Amateur's Abstract:
Using my "hacker's" assumptions and methods on my own personal
data, it is probably fair to say that buying a simple deferred annuity at my current
age to hedge out a lot of late-life longevity risk vis-à-vis spending will
reduce my fail rate risk by some amount that might be "worth it," it
is not fair to say that it matches, dollar for dollar in present value
terms, the gain in spending capacity that it (the deferred annuity purchase
using my own assumptions) engenders. In other words, when it comes to buying a
deferred annuity, the risk reduction benefits might have a case but spending
increases might not given how I'm looking at it.
BACKGROUND
Let's call this analysis a type of personal finance arbitrage
using annuities. I wrote on this before
and the generalized conclusion at the time, subsequently confirmed by other
people's research (I'll link it later), is that one could maybe increase
spending around 14 or 15 %, more or less, by hedging out age 85+ longevity risk
with a deferred annuity. Here is another
take on that same question. Here, I
wanted to see if an investment in the annuity (for me anyway) was
"worth" the incremental increased spending capacity in NPV terms but
now using my new simulator which has a little more "resolution" than
the last time I did this.
ASSUMPTIONS
In this personal case, let's look at some assumptions[1] of
the analysis:
0. Spending is otherwise constant and inflation adjusted, except…
1. I deflect spending down at age 68 when last child
hopefully leaves home
2. I also deflect spending down again to a bare-bones baseline
at age 85+, then…
3. I run a base case with my current assumptions on spending
(and other), then…
4. I run a second case with deferred annuity income that
hedges ~90% of 85+ spending[2]
5. In the second case I reduce assets available by the
amount of the annuity purchase
6. Then, in the third and final case I run trial-and-error sims
to find a spending
level where the
fail rate ~= base case fail rate
and, some other assumptions…
- spending is inflation adjusted from age 59 to ∞ in this analysis, including deflections
- when changing spending in case three, only age 59-85 is
modified
- annuity is
o 25 year deferred, …so annuity
starts at age 84
o assumes I could buy in 3 pieces
due to online quote limits
- assumptions for both inflation and for a discounting
factor are 3%. They wash.
- age 85 - current age=59 is 26, so 26 years of spending
comparison for PV calc
- 30k sim runs are used to speed it up a bit
- contra the last time I tried to do this analysis, where
spending "stopped" at 85, now:
o spending
continues at and past 85 but now all I do is…
o layer on
a non inflation adjusted annuity income source age 84+
- annuity pricing used immediateannuities.com 12/18/16
RESULTS and CONCLUSIONS
Base case:
- fail rate
is around 2.5% given baseline assumptions
- (I think the smaller fail nbr will
skew conclusions a bit…)
Second case (buy a 25yr deferred annuity for $x and reduce
assets by same $x) :
- fail rate
is around 1.9% so let's call it a 24% reduction in "risk"
- that last
bullet point is a sketchy conclusion but let's go with it for now
Third case (increase spending by trial and error to make
fail rates ~= base case):
- spending
can be increased around 6.7% to get to fail rate parity (+/-)
- the PV of
the incremental difference in increased spending age 59-85
is around 23% below annuity purchase cost at time-zero.
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[1] private data but mostly, other than endowment and
personal spending, stuff like: 60/40 portfolio assumption, some tax and fee
effects, SS at age 70, some return suppression first 10 years, random longevity
within a SS distribution, starting age = 59+, etc…
[2] I say 90% because there are some quirks in how annuities
are quoted and the fact that in this post the annuity assumption is not
inflation adjusted so I have to have a little more than I need at age 85 and
less at 100 or 105… There are a bunch of
PV calcs and assumptions that make me say 90%. Let's just call it 90%. This is not really academic research.
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