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Variable Retirement Withdrawal Rates - by Bob Herlien


Variable Retirement Withdrawal Rates - by Bob Herlien

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This article was posted on December 10, 1999.

Bob Herlien (BluesH on the Motley Fool) agreed to let Retire Early post the following article and accompanying Excel spreadsheet describing his model for variable retirement withdrawals. It's well worth your consideration.


This is the first of a series of articles in which I describe a hypothesis of mine about withdrawal rates in retirement, and how I modified the REHP safe withdrawal spreadsheet to test that hypothesis.

To see where I'm coming from, I suggest you first go back and read my message #874 TMF Retire Early Home Page board at http://boards.fool.com/Message.asp?id=1380025000142001&sort=postdate Basically, I'm looking for a middle ground between the fixed (but inflation adjusted) withdrawal rates calculated by the REHP safe withdrawal calculator, which leads to rates of 4% and below; and the variable withdrawal scenario as described toward the end of http://www.efficientfrontier.com/ef/998/hell.htm In the latter case, we can take much larger withdrawals, but in a market downturn, your allowable withdrawals can get very small (Alpo, anyone?).

The middle ground I'm looking for is to use something that looks like the variable withdrawal scenario, but with upper and lower bounds on the withdrawal rates.

But first, a disclaimer. I have a bias going into this. I've already determined that I want to retire sooner rather than later, and so have determined to retire when I achieve a 5% withdrawal rate, despite the safe withdrawal calculation (which comes out to 89% safe for a 40 year horizon, BTW). I've justified this to myself in several ways.

1) I'm flexible. If a market downturn occurs, I can trim a lot of fat out of my retirement budget. BTW, this is my biggest reservation about a strictly fixed withdrawal calculation. Would anybody really continue to blithely withdraw the same amount from their portfolio after the onset of the Great Depression? Considering history (soup kitchens, panhandlers on the streets, etc), I'd be happy to have a roof over my head.

2) I'm young. If worse came to worst, I could still go back to work. I wouldn't want to, but I'd be willing to take a 10% chance that I would have to, in order to retire early. More likely, the worst case scenario would be to take an occasional consulting contract.

3) I have other assets; namely, my house. We may move out of high cost of living coastal California once we have a chance to look around the country to see where we'd like to move. That will decrease expenses, while freeing up some home equity.

Withdrawal Calculations

I set the stage above for figuring withdrawals from a retirement portfolio in a way that's different from either the fixed, inflation adjusted withdrawals or purely variable withdrawals. The problem is how to quantify that for a spreadsheet calculation.

First, some definitions, abbreviations, and observations. Let's call the initial value of the portfolio IV. At any point in time, the portfolio will have a current value, CV. I need to define one more term. At any point in time, you can calulate the inflation-indexed initial value, or IIIV, which is IV multiplied by the inflation factor from the start date to the current date.

The variable withdrawal scenario is, for each year, to simply take a percentage of CV.

The inflation-adjusted fixed withdrawal scenario, as in REHP, is to take a percentage of IV, and index that amount for inflation. I make the observation that this is mathematically identical to taking a fixed percentage of IIIV. That is, (rate * IV) * (inflation factor) = (rate) * (IV * inflation factor).

I modified the REHP withdrawal calculator to use three rates: nominal (or initial) withdrawal rate, maximum and minimum withdrawal rates. All these are percentages of IIIV. An example is 5% nominal rate, 6% maximum, and 4% minimum, which I denote as 6%/5%/4%.

OK, so how do you know when to increase or decrease your withdrawal rate? Quite simply by taking the amount of true market increase or decrease after inflation. This is calculated in the spreadsheet as the ratio of of CV/IIIV, and then applying max/min limits. That is, if the market value of your portfolio (CV) has increased by 20% after accounting for inflation (IIIV), then you can increase your withdrawal rate to 20% above 5%, or 6% of IIIV (120% * 5% = 6%). Conversely, if you suffer a 20% real decline in value, you must reduce your withdrawal rate to 4% of IIIV (in this example). Once you reach either the upper or lower limit, you don't increase or decrease your rate further, although you do continue to apply these rates against IIIV. That is, you continue to adjust for inflation.

Some results

The first result from the calculation described in above is truly remarkable. In fact, I had to stare at the data and scratch my head for quite a while before I believed it. Here it is:

The safe result calculation does not change with the upper limit of withdrawal rate!

Huh? The h*ll you say? Strange, but true. I can put in maximum withdrawal rates of 100%, and the results don't change. But that's not quite as strange as it sounds at first.

Consider a 5% withdrawal rate from a $1M initial value, yielding an initial withdrawl of $50K. A 100% withdrawal rate is 20 times larger than a 5% rate. To get there, CV/IIIV has to be greater than 20. If CV/IIIV = 20, then CV has to be $20M (plus inflation, which we'll ignore for the moment). But the withdrawal will be 100% of IIIV, or $1M. That's still a withdrawal rate of 5% of current value.

In fact, it's another mathematical truism that, as long as you don't hit either the upper or lower limit of withdrawal rate, my algorithm actually becomes identical to the variable withdrawal scenario.

(CV/IIIV) * (rate * IIIV) = rate * CV

Until you hit the upper or lower limit, you'll always take out the initial rate times the current value. Another mathematical truism is that a variable rate of < 100% is always survivable. Think about it -- if you take out 90% of CV per year, you'll always have SOMETHING, although that something gets very small very fast, as does the withdrawal.

So, as long as your portfolio has real (inflation indexed) gains, your withdrawals can continue to go up. The point is really twofold: 1) the method of calculating rate increases is fairly conservative, and consequently 2) you can ride this curve up almost indefinitely according to the data.Oops, what's that last point? Simply that this is calculated from historical data, and isn't necessarily an indication of what will happen in the future. I can think of scenarios where taking out these gains will still yield portfolio failure, whereas leaving them in will allow success. Basically, you'd need a bull market right after retirement (to allow the increased withdrawal), followed by a deep protracted bear market that not only wipes out the gains, but continues to go on and wipe out the portfolio itself. The Roaring 20s followed by the Great Depression comes to mind. The spreadsheet simply says that it has not historically happened that such an event would lead to failure with the increased withdrawals, while still being survivable without those increases. And that includes the 20s & 30s. So we would need an event worse than that to cause a problem. Wow.

But that doesn't mean that it won't happen. Take any increase in withdrawal rate with a huge amount of caution. I know I will.

The big question.

OK, believe it or not, the calculated results don't depend on the upper limit on withdrawal rate. So I can express my results as based on two numbers: initial rate and minimum rate. My earlier example of 6%/5%/4% can be expressed as 5%/4%, since the upper number doesn't matter.

Now, it should be obvious that if you start your withdrawals at 5%, with the intention of reducing to 4% if conditions warrant, that you won't fare as well as if you'd been withdrawing 4% from the start. So, the big question is:

What penalty do I pay for starting at a higher withdrawal rate?

Or, how big a stomach ache do I get from eating my dessert first?

The answer, for a 5% initial rate, is about 1/4%. A 5%/3.75% rate looks remarkably like a 4% rate from the REHP safe withdrawal calculator. That is, if you want the safety associated with a fixed withdrawal rate of 4%, you can start at 5% but must be willing to reduce it to 3.75%. 5%/4% looks like 4.25%, etc. Starting at 6% costs you more.

Fixed Withdrawal (REHP)	Survivability
Rate		10 Yr	20 Yr	30 Yr	40 Yr	50 Yr
3.50%		100%	100%	100%	100%	99%
3.75%		100%	100%	100%	99%	96%
4.00%		100%	100%	99%	97%	95%
4.25%		100%	100%	97%	95%	95%
4.50%		100%	100%	95%	95%	91%
5.00%		100%	97%	91%	88%	77%

Variable Withdrawal	Survivability				
5%/3.5%		100%	100%	100%	99%	96%
5%/3.75%		100%	100%	99%	97%	95%
5%/4%		100%	100%	99%	95%	95%
6%/3.5%		100%	100%	100%	98%	95%
6%/4%		100%	100%	97%	95%	90%

We've seen that you can afford to start at a higher initial withdrawal rate and still achieve a safe withdrawal scenario, but only if you're willing to reduce the withdrawal rate when the market turns bad. You can get the effect of a 4% withdrawal rate by starting at 5%, if you're then willing the reduce it to 3.75% at the appropriate time. The key is that you really must be prepared to reduce your budget when times get bad. The question now becomes, why would you want to do this?

Well, you may not. Retirement plans are very individual things; your plan is undoubtedly different than mine. I'm in the camp that says one's standard of living should go up in retirement, not down. As a result, the budget that leads to my planned 5% withdrawal rate has a lot cushion in areas that are important to me and my wife, particularly travel. I could reduce the budget by 20%, down to a 4% rate, and still have more travel budget than we typically spend annually right now. In a pinch, I could achieve a survival budget of 3.5%, thus achieving a 99% survival probability over 40 years. At that point, we would have a choice. We could either a) spend our time at home, play in the garden, take long walks on the beach, hike in Big Sur, and then come home and sip an inexpensive glass of wine while soaking in the hot tub, or b) take some consulting contracts long enough to earn travel money. Hmmm, life's full of tough choices.


The first disclaimer I've already stated, but it bears repeating. The withdrawal scenario I've outlined only works if you're really prepared to reduce the rate to a safe one. If not, you're just kidding yourself.

Secondly, I should note that even continuing the inital rate is far from automatic. If your withdrawal rate is 5%, and you have 3% inflation, there's an 8% portfolio drag that must be overcome just to continue with the initial rate. If your investments don't do at least that well, your withdrawal rate must still go down.

So your withdrawals in this scenario are only assured to be above your minimum rate -- continuing at the initial rate is far from assured. In that sense, this is a riskier strategy than the fixed withdrawal scenario of REHP. Being somewhat a gambler (but not enough of one to use 8%, LOL), it's a risk I'm willing to take. But everyone has to make his/her own decision.

------------- by Bob Herlien -------------

Download the Variable Withdrawal Rate Calculator

This Microsoft Excel 5.0/7.0 spreadsheet allows you to run some scenarios on your own. Click below to download the file.

Download the Variable Withdrawal Calculator
(withd5.zip, filesize=1,164kb, expands to withdraw5.xls, filesize=2,550kb)

Note: You will need pkunzip.exe, or some similar program, to expand the zip file into Excel format.

filename = varwith.html
Copyright 1999 Bob Herlien, All rights reserved.

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