Article

A basic question about life expectancy that even actuaries struggle to answer

December 4, 2018

A basic question about life expectancy that even actuaries struggle to answer

Willis Towers Watson Media  
Bob Collie
 
Do you know what the average life expectancy at birth is where you live? Most people can make a decent guess; most actuaries can tell you pretty accurately. (Answers are at the end of this post, for a few of the larger countries.)

But do you know what the standard deviation of that number is? Not many people do. It’s a new concept to most people: for some, their first response is to wonder whether life expectancy even has a standard deviation. The typical actuary says something like “Hmmm… I’ve never thought about that before.”

Don Ezra has told the tale of hitting age 60 and wondering about this. So he worked out the standard deviation of a 60-year-old’s life expectancy himself, and then asked five friends what they thought it might be: “Three of the five people thought 5 years, one thought 10, one thought 15. It turned out to be a little more than 9 years.” So most of the guesses were pretty far off.

Contrast that situation with investment returns. Investment professionals spend a lot of time thinking about the expected return on investment strategies, and those expected returns almost always come accompanied either by an expected standard deviation or by some other measure of uncertainty. It’s usually not enough to know what the average outcome is likely to be: you also need some idea of the distribution around that average.

As Don (along with Matt Smith and myself) went on to note: “We would make completely inappropriate asset allocation decisions if our estimates of the standard deviation [of investment returns] were 50 percent off the mark. Yet that may be the state of affairs with the uncertainty of longevity. If we don’t have a rough, intuitive idea of how large the uncertainty is, we will make decisions that are totally inappropriate.”1

Now that three of the largest pension markets (US; UK; Australia) are firmly on the path to becoming mainly DC systems, the standard deviation of life expectancy has become just as important as the standard deviation of investment returns.

That’s because a DC plan is supposed to be able to support participants throughout retirement. TAI’s latest research paper Lifetime income – the DC system’s missing design feature notes:

“When a DC plan participant retires, they move from the accumulation phase into the payout phase, and this introduces an additional unknown into the pension management equation: we do not know how long an individual will live.

“This is a bigger challenge for the DC system than it was for the defined benefit (DB) system. DB is a pooled system, so the uncertainty associated with longevity revolves around how long the average participant lives. That’s something that we can be reasonably confident about. In contrast, DC is focused on the individual.“

So the uncertainty in life expectancy should be just as basic a planning consideration as the uncertainty in investment returns. It’s time to pay more attention to the standard deviation of life expectancy.
 
Exhibit 1. Average life expectancies – and standard deviations – at birth for selected countries:
Country Life expectancy
(female) 
Standard deviation Life expectancy
(male)
Standard deviation
Australia 84.8 13.3 81.0 14.8
Germany 83.3 12.7 78.7 14.1
Japan 87.1 12.7 81.1 13.8
UK 83.2 13.5 79.7 14.7
United States 81.0 15.9 76.0 17.6
Source: WHO Global Health Observatory (2016 data) & author’s calculations
 

Exhibit 2. Average life expectancies – and standard deviations – at age 65 for selected countries:
Country Life expectancy
(female) 
Standard deviation
Life expectancy
(male)
Standard deviation
Australia 22.5 8.3 20.1 8.5
Germany 21.1 8.1 18.1 8.3
Japan 24.4 8.3 19.6 8.5
UK 21.2 8.4 18.9 8.5
United States 20.7 9.1 18.1 9.0
Source: WHO Global Health Observatory (2016 data) & author’s calculations
 
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1 Ezra, D., Collie, B. and Smith, M.X. (2009) “The Retirement Plan Solution: The Reinvention of Defined Contribution” John Wiley and Sons.