I have taken a new set of data using the equations for Safe Withdrawal Rates. The results remain encouraging.I used a flawed procedure in this study. I used the actual Half-Failure Rates from the historical record. Such information would not have been available at that time. I should have used calculated values derived from the historical record.

**Using both Initial and Current Valuations**

I have been looking at a new variable withdrawal algorithm. I have combined two ideas. The combination looks good.

The first idea is to use 30-Year Half-Failure Rates instead of the conventional withdrawal approach that permits the portfolio to be depleted at the end of 30 years. In accordance with our standard procedures, I determined Half-Failure Rates as a function of the percentage earnings yield 100E10/P (which is 100 / [P/E10] ) at the beginning of retirement.

[Withdrawing at the Half-Failure Rate keeps the portfolio balance at or above 50% of its initial (real) balance throughout the time period being examined (in this case 30 years). Withdrawing at a rate that is higher by 0.1% causes the portfolio balance to fall below 50% of its initial (real) balance.]

Next, I incorporated Gummy's concept of varying withdrawals in accordance with the current earnings yield. [I have reported such results for portfolios consisting of the S&P500 and TIPS.]

This combination, using both the initial valuation and the current valuation to determine withdrawal rates, is a winner.

**Early results**

I used a portfolio that consisted of 80% stocks and 20% 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 2.5%. That is, I make withdrawals of (0.25)*(100E10/P-2.5%)*(the portfolio's current balance).

In addition, I make standard withdrawals based upon the Half-Failure Rates of this portfolio. Standard withdrawals equal (the portfolio's initial balance)*(the standard withdrawal rate) in terms of real dollars (that is, after adjusting for inflation).

I had originally determined the 30-year Historical Surviving Withdrawal Rates HSWR for 1921-1980. I kept the varying portion the same while I varied the (standard) withdrawal rates in increments of 0.1%. Later, I determined Half-Failure Rates. I noticed that the curve of calculated rates for Half-Failures was an excellent approximation of the lower confidence limit of the 30-year HSWR.

**Applying the numbers**

The curve for the 30-year Half-Failure Rate HFR is HFR = 0.6 431x + 0.0815 where is the percentage earnings yield 100E10/P.

Applying today's earnings yield, which is close to 3.5%, to this equation, the standard portion of withdrawals is 2.3% of the portfolio's initial balance (plus inflation).

Applying today's earnings yield to Algorithm G1, we withdraw an additional 0.3% of the portfolio's current balance (since 0.25*(3.5%-2.5%) = 0.25%, which is rounded to 0.3%).

For a person beginning retirement today, his total withdrawal amount would be 2.6% (or 2.3% + 0.3% since the current balance equals the initial balance). This is only slightly less than the calculated Half-Failure Rate under normal conditions (i.e., with constant withdrawals in terms of real dollars). This is slightly higher than the Safe Withdrawal Rate under normal conditions.

Including the variable withdrawal component has increased the initial withdrawal amount above what would have been the Safe Withdrawal Rate initially (which would have been slightly above 2.4% with 2% TIPS). However, the withdrawal amount could fall to 2.3% of the initial balance and it could result in the portfolio's balance falling below 50% of the initial balance.

**Looking at the worst case of the past**

If I set my standard (constant) portion of withdrawals equal to the 30-year Half-Failure Rate, the worst case is in 1969. Based on an initial balance of $100000, the five-year rolling average withdrawal amount are $2541 at year 5, $2976 at year 10, $3021 at year 15, $2677 at year 20, $2389 at year 25 and $2041 at year 30. The balances are $78706 at year 5, $59555 at year 10, $61563 at year 15, $80551 at year 20, $105028 at year 25 and $213676.

[There were other sequences with lower balances, but not with lower withdrawals.]

This establishes a baseline for comparison.

Next, I applied the formulas. For 1969, the Half-Failure Rate was 3.12% using the curve for calculations. The variable portion was 0.56%. This totals 3.68%, which is rounded to 3.7%.

Here are the total withdrawal amounts using the formulas. Based on an initial balance of $100000, the five-year rolling average withdrawal amount are $3910 at year 5, $4208 at year 10, $4058 at year 15, $3656 at year 20, $3399 at year 25 and $3214 at year 30. The balances are $72502 at year 5, $47442 at year 10, $39045 at year 15, $39292 at year 20, $38152 at year 25 and $58037 at year 30.

We improved the withdrawal sequence substantially. We were able to do this only because we violated our constraint on the portfolio's balance. However, the balance always remained above $38000 (assuming an initial balance of $100000).

**Here are some references for background**

**HFWR80 versus Earnings Yield**dated Monday, Aug 02, 2004.

http://nofeeboards.com/boards/viewtopic.php?t=2846

80% stocks and 20% commercial paper.

For 1969 Half-Failure Withdrawal Rates HFWR80

Safe: 1.88%

Calculated: 3.75%

High Risk: 5.61%

In 1997, P/E10 = 29.16 and 100E10/P = 3.43% Half-Failure Rates:.

Safe: 1.00

Calculated: 2.87

High Risk: 4.73

**Calculated Rates of the Last Decade**dated Wednesday, Jun 23, 2004.

http://nofeeboards.com/boards/viewtopic.php?t=2657

For 1997 and HDBR80:

Safe: 2.42

Calculated: 4.00

High Risk: 5.58

Have fun.

John R.