A riff on Hoffstein's "Lie of Averages"

The other day, Corey Hoffstein did a great piece over at thinknewfound on the concept of the lie of averages. And I'm not just saying that because it did a big favor to me by highlighting and complimenting one of my better posts (but, well, ahem...ahem, you know, um, well....[dialogue drifts off...we hear whistling and someone kicking the dirt while drooping their head over their feet]).  So I thought I'd do a little riff on the lie of averages concept, too.  In this case I'll be looking at how calculating means can be deceiving in retirement planning if more extreme realities were to come into play for two particular variables (portfolio and personal longevity) for some given individual.  I don't know if this is exactly his point but it's probably a good tangent either way.

For this we will look at two things: 1) the concept of portfolio longevity and its possible distribution, profiled in one of my recent posts, and 2) the distribution of personal longevity expectations for a 59 year old male (me) using SOA annuity table data.  Using the same illustrative but very conservative, maybe unrealistic assumptions for returns (2% real, 10% vol) and a rudimentary spreadsheet sim for wealth depletion (along with a 4% spend) we might expect a mean portfolio longevity of something around 38 years or let's call it to age 97. We might also expect a mean personal longevity, using the more conservative SOA table (vs the SS life table), of around age 86 or 87.  Looks pretty good. This should work, right?  If we were to plot the PDFs of personal and portfolio longevity with the mean expectations of each highlighted in the same color it'd look something like this:

So far so good.  But now let's play a different version of the same game. Let's say a certain reality were to come into play where the portfolio longevity happens, in real life, to fall into the 5th percentile (that's bad) and where the personal longevity happens to fall into the 95th percentile (that's good, I want to believe, but that's also kinda bad from a financial planning perspective). Keeping the other assumptions the same it'd look more like this with the vertical lines representing the 5th percentile (blue) and 95th percentile (green) of their respective distributions:

Hmmm.  Depending on how you do the math and round and stuff, there is potentially a 21 year gap between when the portfolio fails and when one (me) actually checks out.  This is why people simulate themselves silly and also why people annuitize optimally sometime before age 85.

But wait, what if we spend less and also engineer a little higher real return in our sim world?  Let's go to a 3% spend (these are constant spends by the way so maybe not flexible like real life but it helps make the point) and a 3 % real return and re run this.  In that case, if I got it right (keep in mind also that I am not doing a very sophisticated sim here) it'd look like this:

Ok, so better, but not perfect. This is the kind of thing that can gnaw at you and why people sometimes keep pestering their advisors for simulation work. This also why, just like I mentioned above, annuitization can play such big (and underappreciated) role in planning[1][2].  It's because that "mean thing" will get ya if you are not careful. While the extreme 5/95 expectations I'm playing with here are a type of "untruth" themselves, the means like to lie a little bit, too.


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[1] said by the guy with no annuities and no annuities on the table...

[2] this is why I also focus so often on spending as a primary lever.  I know I can't do much about longevity (sort of not true but also why I joke that my new year's resolution should be "drink more and start smoking") but I can influence that portfolio longevity part by making intelligent choices about: 1) spending, 2) wealth in terms of working or working longer, and 3) portfolio returns via asset allocation and any related tactical maneuvers. BUT, since sometimes #2 is out of our control and since #3 comes with baggage in the sense that higher return often comes with a higher vol that'll do funky things to that portf. longevity distribution curve, that means that spending is the one clear way to influence that time gap implied in the charts above.  You know, I gotta say here in my little footnote cum rant that I've been disappointed recently that I've had way too many people chide me for my grip on spending but here's the deal: a) I know they won't be there for me if and when it doesn't work out, b) I know also that they are blind and cannot see...they have no clue about their own risk (heh heh heh...) b) they are not parents to my children, and c) my spending is already (statistically, temporarily, and intractably for now) pretty high so I don't really feel like a life-sucking solipsistic tightwad yet.  I actually think I should still be cutting hard even more and if there are any cuts that do not somehow accrue to my plan for me and my kids then that windfall, such that it would be, should really go to help others that need to solve this problem themselves rather than to some kind of unnecessary consumption that would supposedly make my personal critics happy.