What I've been using

I was on the plane back to FL from MT on Wed. (damn, I'm already ready to go back) and was thinking about my 5+ years of ret-fin blogging. With all that analytic stuff more or less in the rear view mirror (is it really?) I thought I should spend a moment thinking about what I actually use for myself. I’ll try, but fail, to keep this brief. I might've blogged on this before.

Heat Scatter of Portfolio Longevity with N=1,000,000

Just for the hell of it this is a portfolio longevity chart

- N = 1,000,000
- r = .04
- sd = .12
- spend rates are uniformly distributed between 2% and 12%
- horizon set to 100 years max where 100 is sorta infinity

Since this is one of the "shapes" of retirement that I set out to see, I wanted to see what it looked like with a really big N for the sim iterations.  Looks like the smaller N of course, just more filled in.  Also it's easier to see that 2% spend is almost, but not certainly, a perpetuity when returns are volatile. Interesting to ponder long retirements like early retirees in FIRE movement or long duration trusts or endowments.   Didn't take too long to run, just a couple minutes or so.

What an advisor might or might not tell you

Let's say, hypothetically speaking, that one's advisor is somehow deficient in speaking to "retirement income solutions" -- keeping in mind that the older I get the less outrageous of an assumption this gets -- rather than to the bread and butter of what they really do.  To be overly reductive and a bit unfair let's say what they really do is collect fees and recommend asset allocation frameworks.  If that is what they do, and if they won't broach the topic of fee negotiation -- which they usually don't...but should -- then pretty much the bulk of what you hear about in a conversation will devolve, again reductively and unfairly, to "asset allocation."

Denominator Wealth

I track my spend rate as a rate [s/W] every month as part of a statistical control process.  That means I need a denominator. I've lost track of what the "official" literature has to say on this so I'll just describe what I do.  It's easy enough to say "use the balance from your brokerage accounts" but I think that's the wrong answer.  Not all financial wealth belongs in the denominator just like not all non-financial wealth is necessarily excluded. 

I keep an enhanced version of an actuarial balance sheet akin to what Ken Steiner recommends.  That means I have assets and liabilities and I also have "flow" items like capitalized SS PV and an estimate of a spend liability among other things. I also have what I might call mezzanine liabilities that are near term 5+ year big ticket spending like college for 3 kids. I could and should do this for LTC but haven't...yet.  So, when I want a spend rate, wealth in the denominator should reflect what I can spend and I call that "net monitizable wealth."  In practice, this means:

  1- Net financial wealth: including flow items in PV form but net of both soft and hard liabilities
  2- A slice of non-financial wealth that I could monetize if I needed to consume it
  3- If I can consume it someday, it's in, if I can't reasonably expect to, it's out.

For #1, the soft liabilities are mostly made up of the estimated PV of a Tier 1 college ed, books, travel, room n board for 2 kiddos (already had one go thru Stanford).  The hard liabilities are things like a stub of a mortgage and a rolling estimate of a tax liability and a working capital LOC I sometimes keep. The spend-liability estimate proper is left out for this exercise -- but not forgotten -- since this is a spend rate effort.

For #2 the only example I have -- other than maybe a couple watches, perhaps a little silver left over from grandparents and some other trivialities like some rugs and astrophotography gear -- is a portion of my house. Some direct private investments in business ventures, valued by a model, used to be in there but I now estimate their value, not to mention monetizability, at zero.  I raised three kids in my current home and I don't need my whole house.   I'd downsize in a heartbeat but only up to a point. I figure in an extreme situation I could ditch half the value and be fine.  In practice I make maybe 30% of my house available as "monetizable" for this exercise. And, in fact, on a recent real estate scouting trip to MT, that's about the differential I think I'll see when I move. 

Brief note on some reasons for the Annuity Paradox

I was doing a little catch-up reading on the plane.  I'd been meaning to enumerate to myself some of the reasons I see in the literature for why people do not allocate to annuities despite the manifest benefits seen when only using theory to think it through. My reading gave me a starter list. Many of these reasons are my own.  Without more granular attribution, the source material are these:

- How best to Annuitize Defined Contribution Assets. CRRB Munnell, Wettstein, Hou 2019
- Annuitization and Asset Allocation with HARA Utility, Kingston & Thorp 2005
- Annuitization and Asset Allocation, Milevsky, M.A. and V.R. Young (2003)
- Optimal asset allocation and the real option to delay annuitization: It’s not now or never, Milevsky, M.A. and V.R. Young (2002) 

- Some others not listed here

The list of issues with annuities that they enumerate, if I've gotten them all, looks like this. There may be some overlap in the items. I'll add to this if I run into more:

- Adverse selection price effect (fairness); healthier people buy, prices reflect the cohort
- Marketing and admin price effects (fairness)
- Capital reserve price effects (fairness)
- Diminishing utility of the product class due to levels of pre-existing wealth
- Self insurance alternatives via family
- Availability of other life income streams eg Soc Sec
- Bequest motives
- The loss of flexibility re large unexpected events especially health
- Preference to retain and control wealth (endowment effect)
- Unawareness of annuity product benefits over full lifecycle, inadequate education
- Bias for lump sums over flows (illusion of control)
- Incomplete markets: unavailability of negotiable contracts, irreversibility
- Personal evaluation of life expectancy is lower than average (related to adverse selection)
- Personal evaluation of life expectancy is higher than average
     o expectations for better returns via risk premia over time
     o expectations for falling annuity prices at later ages
- Price effects (fairness) from incompleteness maturity/contingency structure of bonds on issue
- Price effect (i.e., high) from the general rate environment (low)
- Complexity and opacity of complex instantiations of the product
- Counter-party risk; insurer bankruptcy
- Misalignment of incentives...your advisor may not be paid to sell or may resent loss of AUM
- Mortality Credits are low at early ages

Retirement finance joke...

On AQR's paper on retirement security in a low expected return world

Here an AQR 2017 paper on Risk and Retirement. 

Intelligent Risk Taking: How to Secure Retirement in a Low ExpectedReturn World, Ilmanen & Rauseo Aug 2017

Read that, then my comments are as follows. This was copy/pasted from some correspondence with DC


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

Here are some superficial comments on the AQR paper

1. I've mostly steered clear in the blog on stuff related to portfolio optimization and design and related component analysis.  You can see this in the "5 Processes" paper I did. An optimized portfolio is "assumed" as input into my quant schema.  That kind of optimization stuff is the bread and butter of the finance industry and I don't add much as an amateur.  It is also something that is generally done before decumulation is considered (though it shouldn't be) and that's what these guys are doing at AQR. They explicitly foreswear things like decumulation and uncertain longevity somewhere in the intro.  They are instead working in the "AQR zone," which is my second point...

2. They are totally shilling for AQR. That's cool, I love AQR and they should shill.  The conclusions of the paper point directly to "buy our funds."  And a lot of retirees probably should buy AQR depending on their plan.  Doesn't mean we shouldn't guess that there is some marketing going on here.  

3. They are 100% focused on "same vol higher return."  That's only one side of vectoring an efficient frontier up and to the left.  I have this theory, that I can prove for no one but me, that before retirement I want my "EF shift" to be up, and after retirement I want it to be left, assuming "r" is adequate to the task. That vol reduction in decumulation is gold in terms of things like sequence risk and portfolio longevity with consumption present. I get why during accumulation one might make a fetish of "return for same vol" but things change afterwards. No W2-analyst or tenured academic is going to understand this in a skin-in-the-game way like I do, this feeling of the difference after the safety-net of work is gone. This sensibility is the missing link in 99% of papers I read.  M Zwecher got it in his book. 

So if I were to be simplistic, 

Before retirement:

- bias, sorta, to single period analysis and MV optimality. MPT dominates conversation

- emphasis on savings rates and the terminal accumulation value of a portfolio at horizon

- focus on returns and net growth rates and terminal value of wealth at horizon

- consumption is often downplayed or ignored and idea of consumption floors are almost unheard of

After Retirement:

- bias towards multiperiod effects, e.g., geometric mean outcomes and median terminal wealth or, say, fail rates etc, and...

- emphasis is really more on portfolio longevity and lifetime consumption utility than it is on terminal wealth (except for issues related to bequest)

- focus here is maybe more on volatility ( vs returns) as well as sequence risk

- consumption should dominate the conversation and the concept of income flooring starts to make more sense

AQR is pandering to the first of these two world's. Makes complete sense. A ton of their audience is institutional. That means fund design and fund management. Almost all of their audience knows squat about spending or annuities and the impact on retirement in decumulation.  Issues related spending and life income over a lifecycle are going to not just dominate fund-design and optimization tricks but are going to crush it.  Except at the margins, where it matters a bit.  

4. The case in the paper for alts and Risk Parity always comes back (they repeated this at least twice) to "averting capitulation and forced sales," not any inherent supremacy of the portfolio statistics over time as such though that discussion might be interesting. So, tongue in cheek here: maybe there is a fund that can be 60/40 instead of, say, Risk Parity, and then part of your 70 bps fund fee or maybe a little spiff on top of that (instead of the 1.25 one might see in an alt mutual) includes mental health and behavioral counseling.  Might be cheaper and more efficient than a RP fund...  But I guess that is what advisors are supposed to do.

On 5 years of Blogging Retirement Finance

You may have noticed that I have been remiss in attending to the blog. I have my reasons.  Among the many I can think of is the location of where I am in the lifecycle of blogging Ret Fin.  Here are the stages of blogging as I see it strictly for me:

Some updates

Yes, the blog has been quiescent lately.  Here are some updates.

Plutarch on Retirement

I cribbed this from someone's tweet but thought it apropos of a retirement mindset:

The future bears down upon each one of us with all the hazards of the unknown. The only way out is through. - Plutarch (allegedly; haven't validated yet)

This reminds me of some thoughts I had about retirement finance where there are varying degrees of risk and uncertainty. Here is my own version of the layer cake so far. I'm not married to this, just thinking out loud:

My layers of uncertainty

a. things known with certainty for which we can and should and usually do plan
b. things known with certainty for which we don't usually plan or needn't bother much
c. things that are associated with risk and probability but that are plan-able and hedge-able and are worth planning and hedging due to the consequences
d. things that are risky or probabilistic but not worth the effort or have lower consequences or cost
e. uncertain things for which few can plan and for which holding resources in reserve is inefficient but where one should probably try to do so, at least for a while until the unknown comes in a bit over time. Longevity risk, up to a point, comes to mind
f. uncertain things for which few can plan but also where one should probably not even bother
g. the pure, impenetrable chaos and unknowns of the universe about which it is probably pointless to even consider either occurrence or response, except as a general phenomenon and mystery associated with being alive. Ask Job about that one.

Supplement to post on the "1970s game"

In "A forward walk through the 70s using two types of dynamic asset allocation" I was playing around with some spend rates and asset allocations in the context of retiring through the 1970s to understand some risk viewed through the lens of the economic utility of consumption during a difficult decade.  I used a constant spend and dynamic (glide up) allocation to test some ideas. One scenario was also fully dynamic. The write-up is in the link.

What I didn't do at any point was test feasibility either at the beginning or along the way.  Feasibility is the test, at some point, of whether A > B or A/B > 1, where A is the present value of net monetizable wealth, and B is the present value of the spending liability.  When I applied the test to the scenarios in the link above, it dawned on me that none of scenarios were feasible to begin with.

If we define the present value of spending reductively to be nothing more than a (conditional) survival probability weighted sum of the real (1964 dollars in this case) cash flow, then the feasibility condition is not met until initial spending is reduced to 30,000 in constant spend terms. At that point the CE spend was, predictably, 30k and terminal wealth in real ('64) terms was 962,804. This outcome, if it had been part of the previous illustration, would have lost the utility war except against the 3.9 and 4% spends, won the bequest war, and won the hearts of feasibility aficionados around the world. The cost, however, would have been a pretty large hit to early lifestyle relative to a desideratum of 40k, but would be a rational, implementable choice if one does not happen to live life in relative terms.

A forward walk through the 70s using two types of dynamic asset allocation

Walk-forwards are the anecdotes of the financial modeling world. At worst they set you up for a naively imagined future that will never repeat but can certainly get worse. At best I suppose they provoke a type of useful anti-nostalgia for a past that was bad enough to pay attention to lest it sticks its nose too far under the tent-wall again.  Better modeling options may lay in something like boot strapping history or engaging in open-ended and less-constrained simulation or even scenerio-based strategic planning. But even these can be false orbuculums where the expectation extracted over 10,000 iterations can "bury the lead" where the lead can be conceived of as the special case in which all iterations and paths are bad news of a particular shape. In this case the shape in question is the 1970s, a period of poor returns and high inflation that's more fun to play with than the GFC.  Plus I lived through it. I remember.

This time I'm throwing some simplified forms of dynamic allocation against the 70s to see what sticks to the wall. I'd been playing around with some ideas on glide-paths in an ongoing dialogue with David Cantor, a dialogue that will bear bigger fruit later.  This time it's just the 1970s walk-thru.

Some Self-Reflection on the Joint Spend-Allocation Choice...For Me This Time

A lot of tech bluster on this blog notwithstanding, most of the count-on-one-hand readers of the blog might be surprised to learn that I directly use very little of the methods on this blog to manage myself on a regular basis. Most of what I do here on the blog comes from mere curiosity, a curiosity that when sated accrues to my general understanding, to be sure. In reality, on a monthly basis I mostly use the following:

Revisiting Backward-Induction-Derived Asset Allocation over Multiple Decumulation Periods

"Arguably, for someone willing to pay careful attention to the evolving funding status of their retirement (the present value of their remaining assets divided by the present value of their remaining liabilities), asset allocation can be adjusted dynamically by matching assets to liabilities in coordination with the client’s risk capacity and risk aversion, rather than just on an arbitrary path. But for those unwilling to take such care, such as users of target date or lifecycle asset allocation funds, or for those whose goals are somewhat more complex in the balancing of current and future, income and legacy goals, what should be the default equity glidepath in the postretirement period?"

Pfau, W. and Kitces, M (2013)

"...the optimal asset allocation moves after significant market events. This means an investor needs to monitor and adjust their asset allocation after such events. They cannot simply follow a glide path."

Irlam, G (2014) 

These quotes are not incompatible. I was considering this today because I was re-reading Irlam (2014) on using backward induction (BI) via stochastic dynamic programming (SDP) so that I could revisit and repair some software I built in 2017 that attempted to replicate what Irlam had done in 2014.  It's a deceptively simple idea that is hard-ish to implement and even harder to figure two years later when you are trying to figure out what you did earlier (note to self: comment one's code better).

Annuities and Random Interest Rates

Just buzzed through this paper (Dynamic Portfolio Choice with Annuities When the Interest Rate Is Stochastic Yannick Dillschneider, Raimond Maurer, and Peter Schober August 29, 2019). It was analytically a little dense for me. I can maybe 20% follow Americans and Canadians in their notation. For Germans writing in English, that drops off to about a 1% follow…on a good day. They lost me pretty quickly. Here are some excerpts, though:

If a sovereign country were to retire...

If a sovereign country were to retire and forgo income, they's have the same issues, except for the immortality thing, as any run of the mill retiree. This was recently covered in

The Optimal Extraction Rate versus the Expected Real Return OfA Sovereign Wealth Fund,  By Knut K. Aase and Petter Bjerksund [2019], a fun but very dense read that has a ton of affinities with retirement finance.  

Here are some selected extracts. Not all of these will make sense out of context and I'm not going to correct copy paste errors in all of the characters. 

Chris Mamula on not knowing

When I think about retirement risk, it's never, or almost never, volatility, it's this: 

https://www.caniretireyet.com/because-you-never-know/

A Middle Path and the Courage to Take it

The following, recent, and unrolled Twitter thread by AJA Cortes (@AJA_Cortes) is a wee bit polemical and maybe a little off path with respect to my usual vibe, and might be vaguely risky here, but it harmonized with some thoughts I had recently about my own journey into, and maybe out of, retirement finance:

Masculinity is RISK taking. To "play it safe" is a negatively feminine quality, the desire to protect oneself from harm and consequence. Operating by fear is always cowardice. What does "negatively feminine" mean? Its means when a feminine trait takes on negative form. Impulsiveness and destructive behavior would [be] the "negatively masculine" equivalent (and complementary inverse). The role of father is to introduce tension to his children so that they might be brave. A son who takes no risks is an emasculated individual. A daughter who takes no risks and is fearful will always be at risk to be manipulated by safety and by group think. Men who don't take risks and live for safety are bitches[; e]veryone is disgusted by them, both men and women. There is an inherent intelligence in us all that recognizes bravery, and is repulsed by cravenness. AJA Cortes 

Cross-section of a hurricane vortex

Here's an image I hadn't seen before. This is a hurricane vortex. It's a cross section of the wind speeds of the system. If I understand this right these readings come from aircraft sampling. Which reminds me that the guys in these planes have some you know what. 

Remember Irma? Here comes Dorian...

From 2017

On the affinities between hurricanes and retirement

Combining Annuities and Tontines

On the Optimal Combination of Annuities and Tontines

33 Pages Posted: 5 Aug 2019

An Chen

University of Ulm

Manuel Rach

University of Ulm - Institute of Insurance Science

Thorsten Sehner

University of Ulm - Department of Mathematics and Economics

Date Written: August 1, 2019

Abstract

Tontines, retirement products constructed in such a way that the longevity risk is shared in a pool of policyholders, have recently gained vast attention from researchers and practitioners. Typically, these products are cheaper than annuities, but do not provide stable payments to policyholders. This raises the question whether, from the policyholders' viewpoint, the advantages of annuities and tontines can be combined to form a retirement plan which is cheaper than an annuity and carries less risk than a tontine. In this article, we analyze and compare three approaches of combining annuities and tontines in an expected utility framework: The “tonuity” introduced in Chen et al. (2019), a product very similar to the tonuity which we call “antine” and a portfolio consisting of an annuity and a tontine. We show that the payoffs of a tonuity or an antine can be replicated by a portfolio consisting of an annuity and a tontine. Consequently, policyholders achieve higher expected utility levels when choosing the portfolio over the novel retirement products tonuity and antine.

Keywords: Optimal retirement products, annuity, tontine, tonuity, antine

JEL Classification: G22, J32

Suggested Citation:

Chen, An and Rach, Manuel and Sehner, Thorsten, On the Optimal Combination of Annuities and Tontines (August 1, 2019). Available at SSRN: https://ssrn.com/abstract=3430546 or http://dx.doi.org/10.2139/ssrn.3430546

Loss Aversion Risk Preferences ... Lead to Greater Retirement Income Certainty [SSRN]

Investing for Retirement: How Loss Aversion Risk Preferences Naturally Leads to Greater Retirement Income Certainty

47 Pages Posted: 30 Jul 2019

William Lim

Australian National University (ANU)

Catherine Donnelly

Heriot-Watt University

Gaurav Khemka

Australian National University (ANU)

Date Written: July 26, 2019

Abstract

We analyze the ability of different investment strategies to give pre-retirees more certainty about their income in retirement, while allowing them to benefit from taking investment risk. Specifically, we look at the optimal strategies that maximize the expected values of a loss aversion utility function and a constant relative risk aversion (CRRA) utility function. We also include a typical lifestyle strategy. 

We find that the loss aversion utility function gives a high degree of certainty about its reference point, the latter chosen to give the desired replacement ratio. Adding in constraints on the income purchased at retirement does not improve the certainty of achieving the desired replacement ratio enough to counter-balance the increased chance of obtaining an income far below it. A CRRA utility function fails to get adequate certainty on the retirement income, and becomes too risk-averse when constraints are added. The lifestyle strategy performs well but is overall out-performed by the loss aversion-derived strategy.

We include inflation in our model, and allow for inflation-indexed bonds in our investment universe. Our results are analyzed in both a Brownian motion-driven financial market model and using UK historical data.

Keywords: finance, retirement planning, optimal asset allocation, stochastic optimal control, constrained optimization

Suggested Citation:

Lim, William and Donnelly, Catherine and Khemka, Gaurav, Investing for Retirement: How Loss Aversion Risk Preferences Naturally Leads to Greater Retirement Income Certainty (July 26, 2019). Available at SSRN: https://ssrn.com/abstract=3426932 or http://dx.doi.org/10.2139/ssrn.3426932

A reminder

I had a really nice recommendation from abnormalreturns the other day to come here for retirement math. I just wanted to remind my readers:

- I have no formal training in math. My last calc class was in 1977.

- I have no formal training in statistics or probability. My last statistics class was intro in grad school circa 1987, probability theory never.

- My formal training in finance is limited to a concentration in an MBA program (again ~1987) which, if you know MBA programs, is typically shallow. Mine was.

- I am a student here, reporting what I learn, rather than a teacher.

- I am not an academic nor am I a finance professional. I have no designations or titles and I make no income off this blog or any profession related to finance other than managing my own wodge.

- Everything I report is incremental, one straw on top of another, all of them no doubt on a camel's back.

- If you come here for retirement math as a reference you will be sorely disappointed if you look too closely.  I'd rather that you defer to someone like earlyrirementnow, in, say, this post.

- The most I can say is that I read a lot and am willing to pick up excel and R for test drives and I have no conflicts of interest.

Fun little artifact from the "Spending, Rules and Habit" post

I don't know if this is just a coincidental, statistical artifact kind of thing or something more meaningful but thought I'd compare -- from the last post Spending, Rules and Habit -- the following:  

(a) The mean real spend from the "close to optimal" scenario using the fake parameters (50k spend on $1M with .05/.12 r and sd and a little bit of spend adaptation) used to generate one of the illustrations in that last post linked above. I took the mean real spend for each of the first 30 periods of the simulation scenario mentioned in that post.  Might be better to use median. Also, note that the distribution is defective btw because some percentage of the spends "fail" or snap to income at some point which creates two distributions, the regular one and the ones that fail.  Mean probably makes less sense in this case but at least it makes a pretty picture below, and   

(b) the Blanchett  (2016) regression formula that fits, or tries to fit, observed evidence for how people spend in real life in retirement.  I was just curious but now the overlay looks interesting. Since the regression model is sensitive to the level of spend I used 50k since that is what we did in (a). Here is the Blanchett (2016) Formula (p 15):  

Charting (a) (orange) and (b) (blue) over 30 periods, it looks like this when rendered in absolute real dollars

Does this mean anything? Probably not but if it did, maybe it means that real retirees are not all that irrational when they try to spend in practice over a lifetime.  Maybe one doesn't need a PhD to get it right after all...  

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

Blanchett, D. (2016), Estimating the True Cost of Retirement, Morningstar

Spending, Rules and Habit

The Point of This Post

I can think of no reason, other than when we consider what is already embedded in common sense, for why this post would be of practical use.  How's that for sandbagging, huh?  But I had a thought and the thought was:

"if I had a 'slider' that could slip spending between "constant" and "percent-of-portfolio" in a continuous fashion, what would happen in a consumption utility model, especially one that knows that wealth depletes and spending snaps to income when that depletion event happens?"

If you are an avid reader of this blog, and I have my eye on all three of you, you may have noticed that I do not trade much in spend rules (except for my own RH40 rule and that was half tongue-in-cheek). Spend rules seem to be a big thing in retirement lit.  I don't trade in them because rules tend to be a wee bit ad-hoc, arbitrary, and not always mathematically necessary, not to mention blind to optimality along some dimension or other.  This is a point that Patrick Collins made in Monitoring and Managing a Retirement Income Portfolio.  But rules, when they are thrown out there into the ret-fin universe, generally try to do one thing if they are honest. They adapt to the circumstances that arise after retirement-initiation vs., say, a Bengen 4% rule or academic papers that use constant inflation adjusted spending for convenience. Let's also ignore a strict application of macro econ and consumption smoothing for now even thought that is more or less what we are doing in this post. In my 5-process paper I made a case (that, embarrassingly, I can't remember) that this smoothing can sometimes be self-contradicting when put into practice. 

Retirement Finance and Herding Goats

The oldest form of capital management on earth is probably, I'm guessing here, goat herding. Me? I think that that particular activity has a lot of affinities with retirement finance.  I even have an academic ag paper somewhere in my pile on the economics of North American goat herding in order to prove that point but I had a hard time penetrating the prose and data for my use here so I thought I'd just do an amateur quick-riff which is what I seem to often do here.

Health, Preventable Disease and Retirement Finance

Having been on a health kick lately for its own merits, whether for vanity or longevity I won't say, I found myself in an interesting Twitter dialogue recently about a nexus between health and retirement finance.

There appears to be a mounting pile of evidence (not provided here maybe start here with PD Mangan or with a book I read) that implicates diet (e.g., sugar, processed food, protein intake, fasting etc) and fitness choices in preventable chronic disease, insulin resistance, inflammation, longevity etc.  That evidence can be translated into a retirement finance discussion in addition to usual one about personal well-being and quality of life.

I originally viewed my own health choices as a quality of life thing but it's more than that as Alli Covington (@allicovington) reminded me in this [edited] thread on Twitter and about which I should have already been aware:

The cost of healthcare after you’ve poisoned your body with years of bad food will astound your retirement savings. Imagine being crippled, unable to move easily, in pain AND broke. Put down the down the donut and pick up a dumbbell. Don’t be left broke and broken  

The real matrix […is…] the trap of eating processed food labeled as “healthy” that eventually leads to disease, which siphons all your available cash preventing you from being free…

That got my attention.  So I asked her what she meant.  She's still working privately on something yet to be published but the concept as I understand it seems pretty sound as she explained in a follow-up DM...   

I researched the annual cost for specific conditions that are 1) prevalent and 2) preventable and reversible with diet and exercise  

If they start fit, they avoid millions in spent dollars with interest. If they allow themselves to get a chronic disease like diabetes, they will lose out on millions.

Ahhh, she's singing retirement finance lullabies to me there. And we can test this a little bit even without the data.  I'd love to see the research and analysis but the underlying dynamic is super simple at its core: this is just retirement spending.  And we've beaten that to death here before. But lets just re-color things a bit and take in hand a subset of health spending in particular (the part attached to preventable chronic disease that can be influenced by self-care choices), which before might have seemed an inevitable and fixed cost of future retirement, and now we make it discretionary! Willful ignorance of health choices and future spending will no longer be tolerated here at RH.

Update on prelim evaluation of real annuitization with stochastic inflation model

I confused a reader in my last post. In a convention that I did not explain, when I ran different spend rates, and used different asset allocations to a stylized efficient frontier, for a parameterization that was unique to me, and therefore not really generalizable, I used a type of shorthand from a prior post. 

For different spend rates for a nominal and for a real annuity, both modeled using stochastic inflation with an autoregressive feature (and compared to a deterministic baseline), I consolidated my moves and took the max utility for each spend rate across all allocations. Easier for me but also easy to misunderstand.  The original chart from (A prelim look at a real annuity and lifetime consumption utility - with a stochastic inflation model) looked like this

A prelim look at a real annuity and lifetime consumption utility - with a stochastic inflation model

Reason for the Post

This is almost the exact same post as the last one (A *very* prelim look at nominal vs real annuities and Lifetime consumption utility) except that I added the ability to make inflation (drawn from history using a table from inflationdata.com) stochastic and, in addition, the ability to stylistically model auto-regressive inflation using an approach offered by Brown, Mitchel and Poterba [2001] in The Role of Real Annuities and Indexed Bonds in an Individual Accounts Retirement Program. The stylized AR(1) process is described in the note in this post (Model Sensitivity: inflation vs lifestyle).

This post is not really research as such. Since modifying existing software is like updating the electrical in a seven bedroom 1911 house not touched for decades (I know whereof I speak and can tell you how long it took and how much it cost) we can consider this post a "software shakeout" rather than anything conclusive. How's that for sandbagging?

A *very* prelim look at nominal vs real annuities and Lifetime consumption utility

I was updating my software for simulating (expected discounted utility of lifetime consumption) and I thought I might as well make it work for a really basic comparison of nominal vs real annuities. I thought it was in the SW but the original amateurism appalled even me.  The mods were really really annoying, though.  I am totally convinced that I should never ever modify software again but do EVERYTHING from scratch.  It's like remodeling houses.

Now, here, I won't give too much detail cuz I don't want to show my own hand on personal data. Mostly this kind of thing uses personal details, though.  Let's at least assume some of the following

Unknowable vs unknown

This is from Crafting Retirement Income That Is Stable, Secure, and Sustainable by Jason K. Branning, CFP®; and M. Ray Grubbs, Ph.D. [2017 SSRN]

Planning against the unknowable offers a different starting point than simply planning for unknowns. We can know that a client will ultimately die, but it is not just unknown as to when, but individually unknowable. The distinction between unknown conditions and unknowable conditions is an important one for financial planners and clients. Unknown implies that there is something that can be done to provide knowledge on which actions can be taken. Unknowable implies that there is nothing that can be done to add knowledge to a particular client situation. The unknowable aptly describes individual client issues such as longevity and conditions within longevity. Conducting empirical tests requires assumptions or constraints to get a meaningful mathematical solution. Math is useful if conditions can be controlled and limited, as math measures quantity.

Tail Risk Hedging

"The takeaway for investors is that the evidence demonstrates that at least, historically, an allocation to time-series momentum and quality (defensive) stocks would not only have improved returns but significantly reduced tail risk, the kind of risk that can lead to the failure of financial plans."

That was Larry Swedroe writing on tail risk hedging at Alpha Architect. The post is here:
Strategies to Reduce Crash Risk in Stocks.

Fecundity and Long-duration Retirements

I was just reading a paper by James Garland (The Fecundity Of Endowments And Long-Duration Trusts) and was struck by the affinities with early retirements. In fact, since I retired early, I myself have always had an eye on endowments and trusts as a model because -- while today at 61 if I were to abandon my DIY approach and plan on sinking a bunch of money into an annuity at age 80, my planning horizon is only maybe 19 years -- for early retirements the planning horizons can be really long, maybe up to 50 years or more.

While I do not 100% agree with what is implied by Garland's approach, since I do believe in "triangulation," this seems like another worthy way to think things through...it's worth a look. Me personally? I still think that the max "fecundity" of consumption portfolios with very long horizons (say 50 years to infinity) happens at a spend rate that is close to or above the horizon-adjusted expectation for multi-period geometric returns -- which depend on the horizon, realized returns, and volatility.  Maybe we are saying the same thing.  TBD.

Try #2 on a rough validation of a 3.6% break-even inflation rate for a real annuity

Before my vacation to MT, I briefly proffered a post that tried to validate Joe Tomlinson’s guess that the current market (ok, it’s only one company and product) for inflation adjusted annuities suggests that there is a “breakeven rate” of around 3.6% inflation when considering those products (Which Annuities Offer the Best Inflation Protection, June 2019). I happened to retract my post because I thought it looked and sounded innumerate and even if it wasn’t innumerate it was at least mixing quantitative apples and oranges and that, at a minimum, felt embarrassing. I also used the wrong name for the insurance company that offers the inflation adjusted annuity. But, I *am* still interested in things like inflation, lifetime income, and consumption utility over a full lifecycle, especially in the decumulation stage. 

A self-frame-of-reference that looks like the hard granite surface of a mountain

While in MT recently with my daughters, I had the chance to watch (Hulu) from a safe distance "Free Solo," the story of an un-roped (i.e., free solo) ascent of El Capitan by Alex Honnold in 2017.   [As an aside, one of the directors went to Carleton College, of which I am an alum.]  The "direct" story of the climbing and the courage necessary to do it is story enough. But there was also a sub-story that I found quite fascinating: that of how Alex holds to his self-defined mission in the face of fairly intense weepy pressure to divert (subvert) it by a committed long-term-relationship girlfriend.

When Retirement Quants Dream...

...when they dream then this, below, in the image (by way of my iPhone last week), is the type of sugar plum fairies that dance in their heads...

In this case we are looking at the Madison Valley in SW Montana. The Madison range (and Ennis, MT) is in front of you, the Tobacco Root range is behind you to the left, the Gravelly Range is behind you to the right. The point of this picture is that it is about :45 from Bozeman. Shit, in south FL it takes me about 45 minutes just to get to the grocery store, about 3 blocks away. An hour of driving and I'm still in Broward county and, if you've ever been to Broward county, you, therefore, know wherefore I dream.

Some thoughts for younger "spenders"

Here is a recent twitter thread on spending....

Bob missed a point right that went right over his head. I wanted to call him a troll after I read this because every once in a while he throws out aggressive tweets of which this is not really one. But nine times out of 10 I totally agree with what he's trying to say. My guess is that he has a point of view developed from working with people that need assertive wealth management help in the Midwest so the trollish-tweets are probably well earned and done in good faith.  At least I'll assume that for now.

In this case the missed point is that sometimes it is not about "spend rates" at all. Spend rates could be all over the place depending on the individual context.  But my guess is that Bob would spend 1M a year without blinking if that was a reasonable construct for a properly constructed age-appropriate decumulation portfolio. I'd maybe agree with that and maybe my own "dream" rate is 1M but my point above was something else entirely.

Let's try this again:

Young people of America. Listen up. Before you even get to the topic of  your future retirement spend rates, make sure that when you complain about spending 150 grand a year, or you complain about having to buy your Porsche used rather than new, you do not do that complaining in front of a family of four that is making 50 or 60 grand a year.  That is somewhere around the median income in this country. And we haven't even gotten to taxes yet.  Your 150k (and I hate to use this next term since it is so loaded these days) is case of privilege.  This has nothing whatsoever to do with whether 3% of 5 mil is "ideal" or a "dream" or not.  I don't really care what your ideal dream spend rate is. This 150 vs 50 thing is a moral position and it is mine. It does not have to be yours. You should be able to make a decent life at 150 in absolute terms. My point still stands. Go find your "dream" but respect others while doing it.

Model Sensitivity: inflation vs lifestyle

In his recent Advisor Perspectives article (Which Annuities Offer the Best Inflation Protection June 2019), Joe Tomlinson, one of the more generous and helpful retirement writers now living, writes:

It turns out by pure coincidence that the 10th percentile for the COLA SPIA almost exactly matches the inflation-adjusted indexed SPIA. So there’s a 90% chance that purchasing the COLA SPIA will generate more real income than the inflation-indexed SPIA and a 10% chance it will do worse. This result is consistent with Blanchett’s findings. The upward-sloping median result for the COLA SPIA indicates that it beats inflation on average; this would be expected given its 3.6% annual increases in payments versus inflation averaging 2.3% overall. The 90th percentile beats inflation by a bigger margin.  

These results look very favorable for the COLA SPIA, but it’s worth cautioning that they are a direct reflection of my particular inflation model, which was built with considerable subjectivity. Higher future average inflation would reduce the advantage of the COLA SPIA and higher inflation volatility would increase the spread between 10th and 90th percentile results. The inflation-indexed SPIA has the unique property of providing a pure hedge against very high inflation, which is a material risk that every retiree must acknowledge and consider. [emphasis added]  

That last sentence is important so the investigations and the conclusions are important as well. Also, if we acknowledge that the inflation-indexed annuity form is the only decent way these days for a retail investor to get access to both a longevity risk pool paired with a pure inflation hedge, it is necessary, imo, to be at least aware of the idea of these products.

Playing around with inflation, part 2

Joe Tomlinson tipped me off to another way to model inflation and sent me the paper that explained it (The Role of Real Annuities and Indexed Bonds in an Individual Accounts Retirement Program [2001] Jeffrey R. Brown, Olivia S. Mitchell,and James M. Poterba).  Also, since the last post I realized I had made an error in the historical inflation model and I wanted to correct that here.  Since I'm goofing around on this and have so few readers, I'm hoping the error did not affect anything anyone does. Doubtful it did.

Starting to play around with inflation...

Note: 

I had an error below where I inadvertently goosed the historical inflation with the extra 1.3% period standard dev. This makes the historical inflation exaggerate a bit. Rather than fix it here I'm moving on and will correct it in the next post (Playing around with inflation, part 2). In that post we see a more reasonable historical inflation effect but when I add on an autoregressive model AR(1) we get back all the multi-period-time-driven vol and then some.  

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

The Point

I just finished 12 posts on lifetime consumption utility and full and partial annuitization. That month-long effort involved, by my estimate, over 100 million iterations of some software I wrote.  That's a lot.  It also put the issue of nominal annuities front and center. While there are many proxies for inflation protected income out there in the market there is evidently only one insurer that writes a true inflation protected annuity.  Nominal annuities, and even the pseudo-protected ones, are an explicit bet on inflation; effectively one is partially or completely short inflation where in extreme inflation it might be better to be long...or employed...or living someplace else.

Most of the models I build factor in inflation a bit but mostly I ignore it or gloss over it.  I wanted to think about it some more. I do not have a sophisticated view. I am, as in my other posts, capable with a spreadsheet or R-script but more or less I am naive most of the time. Nothing has changed in that area yet.  But let's take a preliminary look-see.

Fitness after 60: Intermittent Fasting was Not Enough

The Point

The point of this post is to describe a recent breakthrough in a recalcitrant fitness goal, a breakthrough that was achieved via some hard discipline along with a little encouragement from a few Twitter connections. The other point is to describe some of the how, why and when involved in getting there.

Another point here is that while intermittent fasting and proper diet, along with resistance training of course, is now an important and permanent part of my routine (see this TedX talk by Cynthia Therlow; follow Alex at foreveralphablog.co.uk or on Twitter @TheForeverAlpha; or follow PD Mangan @Mangan150 or roguehealthandfitness.com) it was not, in the end, enough for me. Alcohol elimination (temporary) and calorie counting were necessary to push me all the way to my goal.

Nominal annuity allocation vs deferral - supplement to last post

This is an addendum to Annuity Allocation and Immediate vs. Deferral in a Lifetime Consumption Utility Context (the very last post).  I couldn't not throw in a 3D.

Without too much comment, this is a representation of the max value function (across all spend rates and allocations to risk) for each combination of (a) allocation to a nominal (fake, in-model) annuity between 10 and 50%  and (b) deferrals including: none(SPIA), to-70, 75, and 80. I skipped 85 since the numbers were not great at that age.

As before, this is not terribly universalizable and was made using some personal and fairly rigid choices for a set of parameters. You'd have to know those parameters and why I used them to get some more intuition on the output.  The link to the last post contains links to all of the past posts.

As before there is a overall maxima area around 30% allocation and deferral to 75 with the edges favoring a direction towards 20%/age75-80 and 40%/age70. The chances, however, that I will annuitize anything this year is still approaching zero.

Annuity Allocation and Immediate vs. Deferral in a Lifetime Consumption Utility Context

The Point of the Post

In two previous posts, using my rigid and personally particular parameters and a custom coded lifetime-consumption-utility simulator (i.e., you need to have a certain amount of skepticism present in your brain starting now) I determined two things among several attempts to try to see this:

1. At a 10% allocation to a nominal SPIA for a 61 year old using current interest regime assumptions, that allocation delivered demonstrably better lifetime utility than no use of a risk pool,

2. At a 0% allocation to a nominal SPIA for a 61 year old deferring to no later than age 80 produced higher econ. lifetime utility than the SPIA,

3. When trying to allocate to an SPIA between 10% and 80% of initial wealth, a 60% allocation to an SPIA seemed to work the best, and

4. Deferring the 60% allocation did not seem to do much good, utility wise.

So, the question today is whether some combination of allocation between 10 and 60% and some degree of deferral produces a utility-driven outcome that is better than either #2 (10% allocation, defer to age 80) or #3 (allocate 60% to an SPIA).

I'll look at the following allocations to annuities to try to answer the question above:

• 10% - 50% in 10% increments
• Deferral to 0(spia), 70, 75, and 80. 85 proved in a past post to be a non-starter for me.

Deferring the optimal SPIA from the last post with DIAs to look for an even better set-up

The point of the post

The point should be that I thought for a second that I had mis-coded the software and that I might have to recant the last several posts. How embarrassing that would be.

The real point was to see if, based on the last post where a 50 or 60 percent allocation of initial wealth to lifetime income (SPIA) worked "best," whether a deferral of the allocation via DIAs would produce any incremental benefits, like it did when we deferred a 10% allocation where the answer was yes. 

The short answer here was a very quick "no," so my goal pivoted to see: (a) if I had made coding or conceptual design errors, or (b) what went wrong or what explained the abrupt loss of lifetime consumption utility when it had worked so well in the allocate-10%-of-wealth-to-an-SPIA post. Originally I was going to see, since the 50 and 60% allocation to SPIAs were neck and neck in utility terms, whether deferring either would create any separation between the two. But basically, I just gave up after the first three scenarios because it was so obvious that this wasn't going anywhere.

Annuitizing Larger Portions of Initial Wealth in a Lifetime Consumption Utility Simulator

The Point of This Post

Almost everything I need to set this up was already done in Lifetime Consumption Utility "Frontier" and DIAs - With Different Deferral Periods on June 23.  Start there first.

The purpose here is to take the exact same set-up as in the link and now find out how much initial wealth I can annuitize (using fake in-model nominal SPIAs as proxies for access to a "risk pool") in increasing increments. I want to see if or where the optimization benefits peter out when adding lifetime income...knowing that the "theory" says you are supposed to be able annuitize all wealth for optimality.  We'll see. 

Theory References

There are a bazillion references on this. I'll mention only two, however, and quote a salient fragment from each.

1. Yaari, M. (1965), Uncertain Lifetime, Life Insurance, and the Theory of the Consumer

"In Case C the consumer has no bequest motive but he is constrained to meet the requirement that his transferrable assets at time of death (i.e., those assets which become a part of his estate) should be non-negative with probability one. It turns out that this case is quite simple to analyse because the consumer's assets (or liabilities) will always be held in actuarial notes [i.e., more or less "annuities," but see Prof. Milevsky's comments below] rather than in regular notes."

2. Yagi & Nushigaki (1993), The Inefficiency of Private Constant Annuities

The consumption stream without any constraints [by which I assume they mean “case C” where wealth is held in actuarial notes], which Yaari derived, is considered to be the first-best optimal consumption stream in an economy where insurance is available. The consumption stream with constraints diverges from the first-best consumption stream, and this divergence can be seen as a distortion created by the constraints. In other words, the constraints imposed by the insurer and the imperfect capital markets create a loss in efficiency.

Divergence from Theory

The theory reference is important here because my post diverges from the famous conclusion in #1 and I need something like #2 or other reasons to to justify my results although it is probably fairly intuitive to understand the divergence at a superficial level. We might set it up like this. If my results differ from the conclusion in #1, we might say one of the following:

J.D. Roth on Retirement Purpose

This post by J.D. Roth is pretty good.

     Beyond wealth: What happens AFTER you achieve financial independence?

I bookmarked this because I'll go back for a second and third look. The post shares a lot of affinities with how I have and how I will think about "financial independence." I do a lot of quant analysis here but that's more hobby than anything else. It's like a guy tinkering with a hog in the garage or a model railroad in the basement or astrophotography on weekends. The real issues in retirement often have more to do with meaning, purpose and identity than they do with optimal spend rates. The latter enables the former but the former gets you out of bed.

Lifetime Consumption Utility "Frontier" and DIAs - With Different Deferral Periods

The Point 

The point of this post is to extend the last several posts by now looking at different deferral periods for an idealized, hypothesized, and entirely fake deferred income annuity (DIA) to see what that change in deferral does to the maximum lifetime consumption utility for different spend rates across different allocations to a (idealized, hypothesized....) consumption portfolio.

I mention the "idealized, hypothesized" thing because this model is doubtful in it's fidelity to anything real that will unfold in the world we live in. Also, note that my goal is not to give myself some perfect consumption rate here. Rather I want to look at the "shapes, movement, and ranges" of spend rates and allocations given the narrow constraints of the software I built.  From that I might be able to intuit how things work a little better. Maybe others have done this kind of thing before me but I need to see it for myself.

Bodie and Cotton on Real Annuities

from ssrn.com

Hedging Against Inflation Risk with Real Annuities

7 Pages Posted: 12 Jun 2019

Zvi Bodie

Boston University - Department of Finance & Economics

Dirk Cotton

Independent

Date Written: May 31, 2019

Abstract

The only retirement contract that both insures against longevity risk and hedges against inflation is a life annuity that is linked to the consumer price index (CPI). It is denominated in the same units of account as Social Security benefits. We call it a “real annuity,” although it is also referred to as an inflation-indexed single-premium immediate annuity (SPIA). In computing a person’s replacement ratio of preretirement income, we can add Social Security benefits and the income produced by a real annuity to arrive at a meaningful number. 

An annuity that is not linked to the CPI we call a “nominal annuity.” It is measured in units that are different from Social Security, so it would be a mistake to add the two in computing a replacement ratio. Despite those obvious facts, real annuities are largely ignored in practice and they comprise a tiny portion of the annuities market. The vast majority of income annuities sold are fixed in nominal dollars. From the perspective of rational economic decision-making, this is a puzzle. Let’s call it the “nominal annuity puzzle.” The purpose of this article is to explore the reasons behind this puzzle and to suggest ways to solve it. The lack of interest in real annuities can be explained by a lack of recognition that the purchase of a nominal annuity constitutes a speculative bet on future inflation rates and that the real annuity is the risk-free asset.

Adding a DIA to the last post that was looking at a consumption utility "frontier"

The Point

Lifetime consumption utility is, inter alia, a function of: allocation (return, vol), spending, longevity, risk aversion, and the presence of lifetime income. In the last post "Lifetime Consumption Utility "Frontier" with both Trend-following (fake) and Partial Annuitization (also fake)" I looked at the impact of partial annuitization (assuming a relatively fair annuity) by consuming 10 or 20% of initial wealth to buy a nominal cash flow by way of a modeled SPIA-like concept.

The point of this post is to compare the "10% of wealth" immediate SPIA with a "10% of wealth" purchase of a cash flow that starts at 85 i.e., a "deferred income annuity" or DIA or DIA-like thing, rather.

Lifetime Consumption Utility "Frontier" with both Trend-following (fake) and Partial Annuitization (also fake)

The Point

In my previous several posts I have been toying around with

 - Simple abstracted 2-asset portfolio choice, along with a jointly made
 - Spend choice (using constant spend for now), and then
 - Adding a highly stylized third asset that might look like trend-following

to see how it plays out using a simulator that evaluates the expected discounted utility of lifetime consumption (EDULC) across the different combinations.

The point of this post is to now add some partial annuitization to the mix to see how it affects EDULC, especially when it is stacked on top of the other things we are working with before.

An attempt at a stylized lifetime consumption utility "frontier"

In the last several posts

- Self-Evaluation of My Own Lifetime Consumption Utility
- Self-Evaluation of My Own Lifetime Consumption Utility, Part 2
- Having Some Fun with Portfolio Choice vs. Lifetime Consumption Utility
- Lifetime Consumption Utility with addition of trend following-like behavior

I was playing around with portfolio choice along with a stylized version of an efficient frontier -- both with and without a third asset class that might resemble a trend following allocation of some amount unknown -- in order to see how an economic consumption utility game might play out. I now want to go back and add some more detail. 

Honors (repost)

Repost...this time with picture. Blogger hates iPhones...


My Father’s Day present from my daughter: Stanford’s John G Sobieski Award for Creative Thinking In Economics for Honors Thesis “Market Timing: Individual Investor and Mutual Fund Performance in the Stock Market.” B.A. with honors with special recognition. Her honors honor me.

 

Lifetime Consumption Utility with addition of trend following-like behavior

This post is going to get very abbreviated treatment since I am headed out to a Daughter's graduation.  In the last post Having Some Fun with Portfolio Choice vs. Lifetime Consumption Utility I was playing around with portfolio choice, spending, and consumption utility.  At the end of that post I wondered what would happen if we added a trend-following-like behavior.  Well, I took a shot at that question, though keep in mind none of this is real; it is highly highly FAKE.

If we were to hypothesize adding a third asset to our two asset portfolio -- and don't ask what or how much, this is just a hypothetical and I am interested in the behavior or movement more than I am the execution or plausibility -- we could re-envision the (old fake) efficient frontier in the last post like this (new fake) one where for the same level of return the vol shifts left but less on the safe end and more on the risk end. If I haven't mentioned it, the exact shift comes from only my imagination:

Figure 1. What adding a trend following allocation might do to an eff frontier???

Having Some Fun with Portfolio Choice vs. Lifetime Consumption Utility

Point of the Post

The question is:

• What combination of portfolio choice and spend rate works the best given a particular set of limiting and probably naive and unstable-in-real-life assumptions 

• for me at age 61 

• using a lifetime consumption utility model?

I know I've done something like this before (e.g., here) but

  - I didn't do it specifically for me, and
  - The 3D surfaces were cool and all, but were also distracting and washed out some of the nuance

So the point here is to now personalize it (with some redactions) and limit it to some finite, reasonable set of parameters just for illustration (and don't do 3D). This will not be too exhaustive or necessarily rigorous or "scientific." I just wanted to see what impact different choices along efficient frontier have on (my) consumption utility for different spend rates over (my) remaining lifetime and then compare it to where I am today. It'll go like this:

1. Create an efficient frontier in 11 allocation increments from 0% risk asset to 100%
2. Go up the frontier one allocation increment at a time
3. At each increment, seek out the spend rate that maxes a lifetime-consumption value function
4. Then: chart it and step back to behold the results...and maybe make some observations

An amateur map of the psychology of irrational spending choice

Point of the Post

Since I was on a roll with this spending-choice thread (here and here, both of which were using my own assumptions rather than generic), and since risk-aversion has such a big impact in risk aversion math (surprise, that, eh?) I thought that I'd take the work I was doing recently with trying to optimize spend rates for a given set of assumptions (those are in the original post)  using a consumption utility simulator...and now push it further.  After the last run I was wondering:

"what would all of the spending optima would look like if they were strung, like pearls, along an axis of risk aversion (RA, or alternatively "gamma") from low RA to high (abbreviated interval, in this case)?"

Self-Evaluation of My Own Lifetime Consumption Utility, Part 2

This inherits everything from Part 1, except here I am focusing on gamma = 2 and changing volatility (standard dev of returns) from .11 to .10.  This might be similar to an incremental move into adding a trend following overlay. I know what will happen but wanted to chart it out, a chart that looks like this: 

The outcome is

- ever so slightly higher optimal spend rate (3.4 vs 3.3) though the "flat ranges" on top are wide-ish

- ever so slightly higher lifetime utility of consumption

We already know that the model is very sensitive to risk aversion* which will push the optimal spend sharply to the left or right depending on the coefficient. Untested are any changes in other portfolio choice parameters, annuity purchase, spending volatility, fat tailed distributions, age, inflation vol and mean reversion, the subjective discount, different longevity structures, SS start age, etc...

*this is why I suggested last time, 95% tongue-in-cheek, that counselling and mental health services might be a powerful tool in a retirement finance tool belt.  Skip the portfolio engineering and trend following overlays and just go get some therapy to get less risk averse: optimal spend rates magically go up.

Self-Evaluation of My Own Lifetime Consumption Utility

I don't recall that I've ever run my lifetime consumption utility simulator on my own personal data. That seems odd given why I do the blog.  So, this post is a stub-run for me and my data. This will not be entirely good practice since I am just winging it but I wanted to see.

The Model

The model has been discussed before but I am using an animated value function based on a survival weighted, subjectively discounted, CRRA utility of consumption over a lifetime where consumption snaps to income when wealth runs out before end of life.  The model was discussed here so I won't belabor it in this post.

100: Holy Crap That Hurt

I decided to take up a twitter challenge from someone today and do 100 push-ups. Not sure if I'm supposed to keep doing it every day but let's talk about today first before we get to tomorrow.

I've been working out every day now for 2 years. I used to be a competitive swimmer. I once challenged myself, and succeeded, to do 1000 pushups a day for three months.  The mirror, to my squinting jaundiced eye, still says "fit." ahem...

So, 100 push-ups, no problem, right? Well, to ask the question is to answer answer it.  First, the issue is not so much muscle strength as such. I mean I started with 10 reps but finished with a strong fast "30" from 71-100 and probably could still have done 50 sequentially if real money were on the line. The whole thing from 0 to 100 took like 20 minutes at the most.  The problem, however, was with the first 10.  And here I know that everyone over 60 is going to absolutely get this and everyone who is 25 or 30 is going to say "pfffft, old men suck."

The problem with the first 10 was the not so much the pec or tricep strength, which I would have expected. It was the other stuff. It was the shoulders, front (front delt and clavicular head) and rotator cuff (both current semi-injuries or at least inflamed or something); it was my elbow tendons; it was some weird injured-bicep pain, though that really shouldn't have come into play here; and it was also my back (sorta broke it 15 years ago). Even my left wrist was bitching: so, "shut up wrist, this is not your fight." 

That really f'n hurt. It also felt like the distance between young-me and me, and the distance between idealized-mirror-me-now and real-old-man-me-now, seemed to be far. So: hurt. Pride and body.

But I think I might do it again tomorrow. Maybe even 200. After some Advil.