A hidden variable

I haven't thought this through very carefully but I thought I'd throw out a quick impressionistic riff anyway.  The idea here came from some past work where I convinced myself that even though the 4% "rule" is common in the personal finance literature and even though consumption smoothing (e.g., the 4% rule's method) is considered to be an expression of risk aversion in the macro-econ lit, a 4% constant inflation-adjusted spend is actually quite risk-seeking due to the compounding effects of errors.


Even though a constant spend is smooth and feels good, the 4% constant spend of the original study just got lucky "historically" using the available data and lasted a min 30 years for a retirement starting in 1966, if I recall. Viewed in dynamic mode, however, scrolling from year to year, one can see that the actual risk in any year, based on portfolio value and updated longevity estimates, varies quite a bit and goes sky-high at times. A more nuanced approach would have lasted longer and been less nerve-wracking along the way.

This kind of awareness is not a vote for percent-of-portfolio rules, though. That approach creates a ton of lifestyle volatility and would likely violate some minimum spend requirement in some years.  Nor is it necessarily a vote for "spend rules" which are often ad-hoc and sometimes un-anchored in economic rationality (though are often more helpful that a willful blindness to a changing environment).

My point about the 4% rule is that in any given year it is almost by definition likely to be the wrong answer if one is making a joint allocation-spend choice where each year (or moment) can be viewed as the beginning of a new retirement.  The difference between the 4% rule and a "better answer" in some future year is more likely than not an error and errors compound just like interest compounds in a positive sense.

The following notation is probably flawed but tries to convey my point.  w here is wealth in units, mu is portfolio return based on allocation choice at the beginning of some period, 1 is one unit of consumption (say the 4% rule) in period t, and epsilon (the hidden variable of the title) would be an error term over the whole net wealth process including both spending and allocation (think of things like errors in rebalancing amounts or timing or maybe inattention to financial marketplace innovation plus spending errors like lifestyle creep or habit formation or the presence of random or chaotic spend shocks, etc etc).  Note that longevity is implicit here and would influence the unit-of-spend choice and maybe the allocation but is otherwise not modeled. Also, it looks like positive and negative errors might cancel but the presence of consumption and sequence risk generally make errors a destructive force in my opinion. I haven't touched on this last concept here, this post is just a straw-man for now:

net wealth process with error

It's doubtful that we'd ever get spending+allocation exactly right at either the beginning of retirement (think 4% rule) or even in doing it dynamically over time, hence the need to acknowledge the error term.  It's just too hard and there are too many moving parts.  So the goal might be to not only swag at least a decent estimate of the allocation+spend at the beginning of retirement using whatever tools are best for the job, but also to: (a) keep doing it every year, and (b) try to keep the errors reasonably low along the way so that they don't unnecessarily compound -- which is where the 4% rule makes its biggest mistake.  Blind allegiance to an initial spend allows the errors to compound and my guess is that they would, via Murphy's law, compound to a tipping point at the worst possible moments. I described this updating effort as a triangulation and continuous improvement project in my 5-process series here.  There's probably more to say on this kind of thing but I just wanted to get the idea down on paper while I was thinking about it.