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.


  1. Note that the IRS RMD tables do actually address this indirectly by basing the RMD on the hypothetical lifespan of a couple for which the spouse is 10 years younger than the account owner. For example, at age 92 the divisor (the assumed remaining lifespan) is still 10.2 and at age 100 it is still 6.3. So for those who are single, or whose spouse is of comparable age, the table already corrects (perhaps overcorrects) for this factor.

    1. Thanks. I'm working with the IRS rules too. I think they're too conservative early on and then too aggressive later on. Note that the 6.3 life expectancy implies a 15.9% withdrawal rate, which seems to suggest that the IRS is more keen on having 100 year olds pay their taxes than they are on ensuring that the someone doesn't outlive their 401(k) balance.

    2. You hit the nail on the head Wade ... the taxation over longevity issue is built into the rules ... and, the withdrawal rates exponentially grow (why Mitchell, Blanchett and I wrote paper on muting the exponential nature of any withdrawal rate method (WR% * (1-1/n)). Both of these are reasons RMD based withdrawals are problematic.

    3. On the question of an easy method to adjust withdrawal rate based on current age and uncertain time remaining: here's website with link to paper John Mitchell, David Blanchett and I published, so it's not so confusing or difficult to find.

    4. Thanks Larry. Your system is certainly a key inspiration for me as I'm seeing what I can come up with by starting from scratch. I also want an easy way to allow users to incorporate their own capital market expectations, as well as all of their resources available from outside their financial portfolio.

    5. A few comments about longevity risk and the IRS RMD
      First, the required distributions from deferred income accounts are not optional, so distribution strategies should take this into account. An extract of the RMD table from IRS PUB 590 is show below. It would be interesting to plot this next to the data that you have computed. The IRS remaining life is lower than your the 90% value, but above the median until about age 95, where it is about equal, and is above your 90% line for the duration. The IRS table extends to age 115+, which is about the maximum human lifespan and addresses the black swans who have extreme longevity. It seems to me that any drawdown strategy that is intended to address longevity risk should extend to the maximum human lifespan.
      Rather than being a tax grab, the IRS tables are more actually conservative that they could be. For instance it may be reasonable for the IRS to use the median remaining life, which would accelerate tax payments from deferred income accounts. I believe that the IRS (actually the Treasury Department) could change the rate to the median to increase tax revenue without Congressional action because the RMDs are an administrative matter and are not set by statute.
      The table also illustrates another aspect of longevity risk for those who live beyond the median life expectancy. Those who die at say, 85 can pass their account balance to a beneficiary so that the RMD clock starts again at the beneficiary’s life expectancy. However, the long-lived account holder faces a much higher RMD, and depending on the account balance and other income, a potentially higher tax rate. One way to avoid the high RMD (other than dying) is to draw the account down to a zero balance by age 85 to 90, perhaps by conversing to a Roth IRA.


      IRS pub 590 Table C III
      Age Remaining life Rate
      70 27.4 0.036
      75 22.9 0.044
      80 18.7 0.053
      85 14.8 0.068
      90 11.4 0.088
      95 8.6 0.116
      100 6.3 0.159
      105 4.5 0.222
      110 3.1 0.323
      115+ 1.9 0.526

    6. Thank you. I agree with what you are saying. You are right that it wasn't fair for me to suggest that the RMD rules are a tax grab at the higher ages, because the RMDs could be higher than they are at the lower ages. This fits into my general view that attempts to use the RMD rules as a general retirement income strategy will result in being too conservative at younger ages and too aggressive at older ages. I believe you're points are suggesting this as well.

  2. Is longevity risk associated with the variance in longevity or the number of years of longevity? At 90, the question might be whether I will live 2 years or 12 years, so I might have 10 extra years to fund. At 65, the question is whether I will live 15 years or 35 years, so I might have 20 extra years to fund. The first is a greater percentage unknown, the second is greater years unknown. In terms of dollars needed, a year is a year, so why isn't the greater risk at the younger age?

    1. Good question...

      Based on the way I'm thinking about it now, I'm framing the current year's withdrawal rate based on remaining life expectancy from that point in time. This leads to problems when there is a greater percentage around the remaining time. For instance, if your median life expectancy is 2 years, but there is a 10% change you will live 5 years, it becomes riskier to use a 1/2 = 50% withdrawal rate that year. This is less of a problem earlier on in life when the percentage differences are not as great.

      Of course, there may be a better way to think about all of this...

    2. There is a way ... see the paper I linked to in the prior response. Alternatively, all these thoughts and observations support the conclusions in the paper you, John Mitchell and I are currently writing. There may be an age to annuitize.. However, the conundrum may be they have only 2 years remaining versus the potential 5. This gets to individual choice between which is more important, their income or their bequest. The utility of the research is deeper insight into what factors affect the decision instead of complete lack of those insights not that many years ago.

      An excellent post Wade!

  3. Wade, it'd be interesting to see how actuarial tables differ for joint survivability with couples born in the 1950s, the 1960s, and so on. You'd hate to come up with a variable withdrawal rule for Boomers and find out that it needs to adjust for Gen X.

    1. Doug, this is a good point. Ideally, one would use the cohort life tables based on the particular birth cohorts for each member of the couple. Otherwise, it will be important to make sure the underlying mortality data is up to date and appropriate for the individuals.

  4. Wade, the first thing that come to mind when you mentioned using the Gompertz equation at advanced ages was this warning by Moshe Milevsky in his book, "The 7 Most Important Equations for Your Retirement", page 48:

    "at advanced ages there are serious problems with the Gompertz law of mortality. Centenarians are especially guilty of breaking that law."

    Have you taken some "behind the scenes" steps to overcome the weakenss that Prof. Milevsky is referring to?


    1. Thanks for the reminder to do that. I think the key is to be a bit more conservative when dealing with these higher ages, but I haven't specifically looked into this year.

  5. Wade, just to add another wrinkle, actual health statuses are likely much more diverse and revealing at 95 than at 65. So there's likely to be quite a bit of individual information available on a group of 95-year-olds that's not revealed by the general statistics. Also, I need to take a look at the Gompertz vs. SOA tables and the Blanchett research. I had started to do that a few weeks ago and got sidetracked. Joe.

  6. To Joe's point: I'm working on a case now where an 83-year-old woman with health issues is considering whether to begin distributions on an annuity. Her husband is 92 with fewer health issues. His pension is joint with her, but her pension is for her life only. Would taking joint life distributions on her annuity provide him with any useful protection if he outlives her? Is there a potential statistical arbitrage here, given the counterintuitive health profiles? (Family longevities are indeterminate.)

    1. Eric,

      I'm not sure I fully follow your question. Do you mean the woman has a choice about whether to annuitize as joint or as single (or not at all)? It seems that if it is joint, the pricing would be based on their respective remaining lifespans, and they would lose out because her lifespan may be shorter than a typical 83 year old. Must she annuitize? If she must, then I think I see your point that there could be potential here for them to be better off with the joint annuity. Is this what you are getting at? It's an interesting question.

    2. Wade,

      The choice is to annuitize or not. Evidently the annuity has reached some kind of maturity date but it can be extended. Or, she can annuitize it, in which case the usual joint or single choices, with or without guaranteed distribution periods, apply.

      I thought this was a vivid illustration of Joe's point that the older one gets, the less generic/statistical and the more situation-specific things become.