On Redundancy
It works like this. Over the full decumulation interval we call retirement, there is both risk (let's call it volatility for convenience, or maybe sequence risk) and uncertainty (maybe: meteor strikes, bankruptcy or pandemics). In the absence of someone to come save us in these situations, or in the absence of adequate lifetime income, a reserve of some level[2], must be maintained to discharge at least some of the uncertainty, and at least early in the cycle. As longevity expectations come in and time gets short, the need for the the redundant reserve maybe starts to go away.
For example, let's say we have $1M and we spend 40k real and that 20k of that 40k was bottom-line "necessary" and that 500k of the 1M discharges that 20k floor. If I created a perfectly redundant pool of money in order to attempt to redundantly-hedge the floor, that'd be an extra (at the outset,anyway and keep in mind this is totally a strawman) 500k we'd need to have. That means that the 40k would now be spent against 1.5M (had to work longer, maybe?) so the spend rate with that redundancy baked in would now be ~2.7%, right? But maybe it's still really 4% ... on the 1M ... and now you just have an idle, redundant 500k sitting around...just in case. This is why redundancy is called inefficient and why the busy bees of the world will seek to use it more "efficiently" by, say, spending it now or perhaps retiring with less. This is the same reason an economist might say two kidneys are inefficient and that even one kidney might be trumped by the idea of a shared community kidney...I mean, only if we are ignoring survival risk in a pinch I guess. Kidneys or cash, both are redundant and inefficient but then in a crisis we are also able live to fight the next battle and seize opportunity.
Think Plague now. I literally did not personally plan for plague. But I did plan for uncertainty. For example, the incremental difference in my net worth over 10 years -- by way of penny-pinching buzz-kill low-spending in order to hang onto a redundant "reserve" for uncertainty -- was maybe 10-12% on February 19th. That 10-12% was maybe a little redundant last year but not now. It allows me to survive from a better baseline...I hope. This is no longer all that funny, is it? This problem is also classic Aesop ant-grasshopper territory; why don't people read anymore? And where are my ex SOs now? Probably not laughing, at any rate. Maybe they are. idk.
On an Interesting Chart
In a recent exercise here at RH I built an amateur reinforcement learning AI algo and then told it to teach itself to spend whatever made sense, as if it: a) had an optimizing principle, b) were starting with a 60 year old's conditional longevity risk, c) had $1M and d) had a guess that initial spend rates are somewhere > 2% and < than 8%, using a middle of the road allocation. [I think this is right, I'd have to look]. I then told it to do it again but now with income starting at age 70 forever.
The machine, when looking at the income-less scenario, intuited the need for what I call an "inefficient redundancy" right away while it also acknowledged that the "inefficiency" can fade away as the years get long and life short. This is what it looked like in the post which I'll try to explain. If not, here is the original post. The basic idea is these are the real dollar amounts spent by the machine under two scenarios - 1) self rolled withdrawals with no income (red), and 2) same but with 15k income starting at 70 (blue):
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| Figure 1. Machine learning on (1st Quartile) real spend amounts with and without income |
The machine was left to its own devices to figure things out. The ONLY difference in the two scenarios (red and blue) was the presence of late age income at age 70 forever (eg SS): so, blue data have income, red data have none. The whole exercise was pretty rough-edged, which partly explains the roughness in the data, but in any case here are some observations I took away from doing this post.
1. Spend rates are really low early here for the red scenario where we do systematic withdrawals with no income. This low spend is called by some people I know a "buzz-kill"[3]. My SOs always thought I was a penny-pincher. But I like N Taleb who calls stuff like this "anti-fragile" because you basically have now created redundant capital, at least for a while (and at least as I framed it above). In Taleb world, one can now withstand at least some of the hard blows that might come later. As I mentioned above, the "low" spend rate is not really "low" if one visualizes the redundant capital as an entirely separate thing. Idle, yes of course, but separate. Ignore how it'd be deployed for now. So I can maybe say that spending in this world is both low and not low depending on how it's framed. It's like light, it has dual nature.
2. In later years (see red), as longevity risk comes in, the data converge with blue and the need for a reserve abates. The capital can be redeployed to consumption or bequest at some point. This makes it clear that we are dealing with an issue related to time and exposure.
3. With late age income present (even small amounts; see blue) so that later age "event uncertainty" is now hedged a bit, the need for redundant capital early goes down. In addition, the need for late age reserves for extreme superannuation horizon risk goes towards zero at some point, say 115-120. That means optimized spend rates can go up early in the cycle (efficient, right?[1]). We can see that the divergence (income vs no income --> spend rates) looks pretty wide in this set-up. And I didn't even tell the machine to do that!
4. This post uses an econ consumption utility framework so the big thing to note here is that at some point red will go to precisely zero which is also a modeling conceit. Zero consumption has infinite disutility and therefore is not really seen in real life and is more or less impossible to model in a fake model world given the math. This concept of infinite disutility is what gives the idea of annuities/life-income scenario it's strength (ignoring the annuity paradox for now, of course) and allows the blue data to take more risk earlier. Note that, in order to deal with this issue, I also usually bake into my models a very very very low floor of survival income from family, friends, associative-groups and government, of which SS can be a major component. Otherwise it's a "I sleep under a bridge and I get food stamps and have panhandling money" situation: not exactly zero, but close.
5. Blue here will never go to zero but will eventually "snap" to the 15k income whenever wealth finally depletes. In utility terms this floor softens the blow of a wealth fail and will almost always evaluate better than no income at all. It also means that wealth will almost always be depleted optimally before life end. No income and you have to reserve to all possible final days. Income? You can spend fairly assertively during the first x% of the lifecycle and then lean on income when the probability of being alive is low and getting lower.
6. We can see a difference here perhaps from the Bengen 4% rule. That rule bakes in known "risk" based on past market history but it is radically non-committal on "uncertainty." It takes no position at all on real survivability, something about which I am quite interested. That means that at an age less than 35, with an uncertain horizon, and unquantifiable unknowns I will always spend less than 4%. For the reserve. That'll change later, though.
7. The main point here, at risk of repeating myself, is that in the absence of life-income one must reserve, up to a point[2], for uncertainty of whatever kind: meteor strikes, plagues, superannuation. These are often un-modelable and un-measurable phenomena. So we reserve. Up to a point[2]. And then we let our grasp on that pile loosen up over time. Early on, it looks, to a naive eye, a little like a lower spend rate but it's really not if you believe my case above. It's just the effect of having a pile of redundant, underused, "inefficient" capital sitting around...for a while.
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[1] In the past post I mentioned, I referenced a paper by LaChance that illustrated the concept of optimal lifetime consumption where, with income presence, spending starts high and then drops to income at some age if we live long enough. The illustration looked like this, without any further explanation. The linked post has the reference:
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| LaChance |
[2] I don't think there is really a "point" where reserving for uncertainty is on or off. One can't hedge meteor strikes so one usually doesn't. The reserve might be infinite in that case. Normal vol in markets? Yeah, sure we hedge that, it's usually called "asset allocation." But we can also set a little bit extra aside in order to navigate the life we know, the life that doesn't really know any finance theory at all. That life is a little like planning for a fast-ball and forgetting the curve...or the covid hit-the-batter move.
[3] I've blogged and tweeted before that I flat out fired an advisor for looking down his nose and condescendingly telling me "live a little, bro." This dude has no idea, and he's an advisor. If anyone deserves the experience of ruin, this is one that I will offer to the gods."
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