Life After Full-time Work Blog

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#144 Annuities, Longevity Risk And Investment Risk

A framework for thinking about some financial implications of long life


Quick Note: There’s a special message at the end on a different subject: a webinar that I’m a part of, on November 4, 2 pm in the UK and 10 am in Toronto (summer time will have ended in the UK but not in Canada). I hope you’ll be able to join it, and take the opportunity to ask me a question.


In an earlier blog post I reproduced an article that appeared prominently in the (London) Financial Times and the (Australian) Firstlinks website. Later I also reproduced my Firstlinks response to three issues raised by readers. There was one other issue that British readers raised, but not Australian ones, so it didn’t appear in my Firstlinks response. It was about the use of annuities to protect against longevity risk. Since it involves aspects of longevity planning that aren’t often discussed, I’ll deal with it here.

In fact the same topic has a second context. On September 9 the Canadian Institute of Actuaries had a webinar on defined contribution plans, and I was asked (to my great delight) to be the first speaker. As I knew I’d be just a little bit older than the average viewer (by a few decades, perhaps!), I thought it might be useful to give them the perspective of an actual retiree – in fact, of someone who graduated from full-time work more than eleven years ago. I told them three things.

  • First, that there’s more to Life Two than financial questions: there’s also the identity question (how would I define myself on a business card today?) and the practical question (how will I fill my time?).
  • Second, what financial advice, in connection with retirement, would be most useful to individuals at different stages of their life? There’s no point, for instance, in telling a recent university graduate about the importance of retirement – that’s like life on a different planet. So I gave the viewers a list.
  • And third, I thought I’d give them some real actuarial stuff, so I showed them how to compare longevity risk with investment risk, a topic they probably have never come across before. That’s what the rest of this blog post is about.


A reminder: longevity risk is the financial uncertainty that comes from the chance that you may live so long that you run out of the money you’ve saved.

If unfortunately you’re in poor health, the uncertainty about the age you’ll survive to is much smaller. Hedging your longevity risk therefore only becomes an issue if you are in at least average health, so I’ll take that as a given.

Also, at the extremes of wealth, longevity isn’t a terribly relevant risk. Why? Well, at one extreme there are some retirees who don’t have enough to satisfy their needs, let alone their wants, so longevity is (unfortunately) no more a problem than everyday life. At the other extreme, there are some who can satisfy both needs and wants for longer than the period to the end of the longevity table, so longevity isn’t a risk that upsets their lifestyle. (I’m ignoring the bequest motive, which may seem unreasonable, but there are ways of coping with it separately that I won’t go into here.)

It’s in the (vast) middle that longevity is a risk that could mean doing without some or much of one’s wants if one’s lifespan is too long. Let’s consider them.

Here’s the problem, in an oversimplified nutshell. Even if you know exactly how much income you require for your needs and exactly how much more for your wants (and I’ll take those as a given to simplify the question), there are still two further large uncertainties in the problem of ensuring sufficient retirement income. One is: how long will I require the income? And the other is: the income will be drawn from my pension pot, and I know how large the pot is today, but what will be the future investment return on the pot?

Together they form a horrendous problem (and this time I won’t quote Bill Sharpe on it).

When I was planning financially for my graduation from full-time work, some 15 years ago (that’s when I planned, not when I graduated), I first defined and then thought about the problem, and I concluded that it was far too complicated for me to solve. The best I could do was to simplify the problem by dividing it into two problems, either of which is still difficult, but at least I could solve them. I did that my conducting the following thought experiment.[i]

Let’s imagine life on two hypothetical and very peculiar planets.

On Planet A, longevity is certain: everybody’s lifespan in exactly predictable. But investment returns are uncertain. So of course there’s financial uncertainty about how much money we’ll need to support our needs and wants, because of those uncertain investment returns.

On Planet B, investment returns are certain: we know exactly what any type of investment will return. But longevity is uncertain. Again, this gives rise to financial uncertainty about how much money we’ll need, because while we know what returns we’ll earn, we don’t know how long we’ll need those returns.

I know we can resolve the uncertainty by buying an annuity. But suppose we actually need some growth-type investment return, because the annuity doesn’t provide us with as much income as we want. (Remember, it’s that vast middle group of people we’re considering, and this is a definite problem they face.) Then we’re forced into some kind of decumulation mode.

And in that context, here’s my question: on which planet will there be more financial uncertainty? On Planet A, with its investment uncertainty, or on Planet B, with its longevity uncertainty?

As you can guess, I gave the actuarial viewers a lot of jargon, involving expected values and standard deviations and coefficients of variation, because that’s their lingo. But actually that isn’t necessary for the explanation. It’s only relevant in showing how to compare the two kinds of uncertainty mathematically.

The underlying explanation is a commonsense one. Consider a large group of people like you. Suppose (I’m picking numbers out of the air, purely for illustration) this group needs, on average, a lump sum today of $100 to provide their desired amount of lifetime income. We know that, on both planets, $100 may be the average but there’ll be a large range of answers, because of the uncertainty on that planet. Suppose we say: let’s remove the extremes of the uncertainty, and capture the range that the middle (let’s say) two-thirds of the people will need. That might mean, for example, a range of $100 plus or minus $20 (so, between $80 and $120) on one planet. What would the range be on the other planet? Would the “plus or minus” amount be bigger than $20, or smaller than $20? Comparing the ranges on the two planets gives us a way to see on which planet the financial uncertainty is greater.

So: back to the original question. On which planet is there greater financial uncertainty? The answer is that it depends on your age.

For a male aged 60 and in at least average health (or a female aged 65 – with most longevity tables females have the same longevity as males five years younger), longevity uncertainty has less financial impact than investing 100% in bonds. OK, for most people that’s easy to live with, and far less risky than what they’ve been used to with their retirement accumulation assets.

As you increase the age, the longevity uncertainty starts to catch up with the investment uncertainty. Then it overtakes the investment uncertainty from bonds. OK then, let’s gradually add equities to the investments. Then it takes longer for longevity uncertainty to overtake it. But by male age 75, or female age 80, longevity uncertainty has a bigger financial impact than being 100% invested in equities.

Most of us at that age would find that amount of equity risk intolerable and frightening. That implies that, by that age, we should definitely hedge our longevity risk. (Remember, I’m talking about people in at least average health, and who need some growth element in their investment returns in order to meet their lifetime needs and wants.)


How should we hedge the longevity risk? Dr Geoff Warren has explored this question in multiple papers. Here’s my summary of his findings. I need to say explicitly: this isn’t specific advice for anyone, just a set of general results over a number of simulations of people’s circumstances and risk tolerance.

If there’s some “must have” minimum income in your mind, in addition to your government age pension (for example, enough to meet your needs), consider locking it in with an immediate annuity, that is, a guaranteed lifetime income starting now. You might then use the rest of your pot a la my approach described in the FT article, which I summarize in the footnote.[ii]

If there isn’t a “must have” minimum income but there is a desirable target income (so, some risk in meeting it is acceptable), then generally for that target income longevity insurance (often called a deferred annuity) commencing at an advanced age such as 85 is the least expensive longevity hedge; next best is an immediate annuity. Whichever you choose, the rest of your pension pot might follow the approach in my FT article. A big problem is that this kind of longevity insurance is difficult to find in most countries.

Guaranteed lifetime annuity contracts are necessarily underwritten by life insurance companies with very conservative investments, so they’re often considered expensive, particularly in the current era of extremely low interest rates. There’s an alternative being developed in a number of countries, under which you contribute a lump sum to enter a “longevity pool” which pays out an income guaranteed to last for life, but with the annual income payments varying according to the actual subsequent mortality experience of the participants. A nice feature of a longevity pool is that it can be invested in growth-seeking assets, not just safety-oriented ones, so the hope is for a higher long-term average income – an reasonable expectation but not a guarantee, of course. I described newly-minted Australian and Canadian versions of such a longevity pool recently.


Does some of this sound vaguely familiar? If so, it may be because I’ve referred to some aspects of these topics before, in Blog Posts #127 and #132, for example. But they come up so often that I thought it would be useful to gather them together here.



If by male age 75 or female age 80 we’re in at least average health, don’t have enough to lock in our needs and wants until the end of the longevity table, and are uncomfortable being 100% in equities (and most of us would be, at that age), we should be even more uncomfortable if we haven’t hedged the long end of our longevity distribution, with at least a deferred annuity.

[i] Subsequently my approach was vastly improved by my friend and colleague, actuary Bob Collie, so if you’re interested, here’s a link to his paper.

[ii] This is a summary of the approach I described that I use for my wife and myself. We selected a planning horizon of 31 years, which according to a much-used longevity table reduced to 25% the chance that one of us might survive longer. In other words, that’s a 75% chance of success in not outliving our pension pot, our acceptable risk level. We calculated the sustainable annual withdrawals that went with a combination of five years of after-inflation (and before-tax) withdrawals invested in short-term securities (our insurance bucket) and the rest in a global equity index fund (our growth pot). Why five years? Because historical statistics suggested that it gave us that same 75% chance of success, in this case that the market would recover after any fall and we wouldn’t have to cash out from a depleted growth pot. There’s lots more about risk, and adjustment to changing circumstances – but that’s the essence of it.


Here’s the note about the webinar, posted on LinkedIn by its host, Stefan Lundbergh, Director, Cardano Insights:



I have written about retirement planning before and some of that material also relates to topics or issues that are being discussed here. Where relevant I draw on material from three sources: The Retirement Plan Solution (co-authored with Bob Collie and Matt Smith, published by John Wiley & Sons, Inc., 2009), my foreword to Someday Rich (by Timothy Noonan and Matt Smith, also published by Wiley, 2012), and my occasional column The Art of Investment in the FT Money supplement of The Financial Times, published in the UK. I am grateful to the other authors and to The Financial Times for permission to use the material here.

2 Responses to “#144 Annuities, Longevity Risk And Investment Risk”

  1. Fascinating. Loved reading your letter. I believe the elephant in the room is a third uncertainty-inflation uncertainty. Given the huge expansion of the money supplies throughout the world this uncertainty must be considered in the future. With equity valuations stretched to the limits stocks may not be the inflation hedge you envision in your letter. Be sure to see my next article on how I plan to hedge both inflation and interest uncertainty. I am very interested in your discussion on mortality uncertainty.


    • Don Ezra says:

      Agreed — I don’t actually see stocks as an inflation hedge, in the sense that a hedge should be highly correlated with whatever it’s hedging. It’s just that, over the long term, they have outperformed inflation, rather than hedging it. Let me know where I can find your article — I’d like to refer readers to it.

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