Page 2 of 2
Posted: Fri Mar 11, 2005 9:46 am
by JWR1945
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: Select all
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: Select all
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.
Posted: Fri Mar 11, 2005 7:56 pm
by Mike
2.4 - 2.9% and soldier on.
Indeed, you play the hand you're dealt.
For most of us.
Yes, the majority cannot outperform themselves.
Observe that the Safe and Calculated Rates are higher with 50% stocks than with 80% stocks at today's valuations.
Using both Initial and Current Valuationsâ€â€High Variability--50%
Posted: Sat Mar 12, 2005 2:52 pm
by JWR1945
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.
Posted: Sat Mar 12, 2005 3:02 pm
by JWR1945
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: Select all
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.
Posted: Sat Mar 12, 2005 3:07 pm
by JWR1945
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: Select all
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: Select all
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.
Posted: Sat Mar 12, 2005 3:14 pm
by JWR1945
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: Select all
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: Select all
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.
Using both Initial and Current Valuationsâ€â€50% Stocksâ€â€lar
Posted: Mon Mar 14, 2005 8:30 am
by JWR1945
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.
Posted: Mon Mar 14, 2005 8:33 am
by JWR1945
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: Select all
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.
Posted: Mon Mar 14, 2005 8:36 am
by JWR1945
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: Select all
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: Select all
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.
Posted: Mon Mar 14, 2005 8:43 am
by JWR1945
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: Select all
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: Select all
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.