**Overview: Using both Initial and Current Valuations**

Scroll down to read the last two sections. Then read the entire post.

**Cursory Data Analysis**

This is a minimal review. It brings out some of the key features about the new algorithm. This provides a starting point from which to build.

Withdrawals have two components.

1) The first depends only on the portfolio's initial balance. Its amount equals (standard withdrawal rate term)*(inflation)*(portfolio's initial balance).

2) The second component depends on the portfolio's current balance. It has the form: (slope term)*(100 E10/P + offset)*(the portfolio's current balance).

The term 100E10/P is the earnings yield of the S&P500 index using Professor Robert Shiller's P/E10. That is, 100E10/P = 100 / [P/E10]. P/E10 is the current price (or index value) divided by the average of the last ten years of earnings.

The portfolios that I have examined are designed to last 30 years. They consist of stocks as represented by the S&P500 index and TIPS at a 2% interest rate. For purposes of analysis, I have assumed that we can still buy and sell 2% TIPS throughout the full 30 years with neither capital gains nor losses.

I assert that, when 2% TIPS are unavailable, it is still possible to put together a suitable portfolio of high dividend stocks, cash, TIPS and Ibonds. I have not proved this. I have not demonstrated this. Putting together an adequate combination of securities that is equivalent to 2% TIPS is far from trivial.

I looked at portfolios with 50% stocks and 50% TIPS and at portfolios with 80% stocks and 20% TIPS. I used the variable withdrawal formula that I have described already. I used a fixed withdrawal formula as well to make baselines. In such cases, I held the second component of withdrawals constant (at 0.20% of the portfolio's current balance to cover expenses).

I followed what has become a standard procedure. I determined the 30-year Historical Surviving Withdrawal Rates (of the first component of withdrawals) for 1921-1980. I calculated regression lines using the 1923-1980 data (for better curve fits) of Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P. I made eyeball estimates of the confidence limits about these regression lines. The Safe Withdrawal Rate as a function of earnings yield 100E10/P is the lower confidence limit.

Because the scatter generally increases with earnings yield, I made my eyeball estimates using 100E10/P values of 10% (or less). That is, I narrowed the confidence limits by excluding bargain levels of stock valuations (with P/E10 less than 10).

[Plots of Historical Surviving Withdrawal Rates versus P/E10 have great statistical characteristics related to the scatter (or standard deviation). But the curves themselves are distinctly non-linear. Plots of Historical Surviving Withdrawal Rates versus 100E10/P (or 100 / [P/E10] ) are wonderfully linear (except for saturation at the very highest levels of earnings yield), but their scatter behaves poorly. It increases noticeably with earnings yield.]

**Selected Data Set**

These are minimal sets of data for purposes of comparisons. There are many other ways of making comparisons, but these are sufficient for our purposes at this time.

80% stocks and 20% TIPS at 2% interest

Slope = 0.25.

Offset = (2.5) or minus 2.5%.

Today's initial withdrawal rate: 2.9%.

Withdrawal amounts for the worst case sequence based on an initial balance of $100000:

1) Start: $3625

2) Peak: above $3900.

3) Minimum: $3183 at year 30.

4) Start year: 1966.

Maximum balance: $259329 at year 20 of the 1948 sequence.

Slope = 1.0.

Offset = (2.5) or minus 2.5%.

Today's initial withdrawal rate: 2.1%.

Withdrawal amounts for the worst case sequence based on an initial balance of $100000:

1) Start: $4770.

2) Peak: above $5400.

3) Minimum: $1792 at year 30.

4) Start year: 1969.

Maximum balance: $200355 at year 15 of the 1950 sequence.

Baseline:

Slope = 0.0

Expenses = 0.20%.

Today's withdrawal rates:

1) Safe Withdrawal Rate: 2.7%

2) Calculated Rate: 4.1%.

3) High Risk Rate: 6.7%.

50% stocks and 50% TIPS at 2% interest

Slope = 0.25.

Offset = (2.5) or minus 2.5%.

Today's initial withdrawal rate: 3.3%.

Withdrawal amounts for the worst case sequence based on an initial balance of $100000:

1) Start: $3838.

2) Peak: above $4300.

3) Minimum: $3365 at year 30.

4) Start year: 1966.

Maximum balance: $155096 at year 15 of the 1950 sequence.

Slope = 1.0.

Offset = (2.5) or minus 2.5%.

Today's initial withdrawal rate: 2.4%.

Withdrawal amounts for the worst case sequence based on an initial balance of $100000:

1) Start: $4566.

2) Peak: above $6100.

3) Minimum: $1908 at year 30.

4) Start year: 1968.

Maximum balance: $134412 at year 5 of the 1924 sequence.

Baseline:

Slope = 0.0

Expenses = 0.20%.

Today's withdrawal rates:

1) Safe Withdrawal Rate: 3.4%

2) Calculated Rate: 4.4%.

3) High Risk Rate: 5.9%.

Excursion:

Slope = 0.25.

Offset = (5.0) or minus 5.0%.

Today's initial withdrawal rate: 2.9%.

Withdrawal amounts for the worst case sequence based on an initial balance of $100000:

1) Start: $3550.

2) Peak: above $4200.

3) Minimum: $3479 at year 30.

4) Start year: 1966.

Maximum balance: $165721 at year 15 of the 1950 sequence.

**Comparisons**

Slopes

With 80% stocks, increasing the slope term from 0.25 to 1.0 caused the following changes:

1) Today's initial withdrawal rate decreased from 2.9% to 2.1%.

2) The minimum amount in the worst case sequence decreased from $3183 to $1792.

3) The initial withdrawal amount in the worst case sequence increased from $3625 to $4770.

4) The peak withdrawal amount in the worst case sequence increased from $3900+ to $5400+.

5) The maximum balance decreased from $259329 to $200355.

We can characterize these results by the following observations:

1) Increasing the slope term increases the spread of the data.

2) At today's valuations, increasing the slope term decreases the initial withdrawal amount.

3) In the past and under worst case conditions, increasing the slope term increased the initial amount withdrawn.

4) In the past and under worst case conditions, increasing the slope term increased the peak amount withdrawn.

5) In the past and under worst case conditions, increasing the slope term decreased the minimum amount withdrawn.

6) In the past, increasing the slope term reduced the maximum balance found within the sequences.

With 50% stocks, increasing the slope term from 0.25 to 1.0 caused the following changes:

1) Today's initial withdrawal rate decreased from 3.3% to 2.4%.

2) The initial withdrawal amount in the worst case sequence increased from $3838 to $4566.

3) The peak withdrawal amount in the worst case sequence increased from $4300+ to $6100+.

4) The minimum amount in the worst case sequence decreased from $3365 to $1908.

5) The maximum balance decreased from $155096 to $134412.

The previous observations still apply.

The most important observation is that increasing the slope term from 0.25 to 1.0 increases the spread in withdrawal amounts too much. The minimum balances under worst case conditions are too low.

In spite of this, some people will prefer the larger slope term. Historically, it has increased withdrawal amounts in the early years at the expense of withdrawal amounts in the later years. At today's valuations, however, the initial amount withdrawn actually decreases. [This is a side effect of a wider standard deviation combined with using a lower confidence limit. Using the lower confidence limit comes from the requirement for safety.]

**Stock allocations**

With a slope of 0.25, increasing the stock allocation from 50% to 80% caused the following changes:

1) Today's initial withdrawal rate decreased from 3.3% to 2.9%.

2) The minimum amount in the worst case sequence decreased from $3365 to $3183.

3) The initial withdrawal amount in the worst case sequence decreased from $3838 to $3625.

4) The peak withdrawal amount in the worst case sequence decreased from $4300+ to $3900+.

5) The maximum balance increased from $155096 to $259329.

We can characterize these results by the following observations:

1) At today's valuations, increasing the stock allocation decreases the initial withdrawal amount.

2) In the past and under worst case conditions, increasing the stock allocation decreased the initial amount withdrawn.

3) In the past and under worst case conditions, increasing the stock allocation decreased the peak amount withdrawn.

4) In the past and under worst case conditions, increasing the stock allocation decreased the minimum amount withdrawn.

5) In the past, increasing the stock allocation increased the maximum balance found within the sequences.

With a slope of 1.0, increasing the stock allocation from 50% to 80% caused the following changes:

1) Today's initial withdrawal rate decreased from 2.4% to 2.1%.

2) The initial withdrawal amount in the worst case sequence increased from $4566 to $4770.

3) The peak withdrawal amount in the worst case sequence decreased from $6100+ to $5400+.

4) The minimum amount in the worst case sequence decreased from $1908 to $1792.

5) The maximum balance increased from $134412 to $200355.

With a slope term of 0.25 or 1.0, the previous observations apply except for the initial amounts withdrawn.

We can characterize these results by the following observations when the slope term equals 1.0:

1) At today's valuations, increasing the stock allocation decreases the initial withdrawal amount.

2) In the past and under worst case conditions, increasing the stock allocation increased the initial amount withdrawn.

3) In the past and under worst case conditions, increasing the stock allocation decreased the peak amount withdrawn.

4) In the past and under worst case conditions, increasing the stock allocation decreased the minimum amount withdrawn.

5) In the past, increasing the stock allocation increased the maximum balance found within the sequences.

Varying the stock allocation changes the spread in withdrawal amounts in the worst case sequence by only a little. In contrast, the maximum balances changed considerably.

At today's valuations, the initial amount withdrawn actually decreases as the stock allocation increases. This has varied in the past. It is a side effect of different standard deviations combined with using a lower confidence limit. [Requirements for safety cause us to use the lower confidence limit.]

**Interactions and other effects**

If we restrict ourselves to looking only at today's valuations and initial withdrawal amounts, we find no interaction between the slope term and the stock allocation.

That is, with a slope term of 0.25, changing the stock allocation from 50% to 80% changes the initial amount withdrawn from 3.3% to 2.9%, a decrease of 0.4%. With a slope term of 1.0, changing the stock allocation from 50% to 80% changes the initial amount withdrawn from 2.4% to 2.1%, a decrease of 0.3%.

Other comparisons show a little bit more variation, but not much more.

I have already pointed out that there is an interaction between the valuations of today versus the past that change the initial withdrawal amounts. It occurs because safety demands our use of the lower confidence limit. This introduces the effects of scatter (and standard deviations) into the comparisons.

**Excursion**

With 50% stocks and a slope term of 0.25, changing the offset from minus 2.5% to minus 5.0% caused the following changes:

1) Today's initial withdrawal rate decreased from 3.3% to 2.9%.

2) The minimum amount in the worst case sequence increased from $3365 to $3479.

3) The initial withdrawal amount in the worst case sequence decreased from $3838 to $3550.

4) The peak withdrawal amount in the worst case sequence decreased from $4300+ to $4200+.

5) The maximum balance increased from $155096 to $165721.

The excursion reduced the variation of withdrawal amounts for the worst case sequence. In that sense, it is similar to increasing the TIPS allocation. It has reduced today's initial withdrawal amount. In this sense, it is similar to decreasing the TIPS allocation.

Baseline Comparisons

With a 50% stock allocation and a non-varying withdrawal amount, the safe withdrawal rate is 3.4% at today's valuations. With a slope term of 0.25, the safe withdrawal rate is 3.3%. With a slope term of 1.0, the safe withdrawal rate is 2.4%.

With an 80% stock allocation and a non-varying withdrawal amount, the safe withdrawal rate is 2.7% at today's valuations. With a slope term of 0.25, the safe withdrawal rate is 2.9%. With a slope term of 1.0, the safe withdrawal rate is 2.1%.

In both cases, I have understated the baseline's performance since it includes expenses of 0.20%, which are not included in the other portfolios.

**An alternative baseline**

These data shout at us to abandon stocks entirely at today's valuations. A portfolio consisting entirely of inflation-matched cash equivalents produces a safe withdrawal rate of 3.33% for 30 years. A portfolio consisting entirely of 2% TIPS produces 4.46% safe withdrawal rate for 30 years (subject only to minor idealizations).

If we were to withdraw 3.4% annually from a portfolio consisting entirely of 2% TIPS, we would end up with $43000 (plus inflation, based on an initial balance of $100000) at the end of 30 years.

I used the formulas from the following post in the

**3% SWR for 56 Years**thread dated Monday, Oct 13, 2003:

http://nofeeboards.com/boards/viewtopic ... 536#p12536

**Summary**

This new algorithm is the kind of thing that an actual retiree is likely to do. He is likely to cut back his withdrawal amount when the outlook for stocks looks bad. He is likely to increase his withdrawal amount when the outlook for stocks looks good.

This approach differs from Gummy's Sensible Withdrawal Rate strategy. This approach depends upon the future prospects for stocks. Gummy's approach depends upon the actual recent performance of stocks.

I expect many retirees to combine the two. They will implement Gummy's Sensible Withdrawal Rate strategy with minor modifications based upon the future prospects of the stock market. That is, if they are convinced that the overall stock market is likely to underperform during the next decade, they are likely to reduce withdrawals below what the Sensible Withdrawal Rate strategy would allow during good years.

We keep coming back to the frustratingly consistent story, however, that tells us to abandon stocks in favor of TIPS at today's valuations. Favorable outcomes are still possible with high stock allocations, but they are not likely.

Alternative choices include careful selection of stocks and other investments that differ significantly from the S&P500 as a whole.

Of course, there is a problem with 2% TIPS. They no longer exist. The issue is whether a person can actually construct a good equivalent portfolio. There is a requirement to be able to handle emergency cash needs. There is another requirement to match inflation. There is an additional requirement to produce sufficient income (above any return of capital that might distort the numbers).

Have fun.

John R.