Some Initial Thoughts on the "Divide by 20" Idea as a Retirement Spending Rule

The 4% rule has been beaten up a lot lately. I think this is for many good reasons that have been covered better elsewhere.  For my part, I think the rule (of thumb) is a little like drug use.  If you do it to yourself (and maybe even if you ruin yourself), it might possibly be OK depending on the point-of-view but once your use affects your family or community or society then maybe it's not OK and someone needs to step in. Except for the occasional Manhattan and my morning coffee, I don't use drugs…or the 4% rule. 

But then again it is only a rule of thumb and a very special-case rule of thumb at that. Here is Wade Pfau on the rule: "…people are often surprised to learn it is specifically designed for a thirty-year retirement. The 4% rule wasn’t necessarily meant to apply to eighty-five-year olds, nor can it be safely used by early retirees who leave the workforce by age forty." So it's not for everyone.  If you are a little older you might have a little more latitude to do whatever you want. If you are younger, you would be taking on a lot of risk, in my opinion, in using 4%.  In this early retiree sense, I view 4% a little like jogging with an IED.  It can be done but you'd better be pretty careful. 

On the other hand the rule has a number of significant advantages going for it.  The main thing, in my mind, is that it is pure simplicity itself.  It can be used without an advisor or spreadsheets or Monte Carlo simulators or internet calculators. It doesn't talk you into buying structured products or variable annuities. It doesn't charge you fees.  It doesn't confuse you and it generally works most of the time for people of a certain age that aren't planning on a bad sequence of returns or inflation.  This kind of simplicity is deeply appealing to some people.  For example, according to Richard Thaler, behavioral economist at the University of Chicago: "For many people, being asked to solve their own retirement savings problems is like being asked to build their own cars." Precisely.  

I do realize, however, that there are endless numbers of practitioners and academics (and the odd retiree like me) that line up to nuance the hell out of retirement research and equations and probably give all of us more to chew on than we can or want to handle (if it is not outright conflicting advice at times), but there are just some people that clearly need a simple rule.  Me? I might like my spreadsheets. And that researcher over there might like utility functions or differential equations. And practitioners and institutions are sometimes over-invested in their simulators and black box proprietary tools. But that's why the 4% rule rules. For better or worse it takes all of that away.  In terms of "people and their tools," it might look like this if one were to try to shake out the different types of users of retirement finance stuff:

So, some people just need rules of thumb. 

Except that in the case of the 4% rule, the rule of thumb under-serves older retirees and can walk younger retirees right over a cliff.  But as I argued above not everyone is up for the constant analysis and recalculations and adaptations and decision rules (especially for the early retiree) necessary to keep risk at bay. What if there was a really simple rule of thumb for those folks that need a simple, conservative rule but that also accounts for age (or, I guess put another way, the expected duration of retirement)? 

Enter "Divide by 20."  The other day I happened to run into an article in the Society of Actuaries Pension Section News (don't ask...or as my girlfriend quipped "omg, why?!") by Evan Inglis (The “Feel Free” RetirementSpending Strategy, Society of Actuaries Pensions Section News May 2016) that pitched the idea of using the formula "Age divided by 20" as a threshold level for safe spending.  The idea here is that, like my grid above, a lot of people want simple answers to retirement questions and they also want to be safe. 4% used to be an answer but for a lot of reasons it is no longer quite up to the job (for example, not everyone retires at 65 and dies at 85, or maybe return expectations aren't what they used to be).  Divide by 20 steps up to the plate because it is really simple, factors in age, and is conservative enough to not only be relatively safe (not foolproof as Mr. Inglis points out) but the conservatism also implicitly factors in the current risk we have in 2016 of potentially lower expectations for future returns.   

"My belief is that most people would rather spend their money at a safe level than they would spend their time on an­alyzing their situation in order to be confident in spending a bit more… The feel-free spending level is an easy-to-determine and -remember guideline for those who do not have the time, expertise or inclination to do a lot of analysis and who don’t want to hire an adviser for help. Hopefully, this simple rule is useful, even for those who do lots of planning around their retirement. It’s simple and it’s safe. One needs to use common sense about their circumstances, but dividing one’s age by 20 should provide a useful spending guideline for most retirees. " -Inglis

So, it's not a supercomputer but I thought it was pretty cool.  You can read the article for the details.  I was curious about a couple things, though.  For one, I wondered where the 20 came from. 20? Why 20? So I asked him. His response:  "The feel free idea originated with the thought that one would be able to safely spend more as one got older, so a function of age made sense.  20 is simply the round number that gets you pretty close to a reasonable level of expected real returns.  You want the spending level to be not too much higher or even a little lower than the expected real rate of return in the early years, and it can be a little higher in later years.  As it happens a simple division gets you quite close to reasonable spending levels, especially in early years."  Sounds reasonable and not over-thought to me.

For another, being analytically inclined, I wondered how divide by 20 looked next to the other retirement equations and tools I have used in the past. Was it even close to tools with which I was familiar and comfortable? I took a look.  Here is a chart of divide by 20 put next to a number of other retirement calcs I have used.  Divide by 20 is the lower dotted line (note that 4% would be a horizontal line at...wait for it...4%):

The various lines on the chart are these tools: 

• Blanchett Simple: this is David  Blanchett's Simple Regression Formula (for retirements > 15 years) based on a bunch of MonteCarlo modeling where Withdrawal = .195 - .03701(LN(years)) + .01255*sqrt(equity%) -.04471 * (probability of success) + .507*alpha.  I'm thinking this is probably simple only to an advisor or actuary or an OCD retiree.

• Kolmogorov: Kolmogorov differential equations for lifetime ruin probability as profiled in Moshe Milevsky's "7 Equations" book. I found them instantiated in a spreadsheet found somewhere on the internet. 

• Flexible Retirement Planner: free internet MonteCarlo simulation tool.

• cFireSim.com: free internet historical rolling model style simulator.

• FireCalc: same as cFireSim give or take a few minor things,

• Custom Sim: I hacked out a basic excel/VB MC simulator using historical returns and inflation but I also added in, among other things I don't see (but want) in other simulators, a random longevity variable using a gompertz distribution.  As an early retiree I got tired of always seeing the fixed XX-year kind of thing.
• Divide by 20: Divide-by-20 is the "feel free spending strategy" suggested by Evan Inglis. Divide by 20 to determine a safe spending rate. The goal here is to be simple and relatively safe but not perfect.

• Divide by 14: Evan used 10 for better reasons than mine. I used 14 to make the line come closer to the other lines, more an aesthetic thing than something analytical.

• ARVA (or Annually Recalculated Virtual Annuity): in an article by Waring and Seigel (The Only Spending Rule Article You Will Ever Need, M. Barton Waring and Laurence B. Siegel, 2015 ) they use the Excel PMT function to calculate spending each year based on endowment, real return, and years. I have one line for "1M to age 100 at 1% real return" and another at 3% real.  These rates are arbitrarily selected to show low real return expectations. Terminal age is a little higher because PMT is a blunt instrument. Maybe that's a little bit of a cheat.  

• Note: For a couple of the lines I only calculated spend rates for 3 or 4 different ages and then interpolated in between.  For example, with my custom sim, 5000+ runs takes something like 10 minutes or so; I got bored waiting especially since solving for fail rates involves some trial and error. I don't think the missing non-linearity ruins the basic idea since the assumptions across all tools are a bit of mix and match non-science anyway.

The assumptions are not lined up in a rigorous way that would satisfy anyone but me, and certainly not anyone "serious" but here they are for what it's worth.  If I were to do this again, which I won't, I'd try harder to be more consistent but it works for me for now. I did not record my assumptions well so I might be off on a few of these:

So, how does the chart line up?  I don't know but it looks pretty good to me.  The first thing I noticed, of course, is that the Age/20 result is linear but everything else is not and Age/20 falls quite a bit below the others at later ages.  As Mr. Inglis reminded me in an email "…it's the price for keeping it simple so that it's useable." More interestingly he also said "The feel free spending level IS too low at older ages, which your chart identifies.  I think that’s OK because most people aren’t going to increase their spending as they age (except for a concentrated spend on LT care perhaps) and most people want to leave a bequest."  I agree. 

Here are some other things that I notice as I step back and squint at this thing: 

• Everything slopes up nicely in a similar, parallel curve kind of way
• All the spend rates are low for early retirees and go up intuitively with age
• All the lines are wide apart to the left and converge to the right reflecting some of the greater risk and uncertainty related to early retirements.
• At age 65 there is a lot of convergence around 3.5-4% which feels about right
• At age 58 the more conservative lines are under 3% which again feels right
• As he implies in his article, the divide-rule is especially useful not so much as a precise answer but as a range boundary, below which (20) is safe territory and above which (10) is a no-go zone. 

By the way, for anyone that is interested in a pretty good economic rationale for why those spending rates for early retirees can be so low and that is made by a leading practitioner/researcher, I highly recommend the recent article by Michael Kitces that explains why ("Why Most RetireesWill Never Draw Down Their Retirement Portfolio" www.kitces.com/blog).  In my own words his point, if I got it right, is more or less as follows:

First, just for fun and background, let's quote Pfau on the 4% rule: "While the original Trinity study concluded that the 4% rule has a 95% chance for success, that only means the 4% rule succeeded in 95% of the rolling historical thirty-year periods. New retirees today should not count on the same 95% chance that the 4% rule will work for them." And as above: "…people are often surprised to learn it is specifically designed for a thirty-year retirement."

So if you do happen to accept the 4% rule for a 30 year retirement (and a 95% level of certainty) and you do accept that longer retirements are riskier and shorter are less so then for longer retirements what you are probably actually doing by spending less at younger ages is accruing (hidden spending!... or saving, really) in the first half of retirement for future liabilities in the second half such as:

• Inflation, especially unexpected inflation (or unexpected really high inflation)
• Spending shocks [chaotic - e.g., downward bankruptcy spirals]
• Spending shocks [probabilistic - e.g., long term care]
• Probabilistically increasing health care costs
• Maybe the 4% rule was based on a "too good" data set (e.g., US 20th century)
• In the absence of annuitization, the risk that longevity will run past expectations
• Other - returning children, etc…

Fortunately, as age increases these risks abate a bit and spending can go up since the accruals (hidden spending or saving) start to go away.  Any way you cut it, though, it makes perfect sense to me that all the lines would slope from lower left to upper right and that, especially for early retirees, the risks are higher and spending is lower and that the 4% rule fails (for me, anyway) as a simple rule of thumb.  Divide by 20 -- as a simple rule that takes age into account -- simply works better in today's world for certain people...if we are limiting ourselves to simple rules, that is.  That the divide-by-20 line drops below the other lines at later ages does not bother me at all because all those risk accruals probably don't go away completely and probably, at that point, I really do want to start thinking about bequests. In any case, maybe at some point I can just divide by 19. Or 18…