Life Expectancy and Uncertainty

A better title to this post is the question I really wanted to ask: "how wide is one standard deviation in life expectancy estimates for a 58 year old guy in Florida." The answer to this kind of question is more than likely covered better elsewhere in some kind of technical finance literature.  It's probably also only one Google search away but I wanted to run it out myself just to see how it went.

A longevity estimate is a big part of the messiness in retirement math because it seems like it is the one number no one knows, or wants to consider, very well.  Me? I'm 58 so I'm often told to put something like 81, the current SSA average life expectancy for my age, into a retirement calculator or maybe 90 or 95 if I want to be conservative. But that's just "one number" and there is a ton of variance in life expectancy so "one number" has always seemed a little suspect to me.  In this post I wanted to get a better handle on how much variance there really is, in normal statistical terms, and then internalize what that means in real-life especially since it is a major retirement risk factor when talking about financial sustainability over a long retirement for early retirees.  Let's keep in mind here that the last "real" statistics class I took, in a non-online classroom, was in 1987 so I am at least 30 years away from being able to do it exactly right. An actuary I am not. Anyone that knows how to do this precisely can perhaps help me out if they want.

Using the Social Security 2013 period life table for the SS area population I looked at the data for age 58.  And keep in mind here that I'm just looking at the table data. I'm not worrying about changes or trends in longevity or other advanced demographic topics. It's just me looking at the data I have.  For example, this is what the table says to me about the probability of dying for the cohort that is left at age 58: 

Doing a probability weighted average of death age for that particular cohort I get a mean age of a little over 81. That's within a tenth or so of what the SS table gives for average life expectancy for a 58 year old so I guess I wasn’t exactly right but I suppose I'm pretty close which is good enough for me today.  The mode is further out at 86-87.  Then, when I calculate the standard deviation (square root of the sum of the weighted squared errors) I get a result of around 10-1/4 years [1].  I couldn't find a quick validation for this -- for this post -- but I do remember that 9.5 years was a longevity dispersion factor in an equation Moshe Milevskey's used in his "7 Equations" book that I read a couple years ago. So 10-1/4 is probably close enough to right for me for now. 

I'm not that great with skewed distributions [again, correct me on some of this if we need to] so let's step up a level now and think about that number in very general terms.  The average life expectancy from the SSA table as well as from my own math says I've got 'til age 81 to manage an "average" retirement. So far so good. The mode says that maybe 86-87 is maybe an even better, conservative estimate. Then, if one were to go to a more-than-reasonable one standard deviation out from the mean, that gets me to 91 or so. Now let's go plus two standard deviations out, where most of the deaths will have already occured (almost 98% or so in a normal distribution looking at everything to the left of 2 stdev, if I got that right), and it looks like terminal age could be something more like 101 or 102 -- for a very conservative but not totally unrealistic planning estimate.  The oldest living person was somewhere around 120 so that is where I'd stop...or at least this year anyway.  This kind of math is why I think that using the "one number" average in retirement planning or retirement calculators is a little nutty. It's because of all this variability.  You just don't know what the end age is going to be...but then again you still have to plan. 

But now, when we start to look at the full range of uncertainty, from the left side of the chart to the right, it gets even more insane.  The possible full age range for one standard deviation (both + and - the average) is more than 20 years! For me that happens to be anywhere between 71 and 91.  That's a pretty freakin' wide range.  It's a really long, long time in planning terms.  Even weirder to me still, the +/- age range for a not-totally-unreasonable two standard deviation departure from the mean is an astounding 41+ years, or , in my case, ~age 61-102.  In the old days, retirements used to only be assumed to be a simple 30 years total planning range[2]. And now, when you look closely, even if you plan for 30 years[2]... now there is up to 40 years of variance around an end date estimate!?  People didn't even used to live for 40 years, if you go back far enough, and now that is the two standard deviation range of planning uncertainty for some one like me?  How does one even plan for something like that?  Save a lot I guess. Or buy an annuity.  Or work in the public sector. Or move to Belize. Or spend less. Or trust Social Security…or your kids.  Or die young[3]. Or don't retire...or for sure at least don't retire early.     

Postscript:

In a later post, since longevity is not normally distributed and mean and standard deviation are less helpful than in a normal distribution, I went back to recast some of the data in quartiles here.  --->

 

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[1] I'm assuming the reader knows a little statistics and what standard deviations are.
[2] Back when there were pensions and everyone retired at 65 and lives were shorter.

[3] I might get some assistance here from my current eating, drinking, and exercise habits.