In honor of Gauss B-day

Since it's his 241st birthday I thought I'd do a little Gaussian mix experiment I've been meaning to try out.  The basic mix concept is described here: Deconstructing one non-normal SPY distribution into two normals -- just for fun -- and then putting it back together again. The purpose was to get a smooth random distribution that has a fat, non-normal tail vaguely akin to market data.

Now I'm going to harness it to a net wealth process starting with $1M and a constant inflated 40k spend rate and see what happens.  The formal notation for the process, if I have it right, looks like this:

which is from Habib, Faisal and Huaxiong, Huang and Milevsky, Moshe A., Approximate Solutions to Retirement Spending Problems and the Optimality of Ruin (March 31, 2017). Available at SSRN: https://ssrn.com/abstract=2944125 or http://dx.doi.org/10.2139/ssrn.2944125.  In the case below alpha will be 100% and pi is zero.

That's a bit much for me so we'll describe a net wealth process with a mean terminal wealth "W" expectation like this since we are going to simulate rather than do calculus:

E(W) = 1/S * sum[1:S](p(w(t),s(t),k(t))) 

where p is a simulated process of wealth, returns and spending iterated S times and where p can be described by this

for (t in 1:30) { w(t) = w(t-1)*(1+k) - s(t) }

given that w(0) = $1M, s(1) = 40k inflated at 3% thereafter, S is 10,000 and k is either 

a) normally (gaussian) distributed return with mean 11.4%, std dev of .198 [1], or 

b) a gaussian mix fit to the Stern data[1] to pick up a non-normal fat left tail 

The question is: "how much impact does adding the non normal fat tail affect the simulated net wealth process given the rather arbitrary and relatively non-scientific mix-fit attempt by an amateur?" The answer appears to be: "not that much" since this below is what the terminal wealth distributions for (a) and (b) look like where (b) is in red. We're using the R density function. 

There are in fact some differences in the summary stats done on the two distributions but (1) they are more artifacts of the simulation than anything else and (2) I don't find them (the differences) all that compelling after stepping back and looking at the picture.  Maybe I mis-fit the tail.  

--------------------------------

[1] data was annual data from A Damodaran at the Stern school, 1928-2016 with 100% allocated to large cap.  

On Risk

"The acceptance of a probabilistic measure of risk was an act of faith.  The persistence of it in the face of its lack of success, and the heroic strategies that are invoked to immunize cherished theories are acts of faith as well.  There is more than the scientific method involved.  One can only guess whether the rejection of a probabilistic measure of risk would lead to a loss in status of the profession, a severe depreciation of painfully acquired human capital, a horror at the absence of any apparent alternative, or some or all of the above. It might certainly lead to a better theory."

Last paragraph from 'The History of Risk "Measurement"' Elton G. McGoun, 1995

RH Links - 4/24/2018

QUOTE OF THE DAY

Monte Carlo simulation of a flawed strategy for an individual household’s retirement plan is pointless. DirkCotton [emphasis added]

GRAPHIC OF THE DAY

RETIREMENT FINANCE AND PLANNING

Exploring the Pros and Cons of Retiring Before Your Spouse. Darrow Kirkpatrick

No decision is without trade-offs. Having one spouse working when the other leaves their career creates new challenges at the same time it solves others. Retiring before my wife produces new relationship stress, limits financial and personal options that would be available if we were both retired, and creates unique risks. There are major personal and financial implications for partners retiring at different times. They need to be considered to determine if this strategy makes sense for you. 

We Only Get to Experience One Version of Reality, J Brown.

One of the core tenets of our money management philosophy is to talk about concentrated investments in terms of regret minimization. When we speak with the employees of companies like Amazon or Google who reach out to us, our job is to frame the issue in terms of what would hurt you more, both emotionally and financially – diversifying away from the company’s stock and watching it soar, or holding on through a company-specific catastrophe. Presenting the pros and cons this way allows for our client to think in terms of two different realities that may or may not occur. We often make a break-through with this technique, but not always.  

Retirement Strategies in Pictures, Joe Tomlinson

Advisors providing retirement recommendations need to evaluate strategies and present options to clients. Communication is key and it can be a challenge to come up with the best way to compare alternatives. One way involves presenting metrics such as expected bequests and plan failure probabilities. However, it may be more helpful to use a graphical approach to show the year-by-year progression of funds available during retirement. I’ll demonstrate a graphical approach by comparing a variety of strategies. 

What, specifically, is the game plan if bad stuff happens?

This (OK, Retirees, What’s Your Plan for Dealing with the Upcoming Bear Stock Market? Ken Steiner) is an incredibly useful point of view.  I had a post on something like this in the past once.  Most financial planning at the retail level has lots of charts and numbers and discussion of asset allocations and fund choices but it, the planning exercise, also (not always, there are good planners out there) sometimes fundamentally violates some of the core principles of basic strategic planning.  If the future is envisioned as a portfolio of some set of possible future scenarios, and then if scenario A or B or C or D... unfolds, then specifically, what are you going to do?* What signal triggers an action, what have you pre-identified on the income statement or balance sheet for cuts and change, how fast and when, what is the material impact, etc etc.  I have a developing idea about some post that could make the case that the batrillion dollar financial services industry sometimes misses the boat on almost everything when it comes to retirement. We perseverate so much on asset allocation and the subtleties of esoteric strategies and products but we ignore the big things that will dwarf all that in the impact on real lives: real strategic planning, spending in all its complex random chaotic glory, longevity risk in its real form, the lifetime utility value of risk shifting via insured solutions...

* I do this at least twice a year.  I stress test to see how bad it can get and then look closely at what, precisely, I would do where the precise to-do might actually be to ignore it all and do nothing.

The Limits of Simulation from TheRetirementCafe.com

This'll be in my links post but I thought I would give it some extra emphasis here.  This is a pretty good cover of the boundaries of simulation. 

The Limits of Simulation - Dirk Cotton 

I have now made it my life's goal to show up as a footnote reference in one of Dirk's posts.  Then I will know I have finally arrived.  

Black Seadevil

Here are a couple paragraphs that I happened to run into a while ago that were so appalling, which means interesting, that I had to save it and pass it along.  The content was from a NYR review of a couple of books:

The Deep: The Extraordinary Creatures of the Abyss by Claire Nouvian, University of Chicago Press, 256 pp.

The Silent Deep: The Discovery, Ecology and Conservation of the Deep Sea by Tony Koslow, University of Chicago Press, 270 pp.

"...

To understand the full extent of the constraints that the abyss places on life, consider the black seadevil. It's a somber, grapefruit-sized globe of a fish—seemingly all fangs and gape—with a "fishing rod" affixed between its eyes whose luminescent bait jerks above the trap-like mouth. Clearly, food is a priority for this creature, for it can swallow a victim nearly as large as itself. But that is only half the story, for this description pertains solely to the female: the male is a minnow-like being content to feed on specks in the sea—until, that is, he encounters his sexual partner.

The first time that a black sea devil meets his much larger mate, he bites her and never lets go. Over time, his veins and arteries grow together with hers, until he becomes a fetus-like dependent who receives from his mate's blood all the food, oxygen, and hormones he requires to exist.  The cost of this utter dependence is a loss of function in all of his organs except his testicles, but even these, it seems, are stimulated to action solely at the pleasure of the engulfing female.  When she has had her way with him, the male seadevil simply vanishes, having been completely absorbed and dissipated into the flesh of his paramour, leaving her free to seek another mate.  Not even Dante imagined such a fate.

 ..."

Spending uncertainty

I see so few articles on spending uncertainty that I thought I'd pass this along:

Where Retirees Underestimate Spending - Underestimating how much you’ll spend can be costly, so it’s key to know the common pitfalls.  WSJ Journal Reports: Retirement. 

Navigating retirement can be difficult for lots of reasons. One of the biggest is that it forces people to make plans based on spending assumptions that won’t become a reality for decades. Guessing wrong can be the difference between a comfortable retirement and one that is a struggle....One of the biggest mistakes people make in estimating retirement expenses is underestimating how long they will live....“Everybody worries about dying young,” says Prof. David Littell of the American College of Financial Services. “People should be more worried about living too long.”

Ceasar as literary artist

From Ceasar's Malice, a review by Barry Strauss of The Landmark Julius Ceasar ed. K. Raaflaub, Pantheon. New Criterion April 2018.  

Not the least of the things to consider about Caesar’s writings is this: He wrote them. Himself. Somehow the man who conquered Gaul, defeated the assembled forces of the Roman Empire and their allies abroad, brought down the Roman Republic and laid the foundations of rule by the emperors whom we know as the Caesars, wooed and won beautiful women from Gaul to Egypt (including Cleopatra), gave the western world its current calendar—somehow, this man also found the time to become a great literary artist. Sure, he had slaves, but he didn’t have computers or washing machines or any other modern time-saving devices, and yet he wrote his own great literature. The next time you hear that some politician has a speechwriter and can’t write his own speeches himself, ask yourself why. Ask what that says about our educational system and what it does and doesn’t teach young people. 

Once upon a time, eloquence was a virtue. Not that it is a guarantee of a happy outcome: Caesar shows that, when combined with arms and vote-getting, persuasiveness can bring down a republic. Eloquence is no guarantee of constitutional government, but can you keep a republic without eloquence? That is a question that Caesar leaves unanswered, but we need to know. Given the current state of our educational system, wherein STEM is proclaimed the supreme discipline and wherein those of us in the liberal arts could use a refresher course in what really matters, I fear that we may find out.

A story that blows away this blog and 99% of anything I've heard lately

I just spent the last two hours listening to my 10th grader interview me and my three older brothers about our separate, individual conscious experiences of things like America and media and student movements during the Vietnam war era.  This is verbal family history that I kind of knew but had never really heard in full sequence and all more or less at the same time.  Me, I was born in 1958 when the French were there and maybe a few Americans and I was maybe 6 for the Gulf of Tonkin Incident. The Peace accords were what, 1973? So I would have been around 15 at that point.  Saigon fell in 75; that would have been the fall of my senior year in high school.  That means my entire existence as a child was permeated by war and images of war as well as thoughts about what would happen when I was of draft age (for which I did register, if I recall).  I remember all of the TV and the violence: war and protest at dinner and then at school the next day, drilling for nuclear war under our desks. Our desks?  Of course I also remember kick-the-can and foursquare too, but then again I was just a kid.

This was really fascinating stuff.  My brothers and I were born, respectively, in 47, 49, 53, and me in 58.  We each crossed that whole generation and apprehended what was going in the world each in our own different ways and at different times and maturities. In brief, at one particular interview cross section, we were: law student and draft-lottery participant, college student involved in the movements and lottery participant, enlisted Air Force North Vietnamese linguist in the Asian theater, and me, a high school kid preparing to be drafted...or run.   Line that up with a good sequence of questions by a good interviewer and it becomes mesmerizing oral history.   Can't wait to hear it edited...

Hindsight 10: meaning, purpose, and identity

This is an addition to my hindsight series: things I should've known or needed to know when I first retired.  The "need to know" was exacerbated by the earliness of the retirement.  All I have to say is that people playing the FIRE game should be clear in their minds about what they are doing before they start.  Me? I was winging it and almost got burned. 

This blog  has been mostly about retirement finance, quantitative finance and trading, and some niche areas of financial economics, areas I knew very little about and in which I have had no formal training whatsoever. Hence the claim to amateur status.  The reasons for these interests are manifold and would probably make a good blog post some day. Not today.  Let's just say it is a personal quirk for which I have been criticized and and questioned by real people that are close to me. 

In some respects my critics are correct.  Retirement finance, radically unknown by a lot of people that really should know, is one of those necessary but not sufficient things.  Where the insufficiencies kick in is in an area I touched on in a recent post: meaning and identity.  It can be jarring to go from a structured career to, well to "fuzz." Who am I now? Think cocktail party: "So what do you do?" I never know how to answer that.  At 53 I just got quizzical looks and not zero times a little bit of judgement. Envy maybe too. But there is almost always a quick end to the conversation (except for FIRE candidates that enthuse) because there is no commercial identity and thus no advantage or edge to be explored by those still ambitious enough to look for advantages and edges.  I exaggerate a bit, of course, because I used to work in an aggressive field, but it at least felt like the above at times.  Entering my 60th year, bald and grey, it's a little easier. I'm older, more people understand, and my cohort is starting to look more and more like me.  And all of us in that cohort, if we are honest with ourselves, have probably struggled with the insufficiency I mentioned. Lucky are those that don't.  So, to repeat myself from my last post, this is the list of things above and beyond the retirement-quant stuff I do that I wish I had spent more time thinking about.  I'll give credit to Darrow Kirkpatrick and my twin sister for forcing me to confront this stuff.  Fortunately I am young enough to have a ton of time to work with this. My personal "workplan" and something that is more foresight than hindsight:

1. find and then re-imagine purpose again and again over remaining lifetime,
2. explore the elusiveness of "meaning" as time passes and age overwhelms,
3. re-forge one's ephemeral identity in a continuous process that really has no hard boundaries,
4. travel and learn and grow a personal universe, one tiny increment at a time,
5. throw something, anything, back to community and world,
6. stay healthy, 
7. meet new people whenever and wherever, 
8. foster the essential bonds of: brothers, sisters, children, significant others, and...friends

3D utility surface in WDT model: return vs spend rate

This is pretty predictable, I think, but I wanted to see it anyway. Go to "3D "utility surface" in a Wealth Depletion Time model: spend rates vs annuity" for background. This time I wanted to see what happens in terms of different combinations of spend rates and really low real return assumptions in the absence of annuitization.  The outcome made sense before I even did it but it was worth looking at.  The outcome in the chart looks choppy and weird, I presume, because of rounding and threshold effects but could also be due to modeling or data-entry errors. No idea yet and I probably won't go back to figure it out unless I think I made a truly stupid error. I think the overall picture makes sense though.

On Ruin and Risk

Just because I felt like it, and because I was in the middle of the Taleb paper, I thought I'd juxtapose these two quotes for contemplation:

This is from The Precautionary Principle (with Application to the Genetic Modification of Organisms) by Taleb, Read, Douady, Norman and Bar-Yam 2014

A way to formalize the ruin problem in terms of the destructive consequences of actions identifies harm as not about the amount of destruction, but rather a measure of the integrated level of destruction over the time it persists. When the impact of harm extends to all future times, i.e. forever, then the harm is infinite. When the harm is infinite, the product of any non-zero probability and the harm is also infinite, and it cannot be balanced against any potential gains, which are necessarily finite. This strategy for evaluation of harm as involving the duration of destruction can be used for localized harms for better assessment in risk management.

This is from Uncertain Lifetime, Life Insurance, and the Theory of the Consumer, Menahem Yaari, 1965.

Now a violation of the wealth constraint S(T) >= 0 is clearly a physical possibility, but some people think that the institutional framework makes it virtually impossible for a man in our society to die with a negative net worth. For this reason it is of interest to see what the consumer's optimal plan looks like given that the constraint S(T) >= 0 must hold with probability one.

I'm a grubby miser

Ever since I saw my real retirement risk back in 2011 at age ~53 I have been a hoarder, protecting my future like the grubby, frightened, penny-pinching old man that I seem to want to become.  Seven years of analytics have barely budged me off that wary retirement crouch. Otoh, I just today applied my own tools (e.g., the WDT tool I've been playing with in some past posts - no data shown of course) to my own situation. The conclusion? If I were to commit myself to a constant, well managed consumption path not too dissimilar from the lifestyle I have right now (recall the penny pinching, though) from age 85 to infinity where 85 is roughly mean life expectancy for me (maybe less if you knew the heart history of the men in my family but the main point here is that over 85 is low or really low probability of being around to consume) then I could probably increase my consumption between now and 85 by up to something like 50%! If I were to also commit to annuitizing a pretty high portion of wealth at 75 or 80, then my consumption capacity from 60-85 would probably be even higher! And get this: it would be higher (in nominal and utility terms) both before and after annuitization as compared to the original plan. That is a serious revelation and should be a motivation to act.

But here is the lie lie lie of utility math.  The utility functions that economists seem to like are power functions that have a positive first derivative and negative second. i.e. it rises forever with higher consumption but there are diminishing returns to utility as you go - a crust of bread when starving is a huge life-altering gain; a second lear jet? ho hum.  My personal opinion is that this is not true or at least not true at the far right side of the curve. I have tried this argument out before in a past post with no takers on the discussion.  Here's the deal: I like being frugal. I think it is a proper moral response to existence in my own weird RH way.  That means that there is likely some point (for me) where an additional dollar of consumption actually subtracts from utility. In the past I tried to frame it as something like this: When you buy a third TV, it is not only pretty much unnecessary but the packaging and materials extraction and distribution logistics means you are probably ruining the world in some small way with that choice.  When you buy your fifth lear jet you are pretty much just a rich jerk incurring an opportunity cost on the the world for the other productive things you could be doing with your wealth. The point is that the utility of consumption for some people (me?) does not rise forever at diminishing rates.  It probably goes down at some point.

So am I going to loosen up? Yeah, maybe a little bit. Certainly the normal retirement risk at 60 is different now than it was at 50. That alone changes the calculus. And anyway, my kids would probably gain from it. But I will probably not loosen up a ton. I still like my miserly life. (I once fired an advisor for literally telling me to loosen up to my face).  Now about that bequest plan...

Retire the Blog? not yet but...

IF I were to bail on the blog, and I'm not saying that I am, but IF I were, I would manage an orderly transition of that process by handing all three of you over into the capable hands of the people I trust the most (listed below for the four categories of my "links" posts).  I guess this is a back-door "best of" again but really I have to do it.

RH Links - 4/14/18

QUOTE OF THE DAY

The primary determinant of retirement cost is longevity. Dirk Cotton

GRAPHIC OF THE DAY

from: 3D "utility surface" in a Wealth Depletion Time model by, well...by me.

RETIREMENT FINANCE AND PLANNING

Inflation Risk for Early Retirees – Part 4: Hedging, ERN

What asset classes – if any – are useful in hedging against inflation? Simple question, not an easy answer. It all depends on the horizon! … In fact, the only asset class that had any chance at all to not just keep up with inflation but also supports a withdrawal rate in the neighborhood of 3.5-4% would be equities.  … With bonds, you trade lower short-term volatility for a higher probability of running out of money in the long-term!  What would I do personally?... I am probably going to increase our real estate investments going forward. 

Exploring the Low-Volatility Phenomenon: An Interview with Pim van Vliet, PhD, fortune financial advisors

How a New Bond Can Greatly Improve Retirement Security, Kobor & Mralindhar

All else equal, individuals retiring a few years apart can have vastly different retirement income outcomes (making retirement outcome a function of one’s conception date). A new bond has been proposed to improve retirement security – with a forward-start (tied to date of retirement), income-only (as individuals need steady income), real cash flow stream (linked to appropriate indices), for a fixed period (tied to average life expectancy). This paper examines standard portfolio choices (60/40, target date funds), along with holding this new bond in isolation, from a retirement income perspective to demonstrate how this new bond, either individually or when used in standard portfolio choices could greatly improve retirement outcomes. The paper concludes with a Monte-Carlo simulation that further validates the value of this new bond given the potential risks to all investment choices given future equity, interest rate and inflation scenarios. [Comment: and after the fixed period?] 

3D "utility surface" in a Wealth Depletion Time model: spend rates vs annuity

This is at least temporarily the end of the road for my WDT (wealth depletion time) model.  While this is still a "play" thing and not really "real" analysis yet, the pictures I derive here below were always my end-game except to the extent I might extend it to my own data some day.  The goal in this post can be stated like this:

The Goal of this Post

If we were to calculate the discounted (and weighted and deterministic) utility of lifetime consumption for a consumption plan that anticipates being reduced to available income  when wealth runs out (income that can be purchased with available wealth while it lasts), what would it look like if we did that utility calc for different combinations of initial (constant) spend rates and fair (but loaded) increments of "annuity payouts purchased" (first at age 80 and then another look is done by doing it at 75) in a rudimentary WDT model with fake-ish data?

That is a big awkward bite. So let's roll with it and see what happens.   Since this is a complex question, we should linger on the assumptions and model rather than merely point back to other posts. The concluding "utility surface" looks cool but don't jump ahead yet.

Stochastic vs Deterministic - Part 2

Subtitle: How I might "wing it" with a deterministic model (knowing something about how return and net wealth processes evolve over time) when lacking a simulation that might add a little more "realistic" randomness.

Let's say we are contemplating a net wealth process over 35 periods (age 60 to 95 maybe) and we have a spreadsheet model that has arithmetic real return expectation of .03 that is modeled deterministically. Standard deviation of return if we had a stochastic model would be maybe .10.  Wealth units are 25 and the spend unit is 1 (4% spend rate).  How could I work the deterministic model to tease out insights that might only be found by randomizing in a simulation?

Sliver of hope for dividends??

If you've been following, you know that I've been playing around with a new model that, among other things, calculates a discounted utility of lifetime consumption in the presence of a wealth depletion framework where spending is forced to income at wealth depletion. Several related posts:

• A trial run of a WDT game prototype
• Optimizing Spend Rates in a simple WDT model
• Supplement to "optimizing spend rates in a WDT model"

In this post I take another un-serious and preliminary look at the use of dividend income in the same analytical mix.  My bias from long ago was that div income was essential to my well being. My take away more recently is that it doesn't matter at all; total return is what it is as is consumption so there is little to no real impact over the long haul.  In my model I try again to make a naive stab at looking at div income in a really really rudimentary way especially now that I have flipped the WDT lifecycle model over to a probability weighted and subjective discount approach.  I thought it'd be worth another look. 

Supplement to "optimizing spend rates in a WDT model"

In optimizing spend rates in a WDT model I was doing some casual play with a prototype of a Wealth Depletion Time model.  Nothing huge to report there; I was just goofing around.  In that post I had a hard coded end age and was doing a simple average of utility to that age and then backing into a certainty equivalent that said something about lifetime consumption utility.

In this post there is also nothing to report...still just goofing around.  I kept everything the same, except for:

1. I changed the interval from 60:(hard coded T) to 60:120 because now we can probability weight
2. I discounted the utility by weighting it with conditional survival probability at each age
3. I added a small subjective discount for a little bit of a symmetrical time preference effect
4. I changed the form of the utility function by adding a constant.

Personal finance links at abnormalreturns.com

Basically...

just read all of the links here: Personal finance links at abnormalreturns.com 4/11/18

How's that for a cheater post?

The marginal cost of procrastination at age 60

After this post, a fair and dispassionate reader might be forgiven for thinking that I spend WAY too much time looking at this stuff. ...and I would share that opinion. The proximal reason for the post was me thinking about the nexus between things like personal relationship games and the time left in one's life to play them (to which the other relationship game players would perhaps say "If you'd put as much energy into the real game as you do the fake-blog-math you wouldn't have a nexus-question in the first place").  But this way of thinking could be just as easily applied to other things like retirement-start, un-pursued hobbies, un-executed bucket lists, whatever.

Optimizing Spend Rates in a simple WDT model

I thought I'd see what happens to spend rates in a simple Wealth Depletion Time WDT model in terms of the certainty equivalent consumption over an (unrealistic) fixed utility horizon.

The Setup (illustrative but not very realistic)

age 60 to age T in [104,96] so lifetime is not random except for the simple toggle here
1$M starting endowment
Spend rate = .04 to .03 in .01 increments
Spend grows nominally at .03 real = 0
Returns are .055 nominal .025 real with a 1% penalty for whatever needs to be penalized
A dumb sequence risk filter is applied: -.01 over 0:(T-60)/2 and +.01 over  (T-60)/2:(T-60)
  (geometric return over horizon is neutral)
Soc Security of 10k (FV) is started at age 70 and inflated
No annuitization of wealth over horizon
Risk aversion coefficient = 2
Importantly: Spending is forced to SS income at wealth depletion

Dividend investing meets Wealth Depletion Time and...nothing

Readers of the blog may have inferred that I like dividends, which is true.  I tried, this morning to prove that div income as part of the mix has some certain superiority in the context of lifecycle econ via my Wealth Depletion Time tool.  I will show none of this because I am too lazy and have done too many posts lately and the results were ambiguous-to-non-confirming anyway.  I threw all the intelligence I could at it.  I even threw all the intellectual corruption at it that I could possibly conjur.  I knew the result I wanted and I tried to contrive setups that would prove my conjecture (honorable, eh!).  But I couldn't do it.  That may say more about the model than anything else perhaps.  Wait! I thought. What about in the presence of sequence risk? Nope (though I did get a good illustration of how sequence risk can suck all by itself).  The thing is, dividends are not magic. One is still consuming a slice of total return no matter how you slice it and the consumption thing doesn't change and the total return is still total return (and this is before talking about taxes or corp finance theory).  I'm sure there are other ways to look at this and anyone that thinks they have a good bead on making a good case, send me ammo. I don't want to lose this fight yet but I think I am. 

Affinities between national defense analysis and retirement?

I thought this paper (Handling and Mishandling Estimative Probability: Likelihood,Confidence, and the Search for Bin Laden Jeffrey A. Friedman and Richard Zeckhauser  Intelligence and National Security, 2014) was an interesting short cover of an area of decision theory dealing with presenting analysis to decision makers in situations with both uncertainty and time-sensitive outcomes.  In particular I thought there were some fun affinities with retirement finance where the seperability of the idea of risk from uncertainty (or confidence) makes some sense.  Retirement is nothing if not probabilities confounded by uncertainty.  Here are some excerpts tied to my highlighting and annotation: 

Buying some extra "certainty equivalent constant" spending given a wealth depletion framework.

See one of my last posts on stochastic vs deterministic models because this post is deterministic so it has some serious weaknesses but is not 100% without insight.  This post leans on the WDT game I built here and from which I inherit some structural model assumptions as well as parameters, the biggest of which we should note is that consumption is coerced to whatever pensionized income is available when wealth is depleted. It might be hard to understand this post without reading the prior work and even then this is pretty opaque.  The goal in this post can be stated like this: 

Starting with some assumptions around $1M in wealth and a baseline 4% spend rate for a particular level of risk aversion (say the coefficient is 2 or 3) for a 60 year old and a particular (fixed not stochastic) real return of say 2%, if I want to then consider an increase in spending in .5% increments, but I also want to keep my certainty equivalent consumption constant (with respect to what it was at 4%) each time I ponder a spending step up increment and I want to consider all of this over a full (fixed not stochastic) life-cycle interval (as defined by [60,T=100]), then: how much of a insured income payout, if any, do I have to buy at age 80 for each spending step-up to make that constant CE thing happen?

Whew...that may be the weirdest and longest framing of a question that I have done here at RH. I'm not even sure I know what I am asking myself (aren't blogs great) nor do I know if this is question is worth asking. Also there are so many variables to play with. But let's roll with what we have. This is in a class of what I want to call "holy grail" questions because it is a part of a quest to manage lifestyle up without blowing out risk at late ages when there is so much uncertainty about the future.  And don't forget: no bequest to the kids...yet. 

What I don't know

If, for each new thing I learn about retirement/financial_economics/quantitative_finance, my awareness of the things I don't know grows with some type of exponent attached to it and if by definition the things I do add to what I know is some imperfect and linear process, then in relative terms I am getting dumber every day and I'm guessing that my knowledge, in relative terms, is probably asymptotically approaching zero.  Encouraging thought, eh?

A Life in Books

There was some original reason for this post that I can't remember.  The proximal reason now is that I found a set of notes in my office from a year ago. They had something to do with my books which used to have a really big role in my life. This idea of books would confuse my thirteen year old for whom screens are the only meaning in life. How far we have come from Gutenberg. But let's roll with my notes.

Recipe - Black Trumpet Omelet

Just had this and I have to recommend it.

Black Trumpet Omelet

Black Trumpet mushrooms, a handful
Butter, a lot
Egg, 1
Parmesan Cheese, handful

Criminal

I was reading some recent econo-blogo-twit content on 'criminally under-read fin-twit related blogs.' My first thought: Hey, over here, look at me look at me! That's me! Hey! -- Second thought: zzzzz crickets: chirrrrp chirrrrp. Maybe going shallow or commercially corrupt is what I need...

On the other hand, third thought: I think I actually prefer my thirteen readers (up from three, that'd be well over a 300% increase; take that!). And then there is the blessing of no criticism (yet), no exposure of my errors or self expression, no erroneously high expectations, and no comments so no time required to respond. I try to imagine trying to stay on the top of the social media heap like some children do these days and I recoil.

On Stochastic vs. Deterministic Models

Ken Steiner took on Dirk Cotton in this recent post (Do Stochastic Models Necessarily Do A Better Job of Helping You Determine How Much You Can Safely Spend This Year?).  Now, I generally would not take on Dirk but that is just because he is one of my top favorite retirement bloggers.  On the other hand I think that Ken, like an awful lot of other things in life, is both right and not quite right here in his defense of simple deterministic spreadsheet models. His post triggered some thoughts and since this is a blog, you get to have them...

I think that the points that Ken makes, that you can read for yourself, are correct. But I also think that it is not really an either-or "oppositional" proposition (I don't think Ken is saying that either, nor do I think Dirk is for that matter) but rather that the retirement analysis task is not only a both-and "dyad" of stochastic plus deterministic but it is possibly better represented as a triad (if not more).  In a past post I implied that for retirement analytics I prefer for myself to have three things in my tool kit -- (1) analytic, fully conceived closed form mathematical expressions; (2) simulation tools; and (3) simple deterministic models or spreadsheets -- rather than none or one or two. Let's take these on one at a time and see where it goes.

10 years of retirement, 3 years of quant-ish blogging and I've only done two things

Anyone that follows the blog knows that I have perhaps over-invested in the quantitative finance that surrounds retirement.  Simulators, spreadsheet models, backward induction programs, financial economics, you name it.  It finally dawned on me what I have actually done with all those thousands of hours of reading, coding, thinking, modeling, worrying...  Pretty much nothing.  Over the last 10 years (this august will be the 10th anniversary of my semi-voluntary move to FL and the related semi-voluntary retirement) I can think of only two real, substantive actions that I have taken based on all the stuff I have learned and blogged about. And it's not tactical allocation tricks, investments in funky hedge funds, or insuring lifestyle via esoteric structured or actuarial notes or even TIPs ladders. Here are the two, and only two, big things I've ever done with all the crud that is now lodged in my over-filled head:

1. I cut spending, sometimes politely referred to as lifestyle...very painfully and aggressively...more than 50%. That was in late 2012. And yes, investment fees were part of that calculus, though that came later.

2. I put management and monitoring processes and systems in place. I consider these best in class because I have often built them myself. These are things that belong to and are controlled and operated by me, not advisors or third parties. The basic underlying processes being managed are not really about portfolios or investments as such (directly, anyway, since these are not "processes," they are financial objects) though I do have stuff like that for my trading systems. The processes are, rather, prosaic: spending, income, feasibility (time series balance sheet), sustainability (risk projected out based on net wealth and longevity processes), and maybe a few others I'm not thinking about.

That's it.  Two things.

The financial services industry gets paid trillions and I personally have paid a kings ransom for almost everything but these two things. And I had to do both myself.

A trial run of a WDT game prototype

Since I went to the effort of building a new toy, I thought I'd take my new "Wealth Depletion Time (WDT)" game out for a preliminary test drive while I work out some of the kinks (see note 1: disclaimers and admissions. Also see "links" below for background on the concept, perhaps starting with Wealth Depletion Time - an Hypothesis and a Self-Challenge).

Short options, LJM, and my lack of interest in a long/short option ratio

I was thinking about a tweet I saw today.  The quote that caught my attention was

"For anyone wondering i finally had a chance to crunch the numbers.... 14.5 short puts for every 1 long puts. $41bn short against $3bn long...No words. 

This was regarding an LJM fund failure due to crushing losses on short options during a vol spike.  I'm sympathetic to the quote and in the context of the tweet he is absolutely correct, but the main thrust of the tweet, the ratio (14.5:1), does not really interest me at all.  Me? I often carry somewhere between zero to six short puts and no long. So what is my ratio? Generally we'd call it "undefined."  So, my risk by that measure is unconscionable. But it's not. That means that what interests me in the quote is the (likely and implied) extreme, unthinking, and probably unsystematic (but I don't really know that) exposure as well as (my guess) a lack of respect for chaos by LJM.

Coming soon -- The Wealth Depletion Time Game?

Since I've sunk so much time into this WDT thing, I thought I'd try my hand at instantiating it in some real numbers and some software just to see what it's like to play around with.  A few hours of Excel and we now have a "WDT Game" prototype. It looks like this so far:

I'm not releasing this yet though and that's not out of some kind of proprietary-secrecy-concern thing. Rather, I'm still too early here and there are some things I'm worried about.  For example:

Wealth Depletion Time - Commentary

These are some of the thoughts I promised myself in Wealth Depletion Time - an Hypothesis and a Self-Challenge.  This post is a response to my hypothesis "b" in that post.

1. WDT get's its full nuanced utility (pun intended) from the use of utility math.  If, like me, one does not use utility math in daily life, the subtlety and usefulness of WDT can fade a bit. But...

2. Some of the messages that come from WDT analysis and that I have read over the last few weeks are worth being aware of since they are slightly counter intuitive and can have an impact on planning over a full life cycle. Here are a select few: 

Is this an easy "Wealth Depletion Time" analysis method by proxy?

To jump way ahead to the answer, I'd say: "no, I don't think so but there is probably at least some usefulness here...."

In Evaluating Retirement Strategies: A Utility-Based Approach - Estrada & Kritzman 2018, Estrada and Kritzman lay out a method for evaluating retirement strategies using a "coverage ratio" that carries a little more information content than a pure "ruin rate" for reasons that are explained in their paper and my linked post.  Their method creates a ratio of all the years a portfolio could sustain spending divided by the years to a planning date L that is a fixed longevity estimate.  Less than 1 would be a depleted portfolio with some added info on "how much" or "how long" everything worked out ok.  Greater than 1 would imply a bequest since, with a ratio > 1, the portfolio lasts beyond L.  In general I think that this is a new and useful way to go about retirement analysis.

RH in Key West (or) How I Read

While I may suffer and toil for the sake of my readers, I do not deliberately self-punish. Here is me reading by the pool in Key West.  While I got teased by several tourists for my "homework" this set-up was not the worst thing that's ever happened to me in life.

Wealth Depletion Time - Selected Excerpts

This is neither synthesis nor explication. This post is just some notes (the items below are direct quotes from the source material) I took in support of the self-commitment I made in Wealth Depletion Time - an Hypothesis and a Self-Challenge to try to understand WDT a little better.  Synthesis, if any, will come later...

1. The Utility Value of Longevity Risk Pooling: Analytic Insights, Milevsky & Huang 2018

• One of the main theoretical contributions in this paper is to argue that when pre-existing (fixed) pensions are included in a lifecycle model one has to be (very) careful about how to define annuity equivalent wealth and the value of longevity risk pooling. This is due to the wealth depletion time which complicates the discounted utility analysis. Although the concept of a wealth depletion time is explained in Leung (2002, 2007) or in Lachance (2012), within the context of the Yaari (1965) lifecycle model, it doesn't appear to be well known.  
• It might seem odd to split up the objective function in this manner, but in fact when p [pensionized income] > 0, there is a qualitative change in optimal consumption at some point during the horizon t ∈ [0, ∞).  That is, liquid wealth is actually depleted and the optimal consumption rate c_t* = p from that point onward. That is the ͳ value we select. Until that wealth depletion time consumption is sourced from from both pension income and wealth. But after t ≥ ͳ consumption is exactly equal to the pension, the individual has run out of liquid (non-annuitized) funds and W_t = 0, for t ≥ ͳ.   
• To be crystal clear we are not imposing this on the problem. It actually is the optimal policy, as elaborated on by Leung (2002, 2007) and carefully explained in the (textbook) by Charupat, et al. (2012), chapter #13. We can't emphasize enough how critical this (seemingly minor) point is to the calibration of lifecycle models in general and the computation of AEW [annuity equivalent wealth] values in particular. At the risk of flogging a dead horse, if one assumes all pension income is capitalized and discounted to time zero, or if the pension income is added to optimal consumption as a scaling afterthought, the wealth depletion time will be lost in the backward induction algorithm.