[recent updates in brackets, see item 50]9/20/21
- 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.
- 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.
- Asset allocation is a softer tool than your advisor, who
gets paid by you to allocate, will often tell you. Even the quants sometimes
have a hard time with this. To get geeky, in a consumption utility evaluative
context, the joint spend-allocation choice, denominated in lifetime consumption
utiles, is a surface. The gradient along the spend dimension is steeper than that
along the allocation in most places (did I say that right?) especially at the
edges. I’ve gone through this a million
times. Spend is a bigger hammer. And even if it weren’t, in consumption utility
terms allocation is pretty meh over a broad middle range of say 40% stocks to
70-80% stocks. The sensitivity of many models in different domains of evaluation
is pretty low, flat, there. I mean, yes, at the extremes, especially all bonds,
one can get smoked but I get bored thinking about the difference between 40/60
and 60/40. Spending dominates that chat bigly.
- Ok, so spending dominates. But I was just talking about
constant spend. Did I mention that the constant spend* assumption in many
academic papers is an active risk-seeking posture? It is. But there are other “shapes”
of spending. Declining (seen empirically
ala Blanchett), rising, hump shaped, U shaped, steps up or down, rules, blah blah
blah. This shape has a HUGE impact on the indicia of success however they are
defined. See Robinson and Tahani 2007/ Shape of spending dominates even more
- Guaranteed income is a big fat trump card. Income solves a
lot of problems and evaluates well in a lot of frameworks. Yeah, sure, everyone
plays the annuity paradox, even me, but it works on paper. The interesting thing
is that it matters less (or is it more, I always get turned around on this) with more wealth than less wealth. If SS is 15k a year
and I spend 20k a year, the drop is to 15 when I run out of un-annuitized assets. That
has less of a penalty (especially when using convex math like cumulative CRRA utility) than if I drop from 100k to 15. But either way it sure beats
panhandling and sleeping under a bridge at least. If we are talking annuities, the thing about
them is that the risk pool is something that individuals cannot recreate on
their own ex private tontines. Every time I’ve looked at this I gain up to 5-17%
in my spend capacity by annuitizing some or all of wealth, now or later. Even
my reinforcement learning AI learned how to do this on its own, an outcome
which hewed very very close to the standard LCM model in economics. Yea me. Yet
I don’t annuitize. Go figure. Paradox poster boy.
- Without income, the more you have to reserve early especially
for early retirements in order to hedge all of the various uncertainties (markets,
longevity, spend shocks etc). This is why 4% spend might be ok at 65 (probably
less now per Blanchett and Pfau) but it is certainly not ok at 50. Per the point above, if one has life income
the spend rate can actually be quite high and then decline rapidly as wealth is
depleted well before end of life. Without it: No, be cheap. This is maybe
counter-intuitive, but it is predicted by the LCM (see Lachance 2012). Even my
RL AI algo spent like a total tightwad at 60 – even less than me if I recall --
for a while until the longevity horizons came in a bit but way more at 60 with
- Advisors and friends sometimes will try to shame you, for
reasons entirely unrelated to your mission, into spending more than you want or
know you should – by either analysis or intuition -- but they don’t understand
the math of lifetime consumption or portfolio theory in the presence of spend choice.
Think of them as quant-finance peasants and be arrogant af. I mean, I’m kidding
but what is up with the shaming. None of these people really understand either
the probabilities or the consequences. What I do in my life is like running a
long duration trust and I am the trustee. I am duty bound to my future self not
to their ignorance. ”Hold!” as Braveheart might say. More specifically, romantic partners are often
a threat to the mission: self, future self, kids, legacy. Kids are technically
a threat but should be framed, rather, as a cross between both providence and
purpose. They are the mission. The grasping middle aged date is not. The only metaphor for this phenomenon I could ever
come up with was “the almost-frozen pond” (played hockey as a kid in MN). The
pond is almost frozen with open water in the middle. One’s advisor or ex-gf
will tell you to skate next to the edge…because you can. Should you? Of course
not. They are shouting from the rocky shore and you are out there on the ice
with skin in the game and cold water below.
- Simple, transparent heuristics, well understood, are better
than complex opaque proprietary expensive solutions.
- Ex-ante “optimal” solutions go stale almost instantaneously.
They were probably hard to understand anyway.
- Using multiple methods, models, and modelers to understand a
particular retirement problem over time in a continuous monitoring and management
process is better than set and forget or “products.”
- Splitting hairs on return factors or allocation sleeves is (often,
not always) a fool's game especially if you don’t understand the impact of
- Some hedging is probably warranted. This can be as simple as
asset allocation where the fixed income is there less for its return than for
its ballast characteristics. Even Markowitz had a 50-50 non MPT portfolio based
on a theory of regret. CTAs for trend following, tail hedges, annuities and
even asset-assigned lines of credit have value to smooth risk and consumption.
- Excess risk aversion is closer to psychiatry than it is to
finance. Think about this for a second. I got savaged for this comment once but
I mean it. I get (sorta) CRRA risk aversion coefficients of 1 or 2 or 4 but 8?
16? 32? This is pathological. This is
the financial equivalent of an agoraphobic who’s never left their home due to
intense fear. That person does not need a coefficient or a different model or a
different finance thing. What they need is some help. That kind of fear does in
fact bend behavior in perverse directions. Plus the math gets a little weird in
a standard CRRA utility function since these are power functions. Idk. Tell me
if I am wrong.
- Travel is (my) biggest discretionary expense in retirement
and the pressure to travel and have a travel-fetish or travel-personality is intense,
especially in romantic partners and the young. It is incredibly difficult to
discuss with people close to you if you don’t share that obsession and have a
weather eye on spend rates and sustainability. I mean, I get that never getting
out is a life-draining-suck but c’mon. Also, for every person that brags about
their trips to the Aamlfi coast or to Antarctica, almost none have ever traveled
to America, especially the mountain west. Shame on them.
- Over-engineering the math and models of retirement has
diminishing returns on the far outer margin.
- Understanding the separate probabilities and processes of
portfolio longevity, spending and mortality has high utility. See my 5-process
paper where I make a case that there are five processes in retirement finance: 1) return generation over time, 2) random spending, 3) portfolio longevity [1 and 2 combined], 4) human longevity, 5) managing and monitoring the processes as a whole.
- Consumption Utility might be too subjective to be useful but
can be useful, idk
- Reframing retirement from a “number” or some optimizable
1-number 1-time task to a continuous process of improvement is both understudied
and underappreciated. Things like Six Sigma, ISO9000, OODA, Deming loops,
Collins “management and monitoring”, etc. Operations research and statistical
manufacturing process control is the domain rather than classical finance, pricing,
hedging and equilibrium models. One could also get a little geeky and get into
something like Whitehead-ian process philosophy. We live and decide in an unfolding
self-refreshing process of life. Best to align with that I think. There are 5 main processes in retirement that
need to be understood IMO. Again, I have a paper on that.
- Managing a household in a financial and retirement planning
context needs to be done a lot like a CEO of a small, closely held company:
balance sheet, income statement, and lumpy cash flow awareness are king in this
world. Highly recommended.
- The valuation of spending in present value terms, stochastic
or otherwise, mortality weighted or otherwise, is a critical task. i.e., we are
talking about an actuarial balance sheet. This, the feasibility calculation
implicit in the actuarial balance sheet, is a threshold input to planning. No balance
sheet, no feasibility. No feasibility, no retirement… yet. Speaking of kings:
see Ken Steiner at his blog howmuchcanIspendinretirement.
- Feasibility and sustainability (think Monte Carlo and fail
rates) are closely related to each other in closed form stochastic calculus but
maybe less so in practice. Interesting topic though.
- Sequence of returns risk is, in fact, a real risk even
though one sad lonely pension actuary says no. Even further, when spending is also
a random variable, another dimension emerges where the phase coherence or
interference of spending and returns get interesting ie I recall 2009 where
returns sucked and my spending was super high. One academic called this
phenomenon perverse, which it is.
- Taxes are hard to model as is a realistic inflation environment.
- Return distributions are not “normal” but it may not matter
much depending on the intervals and horizons and need for precision. The fat
tail discussion is important but gets over-done usually by the usual suspect. The
fat tail is sometimes an understandable (underappreciated) stochastic phenomenon
but more likely it really comes from weirder chaotic forces that will never be
modeled but probably need to be appreciated.
The few times I’ve modeled it myself the result is the same: retire
later, spend less early, inherit wealth, or get luckier.
- Understanding the dynamics of portfolio longevity over
infinity is better than looking at fail rates.
- Annuities are not nearly as wicked as people make them out to
be. Opaque and sometimes expensive, yes. Handing wealth to an insurer sucks,
yes (tho there are ways around this). The interest rate environment is a little
wanky right now, yup. But annuities will, from the proper perspective, almost
always enhance consumption utility over a lifetime.
- The other side – relative to abandoning wealth to an insurer
to the disadvantage of legatees -- of the annuity problem is that your legatees
may have to pick up the tab for you if you live too long and haven’t annuitized.
If they were fully aware they might goad you into buying that annuity.
- Spending has a moral component. I got raked over the coals
for this once but I believe it to be true. Look at it this way. In utility terms
there are diminishing returns to consumption. Going from starvation to a loaf
of bread has high utility. So does going from street to shelter but maybe less.
At the other end buying a second lear jet gets an appropriately and stupidly
small increment of additional utility. But that utility approaches a limit and
the 1st derivative goes towards zero. Now, lets say I have an
iphone. I buy a second one I don’t really need. I know that the metals and rare
earths needed to build or waste it savage the environment and that the servitude
of the labor wherever is probably not great. I don’t need the phone but in
utility terms maybe the redundancy has some worth, idk. On a net basis I could
perhaps now make a case that relative to my sense of the world there might be
some disutility starting to kick in. The first derivative goes to and through
zero. Maybe. Anyway that’s how I am doing it. I don’t spend just to spend and never
will. The unspent goes to future me, kids, or philanthropy.
- Learning a little finance math along with some basic
spreadsheeting – let’s ignore coding which can unleash explosive productivity –
is better than listening to a 30yo advisor tell you: “Live a little, bro” or “it’ll
cost you 4 grand to re-run that dressed up Monte Carlo.”
- Almost everyone in academic finance from tenured professors
to advanced professionals is incredibly helpful, friendly and responsive. The
exceptions are more along the lines of community or state college adjunct finance
profs who can’t be bothered with peasants like me.
- Advisors who won’t discuss fees, or those who respond to the topic, when raised, with a focus on their own income, need to be considered very
carefully for termination. Advisor alpha does exist but that is a separate
discussion with better advisors.
- RetFin is often mistaken for a precise discipline. Better to
think of things (idk, spend rates, portfolio choices, whatever) within zones or
clouds of answers, all of which might be right in different ways. This is not
just about parameters but different views of the world. I’ve used many evaluative frameworks – Monte Carlo
and fail, Life consumption utility, perfect withdrawal rates, Stochastic Present Value balance sheets, closed form
expressions etc – and were I to have an army of people construct and code all of these
in overlapping ways then each person would introduce biases and assumptions – this is a type of model
risk I guess – and all be sorta right. For a spend rate at age 60 for $1M etc
etc the answers would be different if only by small amounts. The answers would be a "cloud" and while some answers might be more correct and while there might be some central
tendency, they could also be all considered correct in some way. Messy reality
meets imperfect models. Hence my tendency to triangulate insight rather than
- The need for deep thinking on retirement finance goes way up
the closer one is to the edge of a financial cliff. The destitute and the
wealthy think about in-depth retirement engineering a lot less than the guy on the right side of a windy path next to the financial gorge with tight resources.
- Many (most) middle class retirees have an intuitive grasp of
tactical adaptation in spending and asset allocation but without all the math.
Many have laughed, probably fairly, at my blog as “preposterous.”
- Quantitative Retirement finance << mission, purpose,
family, creativity & relationships.
- Simple problems have a way of working out in retrospect. 13
years since I “retired” at 50 during a personal debacle and, while there were a
couple years of anxiety and discovery, it all worked out so far at 63, an age
closer now to a more realistic retirement. I will try to carry that confidence
forward. Speaking of confidence, I’ll add that physical fitness is >>
retirement finance in some way I have yet to articulate here. The best I can say now is
that it accrues hugely to confidence. All those years coding in R and I should
have been doing more curls.
- While “mathematical fail” is not really real in some way I mentioned above, bankruptcy is
and when it happens it starts slow and unseen then it goes fast into a final cascade,
often with interlocking debt/leverage involved. Best to be wary, especially
when borrowing money. My friend Dirk wrote about this when he was alive.
- Prenups are better than nothing and not marrying/cohabiting
is even better if you don’t want one. A second divorce would have been a total
hydrogen-bomb-nuke-strike on not only my sustainability but also in my ability to
raise and then hedge out my kid’s flight from the nest. Given its impact on retirement as well as the
sorry state of dating along with the camouflaged rent seeking behaviors out there
(maybe this is just a commentary on late middle age FL) I’d say this blog does
not currently endorse second marriages from a retirement finance perspective.
- The 4% rule is not a rule and is absolutely meaningless
without context (anyway, they say it is lower today). If you are under sixty,
try 4% out for a random lifetime and tell me how it goes, especially starting
- Topophilia is a real thing and, in my opinion, a more
fruitful domain of personal introspection, post-retirement, than quantitative retirement
finance. Would that I had started to dote earlier on where I belong for what time I
have left in life. I know where that is now and the whole concept of discovering it,
planning it, and (future) executing it is waaaay more fascinating that fail
rates or consumption utility.
- At long time horizons the geometric mean return of a
portfolio is less than the average of the component geometric means which is less than the arithmetic portfolio return.
- A portfolio with a *lower* estimated forthcoming arithmetic
return might but might not, at a long enough time horizon, have a better
outcome than a portfolio with higher estimated forthcoming arithmetic returns
with higher volatility. Whether this happens at all is uncertain and when it
happens, if it does, is also uncertain. Can be estimated though (geo mean
return analysis) and it might be either: soon or beyond a human lifetime. Best to
think about it. Has implications for dealing with taxes embedded in single
asset holdings. Richard Michaud 2003(?) wrote on this in a great piece.
- The geometric return of a portfolio and median (not mean)
terminal wealth are tied at the hip and are mathematically connected. The terminal “mean” is useless due to extreme
- Maximizing the geometric return in multiperiod time is an
optimizing theory in Finance, something known for a while by folks like John
Kelly, Latané, Hakansson, Markowitz, and a bunch of others but is otherwise
underappreciated by too many. Samuelson savaged it on some kind of rationality
principle. People forget that Markowitz (2016, where he got his final
post-humous dig in on Paul) advised only that one wouldn’t go any higher than [max(geo)]
on the efficient frontier and that lower might be indicated if risk aversion is
present. That latter is germane because the volatility of the portfolio could
be psychologically ruinous until that max idea (vs alternatives) kicks in
forever thereafter keeping in mind that the "kick-in win" might occur at a horizon
relevant only to immortals. This is why traders, using Kelly for bet sizing,
often opt for a “half-kelly” when sizing their bets; sizing is akin to asset
allocation and might explain Markowitz's 50-50 theory of regret.
- Ergodicity Economics sounds like it thinks they discovered cold fusion in the “time
average” but didn’t really. It is, to my amateur eye, the geo mean max principle from above dressed
in party clothes. They (EE) exist, rather, on an arc of discovery embedded in
the last point. This is perhaps gratuitous and petty of course but needs to be said.
- Question: was 10 years of quantitative retirement finance "worth it" given there was no money, no credentials, and no significant recognition?
Probably, idk. I learned some stuff and
met some people. I gained some confidence and learned how to code. I changed
almost nothing in what I do in my own plan except relax. I can see “shapes and
flow” now, though, in ways I couldn’t before which I guess was always a type of
goal. Most of my family think I am a nut and no one asks me for advice. Heh. Being
a top US amateur, a designation that only I give to myself, means almost nothing to anyone. I
mean, yes, I have been acknowledged in one book and a number of academic or professional
papers and one mainstream publication. That is good enough for now. Listen, the purpose for this whole
quixotic thing was always a combination of four things: 1) a fear (reasonable
in retrospect) of my unknown emerging financial situation in ~2011, 2) anger at
bankers who were condescending and arrogant and money-grubby and blind, 3) intense curiosity
about how it all worked, and 4) I wanted, at one point, to stack my LinkedIn resume with
creditable things that would look legit were I to seek employment.
- Learning to Code in R unleashed in me explosive
productivity, capability and insight. Should have done it sooner. You should have
seen the simulator I once coded in VBA. Beast took 3-4 hours to run where in R
it was a minute. Plus it was easier to do in R.
- My favorite paper over the last 10 years was “Uncertain
Lifetime, Life Insurance, and the Theory of the Consumer.” Menahem Yaari, 1965.
I don’t know if I can say exactly zero advisors have read this, but I’ll bet
the number is vanishingly small. I had
to read it about 40 times before I could divine the meaning and internalize the
conclusions. This f’r should’ve gotten a Nobel for something like this. I mean
- I had coffee once with the freakishly capable and energetic
Moshe Milevsky. I thought that was great. He generously explained to me the
math of the Kolmogorov equation for Life Probability of Ruin, an obscure
partial differential equation I had happened to accidently decode by way of
simulation but without truly knowing what I had done or how or why. I think it
was later but he also once pointed out that the ideal retirement advisor would
combine quant finance, economics and actuarial science. This is a rare trifecta
indeed, but I agree. That is a strong three legged stool on which to view the
landscape I was considering. Add some data/computational science and we got
some serious game goin. Go check out his recent book on coding retirement in R
and you’ll see my name in there somewhere, heh.
- [recent updates in brackets] My favorite projects were always the ones where I don’t think any human had (or has still?) really done what I did. I don’t know for sure if I can make the claim but given the giant pile of papers in my garage that I've read over the years I think I can. Let’s say – refute me if you can – that it is like this for the new stuff: 1) Reinforcement learning algo for optimal spend over a defined age interval [Wrong. Gordon Irlam was clearly here first], 2) backward induction and stochastic dynamic programming to find optimal *spend* rates by age [Wrong. again, Gordon Irlam did this first], 3) combining “Perfect Withdrawal Rates” with stochastic longevity, 4) my age-based non-linear spending rule of thumb, 5) my insertion of a Gutenberg Richter model into a net wealth process to capture some negative chaotic force that looks well beyond Talebian fat tails and deep into the darkness of a real world process that has little to do with return distributions as it is commonly practiced, and 5) I’ll add my “paper” on the 5-Processes of retirement…but that paper is more a meta filter on previously existing worlds. Otoh, I haven’t seen any paper like it and I am certain no blog reader has made it this for so…claim it I will. There might be some other new things, idk.
 mine was a little different and way more naive. Gordon's published notes inspired me on this fwiw. For some reason I had imagined he'd done only asset allocation rather than the more comprehensive thing one sees on aiplanner.com. He gets the props on this. I was trying to own the spend side of things and didn't do my homework. This was a fun effort though and in the end my only goal was to get a program to teach itself what to do, something I accomplished for me and my curiosity more than anything else.
 I had attempted my stripped down version of SDP after I had tried to replicate Gordon's published work on SDP for asset allocation and then later, after I was comfortable that it worked, I adapted the approach to spending -- again I had wanted to do something strong on spending -- using a consumption utility framework. I thought he hadn't done spending so claimed it but I just read (9/19) an interview where he said he did exactly that and again no doubt in a less naive way than what I had done. Again, props to Gordon. This was another example of a fun project that came at spending from a different perspective than once sees in the lit. Too many finance guys over-focus on mere slivers of the portfolio problem and skip the big stuff.