7645.
All months 1961-1970: R-squared = 0.105.
All months 1971-1980: R-squared = 0.8727.
These are the values of R-squared when you thin the data so that 100E10/P<10%.
All months 1923-1980, thinned: R-squared = 0.5098.
All months 1923-1930, thinned: R-squared = 0.821.
All months 1931-1940, thinned: R-squared = 0.5187.
All months 1941-1950, thinned: R-squared = 0.1162.
All months 1951-1960, no thinning needed: R-squared = 0.7645.
All months 1961-1970, no thinning needed: R-squared = 0.105.
All months 1971-1980, thinned: R-squared = 0.839.
These are the values of R-squared when you sort the data based on Ed Easterling's Research.
All months 1921-1980: R-squared = 0.3795.
All months 1921-1928: R-squared = 0.4468.
All months 1929-1932: R-squared = 0.8672.
All months 1933-1936: R-squared = 0.5296.
All months 1937-1941: R-squared = 0.7269.
All months 1942-1965: R-squared = 0.6813.
All months 1966-1980: R-squared = 0.8981.
Equations at Year 20
Basic Approach:
All months 1923-1980:
Year 20:
y = 1.0795x-1.332 plus and minus 4%.
R-squared = 0.577.
All months 1923-1930:
Year 20:
y = 0.636x+0.4492 plus and minus 2%.
R-squared = 0.8445.
All months 1931-1940:
Year 20:
y = 0.1654x+6.8715 plus and minus 3%.
R-squared = 0.0987.
All months 1941-1950:
Year 20:
y = 0.4305x+7.0815 plus 1% and minus 2%.
R-squared = 0.3092.
All months 1951-1960:
Year 20:
y = 2.0731x-9.0738 plus and minus 2%.
R-squared = 0.8289.
All months 1961-1970:
Year 20:
y = 1.1421x-3.1477 plus and minus 2%.
R-squared = 0.3952.
All months 1971-1980:
Year 20:
y = 1.2292x-2.5805 plus and minus 2%.
R-squared = 0.8555.
Thinned Data
All conditions with 100E10/P<10%.
All months 1923-1980, thinned:
Year 20:
y = 1.5629x-4.3692 plus and minus 4%.
R-squared = 0.6707.
All months 1923-1930, thinned:
Year 20:
y = 0.9661x-1.3208 plus 2% and minus 1%.
R-squared = 0.9117.
All months 1931-1940, thinned:
Year 20:
y = 0.2141x+6.5824 plus and minus 2%.
R-squared = 0.0421.
All months 1941-1950, thinned:
Year 20:
y = 0.4601x+6.8381 plus 1 and minus 2%.
R-squared = 0.2228.
All months 1951-1960, no thinning needed:
Year 20:
y = 2.0731x-9.0738 plus and minus 2%.
R-squared = 0.8289.
All months 1961-1970, no thinning needed:
Year 20:
y = 1.1421x-3.1477 plus and minus 2%.
R-squared = 0.3952.
All months 1971-1980, thinned:
Year 20:
y = 1.1033x-1.7509 plus and minus 2%.
R-squared = 0.8815.
Sorting based on Ed Easterling's Research
All months 1921-1980:
Year 20:
y = 0.7885x+0.6586 plus and minus 5%.
R-squared = 0.4455.
All months 1921-1928:
Year 20:
y = 0.3763x+2.6001 plus 3% and minus 2%.
R-squared = 0.6779.
All months 1929-1932:
Year 20:
y = 0.6516x+0.496 plus and minus 1%.
R-squared = 0.8998.
All months 1933-1936:
Year 20:
y = 0.1696x+6.5767 plus and minus 2%.
R-squared = 0.0929.
All months 1937-1941:
Year 20:
y = 0.89x+3.1211 plus and minus 1%.
R-squared = 0.6683.
All months 1942-1965:
Year 20:
y = 1.9807x-7.78 plus 5% and minus 3%.
R-squared = 0.8469.
Complex.
All months 1966-1980:
Year 20:
y = 1.2435x-2.7529 plus and minus 2%.
R-squared = 0.918.
Year 20 Comparisons
These are the data spreads using the basic approach:
All months 1923-1980: plus and minus 4%.
All months 1923-1930: plus and minus 2%.
All months 1931-1940: plus and minus 3%.
All months 1941-1950: plus 1% and minus 2%.
All months 1951-1960: plus and minus 2%.
All months 1961-1970: plus and minus 2%.
All months 1971-1980: plus and minus 2%.
These are the data spreads when you thin the data so that 100E10/P<10%.
All months 1923-1980, thinned: plus and minus 4%.
All months 1923-1930, thinned: plus 2% and minus 1%.
All months 1931-1940, thinned: plus and minus 2%.
All months 1941-1950, thinned: plus 1 and minus 2%.
All months 1951-1960, no thinning needed: plus and minus 2%.
All months 1961-1970, no thinning needed: plus and minus 2%.
All months 1971-1980, thinned: plus and minus 2%.
These are the data spreads when you sort the data based on Ed Easterling's Research.
All months 1921-1980: plus and minus 5%.
All months 1921-1928: plus 3% and minus 2%.
All months 1929-1932: plus and minus 1%.
All months 1933-1936: plus and minus 2%.
All months 1937-1941: plus and minus 1%.
All months 1942-1965: plus 5% and minus 3%.
All months 1966-1980: plus and minus 2%.
These are the values of R-squared using the basic approach:
All months 1923-1980: R-squared = 0.577.
All months 1923-1930: R-squared = 0.8445.
All months 1931-1940: R-squared = 0.0987.
All months 1941-1950: R-squared = 0.3092.
All months 1951-1960: R-squared = 0.8289.
All months 1961-1970: R-squared = 0.3952.
All months 1971-1980: R-squared = 0.8555.
These are the values of R-squared when you thin the data so that 100E10/P<10%.
All months 1923-1980, thinned: R-squared = 0.6707.
All months 1923-1930, thinned: R-squared = 0.9117.
All months 1931-1940, thinned: R-squared = 0.0421.
All months 1941-1950, thinned: R-squared = 0.2228.
All months 1951-1960, no thinning needed: R-squared = 0.8289.
All months 1961-1970, no thinning needed: R-squared = 0.3952.
All months 1971-1980, thinned: R-squared = 0.8815.
These are the values of R-squared when you sort the data based on Ed Easterling's Research.
All months 1921-1980: R-squared = 0.4455.
All months 1921-1928: R-squared = 0.6779.
All months 1929-1932: R-squared = 0.8998.
All months 1933-1936: R-squared = 0.0929.
All months 1937-1941: R-squared = 0.6683.
All months 1942-1965: R-squared = 0.8469.
All months 1966-1980: R-squared = 0.918.
Analysis
Understand that the 1921-1980 data does not include sorting. Keep in mind that the years 1921 and 1922 exert an undue influence on the curve fitting process because of their very high earnings yield.
Sorting based on Ed Easterling’s research did the best. Looking at R-squared, it performed exceptionally well except for 20-year projections from the 1933-1936 bull market.
The alternatives performed poorly at year 20 when starting from the 1930s. Nor did they perform well at years 10 and 20 when starting from the 1940s and the 1960s.
Conclusions
The reason that the Forsey-Sortino Model projections (in Current Research E) varied from one decade to another is that stock returns varied from one decade to another.
It is a good idea to analyze secular bull markets and secular bear markets separately.
In terms of the months of a year, the relationship between returns and valuations is stable. In terms of decade to decade, returns vary. Separating bull markets from bear markets improves your forecasting ability.
Interpreting the Equations
The best method to interpret these equations is to stick earnings yield numbers into them and then see what happens. Today’s valuations are higher than the pre-bubble historical range. P/E10 is close to 28 or 29. The percentage earnings yield is (approximately) 3.5%. The typical range historically has been P/E10=10 (earnings yield = 10%) for bargains and P/E10 = 20 (earnings yield = 5%) for overpriced stocks.
Tables at Year 10
Years / Earnings Yields of 3.5% and 5.0% and 10%:
Basic Approach
1923-1980: 0.96% and 2.99% and 9.78%.
1923-1930: 2.58% and 4.05% and 8.92%.
1931-1940: 1.61% and 2.59% and 5.86%.
1941-1950: 7.71% and 8.93% and 13.00%.
1951-1960: 2.29% and 5.75% and 17.29%.
1961-1970: -1.77% and 0.34% and 7.36%.
1971-1980: -5.70% and –2.72% and 7.22%.
Thinned Data
1923-1980: -1.23% and 2.02% and 12.85%.
1923-1930: 1.18% and 3.90% and 12.97%.
1931-1940: 0.10% and 1.81% and 7.51%.
1941-1950: 6.84% and 8.31% and 13.21%.
1951-1960: 2.29% and 5.75% and 17.29%.
1961-1970: -1.77% and 0.34% and 7.36%.
1971-1980: -6.98% and –3.42% and 8.44%.
Sorting based on Ed Easterling's Research
1921-1980: 1.75% and 3.42% and 8.98%.
1921-1928: 4.81% and 5.67% and 8.58%.
1929-1932: 1.50% and 2.34% and 5.14%.
1933-1936: 2.05% and 3.19% and 6.96%.
1937-1941: -2.53% and 0.39% and 10.12%.
1942-1965: 1.43% and 4.60% and 15.15%.
1966-1980: -4.69% and –1.96% and 7.17%.
Comparisons at Year 10
At Year 10 with today’s earnings yield 100E10/P of 3.5%:
Assuming that 100E10/P = 3.5%, the basic approach (1923-1980) predicts a real, annualized, total return of 0.96% at Year 10. The calculated returns using individual decades vary from -5.70% (1971-1980) to 7.71% (1941-1950).
Assuming that 100E10/P = 3.5%, the thinned data prediction (1923-1980) is a real, annualized, total return of 12.85% at Year 10. The calculated returns using individual decades vary from -6.98% (1971-1980) to 6.84% (1941-1950).
Assuming that 100E10/P = 3.5%, sorting (1921-1980) based on Ed Easterling's Research results in a predicted real, annualized, total return of 1.75% at Year 10. The calculated returns using individual periods vary from -4.69% (1966-1980) to 4.81% (1921-1928). The calculated returns assuming a secular (long lasting) bear market vary from -4.69% (1966-1980) to 1.50% (1929-1932). The calculated returns assuming a secular (long lasting) bull market vary from 1.43% (1942-1965) to 4.81% (1921-1928).
At Year 10 and with an earnings yield 100E10/P of 5.0% (P/E10=20):
Assuming that 100E10/P = 5.0% (P/E10=20), the basic approach (1923-1980) predicts a real, annualized, total return of 2.99% at Year 10. The calculated returns using individual decades vary from –2.72% (1971-1980) to 8.93% (1941-1950).
Assuming that 100E10/P = 5.0% (P/E10=20), the thinned data prediction (1923-1980) is a real, annualized, total return of 2.02% at Year 10. The calculated returns using individual decades vary from –3.42% (1971-1980) to 8.31% (1941-1950).
Assuming that 100E10/P = 5.0% (P/E10=20), sorting (1921-1980) based on Ed Easterling's Research results in a predicted real, annualized, total return of 3.42% at Year 10. The calculated returns using individual periods vary from –1.96% (1966-1980) to 5.67% (1921-1928). The calculated returns assuming a secular bear market vary from –1.96% (1966-1980) to 2.34% (1929-1932). The calculated returns assuming a secular bull market vary from 3.19% (1933-1936) to 5.67% (1921-1928).
At Year 10 and with an earnings yield 100E10/P of 10.0% (P/E10=10):
Assuming that 100E10/P = 10.0% (P/E10=10), the basic approach (1923-1980) predicts a real, annualized, total return of 9.78% at Year 10. The calculated returns using individual decades vary from 5.86% (1931-1940) to 17.29% (1951-1960).
Assuming that 100E10/P = 10.0% (P/E10=10), the thinned data prediction (1923-1980) is a real, annualized, total return of 12.85% at Year 10. The calculated returns using individual decades vary from 7.36% (1961-1970) to 17.29% (1951-1960).
Assuming that 100E10/P = 10.0% (P/E10=10), sorting (1921-1980) based on Ed Easterling's Research results in a predicted real, annualized, total return of 8.98% at Year 10. The calculated returns using individual periods vary from 5.14% (1929-1932) to 15.15% (1942-1965). The calculated returns assuming a secular bear market vary from 5.14% (1929-1932) to 10.12% (1937-1941). The calculated returns assuming a secular bull market vary from 6.96% (1933-1936) to 15.15% (1942-1965).
Tables at Year 20
Years / Earnings Yields of 3.5% and 5.0% and 10%:
Basic Approach
1923-1980: 2.45% and 4.07% and 9.46%.
1923-1930: 2.68% and 3.63% and 6.81%.
1931-1940: 7.45% and 7.70% and 8.53%.
1941-1950: 8.59% and 9.23% and 11.39%.
1951-1960: -1.82% and 1.29% and 11.66%.
1961-1970: 0.85% and 2.56% and 8.27%.
1971-1980: 1.72% and 3.57% and 9.71%.
Thinned Data
1923-1980: 1.10% and 3.45% and 11.26%.
1923-1930: 2.06% and 3.51% and 8.34%.
1931-1940: 7.33% and 7.65% and 8.72%.
1941-1950: 8.45% and 9.14% and 11.47%.
1951-1960: -1.82% and 1.29% and 11.66%.
1961-1970: 0.85% and 2.56% and 8.27%.
1971-1980: 2.11% and 3.77% and 9.28%.
Sorting based on Ed Easterling's Research
1921-1980: 3.42% and 4.60% and 8.54%.
1921-1928: 3.92% and 4.48% and 6.36%.
1929-1932: 2.78% and 3.75% and 7.01%.
1933-1936: 7.17% and 7.42% and 8.27%.
1937-1941: 6.24% and 7.57% and 12.02%.
1942-1965: -0.85% and 2.12% and 12.03%.
1966-1980: 1.60% and 3.46% and 9.68%.
Comparisons at Year 20
At Year 20 with today’s earnings yield 100E10/P of 3.5%:
Assuming that 100E10/P = 3.5%, the basic approach (1923-1980) predicts a real, annualized, total return of 2.45% at Year 20. The calculated returns using individual decades vary from -1.82% (1951-1960) to 8.59% (1941-1950).
Assuming that 100E10/P = 3.5%, the thinned data prediction (1923-1980) is a real, annualized, total return of 1.10% at Year 20. The calculated returns using individual decades vary from -1.82% (1951-1960) to 8.45% (1941-1950).
Assuming that 100E10/P = 3.5%, sorting (1921-1980) based on Ed Easterling's Research results in a predicted real, annualized, total return of 3.42% at Year 20. The calculated returns using individual periods vary from -0.85% (1942-1965) to 3.92% (1921-1928). The calculated returns assuming a secular (long lasting) bear market vary from 1.60% (1966-1980) to 6.24% (1937-1941). The calculated returns assuming a secular (long lasting) bull market vary from -0.85% (1942-1965) to 7.17% (1933-1936).
At Year 20 and with an earnings yield 100E10/P of 5.0% (P/E10=20):
Assuming that 100E10/P = 5.0% (P/E10=20), the basic approach (1923-1980) predicts a real, annualized, total return of 4.07% at Year 20. The calculated returns using individual decades vary from 1.29% (1951-1960) to 9.23% (1941-1950).
Assuming that 100E10/P = 5.0% (P/E10=20), the thinned data prediction (1923-1980) is a real, annualized, total return of 3.45% at Year 20. The calculated returns using individual decades vary from 1.29% (1951-1960) to 9.14% (1941-1950).
Assuming that 100E10/P = 5.0% (P/E10=20), sorting (1921-1980) based on Ed Easterling's Research results in a predicted real, annualized, total return of 4.60% at Year 20. The calculated returns using individual periods vary from 2.12% (1941-1965) to 7.57% (1937-1941). The calculated returns assuming a secular bear market vary from 3.46% (1966-1980) to 7.57% (1937-1941). The calculated returns assuming a secular bull market vary from 2.12% (1941-1965) to 7.42% (1933-1936).
At Year 20 and with an earnings yield 100E10/P of 10.0% (P/E10=10):
Assuming that 100E10/P = 10.0% (P/E10=10), the basic approach (1923-1980) predicts a real, annualized, total return of 9.46% at Year 20. The calculated returns using individual decades vary from 6.81% (1923-1930) to 11.66% (1951-1960).
Assuming that 100E10/P = 10.0% (P/E10=10), the thinned data prediction (1923-1980) is a real, annualized, total return of 11.26% at Year 20. The calculated returns using individual decades vary from 8.27% (1961-1970) to 11.66% (1951-1960).
Assuming that 100E10/P = 10.0% (P/E10=10), sorting (1921-1980) based on Ed Easterling's Research results in a predicted real, annualized, total return of 8.54% at Year 20. The calculated returns using individual periods vary from 6.36% (1921-1928) to 12.03% (1942-1965). The calculated returns assuming a secular bear market vary from 7.01% (1929-1932) to 12.02% (1937-1941). The calculated returns assuming a secular bull market vary from 6.36% (1921-1928) to 12.03% (1942-1965).
Analysis
Thinning the data did not change predictions much. It increased predicted 1923-1980 and 1923-1930 returns when the earnings yield 100E10/P is 10% (and P/E10=10). But that might have been expected. The reason for thinning was that the curve tends to saturate at higher earnings yields. That is, the benefit of increasing the earnings yield tapers off at highly favorable valuations. Thinning the data improves the accuracy of equations at lower earnings yields (i.e., at higher valuations). It reduces the accuracy of equations at higher earnings yield (i.e., at lower valuations).
Projections vary a lot. This is in accordance with underlying uncertainties. The basic approach has the largest variation, thinned data approach is next and sorting based on Ed Easterling’s research does best. At year 10, the total variations are in the neighborhood of 12%, just under 12% and 9%, respectively. At year 20, the total variations are in the neighborhood of just under 8%, 7% and 6%, respectively.
The really interesting effects are what happens to (secular) bull market and (secular) bear market projections. Year 10 projections are distinct. Year 20 projections are the same.
Sorting by Bull and Bear Markets
Ed Easterling’s sorting approach assures a wide range of valuations. This reduces errors from extrapolation.
Here are the extreme values of P/E10:
1921-1928: from 5.1 to 25.3.
1929-1932: from 32.6 to 5.6.
1933-1936: from 7.8 to 21.5.
1937-1941: from 22.2 to 10.1.
1942-1965: from 8.5 to 23.9.
1966-1980: from 24.1 to 7.8.
Here are the Year 10 (secular) bull market projections for earnings yields of 3.5%, 5.0% and 10.0%, respectively:
1921-1928: 4.81% and 5.67% and 8.58%.
1933-1936: 2.05% and 3.19% and 6.96%.
1942-1965: 1.43% and 4.60% and 15.15%.
Here are the Year 10 (secular) bear market projections for earnings yields of 3.5%, 5.0% and 10.0%, respectively:
1929-1932: 1.50% and 2.34% and 5.14%.
1937-1941: -2.53% and 0.39% and 10.12%.
1966-1980: -4.69% and –1.96% and 7.17%.
Year 10 bull market projections are more optimistic, in general, than Year 10 bear market projections.
This is as expected. Multiples (P/E and P/E10 and other measures of valuation) increase during bull markets, giving investors a boost. They contract during bear markets, dragging down investment returns.
Now look at Year 20 (secular) bull market projections. Again, the earnings yields are 3.5%, 5/0% and 10.0%, respectively:
1921-1928: 3.92% and 4.48% and 6.36%.
1933-1936: 7.17% and 7.42% and 8.27%.
1942-1965: -0.85% and 2.12% and 12.03%.
Here are the Year 20 (secular) bear market projections for earnings yields of 3.5%, 5.0% and 10.0%, respectively:
1929-1932: 2.78% and 3.75% and 7.01%.
1937-1941: 6.24% and 7.57% and 12.02%.
1966-1980: 1.60% and 3.46% and 9.68%.
Can you tell them apart? If so, which is which?
The Next Step
Sorting by secular (long lasting) bull and bear markets is a good idea. My next step will be to combine the data from all of the secular bull markets together to derive one set of equations. I will combine the data from all of the secular bear markets together to generate another set of equations.
Sorting by Bulls and Bears
I divided the 1921-1980 data into two groups: one with secular (long lasting) bull markets and another with secular (long lasting) bear markets. I used Ed Easterling’s divisions. The bull markets were in 1921-1928, 1933-1936 and 1942-1965. The bear markets were in 1929-1932, 1937-1941 and 1966-1980. [I selected a cutoff date of 1980. The 1966 bear market extended through 1981.]
I plotted bull and bear market returns at years 10 and 20 versus the percentage earnings yield 100E10/P and also versus P/E10. I plotted bull market returns at years 10 and 20 with thinned data (that is, restricted to 100E10/P>10% and P/E10>10 or equal to 10).
Equations at Year 10
Here are the Bull Market equations at Year 10:
100E10/P Bull Market Composite 1921-1980:
Year 10:
y = 0.864x+1.7706 plus and minus 7%.
R-squared = 0.3202.
Distinctly bimodal.
P/E10 Bull Market Composite 1921-1980:
Year 10:
y = -0.7161x+18.74 plus and minus 7%.
R-squared = 0.5279.
Complex.
100E10/P Bull Market Composite 1921-1980, thinned:
Year 10:
y = 2.1057x-6.4098 plus 5% and minus 7%.
R-squared = 0.6055.
Distinctly bimodal.
P/E10 Bull Market Composite 1921-1980, thinned:
Year 10:
y = -0.9439x+22.719 plus and minus 5%.
R-squared = 0.6729.
Complex.
Here are the Bear Market equations at Year 10:
100E10/P Bear Market Composite 1921-1980:
Year 10:
y = 1.3205x-6.5464 plus and minus 5%.
R-squared = 0.688.
P/E10 Bear Market Composite 1921-1980:
Year 10:
y = -0.6205x+12.683 plus and minus 5%.
R-squared = 0.6088.
Here are the Baseline equations at Year 10:
All months 1921-1980:
Year 10:
y = 1.1124x-2.1393 plus and minus 8%.
R-squared = 0.3795.
Complex.
All months 1923-1980:
Year 10:
y = 1.3568x-3.7928 plus and minus 7%.
R-squared = 0.4042.
Distinctly bimodal.
All months 1923-1980, thinned:
Year 10:
y = 2.1659x-8.8103 plus and minus 7%. R-squared = 0.5098.
Distinctly bimodal.
Tables at Year 10
Years / Earnings Yields of 3.5% and 5.0% and 10%:
100E10/P Bull Market Composite 1921-1980, Year 10:
4.79% and 6.09% and 10.41%
P/E10 Bull Market Composite 1921-1980, Year 10:
(1.72)% and 4.42% and 11.58%
100E10/P Bull Market Composite 1921-1980, thinned, Year 10:
0.96% and 4.12% and 14.65%
P/E10 Bull Market Composite 1921-1980, thinned, Year 10:
(4.25)% and 3.84% and 13.28%
100E10/P Bear Market Composite 1921-1980, Year 10:
(1.92)% and 0.06% and 6.66%
P/E10 Bear Market Composite 1921-1980, Year 10:
(5.05)% and 0.27% and 6.48%
All months 1921-1980, Year 10:
1.75% and 3.42% and 8.98%
All months 1923-1980, Year 10:
0.96% and 2.99% and 9.78%
All months 1923-1980, thinned, Year 10:
(1.23)% and 2.02% and 12.85%
Equations at Year 20
Here are the Bull Market equations at Year 20:
100E10/P Bull Market Composite 1921-1980:
Year 20:
y = 0.72x+0.8718 plus and minus 5%.
R-squared = 0.3724.
P/E10 Bull Market Composite 1921-1980:
Year 20:
y = -0.5869x+14.875 plus and minus 4%.
R-squared = 0.5937.
100E10/P Bull Market Composite 1921-1980, thinned:
Year 20:
y = 1.8196x-6.4813 plus and minus 5%.
R-squared = 0.7227.
Distinctly bimodal.
P/E10 Bull Market Composite 1921-1980, thinned:
Year 20:
y = -0.7524x+17.72 plus and minus 4%.
R-squared = 0.6939.
Here are the Bear Market equations at Year 20:
100E10/P Bear Market Composite 1921-1980:
Year 20:
y = 0.9695x-0.1717 plus and minus 3%.
R-squared = 0.6505.
P/E10 Bear Market Composite 1921-1980:
Year 20:
y = -0.508x+14.748 plus and minus 3%.
R-squared = 0.7158.
Here are the Baseline equations at Year 20:
All months 1921-1980:
Year 20:
y = 0.7885x+0.6586 plus and minus 5%.
R-squared = 0.4455.
All months 1923-1980:
Year 20:
y = 1.0795x-1.332 plus and minus 4%.
R-squared = 0.577.
All months 1923-1980, thinned:
Year 20:
y = 1.5629x-4.3692 plus and minus 4%.
R-squared = 0.6707.
Tables at Year 20
Years / Earnings Yields of 3.5% and 5.0% and 10%:
100E10/P Bull Market Composite 1921-1980, Year 20:
3.39% and 4.47% and 8.07%
P/E10 Bull Market Composite 1921-1980, Year 20:
(1.89)% and 3.14% and 9.01%
100E10/P Bull Market Composite 1921-1980, thinned, Year 20:
(0.11)% and 2.62% and 11.71%
P/E10 Bull Market Composite 1921-1980, thinned, Year 20:
(3.78)% and 2.67% and 10.20%
100E10/P Bear Market Composite 1921-1980, Year 20:
3.22% and 4.68% and 9.52%
P/E10 Bear Market Composite 1921-1980, Year 20:
0.23% and 4.59% and 9.67%
All months 1921-1980, Year 20:
3.42% and 4.60% and 8.54%
All months 1923-1980, Year 20:
2.45% and 4.07% and 9.46%
All months 1923-1980, thinned, Year 20:
1.10% and 3.45% and 11.26%
100E10/P versus P/E10 Comparisons
If you compare 100E10/P results with P/E10 results, you will notice that they are similar EXCEPT when 100E10/P = 3.5%. Lines drawn using 100E10/P place more emphasis on what happens at higher earnings yields (bargain prices, favorable valuations). Lines drawn based on P/E10 data place a greater emphasis on what happens at higher prices (unfavorable valuations).
The actual range of P/E10 is from 5.1 to 32.6. The range of 100E10/P is from 19.52% to 3.07%.
An earnings yield of 3.5% is at an extreme. But earnings yields of 5% and 10% are in the central region of the curve fit.
At high valuations, Year 10 Bull Market graphs show that there were many actual returns lower than projected using both 100E10/P and P/E10. [Many others were close to projections.] Year 10 Bear Market returns showed the opposite.
What has happened is that the market has changed from Bull to Bear or from Bear to Bull at the extremes. There is a problem with this explanation, however. It works when going starting at high valuations in a bull market. Multiples cease expanding before year 10. But if we start from high valuations in a bear market, multiples are already contracting. It could be that they stop contracting as rapidly as at first. That would happen if the really sharp decline happens early.
In addition, several bull and bear markets lasted less than 10 years.
These effects are present at both years 10 and 20.
Year 10 Bull Market versus Bear Market Comparisons
Here are the four sets of bull market predictions at earnings yields of 3.5%, 5.0% and 10.0%, respectively:
4.79% and 6.09% and 10.41%
(1.72)% and 4.42% and 11.58%
0.96% and 4.12% and 14.65%
(4.25)% and 3.84% and 13.28%
Here are the Year 10 bull market averages:
(0.06)% and 4.62% and 12.45%
Here are the two sets of bear market predictions at earnings yields of 3.5%, 5.0% and 10.0%, respectively:
(1.92)% and 0.06% and 6.66%
(5.05)% and 0.27% and 6.48%
Here are the Year 10 bear market averages:
(3.49)% and 0.17% and 6.57%
Here are the differences of the averages: Bull Market-Bear Market:
3.43% and 4.45% and 5.88%
This is in qualitative agreement with the dividend discount model and its variants.
In its most basic form: the investment return = the initial dividend yield + the rate of dividend growth. Smoothed earnings yield makes a good proxy for the initial dividend yield since (a) dividends come out of earnings and (b) using smoothed earnings avoids the problem of surprise dividend cuts.
Lower earnings yields (higher prices) translate into lower dividend yields. Higher earnings yields (lower prices) translate into higher dividend yields.
The real, smoothed growth rate of the S&P500 index has been remarkably stable. It has been close to the real growth rate of the GDP.
John Bogle refers to this as the investment return. There is another component of the stock return. It is the speculative return. It comes from changes in the price to earnings ratio. When the price to earnings ratio increases, the speculative return adds a bonus. When the price to earnings ratio falls, the speculative return drags down the overall return.
The differences between the bull market and bear market returns are related to the speculative return. If valuations double in a decade, it adds 7.2% (annualized) to the speculative return. If valuations fall in half in a decade, it subtracts 7.2% (annualized) to the speculative return.
We see from the numbers that valuations change less than that on average.
The overall trend that the differences between bull markets and bear markets increase as earnings yield increases makes sense because limits exist. That is, earnings yield is unlikely to stray far from its historical bounds for an extended amount of time. The normal range is 5% to 10% (P/E10 = 10 to 20). Outside of this range, returns are likely to disappoint (when P/E10>20) or please (when P/E10<10).
When earnings yield starts high (low P/E10), the initial dividend yield is high and there is a lot of room for P/E10 multiples to grow during bull markets. There is little room for P/E10 multiples fall during bear markets.
That is, if you start with a high earnings yield (low P/E10) in a bear market, the bear is almost over. If you start with a high earnings yield (low P/E10) in a bull market, the bull is just beginning.
Similarly, when earnings yield starts low (high P/E10), the initial dividend yield is low and there is little room for P/E10 multiples to grow during bull markets. There is a lot of room for P/E10 multiples to fall during bear markets.
That is, if you start with a low earnings yield (high P/E10) in a bull market, the bull is almost over. If you start with a low earnings yield (high P/E10) in a bear market, the bear market has a long way to go.
Bull and bear markets do not differ simply because of changing multiples. They differ because there are limits to how much multiples can change.
That is, if you start at a high earnings yield (low P/E10) in a bear market, the bear is almost over. If you start at a low earnings yield (high P/E10) in a bull market, the bull is almost over.
Year 20 Bull Market versus Bear Market Comparisons
Here are the four sets of bull market predictions at earnings yields of 3.5%, 5.0% and 10.0%, respectively:
3.39% and 4.47% and 8.07%
(1.89)% and 3.14% and 9.01%
(0.11)% and 2.62% and 11.71%
(3.78)% and 2.67% and 10.20%
Here are the Year 20 bull market averages:
(0.60)% and 3.23% and 9.75%
Here are the two sets of Year 20 bear market predictions at earnings yields of 3.5%, 5.0% and 10.0%, respectively:
3.22% and 4.68% and 9.52%
0.23% and 4.59% and 9.67%
Here are the Year 20 bear market averages:
1.73% and 4.64% and 9.60%
Here are the differences of the averages: Bull Market-Bear Market:
(2.33)% and (1.41)% and 0.15%
These differences may be an artifact of the data. There are thinned bull market data but no thinned bear market data. The differences may be real. If so, the reason is most likely to be the amount of time. Twenty years is long enough for a bull market to change to a bear market and vice versa.
Year 10 Baseline Comparisons
Here are the three sets of baseline market predictions at earnings yields of 3.5%, 5.0% and 10.0%, respectively, at year 10:
1.75% and 3.42% and 8.98%
0.96% and 2.99% and 9.78%
(1.23)% and 2.02% and 12.85%
Here are the Year 10 baseline averages:
0.49% and 2.81% and 10.20%
Here are the Year 10 bull market averages:
(0.06)% and 4.62% and 12.45%
Here are the Year 10 bear market averages:
(3.49)% and 0.17% and 6.57%
Identifying bull and bear markets appears to be helpful at Year 10. [The range of the data is in the neighborhood of plus and minus 7% and the number of degrees of freedom should be enough to bring the confidence limits down to plus and minus 1%.] There is still a lot of scatter in the likely outcomes.
Year 20 Baseline Comparisons
Here are the three sets of baseline market predictions at earnings yields of 3.5%, 5.0% and 10.0%, respectively, at year 20:
3.42% and 4.60% and 8.54%
2.45% and 4.07% and 9.46%
1.10% and 3.45% and 11.26%
Here are the Year 20 baseline averages:
2.32% and 4.04% and 9.75%
Here are the Year 20 bull market averages:
(0.60)% and 3.23% and 9.75%
Here are the Year 20 bear market averages:
1.73% and 4.64% and 9.60%
Identifying bull and bear markets does not appear to help at Year 20. The best that we can say is that if you start in a bull market at a low earnings yield (high P/E10), you are likely to see it end and wind up in a bear market. If you start out at a low earnings yield (high P/E10) in a bear market, you are likely to recover somewhat by Year 20.
Summary
Separating projections based on secular (long lasting) bull markets from secular (long lasting) bear markets can be worthwhile, especially at Year 10.
You are likely to encounter both a secular bull market and a secular bear market by Year 20.
Repeatedly, the story at today’s valuations (100E10/P = 3.5%) is bad news. We can expect to see the effects of the current secular bear market at year 10. The most likely outcome will be a net loss (of 3% annualized) between 2000 and 2010. The bull market that follows is likely to bring the overall annualized return to 1.7% (plus inflation) by year 20. That would almost match today’s TIPS.
Repeatedly, the story is that markets reverse themselves at extreme valuations. We see this in projected returns by Year 10. Even then, there is still a lot of randomness even at Year 10. Outcomes can easily vary plus and minus 5% (annualized) about projections.
Have fun.
John Walter Russell
January 8, 2006