First whack at cost of stochastic inflation in decumulation

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note: some errors have been corrected since initial post
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Ok, let's sandbag right away. I don't know if I got this in the right groove but let's roll anyway.

Using a life consumption utility model, and a simple model for auto-regressive inflation based on historical data, I ran a few new models today:

1. a baseline with deterministic inflation set to the mean of the random distribution I'll use for #2

2. a simulation using stochastic inflation that is bootstrapped from history (1914-2018) with a coefficient of auto-regression over 1 period of .64. (see the link above on inflation)

3. This scenario is the same as #2 except that the initial wealth is stepped up a bit (+25%) to get the life consumption utility up back towards #1 levels (not done analytically. Pretty much just eyeballed it). This is more or less like evaluating "certainty equivalent wealth" but I'm not totally sure about that so I won't precisely make that claim.

The goal was to determine how much extra wealth might be necessary at retirement-start to make the life consumption utility roughly the same as the baseline i.e., that is, either: a) we implicitly spend less...I realize that I have not really shown that here, or b) we have some amount of "redundant" (higher) wealth (vs the baseline) that is held in reserve in a way. Either way, same thing. I might have to expand on this because I know it's a little fuzzy.

My mini fake unrealistic economy

Basic idea: valuation is discounted cash flows, aggregate value is a fake economy

Question: what happens if you kill a couple close-in periods of cash flows, take some time to ramp up, discount rates rise over the interval, there is a 20% extinction rate, and no new entrants?

- 40 periods
- 10 independent cash flows
- $100 cf
- discount 3-->6% over first 10 per, then steady
- first 2 periods of cf get vaporized
- next 7 periods ramp up 0 --> 100; linear
- 2 cash flows go extinct

aggregate difference:  -49%

None of these assumptions are remotely realistic except maybe the cash flow, rates and extinction

My inadvertent pandemic hedge

I was catapulted semi voluntarily into early retirement in 2009 at ~50. This was before I knew a whit about retirement or life-cycle finance which, in the end, would have confirmed my behavior anyway. The behavior in question was my very very conservative spending early in my retirement.  The basic idea was:

My Indolence in Quarantine

From age 50 to 61, under the full force of life's un-quarantined pressures, I embarked on a process of self-ed for reasons that only Richard Dreyfus in "close encounters" might understand. Even though I'd had a full career and a very old MBA with special recognition in finance, it was not enough. I don't know if it was intellectual boredom or insecurity or the need to feel challenged that drove it but I powered through stuff like this below, which is all I can remember. There were no doubt other topics. There's always something. Here is what I remember, though:

On Redundancy, Robustness, and an Interesting Chart I Once Did

In a blog post long ago and far away I made the case that early retirement -- one with only systematic withdrawals and no life income -- needs the redundancy and inefficiency of "extra" capital early in a retirement cycle in order to be robust and immunize itself against the life-cycle uncertainty that can't always be modeled (plague?). The basic idea is that spend rates in the literature often seem over-optimized in a way that is a little like skating too close to open water...because you can and because you can't imagine anything happening except what you expect.  I've struggled with this socially in terms of others because I tend to be cautious where others are not. Every partner I've had over the last 30 years has tried to shame me for my caution and my attempt to build in financial robustness.  I'm guessing that they are not laughing now. I'll take a stab at explaining why I think they were wrong. 

A change in the wind?

The current events unfolding in real time are more or less what I've worried about for a good long while in my personal planning and this blog. It's exactly why I fired an advisor for once glibly saying "c'mon, live a little" to me when I laid out my spending approach that conserves early for the possibilities for later risk and uncertainty. That the banker-peasant could not see the convexity of model-able risk as well as being totally blind to the hammer blows that can come from unmodel-able uncertainty was and is certainly his problem, between him and his family (and no doubt between him and the other co-clients I left behind), but me? I did not want that kind of cavalier attitude to infect my family where "infect" seems to be the appropriate analogy in 2020.

But a big question for a lot of people, myself included, is to what extent extreme volatility is already baked into a plan and just needs to be ridden vs being a situation where there have been material changes in the world and the plan no longer obtains, the plan in broken. Spoiler: that distinction is more art than science in my humble opinion and one will never 100% know, except maybe in retrospect.

A riff on the shift from accumulation to decumulation in an early retirement setting...

Those who know me know that I went through a fraudulently-induced move to FL in '08 for reasons I will still hold back with respect to the exact detail. During that time of separation, divorce, betrayal, global financial crisis, and, of course, the move, I also took a lot of Pepcid, a few cocktails, and some unpleasant prescription pharmaceuticals I didn't like at all and quit cold soon enough. I do not recommend this kind of phase-shift in life to anyone. The decision to "retire" at that time was mine alone. Mostly this decision was made because I had been primary caregiver -- almost entirely solo on a 5x24 basis -- for 12 years and I decided that continuity of care would therefore trump money; a lot of money. But whatever.

That shift, at 50, was naive and uninformed. I've learned things since then. Over the last 12 years or so I've done many things, including this blog. One of the many things I've done as well has been to ruminate on the transition from accumulation to decumulation before an age where it totally makes sense to do that.  This post is not designed to be systematic or exhaustive. Mostly I just wanted to seed my own thoughts for a post later on that will be in more detail. The goal here is to think about some of the off the cuff differences between the two states, differences that are filtered through my personal experience as well as through my amateur finance capabilities.  I may add to this post later.

My points are more or less extemporaneous but are also informed by some work by Michael Zwecher and a body of work by Moshe Milevsky, not to mention everything I've read over the last 6 years.

Does allocation matter?

The recent downdraft in markets spooked people. It spooked me. A woman I know, retired, was going to call her advisor and was dead convinced he had her in too much risk. She pressed me: "You do all that blog math magic stuff, tell me..."  I did NOT want to get between her and her advisor but with enough disclaimers, I obliged, especially since my guess is that the advisor, while competent, probably does not dabble in economics or actuarial science and my perspective would be different rather than necessarily conflicting. 

I told her as a prior that my guess was that the allocation probably did not matter much and that spending was a stronger lever. But I took a look. I won't divulge personal details but let's say we have someone in mid to early 60s, a reasonable wodge of financial assets, social security, a few small deferred annuities in the future, a risk position that was relatively high[1], and a spend that as far as I could tell, was at or under 4%.  The exact numbers were less important than the general sense.

I plugged that into a consumption utility simulator[3] and got this in the figure below. Based on this I figured she probably could trim her risk and I think she got him to give in on that.  Otherwise, the idea that allocation doesn't matter too much over a broad range still (sorta) stands. For her spend rate, if it were me, I would (tax issues excepted) trim risk way back, which is what I do for myself but i think she'll be OK but only over the long run and only if the world stays normal. That last assumption is key and my guess is that the world will not be normal for a good long while.

The commentary in the figure speaks for itself in terms of residual conclusions[2] so I'll leave it at that. The third unspoken lever (besides allocation and spending) that is not imagined here is "when to retire" but that was mooted in this case.  I could have broached the idea of immunizing spend via life income (annuities) but didn't. Probably should have.

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[1] Let's arbitrarily call it like this on "levels" of risk:

- 0-30%        Low risk position
- 30-80%      Mid risk
- 80-100%+  High risk

I just made that up but it's not totally unreasonable.

[2] It's implicit in the figure but I'll make it explicit. High spend rates with very low allocations to risk are a bad combo. Low spend rates with either low or high risk are a better bet than that.  Spend rates move the needle in the middle more than allocation does.

[3] covered here in more detail:

• A Wealth Depletion Time Model

How far?

Message in a bottle

I didn't know my father well. I was seven when he had his third and final heart attack in 1965. He was 47.  Here are some of the few things that come from my direct memory:

- bald
- had a fedora on the top closet shelf and long heavy overcoats, some with a fur collar
- liked shish-kebobs
- had some big-shot job at Prudential on highway 12
- liked his Cadillacs with fins
- loved to fish
- terrible cologne
- most of the time leave him alone but solid otherwise (like me)
- drove us all on an epic western road trip in ~1963
- turned purple some night in '65; wasn't there in the morning

Comments on the Floor Leverage Rule

I was sent a link to a paper from the Stanford Institute for Economic Policy Research by a friend the other day. 

SIEPR Discussion Paper No.13-013
The Floor-Leverage Rule for Retirement
By Jason S. Scott and John G. Watson
Stanford Institute for Economic Policy Research
2013

The abstract is thus:

The Floor-Leverage Rule is a spending and investment strategy designed for retirees that can tolerate investment risk, but insist on sustainable spending. The rule calls for purchasing a spending guarantee with 85% of wealth and investing the remaining 15% in equities with 3x leverage. Surprisingly, this leverage is a tool for managing risk. We compare our rule to some popular strategies, illustrate it for a variety of retiree preferences, and evaluate its historical performance.

The following is neither comprehensive nor exhaustive, just a riff based on some thoughts as I read my friends email.

My first kinda botched attempt at backward inducting spending via SDP

Preliminaries and Intro

The purpose for this post is to write up my attempt to try to use an "optimal control theory" technique (e.g., stochastic dynamic programming and backward induction - BI/SDP) to evaluate lifecycle  spending choice (or the decumulation half, anyway).  I had tried this BI/SDP technique once before with "asset allocation choice" when I tried a couple years ago, with a modestly successful outcome, to replicate Gordon Irlam's description of the method in his article Portfolio Size Matters [2014] article.

The goal here is not replication (I'm not sure I've actually ever seen this kind of BI thing done before for spending) nor is the goal necessarily usable functional results. No, I am mostly just trying to: 1) build new skills or stretch old ones, 2) see if I can do it at all, and 3) maybe provide another avenue of confirmation for the shape of spend rates in the mid-to-late age retirement process.   Since the method is considered to be quantitatively and intellectually robust in some circles of academic econ, it is probably therefore worthy in my mind of some examination. It can then be placed in the toolbox that I have for "triangulating" around my understanding of the retirement spending problem.

Twitter broke my pinned thread

"Todo dia um leão, vovô." from a twitter follower: "every day a lion, Grandpa"

Twitter is the new censor (and jester) of the kingdom.  I had a "pinned tweet" that put myself out there a bit and they broke the thread entirely.  I figured it was going to be there for a while but I keep forgetting that Twitter is a "gaming platform" and they own the game.

Just for fun here is the original thread to the extent that I can reconstruct it. Most of this is redundant with my page above with my fitness stuff as well as a previous post on the same topic. I just felt obligated to rebuild what Twitter broke apart. Edits added for clarity and flow.

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see also:

 - some late-age core work 

 - fitness post-60 page 

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1/  My Path

I burned myself to ash in a crucible of my own making, with 11 years of dead-walking, to find my own path mentally and physically. That’s a really long time. Now? Examples of fitness-follows I use at 61 to stay alive:

@TheForeverAlpha
@Mangan150
@_CynthiaThurlow
@jerryteixeira

2/ The Game…

Fast: consistently, not obsessively >=18:6
Eat: high protein, low other. Count calories, nix alcohol
Lift: often, progressively, with ROM. Recover
Balance: hormones, sleep, stress
Excellence: attempt it always and everywhere, with purpose

all that = hope for 60+ crowd

Results [maybe Q3 2019]:

/3 Some other follows:

@allicovington

@Mattvjohnson

@Chris_DFB 

@HynesDm

@tellquint

@DanielKellyTRT

@FitzgeraldSTA

@IngriPauline

@ClintShelton5

@SBakerMD

@FKetogenics

@ThePrimalMan

@anymanfitness

@jackdcoulson

@MasculineDesign

@Rob_NBF

@Matt_S_Stephens

@AJA_Cortes

4/  Why Those Follows?

It’s not exactly that I do what they recommend or buy their programs, it’s that they seem to be the closest confirmation of what I figured out long before I even knew what a Tweet was a year or two ago.

/5 Some Side Benefits

To round out thread, some of my follows (e.g., @_CynthiaThurlow) enabled me to open a dialogue on this stuff with three teenage girls. Try THAT in your house sometime without being murdered. Note that I am not selling any program and receive nothing for my plugs. Twitter, eh?

6/ Post script to 1-5: 

pic on left [above] was Xmas 2016 close to 200lb. Right was this week [Q32019] at ~169. Turned 61 in July[2019]. Started program casually from zero Q3 2017, seriously in early-mid 2018. BF in mid 2018 was 23%. Now approx 15, maybe less [under 15% by Dec 2019].   5’11” tho I bet I’ve shrunk. My 6-6 bro is now 6-5

7/ Chaining something else to my pinned tweet... 

I hit another fitness goal in mid-to-late 2019: For older dudes that follow: I'll assert age is not an excuse, though it may take a good long while. 61 and I *finally* hit all but 1 goal today. Down 35lb plus strength goals hit. Took me about 2.5 years with periodic caloric and alcohol suppression.  Now legs ;-)

[The reason for the two pics, other than pure vanity, was to show the difference between ~15-16% above and a punch down to ~14% below. If I hit 10% I'll do it again...]

8/ Update 02 05 2020: 

1) still at ~167. Body fat is a little lower I think but haven't checked. Using more recovery.

2) will never trust twitter again even as a small inconsequential account. They move goal posts.

9/ My fitness Page

At the top of the blog there is a tab with a cover of my fitness program. Covers the same ground with more detail on the plan.

Increasing the machine's interval of interest to age 60-->95

Reason for this Post

See the integrated cover of what I'm doing here:

• Machine Spending  

In the last post

• Adding some lifetime income to the machine learning model

I wondered what would happen if I looked at the interval not just from 60-80 but from 60-95 because I wondered if the machine could make itself converge, when presented with the beneficence of lifetime income, towards a "shape" of spending that looks more or less like optimal consumption in a formal economics LCM (life cycle model) context.  The mental frame-of-reference that I have for "the shape" -- though there are other sources for this -- is from a 2010 paper by Marie-Eve LaChance titled 

Optimal onset and exhaustion of retirement savings in a life-cycle model; Cambridge U Press. 2010 

On page 35 she sketches it out like this:

Adding some lifetime income to the machine learning model

Premise

The original set up, with the references and links to other posts, is here:

• Machine Spending

In this post I added 15k  (real) in lifetime income starting at age 70 to the other parameters. This can be viewed as exogenous income like Social Security or some other external pension or annuity.

Something to keep in mind is that:

a) This move to add income with no other changes is more or less like adding new wealth to the balance sheet since the probability weighted present value of that stream at 60 is something like 226k, money that we didn't have before. 

b) the income really isn't like a static wealth PV since it is a "flow" that, in the model, is set up to last forever. I mean except that at some age the survival probability goes to zero...which moots the forever aspect.

The game is still the same as before:  recommend to the machine that it spend 4% but also let it learn, via some randomizing and an evaluative reinforcing value function, what might be better given random returns and lifetime, now this time with life income present.

Some Observations on my Machine Learning Project

The original post and all the associated links and references, for context, are here:

• https://rivershedge.blogspot.com/p/machine-spending.html

A recent question from a correspondent, one that I asked myself in the last post was:

"Why bother to run a sloppy, slow, imprecise machine when one can access the insight directly, accurately and faster by other means?" [paraphrased h/t to David Cantor]

Good question; cuts to the core of my project.  Let's see if I can rationalize what I call "riding a bike in first gear:" a lot of motion and heat for very little forward progress.

What happens when you try to improve the machine by suppressing outliers

Intro

The short answer to the title is that it looks like the machine's output shifts from finance to economics. That confused me at first but I think I have a bead on this. First we'll look at where we've been with: a) lower risk aversion (small, error prone sampling), and b) slightly higher risk aversion (again with smaller sampling. Then I'll change the sampling a bit to see what happens. Then finally I'll try to explain what I think I'm seeing.

What do I mean by sampling and outliers?

In the machine/model as it walks through the meta-sim -- where  "1 iteration = 1 life" and then "year by year within a life" -- it is, at each age for whatever wealth level and spend rate it is at, checking by way of a forward consumption utility simulation for an estimate of the lifetime consumption utility. It does this in order to compare a course of action (changing the spending) to a baseline (what it would have done notwithstanding the change). Since that is a heavy use of the processor and since I was just playing around I originally kept the iterations for that internal mini-sim low, say 100.  That is "the sample" and since it it is technically sampling from infinity, it is a laughably low sample.  In this post I increased that to 300 which is still laughably low but also painfully slow. On AWS with 4x4core so 16 CPUs it takes about 50 minutes for 1000 iterations of the meta-sim. I later nudged it down to 200 due to impatience but that didn't change the conclusions much. 

The main difference, an obvious statistical thing, is that the dispersion of the sampling distribution narrows a bit and the relative impact of outliers (of lifetime consumption utility) comes in. I'll try to interpret that later.

Machine v Merton at RA=2

see original post for set-up and assumptions

• Blue is learning machine at around 300000 sim years, risk aversion coeff set to 2
• Grey is my RH40 rule of thumb
• Orange is the Merton optimum with RA=2 and years tuned to SOA annuitant 90th percentile

Choppy output but still looks like it's getting it done one way or another...

...although in runs after this, I'm noticing that the bend up at later ages here may be more pronounced than it is in my future runs because the mini sim is prone to sampling errors and the high value/utility "errors" are more likely to be captured as an advantage. In adding more cycles, which makes it really really slow it looks like it might not curve up as much as this chart.  On the other hand I've noticed that late iterations are pretty strongly related to what unfolds in the first few so maybe that's part of the problem. No idea yet. TBD

Digging a bit more into the Machine-derived chart for higher risk aversion

Start here for background:

• An early look (too early) into my amateur mini-machine-learning project

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I ran a few more cycles (up to 16000 now so ~320000 sim years) of my machine where the Risk Aversion Coefficient (RA) was now set to "2". So at this point in my iterations, I thought I'd hazard some opinions on what I think the machine is doing at this RA level. Here is the current chart, as of my most recent run, of the spending policy at different ages for $1M in starting endowment at each of those ages:

My machine digesting some higher risk aversion

Start here:

• An early look (too early) into my amateur mini-machine-learning project

I've been playing with this thing just for fun to see where it goes. The first versions were too discrete in it's approach to spending exploration and therefore a little unstable.  Also I had only designed it for log utility (i.e., low or RA=1 in CRRA math). This increment of coding added RA > 1 where the formula is [C^(1-ra)-1]/(1-ra) if I recall correctly.

For this really fast, too-short, too-few-iterations run I flipped RA to 2. Not much of a change but: a) going up a bit in RA has convex and significant effects, b) in my own work a RA=2 is about how I behave based on what I see, and c) my opinion is that really high RA needs fewer models and more counselling.  Think of it this way. If I wear a seat belt I am prudently risk averse. If I am an agoraphobic and never leave the house, I am risk averse and I need help.  I have an unfounded opinion that over about RA=3 it starts to get a little odd, but that's just me.