Let's start with some ruin estimates just to set the stage. Here are 5 methods of estimating lifetime risk of ruin for a plausible set of assumptions[1] for a 60 year old with a balanced portfolio and a 4% constant spend:
| Method | Age | Longevity | Returns | Vol | Spend | Ruin est |
| sim | 60 | 95 fixed duration | Hist 50/50 | hist | 4% | 0.270 |
| sim | 60 | Soc Sec table | Hist 50/50 | hist | 4% | 0.100 |
| sim | 60 | SOA Annuitant | Hist 50/50 | hist | 4% | 0.142 |
| JPA | 60 | Gompertz 90/8.5 | 4% net real | 10% | 4% | 0.127 |
| Kolmog. | 60 | Gompertz 90/8.5 | 4% net real | 10% | 4% | 0.132 |
Ok, so there is some moderately low level of risk here, nothing too scary except maybe that to-95 estimate and even that is probably manageable with some spending flexibility, some good portfolio design, and maybe a little tactical allocation thrown in if that can actually be pulled off.
The Quiz
Now, the quiz. What happens to the probability distribution of portfolio longevity in years if we get a bad diagnosis from the doctor and now have a shorter life expectation? Trick question; the answer is "nothing." The longevity of the portfolio is independent from the lifetime expectation. What happens to the probability distribution of portfolio longevity in years if we take a super-pill that allows us to live to 200? We should have the hang of this now: nothing. Lifetime ruin is the intersection of two independent probability processes -- life and portfolio -- and the portfolio portion has its own nature that is worth examining.
4% Rule -- Conventional
The 4% rule "worked" it its day because of artifacts of time and place (US market history in the 20th century) and the selection of a 30 year time frame. I can't remember if the original study had a fail estimate or a confidence interval but it should have if it didn't since this retirement thing is a probabilistic process. I have seem some in the lit refer to a 5% or less fail estimate when talking about the study but I'd have to go look. Many in the press, academia and the profession of advisory now seem to be cautioning retirees about the current environment as they hazard guesses that lower spend rates are more likely to work than not going forward from here. That is good and proper. But that is not what we are looking at today.
4% Rule - 1000 years of naked ugly glory
Since ruin estimates are a joint probability of both life and portfolio I wanted to look at just the portfolio side. This is because the success of the 4% rule crucially depended on that 30 year lifetime estimate. And even if we add stochastic longevity (probably good; maybe less conservative) or a fixed-to-age 95 or 100 (maybe good depending on your planning philosophy; a little more conservative) we still do not have a real measure of the destructive force of a 4% spend constraint on a wealth process over time independent of the life-cycle assumptions. Just for fun so that we can see this, let's wildly exaggerate things (my S.O. hates it when I do this) and look at the whole process, both life (for context) and portfolio (what we are looking at), over 1000 years. If I take the 4th row in the estimate table above and instead of setting the number of periods I use for my mini-sim to 200 and instead of setting an age cap to 120 (typically used for max longevity), lets now set those to 1000 and see what happens. When we do that it looks like this:
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| view of lifetime ruin estimate over 1000 years |
Obviously the lifetime estimate fades towards obscurity when we do this. But this also shows that the reason that the 4%/30 year thing worked, and the reason that other planning estimates work too, is that we are here too briefly on this beautiful blue planet, something that we are unlikely to radically change anytime soon[2]. Then, if we follow the net wealth process all by itself and without reference to the lifetime estimate and let it continue, we see that the risk of "portfolio longevity in years" in fail rate terms is not really 5%. That was a joint estimate not to mention that it was also because we were slicing only the first 30 years off the front of the portfolio probability process. And it's not even 12 or 14 or 27%. Over time it looks like it limits out at something closer to 70% (a little less here but 70 is easier). That's a sobering view of a 4% spend process (with these assumptions). For what it's worth, notice, too, that the limit is approached pretty quickly within this long-arc view of time, probably within the first 100 years or so[3]. This happens to be what Prof Milevsky told me was a defective distribution. Over enough time the cumulative probability (here) is pushing 70%. The other 30% (that allow us to sum to 1) last forever. The two go together but I'll call it what it is: long odds -- even with our immutable, brief life expectations. I wonder what retirement planning would look like if we lived for even 200 of those 1000 years?
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[1] returns are assumed to be an initial linear return estimate for a moderate risk portfolio net of inflation, fees and taxes. Let's call it .04 with a std dev of ~.10.
[2] notice that the lifetime risk of ruin, based on the joint distribution, doesn't budge much because it is tied at the hip to longevity expectations.
[3] I should mention again that these are expected value paths and that individual paths can be better or worse. Also note that reducing spending to, say, 3% helps but does not change the long term picture too much or at least not without changing other assumptions like returns and vol.
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