## A Second Survey using Minimum Balances

Research on Safe Withdrawal Rates

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JWR1945
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A Second Survey using Minimum Balances
I have collected these numbers easily using my latest calculator update, which I call the Deluxe Calculator V1.1A02. It is available for downloading from the special SWR Research area. It replaces Deluxe Calculator V1.0A and V1.1A.

I have added numerous data summaries similar to what was already available in rows 1 through 9 and columns L through P. The PORTFOLIO BALANCE data summary box is in columns V through Z. The range of years is still specified in cells M1 and M2. I looked at the TOTAL AMOUNT WITHDRAWN in columns AB through AF in all cases. I looked at the DIVIDENDS WITHDRAWN in columns AF through AL and the INTEREST WITHDRAWN in columns AN through AR, as applicable.

I set the initial balance equal to \$100000. I set the minimum balance threshold at \$50000. I chose to use inflation adjusted (real) dollars (in accordance with the CPI). I selected start years 1921 through 1980. I set expenses equal to 0.20%. I rebalanced annually.

I looked at a variety of portfolios.

Except for one condition and as noted, I used portfolios consisting of 50% stocks and 50% commercial paper. Unless otherwise mentioned, 100% of all dividends were reinvested, 100% of all interest was reinvested and 0% of the year-to-year portfolio gains were removed.

I varied many different withdrawal percentages. I have focused on 30-year portfolio lifetimes. I determined the maximum withdrawal percentages that would have resulted in 0 failures, 6 failures and 12 failures to stay above the \$50000 minimum balance. I refer to such failures as Half Failures (since \$50000 is one half of \$100000).

Once I had determined a withdrawal percentage, I determined the maximum TOTAL AMOUNT WITHDRAWN threshold within \$5 that would have had the same number of Half Failures (at the same withdrawal percentage). I did the same for the DIVIDENDS WITHDRAWN threshold and the INTEREST WITHDRAWN threshold, as applicable.

I determined withdrawal rates in increments of 0.1% except for PORTFOLIO GAINS, DIVIDENDS WITHDRAWN and INTEREST WITHDRAWN, where I used increments of 1%.

Data collection was very simple. I set up a portfolio in the traditional manner. I varied withdrawal percentages. I read the number of 30-year Half Failures from cell W6. Then I went to the summary boxes for the TOTAL AMOUNT WITHDRAWN, which is always applicable, and for the DIVIDENDS WITHDRAWN and INTEREST WITHDRAWN, as applicable.

Conventional Strategy

With the conventional strategy, one specifies a withdrawal rate based upon a portfolio's initial balance and puts that in cell B9. Withdrawals vary so as to match inflation.

For 0 Half Failures, the maximum Initial Withdrawal Rate was 2.8%. The corresponding Total Amount Withdrawn threshold was \$2900.

For 6 Half Failures, the maximum Initial Withdrawal Rate was 3.6%. The corresponding Total Amount Withdrawn threshold was \$3705.

For 12 Half Failures, the maximum Initial Withdrawal Rate was 3.7%. The corresponding Total Amount Withdrawn threshold was \$3710.

If it were not for the 0.20% in expenses, the thresholds would equal the Initial Withdrawal amount. [All amounts are in real dollars. That is, they are adjusted to match inflation.]

Percentage of Current Balance

With this strategy, one withdraws a percentage of a portfolio's current balance, which fluctuates. One places a 0% into cell B9. One adds the existing Investment Expenses of 0.20% to his withdrawal percentage (of a portfolio's current balance) and puts that into cell B15.

When making comparisons, remember that the conventional strategy includes 0.20% of Investment Expenses.

For 0 Half Failures, the maximum for Investment Expenses was 4.0%. The corresponding Total Amount Withdrawn threshold was \$2110.

For 6 Half Failures, the maximum for Investment Expenses was 4.8%. The corresponding Total Amount Withdrawn threshold was \$2490.

For 12 Half Failures, the maximum for Investment Expenses was 5.0%. The Total Amount Withdrawn threshold was \$2585.

Notice that, although the withdrawal rate is higher when using a portfolio's current balance, the corresponding Total Amount Withdrawn threshold has fallen.

Blended: Percentages of Initial Balance and Current Balance

With this strategy, one specifies an income floor as a percentage of a portfolio's initial balance. He places that number into cell B9. He withdraws an additional amount depending upon the portfolio's current amount. This additional amount is combined with the 0.20% in Investment Expenses and placed into cell B15.

I set the income floor at 2% and placed it into cell B9 as the Initial Withdrawal Rate. I varied investment expenses in cell B15.

When making comparisons, remember that the conventional strategy includes 0.20% of Investment Expenses.

For 0 Half Failures, the maximum threshold for Investment Expenses (in addition to 2% of the initial balance) was 1.4%. The corresponding Total Amount Withdrawn threshold was \$2715.

For 6 Half Failures, the maximum threshold for Investment Expenses (in addition to 2% of the initial balance) was 2.2%. The corresponding Total Amount Withdrawn threshold was \$3180.

For 12 Half Failures, the maximum threshold for Investment Expenses (in addition to 2% of the initial balance) was 2.4%. The corresponding Total Amount Withdrawn threshold was \$3275.

The Total Amount Withdrawn threshold of this blended strategy is less than when withdrawing a percentage of a portfolio's initial balance and more than when withdrawing a percentage of a portfolio's current balance.

Blended: Percentages of Initial Balance and Portfolio Gains

With this strategy, one specifies an income floor as a percentage of a portfolio's initial balance. He places that number into cell B9. He withdraws 0.20% in Investment Expenses (in cell B15). He withdraws a percentage of a portfolio's gains from the previous year (but nothing when the portfolio has a loss in nominal dollars). The percentage of the gains that are removed is in cell B17.

I set the income floor at 2% and placed it into cell B9 as the Initial Withdrawal Rate. I varied the Percentage Gains Removed in cell B17. I set the Investment Expenses in cell B15 equal to 0.20%.

When making comparisons, remember that the conventional strategy includes 0.20% of Investment Expenses.

For 0 Half Failures, the maximum Percentage Gains Removed was 40%. The corresponding Total Amount Withdrawn threshold was \$2100.

For 6 Half Failures, the maximum Percentage Gains Removes was 50%. The corresponding Total Amount Withdrawn threshold was \$2110.

For 12 Half Failures, the maximum Percentage Gains Removed was 58%. The corresponding Total Amount Withdrawn threshold was \$2100.

The Total Amount Withdrawn is limited to 2% of the portfolio's initial balance and its expenses whenever the (nominal, initial) balance has fallen from that of the year before.

Blended: Percentages of Initial Balance and Dividends

With this strategy, one specifies an income floor as a percentage of a portfolio's initial balance. He places that number into cell B9. He withdraws 0.20% in Investment Expenses (in cell B15). He withdraws a percentage of his dividends and reinvests whatever is left. The Dividend Reinvestment percentage is in cell B22.

I set the income floor at 2% and placed it into cell B9 as the Initial Withdrawal Rate. I set the Investment Expenses in cell B15 equal to 0.20%. I varied the Dividend Reinvestments in cell B22.

When making comparisons, remember that the conventional strategy includes 0.20% of Investment Expenses.

For 0 Half Failures, the minimum in Dividend Reinvestments was 56%. The corresponding Total Amount Withdrawn threshold was \$2575. The corresponding Dividends Withdrawn threshold was \$150. [This was unduly affected by dummy data. The first Half Failure occurred in 1977. At \$400 in Dividends Withdrawn, there were only two Half Failures, 1977 and 1980. But at \$450 in Dividends Withdrawn, there were failures in 1937, 1969 and 1977-1980.]

For 6 Half Failures, the minimum in Dividend Reinvestments was 4%. The corresponding Total Amount Withdrawn threshold was \$2800. The corresponding Dividends Withdrawn threshold was \$655.

To generate 12 Half Failures, I removed all dividends and I withdrew a percentage of the interest as well.

For 12 Half Failures, the Dividend Reinvestments percentage was 0% and the minimum in Interest Reinvestments was 91%. The corresponding Total Amount Withdrawn threshold was \$2935. The corresponding Dividends Withdrawn threshold was \$650. The corresponding Interest Withdrawn threshold was \$15.

Blended: Percentages of Initial Balance and Interest

With this strategy, one specifies an income floor as a percentage of a portfolio's initial balance. He places that number into cell B9. He withdraws 0.20% in Investment Expenses (in cell B15). He withdraws a percentage of his interest (from commercial paper) and reinvests whatever is left. The Interest Reinvestment percentage is in cell B23.

I set the income floor at 2% and placed it into cell B9 as the Initial Withdrawal Rate. I set the Investment Expenses in cell B15 equal to 0.20%. I varied the Interest Reinvestments in cell B23. [I set the Dividend Reinvestments in cell B22 at 100%.]

When making comparisons, remember that the conventional strategy includes 0.20% of Investment Expenses.

For 0 Half Failures, the minimum in Interest Reinvestments was 59%. The corresponding Total Amount Withdrawn threshold was \$2220. The corresponding Interest Withdrawn threshold was \$85.

For 6 Half Failures, the minimum in Interest Reinvestments was 41%. The corresponding Total Amount Withdrawn threshold was \$2330. The corresponding Interest Withdrawn threshold was \$160.

For 12 Half Failures, the minimum in Interest Reinvestments was 29%. The corresponding Total Amount Withdrawn threshold was \$2450. The corresponding Interest Withdrawn threshold was \$240.

Excursion: 80% Stocks

This was the same Blended: Percentages of Initial Balance and Dividends strategy except that the portfolio allocation was changed from 50% stocks and 50% commercial paper to 80% stocks and 20% commercial paper.

With this strategy, one specifies an income floor as a percentage of a portfolio's initial balance. He places that number into cell B9. He withdraws 0.20% in Investment Expenses (in cell B15). He withdraws a percentage of his dividends and reinvests whatever is left. The Dividend Reinvestment percentage is in cell B22.

I set the income floor at 2% and placed it into cell B9 as the Initial Withdrawal Rate. I set the Investment Expenses in cell B15 equal to 0.20%. I varied the Dividend Reinvestments in cell B22.

When making comparisons, remember that the conventional strategy includes 0.20% of Investment Expenses.

For 0 Half Failures, the minimum in Dividend Reinvestments was 78%. The corresponding Total Amount Withdrawn threshold was \$2480. [With the Dividends Withdrawn threshold at \$180, there was a single Half Failure in 1977. At \$350, there were Half Failures in 1977 and 1980. At \$400, there were Half Failures in 1964, 1966, 1968, 1969, 1973, 1979 and 1980. When looking at 30-year sequences, dummy data can influence results from the start year of 1973 and later.]

For 6 Half Failures, the minimum in Dividend Reinvestments was 55%. The corresponding Total Amount Withdrawn threshold was \$2915. The corresponding Dividends Withdrawn threshold was \$705.

For 12 Half Failures, the minimum in Dividend Reinvestments was 32%. The corresponding Total Amount Withdrawn threshold was \$3165. The corresponding Dividends Withdrawn threshold was \$980.