http://nofeeboards.com/boards/viewtopic.php?t=2676

I will start out with a series of tables followed by an analysis. My conclusion is that calculations based on the percentage earnings yield (as defined by 100E10/P or 100/[P/E10]) produce reliable results with the kind of errors typical for extrapolations.

Values of P/E10

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```
January 2000 43.774387
January 2003 22.894158
This week 27.851533 (estimated)
```

y = HDBR80 Calculated Rate (percent) and x = percentage earnings yield = 100/[P/E10]

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```
1941-1950
y = 0.7318x + 2.3723
1941-1960
y = 0.9635x + 0.3354
1941-1970
y = 1.0644x - 0.5469
1941-1980
y = 0.7842x + 0.9624
```

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```
1951-1960
y = 1.201x - 1.2943
1951-1970
y = 1.1936x - 1.2958
1951-1980
y = 0.649x + 1.562
```

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```
1961-1970
y = 0.6831x + 1.1174
1961-1980
y = 0.5835x + 1.5399
```

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```
Degrees of freedom Confidence Limits
10 1.71%
20 1.63%
30 1.60%
40 1.59%
50 1.58%
60 1.58%
```

**January 2000 Results**

January 2000 Rates (Safe, Calculated and High Risk)

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```
1941-1950
2.33% 4.04% 5.75%
1941-1960
0.91% 2.54% 4.17%
1941-1970
0.28% 1.88% 3.48%
1941-1980
1.16% 2.75% 4.34%
```

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```
1951-1960
(0.26)% 1.45% 3.16%
1951-1970
(0.20)% 1.43% 3.06%
1951-1980
1.44% 3.04% 4.64%
```

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```
1961-1970
0.97% 2.68% 4.39%
1961-1980
1.24% 2.87% 4.50%
```

January 2003 Rates (Safe, Calculated and High Risk)

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```
1941-1950
3.86% 5.57% 7.28%
1941-1960
2.91% 4.54% 6.17%
1941-1970
2.50% 4.10% 5.70%
1941-1980
2.80% 4.39% 5.98%
```

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```
1951-1960
2.24% 3.95% 5.66%
1951-1970
2.29% 3.92% 5.55%
1951-1980
2.80% 4.40% 6.00%
```

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```
1961-1970
2.39% 4.10% 5.81%
1961-1980
2.44% 4.07% 5.70%
```

This Week's 2004 Rates (Safe, Calculated and High Risk)

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```
1941-1950
3.29% 5.00% 6.71%
1941-1960
2.16% 3.79% 5.42%
1941-1970
1.67% 3.27% 4.87%
1941-1980
2.19% 3.78% 5.37%
```

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```
1951-1960
1.31% 3.02% 4.73%
1951-1970
1.36% 2.99% 4.62%
1951-1980
2.29% 3.89% 5.49%
```

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```
1961-1970
1.86% 3.57% 5.28%
1961-1980
2.00% 3.63% 5.26%
```

**Safe Withdrawal Rate Comparisons**

January 2000

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```
1941-1950 2.33%
1941-1960 0.91%
1941-1970 0.28%
1941-1980 1.16%
1951-1960 (0.26)%
1951-1970 (0.20)%
1951-1980 1.44%
1961-1970 0.97%
1961-1980 1.24%
```

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```
1941-1950 3.86%
1941-1960 2.91%
1941-1970 2.50%
1941-1980 2.80%
1951-1960 2.24%
1951-1970 2.29%
1951-1980 2.80%
1961-1970 2.39%
1961-1980 2.44%
```

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```
1941-1950 3.29%
1941-1960 2.16%
1941-1970 1.67%
1941-1980 2.19%
1951-1960 1.31%
1951-1970 1.36%
1951-1980 2.29%
1961-1970 1.86%
1961-1980 2.00%
```

**Calculated Rate Comparisons**

January 2000

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```
1941-1950 4.04%
1941-1960 2.54%
1941-1970 1.88%
1941-1980 2.75%
1951-1960 1.45%
1951-1970 1.43%
1951-1980 3.04%
1961-1970 2.68%
1961-1980 2.87%
```

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```
1941-1950 5.57%
1941-1960 4.54%
1941-1970 4.10%
1941-1980 4.39%
1951-1960 3.95%
1951-1970 3.92%
1951-1980 4.40%
1961-1970 4.10%
1961-1980 4.07%
```

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```
1941-1950 5.00%
1941-1960 3.79%
1941-1970 3.27%
1941-1980 3.87%
1951-1960 3.02%
1951-1970 2.99%
1951-1980 3.89%
1961-1970 3.57%
1961-1980 3.63%
```

**High Risk Rate Comparisons**

January 2000

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```
1941-1950 5.75%
1941-1960 4.17%
1941-1970 3.48%
1941-1980 4.34%
1951-1960 3.16%
1951-1970 3.06%
1951-1980 4.64%
1961-1970 4.39%
1961-1980 4.50%
```

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```
1941-1950 7.28%
1941-1960 6.17%
1941-1970 5.70%
1941-1980 5.98%
1951-1960 5.66%
1951-1970 5.55%
1951-1980 6.00%
1961-1970 5.81%
1961-1980 5.70%
```

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```
1941-1950 6.71%
1941-1960 5.42%
1941-1970 4.87%
1941-1980 5.37%
1951-1960 4.73%
1951-1970 4.62%
1951-1980 5.49%
1961-1970 5.28%
1961-1980 5.26%
```

**Analysis: Calculated Rates**

There are two effects that cause these predictions to vary. The first, and more important, is that of extrapolation. Similar data produces better predictions than differing data. When we examine the valuations in 2000 and later, the valuations are very high and the earnings yields are low, of the order of 2.5% to 4.5%. Now look at the decades starting from 1941:

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```
Decade Minimum Earnings Yield Range of Valuations (P/E10)
1941-1950 6.41% 10 to 16
1951-1960 5.46% 12 to 18
1961-1970 4.15% 17 to 24
1971-1980 5.35% 9 to 19
```

As you look at the Calculated Rates for January 2003, notice that they are clustered together as compared to January 2000 and this week in 2004. The greatest variation is for January 2000, which is priced farthest from the historical range. [The historical range does not include bubble level valuations. The historical range peaked in 1929 at 27. Otherwise, it is topped around 24.] This week's 2004 valuation was almost touching the top of the historical range. January 2003 valuation was within the historical range.

The other effect is that the median of the data depends upon the nature of each decade. Good times will produce more examples of successful retirements at higher withdrawal rates than bad times. This causes the mean (and median) of the data to be higher before the decade of the 1960s than after. This introduces a slowly varying secondary effect.

This is quite apparent throughout the data as decades are added. As we add decades, earlier Calculated Rates get revised downward, sharply downward in the 1960s and then reverse themselves and begin to climb as the 1970s are introduced.

**Analysis: Safe Withdrawal Rates**

Now let us use the 1941-1980 Calculated Rates as references.

1941-1980 Calculated Rate

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```
January 2000 2.75%
January 2003 4.39%
This week 2004 3.87%
```

Do not be disturbed that some of the Safe Withdrawal Rates are negative. That simply means that there was not sufficient data to establish anything except that it was very low. [Approximating the underlying statistical distribution with a normal distribution has failed because it allows for a nontrivial percentage of the data to be negative.]

The Safe Withdrawal Rates for January 2003 ranged from 2.24% to 3.86%. All of these are lower than our reference rate of 4.39%. If we exclude the 1941-1950 estimate, the highest January 2003 rate was 2.91%, which is well away from our referenced calculated rate and close to the 1941-1980 Safe Withdrawal Rate of 2.80%.

The Safe Withdrawal Rates for This Week in 2004 ranged from 1.31% to 3.29%. All of these are lower than our reference rate of 3.87%. If we exclude the 1941-1950 estimate, the highest 2004 rate was 2.29%, which is well away from our referenced calculated rate and close to the 1941-1980 Safe Withdrawal Rate of 2.19%.

**Analysis: High Risk Rates**

The High Risk Rates for January 2000 ranged from 3.06% to 5.75%. All of these are higher than our reference rate of 2.75%. If we exclude the 1941-1950 estimate, the highest January 2000 rate was 4.64%, which is well away from our referenced calculated rate and close to the 1941-1980 High Risk Withdrawal Rate of 4.34%.

The High Risk Rates for January 2003 ranged from 5.55% to 7.28%. All of these are higher than our reference rate of 4.39%. If we exclude the 1941-1950 estimate, the highest January 2003 rate was 6.17%, which is well away from our referenced calculated rate and close to the 1941-1980 High Risk Withdrawal Rate of 5.98%.

The High Risk Rates for This Week in 2004 ranged from 4.62% to 6.71%. All of these are higher than our reference rate of 3.87%. If we exclude the 1941-1950 estimate, the highest 2004 rate was 5.49%, which is well away from our referenced calculated rate and close to the 1941-1980 High Risk Withdrawal Rate of 5.37%.

**Remarks**

This adds more light about how the time period chosen affects projections based on earnings yield. All of the results are reasonable. None of the projections, including the very worst projections, would have caused a serious error.

This review shows that projections outside of the range in the database become less and less reliable as they move farther from the database. This is typical of any extrapolation.

The odds of success at a 4% withdrawal rate are less than 50-50 for the peak of the bubble and during this week of 2004. We see that from looking at the Calculated Rates. Those who are withdrawing 6.00% are already in the High Risk area. They are in serious danger. Those who are withdrawing 3.00% or more are outside of the Safe Withdrawal area unless we rely on the 1941-1950 projection (which requires us to make the greatest extrapolation). The Safe Withdrawal Rate was well below 2% at the peak of the bubble unless we rely on the 1941-1950 projection (which requires us to make the greatest extrapolation). Those withdrawing 4.5% or more are in danger.

Have fun.

John R.