Another Stab at a Longevity Hedge Analysis Using Simple DIAs

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.

(Apologies in advance.  I tested this on my own data which means I'm not giving personal details to the internet.  I'll give general % changes and other vague results but that's about 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.

           

notes

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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.