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 Using both Initial and Current Valuations Goto page Previous  1, 2
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JWR1945
***** Legend

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

Posted: Fri Mar 11, 2005 9:46 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%
SWR = HSWR-0.8 (the lower confidence limit)

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

 Code: 1921   8.8     87451     69357     21338 1922   7.5     99107     76960     76888 1923   6.2    112786     79354     80855 1924   6.2    144426    100984     91904 1925   5.5    131023     91894     95893 1926   4.9    113404    106389     85222 1927   4.5     90713    120895     77753 1928   3.7     77073     90126     71405 1929   3.1     76276     78227     61784 1930   3.4     72191     78113     61254 1931   3.9     94347     76109     69993 1932   5.6    124977     73488     57278 1933   5.9    111927     83181     65974 1934   4.5    100869     77675     62155 1935   4.9    109469     87544     70161 1936   3.9     84499     84257     65026 1937   3.4     66100     63656     60514 1938   4.4     77705     66334     66352 1939   4.1     78084     63822     63900 1940   3.9     83236     70781     84315 1941   4.3    104018     85373    109605 1942   5.3     97314     93975    111252 1943   5.3     88402     93325     98325 1944   5.0     83792     86965    109785 1945   4.8     84625    100164    108467 1946   4.1     83525    109316    113758 1947   4.9    100359    123952    135972 1948   5.2    109785    120852    134715 1949   5.3    106205    137491    140906 1950   5.1    123794    140417    155096 1951   4.8    127860    129957    146776 1952   4.6    122537    133298    131565 1953   4.5    111362    125693    134463 1954   4.8    131058    136170    135696 1955   4.0    112409    122937    107043 1956   3.7    101671    114869     95628 1957   3.9    108640    107074     96472 1958   4.4    110972    116454    103191 1959   3.8    103492    102664     77748 1960   3.7    108819     94195     64644 1961   3.7    112150     92513     70361 1962   3.4     99146     90016     66613 1963   3.6    106969     97257     60887 1964   3.4    100658     77812     54575 1965   3.3     87091     60314     48707 1966   3.2     83426     64564     47870 1967   3.5     90830     67262     43422 1968   3.4     91223     57433     43546 1969   3.4     78011     55616     43883 1970   3.9     69313     56062     42720 1971   3.9     77043     56658     44903 1972   3.8     74321     48305     47979 1973   3.7     63888     49772     45209 1974   4.4     72170     58210     52613 1975   5.8     80410     60585     51938 1976   5.0     74351     60136     48148 1977   4.9     66736     69332     58044 1978   5.7     78338     71781     62886 1979   5.6     83750     80034     74376 1980   5.8     84191     86225     73347

Year, SWR, At Year 20, At Year 25, At Year 30

 Code: 1921   8.8    (26928)   (104825)  (180504) 1922   7.5     28120     (6522)   (57335) 1923   6.2     50960     27742      2297 1924   6.2     58834     32243      8615 1925   5.5     70432     48646     40431 1926   4.9     77347     50657     46599 1927   4.5     71686     63520     67456 1928   3.7     62779     65738     68599 1929   3.1     51358     52703     65685 1930   3.4     47576     49646     45956 1931   3.9     47034     45414     30689 1932   5.6     34897     13611    (19314) 1933   5.9     57859     46458     30848 1934   4.5     60240     70016     62510 1935   4.9     76906     76093     70660 1936   3.9     77549     72944     75142 1937   3.4     70339     72072     66298 1938   4.4     65384     63581     55840 1939   4.1     77362     73064     64423 1940   3.9     91933     97092     81031 1941   4.3    111872    126930    106218 1942   5.3    116472    110008     93517 1943   5.3    104247    103499     84529 1944   5.0    109267    103383     72856 1945   4.8    113621     93843     59765 1946   4.1    131746    112979     91051 1947   4.9    135441    123702     92406 1948   5.2    142100    126806     76826 1949   5.3    138182    102915     67208 1950   5.1    136600     96161     79956 1951   4.8    122140     94160     69328 1952   4.6    118760     87071     55148 1953   4.5    122268     76559     57447 1954   4.8    103432     70677     51353 1955   4.0     74108     59811     45389 1956   3.7     73769     54377     43285 1957   3.9     70517     44401     41593 1958   4.4     61723     42152     29754 1959   3.8     52474     37144     26304 1960   3.7     51334     37731     30842 1961   3.7     50522     38213     27015 1962   3.4     42948     42048     31772 1963   3.6     45672     38951     29969 1964   3.4     41766     34589     24939 1965   3.3     37005     32209     20221 1966   3.2     38519     30572     24412 1967   3.5     42610     32336     23414 1968   3.4     37833     30180     24591 1969   3.4     38295     30662     29359 1970   3.9     37384     23767     18261 1971   3.9     34705     26103     17563 1972   3.8     37223     28361     17303 1973   3.7     39039     37390     22828 1974   4.4     44814     48182     22197 1975   5.8     31426     20497     (8199) 1976   5.0     39168     31759      1149 1977   4.9     51424     41936      7708 1978   5.7     61792     39422      3585 1979   5.6     91405     52877     13228 1980   5.8     98761     46342      8039

This completes the 50% stock data when the slope is 0.25.

Have fun.

John R.

Mike
*** Veteran

Joined: 06 Jul 2003
Posts: 278

Posted: Fri Mar 11, 2005 7:56 pm    Post subject:

 Quote: 2.4 - 2.9% and soldier on.

Indeed, you play the hand you're dealt.

 Quote: For most of us.

Yes, the majority cannot outperform themselves.

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

JWR1945
***** Legend

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

 Posted: Sat Mar 12, 2005 2:52 pm    Post subject: Using both Initial and Current Valuationsâ€”High Variability--50% This continues my investigation of 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 also 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 1.0 and an offset of minus 2.5%. That is, I make part of my withdrawals equal to (1.0)*(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). These amounts are constant in real dollars. I determined those Safe Withdrawal Rates from 30-year Historical Surviving Withdrawal Rates HSWR. 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 HSWRs, I left the portion of withdrawals that varied with the portfolio's current balance unchanged. The slope remained 1.0 and the offset remained minus 2.5%. Applying the numbers The curve [or regression equation] for the 30-year Calculated Rate is HSWR = 0.2449x+1.2658 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 0.7%. Higher confidence limit = plus 1.2%. In addition, R-squared = 0.5017 The Safe Withdrawal Rate is the lower confidence limit of the Calculated Rate. Its formula is: SWR = (0.2449x+1.2658)-0.7. Applying today's earnings yield, which is close to 3.5%, to this equation, the standard portion of withdrawals is 1.42% 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 2.42% (or 1.42% + 1.0%) since the current balance would equal the initial balance. Rounded, this becomes 2.4%. This is much less than 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 using the new approach varies. It could fall to 1.4% of the initial balance. 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, but less than what I used. Data Analysis The lowest (five-year average of the) withdrawal amount occurred at year 30 of the 1968 historical sequence. It was \$1908. The amount started at \$4566 and briefly exceeded 6.1% (of the initial balance of \$100000). The lowest balance in the 1968 sequence (in five-year increments) was \$10873 at year 30. Among conditions with earnings yields starting below 10%, there were five valid sequences (1967, 1970, 1971, 1972 and 1973) with balances below \$10000 at year 30. There were numerous conditions with balances below \$20000. The highest balance (in five-year increments) was \$134412 at year 5 of the 1924 sequence. This was not because withdrawal amounts were unduly limited. In that particular sequence, withdrawals started at \$8482. Assessment 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. The smallest initial withdrawal (i.e., the five-year average amount at year 5) was \$3800 in the 1964 historical sequence. Using a large slope emphasizes the portfolio's current valuations. It overcompensates. An offset term with a magnitude larger than 2.5% might correct this deficiency. Have fun. John R.
JWR1945
***** Legend

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

Posted: Sat Mar 12, 2005 3:02 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 = 50%
TIPS at a 2% interest rate = 50%
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    3.0    5.4    6.1 1922   15.87    3.4    4.5    5.2 1923   12.20    3.4    3.6    4.3 1924   12.35    3.6    3.6    4.3 1925   10.31    3.5    3.1    3.8 1926    8.85    3.2    2.7    3.4 1927    7.58    3.2    2.4    3.1 1928    5.32    2.7    1.9    2.6 1929    3.69    2.2    1.5    2.2 1930    4.48    2.2    1.7    2.4 1931    5.99    2.3    2.0    2.7 1932   10.75    3.0    3.2    3.9 1933   11.49    3.7    3.4    4.1 1934    7.69    3.1    2.4    3.1 1935    8.70    3.5    2.7    3.4 1936    5.85    2.9    2.0    2.7 1937    4.63    2.5    1.7    2.4 1938    7.41    3.0    2.4    3.1 1939    6.41    2.9    2.1    2.8 1940    6.10    3.0    2.1    2.8 1941    7.19    3.6    2.3    3.0 1942    9.90    4.2    3.0    3.7 1943    9.80    4.1    3.0    3.7 1944    9.01    4.0    2.8    3.5 1945    8.33    3.9    2.6    3.3 1946    6.41    4.0    2.1    2.8 1947    8.70    4.5    2.7    3.4 1948    9.62    4.5    2.9    3.6 1949    9.80    4.5    3.0    3.7 1950    9.35    4.8    2.9    3.6 1951    8.40    4.4    2.6    3.3 1952    8.00    4.1    2.5    3.2 1953    7.69    3.9    2.4    3.1 1954    8.33    4.0    2.6    3.3 1955    6.25    3.3    2.1    2.8 1956    5.46    3.0    1.9    2.6 1957    5.99    3.0    2.0    2.7 1958    7.25    3.1    2.3    3.0 1959    5.56    2.6    1.9    2.6 1960    5.46    2.6    1.9    2.6 1961    5.41    2.5    1.9    2.6 1962    4.72    2.3    1.7    2.4 1963    5.18    2.3    1.8    2.5 1964    4.63    2.1    1.7    2.4 1965    4.29    2.0    1.6    2.3 1966    4.15    1.9    1.6    2.3 1967    4.90    2.0    1.8    2.5 1968    4.65    1.9    1.7    2.4 1969    4.72    1.9    1.7    2.4 1970    5.85    2.1    2.0    2.7 1971    6.06    2.1    2.1    2.8 1972    5.78    2.0    2.0    2.7 1973    5.35    2.1    1.9    2.6 1974    7.41    2.5    2.4    3.1 1975   11.24    3.0    3.3    4.0 1976    8.93    2.7    2.8    3.5 1977    8.77    2.8    2.7    3.4 1978   10.87    3.3    3.2    3.9 1979   10.75    3.7    3.2    3.9 1980   11.24    3.8    3.3    4.0

Notice that some conditions with earnings yields above 10% have Historical Surviving Withdrawal Rates that are less than their corresponding calculated Safe Withdrawal Rates. This happened because I based the lower confidence limit only on data with earnings yields less than 10%.

Have fun.

John R.

JWR1945
***** Legend

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

Posted: Sat Mar 12, 2005 3:07 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 = 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 =0.2449x+1.2658
where x is the percentage earnings yield
100E10/P and R-squared = 0.5017
Eyeball estimates when 100E10/P is below 10%:
Lower confidence limit = minus 0.7%
Higher confidence limit = plus 1.2%

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

 Code: 1921   5.4    13014    7254    7560 1922   4.5    11770    7641    7493 1923   3.6     9725    7987    6646 1924   3.6     8482    9048    6846 1925   3.1     7009    9406    6227 1926   2.7     5978    8374    5831 1927   2.4     6475    6917    6261 1928   1.9     6388    5355    5368 1929   1.5     5702    4269    4533 1930   1.7     6255    4070    4628 1931   2.0     6705    4652    4864 1932   3.2     7893    7016    6238 1933   3.4     8445    8298    7290 1934   2.4     6599    6963    5961 1935   2.7     6847    7901    6535 1936   2.0     5717    6227    5445 1937   1.7     5558    5195    4600 1938   2.4     6999    6272    5406 1939   2.1     6775    5854    5004 1940   2.1     7129    5968    4858 1941   2.3     8095    7169    5481 1942   3.0     9165    8114    6211 1943   3.0     8827    7708    6135 1944   2.8     8385    7216    5620 1945   2.6     8073    6602    5440 1946   2.1     7951    6092    5359 1947   2.7     8987    6887    6006 1948   2.9     8957    7171    5884 1949   3.0     8819    6865    5835 1950   2.9     8683    7180    5897 1951   2.6     7542    6634    5184 1952   2.5     6965    6092    5042 1953   2.4     6910    5653    4886 1954   2.6     6827    5795    5210 1955   2.1     5720    4679    4706 1956   1.9     5308    4117    4667 1957   2.0     5264    4344    4935 1958   2.3     5436    4698    5511 1959   1.9     4511    4059    5116 1960   1.9     4332    4368    5681 1961   1.9     4127    4681    5848 1962   1.7     3886    4462    5695 1963   1.8     4009    4805    6431 1964   1.7     3800    4854    6002 1965   1.6     3887    5137    5384 1966   1.6     4142    5241    5214 1967   1.8     4638    5891    5653 1968   1.7     4566    6121    5171 1969   1.7     4977    6191    4914 1970   2.0     6187    6446    5089 1971   2.1     6517    6432    4810 1972   2.0     6619    6362    4156 1973   1.9     7132    6052    3832 1974   2.4     8751    6947    4326 1975   3.3    10322    8125    5018 1976   2.8     9210    6921    4305 1977   2.7     9628    6275    4234 1978   3.2    10910    6884    4791 1979   3.2    11183    6852    4875 1980   3.3    11184    6604    5010

Year, SWR, At Year 20, At Year 25, At Year 30

 Code: 1921   5.4    5623    5400    5400 1922   4.5    6254    5069    4500 1923   3.6    6148    5114    3992 1924   3.6    6642    5386    4208 1925   3.1    6725    5391    4231 1926   2.7    5991    5004    3794 1927   2.4    5706    4891    3737 1928   1.9    4795    4115    3255 1929   1.5    3895    3305    2575 1930   1.7    3803    3048    2488 1931   2.0    4121    3132    2645 1932   3.2    5175    3945    3335 1933   3.4    6121    4802    4004 1934   2.4    5033    3924    3351 1935   2.7    5267    4310    3625 1936   2.0    4156    3588    2903 1937   1.7    3521    3046    2559 1938   2.4    4282    3544    3097 1939   2.1    3898    3322    2970 1940   2.1    3994    3324    3189 1941   2.3    4773    3801    4023 1942   3.0    5373    4513    4636 1943   3.0    5057    4403    4632 1944   2.8    4785    4284    4752 1945   2.6    4504    4383    5066 1946   2.1    4187    4658    5650 1947   2.7    4991    5456    6431 1948   2.9    5101    5729    6902 1949   3.0    5235    6152    6890 1950   2.9    5866    7310    7335 1951   2.6    5767    6994    6741 1952   2.5    5634    6887    6417 1953   2.4    5726    7405    6143 1954   2.6    6435    7664    5955 1955   2.1    6071    6252    4897 1956   1.9    5827    5740    4288 1957   2.0    6196    5893    3857 1958   2.3    7136    5924    3800 1959   1.9    6235    4900    3086 1960   1.9    5884    4627    2863 1961   1.9    5765    4308    2719 1962   1.7    5484    3582    2451 1963   1.8    5429    3448    2447 1964   1.7    4750    2968    2189 1965   1.6    4268    2603    2032 1966   1.6    3916    2440    1921 1967   1.8    3694    2538    2048 1968   1.7    3283    2326    1908 1969   1.7    3060    2244    1854 1970   2.0    3126    2455    2066 1971   2.1    3031    2416    2127 1972   2.0    2850    2293    2021 1973   1.9    2695    2186    1866 1974   2.4    3171    2619    2336 1975   3.3    3957    3386    3304 1976   2.8    3384    2864    2711 1977   2.7    3326    2775    2324 1978   3.2    3821    3099    2780 1979   3.2    3781    2826    2539 1980   3.3    3646    2650    2592

Have fun.

John R.

JWR1945
***** Legend

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

Posted: Sat Mar 12, 2005 3:14 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 = 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 =0.2449x+1.2658
where x is the percentage earnings yield
100E10/P and R-squared = 0.5017
Eyeball estimates when 100E10/P is below 10%:
Lower confidence limit = minus 0.7%
Higher confidence limit = plus 1.2%

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

 Code: 1921   5.4     70450     57302    19288 1922   4.5     83091     62131    56382 1923   3.6     98427     62902    58673 1924   3.6    134412     83494    70716 1925   3.1    126320     76057    74833 1926   2.7    111572     90515    68109 1927   2.4     86661    103907    60142 1928   1.9     70058     75452    52675 1929   1.5     67768     64786    44584 1930   1.7     62712     64922    44188 1931   2.0     82597     63509    51544 1932   3.2    115051     62990    44686 1933   3.4    104731     70215    48922 1934   2.4     94998     64750    45200 1935   2.7    104800     72827    50259 1936   2.0     80256     70210    46295 1937   1.7     60600     51574    42027 1938   2.4     70316     53090    45855 1939   2.1     69781     50526    44513 1940   2.1     71909     52330    53902 1941   2.3     89704     61476    68933 1942   3.0     85099     69335    72933 1943   3.0     78018     71055    67488 1944   2.8     73756     66800    77914 1945   2.6     74404     79042    80146 1946   2.1     71338     83886    80405 1947   2.7     86042     96469    98186 1948   2.9     95894     96682   102399 1949   3.0     93935    114082   112572 1950   2.9    110637    117026   124265 1951   2.6    117587    112708   125099 1952   2.5    114221    118580   115298 1953   2.4    104036    113920   120876 1954   2.6    125143    127565   126816 1955   2.1    107615    116400   100029 1956   1.9     97335    109779    89222 1957   2.0    105238    103781    91353 1958   2.3    109568    116334   101342 1959   1.9    103104    103745    76241 1960   1.9    108595     93725    59602 1961   1.9    112830     91745    63564 1962   1.7     99428     88381    58215 1963   1.8    107764     95617    51362 1964   1.7    101360     75200    44317 1965   1.6     87031     55995    38277 1966   1.6     81921     57388    34940 1967   1.8     88642     58134    29504 1968   1.7     88807     47776    28408 1969   1.7     74469     44188    27157 1970   2.0     63962     43242    25829 1971   2.1     69390     41478    25278 1972   2.0     65722     33500    26973 1973   1.9     54221     32765    24734 1974   2.4     59352     36497    27150 1975   3.3     67053     39336    28999 1976   2.8     61041     38933    27540 1977   2.7     52723     45370    34292 1978   3.2     61726     48409    39364 1979   3.2     65486     54298    47010 1980   3.3     66756     61913    50503

Year, SWR, At Year 20, At Year 25, At Year 30

 Code: 1921   5.4   (10931)  (56502) (101892) 1922   4.5    19176    (3594)  (33958) 1923   3.6    32091    13286    (4592) 1924   3.6    39217    17331      319 1925   3.1    46352    25664    14558 1926   2.7    53035    28113    20097 1927   2.4    47439    33818    29261 1928   1.9    39319    33300    28709 1929   1.5    31600    26918    29111 1930   1.7    29456    26366    21317 1931   2.0    29782    25704    15552 1932   3.2    24884    11128    (7335) 1933   3.4    36282    24841    12679 1934   2.4    37546    39241    31707 1935   2.7    47736    42183    35184 1936   2.0    49383    42405    41286 1937   1.7    44215    41792    36426 1938   2.4    40649    36570    29924 1939   2.1    50243    45366    38868 1940   2.1    52797    51185    38454 1941   2.3    62800    65867    48910 1942   3.0    68922    60057    44492 1943   3.0    66659    62632    45639 1944   2.8    73337    66424    41715 1945   2.6    81102    64477    36045 1946   2.1    89247    71195    47903 1947   2.7    93458    78699    47364 1948   2.9   104772    86943    41211 1949   3.0   107950    74204    37350 1950   2.9   104626    64178    39877 1951   2.6    99795    67144    37674 1952   2.5    99754    62911    29311 1953   2.4   105212    54655    30091 1954   2.6    91710    51471    27902 1955   2.1    63223    41773    23698 1956   1.9    61773    36763    22182 1957   2.0    59255    29388    22303 1958   2.3    52722    29126    18170 1959   1.9    44141    25738    17182 1960   1.9    39851    23231    16894 1961   1.9    37880    22928    14585 1962   1.7    29809    24226    16461 1963   1.8    30445    22156    15627 1964   1.7    26852    19416    13048 1965   1.6    23407    18750    11718 1966   1.6    22164    15517    11099 1967   1.8    23543    15396     9148 1968   1.7    20800    14860    10873 1969   1.7    20182    14388    12212 1970   2.0    19765    11058     6919 1971   2.1    16321     9295     2043 1972   2.0    17979    11291     4396 1973   1.9    18777    15850     8421 1974   2.4    19395    16543     4465 1975   3.3    14609     5196    (9038) 1976   2.8    20187    14793    (1020) 1977   2.7    28672    23253     5356 1978   3.2    37920    25777     5405 1979   3.2    56856    35106    12320 1980   3.3    70323    38014    13722

This completes the 50% stock data when the slope is 1.0.

Have fun.

John R.

JWR1945
***** Legend

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

 Posted: Mon Mar 14, 2005 8:30 am    Post subject: Using both Initial and Current Valuationsâ€”50% Stocksâ€”lar 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. My latest investigation 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 5.0%. That is, I make part of my withdrawals equal to (0.25)*(100E10/P-5.0%)*(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 5.0%. Applying the numbers The curve for the 30-year Calculated Rate is HSWR = 0.3859x+2.7967 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 0.9%. Higher confidence limit = plus 1.5%. In addition, R-squared = 0.6488. The Safe Withdrawal Rate is the lower confidence limit of the Calculated Rate. Its formula is: SWR = (0.3859x+2.7967) - 0.9. Applying today's earnings yield, which is close to 3.5%, to this equation, the standard portion of withdrawals is 3.247% of the portfolio's initial balance (plus inflation). Applying today's earnings yield to Algorithm G1, we will put back 0.375% of the portfolio's current balance (since 0.25*(3.5%-5.0%) = (0.25)*(-1.5) = -0.375%. That is, a negative withdrawal of (0.375%) is the same as making a deposit of plus 0.375%. For a person beginning retirement today, his total withdrawal amount would be 3.247-0.375 = 2.872% since the current balance starts out equal to the initial balance. Rounded, this becomes 2.9%. This is less than 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. 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% The withdrawal amount varies when using the new algorithm. The variable part can be written as (slope term of 0.25)*(100E10/P-2.5%-2.5%) = (0.25)*(100E10/P-2.5%) - 0.625%. We have been looking at the first part of this all along: (0.25)*(100E10/P-2.5%). We are now reducing the amount withdrawn by 0.6% (more precisely, 0.625%) of the portfolio's current balance. My confidence limits were determined from data with earnings yield less than 10%. Among such conditions, there were no failures [if we exclude the effect of dummy data for 2003-2010]. 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, but not the large amounts that I chose. Data Analysis The lowest (five-year average of the) withdrawal amount occurred at year 30 of the 1966 historical sequence. It was \$3479. The amount started at \$3550 and briefly exceeded 4.2% (of the initial balance of \$100000). The lowest balance in the 1966 sequence (in five-year increments) was \$28754 at year 30. Among conditions with earnings yields starting below 10% (and at valid data points), the lowest balances were all above \$20000. Among those conditions with earnings yields less than 10% and not contaminated by dummy data (2003-2010), the lowest balances at year 20 occurred in 1965, 1968, 1970, 1971 and 1972. The lowest was \$37682 in 1971. The others were between \$40000 and \$41000. The highest balance (in five-year increments) was \$165721 at year 15 of the 1950 sequence. This was not because withdrawal amounts were unduly limited. In that particular sequence, withdrawals started at \$6295. 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. In terms of today's valuations, moving the offset from minus 2.5% to 5.0% has reduced the initial withdrawal amount. It has also extended the life of the portfolio since the relevant balances at year 30 were above \$20000. [Portfolios with relevant balances start out with earnings yields below 10%. They are not contaminated by dummy data.] Reflecting on these numbers and today's valuations, this approach is a comfortable alternative to dividend-based strategies. Using this approach, withdrawals would start out today at 2.9% of the initial balance. Have fun. John R.
JWR1945
***** Legend

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

Posted: Mon Mar 14, 2005 8:33 am    Post subject:

2% TIPS

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 (5.0) or minus 5.0% in cell B17

Stocks = 50%
TIPS at a 2% interest rate = 50%
With Rebalancing
Historical Surviving Withdrawal Rates are determined by varying the rates in cell B9.

1923-1980 HSWR Curve Fit Equation:
HSWR = 0.3859x+2.7967
where x is the percentage earnings yield
100E10/P and R-squared = 0.5017
Eyeball estimates when 100E10/P is below 10%:
Lower confidence limit = minus 0.7%
Higher confidence limit = plus 1.2%
SWR = 0.3859x+2.7967-0.7

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

 Code: 1921   19.61    6.5    9.5   10.4 1922   15.87    7.0    8.0    8.9 1923   12.20    6.7    6.6    7.5 1924   12.35    6.8    6.7    7.6 1925   10.31    6.7    5.9    6.8 1926    8.85    6.0    5.3    6.2 1927    7.58    5.9    4.8    5.7 1928    5.32    5.2    3.9    4.8 1929    3.69    4.3    3.3    4.2 1930    4.48    4.3    3.6    4.5 1931    5.99    4.6    4.2    5.1 1932   10.75    5.7    6.0    6.9 1933   11.49    6.8    6.3    7.2 1934    7.69    5.8    4.9    5.8 1935    8.70    6.3    5.3    6.2 1936    5.85    5.3    4.2    5.1 1937    4.63    4.6    3.7    4.6 1938    7.41    5.5    4.8    5.7 1939    6.41    5.3    4.4    5.3 1940    6.10    5.5    4.2    5.1 1941    7.19    6.6    4.7    5.6 1942    9.90    7.4    5.7    6.6 1943    9.80    7.1    5.7    6.6 1944    9.01    6.8    5.4    6.3 1945    8.33    6.6    5.1    6.0 1946    6.41    6.8    4.4    5.3 1947    8.70    7.5    5.3    6.2 1948    9.62    7.6    5.6    6.5 1949    9.80    7.4    5.7    6.6 1950    9.35    7.9    5.5    6.4 1951    8.40    7.2    5.1    6.0 1952    8.00    6.7    5.0    5.9 1953    7.69    6.6    4.9    5.8 1954    8.33    6.7    5.1    6.0 1955    6.25    5.7    4.3    5.2 1956    5.46    5.2    4.0    4.9 1957    5.99    5.3    4.2    5.1 1958    7.25    5.6    4.7    5.6 1959    5.56    4.8    4.0    4.9 1960    5.46    4.7    4.0    4.9 1961    5.41    4.7    4.0    4.9 1962    4.72    4.4    3.7    4.6 1963    5.18    4.6    3.9    4.8 1964    4.63    4.2    3.7    4.6 1965    4.29    4.0    3.6    4.5 1966    4.15    3.9    3.5    4.4 1967    4.90    4.2    3.8    4.7 1968    4.65    4.1    3.7    4.6 1969    4.72    4.1    3.7    4.6 1970    5.85    4.4    4.2    5.1 1971    6.06    4.4    4.2    5.1 1972    5.78    4.3    4.1    5.0 1973    5.35    4.4    4.0    4.9 1974    7.41    5.2    4.8    5.7 1975   11.24    6.0    6.2    7.1 1976    8.93    5.4    5.3    6.2 1977    8.77    5.5    5.3    6.2 1978   10.87    6.2    6.1    7.0 1979   10.75    6.5    6.0    6.9 1980   11.24    6.6    6.2    7.1

Have fun.

John R.

JWR1945
***** Legend

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

Posted: Mon Mar 14, 2005 8:36 am    Post subject:

TIPS at 2% Interest

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 (5.0) or minus 5.0% in cell B17

Stocks = 50%
TIPS at a 2% interest rate = 50%
With Rebalancing
Historical Surviving Withdrawal Rates are determined by varying the rates in cell B9.

1923-1980 HSWR Curve Fit Equation:
HSWR = 0.3859x+2.7967
where x is the percentage earnings yield
100E10/P and R-squared = 0.5017
Eyeball estimates when 100E10/P is below 10%:
Lower confidence limit = minus 0.7%
Higher confidence limit = plus 1.2%
SWR = 0.3859x+2.7967-0.7

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

 Code: 1921   9.5   11047    9573    9897 1922   8.0    9342    8243    8519 1923   6.6    7592    7166    7037 1924   6.7    7255    7514    7101 1925   5.9    6136    6974    6203 1926   5.3    5393    6262    5638 1927   4.8    5081    5443    5394 1928   3.9    4410    4324    4506 1929   3.3    3884    3616    3881 1930   3.6    4333    3814    4199 1931   4.2    4968    4471    4765 1932   6.0    6624    6518    6557 1933   6.3    6844    7021    7030 1934   4.9    5314    5632    5578 1935   5.3    5618    6189    6055 1936   4.2    4530    4922    4923 1937   3.7    4181    4296    4312 1938   4.8    5421    5455    5408 1939   4.4    5094    5055    4980 1940   4.2    5012    4924    4740 1941   4.7    5626    5670    5250 1942   5.7    6652    6692    6179 1943   5.7    6586    6560    6139 1944   5.4    6258    6176    5700 1945   5.1    5961    5738    5365 1946   4.4    5385    4969    4709 1947   5.3    6342    5820    5535 1948   5.6    6557    6108    5694 1949   5.7    6583    6049    5727 1950   5.5    6295    5843    5433 1951   5.1    5686    5410    4941 1952   5.0    5464    5207    4866 1953   4.9    5357    4985    4729 1954   5.1    5431    5126    4933 1955   4.3    4552    4252    4250 1956   4.0    4234    3881    4061 1957   4.2    4372    4089    4309 1958   4.7    4775    4552    4852 1959   4.0    4020    3874    4258 1960   4.0    3958    3956    4450 1961   4.0    3889    4056    4540 1962   3.7    3602    3796    4320 1963   3.9    3768    4038    4737 1964   3.7    3581    3945    4542 1965   3.6    3560    4008    4361 1966   3.5    3550    3990    4285 1967   3.8    3897    4425    4722 1968   3.7    3830    4486    4567 1969   3.7    3952    4572    4540 1970   4.2    4675    5086    5024 1971   4.2    4775    5115    4950 1972   4.1    4776    5098    4661 1973   4.0    4892    5001    4480 1974   4.8    5960    5928    5250 1975   6.2    7467    7363    6524 1976   5.3    6496    6293    5548 1977   5.3    6674    6091    5510 1978   6.1    7644    6844    6252 1979   6.0    7602    6670    6089 1980   6.2    7758    6692    6247

Year, SWR, At Year 20, At Year 25, At Year 30

 Code: 1921   9.5    9501    9500    9500 1922   8.0    8300    8138    8000 1923   6.6    7112    7030    6832 1924   6.7    7315    7148    6927 1925   5.9    6711    6530    6288 1926   5.3    6003    5930    5591 1927   4.8    5526    5530    5138 1928   3.9    4571    4572    4257 1929   3.3    3867    3824    3509 1930   3.6    4107    3954    3735 1931   4.2    4711    4439    4296 1932   6.0    6432    6122    6016 1933   6.3    6932    6567    6339 1934   4.9    5484    5110    4916 1935   5.3    5829    5503    5268 1936   4.2    4590    4395    4109 1937   3.7    3992    3826    3624 1938   4.8    5090    4849    4719 1939   4.4    4617    4417    4305 1940   4.2    4426    4158    4156 1941   4.7    4992    4549    4779 1942   5.7    5910    5570    5823 1943   5.7    5779    5552    5844 1944   5.4    5423    5259    5672 1945   5.1    5051    5049    5596 1946   4.4    4236    4489    5293 1947   5.3    5145    5457    6328 1948   5.6    5412    5796    6789 1949   5.7    5528    6049    6875 1950   5.5    5430    6252    6965 1951   5.1    5182    5911    6441 1952   5.0    5132    5854    6275 1953   4.9    5080    6005    6144 1954   5.1    5446    6296    6250 1955   4.3    4827    5301    5265 1956   4.0    4593    4965    4821 1957   4.2    4901    5239    4787 1958   4.7    5605    5662    5123 1959   4.0    4881    4827    4313 1960   4.0    4839    4778    4221 1961   4.0    4856    4696    4167 1962   3.7    4620    4221    3835 1963   3.9    4826    4336    3986 1964   3.7    4500    4009    3737 1965   3.6    4308    3802    3618 1966   3.5    4151    3662    3479 1967   3.8    4317    3931    3755 1968   3.7    4105    3779    3626 1969   3.7    4031    3741    3577 1970   4.2    4435    4221    4063 1971   4.2    4382    4178    4037 1972   4.1    4243    4051    3921 1973   4.0    4097    3895    3705 1974   4.8    4857    4616    4452 1975   6.2    6229    6047    6133 1976   5.3    5267    5039    5072 1977   5.3    5218    4964    4954 1978   6.1    5934    5622    5763 1979   6.0    5651    5225    5462 1980   6.2    5678    5390    5757

Have fun.

John R.

JWR1945
***** Legend

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

Posted: Mon Mar 14, 2005 8:43 am    Post subject:

TIPS at 2% Interest

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 (5.0) or minus 5.0% in cell B17

Stocks = 50%
TIPS at a 2% interest rate = 50%
With Rebalancing
Historical Surviving Withdrawal Rates are determined by varying the rates in cell B9.

1923-1980 HSWR Curve Fit Equation:
HSWR = 0.3859x+2.7967
where x is the percentage earnings yield
100E10/P and R-squared = 0.5017
Eyeball estimates when 100E10/P is below 10%:
Lower confidence limit = minus 0.7%
Higher confidence limit = plus 1.2%
SWR = 0.3859x+2.7967-0.7

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

 Code: 1921   9.5     86398     66579     14495 1922   8.0     99934     78724     79705 1923   6.6    114415     82248     86090 1924   6.7    145981    103604     95968 1925   5.9    133212     95363    102175 1926   5.3    115203    109949     90122 1927   4.8     92619    126434     83858 1928   3.9     78953     94991     78010 1929   3.3     77934     82019     66890 1930   3.6     73715     81893     66432 1931   4.2     95672     78656     73881 1932   6.0    126535     75591     59903 1933   6.3    113825     86349     70315 1934   4.9    102295     79937     65055 1935   5.3    111252     90461     74004 1936   4.2     86056     87489     69192 1937   3.7     67100     65621     63523 1938   4.8     78557     67757     68475 1939   4.4     79329     66060     67742 1940   4.2     84553     73273     89433 1941   4.7    105370     87770    114992 1942   5.7     98801     97122    117837 1943   5.7     89669     96261    103845 1944   5.4     84875     89462    115486 1945   5.1     86156    104361    116518 1946   4.4     85008    113874    121987 1947   5.3    101755    128210    144304 1948   5.6    111357    125132    143221 1949   5.7    107729    142405    149877 1950   5.5    125793    145951    165721 1951   5.1    130469    136158    158737 1952   5.0    124354    138041    139721 1953   4.9    113059    130250    142890 1954   5.1    133842    142805    146938 1955   4.3    114602    128401    115098 1956   4.0    103562    119747    102478 1957   4.2    110719    111751    103581 1958   4.7    113246    121876    111342 1959   4.0    105997    108260     84973 1960   4.0    110876     98196     69215 1961   4.0    114302     96448     75322 1962   3.7    100984     93661     71007 1963   3.9    109051    101378     65093 1964   3.7    102526     80898     58014 1965   3.6     88641     62560     51532 1966   3.5     84860     66849     50471 1967   3.8     92478     69786     45978 1968   3.7     92819     59441     45865 1969   3.7     79353     57483     46117 1970   4.2     70558     58092     45195 1971   4.2     78364     58609     47364 1972   4.1     75510     49806     50320 1973   4.0     64851     51220     47315 1974   4.8     72955     59286     54003 1975   6.2     81510     62199     54193 1976   5.3     75628     62389     51409 1977   5.3     67375     70592     59690 1978   6.1     79299     73718     65829 1979   6.0     84871     82496     78420 1980   6.2     85347     88994     77538

Year, SWR, At Year 20, At Year 25, At Year 30

 Code: 1921   9.5    (38056)  (125732)  (209116) 1922   8.0     29669    (6846)   (61004) 1923   6.6     56567     33783     9372 1924   6.7     62790     35676    11429 1925   5.9     77788     56939    52964 1926   5.3     84182     57664    57325 1927   4.8     80537     75793    87313 1928   3.9     71880     80226    90369 1929   3.3     57974     62892    83750 1930   3.6     54147     60686    61969 1931   4.2     51142     51792    38190 1932   6.0     37339     15655   (19079) 1933   6.3     64190     55148    42273 1934   4.9     64425     77214    71953 1935   5.3     83396     85739    83993 1936   4.2     85263     83657    90938 1937   3.7     75719     80174    76883 1938   4.8     68548     68149    61727 1939   4.4     84738     83550    78065 1940   4.2    100650    110508    96744 1941   4.7    120513    141127   122610 1942   5.7    127326    125047   111822 1943   5.7    113549    117238   101025 1944   5.4    118298    116054    85904 1945   5.1    126767    109762    74767 1946   4.4    146116    130271   110119 1947   5.3    148243    140460   110014 1948   5.6    155990    144779    92706 1949   5.7    151839    117831    81953 1950   5.5    150799    110474    97043 1951   5.1    137186    111034    87832 1952   5.0    129971     98986    66332 1953   4.9    133863     87061    69119 1954   5.1    116511     84285    67451 1955   4.3     82561     69993    57434 1956   4.0     81755     63112    53991 1957   4.2     78447     52031    53079 1958   4.7     69376     50729    40907 1959   4.0     60357     46669    39089 1960   4.0     56882     44099    39546 1961   4.0     55983     44709    34826 1962   3.7     47185     48292    39271 1963   3.9     50475     45255    37981 1964   3.7     45680     39506    30835 1965   3.6     40127     36264    24465 1966   3.5     41508     34027    28754 1967   3.8     46357     36719    28928 1968   3.7     40784     33716    29387 1969   3.7     41152     34076    34598 1970   4.2     40779     27414    24147 1971   4.2     37682     29869    22671 1972   4.1     40003     31766    21131 1973   4.0     41813     41486    26872 1974   4.8     46362     50293    23426 1975   6.2     33583     23210    (7670) 1976   5.3     43897     38961     5150 1977   5.3     53485     44418     8368 1978   6.1     66507     44367     5788 1979   6.0     99417     60085    17236 1980   6.2    107881     53158    11623

This completes the 50% stock data with a slope of 0.25 and an offset of (5.0%).

Have fun.

John R.

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