STUMP » Articles » Geeking Out: Public Pension Mortality Assumptions » 27 June 2018, 07:53

Where Stu & MP spout off about everything.

Geeking Out: Public Pension Mortality Assumptions  


27 June 2018, 07:53

You guys.




Some years back, I noticed the Society of Actuaries asked for public pension plans to submit their mortality experience. The SOA has done a deep dive on private pension mortality experience, and their studies there have been very interesting. But they haven’t yet done a public pension mortality experience study.

Now, what they have to show is not necessarily experience… but it’s something.

The new SOA report: U.S. Public Pension Plan Mortality Assumptions

But before I get to that, check this out: The Kinks frontman Sir Ray Davies reveals the group are getting back together after being disbanded in 1996

The group had a string of hits in the 1960s including You Really Got Me
Sir Ray, 74, said he was inspired by Rolling Stones who just finish a tour
The Waterloo Sunset and Sunny Afternoon singers disbanded in 1996

As Bill Berman remarked to me: “yet another reason to update mortality tables”

A comment, for a moment: life expectancy in retirement has been increasing – but it’s not just longevity that has been increasing, but the length of healthy life has been increasing. I may discuss this another time, but not today.


The SOA had these two key findings from their initial investigation:

The Retirement Plans Experience Committee (RPEC) and the SOA are working on a mortality study specifically for public pension plans in the United States. Based on RPEC’s preliminary findings, results of this analysis suggest that mortality assumptions for many plans may be lagging behind current aggregate mortality experience among public plans.

Mortality assumptions for teachers tend to reflect longer life expectancies than for other job categories. For females, mortality assumptions for public safety employees tend to reflect shorter life expectancies than for general employees. Assumptions for males reflect the opposite.

Yes, that bolded is key, but this is more an investigation into valuation assumptions than an analysis of actual mortality experience. I’m going to focus on the assumptions and what they mean.


The report is actually here, and I’m going to walk through the exhibits and explain what they mean.

First, they do not show life expectancy… because, frankly, life expectancy is not what we use when we actuaries calculate what is called “actuarial present value”.

What they show are annuity factors and here is what they have to say:

All annuity factors shown are for immediate single life annuities at 7% interest with 2% annual benefit increases. These assumptions are for comparison purposes only and not intended as endorsement of their appropriateness for funding these plans or for any other purpose.

Actuarial Present Value (APV) is like regular old present value (PV), but in regular PV, you have certain cash flows, and you’re discounting those certain cash flows at a certain interest rate.

In APV, you’re also factoring in the probability that the cash flow will be paid.

So APV can help you get an idea of how much a contingent promise is worth — given certain interest rate and mortality assumptions, and in this case we have a cash flow increasing 2% per year as well. I didn’t see if the payments were monthly ot annual, but that has a minor effect on the final factor.

The higher the interest rate, btw, the less small differences in mortality assumptions matter. The lower the interest rate, the more it does matter.

Anyway, the annuity factor tells you what a $1 annual base payment is worth — so if you want to know what a pension is “worth”, you multiply that initial payment by the annuity factor. (Again, assuming the mortality, interest, and COLA – a lot of pensions have COLAs greater than 2%).

So if the annuity factor is 15.5, and the initial annual pension amount is $100,000, that would mean that the benefit (assuming mortality, interest rate, and COLAs) would be worth $1.55 million.

They used information available through the Public Plans Database, and they used RP-2014 with mortality projection scale MP-2017 as comparison. Note: RP-2014/MP-2017 were developed from private pension plans.

Finally, obviously, you’re calculating an annuity factor from a specific age. They do their comparisons at age 55, 65, and 75.


Here we go:

Let me walk you through this graph. There are three types of plans/employees: teachers, safety officers (police/fire), and general (everybody else).

Yellow diamonds are unweighted averages for all the plans. It would be hard to decide what an appropriate weighting would be: # of total participants (active and retired), # of retirees, # of retirees age 55. And in some of these cases, the SOA does not have access to the appropriate stats to do that weighting. So fine for unweighted average.

Next, the lines are from calculating the annuity factors using RP-2014/MP-2017 with the 7% interest rate and 2% COLA. The RP-2014 tables have three main categories: white collar, blue collar, and aggregate (a combo of white/blue with weighting by population).

So let’s look at the male graphs and look at the yellow diamonds: pretty damn close to the aggregate result for RP-2014/2017 for both general and safety officers. And teachers are between the aggregate and white collar levels for RP-2014/2017.

On the female side… not quite so much. The averages for general and safety are close to blue collar annuity factors, and the teachers are similar to male: between aggregate and white collar.

What about the specific dots?

I would have liked to have seen a box-and-whisker plot for these (and I’m going to see if I can get a copy of the calculated annuity factors), but there really aren’t a huge number of dots, and it’s good to look at the different colors.

The black dots are for plans that use RP-2014 as the underlying tables, but they could be projecting future mortality differently from using MP-2017, they could be off by a year, they could be blending the blue collar/white collar tables differently, do setbacks/setforwards, yadda yadda.

But just by eye, I don’t see that using other tables gives a biased result compared to those using RP-2014 as their base table.

For comparison, here are the age 65 factors:

Age 75 factors:

A few observations:

It seems that at older ages, the annuity factors are lower than the reference RP-2014/MP-2017 results.

Let’s see what the report writers said:

For all job categories combined, the unweighted average age-65 annuity factor for mortality assumptions in use is 99.3% for males and 99.1% for females of the annuity factor for aggregate RP-2014 rates.2 Compared to RP-2014 white-collar tables, percentages are 94.8% for males and 96.4% for females. Based on RPEC’s preliminary findings, these percentages suggest that mortality assumptions for many plans may be lagging behind current aggregate mortality experience among public plans.


Let’s look at a table about what tables were used.


Here is the tally:

So let’s see, the totals seem to work out.

But I want to point out something: just because an actuary is using one of the 1994 tables, doesn’t mean they’re giving you 1994 mortality. Look at the second part: the mortality projection scales.

Different scales were developed for use with different base tables, and projected in different ways. You’ll see there are two types of projection: generational and static. The static scale gives you factors for different ages, and you’re assuming that, for example, whatever reduction in mortality for somebody age 65 (that is, the probability of dying before age 66 given you’re now 65) is a constant multiplicative factor.

Generational scales will differ by both the age you’re applying it to, and the year you’re applying it in. That’s a little more realistic. But again, these are all projections. We don’t know what future mortality will be, but we’ve got an idea from past mortality trends.

Out of the 192 assumption sets, only 9 had no mortality improvement trend. Not great, but not as bad as I thought it might be.

Anyway, this doesn’t tell us how they combine (the annuity factors give us an idea).

Let’s look at relative differences.


Before the comparisons are made in a relative sense, here are the annuity factors:

Now let’s look at the relative difference:

In most cases, the average annuity factors that are a little higher than the blue collar assumption set.

Also, in most cases, the average annuity factors are a little less than the white collar assumption set.

These aren’t huge differences — there are less than 10% deviation either way.

Also, these differences are very minor compared to what happens when one changes the valuation interest rate by one percentage point.

That is really not too bad… but we don’t know what the actual mortality experience for these plans. Private pension experience, even split out as white collar vs. blue collar, may not be an appropriate comparison.

That said, I’d like to see the data points (I don’t need plan id, I’d just like the data set of annuity factors) – some obviously deviate a lot more and some a lot less. Again, it can be that mortality does vary quite a bit — if nothing else, I wouldn’t be surprised if fire fighters had worse mortality than police (sometimes police & fire plans are combined, and sometimes they’re separate). No, not because of deaths on the job, but because I think fire fighters are more likely to smoke than police officers. [I could be wrong about that… but fire fighters are more often sitting around with down time than are cops.]


From the study:

The Retirement Plans Experience Committee (RPEC) and the SOA are working on a mortality study specifically for public pension plans in the United States. RPEC expects to release an exposure draft report in late summer or early fall 2018. In the August 2017 edition of Pension Section Update, the SOA preliminarily indicated that across all data collected and across all job categories, results were generally closer to RP-2014 white-collar mortality rates than to aggregate RP-2014 rates. Upon deeper analysis, RPEC has found clear differences in mortality experience among the following three job categories: general employees, safety employees and teachers.1 Consequently, this analysis is split by the same job categories.


I’m looking forward to that.

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