Cage Match: PMT function, RMD formula, and Divide-by-10 Rule

The other day a former colleague posed a hypothetical question related to teasing out ideas for a trust rule that would provide for an orderly, sustainable and mostly full disgorgement of assets later in the life of a beneficiary if anything sizable enough were to be left at that age for him or her.

(A big fat disclaimer: It's not that I know exactly zero about trust law and practice but it is pretty close to zero. The same is true for the person asking me, too.  That means that any comments I have here on this kind of thing would fall into that "amateur hack" type of category which I seem to do quite a bit of lately.  I'm not sure how a real live estate-planner would do it or if any of this could be instantiated in a legal doc or if there is a standard practice in this type of scenario.  But all that was never the point of the conversation anyway.)

With the big fat disclaimer out of the way, I did have a couple ideas. The requirements seemed simple enough, which they should be since it's a fake setup:

1. Start a full distribution of resources to the beneficiary later in life (say 55+);
2. Seek to match distributions to longevity
3. Attempt to disgorge most or all resources before death
4. Try to keep it sustainable by not running out of money; a small residual legacy is probably ok. There is probably some benefit to having a discretionary reserve.
5. Early, higher distributions might be favorable, ex taxes
6. Maximize the early reduction of greedy and destructive trustee fees asap, all else being equal
7. The idea has to be extremely simple, understandable and executable by a family member or back office administrator 30-40 years hence
8. Conveniently for this hypothetical, ignore tax effects.

To me, all that just looked like a normal retirement spending problem, even though it really isn't, but with a couple twists.  My first impulse was to say buy a deferred annuity.  But that fails because I don't know of any 40-year (give or take a decade) deferred annuities.  If you do let me know, I might be interested.  Then as I thought about it as a retirement-like spending problem I thought about constant inflation-adjusted spending (e.g., 4% rule) but that would fail at least B & D.  Complex decision rules might be fine for the right trustee and trustee discretion might be OK but that might fail G along with a couple others.  Running simulations to gauge the right amount each year doesn't feel like it fits this situation. Milevsky in his "7 Equations" book uses Komogorov differential equations to dynamically evaluate spending plans; it's great and supple and elegant math but it is probably a non-starter for obvious reasons.  David Blanchett has a simple formula (effectively a simulator packed into a small static form) that I think is effective and very simple but it is a regression-style formula that would scare off some people. That left, I thought, simple rules of thumb or formulas, though there may be other ways to do this that I haven't considered.  For this post, I decided to throw three formulas that I know at the question: 1) the Excel PMT function, 2) the RMD formula, and 3) the Divide-by-10 rule, that last one because I've been wanting to see how it might work in some semi-real application.

1. Excel PMT function.  This is an annuity formula that's been around forever that people call the Excel PMT function because the Excel function is the annuity formula.  Waring and Seigel use it in their Annually Recalculated Virtual Annuity (ARVA) as applied to retirement. Moshe Milevsky uses an inside-out version attributed to Fibonacci to calculate how long money will last for a retiree. Though it's simple, it might be a minor stretch for the wrong trustee. It has the characteristic of ensuring money runs to zero while dynamically adjusting to longevity and return expectations.   The inputs are: endowment (at end of prior period), rate (real rate expectation at any given time, say), and period. Note that for period I used the expected mean terminal age (at whatever age level the formula is being used[1]) minus current age. This (and maybe using excel in the first place) is where it might start to get hard for someone that is not a professional trustee or financial planner.

2. RMD. The Required Minimum Distribution as it is used here has nothing much to do with IRAs or tax policy. It is here because it is a simple formula (end of last period endowment / a value from the IRS RMD table that varies by age) and has publicly available tables to make the calculation simple and easy to implement in 40 years if someone non-pro needs to figure it out.  It also happens to drive the endowment towards zero.  I used the single life table for the illustration.

3. Divide by 10.  This rule (divide your age by ___ to get a spend rate percent that is applied to the current endowment) is the other side of a "divide by 20" rule pitched by Evan Ingliss in a Society of Actuaries publication this year (here) and then covered by me (here). While the divide by 20 rule (a genius-monument to elegant simplicity, I think) is an age-adjusted "feel free" safe spend rate, Evan calls Divide-by-10 the "no more" rate[2] or the spend rate near an annuity-type solution, above which the portfolio is in peril or, rather: the /10 level might possibly work out for someone's spending plan somewhere but "no more" than that, please, and it probably won't work for you.  On the other hand, it might not actually spend down the endowment in the end...but it gets close. Also, it is really, really simple and, I think, well suited to the task above. Inflation is not friendly to this rule.  

To cut to the chase, this is what it looks like if charted out.  The analysis is hopelessly static.  I could have tried to create simulations or varied the charts a bunch, but then again: why? The main assumptions include:

Endowment                   $1M

Spending Inflation         3%

Asset Growth                5%

Real Rate exp                2%

RMD                             single life table

Life expectancy            for PMT function it varies by age based 2013 SS tables[1].

Beneficiary Age           start with 55 and end at 100

Constant Spend            for the one chart where it is shown, see this note: [3]

Without getting into detailed quantitative analysis and comparisons -- which I won't because nothing is really at stake here and no one depends on the outcome -- I can probably make some general conclusions just by eyeballing it...that's assuming I got the modeling right[4].  

• All three are more or less the same thing. They all start with the same pile and just push it around over time differently although obviously with enough time interesting things start to happen.
• RMD seems like it might under-distribute early and over-distribute later but that is pretty subjective. Looks like it can leave a little legacy as well which will satisfy at least one of the conditions.
• PMT seems to do the job pretty well but then again, that's been its job for a long time. Maybe it is too efficient in plowing the endowment towards zero?
• Divide by 10 looks like it gets more money out early at ages when it can be used by a still (hopefully) vigorous beneficiary and it keeps a small reserve available for discretionary payments and residual legacy but it will clearly be weak in the face of inflation. 

In the end I think Divide-By-10 satisfies more of the requirements, especially when it comes to simplicity, and it feels like a more "tempered" solution overall. I'd love to see sometime what taxes would do and also how Db10 would interact with the NPV of lifetime fees paid to the trustee…but not today. Db10 also seems to leave more discretion in the hands of both the beneficiary (unused early money can be saved for whatever later) and the trustee (there is still a reserve for unforeseen emergency spending needs, for example) at the same time. That's a pretty neat trick to pull off.  

Keep in mind that this post is more question than answer.  I'd be curious what the pros would do.

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[1] Graphical view of how the mean longevity expectation, using 2013 SS life table, rises with each new age attained.  I used this for the PMT function because it is maybe a little closer to how someone might use it in real life at the beginning of any given planning year. 

 

[2]  From The “Feel Free” Retirement Spending Strategy Evan Inglis, 2016: "At the other end of the spectrum, divide your age by 10 to get what I call the “no more” level of spending. If one regularly spends a percentage of their savings that is close to their age divided by 10 (e.g., at age 70, 70/10 = 7.0 percent) then their available spending will almost certainly drop significantly over the years, especially after inflation is considered. Except for special circumstances like a large medical expense or one-time help for the kids, one should not plan to spend at that level. Purchasing an annuity may allow spending at close to the “no more” level, but no more than that."

[3] Note that in the "$ spend chart" I snuck in a constant-spend line (dotted) as a baseline comparison.  I used a 3.5% spend rate (the person starts at 55 so I would never use 4%, especially in 2016) which is inflated at 3%.  Then at age 65 I bake in 2% annual real spend declines which is what research seems to show happens in real life.  I have a blog post on this somewhere.  David Blanchett, among others, did a paper on this.

[4] There is no model or analysis I've ever done where I have not made at least one mistake. Not even once...ok, well, maybe once, but I don't remember it. So, who knows.  For example, in the 3rd chart, the RMD formula seems to defy gravity vs. PMT.  Did I get that right? I'll check when it's important enough to someone that I need to do that. Fortunately for me that's not today.