Tuesday, July 9, 2013

Life Expectancy Grows with Age

This post provides an illustration of a simple idea that many readers will understand, but it may still provide "Aha" moment for some readers.

The idea is that your life expectancy continues to grow as you age, so that the number of expected remaining years in your life will decline, but it declines at a slower rate than your increasing age.

This is illustrated below using median life expectancies, where there is a 50% probability of living past a certain age. This distribution is based on the Gompertz probability distribution function (which I will write more about that later time). The idea is that age 65, the person has a 50% chance of living 21.85 more years to just below age 87. The blue curve shows the remaining lifespan based on this age 65 calculation. By age 87, the number of remaining years is zero. Subsequent ages are beyond the age 65 life expectancy.

The red curve, on the other hand, shows the number of remaining years one has a 50% chance of still living, given that they've already survived to each subsequent age beyond 65. This is how things really work. Someone who is age 80 now has more than a 50% chance of living beyond age 87. They actually have a 50% chance of living to age 90. They can expect 10 more years. For someone who has lived to age 90, the remaining life expectancy is not zero. Given their age, they can still expect a 50% chance of living five more years.

This explains why it is a big mistake to use life expectancies at birth when thinking about how long one will live in their retirement. Once one has reached their retirement age, they should to live much longer than their life expectancy at birth because they were not a part of the population that died before the retirement age.

 

11 comments:

  1. Excellent post Wade, and to the point. The dynamics of a changing distribution period, based on remaining life expectancy, has big implications for managing resources so one doesn't outlive them. A big reason for annual reviews to update everything that were last year's assumptions, with this year's facts.

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    1. Thanks Larry, I wrote this as I was reading the big article, about which you should now have an email.

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    2. Gompertz - interesting. Are you planning to go hardcore and address the potential failings at more extreme ages? IIRC, Gompertz had some issues with Centarians/Supercentarians (but what model doesn't?)

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    3. Hi, thanks for the comment. No, I'm not really aiming to dig into that. It's a better topic for demographers to worry about. I'm just looking for something that is "good enough" to give helpful results.

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    4. Works for me, haha. I think living past 100 (or 110) would be quite an interesting problem to have. Nice piece.

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  2. Hi Wade, judging by the fewer comments on this post compared to other posts I'm wagering a guess that the implications about longevity to retirement planning this post brings up hasn't resonated with many readers.

    Retirement income withdrawal rates, using any method including stochastic or deterministic, require that a time be set for the distribution period. The implication of the red line is that the time period does not shrink as fast as the blue line. Thus, if one uses the blue line approach/assumptions in income calculations, the result is over spending relative to how much life may be remaining.

    It may be tempting to think that the retiree doesn't need to worry about this until they reach 80, for example. However, the overspending will have occurred prior to that and thus, the remaining portfolio balance would be less compared to properly adjusting the time period for probable years remaining. The result of a lower balance is a much lower retirement income ... relative to managing the amount of the income over the prior years based on probable time remaining.

    In sum, the effect of returns on income may be more exciting. However, the impact of which distribution period is used has a much greater relative effect on the question of prudent and sustainable income into future older years.

    A great post which illustrates why distribution period is as much, or more, important to evaluation of retirement income. This is not a set and forget process, rather a dynamic one that requires annual review.

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  3. The red curve is defintely an improvement but perhaps the most practical curve would be one that shows not the average life expectacy but the age that one will have a 95% chance of not living beyond.

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    1. Thanks, I will try making one of those once I'm back to my work computer. I do have a feeling that such a figure will be less sensitive, i.e. the age that you have a 5% chance to outlive will increase more slowly over time as it will mostly be affected by the higher mortality rates coming at the later ages. In some sense that could get back to the idea people have of assuming a long retirement horizon which one is unlikely to outlive and then holding off making further adjustments until one is quite old. Though as one becomes quite old, at some point they may have a much harder time managing their retirement income strategy and maybe their advisor is getting old and entering retirement too.

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  4. So true. I remember reading this article on Cracked saying how the "every died at 40 during the Middle Ages" is just a myth. The reason why the average life expectancy was so low is because a lot of people died as children. If you made it past your first couple of years, 50 or 60 years was reasonable to expect.

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  5. Hi Wade.

    In response to your post, I crunched a few numbers using the Society of Actuaries life expectancy calculator to quantify the risk associated with developing a spending plan based on life expectancy (recalculated every 5 years with approximately a 50% probability of outliving the payout period) vs. one based on a 30% probability of outliving the payout period. I believe that the tables included in my post

    http://howmuchcaniaffordtospendinretirement.blogspot.com/2013/07/plan-on-living-to-95.html

    support your post and Mr. Frank's comments

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