## Why do so many people misunderstand life expectancy? Is it the arithmetic or the concept? Let’s take a look. (Spoiler alert: the arithmetic is simple.)

I’ve found that many people have a vague idea about how long life expectancy is, and that typically they underestimate it. It’s an important subject, because if you’re going to plan to make your assets last a lifetime, you need to make some estimate about how long that lifetime may be.

This is an attempt to explain it. I know that it’s too simple for geeks. I have no idea if it’s the right level or too complicated for the non-expert reader. So I’d really like your reaction to it — please!

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Let me make three points about life expectancy.

The *first* is that *most people misunderstand it*. Even if they have heard that in some country life expectancy at birth is 80 years, they don’t understand that, at age 65, the average person there can expect to live more than another 15 years (in fact, probably more like 20 years). How does the arithmetic work?

Here’s a way to understand it.

Suppose I were to ask you what’s the average of the numbers from 0 to 100. It’s not a trick question. It’s simple arithmetic. You know the answer: it’s 50.

Now suppose we leave out the lower numbers. What’s the average of the numbers from 40 to 100? Obviously, it’ll be higher; in fact, the average now rises to (yes, you know this answer too) 70.

It’s similar with life expectancy.

Suppose we encountered a peculiar population of 100 people in which one person dies before the first birthday, one dies between ages 1 and 2, and so on, the last one dying between 99 and 100. What would be the average age at death? Again, not a trick question: it’s 50.

Now suppose we leave out all of those who die before age 40. What’s the average age at death of this smaller group? Again, not a trick question: it’s 70.

So, what does this tell us about the life expectancy of this peculiar population?

It tells us two things. First, at birth, if we don’t know which person we’re talking about, all we can talk about is the average, and for the average person, then, the life expectancy is 50 years. Second, if we consider only those who have survived until age 40, and again we don’t know which individual we’re talking about, their average age at death is 70. Their *future* life expectancy, once they’ve reached 40, is another 30 years, because that’s what “life expectancy” means: it’s the average number of *future* years to be lived by the average member of a well-defined group.

Notice that the people in the second group (those who have survived to age 40) are also members of the first group (the entire population). But the two groups are not the same, even though they contain some identical members. The second group excludes those who have already died before 40; that makes it a different group, and a longer-lived group. So, if we are to define life expectancy, it’s important to define the group we’re talking about very clearly.

OK, now let’s go back to the country in the first paragraph, and interpret those numbers.

What the numbers tell us is two things. First, if you include the entire population, the average age at death is expected to be 80. Second, if you exclude those who have already died before age 65, and include only those who survive past that age, their average age at death is of course higher than 80; in this case it’s around 85. And that’s why the future life expectancy of someone in this country who has already survived to age 65 (a smaller group) is a further 20 years, not the 15 years that people often misunderstand it to be.

Life expectancy tables vary by gender (typically, the life expectancy of a female is longer than that of a male), by country, by race – all kinds of factors, in addition to age.

Talking about the average conceals the fact that, for any individual, the actual date of death is uncertain. If there’s something in your family history, or your personal health record, that makes you suspect you may be longer-lived or shorter-lived than the average group of people who have survived to your age, see if you can find a way to estimate what this might mean for your future life expectancy.

Your doctor may be able to help. There are websites with calculators that purport to help you make adjustments.

Whatever they do, however, is still not a prediction. For most people, until they’re near death, their specific future life expectancy is still pretty much unpredictable.

And so, here’s my *second point*: when you make financial plans about the future, *it’s important to take this unpredictability into account*. (I’ll show how, in the book, perhaps also in a later posting on this website, if readers request it.)

My *third* and *final point* relates to the life expectancy of a couple. More specifically, this relates to how long before the *second *death of the couple. Techies call this the “joint and last survivor” life expectancy. It’s important because it’s necessary to provide for the longer-lived member of a couple, whichever one that may turn out to be.

Suppose there’s a couple whose individual future life expectancies, at some point in time, are roughly 15 years and 20 years. How long until the second death?

Most people say: well, after 15 years you expect one to die, and after 20 years the second one will die; so it’s 20 years to the second death, right?

It actually turns out to be a little more complicated than that. So I won’t go into the arithmetic, I’ll just try to give you a general explanation of why the expected time to the second death is *longer* than 20 years.

Consider the person with the longer (20 year) expectancy. For this person, it’s more or less a 50/50 chance of living longer than, or less than, 20 years. (That’s why the expectancy is 20 years for a group of people like that person.) Now, what about the other partner in the couple? That partner has a 50/50 chance of living longer than 15 years. And a smaller chance than 50/50, obviously, of living longer than 20 years. A smaller chance, yes, but *some* chance nevertheless. And it’s that *some* chance of living longer than 20 years that, combined with the first partner’s 50% chance of living longer than 20 years, means that the couple has *more* than a 50% chance of having one of them live more than 20 years.

And that’s why, for the couple together, *the average expectancy to the second death is longer than the longer of the two individual life expectancies*.

As part of your overall education, I’ll include in the book a table showing not only average life expectancies and average-to-second-death expectancies, but also something about the amount of uncertainty in those averages. For now, here’s the takeaway.

## Takeaway

*Life expectancy is not only uncertain, it’s also typically underestimated, particularly for a couple*.

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By the way, one of the things I’d like to do in the book is to provide a list of resources available on the internet for people in different countries to get an estimate if their future life expectancy. If you know of, or have used, a useful resource in your country, do let me know about it. Thanks!

### 8 Comments

I have written about retirement planning before and some of that material also relates to topics or issues that are being discussed here. Where relevant I draw on material from three sources: The Retirement Plan Solution (co-authored with Bob Collie and Matt Smith, published by John Wiley & Sons, Inc., 2009), my foreword to Someday Rich (by Timothy Noonan and Matt Smith, also published by Wiley, 2012), and my occasional column The Art of Investment in the FT Money supplement of The Financial Times, published in the UK. I am grateful to the other authors and to The Financial Times for permission to use the material here.

I like this explanation of life expectancy. I think it could be improved by mentioning the point about the 50/50 aspect of life expectancy nearer the front. In your example you could add to the calculation of the average of 50 the fact that 50 of the people, which is half the group, live longer than the average and half live shorter than the average. This will help cement this idea for when you later talk about it in the context of couples.

Thanks, David. Now that you’ve pointed it out, yes, it’s the obvious place to explain that the expectancy is the average, not (as some people think) a prediction of the limit of life; so half of the group in question will outlive it and half won’t. Thanks for doing it for me!

Since you asked for readers’ reactions, I thought I would share mine: I found the explanations simple and easy to understand (and perhaps even more so when David Hartley’s comments are taken into account). And they wetted my appetite for what is coming and for incorporating this into my own retirement planning.

I am assuming from what you have written here, that this is how companies selling retirement products operate. By way of example, if I were the sixty-five year old you mention and was about to buy an annuity, the provider of the annuity would do its calculations on the basis that I would survive until eighty-five (the average number of future years to be lived by the average member of sixty-five year olds), not eighty. Have I got that right?

Great question. In principle, yes, you’ve got that right. The provider would actually take it a step further. Since they’re providing a guarantee, they want more than a 50/50 chance that your purchase price is adequate. So they’d base it on your living beyond age 85 — let’s say 88 or 90.

Don, great section on life expectancy. I now understand it a lot better. Given that “the average expectancy to the second death is longer than the longer of the two individual life expectancies”, I have decided to go second. This will save me a lot of money as I was planning to move to Japan when I reached the average age expectancy for men in Canada, as Japan’s average age expectancy for males is two years longer than in Canada. I could use those extra two years.

Oh, to have your sense of humour! I love it! You deserve the extra two years, for that alone.

Don, From my observations married men who outlive their spouses tend to die sooner than their normal life expectancy.

Probably we have to be “nagged” to see a doctor, take their meds or to put on a sweater.

That’s an interesting angle! I’ve never seen statistics on it. Presumably one would identify three categories of men alive at any age: (a) married men with the spouse alive; (b) married men who have outlived the spouse; (c) men who were never married. It’s purely a guess, but I wouldn’t be surprised if the life expectancy is highest for (a), then (b), then (c), since marriage seems to increase expectancy. Whether (b) is lower than the average of a, b, c is something I have no idea about. (But from a personal perspective, I’m grateful to belong to category a!)