P/E10 Predictions

My first excursion into Monte Carlo modeling produced Retirement Trainers. There is a side benefit. We can learn how P/E10 is likely to behave in the future.

The Retirement Trainer Screens

The Retirement Trainers generate random sequences of returns based on the initial value of P/E10. The numbers have the mean estimated by the Stock-Return Predictor for year 30. The standard deviation is 20%, the single-year standard deviation of the S&P500 index. I generate 30-year sequences from these returns.

I require the sequences to pass through three screens: at Years 10, 20 and 30. In all cases, I require that an acceptable sequence remain within the outer confidence limits of the Stock-Return Predictor. This corresponds to the 5% and 95% probability levels. I have additional restrictions (in the logic placed) on my screen at Year 10.

If a sequence is within the inner confidence limits at Year 10, I allow it through the screen. The inner confidence limits correspond roughly to probability levels of 20% and 80%. If the sequence is outside of the inner confidence limits at Year 10 but within the outer confidence limits, I accept the sequence only if it is within the inner confidence limit at Year 20.

These screens simulate Mean Reversion. My implementation was inspired by Raddr’s Monte Carlo modeling approach. The detailed selection criteria for my screens were based on Rob Bennett’s discovery related to stock returns and Mean Reversion.

P/E10 Calculations

I calculate the cumulative return of stocks from the random sequences. The cumulative return is the product of gain multipliers, where each year’s gain multiplier equals 1+that year’s return. I compare this product to the (real) long-term annualized return of stocks, which is 6.8%. After N years, this equals 1.068^N. I assume that the relationship between P/E10 and the long-term return of stocks remains stable. I scale the initial P/E10 accordingly. At year N, P/E10 equals the initial P/E10 times the product of gain multipliers generated from the random sequence divided by 1.068^N.

Sequence Summaries

I generated 20 sequences that satisfied the screens. In all cases, the initial P/E10 level was 26.0.

Each summary below has the form: year/value of P/E10.

Below 15: tells us when P/E10 fell below 15.0 for the first time.

Below 14: tells us when P/E10 fell below 14.0 for the first time.

Low: tells us when P/E10 hit its low throughout the entire time period. I excluded the Year 0 level of P/E10=26. The number of years was 31.

High: tells us when P/E10 hit its high throughout the entire time period. I excluded the Year 0 level of P/E10=26. The number of years was 31.

Sequence 1:
Below 15: 4/14.6
Below 14: 5/10.4
Low: 28/9.8
High: 16/30.7

Sequence 2:
Below 15: 11/14.3
Below 14: 12/13.9
Low: 21/12.6
High: 6/32.3

Sequence 3:
Below 15: 15/13.6
Below 14: 15/13.6
Low: 15/13.6
High: 1/26.5

Sequence 4:
Below 15: 3/13.5
Below 14: 3/13.5
Low: 21/8.4
High: 2/32.4

Sequence 5:
Below 15: 17/11.8
Below 14: 17/11.8
Low: 27/8.8
High: 7/28.8

Sequence 6:
Below 15: 5/14.5
Below 14: 7/11.6
Low: 7/11.6
High: 28/30.1

Sequence 7:
Below 15: 12/14.8
Below 14: 15/12.4
Low: 16/11.1
High: 4/29.4

Sequence 8:
Below 15: 14/14.6
Below 14: 31/11.4
Low: 31/11.4
High: 2/33.3

Sequence 9:
Below 15: 3/13.4
Below 14: 3/13.4
Low: 28/8.2
High: 2/27.7

Sequence 10:
Below 15: 15/11.5
Below 14: 15/11.5
Low: 18/6.0
High: 2/30.9

Sequence 11:
Below 15: 18/13.6
Below 14: 18/13.6
Low: 24/12.3
High: 2/36.6

Sequence 12:
Below 15: 16/13.7
Below 14: 16/13.7
Low: 30/10.4
High: 1/26.1

Sequence 13:
Below 15: 25/14.2
Below 14: 26/11.1
Low: 30/6.7
High: 16/30.1

Sequence 14:
Below 15: 18/12.7
Below 14: 18/12.7
Low: 18/12.7
High: 9/42.1

Sequence 15:
Below 15: 19/13.8
Below 14: 19/13.8
Low: 21/10.7
High: 3/53.0 and 4/53.0

Sequence 16:
Below 15: 7/14.0
Below 14: 25/13.9
Low: 31/10.3
High: 4/35.5

Sequence 17:
Below 15: 11/13.1
Below 14: 11/13.1
Low: 21/7.6
High: 3/47.2

Sequence 18:
Below 15: 21/13.7
Below 14: 21/13.7
Low: 26/7.5
High: 2/32.4

Sequence 19:
Below 15: 10/14.5
Below 14: 11/12.2
Low: 20/8.3
High: 2/32.8

Sequence 20:
Below 15: 7/14.7
Below 14: 14/13.0
Low: 17/10.1
High: 5/22.7

Observations

The results were shocking because P/E10 failed to fall to typical valuations (below 14.0) within 20 years four times.

Even when the threshold was lifted, P/E10 failed twice to fall below 15.0 within 20 years.

There were 20 sequences. Roughly speaking, the probability that P/E10 will stay above 15.0 for two decades is 10%. The probability that P/E10 will stay above 14.0 for two decades is 20%.

Similarly, the probability that P/E10 will stay above 12.0 throughout the entire 31 years is 20%.

There were 3 sequences in which P/E10 rose above 40. There were 2 sequences in which P/E10 rose above the year 2000 January high of 44. The model indicates that there is a 10% chance that the bubble will be followed by a super bubble.

Interpretation

These results have come from rules extracted from the historical record. According to that record, P/E10 has varied slowly.

Much of the information contained in P/E10 relates more to human learning and human reactions than to straightforward calculation. A person who has had success while invested in stocks is likely to continue investing in stocks. A person who has been hurt badly or who was hurt consistently when he first started out is likely to avoid stocks. We now have investors who benefited from the run-up to the bubble and those who got in later. Some recent participants were hurt seriously. Others have experienced only a sideways market.

We can look at Professor Robert Shiller’s plot of P/E10 at his web site (in his S&P500 database) or at a copy in Microsoft Word format that I have placed into my Yahoo Briefcase. NOTE: Professor Shiller labels his data as the price to earnings ratio. It is P/E10, not the single-year P/E.

We should place our greatest emphasis on cause and effect. The psychological factor is important. Demographics are important. Both point consistently toward more attractive prices in the future.

Is there something that my numbers did not capture? Possibly so.

If you look at Ed Easterling’s charts at his Crestmont Research web site, you will find that the stock market has two distinct probability distributions. Both are approximately normal (in terms of percentages, actually lognormal). One distribution applies during long lasting (secular) bull markets, the other during long lasting (secular) bear markets.

I did not include a directional factor in my model.

The market has long-term memory. It is human memory. It is visible in the plots. It makes sense.

My model has overstated the probability that the prices will remain high. However, it places an upper bound on such possibilities. The probability that stock prices will fail to return to their typical levels (P/E10 between 13 and 14) is not really as bad as 20%. Perhaps, it is 5% or 10%. We cannot ignore it. It is big enough for us to pay attention.

Have fun.

John Walter Russell
August 27, 2006

Professor Shiller’s Web Site
Yahoo Briefcase
Crestmont Research
Crestmont Research Secular Swings