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School was never my thing, but I have always had a curiosity about how things work.  Long after school ended for me I discovered that reading is the road to satisfying my curiosity and I spend several hours a day reading all sorts of things – partly because my ADD doesn’t make it easy to focus on one subject for a long period of time and partly because I am interested in a wide range of subjects beyond just ‘DB pensions’ which is largely how I have made my living and focused my professional practice.

When it comes to academic papers, I like the easy ones.  When I encounter one with hard math, I just remind myself why no professors at UWaterloo suggested that I stay longer and limit my reading to the abstract and maybe the executive summary.  Towards the end of 2023, the Canadian Institute of Actuaries published a paper Exploration of Lifetime Pension Pool Design Elements.  I know many of you wouldn’t be grabbed by that title, but as someone who has been wrestling with the decumulation problem for a while now I couldn’t resist looking.

I want to be honest right up front: I can’t do the math in the paper.  Thankfully, the authors Bégin and Sanders use words to help explain their thinking and help me navigate how they did the math.  I trust them 100% that the math is right – which lets me focus on what the paper teaches us.  Let me tell you at the outset that I loved this paper.  There was so much good thinking that went into the modelling and so much learning that came out the other side for me.

The Problem

My readers are reminded of the problem that we are trying to solve.  In the old days when defined benefit plans were prevalent, the plan administrator navigated the world of balancing the assets available to pay lifetime pensions reflecting the emerging experience of people living longer than expected and dying sooner than expected.  Actuaries are well versed in the truth that people rarely die right on schedule and the whole point to our work is playing the averages.

In the defined contribution world, there is no ‘law of large numbers’ – every account holder is funding their own lifetime and there is no pooling with others of the risk of living too long.  When the DC industry started to take hold in the 1990s, accumulation was the focus and from a design perspective it was assumed that at retirement, workers would take their lump sum account and solve decumulation on their own time – no longer the responsibility of employers.

Over the last decade the conversation around decumulation has gotten increasingly louder as the industry comes to grips with the ill-advised strategy of letting retirees figure out one of the most impossible math problems on their own.  People who think there is a way to design a perfect decumulation strategy on an individual basis are misinformed.  The variability in how long any one individual will live is too great to properly predict how much money can be drawn down from the nest egg each year.  Layer on the wild fluctuations in account balances that occur when equities make up a large portion of the investment bundle and you have something a little harder than the Caramilk Secret on your hands.

The Solution

The first surprise in the paper is that there isn’t a ‘right answer’ to how to design a longevity pool.  I should have figured it out when they didn’t share a clear conclusion up front in the executive summary.  I mistakenly thought that it was either an oversight by the authors or a way to hook me to keep reading.  It turns out they don’t tell you an answer because there isn’t one.  The second surprise is that there is a wide range of choices to be made designing a longevity fund.  I mistakenly thought that the academic community, led by tontine guru Moshe Milevsky, had come up with a clear line of attack to the decumulation problem.  Not so much.

Because the math was so hard, because there was no clear solution offered and because I really care about this subject, I reached out to the authors to see if they would walk me through the paper.  They kindly obliged and I am surely smarter for the time we spent.  Thanks to JF and Barbara for taking the time.

The Choices

It turns out there are many design features to consider when setting up a longevity pool.  I am going to give a quick glimpse into three that highlight the complexity of the problem.

Choice 1 – Open or Closed Group.  A longevity pool can be closed where a cohort comes on board at the outset and the pool winds down over time as the cohort reduces to zero.  Alternatively, the pool can be open with new entrants coming in to offset those departing the pool at the end of their lifetime. 

Choice 2 – The Hurdle Rate.  In designing a longevity pool, you must develop an investment strategy and predict the average investment return the pool will earn.  Separately, you must establish a ‘hurdle rate’ which is the rate above which investment gains can be distributed in the form or additional benefits.  A lower hurdle rate increases the likelihood of rising benefits over time – some might think that this is reasonable, like an indexed pension.  The downside here is a lower income at the start and those dying after a short retirement ‘over-subsidize’ the long lifers.  In the other direction, starting with a higher hurdle rate you get higher benefits right out the gate, but you bias the path towards benefit cuts longer term if the investments can’t keep up.  This is the model the salespeople like.

Choice 3 – Group vs Cohort Distribution of Mortality Gains and Losses.  Yikes – this is the really hard math in the paper.  I went through it three times – once before talking with the authors, once on the call and a third time when I was trying to write out this commentary.   Basically, in the Group Based Adjustments everyone shares in the mortality gains and losses in the pool proportionate to the amount of their benefit.  This means that when we see a greater number of deaths than expected, everyone in the pool sees their benefit increase by the same percentage.  In contrast, Cohort Based Adjustments look at the mortality risk for each cohort in distributing the mortality gains.  This means larger adjustments to older members of the group who have a greater risk of ‘not making it’ another year.

If this sounds too easy, there are other nuanced decisions around spreading gains and losses over time and using an adjustable hurdle rate to better reflect the yield curve structure.  There is just too much to talk about in one commentary – maybe next time.

Who Choses?

There aren’t many longevity pools in operation yet, partly because the legislation isn’t fully in place to allow for all the options that we are discussing.  In theory our federal government has promised to create legislation in the Income Tax Act to allow these programs to exist.  Assuming this happens, there are two stages in choosing a longevity pool design.  First, the ‘promoter’ will design the pool they think works best and that can be marketed.  Second, everyone will be able to choose from different pools the design that best suits their preferences.

On the first decision, if I were the promoter, here are the decisions I would make on the three choices discussed above.

Open Group – It should be intuitively obvious that if you have a closed group, the final survivors will have a volatile benefit level as people refuse to die exactly when the actuaries predicted.  The authors kindly back this intuition with a mathematical proof.  To me, when you see in the paper the volatility of the benefits as the closed group winds down under ten members, it only makes sense to run an open group.  I shared this opinion with my buddy Fred, and he disagreed – he thought that those final participants were the ‘winners’ in the pool and as the benefit rose and fell from ‘more’ to ‘lots more’ there was no need to worry.  Fred is smart, but I still disagree – the point to a ‘pension’ is to provide a predictable income throughout retirement.  A longevity pool won’t be as predictable as an annuity but let’s not make it wildly fluctuate in someone’s final years.

Hurdle Rate – this is the toughest one for me to decide.  It is the easiest math and the easiest to explain the choice that is made – conservative start with more upside or aggressive start with more downside.  There are two actuaries inside my brain struggling to choose on this one.  One actuary is ‘old school’ and wants to put in a margin against losses and start conservative, largely because benefit cuts hurt three times as much as benefit increases feel good.  The other actuary is the one that is a disciple of financial economics and thinks the fairest thing to do is to take the ‘expected’ hurdle rate and tell buyers that ups and downs are both likely outcomes.  So, the marketer in me is casting the deciding vote and going with the neutral hurdle rate to market ‘actuarial fairness’ and higher starting incomes compared to building in conservatism in advance.

Mortality Adjustments – this one is almost as easy for me to decide as the open group – even though the math is a little mind blowing.  The best way I can describe the difference between the two approaches is that the Cohort Based Adjustments could be called ‘actuarially fair’ whereas the Group Based Adjustments would likely be seen as ‘fair’ by most non-actuaries and is how things worked in the traditional DB plan.  Like the financial economics disciple mentioned in the hurdle rate discussion above, the pure actuary in me can get onboard easily with the ‘risk-based approach’ of the Cohort Adjustments.  But Cohort Adjustments are just way too complicated to explain and delivers value at the tail when it is likely less valuable than in earlier years.  The marketing man has over-ruled the actuary and we are going with the Group Based Adjustments.

The Road Ahead

The discussion above is all I could fit into one commentary.  The paper explores different ways to measure risk and reward but in the end what you really learn is three things:  First, as Barbara pointed out on our call “if you want a longevity pool to work, you need to be careful in the design”.  Second, as JF observed “at the end of the day people have to decide what they care about” referring to the balance between risks and rewards.  And finally, my biggest conclusion is that whatever design is chosen, communication, communication, communication.

I am smarter now than when I first picked up the paper.  I have enjoyed the read and taking the time to write this commentary.  However, I am not convinced yet that longevity pools are the answer to the decumulation problem.  These products are going to be necessarily complicated which will make them hard to explain.  I fully expect there to be complaints from buyers that later tell us they didn’t understand what they were buying. 

It is hard to imagine that individuals should be entering these pools without personal advice on the appropriateness of the product to their circumstances.  But to make headway in decumulation we are going to need a group product where everyone joins and not an individual product where anti-selection will mean that the broader universe of savers will not see the product as meeting their personal ‘fairness’ test.

More discussion ahead as the legislation and the products evolve.