A fantasy of exogeneity

The Setup

Past this sentence there is no modeling of real financial phenomena. This is just playing around with an idea just to see what it looks like.  This is also the second whack at an idea about modeling "critical states" like forest fires, sand pile avalanches and earthquakes.  Here is the idea: most research papers I read perseverate on returns and return distributions.  The normal distribution is the flawed baseline but usually close enough. There are others. T-distributions have usable fat tails but need to be fit. Gaussian mixes (GM) are often very usable but also need to be fit. I like GM since there is a "high note" of a relatively regular, probabilistic, narrow variance return process and a "low note" of much lower and/or very wide variance returns. This is easy to model but conceiving of the low note as a stochastic process might be "fittable" in the end but also wrong. What if the world had darker forces -- sometimes related to returns -- that are not a regular random process and not always a function of returns.  What if the earthquakes that hit us financially come from things other than returns (or regular spending).  Here we can take a stab at some ideas for what I mean:

Estimating geometric returns and wealth over time vs a simulated path

No grand goals here, just looking at an estimator for geometric returns over time (what we really earn) as well as it's correlate - wealth accumulation - and then compare to one very arbitrary simulated path.  Just for fun and to get the formulas into a spreadsheet.  For the estimator I am using R Michaud's estimator for the Nth period geo return and it's variance. Like this:

On Snow

“In any man who dies there dies with him, his first snow and kiss and fight. Not people die but worlds die in them.”   Yevgeny Yevtushenko quotes (Russian Poet, b.1933)

"Maybe it's wrong when we remember breakthroughs to our own being as something that occurs in discrete, extraordinary moments. Maybe falling in love, the piercing knowledge that we ourselves will someday die, and the love of snow are in reality not some sudden events; maybe they were always present. Maybe they never completely vanish, either.”  Peter Høeg, Smilla's Sense of Snow

On May 1st, 20__, I happened to walk out of my house directly into snow. Snow seemed, on May 1st, as improbable as a rain of frogs, but in Minnesota, in May, that might be a slight exaggeration. The improbability caught my attention, however, because it reminded me that whenever I go into my head and pull the name "X" from the catalogues of memory, as I had done just moments before I walked out the front door, the image of snow always comes with it. I am always amazed at how the brain works like that. I’ve been told, or read somewhere, that unrelated neurons can be triggered just by recalling the memory of another thing held in closely adjoining brain space. In this case I could almost feel the neighborly neurons firing and bringing up their dual images, the name and the image, X and snow. 

Playing with Gaussian Mixes and "jumps" again

There is no real hard science or rigor past this sentence so begone if you need that sort of thing.  

The reason to fling blog crud today was that I was coerced into reading a paper[1] on jump-diffusion processes by the inimitable David Cantor. I know nothing, really, of those processes but I came to the conclusion that my amateur attempts at doing a Gaussian mix in the past was kinda close. I mean, my vol was not really stochastic but both the return and vol "jump" within a random process and so we can, over time, with either jump modeling or mixes - close enough, right? - more or less mimic the fat tails of real world distributions, which in modeling-for-retirement terms is desirable. I think. 

Merton and a special case of optimal consumption

I think I've done this before but what the heck? If a retirement blog can't drool and repeat itself every once in a while, then is it really a retirement blog?[1] The occasion here is some thoughts coming out of reading Merton's 1970 paper on "Optimum Consumption and Portfolio Rules in a Continuous Time Model."  Either a hat tip or an accusatory finger pointed at David Cantor for this outrage  

In Memoriam - Dirk Cotton 195? - 2021

Dirk Cotton, one of the great retirement bloggers of recent years, was not really a close friend or an accomplice in Ret-fin crimes. But I did know him.  Here are some of my memories. 

Using an N-period Geometric Mean Return Estimate for Median Horizon-Wealth Outcomes

A reader of my last post (wow, I'm surprised I still have any; one is good, though) pointed out that even with spending set to zero, there is radical uncertainty about future outcomes (of course, because no one can predict the future) and he pointed to page 32 of Michael Zwecher's great book on retirement portfolios where he, Zwecher, starts to introduce the useful concept of income floors. That reader comment in turn reminded me that: 1) straight up terminal wealth sans spending can be estimated by way of the geometric mean without recourse to black box simulators, something I often blather on about here and then point, vaguely, to R. Michaud's work, and 2) I had never actually taken a direct look at the link between the two. Today is the "look."

Geometric Returns vs Net Wealth over Human Horizons

This post won't add much new to what is in a million other papers or posts, just working some personal stuff out. So this is just for me and the nerds.

In a past post I profiled how the annualized geometric return of a (stable) return engine is diffuse even at long horizons but maybe less so at very long horizons. My original point was that -- in terms of human horizons of, say, 20 or 30 or 40 years -- it is really risky to have volatile returns if you have a goal that depends on achieving a particular return (think "locking in a guaranteed lifestyle by purchasing an annuity at age 80"). The individual portfolio return you earn on your one path -- what Zwecher called "one whack at the cat" -- is wildly uncertain. Yes, if you held it to infinity and had some unwarranted conviction that the "return engine" would be stable that long, it would produce a mildly predictable result. This is the basis for the optimization framework of max{E[log(1+r)]} of Kelly, Markowitz, Hakansson, Latane, etc. 

Heat map of the expected time average of a non-ergodic process

This not really a dig on Ergodicity Economics. I did dig in the past but my point here today is to continue to look at the reality on the ground for human retirees when it comes to finance. EE makes the proper point that the time average matters more than the ensemble average and then they make maybe a teeny tiny bit of a "stretched point" that there is only one (ie log) utility function that matters.  So, I quibble, but only on the edges.  And as before, EE was not the first to the world on time averages in finance. Others were into this point well before EE. I don't know the proper list but let's say Kelly, Hakansson, Latane, Markowitz, Thorp, and a host of others. 

I mean, the geometric mean in finance matters and is also, notably, also a reasonable proxy for Monte Carlo simulation in the right hands (not 25 year old advisors, btw) because the geometric time-averaged mean is also representative of the distribution of terminal wealth outcomes. It is, in that sense, directly correlated to median terminal wealth (cuz of course the average is meaningless due to extreme wealth outcomes on the upside). 

10,000 years of a geometric return series - revisited now for time in years to get above a threshold

This is a re-look at a post I did in September. Then, I ran a "return engine" 10,000 years x 1000 times to look at the shape of the annualized geometric return paths that come out of that multiplicative process. The idea then was that there were a ton of differences in the paths that kinda iron themselves out over ~infinite time. The problem now being: none of us have infinite time and the early years -- economists or physicists new to econ or finance notwithstanding -- can be pretty hard or unnerving.  So now, the question today: how bad can it be -- or how long can it take -- over the foreseeable and unforeseeable future? I am sure there are better mathy ways to do this kind of post but I don't know. As I have beat my own drum before, I am an amateur!

Reminiscence of my Brother in Law.

Some thoughts about a recent Zoom memorial

A dream about pain and war

I had a dream a few nights ago about pain and war and raising a family. None of these ideas cohere, really, but here are some post-waking remnants of thought that eventually, after a few minutes, evanesced a bit like smoke in a high-ceilinged, well ventilated room. 

To whom does a man say “I’m in pain” these days? His kids? No, they’re to be 100% shielded; their world is the future. Wife/girlfriend? Maybe, I suppose, but it’s always fraught; with enough prodding they will eventually desire stronger, higher status men, their princess-day vows and protestations and fake “unconditionality” notwithstanding...I mean, eventually even the feminists will turn away though we know they already have. A boss or co-worker? You’re fired! or passed over. Social media? Even cannibals will eat less of you. Other dudes? Maybe not in this weak age. Anyway, other men should generally be brothers and partners not therapists or confessors. Only one vector remains I think: inward deeply, like Augustine or Buddha or Montaigne, though none of these were warriors (well, Montaigne did serve at the siege of Rouen)...then out...out to the world, like the steppe Khans with horse and bow and a vast continent opening in front or maybe like the scourge of the North Sea, complete with longboat and axe and seax and spear. F’n McClay, and Goldmund, had it right all along but maybe I already knew it; idk. Thus sprouts the toxic, stoic myth of men, of course, but none who are not men or God can really judge any of this and I submit judgment of me, now, to me and God alone. My kids can vote, if they want, but I own the deciding one.

Even my second coffee could not shake me of the faint scent of the saddle or of the North Sea and polished seax. I fold laundry, now, and complete a dishwasher load. Then I oil my four seax with a fine textured mineral oil that is well-matched to their carbon steel. 

On Adverse Possession

In 2004 I moved into a new house with a peach of a neighbor.  He lived next to me in a 7br mansion on the river. The houses across the street from us were 1 or 2bedroom econo homes, so a bit of a class divide depending on how you look at it if I can still say that kind of thing.  To give a flavor of the man, the neighbors across the street told me that when they complained about his contractors backing into their driveway – drives that were over a peat bog and thus degrade easily – his response, as paraphrased by one man that heard it, “I don’t care about you little people, I’m rich.”  Maybe he was or wasn’t, idk. The house signaled status but more on that later. In appearance he was a blue blazer, tan pants, and bow-tie guy.  But sartorial descriptions are banal. Here is a better way to frame it: he had a condescending smirk perfectly located halfway between his Harvard MBA bowtie and a mop of past-the-right-age prep-school hair that Tyson would have loved as a target. 

On rebuilding eyelids

This for all zero of you interested in how an eyelid is reconstructed. I only know the details because I had most of a lower one removed a few years back (skin cancer of the lid margin which I heard is more common than one would think; remind your kids to wear UV sunglasses...) . This post, of course, has nothing to do with retirement finance.

Stochastic Present Value with a Floor

As I try to wind down my quant ret-fin stuff to focus on act IV of my V acts of life, I still, every once in a while, have that "I wonder what ___ would look like" moment. Today I wondered, without any real strong goal in mind, what a stochastic present value (spv) of spending would look like with a floor added in.   I had a guess but I wanted to see. In the end it probably doesn't matter since I don't manage a pension fund and as my ret-friend Ken Steiner reminded me sometimes simple is better especially when working with humans. In other words, if present value is a step too far for many retirees, then spv is an alien. But I still had that "wonder" thing.  

On inflection points

The astute will know that I have been bitchin about my blogging for maybe 2 years. The hyper-astute will recognize that I haven't done much since then. What gives?  Good question. Writing, as they say, is thinking and so therefore I will write.  

On an "early" retirement

Periodically I get asked if I am or was "FIRE" or alternatively "why did I voluntarily retire at such a risky age." Neither FIRE nor voluntary are completely true but neither are they entirely false. This kind of fuzz, and the question, demands -- even if it's only me consolidating my own thoughts by way of writing it down -- an explanation.  

On the affinity between PWR and SPV

This is a guest post from a reader that contacted me after I did some posts on the affinity between a net wealth dispersion process (aka MC sim if it is done right) and stochastic present values (SPV or feasibility).  The reader, self-described as "You can list me as "Rodney Smith, another (very) amateur retiree interested in retirement finance" made the case (said he had a short proof) that PWR and SPV are allied as well.  Doesn't surprise me, I think. Most of the math in the retirement stuff I see uses same or similar parameters for vaguely related ends. I told him "cool, send it up and I'll put it on the blog for my three readers." Heh.

Here, without comment or checking his work (I am not an instructor, just a corner-cutting old-man blogger), is his proof. Thanks Rodney. 

Real option value of spending less over 20 year horizon

The basic premise here is me trying to figure out the "real option value" of different allocation and spend choices over a 20 year horizon (65->85...ie when I might annuitize stuff) where the strike is the then cost of annuitizing $1 of consumption conditional on a longevity estimate at age 85 plus some margin of error (the strike). 

The absurd simplicity of my own retirement process

This from a PhD-pension-dude yesterday to someone else about my last post: "...he could use some help..."  Heh. No doubt. But probably not in the way he thinks.  What I need help with is getting firmly into what I call act IV of my V-act life and/or monetizing what I've learned.  What I need less help on is blogging or retirement finance.  And anyway, PhD dude is still young and getting paid. He doesn't feel any of this in a real way yet.