This is an add on to the past cpl posts. Assumptions are the same except where called out. The past two posts are here:
Again,
This is a follow on to the last post
I swear I've done this before but idk. I did a quick spreadsheet the other day on asset growth and asset allocation for a conversation with a friend and I thought I'd flesh out the idea a little more [3]. The basic idea is what is the expected CRRA utility of wealth, in certainty equivalent terms, at T=20 (arbitrary) for a given simple 2 asset portfolio with return and std dev of .01/.04 and .07/.25 corr coeff = -.20 (really really arbitrary) in real terms? For my conversation I had used coefficient of risk aversion of 2 (another arbitrary but I've always thought of 2 as "mine" but whatever). Here the goal is to push the RA coeff up and down to see what happens to asset allocation.
Here is another reflection after 12 years of retirement finance. Me? I feel like I took this stuff pretty far for myself, from: rules-of-thumb to formulas to spreadsheets to automated spreadsheets to R code to esoterica like backward induction and pseudo-reinforcement-learning. But I don't think, with the remove of a year or two now, that those latter efforts were as additive as I thought they were at the time. I would call them more "confirmatory" of things already known or at least more easily known.
I was in my kitchen cleaning up the last of the post-thanksgiving turkey grease and I was thinking about my dormant-to-deadish blog and 10 or 12 years of me stepping into retirement finance. Did I learn anything? A little math and some coding, certainly. But in the end it wasn't the numbers or models or code or optimal this or that that stood out. It was that some things were more important than others. Some things dominated others if only in tiny ways that would probably matter somehow at some cumulative straw-and-camel[1] level.
I sat down after washing the grease off my hands and jotted down a starter list of "what dominates what" in my amateur opinion. Many of these probably need some additional explanation but I won't do that so don't ask :-). This is what I came up with, some of which is tongue-in-cheek, others I mean sincerely while others still are maybe incoherent. So then this:
My older brother, now pushing 70, was (and I think still is) an extreme skier, competitively so in his youth. That means I grew up surrounded by the various indicia of the skiing life: equipment, magazines, posters etc. All that, stacked into my childhood home, had that ubiquitous vibe of alpine rock and snow and pine. That was, and still is, intoxicating to me. So, at 10 or 15 or whatever, I was like: “I want that…” My problem was, I suppose: lethargy, procrastination, enervation, and other distractions. At 15 or 20 or 30 or 40 I would always tell myself “yeah! Let's go, I still want it, but, um, later.”
This post is part 5 of a series on Portfolio Longevity, a series made up of these links:
The point of this post is to
- 1) drop the spending from 4% to 3% (i.e., lower spending). and
- 2) look at the impact of "asset allocation choice" on portfolio longevity, using the same set-up we started with in the first link but with the following provisos for what I have changed since then. Here is what is different now:
Warning: this is unfinished so TBD...
This post is an extension of the previous three posts:
where the main explanation of the set-up is in the first link and a revision to some key parameters in the third link. The quick explanation for this post is that I am trying to look at the interaction between: a) an oversimplified and reductive and not all that realistic set of portfolio choices and b) portfolio longevity in years. And I want to take that look without dwelling on planning horizons or human mortality (might here though).
This is an addendum to the last post
The point of this post is to use one alternative way to visualize the interior of the distributions in Figure 2 of the last post
Let's look at the response of a particular metric "portfolio longevity in years" (unbounded by human life scales, btw) to asset allocation along an arbitrary but not totally unrealistic efficient frontier...but: in the presence of high spend rates.
Like a tongue seeks out those annoying imperfections in a tooth, I tend to go back to two things over and over here on the blog:
1) the Nikkei index after 1989 as an example of a tough market that never recovers (yet), and
2) the Ed Thorp 2% rule which -- along with simulation I've done a million times -- says 2% is pretty close (on average anyway) to a perpetual spend rate for endowments or long-dated trusts.
In generating our forecast distributions, we’ll use 50 years as our simulation horizon, but that number is arbitrary—we felt it to be a horizon that should represent three to five “generations” of board members or trustees, and one that is also long enough to show the long term trend as time marches on towards the endowment’s hoped-for immortality.50 is arbitrary so right there he is pitching us an ever so slight preference for the near future over infinity. And in fact in most of the consumption utility math I've ever seen there is a factor or discount for biasing us towards the present a bit. LaChance, following Yarri, presents the evaluative goal like this in continuous form:
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| Eq1. Value Function from LaChance 2012 |
From a reader (always surprised when I have a reader...)
"Curious as to why you have an advisor. What services do you think you can't or don't want to do that your advisor provides? Other than handling your divorce which was bungled anyway you seem more than capable of managing your retirement drawdown.
I'm an advisor and big fan of yours thank you for your content and contributions to our industry. I have huge problem with our industry that is focused on training salesman as opposed to actually....advisors..."
"Live a little bro..."
"I gotta make a (commission) living, too"
These epigraph statements came from the same, now fired, financial advisor. The first one was in response to me describing my careful spend rate -- which I will humbly assert was pretty well-informed at 57 when he said it...after more than 5 years of me doing this blog -- that was designed to confront my long-horizon superannuation risk since I have no major hedge like a pension or annuity. The second statement came not long after -- this after 25 years of paying something like a point and a quarter, btw -- when I insisted that we discuss (negotiate, reduce) fees. After my divorce and retirement fees became an absolute yoke and on the forefront of my consciousness because fees are no more and no less than part of our spend rate.
After running through a few posts lately, what do I have? Basically this:
Based on an email from David C, I had forgotten that a rule of thumb for spending is 1/e where e is remaining lifetime. The super quick look here is from a page from Gordon Irlam's aacalc.com site:
where the operative text is this:
Perhaps less well known than Markowitz's modern portfolio theory (MPT) is the subsequent work of Merton and Samuelson. This is a shame because while MPT only concerns itself with optimizing investing in a single time period, Merton's portfolio model concerns itself with optimizing over time, where it is possible to change asset allocation and consumption in response to portfolio performance. This is far closer to the problem faced by most investors. Unfortunately the math involved is quite complex. I've been trying to derive some very simple rules of thumb for stock/bond asset allocation and consumption planning using Merton's portfolio model and the current returns environment as a guide. Here is what I came up with:
This post, still about "Long Horizon Spending," follows the last post on the same topic:
where I was playing around with what a percent-of-portfolio approach does to spending and portfolios at a 50 year mark. 50 is pretty arbitrary but one of the cited papers used 50 years for some kind of reasonable endowment policy cycle. 50 years is pretty long and not a typical assumption in the retirement finance I read but it is not terribly unreasonable were we to be given both early retirements and extended longevity.[1]
I always assume that the constant spend assumption -- set spending at the beginning of some interval and then adjust it for inflation -- is well known to be an active risk position because that approach guarantees, in the absence of mortality, that it will someday stop working where "stop working" means zero[1]. But maybe that isn't as obvious as I think since I look at this stuff all the time and others don't.
On the other hand, I've also heard "% of portfolio" touted often because it kinda-sorta lasts forever. But that is an active risk position as well for a couple reasons:
I spent the better part of an afternoon trying to excelify some math on consumption smoothing, succeeded, and then gave up after the fact for reasons below.
Let's say, as a convenient-for-me strawman, that there are four broad categories of spending in Ret-fin models:
I know I've done the kind of charts in this post before, but whatever. David C pointed out to me I've been kinda re-hashing my past stuff lately but sometimes that's necessary to pound it into one's own head. Here (Figure 1) I was running a "portfolio longevity" calc for a .04/.12 consumption portfolio (different spend rates) 4 million times (uh, there is a reason for that big nbr) to see how many portfolios "tip over" into portfolios that last to infinity (or in this case 100 years which is a convenient proxy for forever but not really).
This is very subjective and depends on both my code correctness and my assumptions/parameters. I am skeptical of everything here but I ran it to see what it looks like anyway.
The goal here was to run a sim to calc the expected discounted utility of lifetime consumption for these main variables:
- different risk aversion coefficients between 1 and 3 [1], and
- two main reductive spending strategies (constant and percent of portfolio)
The assumptions are in digest form:
Over the last six decades I have certainly had my fair share of competition with other people but the main competition was always the mirror ... in other words with myself. It certainly wasn't with my pretty grey face. Self-drive is a powerful engine to which to harness what one does in the world and I have worked pretty hard at it in various fields of human endeavor since 1958. But I am starting to see some fraying among the threads I have woven for myself and I am starting to second guess the idea of personal records or personal bests. At least in the gym.
I usually trade in "constant spend" because it is easy to work with. A % of portfolio isn't all that much harder and lasts forever, right? Sorta. The trade off is consumption volatility and the possibility of really low consumption in absolute terms late in the game. In this post I am simulating (50k times) randomized spend rates against a .04/.12 portfolio over 100 years. Lifetime is a survival probability laid over the 100 years, an interval which is arbitrary and used here as a proxy for forever. The utility score is sum of "consumption utility results over all 100 years weighted by the life survival probability in each year." The lifetime parameters are somewhere in a generic middle between average health and annuitant. Risk aversion coefficient is arbitrarily set to 3 in Figure 1.
[note: fixed an error post-publ]
Summary stats might mislead given the defective distribution so I just dropped the image. The finite P mode bumps out a bit but not much but the whole thing does shift right a little bit. This is why I fold some trend-following into my Portfolio. In theory -- tho no guarantees -- the payoff structure can hedge portfolio vol a bit and goose portfolio longevity as a result. Here I am merely asserting a vol reduction rather than simulating something more complex. Note that more pink portfolios will tip over to infinite (using 100 as a proxy here) but are not shown due to the cropping.
This is the third post on fuzzy clouds, the first two being:
Here I am modifying the code a bit by
In the last post "the challenge of retirement finance in a few charts" I tried to make a case that behind the fancy precise answers that advisors and academics devise for us there is really a big fat cloud of possibilities that we have to navigate by way of judgement and a continuous process of evaluation and adaptation. Actually I didn't make the case for that last part very well, it is implicit. Here is another example in this post, though.
I won't repeat Sharpe's over-used quote about the "retirement problem" but let's at least stipulate that retirement finance is a bit of a challenge. The intersection of uncertain returns, uncertain longevity and uncertain consumption in the absence of lifetime income creates a difficulty in how much to save, how much to spend and how to allocate resources. The self-serving illusion articulated by much of financial services or in academic studies is that there is "a" solution -- i.e., your "number" or some other optimal calculation distilled down to a point -- where in reality there is just fuzz: fuzz now and then even more fuzz as time unfolds. The point here is to highlight some of the idea of "fuzz" rather than solutions or points.
I got confused the other day, when playing around with an Rscript for portfolio longevity. I've always used discrete returns (1+r(t)) in simple sims because 1) it's easy, 2) I don't know continuous time(CT), and 3) I am working inside the sim with very discrete annual steps. In the script I got from Professor Milevsky he uses e^(vt), a continuous form of return, but told me later that either approach is fine as long as the rates are matched to the compounding intervals.
So, why either? What difference does it make?
This is a back of the cocktail check of implied annuity discount rates. Not sure I'm doing this right. If I trust immediateannuities.com ("IA")(not sure how those are priced? market products available to IA? CANNEX? idk) and AAcalc.com (guess based on a number of inputs including the current yield curve which gives a price close to the former) and if for my model I use SOA annuitant conditional survival probabilities for 65yo male and a 5% load and assume a simple immediate annuity and if I solve for the average simple discount that matches my (discrete) model to the basic IA price, the discount looks like it is around 3.6%. I can't remember the last time I did this, maybe a couple years ago and it was under 3%. I have not looked at the yield curve but if I did I'm not sure how an insurer or AAcalc uses it because the current 30 year is still just a little over 2.5. Anyone know how observable rates work in pricing annuities?
"10 years ago at ~52ish I fired up a broad attack on learning stuff in several quant disciplines along 3-4 fronts. No school, no degrees, no credentials. 10 years study! Whatever. I was just curious. I am comfortable with my capability in that domain."Just a cast-off comment but a dude asked "what disciplines?" I have a placeholder on LinkedIn for that but that was in bullshit-speak so I condensed it for my asker more succinctly:
My friend David C says I sandbag on this blog way too much. Otoh, it is sometimes warranted. So, here is the real-deal as I wind down my blog:
Do I know what I'm doing? No idea. Maybe. Probably. Pretty sure. Yes. So there! My sandbagging is out of the way. If you want more cred than that, read ERN or SSRN.
Also, I have to say that I am, as I hinted in the last bullet above, pretty much done with this whole blog thing. Why am I "done?"
