So here below is the test I proposed[1]. The idea or question is that, for any given spending formula, if it were to be applied in a given year and then followed forever (inflation adjusted), what would the simulated fail rates look like? Ignore that some of these formulas, if applied in continuous time, might actually take risk to zero...or close. In the test I am thinking about I take something like the 4% rule or an RMD rule or even my own RH40 rule and I'll say, if I applied this (in a simulator) at age 50 or 60 or 70 forever (inflation adjusted), what would happen if I simulate that process over time[2].
The hypothesis here is that the 4% rule will suck at 50 in terms of risk and is maybe ok at 80 and that the "divide by 20" is maybe better but too conservative at 50 and too generous in terms of bequests at 80 and that my RH40 formula might actually "hang in there" over the whole time frame. Or, rather, the hypothesis is really that a rule that is honestly aware of retirement concerns will be more or less constant when it comes to the risk of failure if applied over spans of time (before getting into continuous time stuff). Let's try it out.
Here is a chart of the fail rates for five (six if you include the adjusted RH40) rules, none of which is applied dynamically. I take each and do the calc-and-apply-forever method. Not great but it makes the math and processing easy. The rules I use here, the selection of which might or might not be self serving (your call), are: the 4% rule, the Excel PMT function using a 2% real return and age 95 as terminal, the divide by 20 rule profiled elsewhere, an RMD style function using wealth / remaining-years, and my own lovely RH40 formula. I do not include here formulas I have used in the past like the Blanchett or Milevsky formulas because they have a constant fail rate baked into the formula. Constant fail is already assumed. Here we go:
Ok, so what do we have? Well first of all we have a bald-faced problem with the 4% rule. If you start that at age 50 and stick with it, you are screwed; at 60 it's still pretty rough; at 70 maybe not so bad. PMT is risky because it is blind to real retirement issues and I am ignoring the fact that is is not supposed to be a forever-calc; in continuous time that formula's risk actually goes towards zero. The /20 rule is awesome but is a tiny bit risky early and too risk averse late -- assuming one never ever adjusts. The RMD looks great but it is conservative early and gives away too much late. I have no idea what it looks like in continuous form and maybe late-age generosity is actually ok. I hate to say it but that crazy RH40 formula looks pretty good (the add-on of my incremental risk aversion math from the last post (dotted line) looks worthless, though). But then again let's totally ignore continuous time and spending volatility here just to be fair. What is the lesson? a) Rules behave differently so use a rule like /20, RMD, or RH40 in the first place but understand what they mean, and probably more importantly, b) a continuously updated plan will generally always work better than one that is not (though that conclusion is not explicitly illustrated here).
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[1] The thing to notice first, though, before I get to anything, about which I was not super clear last time, is that when doing some of this risk analysis, I often talk about fail rates but they are not based on continuous theory. For example, in this post I calculate fail rates but they are not continuously updated over time. For a given age I merely calculate a fail rate based on a rule as if I adhere to that conclusion (and spend rate) "forever." No one does that. It is interesting in a chart but it's not real. In fact, if I were to be totally honest I would now digress into some weird stuff like game theory (say Nash), philosophy of time (say Whitehead), and continuous time finance (Merton). The point here is that the 4% rule, against which everyone tests their own thoughts, was always flawed and not because it does or doesn't work some of the time. It is because it misconceives time. 4% assumes retirement is one thing that does not ever change. It assumes that the retiree is stupid and hates to think. All of that is bunk. Whether one is reading Merton (I actually, stupidly, tried to read his continuous time finance paper last month and I understood -- except for "and" and "the" -- almost nothing), game theory, or philosophy, one has to realize that a 30 or 40 year retirement is not "one thing" it is many. Break it down into discrete years and it is a game of x steps based on years left and each year is a new game. Game theorists revel in this stuff. That is an improvement right there. Use Merton and the increments of finance time compress down to infinite instants and the math gets incomprehensible but more accurate. Here, retirement is not one thing or chunks, it is infinite. Now let's get philosophical...then one will realize that retirement is not even a infinite number of chunks and there is no such thing as early middle and late retirements (though there really is because longevity probabilities change towards zero if you get old enough) there is only a continuous process of "becoming" where in each instant a retirement is created anew. Ok enough of that. My point is that constant spending was always a bad assumption (even though I use that assumption sometimes) and that most retirees know this stuff intuitively: they adapt based on the game that is presented to them in each moment. They are smarter than the practitioners and academics probably think they are.
[2] some standard, generic sim assumptions: 1M endowm, 60/40 allocation, a fee and tax effect, constant spend, no return suppression, a little bit of Soc. Sec, no spend shocks or trends or variance, a fixed terminal age of 95, etc.
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