Some Core Work in My Mid 60s

In my 64th year on earth I am not exactly where I want to be either physically or geographically. I thought I would be wrapped a little tighter than I am after four years of hitting it pretty hard. I also thought that I would be able to be out of FL a little sooner than 2023.  On the other hand I've come pretty far physically since 210lbs in 2017 as well as since a little retrograde weight-add during covid season. Geographically I now have an active plan to move with realtors actively engaged on both ends.  So, all good, right? 

Contradictions in longevity expectations and longevity vol as we age

David Cantor sent me a piece today on pensions and annuities which reminded me about how longevity expectations are more or less dynamic in odd ways I often avoid. While it is true that as one ages one's prospective longevity "interval" comes in a bit in absolute terms -- one has a shorter expected remaining interval at 90 than 60 -- in relative terms the uncertainty actually gets a little bigger or has more prospective "volatility," if you will. 

On Not Building and Memory

Most of the people I interact with in life and on social media are younger than I am, maybe 30ish to mid 50s, sometimes older but that is rare. I get teased, or sometimes aggressively chastised, for my comments about being old. Generally speaking I am joking because 63 is the new 61, right?  Even that is a joke. I get that I have a young mind and fit appearance (I'd go toe to toe with an "average" 30 year old on pull ups: yesterday I did 21 full extension pull ups in one set, 51 in three sets. Try that at any age) and a looong way in life to go still. This means I probably have some room and some basis on which to play the old man game as a big fat tease because I know I've still got the goods.

Fragment On Monte Carlo

David Cantor recently sent me a decent piece on Monte Carlo analysis by Sandidge, Tharp and Powell in the Investments and Wealth Monitor that covered the limitations of Monte Carlo analysis in retirement situations. It's pretty good and takes a proper posture of caution about overthinking MC. I myself once imputed magic to MC after my divorce. I did not gain a proper skepticism on this until I had built quite a few simulators of different types and became intimate with the black box: its coding, its errors, its flaws, its assumptions, its biases, its inability to say much, really, about the future.  

A Bunch of Random Thoughts in my 64th Year

Just thinking about a couple things and jotted them down. Might add later 

On My Divophilia

“Classical models of finance and consumption-saving decisions predict that [a] dividend will have little effect on…consumption... Under the assumptions of Merton Miller and Franco Modigliani, for example, investors can always reinvest unwanted dividends, or sell shares to create homemade dividends, and thereby insulate their preferred consumption stream from corporate dividend policies. Thus, in traditional models, the division of stock returns into dividends and capital gains is a financial decision of the firm that has no “real” consequence for investor consumption patterns.” Baker 2007 [who then goes on to critique the proposition]  

We use the term fecundity here to refer to a portfolio's long-term ability to generate spendable cash for its owner, because fecund means "fruitful or fertile," and cash withdrawals from a portfolio are effectively its fruit… This paper will demonstrate that the fecundity of an equity portfolio — before expenses and (if applicable) taxes — lies somewhere between the earnings yield and the dividend yield of the portfolio.” Garland 2004 [1]

Dividends and Retirement – Some First Pass Thoughts


I’ve been retired for 13 years now and I have always had an unexamined – and according to others an unreasonable and un-theoried -- love for my dividend income stream (my made-up term for this is divophilia). It just feels like it is a good thing. I have rationalized myself into believing that goodness even though I am fairly conversant with financial theory and retirement finance…enough so to be quite skeptical of my own flawed inclinations and behaviors, a skepticism which might be warranted in this case. TBD

Component Analysis #3 - Mortality

“….One need hardly be reminded that a consumer who makes plans for the future must in one way or another take account of the fact that he does not know how long he will live…” - Menahem Yaari 1965

Up until maybe 5 or 10 years ago, most papers I've read in RetFin did not take random lifetime seriously (might be wrong, just an amateur observation) which is not a great place to start a conversation with people that don't live exactly 30 years after a retirement, the start date of which is itself uncertain for some. 

In chapter 8 of Moshe Milevsky's Retirement Recipes in R (RinR), he gives a slick tool, divorced from formal "life tables" and based on "the Gompertz Law of Mortality," that can model conditional - and continuous - survival probabilities (CSP) with some nice malleable parameters. Probably won't land a rocket on Mars but very effective for RetFin models. 

Talebian Redundancy - redux

Like the last post, don't take this post too seriously. This is playtime with Taleb and one of his anti-fragility ideas now expanded a bit.  As in the last post, it is more or less like this with some changes highlighted in blue: 

IF

- robust systems are identifiable by the reduction of single points of failure and redundancy of resources at critical points, and

- we assume a $1M portfolio P1 for a 60-95yo, spending an age adjusted spend[1], and

- of that 40k (in t(0) only) in spend, 20k (real, all periods) is a life-or-death floor forever, and

- we use SS-like life table to assess the probability of spending anything at a future time but now conditional on advancing age, and

- the PV at t(0) of the probability-weighted cashflow of the floor is variable by age , and

- we simply and blindly double that part of the portfolio (.43) that defeases the floor at t(0), and then we also, as age advances:

- recalculate the spend as the "heuristic rule spend amt" divided into the "total" capital, where the total now includes the extra redundancy

A Talebian Spend Rate

First of all, don't take this post too seriously. This is playtime with Taleb and one of his anti-fragility ideas. I think I have done this before but I wanted to mentally run through it again. 

IF

- robust systems are identifiable by the reduction of single points of failure and redundancy of resources at critical points, and

- we assume a $1M portfolio P1 for a 60yo, spending a deterministic (real) 40k, and

- of that 40k in spend, 20k is a life-or-death floor, and

- we use SS-like life table to assess the probability of spending anything at a future time, and

- the PV at t(0) of the probability-weighted cashflow of the floor is .43 of the initial P1, and

- we simply and blindly double that part of the portfolio (.43) that defeases the floor at t(0),

THEN

- the initial portfolio P1 is now 1.43 x P1 = P2

- The spend rate of 40k of P1 is now .028 of P2 at age 60

- The need for redundancy will decline towards zero at later ages. I haven't gotten into that.

Visualizing Simulated Spend Crashes

Here in Figure 1 [note 1] is a quick visualization of a couple retirement process: 

1. in grey, different spend paths from a portfolio without any "life constraint" over time, and 
2. in red dashed, the "life constraint" in terms of a survival probability conditional on achieving (here) age 68 and parameterized to look a little like a Social Security life table.  

On the left-Y axis we have the spend (using .045) i.e, #1. Fwiw, in this case the spend is an amount not a rate, even though it looks like a rate, because initial wealth is = 1.  On the right-Y axis we have the conditional survival probability, red dashed line, for a 68yo. i.e., #2. The X axis is an arbitrary 50 years, long enough to capture early retirements but not too absurdly long.

Shapes and Flow

Comment from feedback: no one needs this post. It is just a weird flourish...

I never really set out to find specific answers when I embarked on my finance mission back in 2012. I was just curious about stuff...and ticked off at my grubby advisor. What I really did want was to be able to see what I call the "shape and flow" of retirement.  So, here is a fun "shape and flow" I was surprised to see, mostly because I never looked for it. It is the shape of consumption utility over time when considering the possibility of wealth depletion. Let's look at it like this in simulation mode:

A 500 year portfolio and min-max spend rates

What is the spend rate that maximizes median terminal wealth at a horizon of 500 years (why 500? idk, just messin' around and anyway that's the game we played in the last post)? Obviously the proper spend rate for doing that is zero. That's why it is sometimes hard to talk about portfolio growth optimality in a retirement spending context, granting that the 500 years here is absurd. Better to discuss portfolio longevity + mortality, and/or (gasp) life consumption utility. 

Ok, what is the threshold spend rate that minimizes median terminal wealth at a 500 year horizon? idk, let's look.

Some Random Thoughts on Growth Optimal Portfolios

“Theorem: If Harry repeatedly invests in a portfolio whose E log(1+R) is greater than that of Paul [i.e., the growth-max proposition], then -- with probability 1.0 — there will come a time (T(0)) when Harry’s wealth exceeds Paul’s and remains so forever thereafter.” Harry Markowitz in a 2016 book poking fun at Paul Samuelson on their past argument about growth optimal investing criteria.

"Mean log of wealth then bores those of us with tastes for risk not real near to one odd (thin!) point on the line of all tastes for risk -- and this holds for each N with N as big as you like...For N as large as one likes, your growth rate can well (and at times must) turn out to be less than mine -- and turn out so much less that my tastes for risk will force me to shun your mode of play. To make N large will not (say it again, not) make me change my mind so as to tempt me to your mode of play. QED"  Paul Samuelson (1979)

Intro

There seems to have been an uptick in the last few years of interest in the growth optimality consideration for portfolios. Ergodicity Economics feels like the new kid on the block, but this topic has a pretty long history, and the general interest bubbling up I find useful because it is an interesting and worthy topic. I won’t recapitulate all the math or notation in this post since it is tedious blogging [7] and one can read it comprehensibly, for the most part, and quite usefully, in the following bulleted references. Or check out the recommended reading list at the end and in particular pay attention to the references inside the various papers: 

A Random List of 50 Things I've Learned over a Decade of Blogging Quant Retirement Finance

[recent updates in brackets, see item 50]9/20/21

1. The planning interval of keen interest in retirement, often pegged at “30 years” by many advisors, academics and retirees, is actually a random variable by way of the dynamics occurring at both ends. The end, and in an underappreciated way the beginning, of retirement are uncertain. This uncertainty has to be acknowledged somehow in the planning process with some method whether it is scenarios, ranges, distributions for key parameters and output variables, probability weighting, random draws, provision for life income, estate planning etc.
   
   
2. Fail rates are a bogus metric. Dirk Cotton, now gone, wrote on this better than I can. No one in the modern world does a real mathematical fail where there is a continuous dive into the ground. People adapt, spending changes, annuity ripcords are pulled if possible, family steps in, institutions – to the extent we even trust institutions anymore in 2021 – of government and association help out. Stuff happens. I mean bankruptcy is possible but that’s a different problem. Also most savvy commentators will mention that magnitude is ignored. Failing by a dollar under some goal on the last day of life is different than running out of money at 72 with another 30 years to go.
   
   

On Anti-travel

I’m interested in anti-travel.

Travel has become a personality and a fetish and a brag (pre 2021 anyway) these days. But look at it this way. In, say, my 1994 world in MN, I might have considered a Mongolian-located herder-yurt “exotic” but we have to also consider the idea that the Mongolian herder next to the yurt would’ve considered my St. Paul back yard exotic as well given the distances in either meters or culture and the relativistic framing. Which was exotic, then, and worthy of "travel" in the western sense we know from the modern decadent world we now live in? Well...both I guess. So that means I needed to have considered my back yard worthy of examination from a travel sense in the same way that the braggarts -- with pictures of the pyramids or Antarctica or the great Wall -- might conceive of things from their superficial iphone perspective from the side of the yurt as they stood with their Apple-product triumphancy. Heh. I mean cmon.

On the Head-Fake of Precision in Spend Rates in Retirement.

The impulse in the retirement finance lit I read seems to be to come up with mega-ultra numbers, the right answer, the unified field theory. I’m not sure that this can be done even though I took my own shot at it for a few years. The following post has exactly zero science so you can more or less blow it off. This piece is just an opinion. The images/charts are completely, entirely illustrative: not real; just trying to make a point.

End of my wine collecting career

Barolo - La Spinetta 2000 Campe

I started drinking wine in 1976, my 18th year. Instantiating my journey, my older brother gave me a glass of wine at dinner once. It was a 1974 Napa cab which had just been recently released. For those that don’t remember, 74 was a remarkable year in CA. I was ~18, dumb, and so I said: “huh, this is pretty good" and that wrapped up my experience for the moment. Then, in 1992 or so, I had a business lunch at an Italian restaurant in Montreal – full linen service with 8 glasses per setting and a tasting menu method – that had 50,000 bottles of Italian wine downstairs in an abandoned subway tunnel; this lunch-wine vignette now had my full attention.

On picking a baby name in 1996

When my ex was about 8.85 months pregnant in 1996, we travelled from Montreal to Gaspe. In a bookstore in Quebec, there were no English titles and few English speakers beyond QC, so I bought a baby name book there in French just cuz and there was some time pressure coming up, too. *I* picked a name because my ex and I ended up taking turns and this was my turn and, in the process that was unfolding in 1996, I had an opinion: Genevieve. This name, btw, is a 2 or 3000 yo pre-Celtic name that means roughly “white wave” or “white woman” or something close to that if we go back far enough. Oops, I had no idea that 2021 was on its way at the time, heh. Sorry D.

Chatwin on The Estate of Maximilian Tod

Would that I had such an estate. I had this story in my "stories" tab but thought I'd push it here...for reasons.

Camus on Sisyphus

The gods had condemned Sisyphus to ceaselessly rolling a rock to the top of a mountain, whence the stone would fall back of its own weight...he [Sisyphus] is accused of a certain levity in regard to the gods.  He stole their secrets. Aegina, the daughter of  Aesopus, was carried off by Jupiter. The father was shocked by that disappearance and complained to Sisyphus.  He, who knew of the abduction, offered to tell about it on condition that Aesopus would give water to the citadel of Corinth. To the celestial thunderbolts he preferred the benediction of water.  He was punished for this in the underworld.  Homer tells us also that Sisyphus had put Death in chains.  Pluto could not endure the sight of his deserted, silent empire.  He dispatched the god of war, who liberated Death from the hands of her conqueror.

It is said also that Sisyphus, being near to death, rashly wanted to test his wife’s love.  He ordered her to cast his unburied body into the middle of the public square.  Sisyphus woke up in the underworld.  And there, annoyed by an obedience so contrary to human love, he obtained from Pluto permission to return to earth in order to chastise his wife.  But when he had seen again the face of this world, enjoyed water and sun, warm stones and the sea, he no longer wanted to go back to the infernal darkness. Recalls, signs of anger, warnings were of no avail.  Many years more he lived facing the curve of the gulf, the sparkling sea, and the smiles of earth.  A decree of the gods was necessary.  Mercury came and seized the impudent man by the collar and, snatching him from his joys, led him forcibly back to the underworld, where his rock was ready for him. (Camus, pp. 88/89)

Three random dumb things I've done that I was thinking about tonight...

 Three dumb things isn't even close to a comprehensive list but it is a start. Here we go:

Contemplating My Stage 3 of Either 4 or 5

Many cultures over thousands of years – and here I won’t back this assertion up. Just assume it’s true for now. Maybe I’ll toss references some other day – have a theory about “stages of life.”  These can range from one monolithic life of whatever length to two stages (childhood and then adult) to four or five or more...like a play in "n" acts.  My favorite framework, for reasons all my own, is the Hindu/Vedic system of 4 life stages which feels about right to me even though advances in tech and medicine might nudge the boundaries and definitions a bit.  It is time tested in the sense that it has been around for a good long while.  Here, stripped directly from Wikipedia, is how the stages are described in that ashrama framework.

Component analysis #2 - the lifecycle

This is my second toe-dip into Milevsky's "Retirement Recipes in R," (RinR) a text book designed for finance and econ undergrad and grad programs with students that go after this kind of stuff but it could just as easily be for you or me (did I brag about my acknowledgement in the book yet? heh). As in my last post, Prof M serves up what it took me months or years to figure out in thousands of lines of code but he does it in just a line or two.  Here is an example.  He provides a simple function in section 3, that builds on a couple others in sections 1->2, one of which I profiled before, in order to estimate the optimal level of financial capital over a lifecycle.  Let's say we have the following:

Stepping into simple component analysis

In a recent post (My Retirement-Finance-Model "Topography" Strawman) I laid out what I thought was a reasonable framework for viewing the concept of retirement finance modeling. I am sure it is actually more complex than this but I wanted a simple way to think about it. It looked like this:

Training differences between me and my younger self

I get teased because I sometimes say I'm old. More chastised than teased, really. That's because me and my interlocutors both know I'm a pretty lean and cut "oldster" that is not really all that old. I mean, I do turn 63 in a couple months which in Twitter years is what? 400? That's a joke but it is true that I am not 25 any more. In my teens and 20s I trained very hard. I was a competitive swimmer, training up to 15k meters in the summer. I also lifted. Post swimming career, I lifted pretty hard. The goal then was to try to max out my shape and size and build max strength. You know, girls and all.  But my goals and body, like everything, have changed. You can't step into the same river twice (note the blog name...). I thought I'd bullet out some of the differences between age 25 and 63 that I see in my own program. I have done exactly zero research into physiology to back up my adjustments but I am comfortable with my mods. There are some legit guys on Twitter I follow in this area but I have not listed them here.  In no particular order, with no particular emphasis or "weighting:"

My Retirement-Finance-Model "Topography" Strawman

A model is best used as a decision-support tool rather than as a return-prediction tool.

- Patrick Collins 

I'll freely admit that the following figure might be naïve or reductive or reflect my biases but I thought I'd take it out for a trial run. Over 10 years of doing this kind of stuff, I might say -- for myself anyway -- that retirement finance models can break down into the kind of dimensionality I see in Fig 1...if we squint our eyes and don't look too close:

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).