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

Posted: Fri Jun 25, 2004 9:41 am Post subject: Stability of Earnings Yield Supplement 


This extends our investigation into The Stability of Estimates Based on Earnings Yield. This time, we look at the effects of not including data from the Great Depression.
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
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: 
19411950
y = 0.7318x + 2.3723
19411960
y = 0.9635x + 0.3354
19411970
y = 1.0644x  0.5469
19411980
y = 0.7842x + 0.9624 
y = HDBR80 Calculated Rate (percent) and x = percentage earnings yield = 100/[P/E10]
Code: 
19511960
y = 1.201x  1.2943
19511970
y = 1.1936x  1.2958
19511980
y = 0.649x + 1.562 
y = HDBR80 Calculated Rate (percent) and x = percentage earnings yield = 100/[P/E10]
Code: 
19611970
y = 0.6831x + 1.1174
19611980
y = 0.5835x + 1.5399 
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: 
19411950
2.33% 4.04% 5.75%
19411960
0.91% 2.54% 4.17%
19411970
0.28% 1.88% 3.48%
19411980
1.16% 2.75% 4.34% 
More January 2000 Rates (Safe, Calculated and High Risk)
Code: 
19511960
(0.26)% 1.45% 3.16%
19511970
(0.20)% 1.43% 3.06%
19511980
1.44% 3.04% 4.64% 
Even More January 2000 Rates (Safe, Calculated and High Risk)
Code: 
19611970
0.97% 2.68% 4.39%
19611980
1.24% 2.87% 4.50% 
January 2003 Results
January 2003 Rates (Safe, Calculated and High Risk)
Code: 
19411950
3.86% 5.57% 7.28%
19411960
2.91% 4.54% 6.17%
19411970
2.50% 4.10% 5.70%
19411980
2.80% 4.39% 5.98% 
More January 2003 Rates (Safe, Calculated and High Risk)
Code: 
19511960
2.24% 3.95% 5.66%
19511970
2.29% 3.92% 5.55%
19511980
2.80% 4.40% 6.00% 
Even More January 2003 Rates (Safe, Calculated and High Risk)
Code: 
19611970
2.39% 4.10% 5.81%
19611980
2.44% 4.07% 5.70% 
This Week's 2004 Results
This Week's 2004 Rates (Safe, Calculated and High Risk)
Code: 
19411950
3.29% 5.00% 6.71%
19411960
2.16% 3.79% 5.42%
19411970
1.67% 3.27% 4.87%
19411980
2.19% 3.78% 5.37% 
More of This Week's 2004 Rates (Safe, Calculated and High Risk)
Code: 
19511960
1.31% 3.02% 4.73%
19511970
1.36% 2.99% 4.62%
19511980
2.29% 3.89% 5.49% 
Even More of This Week's 2004 Rates (Safe, Calculated and High Risk)
Code: 
19611970
1.86% 3.57% 5.28%
19611980
2.00% 3.63% 5.26% 
Safe Withdrawal Rate Comparisons
January 2000
Code: 
19411950 2.33%
19411960 0.91%
19411970 0.28%
19411980 1.16%
19511960 (0.26)%
19511970 (0.20)%
19511980 1.44%
19611970 0.97%
19611980 1.24% 
January 2003
Code: 
19411950 3.86%
19411960 2.91%
19411970 2.50%
19411980 2.80%
19511960 2.24%
19511970 2.29%
19511980 2.80%
19611970 2.39%
19611980 2.44% 
This Week 2004
Code: 
19411950 3.29%
19411960 2.16%
19411970 1.67%
19411980 2.19%
19511960 1.31%
19511970 1.36%
19511980 2.29%
19611970 1.86%
19611980 2.00% 
Calculated Rate Comparisons
January 2000
Code: 
19411950 4.04%
19411960 2.54%
19411970 1.88%
19411980 2.75%
19511960 1.45%
19511970 1.43%
19511980 3.04%
19611970 2.68%
19611980 2.87% 
January 2003
Code: 
19411950 5.57%
19411960 4.54%
19411970 4.10%
19411980 4.39%
19511960 3.95%
19511970 3.92%
19511980 4.40%
19611970 4.10%
19611980 4.07% 
This Week 2004
Code: 
19411950 5.00%
19411960 3.79%
19411970 3.27%
19411980 3.87%
19511960 3.02%
19511970 2.99%
19511980 3.89%
19611970 3.57%
19611980 3.63% 
High Risk Rate Comparisons
January 2000
Code: 
19411950 5.75%
19411960 4.17%
19411970 3.48%
19411980 4.34%
19511960 3.16%
19511970 3.06%
19511980 4.64%
19611970 4.39%
19611980 4.50% 
January 2003
Code: 
19411950 7.28%
19411960 6.17%
19411970 5.70%
19411980 5.98%
19511960 5.66%
19511970 5.55%
19511980 6.00%
19611970 5.81%
19611980 5.70% 
This Week 2004
Code: 
19411950 6.71%
19411960 5.42%
19411970 4.87%
19411980 5.37%
19511960 4.73%
19511970 4.62%
19511980 5.49%
19611970 5.28%
19611980 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:
Code: 
Decade Minimum Earnings Yield Range of Valuations (P/E10)
19411950 6.41% 10 to 16
19511960 5.46% 12 to 18
19611970 4.15% 17 to 24
19711980 5.35% 9 to 19 
When looking at projections with earnings yields from 2.5% to 4.5%, we would expect projections that include 19611970 to be more accurate than projections that end in 1950 or 1960.
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 19411980 Calculated Rates as references.
19411980 Calculated Rate
Code: 
January 2000 2.75%
January 2003 4.39%
This week 2004 3.87% 
The Safe Withdrawal Rates for January 2000 ranged from (0.20)% to 2.33%. All of these are lower than our reference rate of 2.75%. If we exclude the 19411950 estimate, the highest January 2000 rate was 1.44%, which is well away from our referenced calculated rate and close to the 19411980 Safe Withdrawal Rate of 1.16%.
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 19411950 estimate, the highest January 2003 rate was 2.91%, which is well away from our referenced calculated rate and close to the 19411980 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 19411950 estimate, the highest 2004 rate was 2.29%, which is well away from our referenced calculated rate and close to the 19411980 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 19411950 estimate, the highest January 2000 rate was 4.64%, which is well away from our referenced calculated rate and close to the 19411980 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 19411950 estimate, the highest January 2003 rate was 6.17%, which is well away from our referenced calculated rate and close to the 19411980 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 19411950 estimate, the highest 2004 rate was 5.49%, which is well away from our referenced calculated rate and close to the 19411980 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 5050 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 19411950 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 19411950 projection (which requires us to make the greatest extrapolation). Those withdrawing 4.5% or more are in danger.
Have fun.
John R.

