# New Calculator - Max Sustainable Withdrawal Rates

#### kmarbach

We've made a new calculator available on our web site, www.zunna.com. The calculator finds the maximum sustainable withdrawal rate from a portfolio. Inputs are investment horizon (in years), account ending value goal (Don't Go Broke, Retain Principal, Retain Buying Power) and historical success rate. Outputs include the optimized asset allocation, the sustainable withdrawal rate and the initial account value needed to meet the ending value goal. The utility was built using a new method of optimization known as simulated annealing, as exists in the Black Box program, the optimizer in the Advisor Edition of WATS.

Keith Marbach

Re: New Calculator - Max Sustainable Withdrawal Ra

Keith, Thanks for the link, and making it available online.

I was playing with it, and have an observation pertinent to Early Retirees (the purpose of this website ). Early Retirees are most likely to be interested in long periods, as they are retiring early .

I inputted:
40 Yrs.
then ran through all 3 scenarios of:
Don't go for broke.
Retain Principal.
100% Prob.
Used the Default \$40K annual withdrawal.

It said:
\$1,047,120 for Don't go for broke.
\$826,446 for Retain Principal.

Don't Go for broke shouldn't require the LARGEST starting funds !!!

I used the same setup, but backed the period down to 35 years, then the results looked like they had the order that one would have expected. But it was interesting to note that the "Don't Go for broke" fund requirement was \$1,047,120, the exact same \$ amount as the 40 year period had.

I tried the above with 38 years, the Retain principal and Retain buying power went up, relative to the values required at 35 years (to be expected). But the "Don't Go for broke" amount required was still the exact same \$1,047,120.

Is there a problem with the web-based interface there, or is there something I am missing?

Retiring Minds want to know :-/

Re: New Calculator - Max Sustainable Withdrawal Ra

Here is the explanation as it appeared in the paper we published:

************* START OF QUOTED TEXT

There is an anomaly in the maximum sustainable rates (MSR) in that longer horizons sometimes show higher withdrawal rates than shorter horizons. For example, in the 36-year horizon there is a portfolio that achieved 100% historical success with an initial withdrawal of 3.99%. In the 35-year horizon, however, the maximum sustainable withdrawal rate is 3.82%. This is counter-intuitive in that, if you cannot survive 35 years at a 3.9% withdrawal rate you should not be able to survive 36 years at that rate.

The anomaly is a result of the rolling period technique used. Each time a year is added to the horizon we lose one observation. In the example, the last 35-year time frame run is 1966-2000. When we increase the horizon by one year the last time frame becomes 1965-2000. It turns out that the 35-year time frame from 1966-2000 is the worst time frame in the cycle—the removal of 1966 as a starting year in the 36-year tests means that the initial withdrawal can increase slightly.

The correct interpretation is to extend the lowest withdrawal rate in each column through the end of the table, so that, in fact, the maximum sustainable withdrawal rate for the 36-year horizon is also 3.82%. We have highlighted the text in the tables to indicate these anomalies.

************* END OF QUOTED TEXT

For the on-line calculator we extended the MSRs in the case of the "Don’t Go Broke" scenario, so that the MSR for all horizons from 35 to 40 years is 3.82% (in the case of 100% historical success). Once you run out of money the game is over in this scenario.

We did not extend the MSRs in the other scenarios ("Retain Principal" and "Retain Buying Power") because our feeling was that, since money was still in the account, you might have been able to recover losses in the next year, and the calculated numbers might hold up. We are open to suggestions as to whether or not MSRs should be extended in these two scenarios as well… It was just a fluke that the longer periods ending in 2000 happened to be the worst periods in many cases, and adding one year to the start of the time frame actually caused a failure to become a success.

The full studies are on our web site at http://www.zunna.com/Research.htm, under the Variations on The Trinity Study.

Re: New Calculator - Max Sustainable Withdrawal Ra

The quirky results for longer periods of analysis are indicative of a basic dilemma in using historical data in an effort to estimate probable future investment results.

The dilemma is this: If you select relatively recent data (such as 1946 thru 2000) that one would hope is most representative of what financial markets are likely to do in the future, then it limits the data set. For relatively short periods of, say 10 years, this shouldn't be too serious a problem; but for longer periods of say 25 years or more, this is a problem because there really are not that many such periods within the data set. Using "rolling" periods is sort of a necessary contrivance to increase the size of the data set, but is not a true substitute for data collected over a very long time period, such as 300 years.

The problems with using a longer time period, such as 1871 to 2001 in FIRECalc, are (1) that the older data are not as reliable (i.e., there was no S&P 500 index in 1871, and inflation was calculated differently than it is now) and (2) fundamental economic factors were presumably quite a bit different than in more modern times.

The conclusion is that a person should not interpret the results of any analysis too literally. If a person is concerned about whether they will be able to sustain a withdrawal rate of, say, 3.82% or one of "only" 3.76%, they don't understand the true nature of the uncertainties that they are dealing with.

One feature of FIRECalc that is better than the work by Mr. Marbach that I was able to access is that it allows a person to input a reduction in their inflation-adjusted spending as they age. I think that most people should conservatively assume that they will live to 100, but that they should also expect to reduce their inflation-adjusted expenditures as they age.

Re: New Calculator - Max Sustainable Withdrawal Ra

There are problems with historical simulations, just as there are problems with monte carlo simulation and other methods. Both historical and monte carlo, though, are much better than the constant-rate-of-return method that until a few years ago (or still does?) dominated the financial planning world.

What method would you recommend?

Regarding withdrawal strategy (that is, how you decide to pull money out of an account) another strategy that is very manageable and less dangerous (in terms of running out of money) is to plan to withdraw a percentage of what's available, rather than to plod along and spend at a rate to keep up with inflation regardless of what the markets are doing. We have some information on this strategy as it compares to the "spend regardless of account balance" in a paper at http://www.zunna.com/Research.htm under the name "A Choice of Risks When Spending in Retirement, Optimizing the Plan for each Retiree," about half-way down the page.

Re: New Calculator - Max Sustainable Withdrawal Ra

I view the approaches as complementary. Each helps. And Ted does very well in recognizing the risk inherent in any projection. I consider it a good idea to pay attention to the market at all times because there are always some qualitative differences between the past and the future. For example, we were on a GOLD standard at one time, but not now. There are many investments available today that have not been available in the past.

I think that Keith is on the right track when he mentions withdrawals based on a constant percentage of the current portfolio balance. I have noticed that many retirees have been cutting back their withdrawals and some are even working part time. I have also noticed that very few retirees have been comfortable selling stocks or drawing down their principle during this bear market. They would much prefer to cut back and live on dividends.

Have fun.

John R.

Re: New Calculator - Max Sustainable Withdrawal Ra

Thanks JWR1945 for the good word.

I've been making posts for a couple of months now, with the general theme that FIRECalc is about as good a tool for estimating retirement financing as is available. I think that it can be improved somewhat in ways that I have previously mentioned. Allowing it to be run on the basis of withdrawing a particular percentage of assets every year would be another helpful modification.

Mathematically, a person would never exhaust their assets totally if they withdrew only a certain percentage every year, but inflation and adverse market conditions could cause the purchasing power of the amount withdrawn to shrink to practically nothing. So that strategy has its potential limitations just like any other.

I have a degree in economics and try to judge how the fundamental economic factors that drive the economy may cause returns on various asset classes to be different than they have been in the past. Three factors that have driven the American economy, as reflected in past long-term gains in stock values, have been (1) a succession of major technological breakthroughs, starting with steam power in the early 1800's, (2) relatively abundant/cheap supplies of oil and other energy sources, and (3) a high ratio of workers to non-workers (particularly, retirees) in the population.

Barring a truly unforeseeable technological breakthrough, oil is going to become much more expensive, and the ratio of workers to non-workers is going to decline dramatically. I think it very likely that this will reduce the average rate of return on stocks, and that politically popular deficit financing will cause reduced real rates of return on bonds. This fundamentally pessimistic view is expressed by William Bernstein on his website, as discussed in this forum by others and myself under the subject "Update on Bernstein Calculator."

About the only investment that I regard as almost totally secure is TIPs, and I think that retired people should include a substantial percentage of TIPs in their portfolios.

I advocate using FIRECalc with generally very conservative inputs. And if FIRECalc indicates an allocation to stocks of, say, 40%, I would use other assets as partial substitutes for the stocks -- particularly REITs and high yield bond funds. (For example, instead of 40% stocks, I'd go with 20% stocks, 15% REITs, and 15% high yield bond funds.)

The only "non-conservative" input that I think is reasonable is for most people to assume that their level of expenditure, in inflation-adjusted dollars, will decline as they age, assuming that they are "active" in their younger retirement years (travelling, dining out, etc.).

For those who really want to be aggressive at hedging against future increases in energy prices, I even recommend being long on a couple of long-term futures contracts on crude oil or natural gas. People need to be very careful, however, not to become caught up in short-term futures trading, because that is practically gambling, and most people lose at it.

Re: New Calculator - Max Sustainable Withdrawal Ra

...Allowing (FIRECalc) to be run on the basis of withdrawing a particular percentage of assets every year would be another helpful modification. ...

Sounds like a good idea. Since "survival" in the way FIRECalc views it is sort of assured, I need to figure out what the useful output should be...

(Maybe suggestions along this line should be in a new thread, so those interested in discussing the calculator in this thread can keep their discussions together.)

Dory36

Re: New Calculator - Max Sustainable Withdrawal Ra

Dory36, it is best if you introduce the subject. We need to know the scope.

My thoughts are limited and specific (so far). Let me suggest that you use dollar amounts as thresholds for selecting colors to display.

For example, someone might consider withdrawals of \$20K as being minimal and \$35K as being good and \$50K as being a luxurious level. If he starts with \$1.0 million with 5% withdrawals, he would start at a luxurious level. We also know that he is likely to be able to continue at that level. But there have been times in the past when he would have ended up bankrupt if he had kept on removing the \$50K (plus inflation).

Use a red color to highlight those years when his withdrawals have fallen below \$20K. In this example, that would mean that the portfolio balance has fallen to \$400K. Use a yellow color to highlight those years when the balance is between \$400K and \$700K.

If someone were planning for a 50 year withdrawal period, I doubt that he would be concerned about a red color around year 40 and certainly not with a yellow color at that time. But if he sees yellows or reds at year 30, he might well look more closely at the numbers.

The weakness is that almost all of the lines (start years) would end up with some color.

If there is a problem with putting different colors in individual boxes (or cells), perhaps we could use a color whenever the balance falls below a set amount before a particular year. In my example, you might make the line turn red if the balance falls below \$400K before year 35. If not, then make the line yellow if the balance falls below \$700K before year 30. Otherwise, there is no color. (The choices of years 35 and 30 are made by the user. They are not preprogrammed.)

I have interpreted your primary concern as being the display of the output data and not the matter of withdrawing a constant percentage of the balance.

Have fun.

John R.

Re: New Calculator - Max Sustainable Withdrawal Ra

I agree with JWR1945 that it is important to highlight years when withdrawals would fall below a particular value (although a user could see this for themself by looking at the detailed output of FIRECalc).

The main thing that I would add is that the results be shown in constant (inflation-adjusted) dollars. For example, a withdrawal of, say, \$30,000 per year might sound pretty comfortable, but if inflation were to return to, say 5% per year (unfortunately, not all that improbable) in 30 years that \$30,000 would be worth only about \$7,000 in constant dollars.

Since each year's historical inflation is in the FIRECalc database, it would be easy to program it to convert the results to inflation-adjusted dollars.

Re: New Calculator - Max Sustainable Withdrawal Ra

Ted, thank you for your kind words.

Dory36 has already satisfied your wishes. If you check FIREcalc closely, you will see that its results are normally in inflation adjusted dollars...although you can choose not to include an inflation adjustment. You can also choose whether to use CPI-U or PPI.

Unfortunately, data is not available for other indices. More precisely, a complete set of data is not available. Many people would like to see something tailored specifically to older people (because of health care expenses). There is another inflation index is for wages, which is not quite the same as for inflation. It exists today, but I doubt that it goes back to 1871.

Have fun.

John R.

Re: New Calculator - Max Sustainable Withdrawal Ra

The way that FIRECalc is presently configured (I think) is that it increases the inputted withdrawal amounts according to the inputted inflation index. However, the resulting portfolio values for each year, as shown in the "detail results," are in actual (non-inflation-adjusted) dollars.

This is fine!

However, if FIRECalc were modified such that a particular percent of the portfolio value is withdrawn each year, the calculated "withdrawal amount" for each year would be in actual dollars unless it were adjusted by dividing it by the inflation index. I think that it would be useful to the user for the FIRECalc program to make this inflation adjustment, since it will provide results that appear less "rosy."

Of course, the results will be based on past inflation rather than estimated future inflation, but the FIRECalc data base includes periods of substantial inflation that might be approached in the future but hopefully will not be exceeded. Thus, if a user determines that a particular withdrawal scenario would have worked 100% of the time in the past, there is a pretty good chance that it will in the future (more so if the portfolio is heavy on TIPs).

Re: New Calculator - Max Sustainable Withdrawal Ra

Ted
The way that FIRECalc is presently configured (I think) is that it increases the inputted withdrawal amounts according to the inputted inflation index. However, the resulting portfolio values for each year, as shown in the "detail results," are in actual (non-inflation-adjusted) dollars.

I checked. You are right! Thanks for catching this and providing the solution as well.

Have fun.

John R.

Re: New Calculator - Max Sustainable Withdrawal Ra

Showing the results in inflation-adjusted dollars does make good sense. I'll add that to the "to do" list.

Dory36

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