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JWR1945
***** Legend

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

Posted: Fri Mar 04, 2005 5:40 pm    Post subject: Using both Initial and Current Valuations

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 Quote: 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

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

Posted: Sat Mar 05, 2005 6:48 am    Post subject:

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: 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

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

Posted: Sat Mar 05, 2005 6:51 am    Post subject:

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: 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: 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

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

Posted: Sat Mar 05, 2005 6:57 am    Post subject:

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: 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: 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

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

Posted: Sat Mar 05, 2005 7:28 am    Post subject:

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: 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: 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

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

 Posted: Mon Mar 07, 2005 1:15 pm    Post subject: 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%. In addition, R-squared = 0.6519. 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

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

Posted: Mon Mar 07, 2005 1:19 pm    Post subject:

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: 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: 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

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

Posted: Mon Mar 07, 2005 1:29 pm    Post subject:

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: 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: 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

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

 Posted: Tue Mar 08, 2005 7:50 pm    Post subject: 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%. In addition, R-squared = 0.5417. 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

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

Posted: Tue Mar 08, 2005 7:57 pm    Post subject:

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: 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

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

Posted: Tue Mar 08, 2005 8:01 pm    Post subject:

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: 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: 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

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

Posted: Tue Mar 08, 2005 8:13 pm    Post subject:

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: 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: 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

Joined: 06 Jul 2003
Posts: 278

 Posted: Wed Mar 09, 2005 7:34 pm    Post subject: Some of those SWR numbers dip pretty low.
JWR1945
***** Legend

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

Posted: Thu Mar 10, 2005 7:48 am    Post subject:

 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

Joined: 06 Jul 2003
Posts: 278

Posted: Fri Mar 11, 2005 3:03 am    Post subject:

 Quote: 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

Joined: 12 Jun 2004
Posts: 231
Location: LA till Katrina, now MO

 Posted: Fri Mar 11, 2005 4:25 am    Post subject: 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

Joined: 21 Nov 2002
Posts: 343
Location: Cincinnati, Ohio

Posted: Fri Mar 11, 2005 4:57 am    Post subject:

Greetings Mike

 Quote: 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.

_________________
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JWR1945
***** Legend

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

Posted: Fri Mar 11, 2005 8:11 am    Post subject:

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: 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

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

 Posted: Fri Mar 11, 2005 9:07 am    Post subject: 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%. In addition, R-squared = 0.6583. 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

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

Posted: Fri Mar 11, 2005 9:24 am    Post subject:

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: 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: 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.

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