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Using both Initial and Current Valuations
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JWR1945
***** Legend


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

PostPosted: Fri Mar 11, 2005 9:46 am    Post subject: Reply with quote

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.


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Mike
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Joined: 06 Jul 2003
Posts: 278

PostPosted: Fri Mar 11, 2005 7:56 pm    Post subject: Reply with quote

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.


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

PostPosted: Sat Mar 12, 2005 2:52 pm    Post subject: Using both Initial and Current Valuations—High Variability--50% Reply with quote

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.


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

PostPosted: Sat Mar 12, 2005 3:02 pm    Post subject: Reply with quote

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.


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JWR1945
***** Legend


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

PostPosted: Sat Mar 12, 2005 3:07 pm    Post subject: Reply with quote

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.


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

PostPosted: Sat Mar 12, 2005 3:14 pm    Post subject: Reply with quote

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.


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

PostPosted: Mon Mar 14, 2005 8:30 am    Post subject: Using both Initial and Current Valuations—50% Stocks—lar Reply with quote

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.


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

PostPosted: Mon Mar 14, 2005 8:33 am    Post subject: Reply with quote

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.


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JWR1945
***** Legend


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

PostPosted: Mon Mar 14, 2005 8:36 am    Post subject: Reply with quote

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.


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View user's profile Send private message
JWR1945
***** Legend


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

PostPosted: Mon Mar 14, 2005 8:43 am    Post subject: Reply with quote

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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