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Three crucial mistakes about life expectancy

Life expectancy is an important subject, because if you're going to make your assets last a lifetime, you need to make some estimate about how long that lifetime may be. This article explores 3 drivers to understanding life expectancy.



I’ve found that many people have a vague idea about how long life expectancy is, and that it is typically underestimated. 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.

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

Let me make three points about life expectancy.

1. Most people misunderstand the arithmetic


Even if they have heard that in some country (call it Country A) life expectancy at birth is 80 years, they don’t understand that if they have reached the age of 65, the average person can expect to live more than another 15 years (in fact, probably more like 20 years). Here’s how the arithmetic works:

Suppose I asked you for the average of the numbers from 0 to 100. It’s not a trick question. It’s simple arithmetic. You know the answer is 50.

Now suppose we leave out the lower numbers and determine the average of the numbers from 40 to 100? Obviously, it’ll be higher; in fact, the average now rises to 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. Half the people will live longer than that, half won’t reach it.

Now suppose we leave out all of those who die before age 40, leaving us with a smaller group. The average age at death of this smaller group is 70. Half of those alive at age 40 will live longer than that, half won’t reach it.

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 Country A, and interpret those numbers.

The numbers tell us 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 higher than 80; in this case it’s around 85. And that’s why the future life expectancy of someone in Country A 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. You may find a website with a calculator that helps you to estimate your future life expectancy. If your health isn’t average (it may be better or worse), your doctor may be able to help.

2. Averages disguise the unpredictability


Talking about the average conceals the fact that, for any individual, the actual date of death is uncertain. For most people, until they’re near death, their specific future life expectancy is still pretty much unpredictable.

When you make financial plans about the future, it’s important to take this unpredictability into account. There are many ways to do so, the subjects of future posts.

3. The longer life expectancy of one member of a couple


More specifically, 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. I won’t go into the arithmetic. I’ll just tell you why the expected time to the second death is longer than 20 years.

The one with the longer expectancy has a 50/50 chance of living longer than 20 years. The one with the shorter expectancy has some chance (though much less than 50/50) of living longer than 20 years. Between them, they have a bit more than a 50/50 chance. And so for the couple together, the average expectancy to the second death is longer than the longer of the two individual life expectancies.
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