The poll however is more thoughtful and revealing than you
might expect, leaving [as shown] most people including AI puzzled, or overly optimistic
in their approach. This is quite
dangerous, as the ability to make up shortfalls later in retirement, including
in the habits one needs to enjoy for a healthy retirement, become more
challenging later. But there are almost
life-saving interlocking concepts that needed to be considered early in your
retirement in order to be on your best path, and this complexity often is
bypassed in anyone’s thinking or models [and they are probabilistic in
nature].
Indeed it turns out you need more money to retire than
imagine [and need to work 2-3 years more as a result], but neither should be
considered by much if you plan correct.
So this article is not just theory; it's a vital reality check, offering
practical takeaways that will empower you to reassess your strategies and
maximize hard-earned savings.
poll question
First, let’s see the results from this poll, which incidentally mirror the many anecdotal conversations I have had from smart people in my own circle:
Worth stating there is a provided comment below the poll clarifies
that withdrawal at age 50 is 3.5% at that time, and the nominal investment
growth is perpetually centered about 4.5%.
Yet anyway look at the range of answers!
Nearly 45%, including AI actually don’t know at all. The second most popular answer was the lowest
stated value of $2.2 million, or -12% less than the age 65 goal. What was yours?
It’s a little bit of a cop out to use or justify the wrong
answer based on really extreme assumptions.
We can further ask secondary questions which is when and at what level
does the portfolio peak, regardless of what is your chosen answer? The answer will likely surprise you, and will
be delved into a little further below.
simplified industry standards
The are popularized ideas on how to answer this. Two in particular we cover below. The first popularized method is simply use say apply a 3.5%
withdrawal at age 50 to match needs at that time, and 3.5% is generally a
little more conservative for retirees and more in the flavor of the popularized
FIRE movement. Recall for decades people
have whispered the “4% rule” at age 65. Recall
again these are coded percents however that completely misalign with the
long-run and serious acceleration instead of retirement expense drivers.
We use Pt to signify principal level at a
given age or elapsed time t, while using P to refer
to principal level in a general sense. The
3.5% of objective P65 [$2.5 million] expectation, is a withdrawal
at that age of $87.5k. We can then
discount this withdrawal back to an age 50 needed value of $87.5k/1.03^15, or $56.1k.
Hence $56.1k/3.5% is a possible P50
of $1.6 million. Note that this is far
below any of the polling choices provided, so what happened?
One large drawback of this method [and its one of the
initial two models that leading AI is aware of and guides users with] is that
it ignores your requirement of wanting to have a P65 of $2.5 million
altogether, just to ensure that there is adequate expense coverage during the
bulk of your retirement years. The math
just completely misses! Instead your
portfolio grows to only P50*[1+r-w(t)]^15
if we assume that W [withdrawal level] grows with inflation
[growing at a slower rate than the principal’s gross rate or r]. w[t] is the withdrawal rate at
future time t. Or if we impossibly
lock-in a w of 3.5% instead, then the portfolio grows to a far
different value versus $2.5 million, completely missing the mark. More importantly the W[t] and w
assumptions in the end are flawed too, particularly over the long run stages of
retirement as we’ll suggest further below.
It’s incorrect for P50 to be as low as $1.6 million,
and see the withdrawals not even growing at the basic cost inflation rate in
the initial years, let alone correctly completely eclipsing investment returns.
At age 50 for example the 3.5% withdrawal is again $56k. Leaving a $1.6 million portfolio at $1.61 million
for age 51 [the $1.6 million grows slightly on a gross basis but then you are
also withdrawing the $56.1k]. So now age
51 the 3.5% withdrawal amounts to less than $56.5k [so not even 3% expense
inflation but a withdrawal inflation afforded of just under 1%]. So the “model” despite the low $1.6 million
goal is severely broken and unusable even by the second year of retirement.
The second major drawback with this simplistic modeling approach, and critically important
tragedy of this framework is that you really need high a $70k’s withdrawal, and
not $56.1k, so leaving beside w[t], the underlying flows W
completely mis-calibrated for your level of needs on day one of
retirement. In other words you can't assume that just because w50 is 3.5% that w65 is as well, and the result is the entire discounting exercise as a result is mis-calibrated and highly sensitive to the values that you incorrectly assumed from a simplistic model.
Now the second popularized modeling type to estimate your
magic number is to start with a future horizon value and working to the present
iteratively. So right off the top we
know our objective of P65, and t of 15 [15 years of
early retirement]. We also assume we
must start withdrawing as a result at age 50, if we are going to assume to be
retiring then. This can be expressed as
a rate or amount at that age. So start
oscillating and experimenting to estimate a r of 4.5%, yet a w
of 3.5%. This gives us an initial effective
growth factor [eg] we can also estimate as [1+4.5%]*[1-3.5%], or
1.0084 [or you can average the two versions shown so far, and simply use 1.009].
And consequently P50 =P65/eg^15,
or $2.2 million. Note this will indeed also
likely zoom to towards the arbitrary P65 of $2.5 million, and keep
growing towards infinity after that. It
also incorrectly maintains the withdrawals as a component of returns. But doesn’t imagine a large and independently
modeled withdrawal level for consistency.
The real challenge again here is that there is no way to
mathematically create the proper second order rate on the expense inflation, and
this is more and more needed over time as one begins to stop being able to work
at all. Also factor in illiquidity of domiciles as you reduce your portfolio to prefer simply liquefying it, and the health
care costs that are very uncertain and convex. But if you don’t stress over your
health early in retirement and start too complacently you will completely be unprepared for life’s ultimate
shortfall.
Despite the popularity of the polling result, in the end
we’ll need more than $2.2 million at age 50 for an early retirement.
ask AI
This question was posed in general ways to AI, with it almost never getting the correct answer despite peppering it with heuristic questions to clue it in. This leaves you defenseless, only you probe it repeatedly and actually know the correct solution in advance [defeating the purpose of asking it for a solution to begin with!] One generic example is show below [when I was stress-testing it for early retirement of 55 with an extremely liberal gross return of 7%, and a baseline P65 of $2X million], but the examples are littered throughout nearly every step among many. They also presents different mathematical results based on the most subtle of word choice differences in the prompt, including the ordering of inputs described to it. See one modern AI output below.
Notice in the answer above the early retirement age concept
wasn’t even accepted by AI [even though most polling respondents above knew to
do that] and the discounting as a result was erroneous. And there were other classification issues
with liquid versus non-liquid assets that are critical and needed to be
streamlined for the results to make sense.
the actuarial insight
The actuarial reserving
concept is fresher and groundbreaking in dismantling misconceptions. However as we’ll see we’ll still need to take
it further. We can at least start with
the visible mathematical variables in the formulas for the first order
impacts of expenses. Like a ship
captain taking into account wind or current, but not both. Start by estimating both the rise of the plan
assets P, accounting for continuous and growing withdrawals. And up through the time of retirement. Again we focus on a common goal, here set for
a single person to achieve a more-than-sufficient, $2.5 million nest egg
through age 65, the typical retirement age framework.
One way to start this is to
decompose the plan gross growth and the future value of this actuarial
withdrawal function. This is because there is a progression in the level of your expenses in retirement and it's not merely an embedded function, but constrained when both the principal and the withdrawl expenses are maintained independently. For example when there is a bear-market, do your mortgage bills or onion prices suddenly drop -20% in lockstep? Of course not. Here's the complexity of this math is shown below:
P65 = P50*1.045^t – sum[over k=0 to t-1] of W50*eeg^k
= $2.5 million
Where eeg is the “solved effective growth” for
all 1+w[t]. And sum[over k=0
to 14] of W50*eeg^k is therefore
still close to the age 65 future value of annuity, or W50*[(1+3%)^15-1]/3%
for shorter horizons such as 15 years.
But the eeg should really should closer to 1.035
for the initial stage to retirement [ie, 3%-4% average expense inflation]. And then about 1.05 if covering the full
horizon [ie, 5% average expense inflation!]
Another way to see this is that P50 needs to
be discounted slightly towards -2% for every ½ decade early retirement [just
towards -15bps per year]. By the way,
there is no condensed and meek formula for P50 as a function of
either P65 or t, but you must simply rearrange the
formula above, which is easy to isolate P50.
So AI uses the short-cuts described the earlier sections
with no second order growth in the rate of withdrawal. It completely misses the actuarial insight
assumptions, and randomly too based on how you prompt it. And last, delivers back from this reserving
method of solving P50 at too low and impractical of a magic
number, at well below $2.4 million.
psychology and portfolio peak
Once your solution is calibrated [as it should for the longer horizon] to include the higher and accelerating withdrawal expenses, you get an answer far closer to just over $2.4 million. In these scenarios the withdrawals are appropriate, and we indeed overshoot to a mid-50s peak of just over $2.5 million [a benign, just under a +5% jump in fact!] While mathematically correct you should not take this initial ramp-up as a sign to be complacent or assume your health care and other in-fact convex withdrawal expenses are fine. They may dangerously not be. See output from another AI below.
issues and lessons
The lesson from this article is that certainly we can have a
$2.4 million principal number that grows to just over $2.5 million through age
60, but then start a slow crank ahead but before-you-know it rollercoaster plunges toward earth, say from unchecked medical exigencies in your much later
future. While it appears that these polling
solutions are only +10% or so apart from one another, the market can be
unforgiving as well during this time and so could your workplace sanity if you
start to internalize the need to work longer right as you arrive at a miscalculated
magic number.
Semi-retirement is a different concept as well, and that
involves simply treading to cover withdrawals only from an initial to a final
retirement. Allowing more of the weight
of the 4.5% return to work for you. And
the concept of reserving applies to be able to match up to how you are doing
against that latter target frankly, versus an on-track measure early in your
career to simply work towards.
The investments you should be making over the time should be
as diversified as possible and still provide liquidity whenever needed. Luckily this liquidity is not needed as much
in the earlier years. Be cautious with
the strain of high mortgages still in your retirement, assuming you still have
a large chunk of your mortgage term left.
Retirement should be a time for celebration, but also strict
prudency. This is the final nest egg you respectably worked your life building, and
the thought of returning to work for lower wages and a loss of productive connection to the workforce can be daunting.
AI tools provide quick and seemingly confident answers, but with large
errors, no different than the simplest of industry rule-of-thumbs. This
We can note that higher initial withdrawal or gross returns instead closer
to expense inflation have similar damaging effects on your retirement
number. This is where one could envision
the higher polling options: the $2.5 million or even $2.6 million variety. Else
significant superannuation or even mild longevity risk, with complete depletion, frighteningly a
decade at least before death.
So last, make sure to audit results in this case from AI models, and test from various perspectives, such as marginal stock and flow, and including at different time frames of your overall life [eg, age 50, 65, 80, 95, etc].
addendum
On the one-year anniversary of copula narratives, and the eight-year anniversary of Google banning me, it is interesting to now see how their top AI describes this book:
A well-regarded collection of statistical essays and articles by Salil Mehta, a prominent statistician, blogger and author.
The analytical collection is a conceptual grouping of his insightful, profound analyses that break down complex statistical concepts through the lens of real-world, and often newsworthy, situations.
copula narratives cross-roads is his metaphor exploring the often-unseen connective pattern between different events and variables, in the urgent world around us.
from google's AI pro [yeah same company that banned me a decade ago]:
— salil mehta (@salilstatistics) August 15, 2025
"a well-regarded collection of statistical essays and articles by salil mehta, a prominent statistician, blogger and author.
the analytical collection is a conceptual grouping of his insightful, profound… https://t.co/hLEM7zn20f
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