Improving the Retirement Trainer

First, I built the Retirement Trainer. It was my first excursion into Monte Carlo modeling. It included Mean Reversion. Then I introduced the Bull Bear Retirement Trainer. It introduced the ability to distinguish among long lasting (secular) Bull Markets, Bear Markets and Neutral Markets.

Retirement Trainer Overview
Bulls, Bears and P/E10 Predictions

Now I have introduced a further refinement in my Type 2 Bull Bear Retirement Trainer. It is fun. It is realistic.

P/E10 and Mean Reversion

I use a lognormal distribution to simulate year-to-year stock market returns. It has a standard deviation of 20%. I use the Most Likely return at Year 30 as the mean.

I introduce Mean Reversion by filtering out unsuitable sequences at Years 10 and 20. I require that a sequence either be within the inner confidence limits at Year 10 or, if outside of the inner confidence limits at Year 10, I require that it be within the inner confidence limit at Year 20. I require that all acceptable sequences stay within the outer confidence limits at Years 10, 20 and 30.

I credit Raddr with the idea of filtering out unsuitable sequences depending upon their spread. I credit Rob Bennett with discovering that sequences that stray far from their projected Year 10 returns end up close to their projected Year 20 returns.

In the first version of the Retirement Trainer, I used the equations from the Stock-Return Predictor at Years 10, 20 and 30. In the Bull Bear Retirement Trainer, I used separate sets of equations for Bull Markets and Bear Markets. I continued to use the Stock-Return Predictor equations for Neutral Markets. I used Ed Easterling’s definitions for the timing of long lasting (secular) Bull Markets and Bear Markets during the twentieth century. Visit his web site, Crestmont Research, or read his book Unexpected Returns for the details.

In this latest version, I use the Year 30 equations from the Stock-Return Predictor for the Year 30 predictions of all types of markets. This allows the market to recover, changing from a Bear Market or a Bull Market to a Neutral Market.

Before the Change

Here is the P/E10 sequence for Run 3 from the Bull Bear Retirement Trainer. All values are the beginning of Years 0 through 30. I specified a Bear Market.

Run 3

27.3

28.0
28.2
28.7
24.2
30.5
19.6
14.4
13.4
12.0
11.4

14.4
8.8
9.7
10.4
14.7
15.3
14.9
14.9
9.9
11.3

13.6
9.3
8.7
10.5
12.6
14.0
12.3
14.9
9.4
12.6

This sequence is plausible. It is useful for training. However, there is no turning around in the third decade. We never see the beginning of a Bull Market.

After the Change

Here are the P/E10 sequences for Runs 4, 5 and 6 from my new Type 2 Bull Bear Retirement Trainer. All values are at the beginning of Years 0 through 30. I specified a Bear Market.

Run 4

27.3

34.8
27.2
22.1
16.2
13.9
11.9
12.6
14.3
11.9
17.4

12.1
15.6
15.7
13.4
16.1
15.8
17.5
20.3
17.8
20.5

23.0
23.5
21.2
22.2
27.0
21.8
18.6
20.7
21.7
19.1

Run 4 is plausible. It is useful for training. Notice that it never falls to the lowest valuations of the past. P/E10 remains at 11.9 or higher throughout. Notice as well that there is a follow on Bull Market. P/E10 reaches 27.0 at the beginning of Year 25. Since Run 4 starts from today’s valuations, the peak occurs in 2031.

Run 5

27.3

31.8
26.9
25.0
20.6
16.8
13.4
12.8
13.8
11.2
12.6

13.2
11.5
14.0
14.5
16.8
14.7
14.4
13.8
13.7
12.1

17.4
19.6
18.7
17.2
18.6
23.4
20.6
16.4
12.6
13.7

Run 5 sequence is plausible. It is useful for training. Notice that it never falls to the lowest valuations of the past. P/E10 bottoms at 11.2. We see a Bull Market. P/E10 reaches 23.4, almost identical to the January 1966 peak of 24.0, at the beginning of Year 26. Since Run 5 starts from today’s valuations, the peak occurs in 2032.

Run 6

27.3

29.9
30.4
39.0
36.3
44.8
35.4
33.6
29.1
23.8
13.0

11.2
9.7
9.6
10.0
10.4
7.7
6.7
7.5
6.4
8.2

7.9
9.0
9.6
8.4
8.9
10.4
12.9
15.9
16.2
20.6

Run 6 is unusual. It is useful for training. It simulates a future Super Bubble. P/E10 peaks at 44.8 in Year 5. Since Run 6 starts from today’s valuations, this peak occurs in 2011.

Following the Super Bubble, valuations fall quickly to reasonable valuations. P/E10 falls below 10 at Year 12, which would be in 2018, only 7 years after the peak. The bottom occurs at Year 19, corresponding to 2025, which would be 14 years after the peak of the Super Bubble. P/E10 falls to 6.4, which is consistent with previous lows.

The market is rising at Year 30. P/E10 is 20.6.

Downloading Details

I have placed this calculator (Type 2 Bull Bear Retirement Trainer) into my Yahoo Briefcase. I made a new Retirement Trainer folder. It is available for downloading by Everyone. My Yahoo Username is jwr19452000.

Yahoo Briefcase

Perspective

Do not be overly concerned that I have made a series of changes. Each improves realism. Each improves the accuracy of your training experience.

Such upgrades should be routine with Monte Carlo models. Typically, they are not.

We do not have a good method of estimating stock market turning points, the exact times when a market changes from a Bull to a Bear or vice versa.

History suggests that markets peak roughly every 30 to 35 years. Previous peaks occurred in 1901, 1929, 1966 and 2000. Theory suggests that this makes sense and that such intervals will continue into the future. Each generation of new investors has its own initial experience with stocks. Some remember a roaring Bull Market. Others remember an exhausting Bear Market. Others, a mixture of the two. Early lessons stick with you. Early lessons are hard to unlearn.

In the absence of information about turning points, the Type 2 Bull Bear Retirement Trainer is doing about a well as we could hope for. It is producing credible sequences. It includes stressful sequences as well.

You can learn a lot from the Type 2 Bull Bear Retirement Trainer. Besides, it’s fun.

Have fun.

John Walter Russell
September 5, 2006