**Price Adjusted Safe WIthdrawal Rates: Overview**

A. Background

1. Back in May 2002

**hocus**started a thread on the Retire Early Home Page discussion board in which he asked for Safe Withdrawal Rates at current stock market prices. That spawned a series of threads and discussions over the next four months. However, as I was reviewing what took place, I realized that no one had answered his original question.

2. The question is non-trivial. It requires a careful review of what has been done already, the use of precise definitions, identification of the proper method for estimating stock market valuation and relating current stock market behavior to the historical record.

3. These posts answer

**hocus's**original question. This is an overview. But pay attention to my other post. It contains useful details related to valuations.

B. The measure of stock market valuation

1. I have selected the price to earnings ratio P/E10 of the SP500 as used by Professor Shiller of Yale for my measure of stock market valuation. He uses the current value of the SP500 index for the price term P. But he uses the average of the past ten years of earnings for E.

2. I examined three possible adjustments. One adjusts P/E10 for inflation. Another adjusts the P/E10 depending upon whether the P/E10 ratio is increasing or decreasing. The third compares P/E10 to the short-term interest rate. In all cases, the unadjusted P/E10 was best.

C. My approach

1. I used the

**dory36**calculator FIRECalc. It gives the year by year results of a hypothetical portfolio with a specified duration for each possible start year in the historical record (1871 to 2000). The portfolio is re-balanced each year to maintain a constant percentage allocation between stocks and one other investment category.

2. I assumed an initial portfolio of $1000, an annual expense ratio of 0.20%, the CPI for inflation adjustments and commercial paper as the non-stock investment. I examined allocations of 80% stock (with 20% commercial paper) and 50% stock (with 50% commercial paper). Most of my analysis was done using a 30-year duration. I also looked at 40 and 50 years. I looked at a variety of withdrawal rates. But the most significant were 4%, 5% and 6% (which would correspond to initial withdrawals of $40, $50 and $60 each year). To adjust to an actual portfolio, one would scale all dollar amounts by the same number. For example, with a $700K portfolio, one would multiply $40 by 700 = $28 000 or $50 by 700 = 35 000 or $60 by 700 = 42 000 since $1000 times 700 = $700K.

3. The withdrawal amount for each year increases (or decreases) with inflation (or deflation). However, all reported results from the

**dory36**calculator are in terms of real (inflation adjusted) dollars, not nominal dollars (without inflation adjustment).

4. For each start year in the historical record, I determined whether a portfolio would have survived and, if it failed, the year (relative to the start year) in which it failed.

5. From Professor Shiller's database I identified the SP500 price to earnings P/E10 ratio for each start year.

6. I formed two lists. Each identified whether a portfolio succeeded or, if it failed, the number of years after the start year in which it failed. One list was ordered by date. The other was ordered by the price to earnings ratio P/E10 of the SP500.

7. During my analysis I grouped failures by decades (i.e., failure in years 1 to 10, 11 to 20, 21 to 30 and so forth depending upon the duration). I ended up focusing on three categories: a) portfolios that survived for the entire duration, b) portfolios that failed in years 21 to 30 and c) portfolios that failed in year 20 or sooner.

8. I then determined the highest price to earnings ratios P/E10 at which a portfolio succeeded. I also determined the lowest price to earnings ratios at which the two types of failure began (early or normal).

D. Results (thirty year duration)

1. For an 80% stock allocation a 6% withdrawal rate is safe if the P/E10 is 10.2 or lower at the start.

2. For an 80% stock allocation a 6% withdrawal rate has some failures for P/E10 ratios from 10.3 to 12.0. But all of those failures occur after year 20.

3. For an 80% stock allocation a 5% withdrawal rate is safe if the P/E10 is 12.0 or lower.

4. For an 80% stock allocation a 5% withdrawal rate has some failures for P/E10 ratios from 12.5 to 18.6. But all of those failures occur after year 20.

5. For an 80% stock allocation a withdrawal rate of slightly less than 4% provides total safety for P/E10 ratios inside the historical range. The top of this range is roughly 24.0 to 27.0.

6. For a 50% stock allocation a 6% withdrawal rate is safe if the P/E10 is 8.1 or lower.

7. For a 50% stock allocation a 6% withdrawal rate has some failures for P/E10 ratios from 8.7 to 10.2. But all of those failures occur after year 20.

8. For a 50% stock allocation a 5% withdrawal rate is safe if the P/E10 ratio is 10.7 or lower.

9. For a 50% stock allocation a 5% withdrawal rate has some failures for P/E10 ratios from 10.9 to 21.5. But all of those failures occur after year 20.

10. For a 50% stock allocation a withdrawal rate of slightly less than 4% provides safety for P/E10 ratios inside the historical range. The top of this range is roughly 21.6 to 27.0.

E. Low withdrawal rate anomaly

1. Most withdrawal rates favor an 80% stock allocation.

2. At a 4% withdrawal rate both a 50% stock allocation and an 80% stock allocation show a single failure. For a 50% stock allocation, the failure is in 1937 in year 28. For an 80% stock allocation, the failure is in 1966 in year 28.

3. At a 4.2% withdrawal rate there are 3 failures with a 50% stock allocation and 4 failures with an 80% stock allocation. All occur after year 20.

4. At a 4.5% withdrawal rate there are 15 failures with a 50% stock allocation and 10 failures with an 80% stock allocation. All occur after year 20.

5. At a 5% withdrawal rate there is one failure within the first 20 years with a 50% stock allocation. At a 5% withdrawal rate there are 5 failures within the first 20 years with an 80% stock allocation.

6. Observe that we are at the edge of the historical range (or at a tail of a statistical distribution) when we make these observations. Conclusions at these extremes have much uncertainty.

7. There is a mechanism that that might explain this anomaly. Portfolios with a high percentage of stocks have high volatility and high growth. Portfolios with a smaller percentage of stocks have lower volatility and lower growth. Withdrawals steadily decrease the amount in a portfolio. They are balanced by the growth from the stocks. When stock returns are poor (i.e., when they lose money), they can cause a portfolio that is heavily weighted with stocks to fail early. A portfolio with fewer stocks will take longer to fail. A greater percentage of those portfolios with fewer stocks will eventually fail (for a given withdrawal rate) because they do not have as much growth. But such failures are gradual. This is a qualitative difference.

F. Adjustments to match the historical range

1. The

**dory36**calculator uses 130 years (from 1871 to 2000) from Dr. Shiller's database. Because Dr. Shiller requires ten years of earnings information to calculate his price to earnings ratio, his P/E10 information starts in 1881. The latest start year that lasts a full thirty years is 1970. The calculator shows that many failures occur when withdrawals start in the 1970s. For that reason I made use of those years as well. My results include 100 data points with start years of 1881 through 1980.

2. The highest P/E10s during period of 1881 through 1980 were 24.0 in 1966 and 27.0 in 1929. That establishes the historical range.

3. In the last decade P/E10s have often exceeded these values. Only recently have they come back down. According to Professor Shiller's recently updated database, the P/E10 in early July 2002 had fallen back to 23.7. The SP500 index was 903.59 at that time.

4. There is an issue as to how to treat portfolios when the P/E10 of the SP500 exceeds 24.0. I suggest using a conservative approach that matches the historical safe withdrawal rate numbers around 4% to an SP500 index value of 900. For higher SP500 numbers, scale by ( 900 / [the SP500 number] ). The formula can be written as a) amount to withdraw = 4% * ( 900 / [the SP500 number] ) * [the portfolio value] and it can also be written as b) the percentage to be withdrawn = 4% * ( 900 / [the SP500 number] ).

5. This formula could be refined somewhat by referring to Professor Shiller's database for the proper SP500 values after inflation adjustments (the inflation adjusted SP500 index in early July 2002 was 846.89).

7. The 4% withdrawal rate from the historical record would have had to be adjusted downward to a level as low as 2.3% to 2.4% in August 2000. Today, we are in the historical range, but we are close to the top.

8. This adjustment is based on the premise that present earnings can still support withdrawal rates based upon historical P/E10 values - even when actual prices are much higher.

G. References

1. I found all of my data sources initially from posts by

**intercst**on the Retire Early Home Page discussion board. In addition, I recommend that you read everything on his web site www.retireearlyhomepage.com. It includes a free version of his Retire Early Safe Withdrawal Rate Study. I recommend that you download the full report. It only costs $5.00.

2. The

**dory36**calculator FIRECalc is available at http://capn-bill.com/fire/.

3. Dr. Shiller's web site is www.econ.yale.edu/~shiller/. You can go directly to his historical SP500 data by using www.econ.yale.edu/~shiller/data/ie_data.xls.

Have fun.

John R.