Bulls, Bears and P/E10 Predictions

In Unexpected Returns: Understanding Secular Stock Market Cycles, Ed Easterling shows that the stock market has two distinct probability distributions. There is one during long lasting (secular) bull markets. There is another during long lasting (secular) bear markets.

Each can be approximated reasonably well by a standard normal (Gaussian, bell shaped) distribution in terms of percentages (i.e., they are lognormal).

The Stock-Return Predictor is based on standard regression equations with no distinction as to the overall market direction.

Very recently, I looked into the future behavior of P/E10. I used the Monte Carlo model from my Retirement Trainers. My Monte Carlo implementation simulates Mean Reversion. My technique was inspired by Raddr’s original approach. I included Rob Bennett’s Mean Reversion discovery.

The predictions were generally reasonable, but overly pessimistic. Prices might remain high indefinitely, not returning to normal valuations. I attribute this to the lack of directional adjustments in my model. It makes no distinction between bull markets and bear markets.

My assessment is that prices have a high probability of returning to their historically typical level of P/E10=13 or 14 within 20 years. This would be consistent with history, demographics and human behavior. The model indicates otherwise. It indicates that there is (close to) a 20% chance that prices will stay above P/E10=14 longer than 20 years.

In this study, I quantify the effect of long lasting (secular) market trends (bull markets and bear markets). This immediately improves our estimates provided that we get the overall direction right.

Bulls, Bears and Composite Equations

I have extracted a list of (secular, long lasting) Bull and Bear Market periods from page 80, Figure 5.1 of Unexpected Returns. Ed Easterling also makes this available at his Crestmont Research web site.

BEAR 1901-1920
BULL 1921-1928
BEAR 1929-1932
BULL 1933-1936
BEAR 1937-1941
BULL 1942-1965
BEAR 1966-1981
BULL 1982-1999

I constructed Bull Market tables, Bear Market tables and a composite table using 1901-1975 S&P500 real, annualized, total returns. I stopped in 1975 so that all of my 30-year sequences would be complete. I used Excel’s plotting capability to determine regression equations versus the percentage earnings yield 100E10/P. I use January values of P/E10. They are in Professor Robert Shiller’s S&P500 database.

BULL MARKET Equations where x=100E10/P

Sequences used: 1921-1928, 1933-1936, 1942-1965.

Year 10 Return: y = 0.6953x+3.2125 plus and minus 4%.
R-squared=0.261.

Year 20 Return: y = 0.6378x+1.5192 plus 5% and minus 3%.
R-squared=0.3278.

Year 30 Return: y = 0.3681x+3.5193 plus and minus 2%.
R-squared=0.4092.

BEAR MARKET Equations where x=100E10/P

Sequences used: 1901-1920, 1929-1932, 1937-1941, 1966-1975 (the bear market extended through 1981).

Year 10 Return: y = 1.1795x-5.7846 plus and minus 5%.
R-squared=0.6129.

Year 20 Return: y = 0.5549x+1.4162 plus 4% and minus 3%.
R-squared=0.4579.

Year 30 Return: y = 0.1242x+5.4433 plus and minus 2%.
R-squared=0.0782.

COMPOSITE MARKET Equations where x=100E10/P

Sequences used: 1901-1975.

Year 10 Return: y = 1.0884x-2.694 plus and minus 6%.
R-squared=0.3969.

Year 20 Return: y = 0.616x+1.3238 plus 5% and minus 4%.
R-squared=0.3913.

Year 30 Return: y = 0.2423x+4.5795 plus and minus 2%.
R-squared=0.2295.

Bulls, Bears and Composite Predictions

Separating Bull Markets and Bear Markets narrows the confidence limits at Years 10 and 20.

Notice the stronger influence of valuations (as measured by 100E10/P) on Bear Market returns at Year 10 (by examining R-squared). Notice the stronger influence of valuations (as measured by 100E10/P) on Bull Market returns at Year 30. Both markets respond to valuations similarly at Year 20.

Here are the most likely returns at today’s valuations (P/E10=26):

Bull Market Equations: 5.89% at Year 10, 3.97% at Year 20 and 4.94% at Year 30.

Bear Market Equations: -1.25% at Year 10, 3.55% at Year 20 and 5.92% at Year 30.

Composite Market Equations: 1.49% at Year 10, 3.69% at Year 20 and 5.51% at Year 30.

Stock-Return Predictor: 1.31% at Year 10, 2.72% at Year 20 and 5.36% at Year 30.

Here are the most likely returns at typical valuations (P/E10=14):

Bull Market Equations: 8.18% at Year 10, 6.07% at Year 20 and 6.15% at Year 30.

Bear Market Equations: 2.64% at Year 10, 5.38% at Year 20 and 6.33% at Year 30.

Composite Market Equations: 5.08% at Year 10, 5.72% at Year 20 and 6.31% at Year 30.

Stock-Return Predictor: 6.34% at Year 10, 6.30% at Year 20 and 6.73% at Year 30.

Here are the most likely returns at bargain valuations (P/E10=8):

Bull Market Equations: 11.90% at Year 10, 9.49% at Year 20 and 8.12% at Year 30.

Bear Market Equations: 8.96% at Year 10, 8.35% at Year 20 and 7.00% at Year 30.

Composite Market Equations: 10.91% at Year 10, 9.02% at Year 20 and 7.61% at Year 30.

Stock-Return Predictor: 14.51% at Year 10, 12.11% at Year 20 and 8.96% at Year 30.

Including the earliest years of the twentieth century has little effect at today’s valuations and only a moderate effect at typical valuations. It lowers return estimates when starting from bargain levels. The first two decades of the twentieth century were dominated by a prolonged (secular) bear market. Stock market behavior versus 100E10/P was anomalous during the first decade.

More Retirement Trainers to Come

Having these equations, it will be easy and straightforward for me to build Bull Market Retirement Trainers and Bear Market Retirement Trainers. It will be straightforward to learn how P/E10 Predictions change when we assume that we know the overall direction of the market.

I believe that we are in the early stages of a long lasting (secular) bear market. Many informed observers agree.

Have fun.

John Walter Russell
August 27, 2006

Crestmont Research
Crestmont Research Secular Cycles
Professor Shiller’s Web Site