I was reading an article recently on maximum spending rates
(Maximum Withdrawal Rates: An Empirical and Global Perspective, Estrada, 2017) and thought I'd take some of his math out for a test drive just for fun. You can read the paper on your own but the
main question he asks himself, as a comprehensive way to assess retirement
strategies, is "Given a desired bequest [say zero, he says later], what
are the maximum inflation-adjusted withdrawals an individual could make during
his retirement?" He points to related literature from Suarez (2015), Clare (2016), Blanchett (2012), and Miller
(2016). His own answer (to cut to the
chase) by a simple derivation you can check out in the link, is that when the
bequest at time T (the end) is 0 the max withdrawal rate (MWR) is:
And here, because I quickly violate his dictum later, let's
be clear that he says that this can "only be calculated ex-post…no retiree
knows what the returns of his portfolio will be." But, before I get to my dictum-violation,
here is his picture of the ex-post global variability of MWRs:
Now, ignoring his self-debate about
simple-fixed MWR vs re-estimated MWR over n periods and violating his advice
that this only makes sense ex-post, let's do this. Let's take a "special case" of his
MWR math (one with an unrealistic assumption of constant returns over n periods)
and project forwards. That means that we'll calc his formula using a constant
(real) return of 1 or 3 or 5 or 7% over different longevity expectations (for a
58 year old) to see what a MWR might look like for me (i.e., this is not
generalizable). If one were to do that,
it might look like this:
The MWR here (solid lines) is calculated using the Estrada
formula for MWR where T is (longevity expectation - current age) and R is
whatever it is.
The minimum (dotted line) on the other hand, which is not in
the Estrada paper, is something I came to my own through simulation exercises
that showed me that anything below about a 2% spend rate has diminishing
returns in fail rate reduction and seems to imply some serious and probably unwarranted
self-deprivation absent a big bequest motive.
I was confirmed in this notion by a comment in Ed Thorpe's new book A
Man For All Markets where he says:
"What if you want the payouts to continue "forever," as you
might for an endowment? Computer simulations showed me that with the best
long-term investments…annual future spending should be limited to the
inflation-adjusted level of 2 percent of the original gift. This surprisingly
conservative figure assumes that the future investment results will be similar
in risk and return to U.S.
historical experience. In that case, the
chance the endowment is never exhausted turns out to be 96% [that's lower than
I expected]. The 2 percent spending limit is so low because, if the fund is
sharply reduced in its early years by a severe market decline, a higher
spending requirement might wipe it out.[I didn't realize Thorpe was a
retirement planner!]"
Some other assumptions implied in the chart I should point
out are that:
- this is an "initial" withdrawal kind of thing so
constant inflation spending
- there is a no-bequest requirement
- really only supposed to consider this ex-post
- variable returns could create sequence risk not in the
chart
- this is based on real return using a 60-40 rebalanced
portfolio
Any conclusions from this?
No mind-bending ones I can think of. Using a
historical 60/40 return expectation of 5.2% and age 58 with a planning range of
95 (conservative) it looks like the min/max range of spending is between 2% and 5.7%. Splitting those two gives me ~3.85% which is
pretty close to the 4% rule so that doesn't surprise me. If I use a 3% real return (conservative
again…maybe) the range is 2.0 - 4.4% with a split difference of 3.2 which is
closer to my own assumptions. Would I
ever use a MWR for any reason? Not for a spending budget, at least, because I do have a
bequest motive and I do have contingent liabilities I still worry about for at
least a few years. But yes I might use it for: a) context setting, and b) creating
the outer boundaries for a spending process control project like one might see in an industrial process or in some kind of 6-sigma sense. So I think MWR is worth being aware
of anyway.
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