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.
