This appears to be an extension of some previous work that Prof. Estrada has done (after naming names in a literature review) that tries to take all of us beyond "fail rates" in a constructive way (that right there makes his paper worthy before anything I say below) . And I think he has succeeded a little bit on this. The extension here is, at first, to use a coverage ratio (fraction of the retirement period a strategy was able to sustain a withdrawal plan) to evaluate retirement strategies rather than a fail rate. Why is this even vaguely interesting? Because it (the ratio) carries more information content than a fail rate does and not just information on "magnitude of fail" but also something about "scale of bequest" as well. I hadn't thought about that before. Here is Estrada and Kritzman:
The appeal of our coverage ratio is that it consolidates in one variable both the frequency and the magnitude of success or failure. For this reason, it provides more information than the failure rate (which measures only the frequency of failure) and shortfall years (which measures only the magnitude of failure). Furthermore, although the failure rate does not distinguish between two strategies that succeeded but left behind very different bequests, the coverage ratio (which would increase with the size of the bequest) does.Not bad I say! But since these guys are academics and not retirees and since this is mathematical ret-fin not real, it should be pointed out that real retirements typically don't, for the most part, really fail as such. Rather they bend and slide and get awkward. Lifestyle is compromised and adjusted, social security becomes a crutch, annuities might be purchased, part time work is sought, etc etc. Where retirements fail (ex spending shocks like medical disasters and bankruptcy) is usually before they even start: not enough is saved; work is not held long enough; feasibility is never tested; spending plans are not judged and found guilty. But given all those caveats, I think that using an analytical framework that carries "more information content" to the advisor-retiree table is not totally a bad idea.
The other extension they do here is that they don't stop with coverage ratios but also render them in utility terms as well (I don't touch in this post on their international empirical testing but that could be considered another extension). Forget for the moment that utility is an economist's shiny new Christmas toy that is fun to play with but rarely, if ever, part of a retiree's daily death march and that risk aversion parameters are, well, are about as firmly solid as the smoke from my Cuban cigar.
While we are confident on the form of the utility function we propose, we understand that there are no universally accepted values for γ and λ.
But in general I believe the Bernoulli-inspired utility approach to be a correct and good one. And they, Estrada and Kritzman, even take it a step beyond boring standard CRRA math, which I actually really appreciate. They proffer a split utility function which I believe to be pretty darn constructive in a retirement context. They point to literature from Alder & Kritzman as well as Czasonis to back this up but I have seen others do this kind of thing as well. I'm not sure but I think Milevsky has done this in something I read once and to which I cannot now point. In addition, and more concretely, I recall that Markowitz does the same thing in his 2016 Risk Return Analysis Vol 2.[1] To my untrained and naive eye they (Markowitz and E&K) are saying almost the same thing here with Markowitz being the more general. The basic point all are trying to make, as far as I can tell, is that failing some "threshold" of retirement wealth at some time T deserves a utility "penalty" in addition to the basic concept of utility increasing at a decreasing rate over some interval. I'm on board with that. With one exception.
As a naive amateur hack, I don't personally -- and I say this with no knowledge of economics or utility functions -- think they take even that (the idea about the split utility function above) far enough though it is a pretty good idea. And before I go any farther here I should mention that I once (in my own private Idaho of utility) tried to do an amateur hack (I need to trademark that expression) on the utility of retirement spending. I tried to make the case that standard CRRA utility sucks and that something that penalizes high spending/lifestyle for the implied ruin risk as well as what I call social-consumption-waste and that, up to a point, also penalizes low spending for its implied self-denial, potentially deferred spending, and the over-fetishizing of bequests made more sense. To me. ...I'm waiting for the call from the Nobel Committee...zzzzz...crickets.
So, while I think that both the Estrada and Markowitz split-utilities are great ideas, I also think that going to the right in both utility frameworks (wealth in Markowitz and Coverage Ratio in Estrada, both of which head deeply into into high bequest, high self denial, high spending-deferral territory) should not really mean that utility necessarily rises monotonically forever. There should be, in my RH amateur-world-naive opinion, a critical point (in the calculus sense) where utility gets ding-ed with a penalty for over saving and over bequesting (if that is even a word) and utility starts to decline at some point. The socially conscious might even say that this kind of thinking is why we have dynasty wealth constraints and so even if there is not a personal utility penalty maybe there should be at some other level. That's social justice logic that I refuse to take on here but it is at least worth mentioning. I'm willing to get swatted down on that. But think about it for a minute: a critical point. Un-examined territory. [2]
But that utility quibble is just that, a quibble. And not a very well informed one at that. Other than that I think this is a well informed, constructive paper and I am glad I got past my blah-blah aversion. The first quote from them above, by the way, carries 99% of the weight (for me) on why someone might find any of this useful.
Postscript -- I forgot to add this earlier. The other thing I like about the E&K approach is that it works with a ratio that is dealing in the interplay between consumption, wealth and portfolio longevity. It is the utility of a net wealth process. Utility of wealth alone misses the point that sometimes incremental wealth come from sacrifices in consumption utility (self denial) and utility of consumption alone misses that an incremental util of consumption might actually tip us over into the abyss (running out of money). Both need to be considered together which looks like the case here. This, when rendered as a probability distribution of "portfolio longevity in years" is one half of a formal analytic "lifetime probability of ruin" calc by the way. The other half would be a conditional survival probability vector. Maybe someday someone will (or has?) come up with a net wealth utility calc that is also somehow adjusted for being within a probable lifetime as opposed to just saying 30 years or something.
-----------------------------
[1] here is Markowitz on page 160 of the mentioned link. This just happened to be on my desk.
Here is Estrada and Kritzman just for reference...
[2] I realize that in a perfect world that the shape of the utility function should match some observed human behavior (and not just the behavior of an economists grad students) but I consider RH to be a behavioral pool of 1 and the idea I mention matches the pool's behavior or at least opinions. Scientific, no? The E&K curve, if rendered like my opinion, would go up and to the right at a decreasing rate, hit a critical point, go down a little and then maybe stay flat forever thereafter. This, of course, is silly and unprovable but why not? This is all just for fun...
No comments:
Post a Comment