Friday, August 19, 2011

“Joint Life Expectancy and the Retirement Distribution Period”


Today’s classic withdrawal rate study is “Joint Life Expectancy and the Retirement Distribution Period” from the December 2008 Journal of Financial Planning. The authors of this study are David M. Blanchett and Brian C. Blanchett.

I just read this article today, but I realize that in answering Mike Piper’s question about the portfolio failure rates when using life expectancies for a married couple, I had replicated the main results of this article.  It is nice to obtain confirmation that my calculations were on the right track.  And this article is quite interesting in its own right for articulating these issues about considering portfolio success (or failure) rates using actual life expectancies rather than fixed retirement periods.

Just one quick note, which I will bring up again later: this paper uses the 2004 Social Security Administration Period Life Tables, whereas the results I will discuss here use the 2007 Social Security Administration Period Life Tables. Already, in that 3 year span, people are living a bit longer, so my results will refer to slightly longer lifespans that what you find in the article. 

Here are the survival rates (at least one member of the couple is still alive) for a 65-year old opposite-sex couple using this data source:



As I’ve explained before, despite the low probability for retirees living so long, many retirement studies assume a fixed retirement duration of 30 years. I’d say that this article has two key points:

1. It is wrong to assume any fixed retirement duration.  Early retirees may expect to live much longer than 30 years.  But for a typical person retiring at around age 65, it is too conservative to assume such a long lifespan as it will needlessly cause someone to use too small of withdrawal rate. Instead, consider how long people might actually expect to live.  The probability of running out of wealth should be defined as the probability of running out of wealth before death rather than for an arbitrarily long period of time.

2. As well (and this was Mike Piper’s point in his earlier comments), don’t use a single individual as a baseline case.  Most retirees will be married and will be more interested to know about the case of their joint life expectancy: how long will both or at least one of them remain alive?

First, about the issue of how assuming a longer lifespan than necessary will result in too low of withdrawal rate, the following figure is a preview from a paper I am halfway through writing now [this is not the withdrawal rates 2.0 paper, but another paper that I was already doing before learning about that one].  It is not part of the main point of the paper, except that it shows a range of asset allocations which get nearly the same withdrawal rate as the optimal asset allocation.  But for now, the point is that if a retiree is willing to accept a 10% failure rate, then with a 10-year horizon a 10 percent withdrawal rate is supported, and this is 7 percent for 15 years, 5.7 percent for 20 years, 4.9 percent for 25 years, 4.3 percent for 30 years, and so on.  As such, someone planning for the 30-year case but who may only reasonably expect to live for 20 years at most will end up using a withdrawal rate that is 1.4 percentage points less, meaning in turn that their annual spending will be 25% less than possible.


 

To see why this can be too conservative, consider the case for a married couple both aged 65. They are willing to accept a 10% chance for failure before death (which means in practical terms that they want to get a bit higher withdrawal rate understanding that they face a 10% chance of running out of wealth at some point and needing to rely only on Social Security or other income sources for the rest of their lives).  Following the traditional path, they plan for a 30-year retirement duration to be conservative.  But, there is only a 17.1% chance that either or both of them will still be alive 30 years later (for men, there is a 5.9% chance to live another 30 years, and a 12% chance for women to live 30 years, and with their lives being of independent length, the math works out to be a 17.1% that one or both of them are still alive).  If we can assume (which is reasonable) that someone’s life length is independent of market returns, then the chance of running out of wealth by 30 years needs to be multiplied by the probability of living that long anyway.  There is really only a:

17.1% x 10% = 0.171 x 0.10 = .0171 = 1.71%

1.71% chance of running out of wealth, given the unlikely nature of living for another 30 years.  Thus, while they were willing to take a 10% chance of failure, by assuming a 30-year lifespan, they are really only taking a 1.71% chance of failure, which is quite a bit smaller than their willingness.

Making this correction by considering survival probabilities in the calculations, here are what the failure rates look like for different withdrawal rates and asset allocations (using Monte Carlo simulations based on the 1926-2010 data parameters from SBBI for large-cap stocks and intermediate-term government bonds). Here, failure is defined as the wealth being depleted while someone is alive. This is based on 10,000 simulations, in which each simulation is accompanied with an age of death for each member of the couple. As I mentioned, this is a visual interpretation of the results provided in Table 3 of the paper (though Table 3 only shows for one asset allocation choice). I do notice that my failure rates are a bit higher than theirs, and this relates to my also getting a bit higher failure rates in the equivalent of their Table 2. They are using a different portfolio of assets, including Treasury bills and international stocks, which probably explains these differences.






A couple willing to accept a 10 percent failure rate could choose a withdrawal rate closer to 5% than to 4%. This figure doesn’t show the exact value.  As can be seen in the first figure above for joint survival rates, there is a 50% chance than one or both will live to age 89, so their joint life expectancy is 24 years past 65.  This supports a bit higher rate than if they had assumed a 30 year retirement length (that first figure above also does show that survival rates plummet rapidly in this age range… while there is a 50% chance that one or both of them makes it to 89, I already mentioned above that there is only a 17.1% chance that one or both of them makes it another 6 years past that to age 95).

So, I think this is a very informative and worthwhile paper.  I basically described the paper’s findings in my own words here, but this paper provides a previously published source for these ideas.

Two quick comments about the data choice, though.  One is found in the paper, and it is that people who will actually be reading this and making thorough plans for retirement will tend to have above average earnings and education, and so they can expect to live longer (on average) than the population-wide averages found in the data. 

Second, my point is that this data choice will underestimate lifespans.  The 2007 data uses mortality rates from 2007.  For instance, what percentage of 80-years alive in 2007 died during the year?  But lives are getting longer and longer each year, and by the time that current 65-year olds reach age 80, they will certainly experience lower mortality rates, which means they will live longer than the data implies. This is already known by actuaries.  The Social Security Administration also provides “cohort” life expectancy data which account for this fact, rather than the “period” data that I and the Blanchett and Blanchett study are using now.  A more complete investigation should switch over to “cohort” life expectancies which incorporate forecasts for future mortality rates.  More about this from the Social Security Administration can be found here.

To bring things into full circle, it might not really be that much longer before the joint life expectancy (at least one is still alive) for a 65-year old couple is another 30 years! Again, though, that doesn’t make things equivalent to assuming a fixed 30-year duration though, because there would still only be a 50% chance of someone making it that long. And that’s the point about using survival rates.  If someone accepts a particular chance of failure, it should be the chance of failure while still alive, rather than the chance of failure for an arbitrarily long period of time.  I’m much more convinced about the usefulness of survival rates now, which makes this blog a nice record (for myself, anyway, I’m not sure if anyone else will care) about the evolution of my views, since I wasn’t too keen on this before.