Wednesday, November 13, 2013

Longevity Risk Increases with Age

There are lots of proposals for variable withdrawal rate systems out there on the Internet. I'm working on adding a version to the growing list, which, if things work out, will be simpler to follow than others and will also pay more attention to the notion that one's assumptions about future market returns will have a big impact on what will be sustainable.

But one issue I'm trying to work through now is that, regardless of the system, drastic changes need to be made as one's age increases to the 90s and beyond. Ultimately, the case for annuitizing will become increasingly compelling as one reaches extreme ages. Nonetheless, I'm still trying to work through what to do with withdrawal rates at later ages. The issue is that longevity risk increases with age. This is an issue which I was introduced to from a 2010 paper by John Mitchell available from SSRN.

I've made a figure below which introduces the problem. These life expectancies are calculated from a Gompertz distribution using the mortality parameters provided by David Blanchett in this article, which he found by calculating the best fit to the Society of Actuaries 2000 Annuity Tables. These are probably the best general numbers to use in terms of applying to my blog readers, who will likely be more educated and have a higher income that the average person in the population (how is that for kissing up to the audience?).

What the figure shows, for a same-age couple, is their median remaining life expectancy for each age beyond 50. For a 50-year old couple, there is a 50% chance that at least one member of the couple will live at least for just under another 42 years to age 92. By the time they reach 75, there is a 50% chance that at least one will live for a little more than 17 more years to age 92. This is the age range where mortality starts to pick up. If both are still alive at age 92, there is a 50% change that at least one will live for at least 4.6 more years to 96.6, and so on.

What is also shown in the figure are the remaining life expectancies at the 90th and 10th percentiles as well. At 50, 10% of couples will see at least one spouse live for more than another 50.3 years, and 10% of couples will experience both spouses dying in less than 30.7 years. And so on.

What is important to highlight is that the relative gap between median life expectancy and the 90th percentile grows with age. This is because mortality rates are lower at younger ages, and the differences between the median and 90th percentiles only start to build up by staying alive at the higher ages.

So at age 50, 50% of couples will see someone live another 41.8 years, while 10% of couples will see someone live another 50.3 years. It's not that big of difference, relatively speaking.

However, by age 100, for instance, the median remaining life expectancy is 2.1 years, while the 90th percentile is 5.7 years. This is a big relative difference. The implication is that a variable strategy in which withdrawal rates are guided by remaining life expectancy, which I think is an important component of developing an optimal strategy, become much more exposed to longevity risk at the higher ages. This needs a correction, which must be simple in nature to be usable in practice. Hopefully my efforts won't collapse for these reasons and you'll be hearing more from me about this in the future.