I have collected data to show the relationship between withdrawing percentage of an initial balance and withdrawing a percentage of the current balance.
I used our standard portfolios HDBR50 and HDBR80 for these comparisons. HDBR50 consists of 50% stocks and 50% commercial paper with expenses at 0.20%. HDBR80 consists of 80% stocks and 20% commercial paper with expenses at 0.20%. Withdrawals are a percentage of the initial balance along with adjustments to match inflation. The 30-year Historical Surviving Withdrawal Rates (formerly, Historical Database Rates) form the x-axis. Balances are zero or higher at the Historical Surviving Withdrawal Rates for each of the first 30 years. Balances are negative when the withdrawal rate is increase by 0.1%.
In these calculations, the initial balances were all $100000.
The y-axes are the 5-year rolling average withdrawal amounts at year 20 for similar portfolios but with withdrawals equal to 5% of the current balances. In one case, the holding other than stocks consists of TIPS at a 2% interest rate. In the other, the holding other than stocks consists of commercial paper. The stock allocations are 50% for comparisons with HDBR50 and 80% stocks for comparisons with HDBR80.
For each year that begins a sequence, there is a value for the x-axis, the Historical Surviving Withdrawal Rate for that year [for portfolios HDBR50 and HDBR80], and the corresponding withdrawal amounts at year 20 [using portfolios with 50% or 80% stocks and with either 2% TIPS or with commercial paper].
Here are the equations of the best straight-line curve fits:
1) When x is with HDBR50, the withdrawal amount y = 968.74*HDBR50-597.96 and R-squared equals 0.5519 with 2% TIPS.
2) When x is with HDBR50, the withdrawal amount y = 1284.9*HDBR50-2726.6 and R-squared equals 0.8623 with commercial paper.
3) When x is with HDBR80, the withdrawal amount y = 1420.8*HDBR80-3085 and R-squared equals 0.7578 with 2% TIPS.
4) When x is with HDBR80, the withdrawal amount y = 1432.2*HDBR80-3367.7 and R-squared equals 0.81 with commercial paper.
Curve fits are better when the stock allocations are higher (80%) and when commercial paper is selected instead of TIPS. This is seen in the higher values of R-squared. A high percentage of stocks reduces the influence of the other component. The comparisons come close to being strictly for stocks, but with different withdrawal rates. The curve fit is better when the non-stock component is commercial paper because the baseline portfolios, HDBR50 and HDBR80, both use commercial paper.
When withdrawals are a constant percentage of a portfolio's current balance, the portfolio will never be depleted although it can become low. With a 5% withdrawal rate, the minimum withdrawal amounts occur around year 20. Portfolio balances recover any losses and rise by year 30. In effect, a portfolio withdrawal of 5% of the current balance will grow enough to last indefinitely.
When withdrawals are based on a portfolio's initial balance, decreasing withdrawals by 0.1% to 0.2% can extend the portfolio's lifetime by a decade. Decreasing withdrawals by 0.3% extends the lifetime by two decades.
Now look at the equations and solve them for a (five-year average) withdrawal amount of $5000 at year 20.
With 50% stocks, a sequence that has an HDBR50 value of 5.8% would produce $5000 at year 20 when using 2% TIPS. It would take a sequence with an HDBR50 value of 6.0% to produce $5000 at year 20 when using commercial paper.
With 80% stocks, a sequence that has an HDBR80 value of 5.7% would produce $5000 at year 20 when using 2% TIPS. It would take a sequence with an HDBR80 value of 5.8% to produce $5000 at year 20 when using commercial paper.
By withdrawing a fixed percentage of a portfolio's current balance, there will be some years with higher withdrawals than in the first. To guarantee a minimum withdrawal amount (in this case 5.0% of the initial balance) at year 20 requires compensation for such excess withdrawals. The total adjustment turns out to be 0.7% to 1.0%. Part of this is to extend the portfolio's lifetime. This accounts for at least 0.4%, possibly more. The remaining adjustment (of up to 0.3% to 0.6%) is to guarantee the minimum at year 20.
Data tables follow.
Have fun.
John R.
Withdrawal Amount Relationships
Moderator: hocus2004
Initial balances are all $100000. The amounts withdrawn correspond to 5% of a portfolio's current balance.
Year, P/E10, 100E10/P, HDBR50 Historical Surviving Withdrawal Rate, Amount Withdrawn at Year 20 with 2% TIPS, Amount Withdrawn at Year 20 with Commercial Paper.
Year, P/E10, 100E10/P, HDBR80 Historical Surviving Withdrawal Rate, Amount Withdrawn at Year 20 with 2% TIPS, Amount Withdrawn at Year 20 with Commercial Paper.
Have fun.
John R.
Year, P/E10, 100E10/P, HDBR50 Historical Surviving Withdrawal Rate, Amount Withdrawn at Year 20 with 2% TIPS, Amount Withdrawn at Year 20 with Commercial Paper.
Code: Select all
1921 5.1 19.61 8.1 6451 8270
1922 6.3 15.87 8.0 6341 7509
1923 8.2 12.20 7.5 5624 6433
1924 8.1 12.35 7.6 5399 6038
1925 9.7 10.31 7.3 4997 5366
1926 11.3 8.85 6.6 4450 4638
1927 13.2 7.58 6.4 4417 4357
1928 18.8 5.32 5.5 3881 3639
1929 27.1 3.69 4.5 3280 2905
1930 22.3 4.48 4.4 3269 2763
1931 16.7 5.99 4.5 3447 2683
1932 9.3 10.75 5.1 4303 3015
1933 8.7 11.49 5.7 5198 3410
1934 13.0 7.69 4.8 4516 2971
1935 11.5 8.70 5.2 5065 3371
1936 17.1 5.85 4.3 4525 3025
1937 21.6 4.63 3.9 4268 2888
1938 13.5 7.41 4.6 5233 3569
1939 15.6 6.41 4.4 5267 3579
1940 16.4 6.10 4.5 5674 3859
1941 13.9 7.19 5.4 6843 4712
1942 10.1 9.90 6.2 7575 5550
1943 10.2 9.80 6.1 7290 5561
1944 11.1 9.01 5.9 6944 5407
1945 12.0 8.33 5.7 6731 5335
1946 15.6 6.41 5.9 6997 5645
1947 11.5 8.70 7.1 7717 6888
1948 10.4 9.62 7.4 7564 7141
1949 10.2 9.80 7.3 7262 6939
1950 10.7 9.35 7.6 7409 7061
1951 11.9 8.40 7.1 6403 6330
1952 12.5 8.00 6.7 5765 5807
1953 13.0 7.69 6.5 5531 5574
1954 12.0 8.33 6.6 5359 5441
1955 16.0 6.25 5.6 4328 4369
1956 18.3 5.46 5.2 3853 3848
1957 16.7 5.99 5.3 3771 3753
1958 13.8 7.25 5.7 3741 3737
1959 18.0 5.56 4.9 3085 3033
1960 18.3 5.46 4.9 3038 2934
1961 18.5 5.41 4.8 2982 2870
1962 21.2 4.72 4.6 2748 2631
1963 19.3 5.18 4.8 2842 2726
1964 21.6 4.63 4.4 2679 2586
1965 23.3 4.29 4.2 2641 2568
1966 24.1 4.15 4.1 2691 2640
1967 20.4 4.90 4.4 3040 3025
1968 21.5 4.65 4.3 3108 3125
1969 21.2 4.72 4.3 3251 3279
1970 17.1 5.85 4.7 3663 3713
1971 16.5 6.06 4.8 3757 3865
1972 17.3 5.78 4.7 3744 3882
1973 18.7 5.35 4.7 3888 3998
1974 13.5 7.41 5.6 4707 4848
1975 8.9 11.24 6.7 5435 5787
1976 11.2 8.93 6.0 4937 5320
1977 11.4 8.77 6.2 5193 5652
1978 9.2 10.87 7.0 6139 6740
1979 9.3 10.75 7.3 6829 7558
1980 8.9 11.24 7.4 7375 8383
Code: Select all
1921 5.1 19.61 9.8 9772 10839
1922 6.3 15.87 9.9 8926 9599
1923 8.2 12.20 8.9 7260 7701
1924 8.1 12.35 9.2 6928 7282
1925 9.7 10.31 8.5 6027 6230
1926 11.3 8.85 7.5 5198 5305
1927 13.2 7.58 7.2 5103 5096
1928 18.8 5.32 5.8 4170 4084
1929 27.1 3.69 4.4 3197 3063
1930 22.3 4.48 4.5 3303 3104
1931 16.7 5.99 5.0 3677 3337
1932 9.3 10.75 6.9 5281 4572
1933 8.7 11.49 8.0 6585 5551
1934 13.0 7.69 6.2 5314 4484
1935 11.5 8.70 7.1 6442 5465
1936 17.1 5.85 5.4 5422 4607
1937 21.6 4.63 4.5 4993 4262
1938 13.5 7.41 6.0 7081 6066
1939 15.6 6.41 5.6 7083 6058
1940 16.4 6.10 5.8 7833 6701
1941 13.9 7.19 7.3 9988 8588
1942 10.1 9.90 9.0 12010 10599
1943 10.2 9.80 8.7 11551 10354
1944 11.1 9.01 8.1 10729 9693
1945 12.0 8.33 7.7 10222 9299
1946 15.6 6.41 7.4 10056 9208
1947 11.5 8.70 9.5 12388 11843
1948 10.4 9.62 10.2 12628 12347
1949 10.2 9.80 10.0 12073 11860
1950 10.7 9.35 10.3 11803 11584
1951 11.9 8.40 9.2 9596 9549
1952 12.5 8.00 8.5 8308 8327
1953 13.0 7.69 8.2 7744 7763
1954 12.0 8.33 8.4 7451 7492
1955 16.0 6.25 6.6 5349 5367
1956 18.3 5.46 5.7 4390 4386
1957 16.7 5.99 5.9 4207 4196
1958 13.8 7.25 6.5 4187 4182
1959 18.0 5.56 5.2 3089 3064
1960 18.3 5.46 5.1 2991 2945
1961 18.5 5.41 5.1 2925 2876
1962 21.2 4.72 4.6 2565 2516
1963 19.3 5.18 4.9 2694 2645
1964 21.6 4.63 4.4 2458 2420
1965 23.3 4.29 4.0 2375 2346
1966 24.1 4.15 3.9 2414 2393
1967 20.4 4.90 4.4 2920 2911
1968 21.5 4.65 4.1 3006 3009
1969 21.2 4.72 4.1 3189 3195
1970 17.1 5.85 4.8 3883 3897
1971 16.5 6.06 4.8 4079 4118
1972 17.3 5.78 4.6 4045 4096
1973 18.7 5.35 4.6 4157 4196
1974 13.5 7.41 5.9 5603 5658
1975 8.9 11.24 7.8 7326 7509
1976 11.2 8.93 6.6 6355 6543
1977 11.4 8.77 6.6 6821 7051
1978 9.2 10.87 7.9 8813 9145
1979 9.3 10.75 8.2 10187 10603
1980 8.9 11.24 8.2 11598 12200
John R.
These comparisons might be more meaningful if we solve for a (five-year average) withdrawal amount of $4000 at year 20.Now look at the equations and solve them for a (five-year average) withdrawal amount of $5000 at year 20.
With 50% stocks, a sequence that has an HDBR50 value of 5.8% would produce $5000 at year 20 when using 2% TIPS. It would take a sequence with an HDBR50 value of 6.0% to produce $5000 at year 20 when using commercial paper.
With 80% stocks, a sequence that has an HDBR80 value of 5.7% would produce $5000 at year 20 when using 2% TIPS. It would take a sequence with an HDBR80 value of 5.8% to produce $5000 at year 20 when using commercial paper.
With 50% stocks, a sequence that has an HDBR50 value of 4.7% would produce $4000 at year 20 when using 2% TIPS. It would take a sequence with an HDBR50 value of 5.2% to produce $4000 at year 20 when using commercial paper.
With 80% stocks, a sequence that has an HDBR80 value of 5.0% would produce $4000 at year 20 when using 2% TIPS. It would take a sequence with an HDBR80 value of 5.1% to produce $4000 at year 20 when using commercial paper.
The excess in the (calculated) initial withdrawal rate to guarantee a withdrawal amount of $4000 at year 20 ranges from 0.7% to 1.2%. This is because withdrawals are based upon current balances instead of only on the initial balance. This excess is the price of the guaranteed minimum. [This is a guarantee only in terms of calculated rates. I have not included the confidence limits that would be necessary to provide true safety.]
Have fun.
John R.