Rule of Thumb?

A Safe Withdrawal Rate is a calculation, not a rule of thumb. We determine Safe Withdrawal Rates from the historical record. Yet, Safe Withdrawal Rates are not the same as Historical Surviving Withdrawal Rates.

We make most of our calculations using the Historical Sequence method. We determine what would have happened to a portfolio by using the stock market returns, inflation rates and interest rates of actual sequences. We look at all sequences of the same duration for every start year considered.

For example, if we are looking at 30-year survival rates over the years 1921-1980, we determine what would have happened to a portfolio that began in 1921 and lasted until 1951. Then we determine what would have happened to a portfolio that began in 1922 and lasted until 1952. And so forth. The last sequence that we look at began in 1980 and lasted until 2010. [We use dummy values in the data after 2002, from 2003-2010.]

In each year, we determine whether the balance would have remained above zero at a specified withdrawal rate. Then we increase the withdrawal rate by one increment, usually 0.1%, and continue until the balance at year 30 becomes zero or negative. This is the withdrawal rate of the first failure. Subtracting one increment gives us the Historical Surviving Withdrawal Rate for that particular year.

There are lots of variations on how much is withdrawn, how long the duration is and what we use for our survival criteria. The most common withdrawal approach is to start with a specified percentage of a portfolio’s initial balance and then to adjust the withdrawal amount each year to match inflation. The most common variant is to withdraw a specified percentage of the portfolio’s current balance, whether or not it matches inflation.

In real life, many retirees are interested in retirements that last 40 or 50 years or even longer. We use 30 years because it is long enough to be useful to traditional retirees and, more important, because it is suitable for data analysis. Market conditions become favorable, turn unfavorable and become favorable again over periods lasting between 30 and 40 years. Shorter time periods are too short. Longer time periods reduce the number of sequences. In addition, having two favorable or two unfavorable conditions in the same sequence makes it difficult to interpret those sequences lasting 40 or more years.

In many cases, we establish criteria other than ending with a positive balance. We have required having an ending balance equal to or greater than the initial balance. We have required maintaining a balance that never falls below one-half (or three-quarters) of the initial balance (plus inflation) throughout a 30-year timeframe.

Early researchers generally focused on 30-year survival rates. They assumed, but did not prove, that a withdrawal rate equal to the smallest of all of the Historical Surviving Withdrawal Rates would be Safe. It was a reasonable starting point. It never was a reasonable ending point. Today, we know that such a rate is not safe at today’s valuations. In fact, it was a risky rate for some of those sequences that survived.

It was widely circulated at that time that the Safe Withdrawal Rate of a stock and bond portfolio was 4% (plus inflation) of the portfolio’s initial value. This was the smallest Historical Surviving Withdrawal Rate for a portfolio beginning in 1871-1970 or 1871-1980 (using dummy data, when necessary).

To reach 4% required an optimal, high stock allocation. The non-stock component was not bonds. It was commercial paper, which is the primary holding of most money market funds. The time period was 30 years. Withdrawals varied to match inflation. The portfolio was rebalanced every year. A low level of expenses were included (such as are available by using index funds).

We have discovered that Professor Robert Shiller’s P/E10 is an excellent indicator of value. Historical Surviving Withdrawal Rates correlate strongly with its reciprocal, 100E10/P, the percentage earnings yield of the S&P500. This allows us to extract the effect of valuation from the data. This leads us to great insights as to what is happening and why. It reduces the degree of randomness dramatically. We have even been able to separate the effects of the sequence of portfolio returns when there are withdrawals from the overall return in the absence of withdrawals.

[Professor Shiller wrote the book Irrational Exuberance. P/E10 is the current price (index value) of the S&P500 divided by the average of the trailing ten years of earnings. He and Professor John Campbell showed that P/E10 and foreign market equivalents have a good predictive capability in the intermediate-term (10 years). He publishes P/E10 and other S&P500 data at his web site.]
Professor Shiller’s web site

Once we isolate the effects of valuation, we can extract a regression equation and determine confidence limits. We limit ourselves to a 90% confidence level because of the uncertainty of the details of market statistics. We call the lower confidence limit the Safe Withdrawal Rate. We call the upper confidence limit the High Risk Rate. Each of these has a 5% (one-sided) probability of error.

We find that the years with the lowest Historical Surviving Withdrawal Rates were closer to the regression line (which we call the Calculated Rates) than to the lower confidence limit, the Safe Withdrawal Rate. We also discover that recent valuations are at the top end (and actually above) the historical range. That is, 4% is not a Safe Withdrawal Rate. It never was a Safe Withdrawal Rate. The original assumption, although plausible, proved to be false.

We made it a goal to create portfolios with 30-year Safe Withdrawal Rates of 4% in today’s market. We have succeeded. The original takeout number (4%) is easy to remember and it is obtainable. BUT THESE ARE DIFFERENT PORTFOLIOS. As a result, many people have started referring to 4% as a rule of thumb. Adding to confusion, many people have started referring to all Safe Withdrawal Rates as Rules of Thumb.

A Safe Withdrawal Rate is the result of a mathematical calculation. Done properly, it includes an estimate of its uncertainty. Safe Withdrawal Rates are distinct from Historical Surviving Withdrawal Rates. The method of calculating Safe Withdrawal Rates is not restricted to applications of the Historical Sequence method. Many people use Monte Carlo models. [Different Monte Carlo models use different assumptions regarding probability distributions. The details are not always reported.] Sometimes, as with portfolios consisting entirely of TIPS, we can make the entire calculation directly from the mathematics. We do not need a model.

We have not stopped with creating a portfolio with a 30-year Safe Withdrawal Rate of 4%. We have continued. We have a low risk portfolio that allows us to withdraw 4% (plus inflation) for 40 years. We have looked into dividend-based strategies. They inherently have lifetimes lasting well into the foreseeable future. We have developed portfolios that have 30-year Safe Withdrawal Rates above 4% even in today’s market. All of these are calculations, not rules of thumb.

Very seldom should individuals use a Safe Withdrawal Rate directly. Many who seek an early retirement should plan to withdraw at a higher rate, but well below the Calculated Rate. Some people will prefer an even higher level of safety than provided at the Safe Withdrawal Rate. Many people should blend several withdrawal rates: one that provides a minimal source of income to cover necessities with absolute safety and other amounts that offer varying degrees of safety.

For early retirement planning, the Rule of 25 is an excellent rule of thumb: build a nest egg that is 25 times as big as the total income stream that you seek. It was an important conclusion from the early research. That is, 4% is 1/25, which means that a nest egg of 25 times the annual amount of the income stream could be expected to last at least 30 years. As I have mentioned, the early research has failed. But because of our effort, we have been able to restore the Rule of 25. Remember, though, that today’s portfolios differ from those of the early studies.

Have fun.

John Walter Russell
July 23, 2005