On Stochastic vs. Deterministic Models

Ken Steiner took on Dirk Cotton in this recent post (Do Stochastic Models Necessarily Do A Better Job of Helping You Determine How Much You Can Safely Spend This Year?).  Now, I generally would not take on Dirk but that is just because he is one of my top favorite retirement bloggers.  On the other hand I think that Ken, like an awful lot of other things in life, is both right and not quite right here in his defense of simple deterministic spreadsheet models. His post triggered some thoughts and since this is a blog, you get to have them...

I think that the points that Ken makes, that you can read for yourself, are correct. But I also think that it is not really an either-or "oppositional" proposition (I don't think Ken is saying that either, nor do I think Dirk is for that matter) but rather that the retirement analysis task is not only a both-and "dyad" of stochastic plus deterministic but it is possibly better represented as a triad (if not more).  In a past post I implied that for retirement analytics I prefer for myself to have three things in my tool kit -- (1) analytic, fully conceived closed form mathematical expressions; (2) simulation tools; and (3) simple deterministic models or spreadsheets -- rather than none or one or two. Let's take these on one at a time and see where it goes.

1. Analytic expressions  

These are the hardest and typically owned and operated by the academics and PhDs and sometimes rarely by amateurs.  But they do offer a degree of transparency as well as some honesty (while being a little abstract or "fake" in some fundamental way) in representing the underlying real-world processes they attempt to describe. They are a guidepost and interpreter in a foreign land.  Here is a quote by Siu Fai Leung in The Dynamic Effects of Social Security on Individual Consumption, Wealth and Welfare

While simulation analysis is certainly valuable, it would be even better if analytical results are available to guide the analysis and interpret the findings.

Maybe this is just PhD-talk defending PhD-rents but I don't think so.  I think the expressions are "fake" but do hold a dim candle up to the truth when they are good.  And sometimes they are good.

2. Simulation.

Simulation is often a short cut for when there is no analytic expression available or the analytic expressions are too complex to be easily accessible.   They (simulation tools) are generally easy to construct and give output that, while "fake," is easy to digest while they also provide valuable insight into the underlying real world processes they are attempting to represent.  But they are also generally kinda opaque (or black box-y, as Ken says).  Here is an example of how I think this works.  Let's do a little mind game. Let's take some real world phenomenon where we think there is some future "option value" to be evaluated where there is no market available to price it (let's say "the option value of not annuitizing" which Milevsky covered and I tried to play with here).  For the first part of the game, try on your own to derive and then apply the mathematics of option pricing (e.g., a Black Scholes model) in order to come up with and then interpret the result.  For the second half, do the same thing but now do it by way of simulating the evolution of the process being modeled.

Part 1 is going to take you a long time if you can even do it -- and it took the world a long time to do it -- and when you are done, you have to stare at the various expressions of the math for a really long time to be able to see what is being done.  But once you do it's like one of those 3D pictures where you can't see it until you can and then it's like "Oh. yeah..."

Part 2 on the other hand, in informed hands, takes about 15 minutes to code and a few more minutes to interpret (how do I know that? I did it). But then again it is pretty hard to see what the sim is really doing inside the box.

So simulation, like analytic expression, is also fake, and possibly more opaque, but it is easy and provides insight -- maybe even more insight than the next item on deterministic models but maybe less than the prior item on analytic expressions.

3. Deterministic "spreadsheet" models

Read Ken's post because I think he does a better job than I could do at defending these spreadsheet models.  My main thought here is that spreadsheet models are sometimes really really fake -- more fake and maybe even more misleading than 1 or 2 -- but they, too provide insight while having the added benefit of being less opaque and sometimes even fun.  Fun? By that I mean that they are visual, interactive, and fast which are underappreciated features. That is why I have called some of my spreadsheet models a game.  BUT, there is a caveat.  It's not just that to deploy them in a useful and honest way that one needs part 1 and 2 above it's that one also needs item #4.

4. Experience

Wait; what? "you said there were only three." Ok, yeah, but I forgot experience.

First, there is just plain life experience in how things work.  You may know things from life that all the analytics in the world can't convey in a meaningful way to the retirement problem

I believe that individuals spend far too much time studying billionaire fund managers and not enough time studying normal people who have successfully retired. -- Ben Carlson

I think you need this kind of thing to successfully deploy all three approaches above and maybe especially for the third but once you have it the whole dyadic controversy of sim v deterministic fades. A lot. Without experience the whole debate is moot.  Neither is good.

Here is another mind experiment but now focused on experience. Let's say there are two foxholes in the middle of a "rain of steel" firefight in a time of war.  Foxhole 1 has a newly minted second lieutenant with a pure mind and powerfully analytic (analytic or sim, take a pick) battle plans. The second hole has a gunnery sergeant with experience from five different battle campaigns over 10 years (and to sustain the metaphor let's say he has only a spreadsheet).  Now you have to go over the lip of one of the foxholes into the fray.  Which foxhole do you choose?

Good choice.  Experience matters.

The second, and not completely unrelated, type of experience I am thinking about here is not so much raw seat-of-the-pants stuff it is, rather, a seasoned and reasoned and studied appreciation for the mechanics of the underlying processes at play. It is maybe like looking at a dead engine and knowing how fuel injectors work. Or the alternator.  When thinking about any one of the three categories above I think it is useful to have a working knowledge of injectors and alternators.  For those imperfect metaphors I will now arbitrarily replace them with three things that I think are important:

1. Return generating processes (not markets, not allocation, not prices...at least not yet)
2. Human longevity probabilities over time, and
3. A fully informed view of the non deterministic retirement spending process

a.  Return generating processes

Forget portfolios or asset allocation or ETFs or funds or fees for a minute.  I think that children in middle school should be taught something about return generation processes.  Ok maybe not that exactly but they should at least be taught things like multiplicative time processes like what we see in geometric return series over time.  They should also be taught how a little bit of random variance can affect a result...again: over time.  In addition I think they should be taught about the difference between an average result and: (a) individual paths [think sequence risk here], and (b) the situational meaning of median outcomes vs mean outcomes [think of the lognormal outcome of prices or wealth here].  If I respect middle schoolers enough that I think that they should and could start to appreciate this type of thing, then I think it should be mandatory on the application to retire.   (there's no application? hmmm)

b. Human longevity probabilities over time

This is a bit of a stretch but I think that every retiree should have at least some working understanding of mortality probabilities.  This is not that easy but I think that using a 30 year fixed assumption is a huge disservice to their future and their intelligence.  Especially if they are 90.  Or 50.  Knowing something about a "distribution" and how it changes with age and how it both does and does not change with the advances in medicine is kind of a big deal. This is a weak point in the industry and it saps the ability to interpret the output of retirement tools.

c.  Fully informed view of the non deterministic retirement spending process

C'mon. 4% constant spend? That was always a joke, right? Retirees should have a general understanding of at least some of the following knowledge about spending processes: budgeting, data collection reporting and analysis, basic random spending variance, chaotic processes singular (think spending shocks), chaotic processes plural (think cascades of self-reinforcing feedback loops that lead to bankruptcy), and, dare I say it: continuous process improvement methodologies for spending (think management and monitoring and change systems).

So, experience.  That means Ken is right. And Dirk is right.  But at least someone in the mix needs to have experience. Hopefully the retiree. The problem, though, is what Thaler described:

For many people, being asked to solve their own retirement savings
problems is like being asked to build their own cars.
—Richard Thaler, University of Chicago

On the other hand, a well informed skeptic with a seasoned sensibility and at least some knowledge of how the underlying processes work can look at any tool's output and use it to their advantage while seeing and then discounting the weaknesses.  There'd be no this vs. that, sim vs. spreadsheet. It would be all of the above and more. I also think that a good candidate for retirement would not need a retirement priest to interpret the runes.  Everything they (retiree) look at should look vaguely familiar to them and inspire a recognition of the underlying processes that they are looking at and also what it means for their immediate choices. In the end, they should:

• know how to interpret results based on both education and experience
• know how to properly frame the choices to be made, and then, importantly
• know how and when to act

End.

Ok, not the end.

My Retirement Bootcamp Idea

This post reminded me that someday I want to create a retirement boot camp if I can't prevent people from retiring without a license.  The syllabus would be more or less tied to the above but let's recapitulate some of it here. But first, let's be clear. The boot camp would have absolutely no discussion of things like

• 401Ks or Social Security claiming
• Nothing (yet) about 4% rules or systematic withdrawals
• Nothing about annuities or insurance
• Nothing yet about asset allocations or ETFs or mutual funds or whatever

These are things about which the current financial industry can opine forever and for which they are paid a pretty penny or two too much and on which they effectively now deliver with only some degree of ambiguity and inefficiency.  No, MY syllabus would, in my idealized world, be something like this:

Workshop 1 - Intro or remediation: basic probability theory

This could be anything that introduces a 50 or 60 year old to probabilistic processes. It could even introduce some history and philosophy as it might be found in something like this book I just read. The sky is the limit. Actually this would be moot if we would teach this in middle school. I would take this class because I need some remediation. 

Workshop 2 - Intro to return generation processes

Discussion and lab-work on geometric returns and multiplicative time-average processes over time.  Some discussion of the modeling of normal return distributions with breakout groups on real returns not really being normal. Some discussion of lognormal price processes and the difference between median and mean end states. Some discussion and lab-work on the weird effects of volatility over time and a bonus class on the effects of volatility within multiplicative processes over non-infinite time horizons.  In addition, there would be self study on things like path dependencies, sequence of returns risk, and other oddities.  No discussion of markets or portfolios or asset allocation or stock prices; just how returns work over multiple periods. Period.

Workshop 3 - Spending in Retirement

This workshop would "break" the recruits and then rebuild them. After the re-build they would know something about what I described above: budgeting; data collection, reporting and analysis; random variance; chaotic processes singular; chaotic processes plural; and continuous process improvement methods.  The deliverable at class end might be a basic income statement and some simple reporting and analysis tools as well as a signed commitment sheet relating what they plan to do when they get home.

Workshop 4 - The Household Balance Sheet

Week 1 - build a basic balance sheet, introduce present value concept to remedial students
Week 2 - day 1-3 discussion and calculations of present value items (SS, spending, pensions)
Week 2 - day 4-5 build a basic actuarial balance sheet

Workshop 5 - Introduction to Longevity Science

This would be mostly lab study and self discovery related to the shape of longevity distributions and conditional survival probabilities, actuarial tables, mathematical representations of same, and the change in conditional survival over the survival interval, etc.  There would be lecture and film on (a) the evolving and expanding nature of longevity with advances in medicine and (b) the shrinking nature of longevity in response to the opioid crisis and also in times of war.  Pre-req: workshop 1.

Workshop 6 - Portfolio theory for the poet

I know I said no asset allocation but I changed my mind.  The workshop would introduce the concepts of MPT in a gentle way.  Students would end the class with a basic understanding of an efficient frontier, the effects of non correlation and the incremental impact of adding either correlative or non-correlative assets to a retirement portfolio without getting into a discussion of things like planning horizons or multiple time periods.  Advanced students might have a half day discussion of arithmetic vs geometric returns as they relate to the efficient frontier. The skulking know-it-alls in the back row would be forced to breakout to explore links and interaction between utility theory, Kelly criterion and the Markowitz mean-variance efficient frontier.

Workshop 7 -  "Wealth Depletion Time" Game Week [optional]

Ok, I know I said no discussion of SS claiming strategies or annuities but I changed my mind again.  Students would be exposed here to simple utility math and theory as well as to the idea of optimal lifetime consumption with and without bequest.  Students would also be exposed to the idea of an interval of time in the late life-cycle where, in the presence of pension income and in a theoretically optimal "plan," wealth is depleted.  There would, through a series of competitive team-oriented games, be learning around the interactions between social and purchased income, longevity, net wealth processes, and lifetime utility of consumption.  Students intuitions about allocating some wealth to insured income solutions would be expected to shift by the end of the workshop. Pre-req: workshop 1, 2, 4.

Workshop 8 - Retirement Management and Monitoring systems

This would be a hands-on workshop for developing personal tool sets for managing and monitoring retirement processes: income, spending, actuarial balance sheets in process, feasibility, ruin risk, annuity boundaries, etc.  Advanced students might study utility and economic models related to dynamic asset allocation over a lifecyle as well as the impact of planning choices on the utility of consumption before and during a late-cycle wealth depletion interval.  Weekend seminars would explore the role of various modeling methodologies and their relation to lifecycle decision making.  Lab work might include building simple spreadsheets. Advanced students might code some simulation tools in R or Python.

The class price would be $1M per head per week.  Meals and lodging would be included.  The student would be expected to emerge from this class fully able to dissect and interpret the Ken Steiner vs Dirk Cotton debate. But, like Dorothy in the wizard of Oz, and notwithstanding all of the above, they already can. They just don't know it yet.

---------------------------------------------------

Stochastic vs Deterministic - Part 2