# Three life tables; how long till you die.

The Withdrawal Efficiency Rate (WER) calculation requires a monte carlo simulation where you need to simulate both market returns and mortality. Then you can combine the two to create a perfect kn0wledge retirement plan, which you then compare various strategies (that don’t have perfect knowledge) against.

Take the following scenario:

- You retire at age 65
- You die 17 years later at age 82.
- The market returns are: 26.0, -9.0, -5.2, 8.6, 14.4, 3.9, 28.7, -5.4, -8.1, 2.0, 14.9, 7.2, 7.8, 3.3, 3.0, -15.6, -2.7.

Then you could **actually** take out 8.9% from your portfolio every year, leaving exactly $0 when you die.

If your withdrawal strategy has you only taking out 3% a year then it’s Withdrawal Efficiency Rate would be 3/8.9 or 33%. You only spent 33% of the money that you ** could** have spent.

One interesting effect of all this is that the life expectancies you use in the monte carlo simulation can have a fairly dramatic impact on the results. In general, the longer a population lives the better most withdrawal strategies fare in a WER analysis. That’s because these strategies are basically trying to self-insure against longevity and if you die early then all that expensive self-insurance goes to waste.

When I first implemented the above, I used a life table I found on Michael Kitces’s great website: https://www.kitces.com/joint-life-expectancy-and-mortality-calculator/. If you download the Excel file you’ll see that it says it is based on the “Period Life Table, 2004”. It doesn’t provide any further attribution.

When I first compared my WER results to those in Blanchett et al’s original paper, they were always off by quite a bit (e.g. instead of 46% WER I would find a 38% WER for a certain scenario).

This caused me a lot of frustration.

Until I figured out the problem: Blanchett et al were using a different life table than I was. After a bit of digging, I have turned up ** three **different life tables.

On the surface, this is a bit surprising. Is there really a disagreement on how long Americans are living? Shouldn’t everyone find the same results?

To show you an example of how the three tables vary, let’s look at the “chance of dying in the next 12 months” for an American male aged 80.

`Table 1: 0.068836`

Table 2: 0.066557

Table 3: 0.046037

That’s a pretty big gap. The difference between Table 1 and Table 2 isn’t large…but even small differences add up. Table 1 gives a slightly higher chance of dying every single year along the way. Starting with 100,000 males, 80 years later Table 1 says only 45,747 are still alive. Table 2 says 46,461 are still alive. That’s an extra 714 people still alive.

But Table 3 has a very large gap. It says there would be 62,565 still alive.

It turns out that Blanchett at al. were using Table 3 (with the most longevity) and I had been using Table 1 (with the least longevity).

Once I switched over to using their data source, I was able to replicate their results more closely.

How can there be disagreement about how many Americans are left alive? Creating these life tables actually has a fair amount of “creative interpretation” to fill in missing gaps and smooth things that are assumed to errors in the underlying data. I have one life table that has the following note:

A loading of 10% was deducted from the Annuity 2000 Male Basic Table and quin ages from 7+ were graduated with Jenkins. Then a Jenkins smoothing and a cubic to close from 95+ The calculated mortality rates were adjusted to remove a small dip in the mortality rates in ages 33–35. The official table runs from ages 5+, unofficial extension values for ages 0–4 were added by R.S.Lumsden using the standard extension of a-1949 as a base.

The biggest factor here is the first sentence: “A loading of 10% was deducted from the Annuity 2000 Male Basic Table”. What this means is: “we took the mortality rates from the basic table and then tweaked things so that everyone lives longer.”

It sounds arbitrary (and I’ve seen no explanation for why 10% was chosen as opposed to 8% or 12%) but there’s actually a method to the madness.

The more money you have, the longer you tend to live. What I’ve called “Table 3” is actually Annuity 2000, which was created by the Society of Actuaries for insurance companies to use. And insurance companies know that the kind of person who buys an annuity generally lives longer than someone who doesn’t buy an annuity. (For instance, people with terminal conditions do not buy annuities.)

When we’re talking about fancy retirement plans we need to keep in mind that very few people in the bottom half of the income scale are in the target audience. So including them in life tables when running simulations skews the picture. It is bad for the person (since they die sooner) but it is good for the portfolio and the withdrawal strategy (since it doesn’t have to support withdrawals for as long).

The most conservative choice is to use the Annuity 2000 life tables in these kinds of conversations. Which were actually created in 1996 and are thus 20 years out of date!