A riff on time...

I know I'm more oblivious than most so I am probably the last reader of finance to have come to this kind of epiphany. For several decades I was under the illusion that the "amount" or the number of things is what matters, which it does of course in some essential way, but really it all seems, in the end, to be a little bit more about time. I mean, yes, in grad school we learned all about managerial accounting and present value analysis and yield curves and stuff like that but any discussion of continuous-time finance or geometric returns or other time effects was more absent than not. MBA is not really where one learns that stuff of course -- or it didn't used to be in the 80s -- but it seems a little odd now in retrospect that I missed it. 

Volatility, spending and horizon wealth

There is nothing necessarily new or systematically thorough or dispositive here. Just curious about something I think I might have already covered years ago.  The idea is to take $1, grow it at 4% with volatility of N[20%, 15%, 10%, 5%] and a spend rate of 4% over 30 years; 10,000 iterations. This is standard MC sim territory. No epiphanies or conclusions out of this. Just wanted to see what these distributions (using R standard density function) looked like when overlaid. Ignore the interpretation of negative wealth for now.  

X is wealth outcome at horizon = 30

Y is density inferred from the simulation. Might have been better to have done a P mass/hist but the lines are easier to see

• black = 20% vol
• blue = 15%
• red = 10%
• green = 5%

Would I pick up a million dollar bill in the street?

I'm one of those oblivious and penurious cheapskate cranks that wants to live more or less forever and spend only portfolio income and then die with way too much unconsidered legacy that will go to the ungrateful and the unaware.  You know, an ex South FL girlfriend once even called me a parsimonious tightwad and killjoy. Ok, she didn't really say that exactly and "parsimonious" was not in her stunted vocabulary anyway. (Heh, Sorry X)  Also, it turned out she was only miffed because I wasn't pointing a flow of nest egg units towards her (this being So FL and all) but rather towards present-me, future-me and my kids -- what I call my razor's edge path. Another "heh" (sorry again X, my kids and razor's edge trumped your self interest!)

How much faith do I have in the forthcoming equity risk premium for planning purposes?

To ask the title question is to probably have an opinion in hand which I do. I've read a lot of finance over the years. The academic papers and the advanced practitioner papers that focus on markets and instruments and factors -- as opposed to those that deal with retirement, consumption and decumulation -- will casually mention the equity risk premium as if it is a Newtonian force or a guarantee. Take risk, must get paid. Heh. I mean, yes there is something to it and certainly in productive and relatively unfettered economies, capital used for growth gets compensated one way or another or at least it has historically been comped in the US. And yes, there is of course risk that is usually measured in standard deviations. But the wise will also consider shocks, chaos and fat tails. But in addition to all that there are also macroeconomic and policy forces along with crud that someone once referred to as "opulence, corruption, extravagance and waste" that might force one to eventually bend a knee in abject submission, forces that could make one doubt the whole enterprise of planning using historical data for conjuring forthcoming return expectations over our human planning horizons.

Visualizing the impact of spend choice

As in the last post, nothing really new to me or the literature here. 

This is how it works at RH: if I go back to old code I wrote -- even if it is well commented -- long ago, I often have no idea what I did then and I usually can't make it work well without a bunch of work and we here at RH are a little lazy. So when I have new code I will sometimes pile on: "hmmm, I wonder what x would look like as long as I have this code up?" That was certainly the case with the last post where a reader, reasonably, asked "what am I missing, this is simple?" yep, just goofin around. 

Geometric mean, simulation, short horizons and portfolio choice

I don't think this post is all that innovative. We see this kind of stuff in thousands of papers because this is basically just simulation but without the spending and fancy parameters one ususally sees. I just wanted to see how some stuff works here. 

In this post I'll look at 2 strategies -- 1) high return, high vol & 2) lower return lower vol -- to see what it all looks like. We know that we can use deterministic N-period geometric return formulas to estimate the N-per geo mean, something typically and probably incorrectly evaluated at infinity, for evaluating portfolios -- especially for the possibility of a "crossover point" where one strategy should dominate another. We also know that we can also construct a geometric efficient frontier in order to try to limit the portfolio choice interval to the one from risk free to the Kelly optimal (growth optimal) portfolio given believable inputs. Even Markowitz says that. But that latter method again often evaluates at infinity. What is missing is shorter horizons. Hence the post.

Using approximations to intuit the output of simple non-spend MC simulation

My first foray into retirement finance was in 2012 with Milevsky's "7 Equations..." book. Those seven equations took me pretty far and I still think that simple deterministic equations (ok, well maybe not the Komogorov equation in that book, but even that can be handled by amateurs) embedded in an adaptive triangulation methodology along with some common sense can go a really long way into teasing out some intuition about the consequences of the portfolio and spend choices that one needs to make over a lifetime.

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.