Wealth Depletion Time - Adding again to my pile with Leung '94

Yeah, I get it. I realize that my recent taste in reading (niche areas of financial economics and quantitative finance) is an acquired one for others.  Certainly my significant others never really quite understood the impulse.  On the other hand I am absolutely bewildered by the recent traffic on my "Wealth Depletion Time - an Hypothesis and a Self-Challenge." That this would be my top 5 all time post (currently, and seemingly, accelerative...and no, I did not click on my own post x00 times) never crossed my mind.  It wasn't even a post, it was a post about a possible future post and a topic about which I know little at this point. Maybe a friendly reader will clue me in on this phenomenon some day.

Since this WDT thing appears to be a popular topic, I'll record some of what I run into as I am on the run.  For example, today and yesterday I read through Notes and Comments - Uncertain Lifetime, the Theory of the Consumer, and the Lifecycle Hypothesis, Leung 1994. Milevsky calls this paper the first to discover the idea of WDT. Those who know me will successfully guess that both of those days I was reading the paper at a bar. Forget the unconstructive personal dynamics of this choice, it at least makes for interesting conversations sometimes.  The last conversation happened to be with someone who, while painfully attractive, is not only too young for me, her mother is probably too young for me as well.  But this is why reading financial economics at a bar can kinda be fun sometimes.

So, with respect to my reporting today, let's be clear. This post is not an explication.  This is really just me reporting on what I'm running into. It is also a placeholder for future posts where I will have a stronger point of view and hopefully a better understanding.  My mental state in apprehending this stuff at this stage of the game can be summarized like this:

Minnesota "Peak-July" is Here Today in FL

My instincts (and analytical skills, I guess) have not failed me.  For almost 50 years I was able to pick out, with nothing other than my eye and maybe my nose, what I called the "top" of the summer in Minnesota.  It was the day when the sky was the bluest and the light the most pure and after which all days led to fall or school or, later, the cold winds that start to come down from Canada. It was the day after which snow became at least a plausible concept -- in the back of a brain that was vigorously denying all of it -- three months hence.  Of course that day is typically summer solstice (but not always because this is a subjective judgment) in MN but I didn't know that as a kid nor did I pay much attention to the calendar later.

I walked out my front door at about 2 pm today (Fort Lauderdale) and thought to myself "huh...this looks like a MN top." But this time I knew it it was only late March and I knew there will be no snow three months hence.  I figured that there must be something about the angle of the sun cutting through the atmosphere.  Sure enough, when I looked, I hit it right on the numbers. Here is the angle of the sun by month in each location (Ft. Lauderdale, St. Paul). Peak angle in MN corresponds to about the end of March in FL.  It's March 30 today. I still got it.

(technically it looks like the peak in MN is in June but let's call it a range...)

I Updated My Retirement Game

In "version 8" (that sounds so formal for something where I'm just goofing around) of my Retirement Game I added a feature where one can start to "fade" income in late career.  For example, starting at age 50 and until age 65, income will decline by x% (say 50%) in equal increments from age 50-60. So 100k becomes 50k over 15 years.  This was just a little dose of reality in an otherwise unrealistic game.  I still want to make the start age something variable other than a hard coded "25" but that would take way more mental energy than I can conjur right now.

3/28 Yield Curve vs. 2016

This is the current yield curve vs. all of 2016 for contrast. Good thing I bought a curve steepener bond... There's still time. This comes from the treasury site.

Pseudo Annuity Boundary for Age 60 Male With 100k Lifestyle?

I took a shot here at trying to visualize a hypothetical series of future, inflation-adjusted, loaded, annuity prices for a 60 year old using an inflating 100k lifestyle over time along with updated mortality assumptions at each age.  The method I am using to price is this, except that I add a load of a(x)*(1+L) where L is 10%:

At t(1) in each series for each age "x," the tCx term is the 100k but inflated to each (x) by 3 or 4%. Then for t[1:(120-x)] for a given x, the tCx series is inflated at 3 or 4%.  tPx is extracted from the SOA IAM table with G2 extension to 2018 and the conditional probabilities are updated for each (x). w is 120.  Other than the load there are no other frictions modeled to help with one's confidence in any type of realism. The annuity discount "d" used to price a(x) is a not very happy assumption of a constant, average .03 but happy or not it makes my life easier to do so right now. The phrase "not a very happy assumption" was one I found in Yaari (1965) on page one where he made a reference to the "unhappy" assumption that consumer preferences were to be independent over time. I thought that his shift in tone by using language like that humanized an otherwise difficult and dry mathematical treatment of life-cycle quantitative econ; I was momentarily amused.

Beach Story

Maybe you can tell that I am starting to weary a bit of hard-core life-cycle finance analytics.  My guess is that is it temporary but who knows?  In the interim, here is another story while we see what happens.  This story below is a wee bit dated. It comes from 2008 when I had the trifecta of divorce/move/econ_crash all at one time. This is a trifecta that I heartily do not recommend to anyone contemplating something similar.  While life has mellowed and improved immeasurably since then, I did just find this story in a hidden corner of my storage drive so I thought I'd roll it out.

Top 7 Posts in March

Here were the top 7 posts in March:

1. My Drowning Man Story -- and a recipe Mar 18, 2018
2. Wealth Depletion Time - an Hypothesis and a Self-C... Mar 24, 2018  
3. More "theory reference points" (Yaari) for my cust...  Feb 21, 2018  
4. The 2017 RiversHedge 20 Best-of Awards  Oct 13, 2017  
5. RH Links - 3/2/2018  Mar 2, 2018  
6. A retirement game for a young adult  Mar 2, 2018  
7. Some thoughts on bequests and fairness: a mini moral theory...  Mar 17, 2018 [+ correction]

This perplexes me a bit.  Item #2 is rapidly becoming one of my top posts at the rate it is getting traffic. Usually this only happens when abnormalreturns.com picks up one of my posts (btw, thanks Tadas...) but (a) this is an esoteric, niche topic area, (b) I don't even really understand it yet, (c) there is no evidence it has been "picked up," and (d) it wasn't even really a post, it was a post about a post I might do some day...in the future...maybe.  Russian ret-fin auto-traffic-bots, perhaps?  If so I will start advertising soon.

A Good Day

67*. INT.    CAR EN ROUTE TO CAVE OF SWIMMERS.    DAY.

LATER - Almásy drives the second car, accompanied by Katharine and Al
Auf.  Katharine breaks the long silence.

KATHARINE
I've been thinking about - how does
somebody like you decide to come to
the desert?  What is it?  You're doing
whatever you're doing - in your castle,
or wherever it is you live, and one day,
you say, I have to go to the desert - or what?

Almásy doesn't answer.  Katharine, who has looked at him for an answer,
looks away.  There's another long silence.

ALMÁSY
I once traveled with a terrific guide,
who was taking me to Faya.  He didn't
speak for nine hours.  At the end of
it he pointed at the horizon and
said - Faya!  That was a good day!

-----

From: screenplay - The English Patient.

18 months of reading research papers...

Here is ~18 months worth of research papers lest anyone second guess my commitment to RH readers.

This is just what I printed minus what is on my office floor or the trunk of my car or thrown away. Online reading is another journey altogether.  I'm guessing I have absorbed maybe 1% of this stuff.

People have often asked me why I print this stuff out. The short answer is that I have a hard time with long session online screen reading. That is partly due to age and partly due to the fact that I had the better part of an eyelid removed and rebuilt from scratch which adds reading stress (skin cancer. You can't tell now because I had a great surgeon. But here is the PSA part: make sure your kids have UVA/B sunglasses. The procedure is as or more un-fun than it sounds). That, and it's hard to annotate online.

My annuity game extended: now vs RMD with 3 different return expectations

This is an extension of a previous spend game, the description and rules of which are here (Early retirement: inflation adjusted annuity vs. 2 SWPs). The game is the basically the same but can be summarized like this:

• For a $1M endowment at age 58: accept the lifestyle implied by an inflation adjusted annuity with a fair price + 10% (which I gather to be somewhere around an initial payout of 33k, but I might be off) 

• Either buy the annuity or replicate the annuity by spending the RMD or the annuity spend rate, whichever is lower between age 58 and 120, 

• Then see how much lifestyle has to be forsaken (in probability weighted PV terms) in the SWP (systematic withdrawal plan) in order to not run out of money at late ages by using the rules of the SWP.

The Extension

The extension here is to use at least three different return assumptions for the RMD plan and note the effects of the different growth rates on the game.  See the prev link for constraints and caveats...like: there is no randomness or vol in the model, the RMD for age 58-70 is an extrapolation, static inflation of 3%, discount of 3%, etc. none of which are all that realistic or maybe even reasonable. Hence the framing of this as a "game" rather than reality.

The choice

I had a choice:

1. retreat to the darkness and solitude of the retiree-quant cave and hover over dark, odoriferous, boiling pots of spreadsheets and retirement math, or

2. step out into the light of day and joint the twitterverse

therefore...

@rivershedge

I suddenly have nothing to say.

RH Links - 3/26/18

QUOTE OF THE DAY

I feel dumber for reading this meaningless drivel.  FriendlyChemist  

RETIREMENT FINANCE AND PLANNING

No Pension? You can pensionize your savings, Ann Carrns NYT. (I thought Milevsky trademarked "pensionize."  No excerpt here since NYT hates copy paste…though I can break that.  The short version is:1) work later, 2) delay SS, and 2) draw down savings using RMD method.) 

When A Client’s Failing Retirement Plan Sometimes Isn’t Really, Kitces

[ I normally like Kitces' posts.  But the idea that I, as a customer, would be somehow "hiding" assets that really "belong" to an advisor's fee generating AUM is appalling. That's fee-blinded irrationality.  Maybe, just maybe, a client can optimize themselves across multiple platforms and/or advisors for reasons that make sense to them. And let's celebrate the ones that take full ownership and responsibility for their own financial education and outcomes.]

Wealth Depletion Time - an Hypothesis and a Self-Challenge, me

I will understand almost none of this and will suffer greatly for my choices. 

Pascal’s Retirement, Jonathan Clements

Indeed, there’s evidence we care more about our future self if we’re pushed to imagine the person we will become. For instance, experiments have found that if folks are shown what they might look like at retirement age, they’re inclined to spend less today and save more for tomorrow. Interested in trying this yourself? Check out your future self with a site like ChangeMyFace.com or in20years.com—and remember there’s almost a 90% chance that one day you’ll be that person. 

Early retirement: inflation adjusted annuity vs. 2 SWPs

This is another quick and dirty spend game...

Assumptions

If we were to be willing to accept these assumptions (and I'm not yet):

1. we are 58 and we have $1M
2. we are potentially willing to commit all capital to a SPIA and cut lifestyle from, say, a hypothetical 4% spend plan to match the annuity cash flow, 
3. the annuity baseline is inflation adjusted and has a 10% load... 
4. our spend rates will be based on either the annuity or the players below
5. the portfolio return is 5% nominal
6. inflation is 3% where it comes into play 
7. the survival probabilities will be extracted from the SOA IAM 2012 table with extension
8. nothing is stochastic here
9. for some reason we trust my annuity pricing, and 
10. we refuse to do any formal utility analysis today...

Constraints

Wealth Depletion Time - an Hypothesis and a Self-Challenge

In several papers I've read lately I keep bumping up against the phrase "wealth depletion time" (WDT) or "wealth depletion age." My guess at the time of reading was that it was more or less the same as portfolio longevity or ruin risk but I gather that it is something quite a bit more subtle than that.  One of the subtleties is evidently that -- if one were to be enamored of utility analysis and formal mathematics, and I am not saying that I am -- capitalizing pension income onto a balance sheet and doing a PV analysis therein misses some of the nuances in evaluating the lifetime utility of wealth and consumption especially when consumption hits a "depletion inflection" and then reduces itself to the available pensionized income for some uncertain amount of time.  And this brings me to my hypothesis, which is:

My Hypothesis

I don't know much yet about WDT,  but my guess, before I start to dig into this, is that:

4% spend vs. survival probabilities and a net wealth process vs. annuity boundary

This is another one of those "I wanted to see what it looks like" posts and is a partial reprise of some "spend games" I did a while back.  This time I wanted to take a closer look at: 1) a very simple visual of a basic spend calc in the context of survival probabilities that change with each year survived, and 2) the net wealth process implied by the spend calc especially as it might plausibly relate to the arc of possible annuity calcs over time...or rather as an annuity might be recalculated if it were priced at each new age for the new level of inflation adjusted consumption at that age as well as the new longevity probabilities.

Some assumptions:

• the portfolio is $1M and returns are dead-flat deterministic (4% 5% or 6% nominal), 
• there are no taxes or fees or insurance frictions or anything else inconvenient  
• inflation is 3% fixed  
• for the "inflated cash flow" annuities, survival probabilities are extracted from the SOA IAM table with G2 extension to 2018. Male.  
• for the "constant cash flow" annuities Gompertz Makeham math is used inside an annuity pricing tool I got from Milevsky
• age range for the net wealth process is 58-105. 
• age range for the annuity calcs is 58-95.  
• consumption is 4% constant

1) 4% spend vs. survival probabilities

Proof that I do more than read SSRN papers and code stuff in R and Excel...

It's not all about the left side of the brain here at RH. This was completed today in my old-retired-man art class that I just started. Project #2...

Acrylic on paper.  I'll part with it for $1M and change. In the real world I should mention, in the interest of being honorable, that while this is my freehand work it is derivative of an original by Mark Mehaffey done for classroom, non-commercial purposes.

Correction - My post on bequests and fairness...esp wrt the delta concept

1. My mistake

In my post "Some thoughts on bequests and fairness: a mini moral-theory story about me vitiating my optimal path - draft 1" on March 17, I mis-analysed some stuff in one section.  In section "B.2.2.2 -- Swap 2: Swapping a SPIA for GLWB product - using the pooling-delta method" I misapplied Milevsky's concept of delta in the first part of that section.  When looking at his table that had the annuitization "delta" cost for wealth that is already 99% pensionized, I mistakenly applied that delta factor to what would have been original wealth forgetting I would have spent all wealth to buy a "defective" annuity like the VA/GLWB product. Figuring out delta, in the presence of prior annuitization, would instead be applied to remaining wealth which might be zero or $100 or $100,000 or something; whatever is liquid, if I have that right, which is now suspect... I had mis-understood what I was trying to do and how to read his table. I'll try to correct this as best I can.

One of the several to many things I didn't know: mathematical life expectancy

This is from "The Utility Value of Longevity Risk Pooling: TECHNICAL APPENDIX" Milevsky and Huang 2018:"  

using the classic actuarial identity that the immediate annuity factor collapses to mathematical life expectancy E[Tx], when the interest rate is zero, recovers the (cohort) life expectancy

I didn't know that. But then again I am not an actuary. This simplifies things for me in that I do not have to extract a pdf and then probability weight ages; I can do it directly. The results match my own calcs and other life expectancy calculators using a similar cohort.  In retrospect I'd say it should have been obvious but it wasn't. Does make sense though. 

Calibrating my annuity calc

Most of the time I'm winging stuff very roughly as a exercise in pure self discovery. A tiny percentage of the time I want to make sure I am not too far off-road.  This is one of those times.  I have been doing annuity math lately in some of the things I have been trying to figure out.  I know the simple formula and spreadsheets I do are "ok" but I wasn't sure how far out of bounds I was.  So, I thought I'd do a quick calibration check on my math vs. two other trusted sources.  Here is the lineup:

1. My amateur hack for annuity price using: sum[t=1:120](tPx*(1+r)^-t) | x=59, r~.0301, SOA data w G2 extension to 2018. CSP is calculated directly from the table for 59+. The rate comes from guessing an average for the result in "3" below. The formula is from any textbook. The mortality function is a simple discrete version of some Gompertz math; the simplest version is the epigraphic equation at the start of chapter 2 of Milevsky's "7 equations book. Data and math are annualized not continuous. 

2. Milevskys ILA function in Rscript (a "discretized (Reimann) version of an actuarial expectation") represented by: 

where w-x is forced to an endpoint around 121 and dt is 1/52. This is from "The Utility Value of Longevity Risk Pooling: TECHNICAL APPENDIX" Milevsky and Huang 2018 which, helpfully, provides the Rscript. 

3. An aacalc.com estimate that uses SOA annuitant cohort data and an interpolated treasury curve with a survival probability wtd avg r as of 3/2018 around .0301.  Annual payout (not continuous) and MWR = 100%. 

Using...

x = 59

m = 89.95 for 2 and 3 which roughly approximates the SOA data for that age...I think

b = 8.4 for 2 and 3

r = .0301

we get the following...

1. -->  17.985

2. -->  17.840

3. -->  18.011

Being sandwiched in between two guys smarter than me does not totally bum me out. I have a long way to go in all this but I at least feel better about my baby steps and now have some slick Rscript in which I can be confident.

The Weltschmerz of geometric returns

This difference [basically the difference between arithmetic and geometric returns over long time frames] is sometimes called the “spurious drift”, but at the London Mathematical Laboratory (LML) we call it the “Weltschmerz” because it is the difference between the many worlds of our dreams and fantasies, and the one cruel reality that the passage of time imposes on us.

From Lecture Notes ergodiceconomics.com p29.

My Drowning Man Story -- and a recipe

The smallest guarantee, the straw at which the drowning man grasps is remembrance.

                                                                                        – Walter Benjamin

Sometime in my 50th year, somewhere in the middle of 2008 -- the “crash” year, though I have to admit that at that precise point in ’08 I had not the slightest clue about the real crashes yet to come -- I lost my desire to cook.  Not lost really, maybe “taken away” is a better way to say it.  And it was not taken quickly, like a punch to the stomach might take one’s breath away with one sharp blow to the gut, but more gradually, in increments, like cold, deep water would do it if one happened to be drowning in the middle of an ocean with the choking waves competing for a share of one’s breath and relentlessly tugging at what’s left of what would be now near-frozen human energy. You know how it goes: once, twice, then a final third.  Bye-bye.

The power and glory of a single word

I've been a parent for 21 years and change.  For most of that time I was all-in or "lean-ed in" in ways that even Sheryl Sandberg would never understand because our current culture radically and willfully and self-blindingly misunderstands the subtleties and essential-ness and power, not to mention the costs and consequences, of all-in male care giving.  That kind of total attention over that much time, however, is not without its side effects.  Not more than 15 minutes ago I was unloading my weekly groceries.  My neighbor and his son were raking or working on their lawn…maybe 20 yards away.  I am not habituated to the male-child voice, having been blessed with the grace of three perfect daughters. All my neighbor's son had to do was say the word "dad," almost under his breath; I could barely hear it. In slow-motion time, like in a movie, I could feel every single muscle in my torso, reflexively and without my consent or direct ratiocination but with my utter and complete awareness, contract and twist towards the word.  

Some thoughts on bequests and fairness: a mini moral-theory story about me vitiating my optimal path - draft 1

I thought I was going to jot down some thoughts on bequest and annuity pricing for around 20 minutes. Five days later and this is one of the longer pieces I've done and probably the second hardest.  There are a ton of mistakes and wrong paths followed but one of the themes of the blog is to use writing to consolidate my memory so let's soldier on if for no other reason than that...

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

The Problem of locking up assets and "cheating" bequestees

I've been told, quite assertively and quite often by an advisor friend of mine, despite my (formerly) shallow, naïve, amateur insights on the value of longevity pooling, to never ever annuitize…ever. Ever!!!  Trying to press on this issue, even for some perspective or to get more info, is a little like a wall-head-banging excercise. So I don't. Or at least not anymore.  My presumption is that, in the absence of a reasoned and calm discussion, the rationale for her position is that: A) there are products and strategies that can provide longevity risk hedging and income flooring similar to a traditional annuity but without the irreversibility of giving your capital to an insurance company "forever" -- and here she used a particular company's GLWB rider with step-ups and minimum withdrawals as an exemplar, and B) not so unrelatedly, the idea is that irreversibly giving your capital away to the evil insurance company is both "unfair" to potential bequestees if you die the day after signing the contract as well as risky if you happen to have spend shocks in the future (the latter part of "B" I will mostly ignore). This is part of the fabric of the annuity paradox, by the way. This is also something I want to understand. Let's hit both A and B and see what happens.

On the delta value of longevity risk pooling

This is basically an update to a previous post on a paper on the utility of pooling (Notes on: Utility Value of Longevity Risk Pooling - Milevsky and Huang 2018). In that paper, which I considered to be useful and innovative, I had one point (ok, a lot of points) where I was particularly confused.  I couldn't completely get my head around one of the important innovations in the paper: his delta [δ0 = √ e − 1 ≈ 64.9%, when r = λ, γ → 1] (this would be in the absence of existing pension income and using exponentially distributed remaining lifetime which would change delta) which he describes as "the value of longevity risk pooling."

I figured this was pretty important so I couldn't let my confusion pass unmolested. And this is where I get to one of the things I like about retirement finance: when one is confused, all ya gotta do is ask, and 9 out of ten times, someone will respond in a helpful way.  So I asked.  To my (paraphrased here) email to Professor Milevsly asking "Can you explain what the heck 65% means and how I should interpret it?" the good professor responded: 

Hi Will. Basically, its DELTA percent of the money you have available to annuitize at retirement. So, if you have $100,000 and decide not to purchase the longevity insurance -- and take the chance of living longer than life expectancy -- you would need to be compensated with $100,000 times DELTA. moshe

Ok, so if his delta was an obscure or odd mathematical object before the email...then, after crossing the line called "ah, now I get it," it seems even odder.  I had been ruminating lately on the percentage of my capital that is "dead" because it is the portion I can't really tap because it self insures a superannuation risk that may never be realized. But this is something different. This is like some kind of shadow capital concept; it's as he says: the value of what I'd need to be paid not to annuitize wealth to cover the chances of living really long. It's like a parallel-universe-through-the-looking-glass version of my dead capital idea. If I have it right. Which always seems in question.  

RH Links - 3/15/18

QUOTE OF THE DAY

Pity the poor fellow who doesn’t write. He likely cannot think. Rayward  

RETIREMENT FINANCE AND PLANNING

Debugging Your Retirement Calculations,  Darrow Kirkpatrick

After all these years of retirement modeling, I still don’t get very fancy when doing my own calculations. I model the basic factors that I can predict with some accuracy. Then I live frugally, maintain a healthy cushion to guard against the unknown, and don’t spend much time or effort trying to predict how the future will unfold… For most of us, a middle way works best 

Developing a Sustainable Spending Plan (SSP) vs. Using a Systematic Withdrawal Plan (SWP) Ken Steiner. 

SWPs provide a retiree with an algorithm for withdrawing funds from their investment portfolio.  Sometimes this is also referred to as “tapping” one’s savings.   Common examples are the 4% Rule and the IRS RMD approach…. A Sustainable Spending Plan develops a spending budget that is consistent with the individual’s (or couple’s) spending goals… The focus of the SSP is on spending, not withdrawals from savings.  [I'm going to have to agree with Ken on this.  Withdrawal methodologies often get confused with spending but are not the same.  An annuity is a type of "withdrawal plan" and a person would be blessed if their spending exactly matched the annuity cash flow...but it won't] 

Increasing Client Withdrawal Rates in Retirement, CFA institute

two recent studies … aim to tip the odds when it comes to spending from a portfolio. 

Evaluating Retirement Strategies: A Utility-Based Approach, Estrada & Kritzman

Retirees need to make two critical financial decisions, namely, the withdrawal rate and the asset allocation of their portfolios. We propose a methodology that retirees, and particularly advisors, could use to make these decisions in an optimal way. We introduce a new variable, the coverage ratio, and a theoretical approach, based on utility. Our approach can be used to make optimal decisions during both the accumulation and the retirement period, but we illustrate it by focusing on the latter, and particularly on the choice of an optimal asset allocation. We find that the strategies selected by our utility-based approach are in general somewhat more aggressive than those selected by the failure rate and other existing approaches. 

The Utility Value of Longevity Risk Pooling: Analytic Insights Milevsky Huang 2018

In this paper we derive some closed-form expressions for the value of longevity risk pooling with fixed life annuities under constant relative risk aversion preferences. We show, for example, that this value converges to the square root of Euler's e -1 (=65\%), when the interest rate is the inverse of life expectancy, lifetimes are exponentially distributed and utility is logarithmic. In general the various formulae we derive match previously published numerical results, when properly calibrated to discrete time and tables. More importantly, we focus attention on the incremental utility from annuitization when the retiree is already endowed with pre-existing pension income such as Social Security benefits. Indeed, due to the difficulty in working with the so-called wealth depletion time (WDT) in lifecycle models, we believe this is an area that hasn't received proper attention from actuarial researchers. Our paper offers tools to explain the value of longevity risk pooling. 

Notes on: Utility Value of Longevity Risk Pooling - Milevsky and Huang 2018

These are some comments on Utility Value of Longevity Risk Pooling: Analytic Insights - Milevsky and Huang, March 2018 [ssrn.com]

• This either is or will be or should be an important paper for some of the reasons they state: "Against the backdrop of declining defined benefit (DB) pension coverage and increasing reliance on defined contribution (DC) investment plans, there is a growing awareness that longevity risk pooling is being lost in transition." I agree with the authors that this awareness is a much bigger deal than people realize. 
• In addition, this paper is a technical tour de force because it basically takes the lower half of Yaari's 1965 matrix (uncertain lifetime with insurance available) and: a) blows it out by extending the concept, and b) makes a (feeble?) attempt to make it accessible to a broader audience (see next point). This is one of those papers that actually does move the ball forward.
• One of the stated non-academic goals of the paper is to extend the dialogue on risk pooling beyond  practicing actuaries and insurance and pension economists to general public, the media, advanced practitioners and regulators. My guess is that it will not find its way past a few research academics and some actuaries and maybe, as a very far stretch, some advanced practitioners.  This is still pretty dense.  I am not exactly a slouch in this area but even for me a lot of this was over my head...even though I could actually follow or at least recognize what they were doing with the math for a change.  So, in my opinion, this does not have a broad audience yet. 
• My bloggie-sense is that longevity risk pooling is a radically underutilized and sometimes mis-characterized tool that is more important today than it was yesterday and will be more important still tomorrow.  This is basically the same as the first point but I thought I'd mention it again.  My guess is also that folks like Milevsky will have an out sized impact on where we all go from here.  I also think we have not gotten anywhere near a creative apex in the area of exploiting the value and goosing the efficiencies of longevity pooling (see my pseudo-tontine post) 

Thoughts on "Bernoulli's error" and Samuelson v. J L Kelly

EUT is the foundation of modern economics. Despite this, I have yet to find a practitioner who uses it.  --ergodicityeconomics

I was reading an interesting post at ergodicityeconomics.com yesterday (The trouble with Bernoulli 1738). If I may be permitted to oversimplify, the poster's point is that there is a possible error in the way Bernoulli deals with fees in the context of the utility curve for a lottery. That means for him that to some extent Bernoulli is not "the same" as modern utility economics which he then uses as a platform to advocate a non-utility approach (time-average growth rates) that is "better."  I can't comment on Bernoilli's error (or lack) but it is definitely worth the read to see the poster pick apart the original paper.

On the other hand the thing that my amateur brain did notice was that in the remainder of his post, where he starts to tease out some of the differences between evaluating utility (disfavored by poster) and evaluating expected exponential rates of growth in wealth (favored) it was starting to smell and sound really, really familiar to me, like someone speaking in some difficult dialect but who also starts to slowly become more and more understandable (usually in the presence of beer).  Here are some excerpts. These may be tendentiously selected in a way that is in my post's favor but are representative I think:

A Pseudo Tontine for Me...But Probably Not for You

I was reading an article on Tontines today (Annuities Versus Tontines in the 21st Century, Milevsky et al, 2018 Society of Actuaries, Retirement Section Research committee -- man that guy is everywhere these days).  I didn't read the whole thing because I have to admit I started to lose interest half way through but it did kick off some thoughts.   This is a blog so blog we will on those thoughts.

Optimal Purchasing of Deferred Income Annuities -- Huang, Milevsky, Young 2015

I was reading today Optimal Purchasing of Deferred Income Annuities When Payout Yields are Mean-Reverting by Huang, Milevsky and Young 2015.  Or, rather, let's say "trying" to read. Over the last couple years I have vastly improved my ability to read and interpret quant-finance notation but me trying to follow these guys, which I attempted for maybe the first 9 pages, is like a dog chasing a UFO: charmingly and endearingly naive, odd, and impossible.

Tincup in the RH lab

Since:

1. I was a binge watcher of season 1 of Jessica Jones on Netflix,
2. One of the top alt risk guys on the planet (Cliff Asness) also appears to be a fan of JJ,
3. Season 2 of JJ just started,
4. In season 2 Jessica drinks about a fifth of Tincup for every 20 minutes of show,
5. My future heart and home belong to Colorado, and
6. Tincup is made in Colorado...

I thought I'd bring some Tincup (or from their site: TINCUP) into the RH lab for testing.  This is the scene:

Keep in mind that Jessica would have a much taller glass and it would be 94% full (before she swills the whole thing).  As for the lab, that's an Asness fund I own in the background. The book is Markowitz (vol 2 of Risk Return Analysis 2016). The keyboard is filthy so I cut it out. The magnifying glass is not a prop. Without it I can't see the 2-factor authentication code I need to log into my broker platform.  The multiple screens are vestigial. I have three but don't need them all. I once had six when I was a GP/LP in a hedge fund startup (lost a ton; learned a lot).  My kids made fun of me for my screens. By the way, it's 3:06pm.  When I was married my now-ex would give me the evil eye for even the smallest drop of alcohol before 5:01pm.  Have I mentioned that I am not married anymore?  

As for the whiskey... they call it an american whiskey in a bourbon style. It was sold in the bourbon section. From the producer's site:

TINCUP is a blend of two great American whiskeys, each aged in #3 charred oak barrels. “High rye” bourbon, distilled and aged in Indiana, is blended with a small amount of Colorado single malt whiskey. These whiskeys are then cut with Rocky Mountain water. TINCUP is named for the Colorado mining pioneers and the tin cups from which they drank their whiskey.

And that makes sense because the first taste came across as pure rye.  The palate is pretty bold and a little spicy.  I can see why they call this an American whiskey. Not sure if I could go toe to toe with Jessica on gulping this straight in 20 ounce increments though.  I'm thinking a couple ounces with a splash of water and a big chunk of good ice might do the trick.  Manhattan or old fashioned style would not offend me either.  A coffee drink done right would be killer.

As a last thought I'll mention that I'm trying to start up an interview series called "RH Five Questions."  I have two people I have asked so far and am waiting to see if I can reel in their responses.  My goal is to canvas some of the quant-finance litterati that have been helpful to me so maybe I can interview Cliff in person over a Tincup with JJ running in the background. Maybe someone can tweet this to Cliff for me since I am not a twitter-god.  

Evaluating Retirement Strategies: A Utility-Based Approach - Estrada & Kritzman 2018

At first glance I was thinking to myself "yawn...another withdrawal rate paper with such and such insight...blah blah blah" but I actually kinda liked this one more than I had expected.  The paper in question is "Evaluating Retirement Strategies: A Utility-Based Approach" by Javier Estrada and Mark Kritzman 2018.

This appears to be an extension of some previous work that Prof. Estrada has done (after naming names in a literature review) that tries to take all of us beyond "fail rates" in a constructive way (that right there makes his paper worthy before anything I say below) .  And I think he has succeeded a little bit on this.  The extension here is, at first, to use a coverage ratio (fraction of the retirement period a strategy was able to sustain a withdrawal plan) to evaluate retirement strategies rather than a fail rate. Why is this even vaguely interesting?  Because it (the ratio) carries more information content than a fail rate does and not just information on "magnitude of fail" but also something about "scale of bequest" as well. I hadn't thought about that before. Here is Estrada and Kritzman:

On RiversHedge and Hobbies

I came to some odd conclusions about RiversHedge yesterday.  Let me run this by you and see what you think.

I retired 10 years ago and at that time, in a difficult situation, for a variety of reasons big and small, I made the care of -- and continuity of caregiving for -- my kids my single, unbreakable focus.  Now, 10 years later, everyone is a little older and a little closer to being on their way into the world.  So, now my thoughts turn to other things, things like maybe an encore career or a hobby or something...you know: golf or glass blowing or maybe canasta.  But about that hobby thing I've had several epiphanies.  I'll enumerate them thusly:

Is Illinois the worst run state?

Don't get me wrong. Some of the small rural towns in Illinois can be pure magic especially those small rural river towns and especially those small rural river towns when they are seen in that infinite span of time that only seems to happen in the midwest...you know, the span between the unexpectedly late end of a hard-bright day and the onset of that dark-dark part of night that never seems to come. And then there is Chicago. Chicago is one of the true jewels of big cities, not just in the US but in the world. On the other hand...

I was thinking about Illinois today for several reasons. First because I have always asked my advisors to steer clear of Illinois bonds (the only state, so far, where I have a hard "no") because of their dysfunctional finances that always seem to favor special interests at the expense of the taxpayers, future taxpayers, children of future taxpayers, and, of course, rural counties. Second, I have recently added corporate and muni bond trading to my personal repertoire, a capability that is among the very last frontiers of what I physically need from a formal advisor (if we skip over things like lending facilities -- though I have solved that too -- or private placements but I have forsworn placements for the foreseeable future). This means that I have recently been perusing bond offerings and have been considering, along with the obvious financial and time terms, their various risks and ratings. Third, because there was a good letter to the editor in the WSJ today about the perverse alice-in-wonderland feats and foibles of the entrenched Illinois political "combine" that made me wonder "how bad can it be, really?"

Here is how bad it can be. This is an excerpt, without any further comment (though I suppose we could discuss New Jersey? ...and the fact that there is currently no interest rate on the planet that would induce me to lend to IL; I'd almost rather lend to Venezuela), from ballotpedia.org/State_credit_ratings: 

RH Links - 3/2/2018

QUOTE OF THE DAY

"Grammar, once a benchmark of basic literacy, is now a luxury...digital communication has inflected written English in the way that the guillotine inflected Marie Antoinette's neck." Dominic Green

RETIREMENT FINANCE AND PLANNING

How to Rescue an Underfunded Retirement, Joe Tomlinson

Americans have under-saved and will need more than withdrawals from savings to survive retirement. An optimal withdrawal strategy and asset allocation, delaying Social Security, annuitizing, tapping home equity and possibly working longer need to be evaluated…The biggest improvements in retirement prospects come from working longer. For those who don’t save enough, it is a big plus to have stable employment in a good job, and to keep building job skills while maintaining good health. More human capital makes up for less financial capital.  

Unraveling Retirement Strategies: Constant-Dollar Spending(4% Rule) ; Dirk Cotton

The idea that we can spend an amount calculated at the beginning of retirement and continue spending it regardless of what happens to our financial situation over perhaps 30 years is not only risky but irrational…SWR is like an annuity from an insurance company with a 5% to 10% chance of going out of business…It’s expensive to tie up 96% of your wealth so you can safely spend 4% of it… it is irrational to ignore new information that comes available as retirement progresses and financially unsound to attempt to derive constant income from a volatile portfolio. The strategy is risky for retirees who are not wealthy and unnecessary for those who are. [Wise words from Dirk.  You may recall that I have suggested that a constant spend strategy is a very active risk accepting posture. Dirk just says it better.] 

What Investment Risk Really Is, Illustrated, Waring and Siegel [2018]

We’re focused here on the task of simply understanding what risk really is, and how it changes with SAA policy choices and with different approaches to spending. Along the way, we’ll examine how risk looks for the traditional single-period capital asset pricing model, as well as for a multi-period consumption-based model…Don’t like the risk? Change the asset allocation. 

Spending, Relationship Quality, and Life Satisfaction in Retirement; Finke, Ho, Huston

this research explores how spending and relationship quality contribute to life satisfaction in retirement, controlling for financial and human capital factors. The results provide evidence to suggest that leisure spending, health status, and spousal and friend relationships have the greatest impact on creating life satisfaction during retirement, while other type of spending and children relationships do not. 

A retirement game for a young adult

Ok, so I've been doing this RH thing for maybe 2 years and thinking about retirement issues for at least 10.  What's the hardest thing I've dealt with so far? Take a guess. And it's not backward induction via stochastic dynamic programming or learning to code R or evaluating stochastic present value or modeling longevity processes or joining stochastic lifetime process probability math with perfect withdrawal rates or portfolio longevity processes.  No, it is trying to answer my 21 year old daughter's question about her future retirement. One would think I'd be equipped to respond to something like this but one would be wrong.  This is all harder than I thought. I've never really had to give advice before to someone that does not speak the same language I've been working with here at RH. Actually I have not, to my recollection, given retirement advice to anyone other than myself. Except for the blog I guess. But that's not advice, just an online diary of sorts.

Putin Targets Florida

Why would Putin pick on a disfunctional state like Florida when there are so many normal states to choose from? https://www.cnn.com/…/putin-nuclear-missile-vide…/index.html

Book Mention - Ten Great Ideas About Chance

First of all, I should say that I neither advertise nor do I have any affiliate programs like some bloggers do with Amazon. This is just me.

I am currently about half way through an interesting new book (Ten Great Ideas About Chance, Princeton University Press. November 7, 2017; amazon link here...I am now starting chapter 7 - Bruno de Finetti). The book is described like this:

In the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact.

The authors are Perci Diaconis and Brian Skyrms, respectively: 1) the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford U. and 2) the Distinguished Professor in the Department of Logic and Philosophy at the University of CA at Irvine, and professor of Philosophy at Stanford.

I say "book mention" and "interesting" above because I can't really review it because I am only half way through and an awful lot of it is over my head. That, and I'm not totally sure I feel great every time I read a page that I have to read again only to realize I don't understand it.   On the other hand this is, in fact, the "intro course" I was looking for. It gives the history. It provides the context. It names names. And it does not shy away from the math and structural concepts.  So, while it is interesting in the sense that interesting is hard like eating kale and pretending to like it, it is also something I am glad I am reading, glad like someone just brought me cheesecake that I didn't order and don't want but will no doubt eat anyway.  

AQR and pulling the goalie

In a recent AQR post (Perhaps the Most Important Essay I Will Ever Co-Author), Cliff Asness rolls out a fun analysis of the mathematics of pulling a goalie in hockey (the math supports an earlier pull than is typical) and takes a slap-shot at applying the insight to investing.  I am friendly to AQR (investor in several funds) and to hockey (hey, I'm from Minnesota) but I am not as sanguine as Cliff on the applicability of "goalie-pulling" to individual retirees and I think the frisson of coming up with what is otherwise a pretty good sports-to-finance metaphor has blinded him to a couple things (If I am reading it right). While there is probably some case for institutions with long time frames to "pull goalies" (i.e., don't disdain the return potential of higher vol strategies or "you can't eat low volatility" or something like that) the problem for me is that for certain retirees in mid retirement: 1) a plausible remaining retirement planning horizon can sometimes be really short (say you are 68 and plan to annuitize at some optimal age such as 76 or 80) so recovery time can be too short as well, and 2) his metaphor looks like it leans pretty hard on expected value so for an individual retiree he hasn't solved the one-whack-at-a-cat problem.  For the individuals that average to the expected value the journey can be one of misery if they are the one stuck with the non EV result.  On the other hand for low levels of wealth and short time horizons, high vol can, in fact, act like the only lotto ticket available and pulling the goalie might be an obligation rather than a choice which probably makes his point. The rich, of course, can pull goalies all day long because they have giant margins for error...but we don't care about that side of the equation. For those in the middle conservative game strategies still seem worthy.  But then I have not really digested the paper so maybe there is more to it that I credit here.