See the line below this paragraph? Below that line will be
very little perfect science or solidly defend-able math (by me, I mean). What you will see is what might be called a
bad case of pseudo-quantitative impressionism.
Ready? Here is the line; you know what you are getting into after you
pass it:
-------------------------------the
line---------------------------------------------
Now that we have that established, what I want to do is
take a look at the eight rules of thumb I have written about before and see how they work with respect to longevity expectations and real return
assumptions. I might have done this before but there are a couple new rules since then. I like rules of thumb
because I hate black boxes and I especially hate being asked to pay for black
boxes that are proprietary. Rules of thumb are freedom. They also give individual retirees a toolbox
that allows them to adapt to changing circumstances…which they should. Here is a super-retirement-quant (my label) on
adaptation.
A [retirement] scheme that does not respond to the performance of the portfolio is likely to underperform one that is responsive to portfolio performance. - Gordan Irlam
That quote might seem thin at first glance but there is a
lot packed into it if you think about it enough, which I have. Here is the link to the writeup on the eightrules of thumb (ROT). Go there to see the actual formulas. Note that it's
really more like six rules because two of them (#4 and 8) are the same and one
of them (#1) is different because it calculates money duration rather than
consumption but we can let #1 stand in as the baseline 4% rule while we calculate duration. In brief, here are the rules:
1. Milevskey's how long will it last formula
2. Excel PMT function used by Waring and Seigel
3. Blanchett's simple formula #1
4. Blanchett's simple formula #2 (and) Irlam's simple
formula 2
5. Evan Inglis divide age by 20 rule
6. Ken Steiner's actuarial formula for consumption
7. Gordan Irlam' simple rule of thumb 1
(8. Gordan Irlam' simple rule of thumb 2 -- same as #4)
I took a generic set of assumptions[1], many of which (but not all) cohere, and ran them through the various rules of thumb (ROT). I tried but failed to be perfectly consistent
and numerate. Oh well. These were the steps I attempted to follow:
a. Run each ROT for different expectations of
longevity sorted into five levels: 1) very early or to age 75, 2) modal age of around 85-87 or
let's call it 85, 3) age 95 which would be about a 3rd quartile expectation for
a 58 year old that survives to 85, 4) the latest planning age I would personally consider
or to 105, and finally 5) the approximate human terminal age or around 115.
b. Do "a" again but for a couple +/- 1% changes in real return
assumptions.
c. Run a custom simulator against the various spend rates in "a" (but using an assumption of a constant spend when in real life these rules of thumb would be adaptive. Weak I know but what can I say?)
d. Then finally see, impressionistically if necessary, what falls out of the data after doing "a" through "c."
For a 2% real rate assumption, the chart looks like this. I'll put the 1% real and the 3% real in the
notes below[2].
Are there any conclusions that can be drawn from this chart?
Not really by me. That's because it depends on your age and longevity expectation. I know mine
for planning purposes (58 to, say, 95) but not yours.
The best I can conclude is that if one were to have a "longish" expectation (early retirees take note) then rules 2, 5, 6, and 7 would have an edge in keeping us a little safer while also letting us spend a little more now than some of the other rules might. If one were to have a shortish expectation
then rules 2, 3, 4 (4 and 8 are the same) and maybe 6 dominate while 5 is a loser[3] in this scenario. Blanchett even pointed this out in his
article on his simple rules (# 4 for example). He said his RMD style
formula worked better for short retirements of < 15 years. Fwiw, the blind use of the 4% rule (implied in #1 because I use a 4% spend rate to calculate duration)
when it is unhinged from a longevity expectation looks like a loser when we look at
the expected duration of the money which would supposedly run out at age 93 for
a 58 year old. That end age is the black triangle on the x axis. [note that rule 6 bends up a bit at longer age expectations; it, along with #7, are the only rules with an assumption about income sources in the future (like SS at age xx-plus) baked into its math. In general, without any proof offered, maybe accept the idea that floor income (SS, pension, annuity) will improve long term longevity-risk management, allow higher spending earlier, and permit higher risk portfolios ]
Now I want to take it a little further but maybe a little
illegitimately so. I want to see what
a simulator with a realistic longevity distribution function would do with each of
the spend rates implied by the various rules of thumb at the different
longevity expectations. This is slightly problematic and not just because simulators are weak retirement tools. It is a problem because: 1) we used the ROT with respect to particular longevity expectations while the simulator is agnostic because
it lets that number vary so there is maybe a slight mis-match in the analysis, and
2) the ROT, in my opinion, are tailor-made for adaptive decision making as the world changes each year while the simulator is
run (for this post anyway) with a hard constant spend assumption which I don't think anyone would do in real life. But
let's press ahead.
Here is the table of results after the sim runs.
The color overlay is this: Green is any consumption that is at least 70% or more of the
4% rule's 40k (i.e., we like to not over-conserve), Blue is fail rates that are less than or equal to 15%, Purple is a median fail duration
(terminal age - money runs out age) less than 8. These numbers are really arbitrary and based on
nothing much (certainly no science that I can think of) except that I wanted to
not spend too little and I wanted to keep fail risk moderate.
The conclusions from the table are a little different from the previous chart but not by very much. For moderate-to-conservative planning horizons, rules 5
(Inglis - divide by 20), 7 (Irlam's sorta simple rule), and 6 (Ken Steiner's
Actuarial formula) stand out to me. Rule 2 (the PMT function suggested by
Waring and Seigel ) is probably ok for the very longest and conservative expectations. The ultra-simple RMD style rule (4 and 8) seems maybe a tiny bit sub-optimal at all expectation levels. For short expectations, rule 5
passes the test but I think, subjectively speaking, that you'd be underspending for that longevity expectation by quite a bit and we'd want to know more about why you have such a short expectation because that would
be better to know that how a particular rule calculates itself out. For normal planning ranges (say mine at 95)
I'll call it a tie between 5 6 and 7 (two actuaries and a hard-core quant can't be all wrong, right?) and then to be totally innumerate about it maybe I'd even average
them (what would that average mean anyway). Not sure that makes sense but it might work this year. Next year who knows. Maybe I'll find a new
rule of thumb. Or make one.
notes
-------------------------------------------------------
[1] These are the assumptions. I won't detail them explicitly since I have
so few readers. If anyone were to be
interested and the other post with the actual formulas does not make sense you can email
me. Some might be highly debatable but I
knew that. Fwiw, "nbr years,"
"Ann real growth" and "inflate rate for $1 over term" were
varied to create the charts.
[2] varying the real rate of growth to 1% and 3% from 2%(above):
[3] calling this ROT a loser in this particular situation (early retiree with a short planning horizon) is unfair because it's not realistic. What is a shortish expectation for a 58 year old? Maybe something related to a cancer diagnosis? Actually this rule works really well because as you age the percent goes up so in the case where one were to be 85 the spend rate is now higher (>4%) because "short expectation" is means something closer to normal mortality assumptions.
No comments:
Post a Comment