Withdrawal Amount Relationships

Research on Safe Withdrawal Rates

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JWR1945
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Withdrawal Amount Relationships

Post by JWR1945 »

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.
JWR1945
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Post by JWR1945 »

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.

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
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.

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
Have fun.

John R.
Mike
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Post by Mike »

Are the year 20 withdrawal amounts inflation adjusted back to year one?
JWR1945
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Joined: Tue Nov 26, 2002 3:59 am
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Post by JWR1945 »

Mike wrote:Are the year 20 withdrawal amounts inflation adjusted back to year one?
Yes. All dollar amounts are inflation adjusted (back to the initial balance of $100000).

Have fun.

John R.
JWR1945
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Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

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.
These comparisons might be more meaningful if we solve for a (five-year average) withdrawal amount of $4000 at year 20.

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.
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