Using both Initial and Current Valuations

Research on Safe Withdrawal Rates

Moderator: hocus2004

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Using both Initial and Current Valuations

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I used a flawed procedure in this study. I used the actual Half-Failure Rates from the historical record. Such information would not have been available at that time. I should have used calculated values derived from the historical record.
I have taken a new set of data using the equations for Safe Withdrawal Rates. The results remain encouraging.

Using both Initial and Current Valuations

I have been looking at a new variable withdrawal algorithm. I have combined two ideas. The combination looks good.

The first idea is to use 30-Year Half-Failure Rates instead of the conventional withdrawal approach that permits the portfolio to be depleted at the end of 30 years. In accordance with our standard procedures, I determined Half-Failure Rates as a function of the percentage earnings yield 100E10/P (which is 100 / [P/E10] ) at the beginning of retirement.

[Withdrawing at the Half-Failure Rate keeps the portfolio balance at or above 50% of its initial (real) balance throughout the time period being examined (in this case 30 years). Withdrawing at a rate that is higher by 0.1% causes the portfolio balance to fall below 50% of its initial (real) balance.]

Next, I incorporated Gummy's concept of varying withdrawals in accordance with the current earnings yield. [I have reported such results for portfolios consisting of the S&P500 and TIPS.]

This combination, using both the initial valuation and the current valuation to determine withdrawal rates, is a winner.

Early results

I used a portfolio that consisted of 80% stocks and 20% TIPS at a 2% interest rate. [I am confident that, if 2% TIPS are not available, it is possible to construct a suitable alternative investment from higher-dividend stocks.]

I applied my version of Gummy's algorithm, which I call G1, using a slope of 0.25 and an offset of minus 2.5%. That is, I make withdrawals of (0.25)*(100E10/P-2.5%)*(the portfolio's current balance).

In addition, I make standard withdrawals based upon the Half-Failure Rates of this portfolio. Standard withdrawals equal (the portfolio's initial balance)*(the standard withdrawal rate) in terms of real dollars (that is, after adjusting for inflation).

I had originally determined the 30-year Historical Surviving Withdrawal Rates HSWR for 1921-1980. I kept the varying portion the same while I varied the (standard) withdrawal rates in increments of 0.1%. Later, I determined Half-Failure Rates. I noticed that the curve of calculated rates for Half-Failures was an excellent approximation of the lower confidence limit of the 30-year HSWR.

Applying the numbers

The curve for the 30-year Half-Failure Rate HFR is HFR = 0.6 431x + 0.0815 where is the percentage earnings yield 100E10/P.

Applying today's earnings yield, which is close to 3.5%, to this equation, the standard portion of withdrawals is 2.3% of the portfolio's initial balance (plus inflation).

Applying today's earnings yield to Algorithm G1, we withdraw an additional 0.3% of the portfolio's current balance (since 0.25*(3.5%-2.5%) = 0.25%, which is rounded to 0.3%).

For a person beginning retirement today, his total withdrawal amount would be 2.6% (or 2.3% + 0.3% since the current balance equals the initial balance). This is only slightly less than the calculated Half-Failure Rate under normal conditions (i.e., with constant withdrawals in terms of real dollars). This is slightly higher than the Safe Withdrawal Rate under normal conditions.

Including the variable withdrawal component has increased the initial withdrawal amount above what would have been the Safe Withdrawal Rate initially (which would have been slightly above 2.4% with 2% TIPS). However, the withdrawal amount could fall to 2.3% of the initial balance and it could result in the portfolio's balance falling below 50% of the initial balance.

Looking at the worst case of the past

If I set my standard (constant) portion of withdrawals equal to the 30-year Half-Failure Rate, the worst case is in 1969. Based on an initial balance of \$100000, the five-year rolling average withdrawal amount are \$2541 at year 5, \$2976 at year 10, \$3021 at year 15, \$2677 at year 20, \$2389 at year 25 and \$2041 at year 30. The balances are \$78706 at year 5, \$59555 at year 10, \$61563 at year 15, \$80551 at year 20, \$105028 at year 25 and \$213676.

[There were other sequences with lower balances, but not with lower withdrawals.]

This establishes a baseline for comparison.

Next, I applied the formulas. For 1969, the Half-Failure Rate was 3.12% using the curve for calculations. The variable portion was 0.56%. This totals 3.68%, which is rounded to 3.7%.

Here are the total withdrawal amounts using the formulas. Based on an initial balance of \$100000, the five-year rolling average withdrawal amount are \$3910 at year 5, \$4208 at year 10, \$4058 at year 15, \$3656 at year 20, \$3399 at year 25 and \$3214 at year 30. The balances are \$72502 at year 5, \$47442 at year 10, \$39045 at year 15, \$39292 at year 20, \$38152 at year 25 and \$58037 at year 30.

We improved the withdrawal sequence substantially. We were able to do this only because we violated our constraint on the portfolio's balance. However, the balance always remained above \$38000 (assuming an initial balance of \$100000).

Here are some references for background

HFWR80 versus Earnings Yield dated Monday, Aug 02, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2846

80% stocks and 20% commercial paper.
For 1969 Half-Failure Withdrawal Rates HFWR80
Safe: 1.88%
Calculated: 3.75%
High Risk: 5.61%

In 1997, P/E10 = 29.16 and 100E10/P = 3.43% Half-Failure Rates:.
Safe: 1.00
Calculated: 2.87
High Risk: 4.73

Calculated Rates of the Last Decade dated Wednesday, Jun 23, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2657
For 1997 and HDBR80:
Safe: 2.42
Calculated: 4.00
High Risk: 5.58
Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
With 2% TIPS

Reference with 80% stocks
1921-1980
\$100000 initial balance
Gummy Algorithm 1 is set for Yes (cell B24 equals 1)

Gummy's Multiplier G1 = 0.25 in cell B25
Gummy's Offset is (2.5) or minus 2.5% in cell B17

Stocks = 80%
TIPS at a 2% interest rate = 20%
With Rebalancing
I used the CPI for inflation adjustments.

I varied the Withdrawal Rate in cell B9.

Reference from previously collected data:
Withdrawal Rate in cell B9 was set at 3.4%.
There were no failures at 30 years with B9 set at 3.4%.
There was one failure at 30 years with B9 set at 3.5%.

Definitions:

All balances are positive at the Historical Surviving Withdrawal Rate. They are zero or negative when the (standard) withdrawal rate (in cell B9) is increased by 0.1%.

All balances are at least 50% of the initial balance at the Half-Failure Rate. They fall to 50% of the initial balance or lower during at least one year when the (standard) withdrawal rate (in cell B9) is increased by 0.1%.

Year, P/E10, 100E10/P, Historical Surviving Withdrawal Rate, Half-Failure Rate

Code: Select all

``````1921    5.1    19.61    7.9    7.2
1922    6.3    15.87    8.3    7.5
1923    8.2    12.20    7.6    6.9
1924    8.1    12.35    7.9    7.1
1925    9.7    10.31    7.4    6.6
1926   11.3     8.85    6.4    5.7
1927   13.2     7.58    6.2    5.6
1928   18.8     5.32    5.1    4.2
1929   27.1     3.69    3.8    2.8
1930   22.3     4.48    3.9    3.0
1931   16.7     5.99    4.5    3.8
1932    9.3    10.75    6.4    6.0
1933    8.7    11.49    7.8    7.3
1934   13.0     7.69    6.0    5.5
1935   11.5     8.70    6.9    6.4
1936   17.1     5.85    5.2    4.5
1937   21.6     4.63    4.4    3.2
1938   13.5     7.41    5.9    5.4
1939   15.6     6.41    5.5    5.0
1940   16.4     6.10    5.7    5.2
1941   13.9     7.19    7.2    6.6
1942   10.1     9.90    8.7    8.1
1943   10.2     9.80    8.4    7.9
1944   11.1     9.01    7.9    7.1
1945   12.0     8.33    7.5    6.4
1946   15.6     6.41    7.2    6.0
1947   11.5     8.70    8.9    7.9
1948   10.4     9.62    9.4    8.3
1949   10.2     9.80    9.3    8.2
1950   10.7     9.35    9.6    8.3
1951   11.9     8.40    8.5    7.2
1952   12.5     8.00    7.8    6.3
1953   13.0     7.69    7.5    6.1
1954   12.0     8.33    7.7    6.4
1955   16.0     6.25    6.0    4.7
1956   18.3     5.46    5.2    3.9
1957   16.7     5.99    5.3    4.0
1958   13.8     7.25    5.8    4.7
1959   18.0     5.56    4.6    3.3
1960   18.3     5.46    4.6    3.3
1961   18.5     5.41    4.5    3.3
1962   21.2     4.72    4.1    2.7
1963   19.3     5.18    4.3    3.1
1964   21.6     4.63    3.8    2.4
1965   23.3     4.29    3.5    1.9
1966   24.1     4.15    3.4    1.7
1967   20.4     4.90    3.8    2.3
1968   21.5     4.65    3.6    1.9
1969   21.2     4.72    3.6    1.7
1970   17.1     5.85    4.1    2.7
1971   16.5     6.06    4.1    2.8
1972   17.3     5.78    4.0    2.4
1973   18.7     5.35    3.9    1.9
1974   13.5     7.41    5.1    4.2
1975    8.9    11.24    6.6    5.6
1976   11.2     8.93    5.6    4.4
1977   11.4     8.77    5.7    4.2
1978    9.2    10.87    6.8    4.9
1979    9.3    10.75    7.1    4.7
1980    8.9    11.24    7.1    4.3``````
Here are the curve fitting equations from the 1923-1980 data:

1923-1980 equation
HSWR = 0.6085x+1.4834
Lower confidence limit is minus 1.0% (eyeball estimate when P/E10 = 10 and higher).
Upper confidence limit is plus 2.5% (eyeball estimate).
R-squared = 0.6519.

1923-1980 equation
HFR = 0.6431x+0.0815
Lower confidence limit is minus 1.6% (eyeball estimate when P/E10 = 10 and higher).
Upper confidence limit is plus 2.2% (eyeball estimate).
R-squared = 0.597.

Combination Algorithm
Set the standard withdrawal rate (in cell B9) equal to the Half-Failure Rate HFR in accordance with the formula. Withdraw an amount equal to this rate times a portfolio's initial balance in real dollars. That is, adjust these withdrawals to match inflation.

Increase the amount withdrawn by a percentage of the portfolio's current balance as determined from Gummy's Algorithm G1. This equals (the slope of 0.25)*([100E10/P] - 2.5%).

Rates to use with today's valuations.
P/E10 = 28 to 29 and 100E10/P = 3.5%.
HFR with today's valuations = 2.33%.

Add (slope of 0.25)*(today's earnings yield - 2.5%) = 0.25%.

Today's withdrawal rate for starting a retirement = 2.33% + 0.25% = 2.58% or 2.6%.

Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
With 2% TIPS

Withdrawal Amounts

Reference with 80% stocks
1921-1980
\$100000 initial balance
Gummy Algorithm 1 is set for Yes (cell B24 equals 1)

Gummy's Multiplier G1 = 0.25 in cell B25
Gummy's Offset is (2.5) or minus 2.5% in cell B17

Stocks = 80%
TIPS at a 2% interest rate = 20%
With Rebalancing
I used the CPI for inflation adjustments.

I set the Withdrawal Rate in cell B9 equal to the Half-Failure Rate of each sequence.

These are the five-year rolling averages of the withdrawal amounts ending at years 5, 10, 15, 20, 25 and 30.

Year, Withdrawal Rate in B9, At Year 5, At Year 10, At Year 15

Code: Select all

``````1921   7.2    9645    8278    9061
1922   7.5    9694    8898    9057
1923   6.9    8632    8479    8221
1924   7.1    8502    8954    8458
1925   6.6    7700    8514    7759
1926   5.7    6618    7316    6786
1927   5.6    6701    6842    6800
1928   4.2    5306    5161    5219
1929   2.8    3756    3553    3690
1930   3.0    4081    3698    3925
1931   3.8    4969    4607    4724
1932   6.0    7318    7269    7146
1933   7.3    8757    8781    8618
1934   5.5    6603    6700    6527
1935   6.4    7544    7802    7526
1936   4.5    5433    5559    5457
1937   3.2    4109    4110    4091
1938   5.4    6561    6459    6284
1939   5.0    6132    5985    5829
1940   5.2    6416    6208    5998
1941   6.6    8056    7876    7524
1942   8.1    9782    9549    9159
1943   7.9    9470    9220    8921
1944   7.1    8550    8344    8048
1945   6.4    7780    7552    7397
1946   6.0    7363    7071    7015
1947   7.9    9510    9159    9014
1948   8.3    9942    9684    9389
1949   8.2    9808    9490    9252
1950   8.3    9879    9696    9367
1951   7.2    8534    8481    8102
1952   6.3    7526    7454    7216
1953   6.1    7346    7140    6973
1954   6.4    7612    7438    7328
1955   4.7    5680    5488    5566
1956   3.9    4789    4561    4782
1957   4.0    4861    4707    4932
1958   4.7    5571    5444    5733
1959   3.3    3988    3944    4304
1960   3.3    3942    4025    4441
1961   3.3    3896    4103    4472
1962   2.7    3274    3479    3880
1963   3.1    3696    3954    4458
1964   2.4    2956    3288    3697
1965   1.9    2493    2878    3115
1966   1.7    2347    2702    2928
1967   2.3    3042    3441    3645
1968   1.9    2638    3134    3203
1969   1.7    2541    2976    3021
1970   2.7    3789    4003    3972
1971   2.8    3935    4110    3983
1972   2.4    3565    3768    3449
1973   1.9    3193    3276    2964
1974   4.2    5822    5642    5076
1975   5.6    7596    7382    6575
1976   4.4    6127    5882    5242
1977   4.2    5822    5642    5076
1978   4.9    7101    6435    5866
1979   4.7    6991    6251    5707
1980   4.3    6613    5776    5367``````
Year, Withdrawal Rate in B9, At Year 20 At Year 25, At Year 30

Code: Select all

``````1921   7.2    8409    8470    8178
1922   7.5    8968    8781    8483
1923   6.9    8224    8047    7764
1924   7.1    8554    8307    8028
1925   6.6    8012    7720    7418
1926   5.7    6899    6726    6412
1927   5.6    6690    6506    6223
1928   4.2    5174    5082    4962
1929   2.8    3670    3678    3613
1930   3.0    3851    3790    3769
1931   3.8    4647    4459    4419
1932   6.0    6943    6635    6462
1933   7.3    8349    8034    7753
1934   5.5    6338    6092    5917
1935   6.4    7242    7023    6782
1936   4.5    5229    5167    4945
1937   3.2    3984    3980    3854
1938   5.4    6076    5874    5716
1939   5.0    5614    5459    5342
1940   5.2    5844    5645    5598
1941   6.6    7394    7090    7110
1942   8.1    8965    8672    8663
1943   7.9    8627    8397    8405
1944   7.1    7832    7672    7805
1945   6.4    7145    7150    7415
1946   6.0    6705    6869    7123
1947   7.9    8723    8858    9052
1948   8.3    9155    9373    9667
1949   8.2    9085    9417    9568
1950   8.3    9403    9856    9780
1951   7.2    8330    8697    8599
1952   6.3    7463    7914    7872
1953   6.1    7288    7852    7562
1954   6.4    7773    8181    7776
1955   4.7    6021    6158    5934
1956   3.9    5170    5294    5058
1957   4.0    5362    5468    4989
1958   4.7    6270    6098    5533
1959   3.3    4719    4604    4132
1960   3.3    4625    4530    4013
1961   3.3    4615    4434    3948
1962   2.7    4055    3708    3367
1963   3.1    4419    4006    3659
1964   2.4    3664    3272    2976
1965   1.9    3156    2733    2523
1966   1.7    2911    2515    2263
1967   2.3    3338    3014    2756
1968   1.9    2898    2592    2325
1969   1.7    2677    2389    2041
1970   2.7    3488    3253    2842
1971   2.8    3520    3254    2883
1972   2.4    3117    2856    2503
1973   1.9    2644    2360    1755
1974   4.2    4700    4405    4046
1975   5.6    6193    5735    5344
1976   4.4    4893    4485    4013
1977   4.2    4700    4405    4046
1978   4.9    5442    4747    4231
1979   4.7    5166    4277    4025
1980   4.3    4579    3619    3653``````
Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
With 2% TIPS

Balances

Reference with 80% stocks
1921-1980
\$100000 initial balance
Gummy Algorithm 1 is set for Yes (cell B24 equals 1)

Gummy's Multiplier G1 = 0.25 in cell B25
Gummy's Offset is (2.5) or minus 2.5% in cell B17

Stocks = 80%
TIPS at a 2% interest rate = 20%
With Rebalancing
I used the CPI for inflation adjustments.

I set the Withdrawal Rate in cell B9 equal to the Half-Failure Rate of each sequence.

These are the balances at years 5, 10, 15, 20, 25 and 30.

Year, Withdrawal Rate in B9, At Year 5, At Year 10, At Year 15

Code: Select all

``````1921   7.2    130097    163915    152394
1922   7.5    127108    107888    170158
1923   6.9    139240     90572    110881
1924   7.1    198950    127583    129316
1925   6.6    162579     99575    115289
1926   5.7    128167    122764     94453
1927   5.6     85908    138312     71264
1928   4.2     67191     86285     63186
1929   2.8     68340     74998     58140
1930   3.0     64849     80115     65403
1931   3.8     98124     77563     81836
1932   6.0    160531     82386     75192
1933   7.3    123896     85808     67251
1934   5.5    102654     71331     51898
1935   6.4    116316     85047     60656
1936   4.5     78578     81984     56850
1937   3.2     55430     57817     62155
1938   5.4     70597     57270     59940
1939   5.0     70387     52376     53835
1940   5.2    148053    183745    196983
1941   6.6    101927     67763     88788
1942   8.1     94321     85420    104440
1943   7.9     81544     86200     89262
1944   7.1     75490     79548    112446
1945   6.4     77773    103110    120537
1946   6.0     71235    102424    104290
1947   7.9     96099    126727    139686
1948   8.3    113956    129516    151689
1949   8.2    110418    164562    174095
1950   8.3    135331    161564    186296
1951   7.2    145588    150160    183715
1952   6.3    140266    165271    168349
1953   6.1    120515    150256    173659
1954   6.4    156689    175005    184322
1955   4.7    125601    152957    130927
1956   3.9    108886    140854    114099
1957   4.0    121783    128227    120036
1958   4.7    126791    149110    138438
1959   3.3    116829    128843     95745
1960   3.3    124832    109663     68753
1961   3.3    130613    106959     79422
1962   2.7    108050    104265     75599
1963   3.1    121027    116445     64822
1964   2.4    112619     85939     61799
1965   1.9     91428     60517     58610
1966   1.7     86178     68827     59574
1967   2.3     97805     72357     50080
1968   1.9    100224     59614     56297
1969   1.7     78706     59555     61563
1970   2.7     64194     59146     56872
1971   2.8     75967     60828     61922
1972   2.4     73741     50774     75872
1973   1.9     59855     57041     73999
1974   4.2     66823     57158     60724
1975   5.6     85678     73345     85900
1976   4.4     76710     73178     74856
1977   4.2     64991     90171     95629
1978   4.9     86275    100496    118582
1979   4.7     94630    113501    136555
1980   4.3     99047    136701    148853``````
Year, Withdrawal Rate in B9, At Year 20 At Year 25, At Year 30

Code: Select all

``````1921   7.2    113173    105009     56976
1922   7.5     85223     74080     55932
1923   6.9     75289     56826     50874
1924   7.1     87803     61219     55456
1925   6.6     83519     58535     65170
1926   5.7     94544     60709     75446
1927   5.6     65533     56369     63953
1928   4.2     54487     63565     74152
1929   2.8     50106     63916    109046
1930   3.0     55703     83220    108727
1931   3.8     57853     82391     83051
1932   6.0     63643     70390     60396
1933   7.3     65613     60297     51665
1934   5.5     51200     66507     58530
1935   6.4     69788     68604     59868
1936   4.5     78973     77470     89489
1937   3.2     92324    114922    123543
1938   5.4     61231     62562     55548
1939   5.0     73815     70344     60452
1940   5.2    188371    134695     51396
1942   8.1    104700     87272     55746
1943   7.9     92981     85198     50318
1944   7.1    111584    101740     55084
1945   6.4    135640    105843     54469
1946   6.0    125801     93508     58711
1947   7.9    132121    106782     54592
1948   8.3    163411    133863     52253
1949   8.2    172429    109299     51118
1950   8.3    149840     81605     52407
1951   7.2    139110     90517     52339
1952   6.3    151193     97212     51191
1953   6.1    157600     78692     53613
1954   6.4    128620     77649     53754
1955   4.7     79010     64930     51421
1956   3.9     83319     62253     56854
1957   4.0     82956     50988     65173
1958   4.7     72273     54400     52240
1959   3.3     65677     58768     66128
1960   3.3     60778     54847     68575
1961   3.3     61163     58709     60485
1962   2.7     50634     73111     80887
1963   3.1     55107     63048     72930
1964   2.4     59532     72760     89178
1965   1.9     60349     86350     97228
1966   1.7     67166     80950    121998
1967   2.3     75300     86672    122762
1968   1.9     72383     94126    161895
1969   1.7     80551    105028    213676
1970   2.7     76217     80609    174942
1971   2.8     67955     93683    154056
1972   2.4     86821    122317    155209
1973   1.9     96991    167891    152701
1974   4.2     63583    106012     55125
1975   5.6     77487    146281     54210
1976   4.4     95363    147872     51248
1977   4.2    124958    150732     50177
1978   4.9    187070    159751     52100
1979   4.7    260692    154122     50943
1980   4.3    330052    149973     50149``````
Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
Here is what would have happened with the worst case sequence of withdrawal amounts if I had applied the formula.

With an initial balance of \$100000, the lowest withdrawal amount (with valid data) is \$2041 at the end of the 1969 sequence. Its initial withdrawal amount was \$2541.

The actual Half-Failure Rate in 1969 was 1.7% and the initial withdrawal (averaged over 5 years) was 2.5%. Using 1.7% and the 0.56% adjustment of the formula, the initial withdrawal rate would have been 2.26%.

In 1969, P/E10 = 21.2 and 100E10/P = 4.72. Using the formulas, the calculated Half-Failure Rate is 3.12%. Then we add (slope of 0.25)*(1969's earnings yield of 4.72 - 2.5%). This adjustment equals 0.56%. The 1969 starting withdrawal rate would have been 3.12+0.56 = 3.68% or 3.7%.

In the following results, I used the formulas and applied them to the 1969 historical sequence. For 1969, using a conventional withdrawal rate of 3.1% in cell B9, we find that:

Year after 1969, Five-Year Rolling Averages of Withdrawal Amounts

Code: Select all

``````5    3910
6    4024
7    4057
8    4105
9    4206
10   4208
11   4137
12   4135
13   4168
14   4109
15   4058
16   4004
17   3937
18   3801
19   3728
20   3656
21   3576
22   3534
23   3492
24   3440
25   3399
26   3375
27   3326
28   3297
29   3259
30   3214``````
Year after 1969, Portfolio Balances starting from \$100000

Code: Select all

``````1    86153
2    83735
3    86856
4    92527
5    72502
6    52605
7    60466
8    59374
9    49152
10   47442
11   44250
12   44238
13   35729
14   38324
15   39045
16   36646
17   38930
18   44127
19   38931
20   39292
21   41017
22   35947
23   40420
24   38625
25   38152
26   34653
27   39821
28   43916
29   49686
30   58037``````
There was year with a balance below \$35000. It was year 26. The balance was \$34653.

Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
Using both Initial and Current Valuations - Corrected

I have been looking at a new variable withdrawal algorithm. It combines conventional withdrawals, which are based only on a portfolio's initial balance, and variable withdrawals that are based on a portfolio's current balance.

I used the market's earnings yield at the beginning of retirement to determine the size of conventional withdrawals. Such withdrawals are fixed percentage a portfolio's initial balance (plus inflation).

I varied withdrawals depending upon the portfolio's current balance and the market's current earnings yield. Gummy came up with this idea.

This combination is a winner. It takes advantage of both initial valuations and current valuations.

Early results

I used a portfolio that consisted of 80% stocks and 20% TIPS at a 2% interest rate. [I am confident that, if 2% TIPS are not available, it is possible to construct a suitable alternative investment from higher-dividend stocks.]

I applied my version of Gummy's algorithm, which I call G1, using a slope of 0.25 and an offset of minus 2.5%. That is, I make part of my withdrawals equal to (0.25)*(100E10/P-2.5%)*(the portfolio's current balance).

In addition, I make standard withdrawals based upon the Safe Withdrawal Rate of this portfolio. Standard withdrawal amounts equal (the portfolio's initial balance)*(the standard withdrawal rate)*(adjustments for inflation). They are constant in real dollars.

I determined the 30-year Historical Surviving Withdrawal Rates HSWR for 1921-1980. I varied the (standard) withdrawal rates in increments of 0.1%. A portfolio's balance remains positive throughout the entire 30 years at a Historical Surviving Withdrawal Rate HSWR. It falls to zero or becomes negative when the withdrawal rate is increased by 0.1%.

I left the portion of withdrawals that varied with the portfolio's current balance unchanged. The slope remained 0.25 and the offset remained minus 2.5%.

Applying the numbers

The curve for the 30-year Calculated Rate is HSWR = 0.6085x+1.4834 where x is the percentage earnings yield 100E10/P. I used the 30-year Historical Surviving Withdrawal Rates from 1923-1980 for a better curve fit.

These confidence limits are eyeball estimated based values of earnings yield below 10% (which means that P/E10 is above 10):
The lower confidence limit is minus 1.0%.
The upper confidence limit is plus 2.5%.

The Safe Withdrawal Rate is the lower confidence limit of the Calculated Rate. Its formula is: SWR = (0.6085x+1.4834) - 1.0 = 0.6085x+ 0.4834.

Applying today's earnings yield, which is close to 3.5%, to this equation, the standard portion of withdrawals is 2.6% of the portfolio's initial balance (plus inflation).

Applying today's earnings yield to Algorithm G1, we withdraw an additional 0.3% of the portfolio's current balance (since 0.25*(3.5%-2.5%) = 0.25%, which is rounded to 0.3%).

For a person beginning retirement today, his total withdrawal amount would be 2.9% (or 2.6% + 0.3% since the current balance would equal the initial balance.

This is substantially higher than the Safe Withdrawal Rate under normal conditions. [However, such numbers were based on using commercial paper, not TIPS.] The withdrawal amount varies. It could fall to 2.6% of the initial balance.

As a point of reference:
Here are the Calculated Rates of the Last Decade dated Wednesday, Jun 23, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2657
For 1997 and HDBR80:
Safe: 2.42
Calculated: 4.00
High Risk: 5.58
P/E10 was closest to today's value in 1997 during the past decade. It was 28.33. Today's value is between 28 and 29.

My confidence limits were determined from data with earnings yield less than 10%. Among such conditions, there was only one failure. It occurred in year 30 of the 1971 historical sequence.

There were several failures among conditions with earnings yields greater than 10%. This happened because of how I defined the lower confidence limit. These conditions could have safely provided large withdrawal amounts, just not so large as I used.

Data Analysis

The lowest (five-year average of the) withdrawal amount occurred at year 30 of the 1966 historical sequence. It was \$3183. The amount started at \$3625 and briefly exceeded 3.9% (of the initial balance of \$100000). The lowest balance (in five-year increments) was \$30719 at year 25.

Among conditions with earnings yields starting below 10%, there were only three sequences (1970, 1971 and 1972) with very low balances at year 30. The other balances (at valid data points) were above \$20000.

The highest balance (in five-year increments) was \$259329 at year 20 of the 1948 sequence. This was not because withdrawal amounts were unduly limited. In that particular sequence, withdrawals started at \$8022.

Assessment

The variation of withdrawal amounts remained within reasonable bounds. The algorithm does what it is supposed to do. It provides a reasonably steady income. It takes advantage of any reward on the upside. It does not increase risk.

Reflecting on these numbers and today's valuations, dividend-based strategies remain an attractive alternative. This approach would start out today at a 2.9% withdrawal rate. With careful stock selection, dividends should be able to do at least as well.

Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
With 2% TIPS

Withdrawal Amounts

Reference with 80% stocks
1921-1980
\$100000 initial balance
Gummy Algorithm 1 is set for Yes (cell B24 equals 1)

Gummy's Multiplier G1 = 0.25 in cell B25
Gummy's Offset is (2.5) or minus 2.5% in cell B17
Stocks = 80%
TIPS at a 2% interest rate = 20%
With Rebalancing
I used the CPI for inflation adjustments.

I set the Withdrawal Rate in cell B9 equal to the Safe Withdrawal Rate of each sequence.

These are the five-year rolling averages of the withdrawal amounts ending at years 5, 10, 15, 20, 25 and 30.

Year, Withdrawal Rate in B9, At Year 5, At Year 10, At Year 15

Code: Select all

``````1921  12.4   14560   13005   12855
1922  10.1   12174   11205   11112
1923   7.9    9597    9350    9025
1924   8.0    9381    9739    9192
1925   6.8    9074    9735    8928
1926   5.9    6814    7493    6952
1927   5.1    6214    6387    6395
1928   3.7    4821    4707    4816
1929   2.7    3659    3462    3610
1930   3.2    4274    3880    4080
1931   4.1    5259    4879    4959
1932   7.0    8290    8159    7924
1933   7.5    8952    8960    8774
1934   5.2    6311    6433    6294
1935   5.8    6958    7270    7062
1936   4.0    4944    5114    5075
1937   3.3    4207    4199    4167
1938   5.0    6174    6108    5983
1939   4.4    5553    5462    5383
1940   4.2    5455    5344    5247
1941   4.9    6419    6417    6232
1942   6.5    8243    8172    7935
1943   6.4    8025    7925    7784
1944   6.0    7490    7396    7192
1945   5.6    7010    6856    6771
1946   4.4    5828    5670    5761
1947   5.8    7498    7317    7326
1948   6.3    8022    7932    7734
1949   6.4    8079    7887    7730
1950   6.2    7851    7811    7549
1951   5.6    6981    7033    6688
1952   5.4    6651    6628    6419
1953   5.2    6472    6305    6168
1954   5.6    6832    6690    6609
1955   4.3    5288    5110    5210
1956   3.8    4691    4466    4693
1957   4.1    4959    4802    5020
1958   4.9    5768    5635    5910
1959   3.9    4578    4515    4826
1960   3.8    4435    4498    4864
1961   3.8    4390    4574    4893
1962   3.4    3965    4137    4462
1963   3.6    4190    4424    4863
1964   3.3    3845    4127    4419
1965   3.1    3675    3979    4072
1966   3.0    3625    3887    3947
1967   3.5    4220    4525    4553
1968   3.3    4012    4378    4251
1969   3.4    4204    4472    4280
1970   4.0    5052    5139    4926
1971   4.2    5293    5321    5014
1972   4.0    5112    5120    4664
1973   3.7    4922    4783    4340
1974   5.0    6587    6307    5697
1975   7.3    9217    8795    7933
1976   5.9    7558    7139    6453
1977   5.8    7580    6908    6367
1978   7.1    9179    8330    7714
1979   7.0    9166    8260    7677
1980   7.3    9456    8442    7964``````
Year, Withdrawal Rate in B9, At Year 20 At Year 25, At Year 30

Code: Select all

``````1921  12.4   12400   12400   12400
1922  10.1   10667   10161   10100
1923   7.9    8887    8533    8042
1924   8.0    9146    8749    8250
1925   6.8    8926    8408    8011
1926   5.9    7033    6822    6478
1927   5.1    6353    6263    6055
1928   3.7    4839    4839    4814
1929   2.7    3604    3631    3580
1930   3.2    3980    3886    3831
1931   4.1    4833    4607    4508
1932   7.0    7566    7130    7000
1933   7.5    8474    8128    7834
1934   5.2    6152    5941    5785
1935   5.8    6858    6721    6493
1936   4.0    4902    4916    4682
1937   3.3    4049    4032    3905
1938   5.0    5827    5649    5508
1939   4.4    5229    5109    5032
1940   4.2    5205    5030    5140
1941   4.9    6311    5991    6414
1942   6.5    7894    7644    8008
1943   6.4    7570    7397    7780
1944   6.0    7033    6934    7402
1945   5.6    6543    6637    7184
1946   4.4    5464    5890    6678
1947   5.8    7097    7571    8504
1948   6.3    7569    8129    9234
1949   6.4    7644    8340    9138
1950   6.2    7748    8683    9168
1951   5.6    7082    7793    8113
1952   5.4    6758    7411    7623
1953   5.2    6579    7377    7289
1954   5.6    7154    7754    7512
1955   4.3    5723    5936    5794
1956   3.8    5096    5240    5021
1957   4.1    5434    5519    5034
1958   4.9    6410    6201    5629
1959   3.9    5136    4917    4442
1960   3.8    4974    4791    4293
1961   3.8    4958    4701    4235
1962   3.4    4514    4116    3787
1963   3.6    4745    4305    3976
1964   3.3    4248    3832    3570
1965   3.1    3926    3516    3324
1966   3.0    3748    3372    3183
1967   3.5    4148    3826    3636
1968   3.3    3858    3575    3411
1969   3.4    3866    3615    3465
1970   4.0    4429    4198    4032
1971   4.2    4542    4319    4209
1972   4.0    4309    4110    4007
1973   3.7    4020    3832    3680
1974   5.0    5325    5100    4968
1975   7.3    7536    7321    7300
1976   5.9    6123    5924    5890
1977   5.8    6046    5832    5694
1978   7.1    7354    7061    6999
1979   7.0    7258    6831    6803
1980   7.3    7445    7053    7155``````
Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
With 2% TIPS

Balances

Reference with 80% stocks
1921-1980
\$100000 initial balance
Gummy Algorithm 1 is set for Yes (cell B24 equals 1)

Gummy's Multiplier G1 = 0.25 in cell B25
Gummy's Offset is (2.5) or minus 2.5% in cell B17
Stocks = 80%
TIPS at a 2% interest rate = 20%
With Rebalancing
I used the CPI for inflation adjustments.

I set the Withdrawal Rate in cell B9 equal to the Safe Withdrawal Rate of each sequence.

These are the balances at years 5, 10, 15, 20, 25 and 30.

Year, Withdrawal Rate in B9, At Year 5, At Year 10, At Year 15

Code: Select all

``````1921  12.4     89875     66922    (14658)
1922  10.1    109353     78884     86209
1923   7.9    131686     80579     89100
1924   8.0    190680    115732    108396
1925   6.8    161176     97433    111016
1926   5.9    127032    119826     90556
1927   5.1     87828    146607     79135
1928   3.7     69117     92260     71374
1929   2.7     68888     76299     59962
1930   3.2     63738     77275     61073
1931   4.1     95714     73578     73523
1932   7.0    151410     71381     54025
1933   7.5    122805     83822     63912
1934   5.2    104317     74555     56923
1935   5.8    119523     92064     71861
1936   4.0     80905     89036     67346
1937   3.3     55008     56688     59841
1938   5.0     72530     61585     70018
1939   4.4     73697     59072     68397
1940   4.2     80945     68119    100318
1941   4.9    113320     89472    144251
1942   6.5    102601    107570    155951
1943   6.4     88747    108322    132423
1944   6.0     80901     94928    150464
1945   5.6     82137    117348    147503
1946   4.4     79980    130598    149564
1947   5.8    109100    164300    207046
1948   6.3    127378    162153    212992
1949   6.4    121729    199577    233059
1950   6.2    149818    196188    248880
1951   5.6    157683    175336    231394
1952   5.4    146637    180386    191777
1953   5.2    125776    163403    196866
1954   5.6    162117    187300    204297
1955   4.3    128098    159103    139045
1956   3.8    109472    142348    115988
1957   4.1    121161    126938    118112
1958   4.9    125665    146438    134351
1959   3.9    113234    121003     86190
1960   3.8    121728    104149     62807
1961   3.8    127497    101563     72208
1962   3.4    104278     96472     65370
1963   3.6    118247    110551     58473
1964   3.3    107646     77456     49917
1965   3.1     85694     51802     42717
1966   3.0     79960     57198     41091
1967   3.5     91671     61146     34988
1968   3.3     92542     48016     35677
1969   3.4     71173     44847     34220
1970   4.0     65799     36549     38877
1971   4.2     69398     46843     34939
1972   4.0     65799     36549     38877
1973   3.7     52044     38919     36966
1974   5.0     63149     48408     43433
1975   7.3     77467     53956     44158
1976   5.9     68888     53787     40887
1977   5.8     57677     66096     53780
1978   7.1     74793     71058     63277
1979   7.0     82353     82952     80660
1980   7.3     83227     93810     80101``````
Year, Withdrawal Rate in B9, At Year 20 At Year 25, At Year 30

Code: Select all

``````1921  12.4    (83174)  (239058)  (363938)
1922  10.1     16212    (35221)  (127444)
1923   7.9     49602     21334    (16098)
1924   8.0     62378     28616     (2881)
1925   6.8     77799     51011     49240
1926   5.9     87323     51876     56164
1927   5.1     79074     79457    110228
1928   3.7     66771     87843    115059
1929   2.7     52621     68604    119102
1930   3.2     49624     69910     86755
1931   4.1     47051     58156     49119
1932   7.0     25383     (8236)   (63374)
1933   7.5     58620     48219     32037
1934   5.2     61130     88340     90118
1935   5.8     95776    112579    127507
1936   4.0    103827    113156    146507
1937   3.3     87340    106974    113257
1938   5.0     79370     92680     99483
1939   4.4    107026    119371    125539
1940   4.2    129490    162031    142688
1941   4.9    163472    219524    185255
1942   6.5    189801    199723    186827
1943   6.4    167455    196398    181706
1944   6.0    170030    181311    128765
1945   5.6    179768    154005     93055
1946   4.4    202739    172770    135898
1947   5.8    225107    218755    160302
1948   6.3    259329    251309    141610
1949   6.4    256909    190803    130744
1950   6.2    222206    142497    131065
1951   5.6    191664    144775    114825
1952   5.4    181611    127880     81389
1953   5.2    188375    103875     86855
1954   5.6    149638     99887     85278
1955   4.3     86528     75458     66587
1956   3.8     85473     64932     60976
1957   4.1     80812     48712     60334
1958   4.9     68554     49115     43179
1959   3.9     54400     41656     37302
1960   3.8     51541     40705     42410
1961   3.8     51248     42571     36062
1962   3.4     38649     46319     40565
1963   3.6     45201     45312     44068
1964   3.3     39888     38370     34706
1965   3.1     34060     36029     27735
1966   3.0     34951     30719     31377
1967   3.5     39494     31283     26084
1968   3.3     33516     29249     30301
1969   3.4     30450     23822     24686
1970   4.0     27366     16415      3092
1971   4.2     24190     13017     (1817)
1972   4.0     27366     16415      3092
1973   3.7     32902     35422     19917
1974   5.0     34561     37268      7933
1975   7.3     16349    (14230)   (30353)
1976   5.9     30305     20068    (10166)
1977   5.8     47507     37641     (2578)
1978   7.1     68185     38395     (5882)
1979   7.0    122927     57423      3325
1980   7.3    142536     47926     (1978)``````
Remember that sequences after 1972 include dummy data for the years 2003-2010.

Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
Using both Initial and Current Valuations - High Variability

I have been looking at a new variable withdrawal algorithm. It combines conventional withdrawals, which are based only on a portfolio's initial balance, and variable withdrawals that are based on a portfolio's current balance.

I used the market's earnings yield at the beginning of retirement to determine the size of conventional withdrawals. Such withdrawals are fixed percentage a portfolio's initial balance (plus inflation).

I varied withdrawals depending upon the portfolio's current balance and the market's current earnings yield. Gummy came up with this idea.

This combination is a winner.

New Conditions

I used a portfolio that consisted of 80% stocks and 20% TIPS at a 2% interest rate. [I am confident that, if 2% TIPS are not available, it is possible to construct a suitable alternative investment from higher-dividend stocks.]

I applied my version of Gummy's algorithm, which I call G1, using a slope of 1.0 and an offset of minus 2.5%. That is, I made part of my withdrawals equal to (1.0)*(100E10/P-2.5%)*(the portfolio's current balance).

Previously, I used a slope of 0.25.

I made standard withdrawals based upon the Safe Withdrawal Rate of this portfolio. Standard withdrawal amounts equal (the portfolio's initial balance)*(the standard withdrawal rate)*(adjustments for inflation). They are constant in real dollars.

I determined the 30-year Historical Surviving Withdrawal Rates HSWR for 1921-1980. I varied the (standard) withdrawal rates in increments of 0.1%. A portfolio's balance remains positive throughout the entire 30 years at a Historical Surviving Withdrawal Rate HSWR. It falls to zero or becomes negative when the withdrawal rate is increased by 0.1%.

When determining these Historical Surviving Withdrawal Rates, I left the portion of withdrawals that vary with the portfolio's current balance unchanged. The slope remained 1.0. The offset remained minus 2.5%.

Applying the numbers

The curve for the 30-year Calculated Rate is HSWR = 0.4107x+0.6173 where x is the percentage earnings yield 100E10/P. I used the 30-year Historical Surviving Withdrawal Rates from 1923-1980 for a better curve fit.

These confidence limits are eyeball estimated based values of earnings yield below 8% (which means that P/E10 is above 12.5):
The lower confidence limit is minus 1.0%.
The upper confidence limit is plus 1.5%.

The Safe Withdrawal Rate is the lower confidence limit of the Calculated Rate. Its formula is: SWR = (0.4107x+0.6173) - 1.0 = 0.4107x-0.3827.

Applying today's earnings yield, which is close to 3.5%, to this equation, the standard portion of withdrawals is 1.1% of the portfolio's initial balance (plus inflation).

Applying today's earnings yield to Algorithm G1, we withdraw an additional 1.0% of the portfolio's current balance (since 1.0*(3.5%-2.5%) = 1.0%.

For a person beginning retirement today, his total withdrawal amount would be 2.1% (or 1.1% + 1.0% since the current balance would start equal to the initial balance.

This is lower than the Safe Withdrawal Rate under normal conditions. [However, such numbers were based on using commercial paper, not TIPS.] The withdrawal amount varies. It could fall to 1.1% of the initial balance.

As a point of reference:
Here are the Calculated Rates of the Last Decade dated Wednesday, Jun 23, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2657
For 1997 and HDBR80:
Safe: 2.42
Calculated: 4.00
High Risk: 5.58
P/E10 was closest to today's value in 1997 during the past decade. It was 28.33. Today's value is between 28 and 29.

My confidence limits were determined from data with earnings yield less than 8%. Among such conditions, there were no failures.

There were several failures among conditions with earnings yields greater than 8%. This happened because of how I defined the lower confidence limit. These conditions could have safely provided large withdrawal amounts, but not as large as I used.

Data Analysis

The lowest (five-year average of the) withdrawal amount occurred at year 30 of the 1969 historical sequence. It was \$1792. The amount started at \$4770 and briefly exceeded 5.4% (of the initial balance of \$100000). The highest (five-year average of the) withdrawal amount at year 30 in the 1965-1969 historical sequences was \$2001. The lowest balance (in five-year increments) among these 1965-1969 sequences was \$16715 at year 30.

Among conditions with earnings yields starting below 8%, the three sequences with the lowest balances at year 30 were 1970, 1971 and 1972. They were \$13192, \$9939 and \$9952. Balances at year 30 for 1965-1969 were close to \$20000.

The highest balance (in five-year increments) was \$200355 at year 15 of the 1950 sequence. This was not because withdrawal amounts were unduly limited. In that particular sequence, withdrawals started at \$9810.

Assessment

Although there were exceptions, withdrawal amounts trended downward with time. Using a large variable component (i.e., a large slope) produces high initial withdrawal amounts at the expense of later withdrawals.

Using a large slope emphasizes the portfolio's current valuations. It reduces the variation in Historical Surviving Withdrawal Rates and the portion of withdrawals that remains constant (in terms of real dollars).

This leads us to a design procedure. One can vary the size of the variable portion, which is the slope term, to control the variation in withdrawal amounts. When the slope term is set to zero, there is no variation. All withdrawals are fixed. As we increase the slope term, the withdrawal amounts vary more. We can look at the data to determine the lowest of these amounts. We select the slope so as to guarantee a desired minimum withdrawal amount.

We still have issues related to our other variables. We are not limited to an earnings yield offset of 2.5%. We have very limited data with a stock allocation of 50%.

Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
2% TIPS

1921-1980
\$100000 initial balance
Gummy Algorithm 1 is set for Yes (cell B24 equals 1)
Gummy's Multiplier G1 = 1.0 in cell B25
Gummy's Offset is (2.5) or minus 2.5% in cell B17

Stocks = 80%
TIPS at a 2% interest rate = 20%
With Rebalancing
Historical Surviving Withdrawal Rates are determined by varying the rates in cell B9.

Year, Earnings Yield, Historical Surviving Withdrawal Rates, Safe Withdrawal Rates, Calculated Rates

Code: Select all

``````1921   19.61    4.1    7.7    8.7
1922   15.87    4.5    6.1    7.1
1923   12.20    4.3    4.6    5.6
1924   12.35    4.6    4.7    5.7
1925   10.31    4.3    3.9    4.9
1926    8.85    3.8    3.3    4.3
1927    7.58    3.7    2.7    3.7
1928    5.32    3.0    1.8    2.8
1929    3.69    2.2    1.1    2.1
1930    4.48    2.2    1.5    2.5
1931    5.99    2.5    2.1    3.1
1932   10.75    3.8    4.0    5.0
1933   11.49    4.7    4.3    5.3
1934    7.69    3.7    2.8    3.8
1935    8.70    4.3    3.2    4.2
1936    5.85    3.2    2.0    3.0
1937    4.63    2.7    1.5    2.5
1938    7.41    3.6    2.7    3.7
1939    6.41    3.4    2.2    3.2
1940    6.10    3.6    2.1    3.1
1941    7.19    4.5    2.6    3.6
1942    9.90    5.6    3.7    4.7
1943    9.80    5.5    3.6    4.6
1944    9.01    5.2    3.3    4.3
1945    8.33    5.0    3.0    4.0
1946    6.41    4.7    2.2    3.2
1947    8.70    5.9    3.2    4.2
1948    9.62    6.3    3.6    4.6
1949    9.80    6.3    3.6    4.6
1950    9.35    6.5    3.5    4.5
1951    8.40    5.7    3.1    4.1
1952    8.00    5.2    2.9    3.9
1953    7.69    4.9    2.8    3.8
1954    8.33    5.0    3.0    4.0
1955    6.25    3.8    2.2    3.2
1956    5.46    3.3    1.9    2.9
1957    5.99    3.3    2.1    3.1
1958    7.25    3.6    2.6    3.6
1959    5.56    2.8    1.9    2.9
1960    5.46    2.7    1.9    2.9
1961    5.41    2.6    1.8    2.8
1962    4.72    2.3    1.6    2.6
1963    5.18    2.4    1.7    2.7
1964    4.63    2.1    1.5    2.5
1965    4.29    1.9    1.4    2.4
1966    4.15    1.8    1.3    2.3
1967    4.90    2.0    1.6    2.6
1968    4.65    1.9    1.5    2.5
1969    4.72    1.9    1.6    2.6
1970    5.85    2.2    2.0    3.0
1971    6.06    2.2    2.1    3.1
1972    5.78    2.1    2.0    3.0
1973    5.35    2.1    1.8    2.8
1974    7.41    2.7    2.7    3.7
1975   11.24    3.7    4.2    5.2
1976    8.93    3.2    3.3    4.3
1977    8.77    3.3    3.2    4.2
1978   10.87    4.1    4.1    5.1
1979   10.75    4.4    4.0    5.0
1980   11.24    4.6    4.2    5.2``````
Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
TIPS at 2% Interest

Conditions
1921-1980
\$100000 initial balance
Gummy Algorithm 1 is set for Yes (cell B24 equals 1)
Gummy's Multiplier G1 = 1.0 in cell B25
Gummy's Offset is (2.5) or minus 2.5% in cell B17

Stocks = 80%
TIPS at a 2% interest rate = 20%
With Rebalancing
Withdrawal Rate in cell B9 is set equal to the Safe Withdrawal Rate

1923-1980 HSWR Curve Fit Equation:
HSWR = 0.4107x+0.6173
where x is the percentage earnings yield
100E10/P and R-squared = 0.5417
Eyeball estimates when 100E10/P is below 8%:
Lower confidence limit = minus 1.0%
Higher confidence limit = plus 1.5%

Five Year Rolling Averages
Year, At Year 5, At Year 10, At Year 15

Code: Select all

``````1921   7.7    15714     9873    9764
1922   6.1    13858    10011    9504
1923   4.6    11001     9740    8221
1924   4.7    10029    11079    8672
1925   3.9     8191    10858    7643
1926   3.3     6937     9242    6901
1927   2.7     7155     7392    7056
1928   1.8     6205     5354    5425
1929   1.1     4806     3778    4063
1930   1.5     5582     3873    4343
1931   2.1     6480     4837    4898
1932   4.0     8970     8300    7276
1933   4.3     9974     9726    8639
1934   2.8     7143     7333    6422
1935   3.2     7776     8600    7322
1936   2.0     6121     5994    4732
1937   1.5     5036     4714    4299
1938   2.7     7273     6627    5828
1939   2.2     6661     5933    5308
1940   2.1     6874     5978    5224
1941   2.6     8309     7567    6345
1942   3.7    10301     9248    7848
1943   3.6     9814     8765    7783
1944   3.3     9031     8096    7044
1945   3.0     8425     7352    6767
1946   2.2     7584     6437    6354
1947   3.2     9584     8263    7875
1948   3.6    10100     9122    8082
1949   3.6     9995     8786    7959
1950   3.5     9810     9156    7950
1951   3.1     8418     8241    6810
1952   2.9     7754     7413    6516
1953   2.8     7746     6883    6276
1954   3.0     7848     7128    6752
1955   2.2     6086     5285    5611
1956   1.9     5394     4447    5264
1957   2.1     5476     4815    5604
1958   2.6     6050     5509    6547
1959   1.9     4606     4368    5563
1960   1.9     4436     4691    6015
1961   1.8     4167     4920    6035
1962   1.6     3865     4547    5612
1963   1.7     4071     4978    6362
1964   1.5     3692     4785    5572
1965   1.4     3709     4841    4818
1966   1.3     3798     4722    4551
1967   1.6     4473     5503    5113
1968   1.5     4328     5511    4543
1969   1.6     4770     5484    4316
1970   2.0     6121     5994    4732
1971   2.1     6363     5993    4508
1972   2.0     6290     5771    3886
1973   1.8     6421     5277    3527
1974   2.7     8620     6735    4470
1975   4.2    11428     8918    5909
1976   3.3     9504     7156    4811
1977   3.2     9774     6584    4765
1978   4.1    11744     7850    5805
1979   4.0    11924     7855    5912
1980   4.2    12104     7797    6189``````
Year, At Year 20, At Year 25, At Year 30

Code: Select all

``````1921   7.7    7734    7700    7700
1922   6.1    8121    6521    6100
1923   4.6    7593    6342    4966
1924   4.7    8271    6794    5317
1925   3.9    7965    6526    5269
1926   3.3    6836    5811    4622
1927   2.7    6411    5619    4676
1928   1.8    5013    4490    3999
1929   1.1    3690    3394    3007
1930   1.5    3730    3208    2905
1931   2.1    4258    3448    3119
1932   4.0    6054    4815    4141
1933   4.3    7336    6155    5302
1934   2.8    5599    4773    4251
1935   3.2    6229    5568    4832
1936   2.0    3101    2499    2085
1937   1.5    3693    3504    3078
1938   2.7    5090    4454    4014
1939   2.2    4611    4150    3877
1940   2.1    4816    4181    4317
1941   2.6    6130    5089    5777
1942   3.7    7329    6430    6986
1943   3.6    6853    6206    6946
1944   3.3    6345    5936    6996
1945   3.0    5875    6048    7305
1946   2.2    5236    6219    7681
1947   3.2    6921    7954    9525
1948   3.6    7352    8654   10511
1949   3.6    7510    9303   10372
1950   3.5    8375   10652   10423
1951   3.1    7951    9617    9087
1952   2.9    7553    9146    8393
1953   2.8    7561    9477    7746
1954   3.0    8551    9742    7625
1955   2.2    7255    7178    5719
1956   1.9    6474    6193    4714
1957   2.1    6823    6290    4237
1958   2.6    8057    6519    4366
1959   1.9    6373    5005    3313
1960   1.9    5919    4693    3063
1961   1.8    5761    4378    2911
1962   1.6    5228    3524    2537
1963   1.7    5254    3509    2574
1964   1.5    4418    2912    2194
1965   1.4    3859    2495    1987
1966   1.3    3483    2296    1805
1967   1.6    3445    2485    2001
1968   1.5    3035    2231    1819
1969   1.6    2854    2172    1792
1970   2.0    3101    2499    2085
1971   2.1    3034    2460    2140
1972   2.0    2825    2317    2035
1973   1.8    2602    2136    1737
1974   2.7    3434    2909    2643
1975   4.2    4806    4259    4200
1976   3.3    3895    3369    3216
1977   3.2    3868    3295    2786
1978   4.1    4791    3981    3709
1979   4.0    4715    3493    3291
1980   4.2    4633    3356    3524``````
Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
TIPS at 2% Interest

Conditions
1921-1980
\$100000 initial balance
Gummy Algorithm 1 is set for Yes (cell B24 equals 1)
Gummy's Multiplier G1 = 1.0 in cell B25
Gummy's Offset is (2.5) or minus 2.5% in cell B17

Stocks = 80%
TIPS at a 2% interest rate = 20%
With Rebalancing
Withdrawal Rate in cell B9 is set equal to the Safe Withdrawal Rate

1923-1980 HSWR Curve Fit Equation:
HSWR = 0.4107x+0.6173
where x is the percentage earnings yield
100E10/P and R-squared = 0.5417
Eyeball estimates when 100E10/P is below 8%:
Lower confidence limit = minus 1.0%
Higher confidence limit = plus 1.5%

Balances
Year, SWR, At Year 5, At Year 10, At Year 15

Code: Select all

``````1921   7.7     77555     65717      9189
1922   6.1     95427     68038     73300
1923   4.6    118163     66724     69428
1924   4.7    180741     98906     87632
1925   3.9    156922     82541     89333
1926   3.3    125889    104561     74945
1927   2.7     84267    128005     62576
1928   1.8     63186     78221     53721
1929   1.1     62152     64946     45331
1930   1.5     56262     65743     45912
1931   2.1     85338     63029     56877
1932   4.0    142785     64397     47518
1933   4.3    116959     73962     51759
1934   2.8     99443     64333     44075
1935   3.2    115399     78830     54230
1936   2.0     77311     75879     49902
1937   1.5     51395     48226     45418
1938   2.7     66913     51556     52456
1939   2.2     67233     48875     51034
1940   2.1     71930     53498     70308
1941   2.6     99477     66751     94830
1942   3.7     91123     82019    106276
1943   3.6     79703     85599     94946
1944   3.3     73010     76701    113557
1945   3.0     74096     96924    114502
1946   2.2     69894    103547    109138
1947   3.2     95310    130719    152141
1948   3.6    112482    130472    160736
1949   3.6    109167    167385    186079
1950   3.5    135718    165461    200355
1951   3.1    145910    151814    194031
1952   2.9    138189    161935    167960
1953   2.8    118143    148000    174493
1954   3.0    155504    175152    187876
1955   2.2    123060    150328    128024
1956   1.9    105136    135662    106680
1957   2.1    117576    122326    109842
1958   2.6    124070    144957    128944
1959   1.9    113001    121583     83205
1960   1.9    121629    103143     57358
1961   1.8    128834    101142     65922
1962   1.6    104801     94895     57714
1963   1.7    118981    108184     49454
1964   1.5    108555     75142     41615
1965   1.4     85557     48188     34359
1966   1.3     79123     52195     32246
1967   1.6     90361     54771     26211
1968   1.5     90756     41345     25600
1969   1.6     68610     37320     23789
1970   2.0     55305     37981     23405
1971   2.1     64011     37194     23868
1972   2.0     59588     27475     26062
1973   1.8     45294     27698     23482
1974   2.7     53408     32695     25482
1975   4.2     66426     37806     28534
1976   3.3     58299     37699     27025
1977   3.2     47120     46718     36250
1978   4.1     60574     50498     42928
1979   4.0     66488     59784     55897
1980   4.2     67970     71004     59644``````
Year, SWR, At Year 20, At Year 25, At Year 30

Code: Select all

``````1921   7.7    (32729)   (118553)   (192184)
1922   6.1     18026    (11817)   (62093)
1923   4.6     35421     13867     (9025)
1924   4.7     45369     18541     (2034)
1925   3.9     53771     28944     20015
1926   3.3     63591     31833     28719
1927   2.7     54104     44488     51909
1928   1.8     43072     46677     52244
1929   1.1     34728     38892     60955
1930   1.5     32696     40602     45700
1931   2.1     32410     37279     29817
1932   4.0     26658     12593    (11014)
1933   4.3     43782     35315     25867
1934   2.8     42034     56248     53934
1935   3.2     64092     68561     72013
1936   2.0     69348     69050     84581
1937   1.5     61590     70938     72399
1938   2.7     54914     60888     63076
1939   2.2     75118     80226     81585
1940   2.1     83400     98328     80775
1941   2.6     96368    120448     91440
1942   3.7    117096    114357     94945
1943   3.6    112019    124441    103663
1944   3.3    121996    124836     79720
1945   3.0    134438    109957     57883
1946   2.2    141146    111262     72977
1947   3.2    156809    139275     81991
1948   3.6    186525    164534     70956
1949   3.6    197095    132112     68367
1950   3.5    169153     93462     64061
1951   3.1    151016     97105     56966
1952   2.9    150285     89601     41365
1953   2.8    156943     70301     41947
1954   3.0    128059     68709     42503
1955   2.2     71635     50403     32736
1956   1.9     69712     42272     29762
1957   2.1     65883     30822     30126
1958   2.6     56542     32098     23540
1959   1.9     45019     28369     23333
1960   1.9     39850     25192     23492
1961   1.8     39767     27702     22547
1962   1.6     27819     28800     23961
1963   1.7     30844     27044     24965
1964   1.5     27543     24590     22750
1965   1.4     22930     23321     18830
1966   1.3     23555     20546     23043
1967   1.6     26776     21820     21818
1968   1.5     22173     20085     24577
1969   1.6     19965     16715     22197
1970   2.0     20852     13192     16373
1971   2.1     16860     12577      9939
1972   2.0     18661     14473      9952
1973   1.8     20543     23811     16169
1974   2.7     18463     18308      3277
1975   4.2     10799     (5240)   (16029)
1976   3.3     20937     18109     (2463)
1977   3.2     33289     30060      3362
1978   4.1     47395     30216       770
1979   4.0     86871     45089      8496
1980   4.2    111873     44678      7446``````
This completes the 80% stock data when the slope is 1.0.

Have fun.

John R.

Mike
*** Veteran
Posts: 278
Joined: Sun Jul 06, 2003 4:00 am
Some of those SWR numbers dip pretty low.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
Mike wrote:Some of those SWR numbers dip pretty low.
Yes. This is a consistent theme of variable withdrawal strategies.

So far, our results have favored limiting the amount of year-to-year variation. [This includes some data that I have not yet presented.] They have also favored higher stock allocations.

These results are not unique to this combination of strategies. Rather, whenever you adjust withdrawal amounts from year-to-year, you are vulnerable to ending up with some very low final withdrawal rates (in times of stress). The message in The 4% Shocker seems to have a lot of generality.

But let's look at this differently. How about the upside?

[OK. This is not for today, but it is still worth knowing.]

From these combination strategies, we can compress the amount of variation in all sequences. This means that we can start out very close to the right withdrawal rate and then make minor adjustments later. We do not have to accept the limitations of the worst-case condition in order to achieve safety. We can start with a realistic withdrawal rate right from the start.

Another way of looking at this is that today's Safe Withdrawal Rate using the traditional approach is 2.4%. Instead, we can start out at 2.9% without giving up safety as long as we are willing to make adjustments later. The downside is 2.6%, which close to the (traditional) constant-withdrawal Safe Withdrawal Rate of 2.4%. [The new number should be closer to the number from the traditional strategy. The discrepancy has to do with the details of how the lower confidence limits were determined. The traditional constant-withdrawal Safe Withdrawal Rate included conditions at low P/E10 (high 100E10/P) values, which widens the confidence interval. It is calculated precisely, according to formula. The rate with this combination approach was based on using only medium to high values of P/E10, which narrowed the confidence interval, and it was made using an eyeball estimate.]

Have fun.

John R.

Mike
*** Veteran
Posts: 278
Joined: Sun Jul 06, 2003 4:00 am
Another way of looking at this is that today's Safe Withdrawal Rate using the traditional approach is 2.4%. Instead, we can start out at 2.9% without giving up safety as long as we are willing to make adjustments later.
Thin gruel either way. There does not seem to be any way to win today by using S&P index funds, with S&P yields so low. The new private accounts are likely to exert a yield lowering effect (as did the private pension laws), so the yields may stay low for a long time. Depending upon future political choices. An interesting puzzle.

unclemick
*** Veteran
Posts: 231
Joined: Sat Jun 12, 2004 4:00 am
Location: LA till Katrina, now MO
Sometimes the best you can do is sit tight and wait.

Looking over the landscape - REITs, junk bonds, emerging markets - both bonds and stocks, new commodities investment vehicles, royalty trusts, timberland, gold, etc., are areas getting fund flows of money - some will succeed and be loudly noted - alas a goodly number will fail and remain silent.

Ala Clint Eastwood -'A man's got to know his limitations.'

2.4 - 2.9% and soldier on. In ER - defense is sometimes a good offense.
Patience sucks - but it is usually better than losing money.

ElSupremo
Posts: 343
Joined: Thu Nov 21, 2002 12:53 pm
Location: Cincinnati, Ohio
Greetings Mike
There does not seem to be any way to win today by using S&P index funds, with S&P yields so low.
Expanding on unclemicks thoughts, we aren't trying to win the battle today. We are trying to win the war tomorrow. I've been a big fan of VFINX for many years. I still am and you could do a lot worse, but the evidence has been piling up for years pointing to the total market approach. So the same long term outlook we've always had, and something like VTSMX makes sense today. And tomorrow. For most of us.
"The best things in life are FREE!"

www.nofeeboards.com

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
TIPS at 2% Interest: Baseline

HDBR50T2 consists of 50% stocks and 50% TIPS at a 2% interest rate.

HDBR80T2 consists of 80% stocks and 20% TIPS at a 2% interest rate.

These portfolios are similar to HDBR50 and HDBR80 except that they use TIPS instead of commercial paper.

These are 30-year Historical Surviving Withdrawal Rates. Expenses were set at 0.20%. These are with rebalancing. The CPI was used for inflation adjustments.

Year, P/E10, 100E10/P, HDBR50T2, HDBR80T2

Code: Select all

``````1921    5.1   19.61    7.1    9.3
1922    6.3   15.87    7.5    9.6
1923    8.2   12.20    7.2    8.7
1924    8.1   12.35    7.2    9.0
1925    9.7   10.31    7.0    8.3
1926   11.3    8.85    6.3    7.3
1927   13.2    7.58    6.2    7.0
1928   18.8    5.32    5.5    5.7
1929   27.1    3.69    4.6    4.4
1930   22.3    4.48    4.6    4.5
1931   16.7    5.99    4.9    5.2
1932    9.3   10.75    6.1    7.3
1933    8.7   11.49    7.2    8.8
1934   13.0    7.69    6.1    6.8
1935   11.5    8.70    6.6    7.7
1936   17.1    5.85    5.5    5.9
1937   21.6    4.63    4.9    4.9
1938   13.5    7.41    5.8    6.6
1939   15.6    6.41    5.6    6.2
1940   16.4    6.10    5.9    6.5
1941   13.9    7.19    7.0    8.1
1942   10.1    9.90    7.8    9.8
1943   10.2    9.80    7.5    9.4
1944   11.1    9.01    7.1    8.7
1945   12.0    8.33    6.9    8.3
1946   15.6    6.41    7.1    8.0
1947   11.5    8.70    7.8    9.9
1948   10.4    9.62    7.8   10.4
1949   10.2    9.80    7.6   10.2
1950   10.7    9.35    8.0   10.6
1951   11.9    8.40    7.3    9.3
1952   12.5    8.00    6.8    8.5
1953   13.0    7.69    6.6    8.2
1954   12.0    8.33    6.7    8.5
1955   16.0    6.25    5.8    6.6
1956   18.3    5.46    5.3    5.8
1957   16.7    5.99    5.4    5.9
1958   13.8    7.25    5.6    6.5
1959   18.0    5.56    4.9    5.2
1960   18.3    5.46    4.9    5.1
1961   18.5    5.41    4.8    5.1
1962   21.2    4.72    4.5    4.6
1963   19.3    5.18    4.8    4.9
1964   21.6    4.63    4.4    4.4
1965   23.3    4.29    4.2    4.1
1966   24.1    4.15    4.2    3.9
1967   20.4    4.90    4.5    4.4
1968   21.5    4.65    4.4    4.2
1969   21.2    4.72    4.4    4.2
1970   17.1    5.85    4.8    4.8
1971   16.5    6.06    4.8    4.8
1972   17.3    5.78    4.8    4.7
1973   18.7    5.35    4.8    4.6
1974   13.5    7.41    5.7    6.0
1975    8.9   11.24    6.5    7.7
1976   11.2    8.93    5.8    6.5
1977   11.4    8.77    5.9    6.5
1978    9.2   10.87    6.6    7.8
1979    9.3   10.75    6.9    8.1
1980    8.9   11.24    6.9    8.0``````
Here are the equations derived from these data:

50% stocks
From 1923-1980 data:
HDBR50T2 = 0.4031x + 2.9478
and R-squared = 0.7048
Eyeball estimates:
Lower Confidence limit = minus 1.0%
Upper Confidence limit = plus 1.5%

Using today's valuations (100E10/P = 3.5%):
Safe = 3.4%
Calculated = 4.35865% or 4.4% when rounded
High Risk = 5.9%

80% stocks
From 1923-1980 data:
HDBR80T2 = 0.6758x + 1.7538
and R-squared = 0.6916
Eyeball estimates:
Lower Confidence limit = minus 1.4%
Upper Confidence limit = plus 2.6%

Using today's valuations (100E10/P = 3.5%):
Safe = 2.7%
Calculated = 4.1191% or 4.1% when rounded
High Risk = 6.7%

Observe that the Safe and Calculated Rates are higher with 50% stocks than with 80% stocks at today's valuations.

At today's valuations, using a variable withdrawal rate portfolio with a slope of 0.25, you would start withdrawing at 2.9% of the initial value but you could end up at 2.6% under worst-case conditions. The baseline HDBR80T2 has a Safe Withdrawal Rate of 2.7%. These numbers are very close.

In contrast, the High Variability portfolio for 80% stocks (with a slope of 1.0) has a much lower starting rate of 2.1% at today's valuations.

Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
Using both Initial and Current Valuations--Revised - 50% Stocks

I have been looking at a new variable withdrawal algorithm. It combines conventional withdrawals, which are based only on a portfolio's initial balance, and variable withdrawals that are based on a portfolio's current balance.

I used the market's earnings yield at the beginning of retirement to determine the size of conventional withdrawals. Such withdrawals are fixed percentage a portfolio's initial balance (plus inflation).

I varied withdrawals depending upon the portfolio's current balance and the market's current earnings yield. Gummy came up with this idea.

This combination is a winner.

Early results

I used a portfolio that consisted of 50% stocks and 50% TIPS at a 2% interest rate. [I am confident that, if 2% TIPS are not available, it is possible to construct a suitable alternative investment from higher-dividend stocks.]

I applied my version of Gummy's algorithm, which I call G1, using a slope of 0.25 and an offset of minus 2.5%. That is, I make part of my withdrawals equal to (0.25)*(100E10/P-2.5%)*(the portfolio's current balance).

In addition, I make standard withdrawals based upon the Safe Withdrawal Rate of this portfolio. Standard withdrawal amounts equal (the portfolio's initial balance)*(the standard withdrawal rate)*(adjustments for inflation). They are constant in real dollars.

I determined the 30-year Historical Surviving Withdrawal Rates HSWR for 1921-1980. I varied the (standard) withdrawal rates in increments of 0.1%. A portfolio's balance remains positive throughout the entire 30 years at a Historical Surviving Withdrawal Rate HSWR. It falls to zero or becomes negative when the withdrawal rate is increased by 0.1%.

I left the portion of withdrawals that varied with the portfolio's current balance unchanged. The slope remained 0.25 and the offset remained minus 2.5%.

Applying the numbers

The curve for the 30-year Calculated Rate is HSWR = 0.362x+2.5395 where x is the percentage earnings yield 100E10/P. I used the 30-year Historical Surviving Withdrawal Rates from 1923-1980 for a better curve fit.

Eyeball estimates when 100E10/P is below 10%:
Lower confidence limit = minus 0.8%.
Higher confidence limit = plus 1.3%.

The Safe Withdrawal Rate is the lower confidence limit of the Calculated Rate. Its formula is: SWR = (0.362x+2.5395)-(0.8 ).

Applying today's earnings yield, which is close to 3.5%, to this equation, the standard portion of withdrawals is 3.01% of the portfolio's initial balance (plus inflation).

Applying today's earnings yield to Algorithm G1, we withdraw an additional 0.25% of the portfolio's current balance (since 0.25*(3.5%-2.5%) = 0.25%.

For a person beginning retirement today, his total withdrawal amount would be 3.26% (or 3.01% + 0.25%) since the current balance would equal the initial balance. Rounded, this becomes 3.3%.

This is essentially equal to the Safe Withdrawal Rate under normal conditions. With 2% TIPS and 50% stocks, the traditional constant-withdrawal amount (in real dollars) has a Safe Withdrawal Rate of 3.4% of the initial balance. The withdrawal amount varies. It could fall to 3.0% of the initial balance.

As a point of reference, from my recently posted baseline:
From 1923-1980 data:
HDBR50T2 = 0.4031x + 2.9478
and R-squared = 0.7048
Eyeball estimates:
Lower Confidence limit = minus 1.0%
Upper Confidence limit = plus 1.5%

Using today's valuations (100E10/P = 3.5%):
Safe = 3.4%
Calculated = 4.35865% or 4.4% when rounded
High Risk = 5.9%

My confidence limits were determined from data with earnings yield less than 10%. Among such conditions, there were no failures.

There were a few failures among conditions with earnings yields greater than 10%. This happened because of how I defined the lower confidence limit. These conditions could have safely provided large withdrawal amounts, just not so large as I used.

Data Analysis

The lowest (five-year average of the) withdrawal amount occurred at year 30 of the 1966 historical sequence. It was \$3365. The amount started at \$3838 and briefly exceeded 4.3% (of the initial balance of \$100000). The lowest balance in the 1966 sequence (in five-year increments) was \$24412 at year 30.

Among conditions with earnings yields starting below 10%, there were only three sequences (1970, 1971 and 1972) with very low balances at year 30. The lowest was \$17303 in the 1972 sequence. The other balances (at valid data points) were above \$20000.

The highest balance (in five-year increments) was \$155096 at year 15 of the 1950 sequence. This was not because withdrawal amounts were unduly limited. In that particular sequence, withdrawals started at \$6622.

Assessment

The variation of withdrawal amounts remained within reasonable bounds. The algorithm does what it is supposed to do. It provides a reasonably steady income. It takes advantage of any reward on the upside. It does not increase risk.

Reflecting on these numbers and today's valuations, this approach challenges dividend-based strategies. Using this approach, withdrawals would start out today at 3.3% of the initial balance.

Most people consider dividend projections far more reliable than stock price projections, especially during the first decade. They would still be competitive using a dividends-based strategy. They are much more likely to be comfortable than with a strategy (such as this) that relies on price increases. They would not panic if prices fell in half. People who depend upon price appreciation are sometimes under great pressure.

Have fun.

John R.

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
TIPS at 2% Interest

Conditions
1921-1980
\$100000 initial balance
Gummy Algorithm 1 is set for Yes (cell B24 equals 1)
Gummy's Multiplier G1 = 0.25 in cell B25
Gummy's Offset is (2.5) or minus 2.5% in cell B17

Stocks = 50%
TIPS at a 2% interest rate = 50%
With Rebalancing
Withdrawal Rate in cell B9 is set equal to the Safe Withdrawal Rate

1923-1980 HSWR Curve Fit Equation:
HSWR = 0.362x+2.5395
where x is the percentage earnings yield
100E10/P and R-squared = 0.6583
Eyeball estimates when 100E10/P is below 10%:
Lower confidence limit = minus 0.8%
Higher confidence limit = plus 1.3%

Five Year Rolling Averages
Year, SWR, At Year 5, At Year 10, At Year 15

Code: Select all

``````1921   8.8   10898    9374    9467
1922   7.5    9472    8436    8474
1923   6.2    7840    7482    7200
1924   6.2    7474    7722    7214
1925   5.5    6504    7238    6466
1926   4.9    5728    6443    5842
1927   4.5    5522    5749    5669
1928   3.7    4845    4688    4784
1929   3.1    4194    3905    4065
1930   3.4    4606    4093    4334
1931   3.9    5154    4671    4810
1932   5.6    6829    6664    6526
1933   5.9    7202    7256    7115
1934   4.5    5580    5768    5626
1935   4.9    5954    6340    6121
1936   3.9    4847    5084    5005
1937   3.4    4397    4409    4358
1938   4.4    5590    5526    5402
1939   4.1    5319    5201    5070
1940   3.9    5237    5090    4895
1941   4.3    5852    5825    5475
1942   5.3    6939    6876    6449
1943   5.3    6835    6726    6379
1944   5.0    6468    6332    5949
1945   4.8    6238    5995    5726
1946   4.1    5667    5329    5203
1947   4.9    6585    6179    6001
1948   5.2    6812    6472    6155
1949   5.3    6837    6422    6170
1950   5.1    6622    6334    6016
1951   4.8    6087    5928    5552
1952   4.6    5756    5588    5320
1953   4.5    5663    5383    5188
1954   4.8    5877    5645    5496
1955   4.0    4922    4678    4689
1956   3.7    4571    4281    4429
1957   3.9    4732    4505    4662
1958   4.4    5190    5003    5209
1959   3.8    4455    4337    4605
1960   3.7    4310    4317    4671
1961   3.7    4257    4393    4725
1962   3.4    3946    4092    4462
1963   3.6    4150    4353    4853
1964   3.4    3922    4195    4597
1965   3.3    3869    4203    4388
1966   3.2    3838    4158    4300
1967   3.5    4214    4597    4726
1968   3.4    4124    4610    4550
1969   3.4    4234    4670    4521
1970   3.9    4972    5192    5007
1971   3.9    5044    5206    4932
1972   3.8    5009    5158    4650
1973   3.7    5098    5055    4494
1974   4.4    6123    5944    5232
1975   5.8    7685    7402    6503
1976   5.0    6734    6389    5611
1977   4.9    6803    6130    5512
1978   5.7    7823    6953    6310
1979   5.6    7812    6845    6237
1980   5.8    7977    6890    6408``````
Year, SWR, At Year 20, At Year 25, At Year 30

Code: Select all

``````1921   8.8    8844    8800    8800
1922   7.5    8114    7712    7500
1923   6.2    7121    6857    6480
1924   6.2    7241    6920    6544
1925   5.5    6744    6444    6109
1926   4.9    6003    5812    5440
1927   4.5    5645    5530    5183
1928   3.7    4750    4669    4426
1929   3.1    3984    3895    3659
1930   3.4    4173    3981    3791
1931   3.9    4666    4369    4197
1932   5.6    6260    5859    5633
1933   5.9    6884    6495    6207
1934   4.5    5468    5139    4942
1935   4.9    5853    5579    5335
1936   3.9    4697    4549    4298
1937   3.4    4087    3956    3779
1938   4.4    5114    4875    4712
1939   4.1    4765    4580    4454
1940   3.9    4675    4453    4439
1941   4.3    5334    4992    5173
1942   5.3    6247    5962    6092
1943   5.3    6073    5862    6006
1944   5.0    5717    5563    5796
1945   4.8    5455    5433    5739
1946   4.1    4853    5072    5609
1947   4.9    5710    5932    6494
1948   5.2    5933    6189    6806
1949   5.3    6005    6342    6794
1950   5.1    6042    6614    6962
1951   4.8    5743    6212    6413
1952   4.6    5508    5983    6125
1953   4.5    5442    6067    5979
1954   4.8    5848    6348    6091
1955   4.0    5093    5316    5124
1956   3.7    4791    4948    4689
1957   3.9    5058    5172    4666
1958   4.4    5702    5553    4974
1959   3.8    4979    4766    4243
1960   3.7    4856    4666    4111
1961   3.7    4852    4583    4056
1962   3.4    4586    4135    3740
1963   3.6    4782    4263    3895
1964   3.4    4434    3923    3624
1965   3.3    4230    3712    3487
1966   3.2    4078    3584    3365
1967   3.5    4261    3853    3638
1968   3.4    4053    3697    3509
1969   3.4    3989    3670    3485
1970   3.9    4392    4125    3936
1971   3.9    4342    4083    3920
1972   3.8    4201    3961    3816
1973   3.7    4083    3855    3677
1974   4.4    4799    4533    4335
1975   5.8    6112    5848    5797
1976   5.0    5265    5031    4942
1977   4.9    5171    4934    4738
1978   5.7    5951    5661    5556
1979   5.6    5832    5455    5370
1980   5.8    5926    5587    5614``````
Have fun.

John R.