On Outliers or a response that got away from me

I received a decent comment from a reader to which I started to reply. But (1) the reply got away from me, and (2) I can't really answer it very well. This is my response and, if anyone is interested, a challenge to the world to help me articulate a better answer. This was in response to what I considered a casual exploratory post
Another half-a** look at trend following and retirement portfolios.  The "half-a**" was the tell on my casualness. 

Here is the comment:

"I guess we can confirm that there is a fat tail, ..." 

Is it really a fat tail, or is it a normal distribution with outliers? Would a Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors, or Anderson–Darling test run on your raw data help you infer an answer?  

Also, you're binning data. That could the assailability of your "fat tail" conclusion, couldn't it? 

Here is my tentative response, tentative because it should properly be the start of a dialogue rather than an answer. I mean, really, how much do I really know about this kind of thing...yet.

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Hi. I’m not 100% convinced I’m well equipped to answer the comment.  All three of my readers know that I have no formal background in stats or probability theory unless we consider 1 bad MBA stats class in 1988 a “formal background.” I’ve also mentioned here before that I am recording a learning journey (starting more or less from scratch) rather than teaching anything of serious use to anyone...without a reader knowing that disclaimer first. I realize that that kind of response could be considered an un-attractive form of sandbagging but I guess the least I can say is that the question would probably be part of a good learning dialogue so I take the comment seriously and welcome it.

 

I have to also note that I feel like I am (lazily?) following a really large herd of people in a lot of domains, that range from naïve to sophisticated, that tend to call market return data not-normal and fat tailed. I haven’t spent much time (yet) thinking about challenging that language.  Maybe others have. In the end, as a retiree and an amateur, my thought is that outcomes and consequences in retirement have a hard time distinguishing between “causes with improperly labeled fat-tails” and “causes with a better-tuned description of a statistical process.”  Here, quick, try this thought experiment: in some year (or years, if we are thinking about sequence risk) a black swan of returns happens to meet a black swan of spending (with asset liquidation to fund the consumption) in which case we have, to a certain degree*, now permanently corrupted in the present our capacity to consume in the future.  Was that corruption due to an outlier or a fat tail or something that a Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors, or Anderson–Darling test could test? Doesn’t matter. Still kinda screwed.  If it’s not hedge-able, that is.

Speaking of spending… Spending is an example of where I think you are quite correct. In a past look at spending distributions that are asymmetrical to the right (like mine…something I called “fat tailed” at the time) we can now look at this through your lens.  And, in fact, this lens (call it “outliers”) was the conclusion I also came to back then.  Spending is not really “fat tailed” as such. What it is is something that is made up of two things: (a) a normally and narrowly distributed and reasonably predictable process that can be described** by modern statistical “stuff,” and (b) another thing that is either: i.) some kind of “outlier” thing, or ii.) some other unrelated non-typical-normal-statistical process that can’t be modeled or, if modeled, we are in Mandelbrotian world, or iii.) it’s just funky curveballs from the universe that we call outliers and then attach to a statistical “process” for our convenience…and then ignore.  As you say, maybe we can then test the “object,” however it’s defined, with sophisticated stats techniques.  Or maybe not. I think this kind of thinking and questioning is useful and as applicable to market returns as it is to spending. I’m sure there is lit out there on this kind of thing, I just haven’t seen it yet. Granted I’m not looking very hard.   

Maybe one other thing to contemplate in all of this is to also consider the evaluation of the consequences of things, to which statistics is typically blind, or at least deaf.  Think about it in trading terms or gambling with uncertainty. One has not only to deal with edge (that can be more or less subjected to statistics) but also odds (that can sometimes be a little more subjective). For example, in trading, I can be objectively wrong in a statistically predictable way 70% of the time but still make money because my payoffs and risk-management are good (and this can be reversed, btw).  Risk management is the big game here in retirement rather than stats because consequences matter quite a bit.  This, for me, is what makes a hard distinction between fat tails and outliers fade a bit. I gotta eat tomorrow, too.

But let me be clear. I very much agree with the push in the comment and take it as constructive. A casual reader should be aware of the issues implied here.  And the “binning” thing, when one has only discrete data, is a really good thing to contemplate. I also agree that I’d like to know more formal mathematics so that, at the very least, I do not embarrass myself too much in the future. On the other hand, at 60, I’m not sure how much motivation I still have for advanced prob/stats/calc etc. I had a ton of motivation for the last four years but it’s starting to fade.  But maybe this is an opportunity to up my game.

So, let me make a counter offer:  (a) you, or anyone, make a digestible “connect” between awareness and manipulation of “Shapiro–Wilk, Kolmogorov–Smirnov…” and “retirement outcomes and consequences” and I’ll guest-post it, or (b) show me how to do it and I’ll post it if I can figure it out, or (c) link me to the lit that an amateur can read and absorb and I might try.  Maybe.

* ignores lifetime income and human capital among other things.

** assuming inter-temporal stability and no state-jumps