I remember reading, over the last year or two, a statement
like the following from one of our leading retirement research luminaries -- I
don't remember which one but all the usual suspects are in play: "In the
absence of annuitization a retiree must spend less in order to hedge the
risk of uncertain longevity." That means that in the presence of
annuitization, a retiree could spend more. Foolish me, I decided to try to figure out how
much more I could spend now if I happened to try to hedge out
longevity risk.
First things first.
I'm pushing 60 so I am running this hack as if we were looking at a 60
year old US
male. In retirement planning one of the more important things is to get one's
arms around longevity and the uncertainty of it and the types of assumptions
one can make about the planning horizon especially since the base case here is
planning without recourse to annuitization in its various forms (annuities, Soc
Security, Pensions, etc). Here is a
probability density function of mortality or longevity or whatever using the
2011 SS life tables. This will change
every year going forward, of course, but let's look at the baseline first:
Exhibit 1. Longevity Distribution
The average life expectancy, the often misused number in
planning, for the 60 year old is somewhere between 81 and 82 depending on the
math used. On the other hand, the mode,
or the greatest number of occurrences, is closer to 87. Going further, 95, a reasonable long range
planning horizon, is thrown in for good measure but even that is not the end of
the distribution which continues on to the right. Note that when one does not have access to anything
other than one's own resources for retirement, going right is better than left
for planning purposes. On the other hand
that is what makes retirement spending so hard -- planning for such a long time
frame makes one necessarily conservative, often too conservative; so
conservative that a lot of money maybe goes unspent earlier in retirement when
the spending is more fun. So, for a 60
year old let's assume the retirement planning horizon is at least 35 if not perhaps
40 years. Let's also assume that,
depending on who you are talking to, most people want to spend more rather than
less and to spend it earlier rather than later.
In retirement that can be a problem.
This, for example, is what it looks like as one tries to raise spending
as a percentage of (generalized, taxable) retirement assets:
Exhibit 2. Constant Spending vs. Simulated Fail Rates
This is simplistic and I was pretty sloppy with the
assumptions and I think I made a couple mistakes in some of the models but the general idea is pretty consistent across all of them. The idea is that (using constant inflation adj spending
and ignoring dynamic spending) fail rates do not just rise, they accelerate
as spending increases all else being equal, and spending more than 3-4% on a
constant inflation adjusted basis can get pretty scary.
Then, in addition, if one were to hold spending constant,
say 4%, and then play around with extending retirement out a few years more,
like an early retiree might, then the fail rates accelerate (success rates fall
in the chart) again with the changes in duration:
Exhibit 3. Retirement Duration vs. Simulated Success Rates
So, certainty and long retirements and higher spending all seem to be at odds, Let's look at a preliminary
list of ways people try to hedge this kind of risk and/or increase
spending:
- Damn the risk, full spend ahead. Depend on Soc. Sec. and
kids to carry the day.
- Spend less at least early in retirement. Perhaps spend
more later…when it's less fun.
- Annuitize now or in the future but maybe squander legacy
or be less flexible
- Get lucky with markets and inflation and the sequence of
those factors
- Take more risk or mortgage the future a bit or reduce
one's legacy plans
- Go back to work at a plan B career
- Die younger
- Ignore the risk of future spending shocks
- Change tax assumptions by moving
- Other?
All good ideas except maybe die younger. Let's ignore them
all except to look at some type of annuitization since that is the point of the
post. First of all let me say that I am
not an expert and I am not even an amateur so proceed with caution. Also there are an infinite number of opinions
on the idea of using annuities in a retirement plan, from Ken Fisher style ads ("I
hate annuities") to financial advisors that say "some are ok for accumulation but
never, ever actually annuitize" to economists that consider them eminently
viable as an abstract concept. The
difference between that last and the first two is often referred to as the
annuitization paradox or puzzle (see Time Inconsistent Preferences and theAnnuitization Decision or If Immediate Annuities Are Such A Great Solution, Why Doesn’t Anyone Want ToBuy One?). There are a lot of reasons for this, many of
which are cognitive/behavioral in origin. I'll leave the reading to you. Me, I'll just point out one big
"con" and one big "pro" that I have seen in the literature.
One of the bigger "cons" that I often hear or read about -- other
than they are expensive right now in a low interest environment (true) or that
they are too complex (often true) or over fee'd or commissioned (usually true)
or that the riders can make it unaffordable (true, I think) -- is that they, in
their pure form, hand money over to an insurance company that you can't get back and
that otherwise would have gone to your heirs (not necessarily true depending on
how you look at it). That last comment and parenthetical insertion can be
illustrated by considering the other side of the coin (i.e., the scenario on the other side of the "short-life, wasted my assets on insurance" scenario)
through a thought experiment: How much would your kids, or you as their proxy today,
pay to avoid carrying your expenses in old age when or if you run out of money
if you happen to live to 100 and have not properly planned for that? Probably
quite a bit and probably, I'm thinking, close to the cost of a deferred income
annuity. Personally, my experience was
that I had a parent that was running down a portfolio at the same time that I
was building a career and caregiving young children. The prospect was and is
daunting when it is lived experience. Annuities are probably less of a paradox in that
kind of situation. Here is Douglas McCormick in his new book "Family Inc." responding to the objection that "Buying an annuity reduces my heirs' inheritance" (p. 175) by making a similar if not the very same point:
"This is flawed thinking. The present value of their expected inheritance is similar regardless of your insurance purchase, but the volatility of the expected inheritance is likely reduced by longevity insurance. For example, if you die early, your heirs would have received a greater inheritance had you not annuitized. However, the opposite is also true -- if you live longer than expected, your heirs will inherit more [sic, I think he meant less here] than they otherwise would have. Moreover, if you avoid longevity insurance and deplete your assets, you may instead become a burden on your heirs, which I view as the worst possible scenario."
If that is not convincing, which it is to me, note also that it is at least technically (practically?? I'm not so sure) possible to create a synthetic "short" annuity with debt and life insurance to offset the long annuity. I seriously doubt anyone would do that in today's market but there it is (The Implications of Annuity Replication for theAnnuity Puzzle, Arbitrage, Speculation and Portfolios, Sutcliffe 2013).
One of the bigger "pros," one that is often hard
to explain and is underappreciated is that one of the very, very few things that an individual
retiree cannot do -- and they can really do a lot on their own, often
more than they realize -- is to pool risk. This is one thing that annuities (or
in a prior age a tontine…See Milevsky on this)
are not only good at but are designed to do and why economists and researchers tend to like them. Annuitants that live longer lives are subsidized by those that live
shorter lives. Again, if you hate this idea
ask your kids once more if they want to subsidize your longevity risk or if they'd rather
have thousands of others do it and forgo but a sliver of legacy. I know my answer and I can guess theirs.
So let's say, for the sake of argument, that the pros
outweigh the cons. There are lots of annuities
and offerings and companies. I am not
going to tutorialize here, though. I am
just going to assume, as a stretch, and with no supporting evidence or argument
(other than proof by intimidation as a former boss of mine called it), that a deferred
income annuity is the lowest cost, purest form of longevity hedging when
considering the "right tail" longevity risk of an early retiree in exhibit 2. I am also considering one of the comments
that I started with: In the absence of annuitization a retiree must spend
less which I take to mean that in the presence of annuitization one can spend more. Whether market timing issues in the current world are good or bad or whether 60 or 70 or 80 is more or less an optimal time to start I'll
leave to others.
Here is the basic idea.
Let's say we have a 60 year old.
The furthest deferred annuity I could see in the market was 25 years out
or starting at age 85. The idea then, in
this post, is to try to hedge out a current spend rate (say 3.5%) inflated to
age 85 and then locked in at 85 and beyond.
In terms of the probability distribution above, it would look like this. The yellowish portion is the probability of living beyond age 85 and is that which we are trying to hedge or annuitize:
Exhibit 4. Hedging age 85+ in the Longevity Distribution
The income we are hedging, with a simple extrapolation, is
35,000 in current dollars (3.5% of $1M, lets ignore taxes and other messy stuff,
or why I picked 3.5%). At age 85 with 3%
inflation, if I got it right, the income requirement is around $73,000/yr rising to
~$98,000 at age 95 and ~114k at 100.
To keep it simple, let's look at a deferred annuity starting
at age 85 using only A++ insurers (i.e., keep counter-party risk down) that covers most of the income need from 85-95, the 73k that rises to 98k and higher. As of June 2016, I found an annuity that
would provide 7983/mo. (or ~96,000/yr). That covers more than the stated requirement at age 85, a little less at 95 and even less at 100. That'll work for now, though. The investment allocation was $175,000. So, if I reallocate 175,000 (or 17.5%,
probably from the fixed income portion of the portfolio) from the $1M endowment into a
deferred annuity I have transformed an uncertain retirement to retirement that
is certain from age 85 forward…if I trust the insurer and don't sweat inflation
or spending shocks. The only thing left for
me to do is plan from 60 to a now certain 85 where there is still some risk, but probably
less. Let's take a look.
First, let's run a baseline Monte Carlo sim for $1M and a
3.5% inflation adj spend, uncertain longevity, .5% fees, 10% avg tax rate,
60/40 portfolio, age 60, no spend shocks or variance, and 5000 runs. First, terminal wealth dispersion (or at
least the first 255 runs of the 5k) looks like this with a vertical line at 85:
Exhibit 5. Wealth Dispersion Sample for a Monte
Carlo Sim Without Annuitization
The longevity distribution in the sim looks like this:
Exhibit 6. Longevity Distribution for a Monte
Carlo Sim Without Annuitization
The fail rate, among other metrics was 8.4%. Not bad but not
great depending on personal thresholds.
Let's say under 10% is good for now.
Now, let's buy the deferred annuity and re run the Monte
Carlo but now with the assumptions as follows
- $825,000 in assets usable to age 85. (still with $1M net
worth including the annuity)
- $35,000 inflated spend rate being spent now from the 825k to age 85
- The allocation of the 825k is nudged to 70/30 to reflect
the annuity allocation
- Age is now capped at 85 since we are not worried about
anything over 85
- All other assumptions are the same
The dispersion looks like this:
Exhibit 7. Wealth Dispersion Sample for a Monte
Carlo Sim With Annuitization at 85
The longevity distribution due to the cap looks like this:
Exhibit 8. Longevity Distribution for a Monte Carlo Sim With
Annuitization at age 85
The result in terms of simulated fail rates (terminal
scenarios where end-wealth < 0) is 5.6% or about a 33% reduction in fail
risk. Not only that, there is now a
fixed certain planning age (85), less uncertainty and worry, and the median end
wealth at 85 is ~1.2M so that we not only have a certain annuity in play we are
more likely than not to have assets above and beyond the inflated 35K annuity
income to spend as well. But even that totally underplays the risk reduction opportunity presented by annuitization because it ignores the magnitude of risk. It would be one thing to run out of money at 84 and live to 100. It is another thing entirely to run out at 84 but have the annuity kick in at 85. One risk is hardly manageable if at all while the other feels like it is acceptable.
That all sounds good but the original question is whether or
how much we can increase spending (for the same or similar risk). If one were to run the MC simulation for
various spend rates on the $825k to age 85, it would look like this if superimposed (dotted red line) on Exhibit
2, the fail rate vs. spending chart I proposed above:
Exhibit 9. Spending Models (Including Annuity Hedge) vs.
Fail Rates
The addition of the annuity has, in effect, pushed out what
we might tentatively call the equivalent of an efficient frontier for retirement spending: same
risk, higher spend; same spend, lower risk.
In this case, for a risk level under 10% (or close enough to the
original 8.4% fail rate) it looks like spending could be raised to about 4% (fail rate around 9.9%) which is about a
14% increase in spending (coincidentally this is also the same as dividing the $1M by the now certain 25 years). Maybe not the big magic I might have hoped for but it's not
trivial either. In practice I probably would not insure 100%
of the spend past 85 (if any), nor would I necessarily buy it all at once right now, but that
is another analysis. Let's just say that
in the presence of annuitization, or pooled risk, spending can increase a little bit…maybe…if
I got the math right.
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