P/E10 Predictions Revisited

My first excursion into Monte Carlo modeling resulted in Retirement Trainers A, B and C. I reported the implications in P/E10 Predictions. After examining the data, I separated Bull Markets and Bear Markets. I calculated a new set of Equations. I published them in Bulls, Bears and P/E10 Predictions. I built Bull Bear Retirement Trainers A and B. They allow you to specify the market’s direction: Bull Market, Neutral Market or Bear Market. They generate a realistic sequence of returns.

P/E10 Predictions
Bulls, Bears and P/E10 Predictions

I have collected two sets of P/E10 data using Bull Bear Retirement Trainer B. The first assumes a long lasting (secular) Bear Market starting from today’s valuations, P/E10=26.0. The second assumes a long lasting (secular) Bull Market starting from P/E10=9.0.

I also ran through a single sequence of each type to get a feel for what happens. There are traps. It is easy to become overconfident in either type of market.

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.

The new equations produce new numbers for the mean return and the confidence limits, depending upon the type of market. Otherwise, the screens are the same. The probabilities, 5% and 95% for the outer confidence limits and 20% and 80% for the inner confidence limits, remain the same.

P/E10 Calculations

P/E10 calculations remain the same.

Bear Market Summaries

I generated 20 sequences that satisfied the Bear Market 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. High: tells us when P/E10 hit its high throughout the entire time period.

Sequence 1:
Below 15: 6/13.1
Below 14: 6/13.1
Low: 7/8.0
High: 2/30.5

Sequence 2:
Below 15: 8/13.5
Below 14: 8/13.5
Low: 12/12.0
High: 1/29.9 and 2/29.9

Sequence 3:
Below 15: 10/12.5
Below 14: 10/12.5
Low: 22/11.4
High: 1/26.9

Sequence 4:
Below 15: 7/13.5
Below 14: 7/13.5
Low: 19/7.6
High: 4/26.4

Sequence 5:
Below 15: 4/14.2
Below 14: 13/13.7
Low: 19/8.7 and 23/8.7
High: 17/26.2

Sequence 6:
Below 15: 5/14.4
Below 14: 8/12.3
Low: 11/7.9
High: 24/26.3

Sequence 7:
Below 15: 2/13.1
Below 14: 2/13.1
Low: 7/7.4
High: 18/50.0

Sequence 8:
Below 15: 6/11.8
Below 14: 6/11.8
Low: 11/9.1
High: 23/32.1

Sequence 9:
Below 15: 8/13.8
Below 14: 8/13.8
Low: 8/13.8
High: 27/28.9

Sequence 10:
Below 15: 13/13.9
Below 14: 13/13.9
Low: 22/10.1
High: 2/29.5

Sequence 11:
Below 15: 6/12.5
Below 14: 6/12.5
Low: 23/8.6
High: 3/27.4

Sequence 12:
Below 15: 11/12.6
Below 14: 11/12.6
Low: 17/7.3
High: 2/30.5

Sequence 13:
Below 15: 3/14.4
Below 14: 5/11.5
Low: 20/8.3
High: 0/26.0

Sequence 14:
Below 15: 8/11.2
Below 14: 8/11.2
Low: 12/8.9
High: 3/27.2

Sequence 15:
Below 15: 7/11.2
Below 14: 7/11.2
Low: 9/9.4
High: 1/33.0

Sequence 16:
Below 15: 10/13.8
Below 14: 10/13.8
Low: 27/7.5
High: 2/29.2

Sequence 17:
Below 15: 5/11.2
Below 14: 5/11.2
Low: 12/7.7
High: 1/27.5

Sequence 18:
Below 15: 3/12.8
Below 14: 3/12.8
Low: 5/8.2
High: 0/26.0

Sequence 19:
Below 15: 9/13.3
Below 14: 9/13.3
Low: 18/5.8
High: 0/26.0

Sequence 20:
Below 15: 6/14.9
Below 14: 10/10.6
Low: 27/6.1
High: 1/26.6

Bear Market Observations

These results were much more reasonable than before. P/E10 fell to a low of 5.8 to 12.0. The average was 9.1. The median was 8.65.

The longest it took for P/E10 to fall below 15.0 and 14.0 was 13 years (two instances and one instance, respectively). Since there were 20 sequences, the chances that it would take 13 years were (roughly) 10% and 5%, respectively.

In one instance, P/E10 rose to 50, which is even higher than in the bubble. But that was only after it had fallen to 7.4 eleven years earlier. This was not a case of having a super bubble follow the bubble.

Bull Market Summaries

I generated 20 sequences that satisfied the Bull Market screens. In all cases, I set the initial P/E10 level at 9.0. This is rounded and consistent with the average low from the Bear Market data.

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

Above 15: tells us when P/E10 rose above 15.0 for the first time.

Above 14: tells us when P/E10 rose above 14.0 for the first time.

Low: tells us when P/E10 hit its low throughout the entire time period. High: tells us when P/E10 hit its high throughout the entire time period.

Sequence 1:
Above 15: 13/15.1
Above 14: 13/15.1
Low: 29/3.9
High: 15/17.8

Sequence 2:
Above 15: 8/17.2
Above 14: 5/14.9
Low: 0/9.0
High: 8/17.2

Sequence 3:
Above 15: 19/18.6
Above 14: 19/18.6
Low: 2/7.9
High: 29/20.7

Sequence 4:
Above 15: 19/15.8
Above 14: 19/15.8
Low: 22/7.0
High: 20/16.8

Sequence 5:
Above 15: 14/17.4
Above 14: 14/17.4
Low: 1/8.3
High: 14/17.4

Sequence 6:
Above 15: NEVER
Above 14: NEVER
Low: 30/5.8
High: 22/13.1

Sequence 7:
Above 15: 16/15.9
Above 14: 16/15.9
Low: 5/6.6 and 7/6.6
High: 30/32.2

Sequence 8:
Above 15: 11/17.4
Above 14: 8/14.3
Low: 29/8.7
High: 14/22.2

Sequence 9:
Above 15: 16/15.5
Above 14: 14/14.4
Low: 29/7.6
High: 20/18.7

Sequence 10:
Above 15: 16/16.1
Above 14: 16/16.1
Low: 7/7.4
High: 25/22.4

Sequence 11:
Above 15: 9/15.7
Above 14: 8/14.2
Low: 29/4.8
High: 19/25.2

Sequence 12:
Above 15: 5/19.2
Above 14: 4/15.0
Low: 0/9.0
High: 23/25.3

Sequence 13:
Above 15: 15/15.4
Above 14: 15/15.4
Low: 2/8.0
High: 26/18.9

Sequence 14:
Above 15: 12/16.0
Above 14: 12/16.0
Low: 1/8.1
High: 24/31.7

Sequence 15:
Above 15: 10/15.4
Above 14: 9/14.2
Low: 3/7.0
High: 18/20.0

Sequence 16:
Above 15: 5/15.3
Above 14: 5/15.3
Low: 15/8.0
High: 22/19.1

Sequence 17:
Above 15: 14/15.2
Above 14: 7/14.4
Low: 1/7.5
High: 17/22.3

Sequence 18:
Above 15: 5/15.6
Above 14: 5/15.6
Low: 23/6.8
High: 6/16.0

Sequence 19:
Above 15: 12/17.3
Above 14: 11/14.2
Low: 4/7.1
High: 13/25.0

Sequence 20:
Above 15: NEVER
Above 14: NEVER
Low: 24/4.9
High: 19/13.5

Bull Market Observations

P/E10 highs ranged from 13.1 to 32.2. The average P/E10 high was 20.8. The median P/E10 high was 19.55.

There were two instances each in which P/E10 failed to rise above 15.0 and 14.0. Since there were 20 sequences, the chance of such a shortfall is (roughly) 10% (in both cases).

These numbers strike me as unreasonably low. I believe that this is because I started at a low, a turning point, instead of waiting until P/E10 had recovered enough to confirm a long lasting (secular) Bull Market trend.

Conclusions

The Bear Market summaries strike me as realistic. They are relevant to today’s investor.

In contrast, the Bull Market summaries strike me as subdued, with valuations remaining below normal much too long.

The reason for the discrepancy is likely to be the starting point. The Bear Market data uses P/E10=26, which is well below the market peak. The Bear Market has been around long enough for us to treat the market’s direction as already established. The Bull Market numbers, in contrast, correspond to a market low, P/E10=9, which was extracted from the analysis of the Bear Market results. This defines a turning point, not an established Bull Market.

In spite of this, the Bull Market data are significant. They confirm that Professor Robert Shiller’s plot of P/E10 is reasonable throughout the entire time period.

Getting a Feel for Retirement Portfolios

I made two quick runs with Bull Bear Retirement Trainer B.

Using what I have learned about stock allocations and valuations, I made it through 30 years OK withdrawing 5% in today’s (secular) Bear Market.

Keep in mind that this was a single run. Keep in mind that the odds were against my running into stressful market conditions.

I held off heavier stock allocations until valuations had improved considerably. I eased into stocks, not making dramatic shifts. Still, I surprised myself. I became complacent. As I was approaching Year 30, I had more than enough, but it was almost entirely in stocks. I ran into a couple of bad years and almost ran out of money. I could have locked in success by transferring funds into TIPS. Instead, I was complacent. I barely squeaked by.

I also discovered that my portfolio never really took off. At a high withdrawal rate (5% of the initial portfolio balance plus inflation), it was stable, but drifted downward.

When I tried starting in a Bull Market, with P/E10=9, it seemed like a breeze. I saw my portfolio double even though I was withdrawing 5% of the original balance (plus inflation). But I got sloppy. I ended up with about one-half of the money that I should have. I delayed transferring money into TIPS during the good years. I returned half of my gains back to the market. I did OK because of the Bull Market. But I could have done spectacularly well.

Of course, nothing like this ever happens in the real world. Investors never become complacent. Investors never become sloppy. Actually, there is one small subclass of investors who fall prey to such errors, but only one. They are the humans.

Have fun.

John Walter Russell
August 28, 2006