Dec 30, 2018

Cotton on Ret-Fin 2018

I love this recent post ( Lessons from 2018 ) from Dirk Cotton. It reminds me that I spoke to him recently and that in addition to discovering that to some minor degree we have led parallel lives, he is also as gracious and intelligent in person as he come across as in his blog posts.  His points in this particular post resonate, probably due to the parallel lives thing. Here are some thoughts.

1. Retirement Finance v Relationships

At first glance, this might seem like an odd opposition. But when I saw Dirk tease his wife in his post for only having an interest in retirement finance as his hobby when engraved knives are at stake (steak?) I realized that it was not the first time I had encountered this concept. When I met Prof. Milevsky in person, he told me that his wife teased him about his odd choice of interest in something so quantishly obscure...and this is probably the top retirement-quant on the planet.  Me? Well, a small part of me kinda sorta maybe thinks that my perseveration on retirement finance is at least a teeny tiny part of the ending of a relationship. That idea is odd from a couple directions. I mean, which is weirder here? My perseveration on ret-fin as a “hobby?” or that someone would be so put off by it.  I have to give some serious consideration to #1 when contemplating weirdness before I start to think about #2.

2. The Power and Glory of Sequence Risk

Dimitry Mindlin scoffs at sequence risk as a dominating issue (The pitfalls of sequence risk, 2016) but I might hazard a guess that Mr. Mindlin is not yet retired and does not feel the full force of no W2 income and almost certainly depleted human capital.  As Dirk points out, does a nice cover of the impact of sequence risk.  I am familiar with the math that ern uses which is basically the same root as the perfect withdrawal rates articulated by Suarez and Suarez in “The Perfect Withdrawal Amount: A Methodology for Creating Retirement Account Distribution Strategies” (2015).  In one of my recent posts I deconstructed their math to show that the intuition on sequence risk can be apprehended directly from just looking at the math itself.  If one were to have an initial endowment of $1 and an ending one of zero, it looks like this below which is also the “perfect withdrawal rate” or what one could spend if one were to know with perfect foresight the sequence of returns that will be realized over a planning interval. I call it the capacity to spend because that is what it is, given full hindsight at the end of life. 

One can see in this that the capacity to spend is entirely a function of returns and how they "stack" in sequence.  Just looking mechanically, there are more “r”s at the end (look "vertically") so that low returns early and high late makes a big number which would make the PWR lower.  It may also be helpful to think of early spending as an opportunity cost of compounding capital (if I have it right. look "horizontally") that hurts us because we could have captured some of the late high returns with money that was otherwise spent early. Me? As a retiree I will clearly be hurt or helped by sequence but there is nothing much I can do about it except to be cautious in my early spending or hedge it out with lifetime income by way of an annuity.  But Dirk points something out here that I have mentioned before in this blog.  Sequence risk is not a "partitioned" risk that only attaches itself to some specific and artificial early-retirement interval.  Given unknown longevity, one’s retirement is in fact always in a continuous state of becoming (let's call it a process, then) so that technically one is always in the early part of retirement which means that one is always exposed to sequence risk. Yes, with two years to go the impact is not as severe as it would be with thirty but the risk is not entirely gone either.  This was a cool point that I have not seen elsewhere (except here at RH, I guess).

3. Beware of MC simulation and ruin.

Dirk, appropriately in my opinion, asks us to temper our enthusiasm for the use of Monte Carlo simulation and risk of ruin metrics.  There are probably three types of users of MC sims: those that know nothing and don’t use it or limit its influence if they do, those that know a little bit and place a little too much weight on it without really understanding it, and those that are steeped in the math and design. The second group is dangerous and the third often have either a misunderstanding of or a limited knowledge of the underlying processes being modeled, the processes that might drive outcomes in real life (hence my proposed "5-process" series). This leaves us with the first group which, counter-intuitively, is maybe the safest place to be when it comes to MC simulation.  

Ruin as a metric is probably less useful than many suppose. It should be obvious that it is neither truth nor the future and for the most part – except in the extreme with things like bankruptcy or seriously unfortunate and expensive life events – people are not really "ruined" all the time in the sudden and extreme sense that one might suppose from the word itself. Behaviors change, jobs are taken, lifestyle degrades a bit, spending snaps to available resources, institutions and social programs step in. That makes ruin more often a mathematical abstraction.  This is fine because it is also an integrative abstraction which means that if one were to happen to have a good grasp of the underlying processes (e.g., return generation, spending, portfolio longevity, random lifetime, and time) that go into estimating ruin probabilities, then the ruin concept is not totally un-useful. It becomes just one more risk metric in a stable of many and it's maybe not even the most important one even though it can sometimes make a lot of "noise." As a generalized risk metric, it is akin to the lane warning systems in modern cars that buzz your seat when you stray from your lane.  The buzz can either be interpreted as “omg you’re going off the road and you are going to die” or maybe it can instead be interpreted as a minor "nudge" designed to get you to change your behavior (just turn that steering wheel a tiny bit…sooner is better than later) before anything really bad happens. This also, by the way, makes ruin evaluation a continuous process, rather than a one-time pronouncement, as long as we make sure it is understood in it's dashboard sense rather than some view into the future.

Dirk is also correct that magnitude (say "years in a ruin state") is often ignored in fail metrics and ret-fin literature. He is also correct that utility in an economic sense gets to the heart of this better than an arbitrary x% fail estimate in N years. I’m not a big fan of utility but the non-linearity of the math does a better job of evaluating consumption plans especially when they are discontinuous due to depletion of wealth before one’s time is up. My model for this type of evaluation is here: A Wealth Depletion Time Model.

Un-mentioned, however, is the idea of "thresholds" on fail rate estimates which is another thing often missing in the literature. It’s missing because no one really knows what it/they should be and no one knows because it is rather arbitrary. It's arbitrary because there is nothing to help us make it less so.  Here is a quote from a recent (unattributed, sorry) paper I read recently: “What do we consider to be an acceptable risk of shortfall? That is a decision for every retiree or planner to think about, but our choice is 10% [I've also seen 30%]. We think that many people would choose 5%, but we know of no formal evidence on this question. [emphasis added].

So, yes, beware of MC simulation and ruin. Or, alternatively, understand the underlying processes on which these concepts are based and monitor those in real time. Since I have literally lost count of the numbers and types of simulation programs I have created in different languages for different purposes I feel relatively comfortable with passing judgement here on simulation and its discontents not to mention its uses and abuses[1]. I am in accord with Dirk on this point.

4. Ret-fin for the Un-wealthy is More Important Than it is for the Wealthy or the Destitute.

The social aspects of retirement finance are underappreciated in the literature I read and I am gratified to see Dirk address this. I have seen some of the work by Pfau, Vernon and Tomlinson that he mentions and appreciate their efforts, too.  I try to tune into the papers and articles I read that come close to this topic but I see so few.  But before we even get to woke issues like inequality, we should at least be aware of the relative importance of retirement finance to different cohorts of age and resource availability.  Retired early or more conventionally retired but lacking resources and living on a razor’s edge is an entirely different situation than being really old, unhealthy and rich.  If we were to over simplify and say that there are three types of retirees – the non-feasible, feasible but just barely, and really rich – only the middle cohort cares about this subject and the closer to the line the bigger deal it is.  This is why I took up retirement finance: fear of the line.  Maybe visualize it like this:

Good post.  Happy new year, Dirk.

[1] This is why closed form analytic expressions are often useful for reasons other than getting tenure or impressing other academics. Simulation is the easy way to get insight into the same thing except that the analytic forms are more transparent and show the relationships involved. From a recent 2018 paper by Bilsen et al "Consumption and Portfolio Choice under Multiplicative Habit Formation:" "Having closed-form solutions has three key advantages: they reveal the roles played by the various model parameters, they are readily amenable to comparative statics analysis, and they facilitate the implementation of the optimal consumption and investment policies." That last point is more debatable than the first two.


  1. "In one of my recent posts I deconstructed their math to show that the intuition on sequence risk can be apprehended directly from just looking at the math itself."

    I think that ERN's analysis is good & useful but I think it does something subtly...well, not wrong exactly. But it means it isn't actually showing "sequence of returns" versus "portfolio returns" the way most people think about those things.

    The key step is that ERN uses real returns. But real returns are actually two things: portfolio return + inflation. When most people think about "sequence of returns" their mental image is about the portfolio return -- big crashes and so on. No one ever says "what if inflation is really high in the first few years of your retirement?"

    A year or so before ERN's article I did a similar look into sequence of returns:

    and came away feeling that when you decompose real returns into nominal returns + inflation, then inflation is ~10-20% more important than sequence of nominal returns.

  2. I think you are probably right. I am following Suarez and Suarez (2007) by thinking in simple real terms here and calling the equation denominator (same eq as ERN, and some work by Blanchett and Estrada for that matter) the sequencing term; from Suarez "To make the interpretation more natural, we’ll say that it is the reciprocal...that captures the sequencing effect." My recent post on "spending processes" does some additional work to separate spending and returns within the sequence topic (when not focusing on a particular bequest) since inflation has an effect on spending more than returns and spending has its own sequence issues. Other than that not sure what to say so I'll offer a story instead... I was born in '58 and my father passed in '65. I watched my mother push 5 kids thru the late 60s, all of the '70s and a bit of the 80s on what would now be called a SWR from a very modest endowment. The combo of low returns and high inflation was extraordinarily destructive to both lifestyle and portfolio longevity. She passed while running on fumes. So, I fear the 1970s more than the 2008-9 GFC and for more than its disco and leisure suits.

    1. *Suarez E., Suarez A., Walz D, (2015) The Perfect Withdrawal Amount: A Methodology for Creating Retirement Account Distribution Strategies. Trinity Univ.