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The Stability of Estimates Based on Earnings Yield

 
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JWR1945
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Joined: 26 Nov 2002
Posts: 1697
Location: Crestview, Florida

PostPosted: Thu Jun 24, 2004 8:57 pm    Post subject: The Stability of Estimates Based on Earnings Yield Reply with quote

This examines the reliability of our Safe Withdrawal Rate estimates based on earnings yield (based on P/E10).

I base my estimates on the years 1923-1980. My exclusion of 1921 and 1922 is of little importance. They are outliers. They have the highest earnings yield (and lowest P/E10) in the data. I exclude them only to improve the linear curve fit at other valuations.

Of greater interest is my exclusion of 1871-1920. Data from that era behave differently from those in later years. There are many possible reasons. My best guess is that the most important was the rise of the Federal Reserve system and its debasement of commercial paper as an attractive investment. Income taxes might have been an important factor. The list goes on. In any event, the data are clear. There has been a change.

Regardless of the details, most people would agree that the Great Depression caused a series of radical changes in the economy. The Federal Government grew in importance. Departments started collecting detailed economic statistics. Therefore, I have included two examinations: one covering the years from 1923-1980 and the other from 1931-1980.

When interpreting these results, remember that it takes about 20 years after the last start date before we can use it in a projection. We are looking at 30-year retirements, which is a standard condition that balances how much we can learn with how much we must exclude. We include some partial sequences since much is known by the end of the first two decades.

My Investigation

What I have looked into is how the various estimates (the Safe Withdrawal Rate, the Calculated Rate and the High Risk Rate) change as a function of how many years of data are included.

First, I generated the same kind of curves that I currently use based on the following sequences. I did this for the standard 80% stocks / 20% commercial paper portfolio HDBR80, which was used in making the previous curves. I did not collect information on HDBR50 (except to verify that it does not behave radically different from HDBR80):
1) From my standard starting point: 1923-1930, 1923-1940, 1923-1950, 1923-1960, 1923-1970 and 1923-1980.
2) From the Great Depression: 1931-1940, 1931-1950, 1931-1960, 1931-1970 and 1931-1980.

Next, I applied the equations to valuations from January 2000 (which had the highest January valuation), from January 2003 (which had the lowest January valuation since then) and from earlier this week. That produced a set of Calculated Rates.

Next, I scaled my previous confidence limits for shorter sequences. I did not go to the trouble of calculating new estimates of the variances and standard deviations. [Our ability to claim safety and/or to declare excessive risk depends upon how much data we have. The adjustment is minor.]

Finally, I applied the new confidence limits to calculate Safe Withdrawal Rates and High Risk Rates.

Initial Results

Values of P/E10
Code:


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


Here are the formulas for the Calculated Rate of HDBR80 as a function of the percentage earnings yield using P/E10 (i.e., 100/[P/E10] or 100E10/P).

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


1923-1930
y = 0.5515x + 2.5346

1923-1940
y = 0.5274x + 2.3765

1923-1950
y = 0.6276x + 2.2028

1923-1960
y = 0.6473x + 2.1637

1923-1970
y = 0.7312x + 1.379

1923-1980
y = 0.6685x + 1.6424


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


1931-1940
y = 0.4456x + 2.7071

1931-1950
y = 0.7189x + 1.5714

1931-1960
y = 0.7459x + 1.5098

1931-1970
y = 0.8419x + 0.6639

1931-1980
y = 0.7117x + 1.3346


I scaled my previous confidence limits of 1.58% (for HDBR80) by taking the ratio of the Student t test confidence limit for a given number of freedom to that with 60 degrees of freedom.

Confidence Limits (approximately 90%, add and subtract these values)
Code:


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)
Code:


1923-1930
2.08%    3.79%    5.50%

1923-1940
1.95%    3.58%    5.21%

1923-1950
2.04%    3.64%    5.24%

1923-1960
2.05%    3.64%    5.23%

1923-1970
1.47%    3.05%    4.63%

1923-1980
1.59%    3.17%    4.75%

More January 2000 Rates (Safe, Calculated and High Risk)
Code:


1931-1940
2.02%    3.73%    5.44%

1931-1950
1.58%    3.21%    4.84%

1931-1960
1.61%    3.21%    4.81%

1931-1970
1.00%    2.59%    4.18%

1931-1980
1.38%    2.96%    4.54%


January 2003 Results

January 2003 Rates (Safe, Calculated and High Risk)
Code:


1923-1930
3.23%    4.94%    6.65%

1923-1940
3.05%    4.68%    6.31%

1923-1950
3.34%    4.94%    6.54%

1923-1960
3.40%    4.99%    6.58%

1923-1970
2.99%    4.57%    6.15%

1923-1980
2.98%    4.56%    6.14%

More January 2003 Rates (Safe, Calculated and High Risk)
Code:


1931-1940
2.94%    4.65%    6.36%

1931-1950
3.08%    4.71%    6.34%

1931-1960
3.16%    4.76%    6.36%

1931-1970
2.75%    4.34%    5.93%

1931-1980
2.86%    4.44%    6.02%


This Week's 2004 Results

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


1923-1930
2.80%    4.51%    6.22%

1923-1940
2.64%    4.27%    5.90%

1923-1950
2.86%    4.46%    6.06%

1923-1960
2.90%    4.49%    6.08%

1923-1970
2.42%    4.00%    5.58%

1923-1980
2.46%    4.04%    5.62%

More of This Week's 2004 Rates (Safe, Calculated and High Risk)
Code:


1931-1940
2.60%    4.31%    6.02%

1931-1950
2.52%    4.15%    5.78%

1931-1960
2.59%    4.19%    5.79%

1931-1970
2.10%    3.69%    5.28%

1931-1980
2.31%    3.89%    5.47%


Safe Withdrawal Rate Comparisons

January 2000
Code:


1923-1930    2.08%
1923-1940    1.95%
1923-1950    2.04%
1923-1960    2.05%
1923-1970    1.47%
1923-1980    1.59%

1931-1940    2.02%
1931-1950    1.58%
1931-1960    1.61%
1931-1970    1.00%
1931-1980    1.38%

The 1923 set of values varied over the range of 1.47% to 2.08%.
The 1931 set of values varied over the range of 1.00% to 2.02%.
Most comparisons ending in the same year that included the 1920s boom were more optimistic than those that started in the Great Depression. The exception was 1940.

January 2003
Code:


1923-1930    3.23%
1923-1940    3.05%
1923-1950    3.34%
1923-1960    3.40%
1923-1970    2.99%
1923-1980    2.98%

1931-1940    2.94%
1931-1950    3.08%
1931-1960    3.16%
1931-1970    2.75%
1931-1980    2.86%

The 1923 set of values varied over the range of 2.98% to 3.40%.
The 1931 set of values varied over the range of 2.75% to 3.16%.
All comparisons ending in the same year that included the 1920s boom were more optimistic than those that started in the Great Depression.

This Week 2004
Code:


1923-1930    2.80%
1923-1940    2.64%
1923-1950    2.86%
1923-1960    2.90%
1923-1970    2.42%
1923-1980    2.46%

1931-1940    2.60%
1931-1950    2.52%
1931-1960    2.59%
1931-1970    2.10%
1931-1980    2.31%

The 1923 set of values varied over the range of 2.42% to 2.90%.
The 1931 set of values varied over the range of 2.10% to 2.60%.
All comparisons ending in the same year that included the 1920s boom were more optimistic than those that started in the Great Depression.

Calculated Rate Comparisons

January 2000
Code:


1923-1930    3.79%
1923-1940    3.58%
1923-1950    3.64%
1923-1960    3.64%
1923-1970    3.05%
1923-1980    3.17%

1931-1940    3.73%
1931-1950    3.21%
1931-1960    3.21%
1931-1970    2.59%
1931-1980    2.96%

The 1923 set of values varied over the range of 3.05% to 3.79%.
The 1931 set of values varied over the range of 2.59% to 3.73%.
Most comparisons ending in the same year that included the 1920s boom were more optimistic than those that started in the Great Depression. The exception was 1940.

January 2003
Code:


1923-1930    4.94%
1923-1940    4.68%
1923-1950    4.94%
1923-1960    4.99%
1923-1970    4.57%
1923-1980    4.56%

1931-1940    4.65%
1931-1950    4.71%
1931-1960    4.76%
1931-1970    4.34%
1931-1980    4.44%

The 1923 set of values varied over the range of 4.56% to 4.99%.
The 1931 set of values varied over the range of 4.34% to 4.76%.
Most comparisons ending in the same year that included the 1920s boom were more optimistic than those that started in the Great Depression. The exception was 1940.

This Week 2004
Code:


1923-1930    4.51%
1923-1940    4.27%
1923-1950    4.46%
1923-1960    4.49%
1923-1970    4.00%
1923-1980    4.04%

1931-1940    4.31%
1931-1950    4.15%
1931-1960    4.19%
1931-1970    3.69%
1931-1980    3.89%

The 1923 set of values varied over the range of 4.00% to 4.51%.
The 1931 set of values varied over the range of 3.69% to 4.31%.
Most comparisons ending in the same year that included the 1920s boom were more optimistic than those that started in the Great Depression. The exception was 1940.

High Risk Rate Comparisons

January 2000
Code:


1923-1930    5.50%
1923-1940    5.21%
1923-1950    5.24%
1923-1960    5.23%
1923-1970    4.63%
1923-1980    4.75%

1931-1940    5.44%
1931-1950    4.84%
1931-1960    4.81%
1931-1970    4.18%
1931-1980    4.54%

The 1923 set of values varied over the range of 4.63% to 5.50%.
The 1931 set of values varied over the range of 4.18% to 5.44%.
Most comparisons ending in the same year that included the 1920s boom were more optimistic than those that started in the Great Depression. The exception was 1940.

January 2003
Code:


1923-1930    6.65%
1923-1940    6.31%
1923-1950    6.54%
1923-1960    6.58%
1923-1970    6.15%
1923-1980    6.14%

1931-1940    6.36%
1931-1950    6.34%
1931-1960    6.36%
1931-1970    5.93%
1931-1980    6.02%

The 1923 set of values varied over the range of 6.14% to 6.65%.
The 1931 set of values varied over the range of 5.93% to 6.36%.
Most comparisons ending in the same year that included the 1920s boom were more optimistic than those that started in the Great Depression. The exception was 1940.

This Week 2004
Code:


1923-1930    6.22%
1923-1940    5.90%
1923-1950    6.06%
1923-1960    6.08%
1923-1970    5.58%
1923-1980    5.62%

1931-1940    6.02%
1931-1950    5.78%
1931-1960    5.79%
1931-1970    5.28%
1931-1980    5.47%

The 1923 set of values varied over the range of 5.58% to 6.22%.
The 1931 set of values varied over the range of 5.28% to 6.02%.
Most comparisons ending in the same year that included the 1920s boom were more optimistic than those that started in the Great Depression. The exception was 1940.

A Sharp Contrast

Notice how rapidly earnings yield snaps down on the range of Safe Withdrawal Rates. Look at the results based on a single decade. Even those results are reasonably accurate.

Now compare this approach with alternative methods. Typically, those methods wildly miscalculate the dangers when entering the 1960s. The 1960s valuations were similar to those of January 2003. Look at our predictions based on 1923-1930 or 1931-1940. We didn't do badly at all.

This is what including valuations buys us. This what using all of the available data points gives us.

Have fun.

John R.


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