The Trail For Enthusiasts

Show Chapters

T 01 Deep risk and shallow risk

T 02 How reliable an income stream can you get from equity dividends?

T 03 Capital markets can’t possibly be efficient all the time

T 04 Longevity risk compared with investment risk

T 05 How a longevity pool would work

T 06 How a lifetime income annuity works

T 07 How much more does it cost to self-insure longevity?

T 08 It’s a better world when annuities are available

T 09 Why a deferred annuity is usually preferable to an immediate annuity

T 10 Equities in the retirement glide path: a tough issue (increasing, decreasing or level exposure to growth assets?)

T 11 The role of an annuity in a sensible retirement portfolio

T 12 Measuring what matters most





Where the route takes us

We can talk about risk as the possibility of a bad outcome, but it really matters whether we’re thinking about the short term or the long term. Here we’ll see why one form of risk is unavoidable.


In Route 2 I’m not precise in the way I refer to risk or uncertainty.[1] Yes, risk means, literally, the chance of a bad outcome, of something going wrong. But all sorts of outcomes are bad. Let’s now be more precise and distinguish between two kinds of uncertainty, the distinction being the time horizon under consideration.

In Stage F 01 we see that the chances are, for many of us, that we may not have enough money to match our retirement ambitions. In practice, the most powerful mechanism (as we see in Stage F 02) to bridge the gap is to take investment risk, in the hope and expectation of creating a multiplier effect from investment returns.

Obviously the big risk is that, over the long term, returns won’t match expectations. The traditional way risk is expressed, in most investment situations, is via short-term volatility – which actually has very little impact on our long-term future.

This distinction (long term versus short term) is captured in a little gem of a book called Deep Risk, by William Bernstein.[2] (I love his entire series of brief books.)

He distinguishes between “shallow risk” and “deep risk”. Shallow risk is the risk that we’re forced to interact with the market at a bad time. We’re forced to buy right after the market has gone up, or to sell right after it’s gone down. Yes, it makes sense for volatility to be a good measure of shallow risk. Much of what’s called “modern portfolio theory” is based on this concept. But it’s an avoidable risk, at least partially, as I’ll show in a moment.


Deep risk is much more serious. It’s the risk that the world’s economy, and therefore its collective stock market, doesn’t perform over the long term. This is what places us all in retirement jeopardy. And it’s unavoidable. There’s nothing we, as individuals, can do about it.

Bernstein identifies four possible causes. Fancifully, think of them as the four horsemen of the deep risk apocalypse: inflation, deflation, confiscation (taxation) and devastation (wars and natural disasters). How likely are they, and what can we do as a partial hedge against each of them? Read his 50-page book. Here’s my very quick summary. I mention it for curiosity; I don’t use it any further, except for the concept of deep risk itself.

  • He sees inflation as the most likely, followed by confiscation, with deflation and devastation as the least likely – at least in America.
  • He also sees inflation as having (relatively) the lowest cost of hedging against. His studies suggest that partial hedges against inflation are to invest in global equities, commodities producers and index-linked gilts.
  • Against confiscation (direct taxation – and also indirect taxation on savers, like the post-2008 regime of financial repression), few would be willing to move abroad or renounce citizenship. In which case he thinks the sensible long-term partial hedge is to invest in foreign-held assets and real estate.
  • A partial hedge against long-term deflation is more costly. He suggests global equities, long government bonds, Treasury bills (short-term assets) and gold.
  • And against devastation: quite simply, foreign-held assets – against local devastation only, of course.

If you follow his thought process, you design an aggregate portfolio that offers you some chance of partially hedging against these forms of deep risk. And every investment in your portfolio will then have a specific job description: this will be your way to survive at least the worst effects of deep risk while giving you a hope and expectation of thriving if deep risk never occurs.


How can you escape shallow risk?

In the accumulation phase, you don’t really need to. It has little effect because you’re investing regularly. Volatility just means that sometimes you’ll buy high and sometimes low. Americans call this “dollar cost averaging” and have analyzed it thoroughly.


One fundamental consequence of this distinction between deep risk and shallow risk is that we should have two (and only two) investment goals. One is to seek short-term safety (that is, to avoid shallow risk), and the other is to seek long-term growth (and therefore to be permanently and unavoidably subject to deep risk). Of course, the mixture of these two goals will vary from one person to another. At one extreme, some will be extremely risk averse and will want to avoid shallow risk entirely, even at the cost of reducing their periodic drawdown significantly. At the other extreme, some (very few, I suspect) will be willing to focus entirely on long-term growth, at the cost of enduring potentially high short-term volatility in their periodic drawdown.

A further consequence, from combining this two-goal principle with Tinbergen’s principle (see Stage F 46) is that we should have two investment instruments. One focuses entirely on avoiding shallow risk; the other focuses entirely on seeking long-term growth. There’s no need to compromise either goal by combining them. In fact, avoiding shallow risk is actually an insurance procedure.

By the way, this is exactly the strategy followed by the world’s most sophisticated defined benefit pension funds. They divide their portfolio into two parts, typically called “liability-hedging” (what we’ve called avoiding shallow risk) and “return-seeking” (what we’ve called seeking long-term growth).

One final comment. After I published these thoughts in my FT Money column “The art of investment”[3] I came across another – and a very accurate – way of distinguishing between the two forms of risk. Stuart Fowler[4] differentiates between “path risk” and “outcome risk,” which to me is an even more instinctive pair of terms than shallow risk and deep risk.



There are really two different forms of risk. One is volatility in the investment path; the other is a poor long-term outcome. The first is bearable if you design your plan appropriately; there is no way to overcome the second, and all you can do is reduce your spending.





Where the route takes us

We’ve looked at equities as an embodiment of seeking growth. But equity returns come in two parts, one part being the dividends paid out and the other part being changes in the value of the investments. Here we’ll look more closely at the dividends, because many people hope that they can use the dividends as a component of their safety-oriented investments.


In Stage F 46 I identify three kinds of financial goals we typically have once we stop working. One relates to longevity protection, that is, not outliving our future income. Investment instruments alone can’t totally satisfy this goal; there needs to be an element of insurance, since our lifespans aren’t certain. But investment instruments are useful for the other two goals: safety and growth. Not surprisingly, in Stage I 12 I suggest that investments have two fundamental characteristics related to their future returns, and yes, they’re safety and growth. And the two are invariably in conflict: the more you want of one characteristic, the less you should expect of the other. In particular, I identify equities in Stage I 21 as having behaved like a good growth-oriented strategy. That means that you can’t rely on equity returns for safety.

Nevertheless, on this trail I’m going to identify a portion of the equity return as being reasonably reliable from a safety perspective. It’s the portion of the return that comes from equity dividends.

What are dividends? They are essentially how profits made by companies are repaid to their investors. In fact it’s not quite as straightforward as simply paying back the profits. There are three things that companies tend to do with their profits: pay some of the profits back, as dividends; retain some, to finance new ventures in the future; and the catch-all, retain some as a contingency reserve. A reserve for what? For the two other purposes. There may be unexpected new venture opportunities, and it’s convenient for a company to have money on hand and not have to go back to its shareholders for more. And a reserve for years when the profits are lower than the last dividend payment, so that the dividend amount can be maintained even if profits are low or negative.

Investors like that last feature very much. In Stage F 43 we saw that human beings are hard-wired to like certainty. That fact reveals itself in many ways, one of which is that equities with reliable dividend streams tend to sell for a higher price (other things being equal) than equities with volatile dividend streams. And therefore companies (other than, for example, those describing themselves or behaving as “pure growth” companies) like keeping their dividends level or increasing.

It’s a fine balance between paying out such a high dividend that its maintenance is imperiled and paying out such a low dividend that a higher stream could be sustainable. So it’s not surprising to find that, from time to time, dividends are cut. But for a country’s equity index, representing a collection of its companies, somewhat greater stability is built into the dividend stream, because it tends to fall only when something negatively affects the economy of the whole country rather than a particular industry.

This suggests that an index’s dividend stream has the potential to act as a source of investment safety, at least partially if not fully.


There are some obvious questions to investigate historically. In particular, how often does an index’s dividend stream fall? And when it falls, by how much? And let’s look at those in real terms, that is, after inflation. We’re already used to the notion of real returns (from Stage I 21), and most of our income needs are expressed in after-inflation terms anyway since a lifestyle spending pattern can only be sustained if it keeps pace with inflation.

It’s surprisingly difficult to find historical data relating to equity dividend streams. One that does exist, fortunately, comes from the US S&P 500 index and a data series compiled by Economics Nobel Prize winner Robert Shiller.[5]

The constructed data series goes back to the 1800s. I used the data starting with 1928, partly because that’s also the starting date for the data series I cited in Stage I 21, and partly because I wanted to make sure that the negative effects of the Great Depression are included. Here’s what I discovered when I analyzed it.


First, and most important: yes, the dividends do look fairly stable, in real terms. In fact, not only do they deliver an average real return that’s positive. They do better than that. Their average annual rate of growth is roughly 2%.[6] (In other words, in real terms the amount of the dividend grows roughly 2% a year.) Compare that with the average Treasury bill real return of 0.5%, and it looks good.

How about its volatility?

The annualized standard deviation of the return series is 10.7%. That compares with 3.9% for T-bills, so dividend yield growth is less stable than T-bill returns.

How often is the growth rate positive? 63% of the years, compared with 61% for positive real T-Bill returns. Extending the time horizon to 5 years or 10 years doesn’t improve the prospects for T-bill positive real returns (strictly, it’s not the prospect but the history that I’m looking at), both producing around the same 60% outcome. But with the dividend stream for equities, extending the time horizon to 5 years shows that 69% of the time real dividend growth was positive, and periods of 10 consecutive years showed positive average growth 81% of the time.

Overall, then, my interpretation is that the S&P 500 index has historically produced a dividend stream that is somewhat better and more reliable, in terms of real return, than an investment in T-bills.


There’s one more question I asked myself. How large a dividend yield is reliable? For this I looked at the real dividend each year and checked what was the biggest drop. And here’s what I found. Over one-year periods, the biggest drop was 34%. Over 5-year periods, the biggest drop was 11%. And it was 4% over 10-year periods.

My interpretation of the one-year number is that, if you had started with two-thirds of the current dividend at any time, you could essentially have taken that amount as sustainable in real terms.

If you can create your own volatility reserve for 5-to-10 year periods to cushion the one-year impact within those periods, then roughly 90-95% of the dividend yield has been sustainable, at least historically.



The equity dividend stream has an important potential use as a source of investment safety.





Where the route takes us

When there’s lots of information available to lots of very intelligent people, why do markets still sometimes swing so wildly? Let’s look at human behavior in general for the answer, and see what it implies for our own desired behavior.


There’s a concept about investment markets called the “efficient market hypothesis.” Essentially (yes, this is an over-simplification) it postulates that all available information is already reflected in the prices of securities. And therefore it isn’t possible to “beat the market.”

In fact, markets for which information and research are quickly and widely disseminated, and in which trading in order to change one’s holdings is quick and cheap, satisfy this definition for all practical purposes. And these are the ones (like the market for large company US equities) in which beating the index is very difficult to do with any consistency.

Not all markets are like this. Some may be informationally inefficient or transactionally inefficient. But more than that, the efficient market hypothesis can’t possibly be a totally accurate description of the way investment markets work, even if they are efficient most of the time.


I need to start with a digression, introducing a couple of notions regarding physics and biology that will be relevant. You don’t need to remember any of the details.

A physical system is one in which the various parts interact with one another. That’s a very simple notion. A complex system is one in which those interactions compound in such a way that the whole system seems to take on a life of its own, different from just being the sum of its parts. Example: the weather is a complex physical system. The molecules in the air interact with their neighbors. But the interaction is so complicated that the weather itself can’t be predicted from the molecules.

You may have heard that a butterfly moving its wings can create a tornado half a world away. Well, that’s one of the characteristics of complex systems. They may have a tipping point that causes the system to spill over into chaotic behavior.

Does that sound like investment markets? As it happens, investment markets are not just complex systems; they have a further level of complication. Their basic molecules are human beings, interacting with one another. But unlike the weather, where the molecules don’t change their behavior from one interaction to the next in response to experience, human beings do. And so investment markets aren’t just complex systems, they’re complex adaptive systems. They’re not just physical systems, they’re biological systems. They change in response to experience.

Complex adaptive systems have feedback loops, which can be positive or negative. A negative feedback loop moves the system in the opposite direction from the initial stimulus. So, for example, in capital markets, buying pushes prices up; then, when prices go up, markets seem less attractive, and that reduces the buying pressure. That’s a negative feedback loop. But the herd instinct is a positive feedback loop, which accentuates movement.

So, depending on the feedback loops, we can have a complex adaptive system that tends towards equilibrium or towards bubbles that eventually burst. What you’re sure of is that equilibrium will never actually be achieved, because someone, somewhere, will have an idea and act on it, and that’ll be the stimulus for a new movement.

So in a complex adaptive system, it’s impossible to model the future with the accuracy of physical systems. There will always be cycles, rather than uniform movement in a single direction. And rather than a permanently efficient market, there will be markets with varying opportunities and varying risks over time.


So we should never struggle to decide whether there’s a “true” equity risk premium (that is, the long-term outperformance of equities over safety-oriented investments), and whether its value is 5% or 4% or 3%, as if we’re physicists comparing experimental results to get the true value of a physical constant. There’ll never be the equivalent of a Higgs boson announcement for capital markets: “Look what we found! After studying the evidence, we’ve determined a value for that particle!” Not with capital markets.

Doesn’t everybody realize this? Certainly it seemed, after the global financial crisis that started in 2007-8, that a tipping point had come and the need for a new paradigm had become irresistible. We observed that markets went crazy from time to time, with bubbles forming and bursting far more frequently than typical statistical distributions predicted. We had so-called “once-in-a-century” events monthly, then weekly, then daily. The equity premium vanished for long periods. Standard deviations of asset class returns suddenly expanded and then shrunk and expanded again. And when markets fell, correlations across countries and across some asset classes rose to almost +1. Nothing was constant.

It became clear that our cherished inputs into asset allocation calculations, such as the normal distribution of asset class returns and the constancy of asset class standard deviations and correlations, no longer held under the extreme capital market conditions we were encountering.

Dr Andrew Lo, of MIT, who had been preaching this for a long time, finally found that his Adaptive Markets Hypothesis,[7] based on biological rather than physical principles, gained legitimacy. And now we understand a number of things. Let me mention four of them.

  • Markets are well behaved most of the time, but they break down from time to time, because logical reasoning is only one human aspect brought to bear on pricing. Emotion is another, and it resides instinctively in the brain, in the amygdala’s fight-or-flight response to change.
  • As intelligent but emotional investors adapt to new economic evidence, they do not necessarily perceive events accurately. Sometimes rationality wins and creates a negative feedback loop; but sometimes emotion wins and creates a positive feedback loop. The wisdom of crowds does not always conquer the madness of mobs.
  • The trade-off between risk and reward is therefore not stable, but varies as a function of the characteristics of the population of market participants and their own business environments.
  • Market pricing efficiency at any point in time is somewhere along a continuum that depends on the proportions of market participants making decisions with their rational neocortex versus their emotional amygdala.

There are strong consequences for investment policy. Here are three.

  • Investment policies should be formulated with these changes in mind, and should therefore adapt to changing degrees of pricing efficiency.
  • Investment opportunities present themselves, but only to investors able to stand apart from the madness of mobs.
  • Denominating asset allocations in risk units is potentially more effective than in asset class units. (But I won’t follow that angle in this tour. Even sophisticated multi-billion-dollar funds are turning to this concept only in an experimental way, rather than replacing their traditional asset allocation concepts.)


How can you use the consequences mentioned above?

  • Periodically (for example, annually) you should re-calibrate where you stand. You might also want to consider whether or not you change the capital market assumptions that you use, though that’s something you ought to get professional input into.
  • It’s possible that changing your capital market assumptions leads to a change in your safety/growth mixture. If so, it’s a change that is made rationally rather than emotionally.
  • Before you choose (or you accede to your financial professional choosing) to try to beat passive investing, be aware that you’re essentially saying you’re taking advantage of the irrationality of most other investors.



At best, capital markets are efficient most of the time. But because human beings are involved, emotion will sometimes trump logic, with prices departing from rationality. But you can only take advantage of these times if you are rational when others are being emotional.





Where the route takes us

When we invest money, the outcome is uncertain. We can measure the financial impact of that uncertainty. But our future lifespan is also uncertain. That too creates financial uncertainty. Can we compare investment uncertainty and longevity uncertainty? Which is more significant? Does the answer vary with age? So many questions! Let’s answer them all.


A standard way of expressing investment risk is to say that it’s equivalent to drawing a single outcome from a distribution of possibilities. In other words, lots of investment outcomes are possible. One of them will happen. We don’t know which one, so that means there’s uncertainty, and that leads to a chance that the outcome will be a bad one for us.

We’re much less familiar with the representation of longevity risk in the same way: as a number selected at random from a specified distribution. It’s like saying, “You don’t know when your number is up.” You might live a long time; you might live an average length of time; you might not live long at all. Each possible outcome affects how much money you will need in order to avoid the single biggest fear of retirees, that of outliving your assets (Stage F 43).

Both investment uncertainty and longevity uncertainty have financial consequences. Here I’ll attempt to roughly compare the financial impacts of the two types of uncertainty.


Here’s one way to make the comparison.

Consider a thought experiment, about life on two hypothetical (and extremely imaginary, unrealistic) planets.

On the first planet, longevity is fixed. Everyone lives to exactly the average life expectancy, with no uncertainty at all. In contrast, on this planet investment returns are uncertain. On the second planet, the reverse conditions hold. Investment returns are fixed. Everyone gets the average return. In contrast, life spans are uncertain.

On both planets, therefore, the amount necessary to finance a given standard of retirement living is uncertain. Each type of uncertainty can be represented by a distribution of possible outcomes. The more uncertain the range of outcomes, the wider is the resulting distribution. But which planet gives rise to the wider distribution?

To measure the width of the two distributions, I use what statisticians call the coefficient of variation – the standard deviation divided by the mean. Essentially, this answers the following question: for each unit of average expected cost, how uncertain is the outcome?

I did my calculations many years ago, while I was still working full time, in order to educate myself about the relative sizes of the risks. (That’s because I couldn’t find any guidance from anyone else who had thought about this question). Consequently, the numbers I used may seem out of date today. But that doesn’t matter. The conclusions, it turns out, are pretty robust, and are as true today as they were all those years ago.


Here I’ll just give you an outline of the process and the results.[8]

At the time I used a 6% interest rate for bonds and a 9% expected return for equities, with bond and equity standard deviations of 8% and 16% respectively. And I used the American RP2000 life tables for healthy annuitants, in which the male life expectancy at age 60 is 22 years and at age 75 is something much shorter – closer to 10 years.

Let me explain the calculation for the first planet, for a 60-year-old male. He will live for 22 years, with certainty. Using an expected annual return of 6% with an annual standard deviation of 8%, I ran 2,000 Monte Carlo simulations of the accumulation of an initial amount of $1 invested in bonds over a fixed 22-year period.

The mean 22-year accumulation was $3.65, with a standard deviation of $1.37. Hence the coefficient of variation was $1.37/$3.65, or 0.38. This is essentially saying that 2,000 people live for the same length of time but have uncertain accumulations; and for each $100 of ultimate average accumulation, the standard deviation of the range of outcomes is $38.

For equities, when I used an expected annual return of 9% and an annual standard deviation of 16%, the coefficient of variation rose to 0.75. So, for each $100 of average accumulation, the standard deviation of the resulting distribution was $75. Yes, equities are much riskier than fixed income, on this first hypothetical planet as on earth.

What would happen to the same 2,000 60-year-old males on the second planet? They all want to draw down $1 a year with safety, over lifetimes of an uncertain length. Those few who die in the first year (let’s say in the middle of the year, on average) will each have drawn down 50 cents, which could have been supported by an investment of 48 cents at the start of the year. Those dying in the second year (a few more) would have needed $1.40 at the outset for their 18 months of drawdown. And so on. Given the distribution of deaths from the longevity table, the average initial amount required would be $11.20 and the standard deviation $3.14. So the coefficient of variation is $3.14/$11.20 = 0.28. That’s lower than for investing in a 100% bond portfolio.

In other words, the financial uncertainty arising from uncertain longevity, for a 60-year-old male, is less than the financial uncertainty inherent in investing in a purely bond portfolio.


Now consider the 75-year-old males. Adjust the projection period downwards, to reflect the lower life expectancy. Now the coefficient of variation for providing the lifetime drawdown rises to 0.46.

(Of course the expected future longevity of a group decreases as their age increases, but because the spread of possible outcomes does not decrease as fast, the coefficient of variation increases.)

And now it turns out that the coefficient of variation for drawdowns is greater than that for the accumulation that results from 100% invested in equities over that shorter time period.

Conclusion: At age 60 longevity uncertainty has less of an impact than investing solely in bonds – so that’s a risk most people will be happy to take. By age 75, longevity uncertainty starts to have a greater financial impact than investing 100% in equities. But investing 100% in equities is a risk most people are not prepared to take. And therefore it’s clear that taking longevity risk after that age isn’t something they should contemplate either.


For techies, I can add to the discussion. I accept that, given the skewness of the distributions involved, the standard deviation is too simplistic a measure of uncertainty. But all I wanted was to reach a couple of initial conclusions, since it appeared that nobody had ever tackled the issue before. In 2015 my friend, colleague and co-author Bob Collie refined the calculations.[9]

He contemplated the same hypothetical planets. He considered a 65-year-old female and a 65-year-old male as well as their joint and last survivor lifespans, using a more up-to-date longevity table. Instead of the standard deviation of the outcomes, he focused on how much less than average they would be able to draw down if they lived longer than 90% of their counterparts. And then he also considered longevity and investment returns as being uncertain at the same time (which is, of course, the way our own world operates.) Finally he varied the age being tested from as low as 50 to as high as 80.

He concluded that, at 65, “longevity risk is smaller than typical levels of investment risk,” and it adds little to investment risk alone. But “the importance of longevity risk increases at older ages. For an 80-year-old, the uncertainty associated with how long they will live is equivalent to a fairly substantial level of investment risk.”

In an appendix he considers a more complex model of investment risk, and concludes that “the age at which longevity risk overtakes investment risk [for a portfolio that is split 50/50 between equities and bonds] is around age 70 for both the female retiree and the male retiree.”

What’s the take-away? It’s simple. If you find holding 100% in equities too risky, you should also find it too risky not to buy some form of longevity protection at some age after retirement, certainly no later than age 75.



Before age 65, typically longevity risk isn’t a significant factor. After age 75, longevity risk is typically bigger than investment risk. If you have any safety orientation in your investment portfolio, you should logically have at least some safety orientation in how you deal with longevity risk.





Where the route takes us

When a risk affects many people and we know that only some of them will be affected by it in a given time period (but we can’t tell in advance who will be affected), sometimes it’s helpful to “pool” the risk by having all the people contribute to it and then use the pooled money to pay those who turned out to be affected. Doing that with longevity risk creates a “longevity pool.” Here’s how it would work, in principle.


Here’s a thought experiment.

Suppose we could gather a large group of 65-year-old males in average health in a particular country. In this fictitious country, their average future life expectancy is 16.2 years. Of course some will live longer than that, some less than that – but today, we can’t tell in advance who will live longer or less than that average period.

Someone in the group has an intriguing suggestion. He has calculated that, with current interest rates of roughly 2%, it would cost roughly $137,500 to buy a series of bonds that would provide (via their interest and maturity payments) $10,000 a year for 16.2 years. He suggests that, if each member of the group contributes $137,500 to a shared pot, they could each draw out $10,000 for as long as they live.

Of course, some would live long and get a great deal for their $137,500. Imagine getting 30 years of $10,000 payments, for example, for $137,500 when it’s only really able to support 16.2 years of payments! And others would get a bad deal: if they die after, let’s say, 5 years, they would only have received 5 years of $10,000 instead of the 16.2 years they really paid for.

But here’s the point. Unless they know in advance who will live longer or less than 16.2 years, having each contribute $137,500 is a fair deal. Yes, there will be winners and losers, but it’s still a fair deal, because it’s not possible to predict who the winners and losers will be. Each one could be a winner, each one could be a loser. As long as the estimated average of 16.2 years works out, the deal works perfectly.


In effect, that’s how a longevity pool works. Everyone contributes whatever is a fair amount for their future life expectancy, and then draws money for life – however long or short that may turn out to be. In practice the amount paid out will periodically be nudged up or down, relative to the $10,000 proposed, depending on whether, at any point in time, the number of survivors is lower or higher than the number expected from the longevity tables. But as long as the longevity tables are accurate, the longevity pool works fine.[10]

In effect, each person has done what investment people call a “swap.” They have promised to pay into the pool an amount that will cover 16.2 years of payments, and they have swapped this for the same payment every year for as long as they live. They’ve swapped an uncertain time period for a fixed time period.

In practice, to the best of my knowledge (which may not be up to date), I’m aware of only one such voluntary longevity pool in existence[11], even though this principle has been around for centuries. Nevertheless, this is the principle on which the annuities issued by life insurance companies work.


What’s particularly interesting is that there is no cheaper way to finance a payment of $10,000 (or any other amount, really – there’s no magic in the number $10,000) to last a lifetime. Why?

Well, if each member contributes less than $137,500, there’s clearly not enough to finance 16.2 years of payments on average, so that won’t work. On the other hand, why have each member contribute more than $137,500? All it achieves is that there’s likely to be money left over in the pool when the last member dies – so why bother to over-contribute?

You’ll recognize, of course, that I’ve said nothing about the expense of organizing such a pool, or the potential desire for some profit margin if a commercial organization creates it. The added payment for those is called a “loading.” But that doesn’t change the principle on which a longevity pool works.



We could reduce the financial impact of uncertain longevity by joining a longevity pool.





Where the route takes us

What we customarily call an “annuity” is a form of longevity pool to which is added a guarantee. Here I explain how the pool and the guarantee work together, and how much we typically have to pay for the guarantee feature.


You need to understand how a longevity pool works (see Trail T 05), because in effect that’s the principle on which life insurance companies’ lifetime income products work. They’re typically called annuities, but people seem to hate that word. (I’m referring here to payments guaranteed to last a lifetime, not to payments for a fixed period, which may also be called annuities. The whole point is to relieve uncertainty about whether the payments will last as long as you live.)

Annuities start by having actuaries select an appropriate longevity table for the group of people likely to buy the annuities being priced. For example, the people may be males or females forced by law to buy an annuity (as used to be the case in the UK until 2015), the specification being necessary because their health is likely to be average. Or males or females not forced, but buying an annuity voluntarily – implying that they are likely to be healthier than average, and to live longer than average, because why would they buy an annuity unless they were concerned that they might live so long that they’d outlive their assets?

Once the appropriate table has been chosen, actuaries calculate how much would be a fair price for each annuity purchaser to pay, given their life expectancy and how large an income they want to receive for life. So far, no different from how a longevity pool would operate, at the start. But then actuaries add amounts to cover four things.


The first is that the longevity table might prove to be wrong. If it overestimates longevity that’s not a problem; but it’s a serious problem if it underestimates longevity, because unlike a longevity pool, in which it’s possible to adjust the payments downwards, the insurance company gives a guarantee that payments will continue for life. So actuaries deliberately add to the longevity that the insurance company guarantees to support, as a sensible margin of safety.

Second, insurance companies have to set up reserves for the guarantees they make, and the authorities who oversee the companies have stringent reserving requirements – they don’t want to see a company fail. Add another margin for establishing stringent reserves.

Third, there are costs involved in running an annuity business: advertising the business, bringing in the business (commission to agents?), paying those involved in all sorts of aspects (management, actuaries, backroom record-keepers, and so on). Only by charging each purchaser for a share of those costs can the costs actually be met.

And finally, if the insurance company has shareholders, those shareholders have contributed capital to establish the company, and their capital is at risk if it fails, so they expect some sort of return for the risk capital.

Add it up, and of course the purchase price of an annuity has what is called a “loading” relative to the fair price that a non-profit (and hypothetically no-expense) longevity pool would charge.


Aha! How large is this loading, typically?

It’s not a surprise that academics have investigated this. Let me give you some of the results.

They use a concept that they call “money’s worth.” It’s the ratio of the pure protection provided to the cost of that protection.

What does that mean? Suppose the value of the protection provided by an annuity of $10,000 a year is $137,500 (exactly the figure we used in Trail T 05, in discussing a longevity pool), and an insurance company actually charges $165,000. Academics would say that, out of the $165,000 paid for the annuity, the underlying pure protection only cost $137,500, which is 83% of the $165,000 charged. So the “money’s worth” of the annuity contract is 83%.

The aggregate “loading” is the difference, $27,500, and this makes up the remaining 17% of the annuity price.

A couple of UK academics, Drs Cannon and Tonks[12], are experts at ferreting out the money’s worth of annuities. They report that, over the years, British immediate annuities (in the days when that was the biggest market in the world) provided money’s worth of about 90% or more.

Those are nominal annuities, with fixed payments. They also looked at inflation-indexed annuities (in other words, annuities that start at, let’s say, $10,000 and then have their payments to the purchaser increased by the amount of inflation each year). The fact is that British index-linked gilts (the bonds purchased by the insurance company in order to match the payments they guarantee) are more scarce than the demand for them, resulting in over-pricing of those gilts. In addition, there are far fewer purchasers of inflation-indexed annuities, so an insurance company’s margin of safety needs to be proportionately a bit larger. Together those facts mean that inflation-protected annuities have had a money’s worth of only 70-75%.

In the US, Dr Olivia Mitchell and others[13] report that (nominal) annuities have tended to have a “money’s worth” in the same 90% ballpark.

Personally, I think that’s pretty good. Why? Because if you don’t enter into that sort of pooling arrangement, the cost of making your money last until some advanced age is likely to be much higher than an insurance company’s loading. See Trail T 07 for an explanation. But also see Trail T 09 to see why a deferred annuity might be preferable to an immediate annuity.



If you want a longevity pool with a guarantee that the amount paid will never decrease, that costs more. And it’s called an annuity.





Where the route takes us

We know that pooling our longevity risk with others is the least expensive way to generate lifetime income. I wanted to test that statement with numbers that applied to my wife and me. Here’s what I found.


In Stage F 43 I mentioned that the biggest fear of retirees is outliving your money. Ensuring that you have an income for life, no matter how long you (and your partner) live is therefore a fundamental goal of retirement finance. And I showed in Trail T 05 that a longevity pool is always the least expensive way to guarantee an income for life.

That’s not quite the same thing as buying a lifetime income annuity, because (as mentioned in Trail T 06) an annuity adds a loading to the pure cost of longevity protection.

Now we’ll examine the question of how much more than the pure cost of longevity protection is involved when you self-insure longevity. And by “self-insure longevity,” what I mean is that you set aside, for yourself, a large enough sum of money that it’ll last for the rest of your life, even if you live to a ripe old age.


Some years ago, to get a rough order of magnitude, I did a quick calculation for my wife and me. (At the time, my wife kindly consented to my using her chronological age for these calculations, rather than the age 39 that reflected her mental outlook and energy.) Our joint-and-last-survivor expectancy (to the second estate event, that is) turned out to be 29 years, according to the then current longevity tables. I wanted to be very safe, so I delved more deeply into the tables and discovered that 5% of couples our age would have at least one partner still alive after 41 years. (I know I talk about the 25% and 10% survival points in Stage L 21, but at the time I did these calculations I was more extreme in my risk aversion and used the 5% survival point.)

For my calculations I used a real (after inflation) interest rate of 0%. Partly this was because we were at the start of the era of financial repression, with governments keeping interest rates artificially low; partly it was because an annuity value at a 0% interest rate is the same as the life expectancy, and that greatly simplified the calculations. So the ratio of 41 years to 29 years (a bit more than 140%) was therefore also the relative value of the two annuities.

In other words, whatever it would cost us to set aside for 29 years, we would have to set aside 40% more than that, to make it last for 41 years. That was an eye-opener. And even then there’d be a 5% chance that we would outlive our savings.

(Incidentally, speaking to an insurance agent at the time, this was when I first encountered the novel phrase “estate event” as a euphemism for death.)

The higher the real return assumption, the lower would be the additional cost, because the payments at the far end would require a smaller amount to be set aside today if a higher return can be earned. But even at a 2.5% annual real return assumption (if only those days would return!), the ratio turned out to be 126%.


I have since done many such calculations, based on single lives and couples, and using a range of different return assumptions. The ratios tend to come out to something between 120% and 150%.

Naturally, they vary enormously depending on the relevant ages and return assumptions. They also vary with the acceptable chance of failure: there’s nothing significant about the 5% figure I used for our own initial calculations.

If you can, I urge you to do your own calculation, or to get your financial professional to do so for you. You’ll find, I’m sure, that self-insurance is expensive. Of course, your professional may well suggest that you seek a higher investment return by taking more investment risk, in the hope of generating additional funds that way. To which I suggest that, before you do that, you should at least consider Tinbergen’s principle (Stage F 46), to the effect that an investment solution is not the best way to combat longevity – unless, of course, no form of risk pooling is available in the country in which you live, in which case you have no choice but to create an investment solution.



Not surprisingly, it costs a lot to be able to make your income survive to some advanced age.





Where the route takes us

Annuities tend to have a bad reputation. Yet, whether or not we use them, just having them available is a good thing. Here’s why.


Most people have never come across the concept that economists call “annuity-equivalent wealth.” Here’s what it means, briefly. Let’s do a little thought experiment.

Imagine two countries, two societies, whatever. Call them A and N (A for available lifetime income annuities and N for not available).

You and your spouse live in A. You’ve worked out your desired post-retirement spending pattern. And you find that you have just enough money to lock it in by buying a lifetime income annuity. And that’s what you do. That gives you a certain amount of pleasure, or satisfaction – or, as economists call it, utility.

Your twin is married to your spouse’s twin. They live in N, and they have exactly the same desired lifestyle and exactly the same amount of money. Get the idea? It’s simple and it’s symmetrical. (Hey, this is a thought experiment.) The difference is, living in N, the twins don’t have annuities available. So they’re exposed to longevity risk. What do they do? Being sensible, they set aside some money each year, against the chance that they live beyond age 95 (or 100, or whatever). So they spend less than you. So they have less utility than you.

How much less utility? It doesn’t matter. That depends on how upset they are at turning down their spending dial – that’s what economists call their utility function. But whatever their utility function, they experience less utility than you do. And yes, they can leave a bequest, because there’ll probably be something left after their second estate event; but if you build saving for a bequest into the lifestyle, then all it means is that they have unused money left at the end. So they have less utility.

Ah, but if they had more money, that would take their utility back up. So, how much more money would they need, to raise their utility back up to your level? That’s what annuity-equivalent wealth measures. It’s expressed as a ratio, like 1.2, or 1.45, or whatever.

The precise level depends on what you assume is their utility function, of course. But the level is always bigger than 1, obviously. And that’s because they have no pooling mechanism for longevity risk. That’s why Society A is better off than Society N. People have higher utility in Society A, with the same amount of money. Neat idea, isn’t it?

That doesn’t mean that everyone will or should buy a lifetime income annuity, as we saw when we discussed wealth zones in Stage F 28. It just means that society as a whole is better off when people have the option to buy an annuity.





Being able to purchase a lifetime income annuity enhances people’s utility, relative to living in a society where these annuities are not available.




Where the route takes us

Two of the four decumulation approaches in Stage F 61 involve buying some form of annuity. Is there anything we can say to compare their respective merits? Yes – and that’s what we examine in this stage.


We saw in Stage F 61 that there are essentially four ways to convert your pension pot into a sustainable stream of income for life. Two of these involve estimating how much you can withdraw every year from your pot, to live on. We’re not dealing with those two ways, in this Trail. Here we’re going to look at the other two ways, both of which involve pooling your longevity risk (as discussed in Trails T 05 and T 06). In other words, you buy a guarantee from an insurance company that they’ll pay you a specified amount for the rest of your life.

In one case (an immediate annuity, Stage F 62) they start paying you immediately. In the other case (variously called a deferred annuity or longevity insurance, Stage F 64) you pay the purchase price and buy the product now, but payments only start at some specified future date (the deferred date), and then they continue after that for as long as you live. Obviously, for any given level of payments, a deferred annuity costs substantially less than an immediate annuity. This is because the insurance company pays you for a much shorter period under a deferred annuity, because it makes no payments until the deferred date. In fact, if you pass away during the deferred period, it makes no payments at all.

In this Trail I’ll explain why a deferred annuity is usually a preferable choice to an immediate annuity.

I say “usually” because there are undoubtedly times when an immediate annuity can make more sense. For example, if your sole focus is to maximize your guaranteed lifetime income, there’s nothing better.

Why consider a deferred annuity? For two reasons.

One is that it leaves you in control and gives you flexibility with the portion of your pension pot that isn’t part of the immediate annuity purchase price. For example, if in your case the required immediate annuity costs $100,000 and the required deferred annuity costs $20,000, you maintain control over the $80,000 difference. It isn’t just the psychological benefit of the feeling of control; it’s also that you have the flexibility of investing the money as you consider appropriate for generating income during the deferred period.

But in addition there’s the fact that, if you should pass away in that deferred period, you won’t have lost the $80,000. I mentioned in Stage F 62 that, to many people, this feels like a gamble, with early death causing a huge financial loss. In fact, it’s not just an emotional feeling. It turns out that, in effect, the $80,000 works exactly as if you were giving the insurance company a policy to be paid to them if you die early. Yes, you’ve effectively written a life insurance policy on your own life, and the insurance company is the beneficiary and you’re the guarantor.[14]

Why would you do that? Imagine going to an insurance company and asking to buy a deferred annuity, and they say, “Yes, but only if you underwrite a ‘whole life’ policy on your own life, with us as beneficiary.” Your first reaction would probably be a confused “Huh?” but your second reaction would probably be: “No, wait, I have no need to do that, all I want is to buy a deferred annuity.”

Let me be clear. I’m not suggesting that this is underhanded at all. It’s a perfectly legitimate financial contract. And you also get fair value for money: it’s not a one-sided deal by any means. The added value you get is that, because you’re putting so much more money into the longevity pool with the immediate annuity than with the deferred annuity ($100,000 versus $20,000, in this example), you get a higher income with the immediate annuity than you would if you bought the deferred annuity and invested the $80,000 yourself in fixed income. The more money you pool, the better off you are if you outlive your life expectancy, and the worse off you are if you live a shorter time than your life expectancy. It’s a fair deal. That’s what pooling is all about.

But this “reverse whole life policy” is such a little understood interpretation of the difference between an immediate annuity and a deferred annuity that I wanted to make sure I referred to it explicitly, even if just on this Trail for Enthusiasts.



If you want to maximise your guaranteed lifetime income, an immediate annuity is usually preferable. For any other goal, you might prefer to just buy guaranteed income after some advanced age.






Where the route takes us

Unlike with the glide path approach while we’re accumulating assets, where the typical saver’s exposure to growth-oriented assets ought to decline as retirement approaches, there’s no consensus as to the shape of the glide path once we start withdrawing money. In this Trail we’ll examine what the experts tell us.


We saw in Stage F 11 that it makes sense for the equity exposure to start high in the accumulation phase and then decline as retirement approaches, because the amount of assets to which the equity exposure applies keeps increasing in accumulation. Hence the equity “glide path” in accumulation. Does that tell us anything about whether there should be something systematic about the equity exposure as we move through the decumulation stage? And if so, should the equity glide path in retirement be a rising, level or falling one? That’s what we address in this Trail.

What’s clear is that there is no agreed answer among experts. Nothing approaching the commonsense “Dad and Son” anecdote of Stage F 11. Instead, experts perform tests to see which systematic path looks best, using many different criteria to rate them. (The criteria are academic rather than based on retirement psychology. See Stage F 71 for a case study based on one couple’s psychology.)

Tests are made in two different ways, one involving actual history and the other involving multiple (“Monte Carlo”) simulations of how the future might evolve if the distribution of possible returns follows some assumed pattern. Each approach has advantages and disadvantages.

The advantage of looking at history is that you can say: “Here is what actually happened,” and that’s very powerful psychologically. The disadvantage, of course, is that the evidence is very sparse because history didn’t occur thousands of times, it only occurred once! And so it could be dangerous to think that the future couldn’t be worse than the past.

The advantage of simulations is that you get a much more complete range of possible outcomes. The disadvantage is more subtle. It’s not simply “None of these actually happened” because in a sense the past doesn’t matter, it’s only the unknown future that matters. The thing is that if many years produce bad outcomes in a row, invariably governments or central banks intervene to attempt to change the pattern. The consequence that, in reality, a long run of really bad outcomes tends not to happen, whereas in theory the next year’s simulation is totally independent of what has happened previously. And so you find that simulations invariably show worse outcomes possible than have actually occurred. And this is important, because the whole purpose of examining your risk tolerance is to ask: “Could you stand a bad outcome?” And if bad outcomes aren’t likely to be as bad or as frequent as the Monte Carlo simulations imply, then yes, that’s a disadvantage of those simulations.

You therefore probably want to take both sets of tests into account.

Am I ducking the issue of being prescriptive and telling you what to do? Yes, for two very good reasons. One is that there is no consensus among experts that one way is totally superior to the other way for testing equity exposures, and equally there is there is absolutely no consensus about whether increasing, level or decreasing equity exposure is best.[15] The fact is, you’d need a crystal ball before you can feel confident, and no such thing exists. My other very good reason is that(as I’ve said so often) I’m not in a position to offer you advice, because I don’t know you, and the crucial element (as we saw in Stages I 31 to I 33) is your risk tolerance. Remember that in P3 in the Prologue, where I explained what it means to be an informed consumer of expertise, I reminded you that you are the expert on the subject of yourself, and it’s your job to educate your financial professional about you.

Here are the arguments in favor of a level growth exposure.

One is intuitive. Let’s assume you have the same risk tolerance throughout your retirement years as far as a decline in your drawdown is concerned. Then a level equity exposure places the same proportion of your future income at risk all the time. The outcome may be good or bad, but in any year the percentage loss of drawdown that you face doesn’t change.

Another is that, both in theory and in practice, it tends to work for much of the time. (Nothing works all the time, of course.) Estrada demonstrates[16] that a level 60/40 mixture of equities and bonds (the idea being that whenever markets cause your allocation to depart from 60/40, you rebalance back to 60/40) works pretty well. In fact, he demonstrates that 100% in equities works pretty well too! Scary, no doubt, but it works.

Next, the arguments for an increasing equity exposure as you age.

One, again, is intuitive. The amount of money that remains in your pension pot decreases over time. If you are willing to place the same amount of money at risk over time, then you need to increase the equity exposure as you age. (Notice the difference between the two intuitive approaches. One assumes constant relative risk tolerance, the other assumes constant absolute risk tolerance.) What’s more, it can be proved that, for any level equity exposure over time, there’s a path of increasing equity that provides the same expected outcome at lower risk.[17]

And once again, another reason is that it tends to works pretty well. In fact, its proponents[18] say that, although it feels spooky (they never actually use that word, but they imply that that’s how many retirees would feel), it works so well that perhaps it needs to be sold in a psychologically appealing way. The financial professional should tell the retiree that in the early retirement years there’s no need to worry about returns, because all the drawdowns will come from safe investments; then let the safe investments run down and run out, and voila, in practice you have an increasing equity exposure, with all the good results that follow!

Finally, here’s the case for a declining equity exposure.

And once again, it’s that it works in practice. Estrada[19] looks not only at an American using US equities, but also at an American using global equities, and then at 18 other countries (including some where some aspect of the economy – like inflation in Germany – went out of control), and demonstrates that historically a systematically declining equity path in retirement has worked better than a systematically increasing equity exposure.

All of which now probably leaves you feeling totally confused! If reliable experts come to three radically different conclusions, how on earth are you to judge which is the way you should go?

One common element in all their analyses is that you should use their approach systematically. That implies that you stick to it, and don’t panic when things start to go wrong – perhaps easier said than done. Risk is always there, but if you use any approach systematically and don’t take more risk than you’re willing to stand, it ought to work reasonably well over the long term.

If there’s no easy answer, what can you say to evaluate a financial professional’s advice to you (no matter which of the three paths is recommended to you)?

That’s where I return to the way in which you can be an informed consumer of expertise and apply the relevant principles to your own situation.

Remember what I said in P3 in the Prologue? I suggested that you can do three things, once you understand the framework (which I hope I have provided in this stage).

First, assess what the expert is saying. What is the main message? Here it could be: “As long as you don’t panic in the middle, pretty much any approach can work in practice.” Or perhaps: “Trust me, I’m the professional.” Or: “There’s no guarantee, so we’ll pick Approach X and adapt as we go.” Or whatever.

Next, challenge the expert. What are the principles on which the proposed strategy is based? That equities ought to outperform safe investments in the future, as they have in the past? That every year’s returns in the future will be independent of the immediate past? Also challenge on the nature of the evidence. Is the projection into the future based on history repeating itself, or on Monte Carlo simulations of the future? And what is the professional assuming about your own risk tolerance? Is it presumed to stay constant or to decline over time (Stage H 62)? Confirm that it’s measured by aversion to fluctuations in your annual spending, not by aversion to asset value fluctuations, which are not directly relevant (Stage F 42).

And finally, apply it all to your own situation. Which wealth zone are you in (see Stage F 28)? How does that affect your goals and your risk tolerance? What is a likely level of sustainable annual drawdown for you, and to what age is it projected? How much of a decline can you stand? And again: do you think your risk tolerance likely to decline as you age?

All of those considerations together should give you your best chance of determining which equity path you are most comfortable with.



Experts don’t agree on whether the equity glide path in retirement should rise or fall or stay level.





Where the route takes us

We’ve looked at the annuity from many perspectives. Let’s gather them together here and identify the essence of what its role should be.


Annuities have more uses than we can imagine, particularly in connection with estate and tax planning in countries where they are singled out for special treatment, like the US. Those are not my focus here. Here I consider only the retirement portfolio, aimed at generating income from a chosen date forward.

You’ll recall the three goals such a portfolio can have (Stage F 46): investment safety, investment growth and longevity protection. And you’ll recall Tinbergen’s principle, that each goal should have its own instrument.

Longevity protection isn’t an investment goal. It’s a “length of lifespan” goal. And therefore ideally it should have its own instrument. That’s the annuity. Not that an annuity is the only possible approach; it’s just that it’s the most efficient, least expensive approach. For example, you can aim to accumulate enough money to reach the Endowed Zone (Stage F 28); then you won’t need longevity protection because you’ll never run out of money. But that’s an expensive way to secure the goal, relative to buying an annuity.

So that’s the sole purpose of an annuity in a retirement portfolio: to secure longevity protection. It’s not an instrument focused on investment safety or growth. Yes, it does have investment characteristics (typically involving a safety orientation), but those are incidental and may even hinder your further pursuit of investment safety and growth. Don’t judge the relevance of an annuity by what its investment characteristics are.

If you do decide to use an annuity for longevity protection, and these instruments are available in your country, two further questions arise. What sort of annuity? And how much to spend on it?

The two main choices as regards type of annuity are the immediate annuity and the deferred annuity (also known as longevity insurance). In Trail T 09 we saw why, for most people, the deferred annuity is preferable. The determining factor in the choice between the two is whether you want to maximize guaranteed income (in which case the immediate annuity appeals) or just focus on longevity insurance and invest the rest of the portfolio with some eye on growth (in which case the deferred annuity appeals).

There is sometimes an indirect form of longevity protection available, sometimes called a Guaranteed Lifetime Withdrawal Benefit (GLWB) or a Guaranteed Minimum Withdrawal Benefit (GMWB), in which the protection is linked to mutual funds. In this form you pay for the protection via an annual fee, typically a small proportion of the remaining asset value, and retain the right for any remainder of the assets after your estate event to go into your estate. But as you can imagine, all you’re contributing to the longevity pool is your annual fees, so that doesn’t buy you much actual longevity protection. In fact these hybrid contracts attempt to offer both longevity insurance and investment growth, and therefore (Tinbergen again) they could be an expensive way to get pure longevity protection.

Finally, the question of how much to spend on an annuity.

Start with a reminder that its purpose is to secure longevity protection. Therefore, unless you fear outliving your life expectancy, it doesn’t seem appropriate at all. For example, if you’re what insurance companies call an “impaired life,” meaning that you suffer from some ailment that is likely to shorten your lifespan relative to the average expectancy at your age, you should see if they will offer you a higher guaranteed income than the average annuity purchaser would get, to compensate for the reduced expectancy. With that higher offer, an annuity may appeal again; without it, you may be better off self-insuring.

OK, let’s assume that you do want longevity insurance. Back to the question of how much.  Inevitably that’s subjective. This is where you have to decide for yourself the relative importance of the three goals.

If you’re in the Bequest Zone (Stage F 28), you have no instant need to secure longevity protection, but it’s something you should monitor because you won’t want to slip down into the Lifestyle Zone just because (for example) equity values fall or interest rates fall. You might like to do a little bit of longevity protection right away, if that makes you feel better.

If you’re in the Lifestyle Zone you might want to do some right away, or wait and hope that growth takes you up to the Bequest Zone first. Some people I’ve discussed this with suggest that it might be appealing to lock in spending that involves essentials, via an annuity that covers that amount of spending. The more you have in pre-annuitized wealth, the lower the appeal of locking in more spending; the less you have in pre-annuitized wealth, the higher the appeal of covering more spending via an annuity.

As you can see, ultimately it depends on psychological factors – exactly as anticipated in Stage I 32 – and perhaps the sequence of thinking in Stage F 42 may be helpful.

One final aspect relates to the timing of purchasing an annuity. We saw in Trail T 04 that the older you are, the more significant longevity risk becomes, relative to investment risk. So at some stage (which might be by age 75, from the examples mentioned in that stage), if you’re unwilling to be 100% invested in growth assets, logic suggests that you ought to be reducing your longevity risk exposure too.

Another timing consideration is simply that if you’re purely in safety-oriented investments and don’t seek any further growth, then it becomes appealing to buy an annuity, if you’re still in at least average health and have made all the preparations you want regarding bequests.

A final timing consideration, one that is likely to be stressed by financial professionals, is that interest rates change, the supply of and demand for annuities change over time (as, for example, big pension funds buy annuities en masse), and so on. Spreading the purchase of annuities over time in order to average out the impact of interest rates, or buying at a time advised by your professional – these become investment-related considerations about timing.



Annuities should be considered purely in their capacity to provide longevity protection, not as investment instruments. The choices then become: immediate or deferred annuities; how you rate the goal of longevity protection relative to the goals of investment safety and investment growth; and when to buy an annuity.


July 1, 2019





Where the route takes us

There are all kinds of technical investment results that professionals like to measure and to report to you. They may be useful as background, but they miss the point, which is to inform you about the extent to which their advice and decisions have improved your standard of living in this phase of life. Here are five often unappreciated ways in which they can help you.


In 2013, on a visit to Australia, I was invited to address a number of gatherings. One was the annual National Conference of the Fund Executives Association Ltd. (known by its initials as FEAL). We agreed on a topic that was of interest to them and to me, and which I had come across and been excited by when I saw an article in 2012. I was later asked to write up my talk as a guest editorial for the University of Toronto’s Rotman International Journal of Pension Management, which I did with great pleasure. Here’s what I wrote in that piece.[20]   


Recently I was asked to comment on what matters most, as far as retirement investments are concerned. My response was simple: what matters most is what investments contribute to the ultimate outcome, which is to enable the investor to enjoy a standard of living without having to work.

Measuring time-weighted returns recognises that product providers don’t control cash flows. Subtracting the market return (which is also not controlled by product providers) then produces excess returns, loosely called alpha. And so the excess return is a conceptually pure measure that enables investment managers to compare themselves with one another – but it is virtually irrelevant to the investor’s lifestyle.

That doesn’t mean investing isn’t important. It is! The 10-30-60 rule[21] reminds us that most of the investor’s lifestyle is funded by investment returns, indeed by investment returns in the post-retirement or drawdown phase. But that just emphasizes that investing creates a multiplier effect that assists the goal; it isn’t the goal in itself. That’s measured by the retiree’s drawdown.

And there are many things other than alpha that enhance the drawdown. As an investment guy myself, I appreciate those other services very much, now that I have – how can I put this? – graduated from full-time work.

Let me refer you to a paper: “Alpha, Beta and Now … Gamma” by David Blanchett and Paul Kaplan of Morningstar.[22] And let me lead you through some of those things that also enhance post-retirement income. They list five. How they apply in any given country will of course vary. But here’s the idea.

The first service is a total wealth framework to determine the optimal asset allocation. What does that mean? It means that, at any time, an investor’s prospective retirement wealth consists partly of money that has been contributed, and is invested in the capital markets, and partly of money yet to be contributed. Taking greater market risk when the amount exposed is small, and reducing market risk as the amount rises (a “glide path”), exercises better risk control than a constant asset allocation. For a given level of expected outcome, the certainty-equivalent utility (think of it as a risk-adjusted added amount) corresponding to a glide path exceeds the certainty-equivalent utility corresponding to a constant allocation.

By how much? Well, that depends on the assumptions, inevitably, because we can’t foretell the future. The authors calculate that it’s worth an extra 6%.

I feel your reaction: all that work, for 6%? Hardly seems worth it, does it? But let me express it another way. You know how much alpha needs to be delivered, every year, consistently, net of fees, to have the same impact? 38 basis points. Certainty equivalent.  Annually, over a lifetime. How many of us have delivered 38 basis points with total certainty, net of fees, year in, year out?

Let me tell you about the other services.

The second is a dynamic withdrawal strategy. A sensible naïve withdrawal strategy might be the 4% rule. You withdraw 4% from your fund in the first year, and increase that dollar amount by inflation each year. What’s more sensible than that? More sensibly, you’d re-evaluate the withdrawal each year, to allow for the actual experience. Guess what: that too increases the certainty-equivalent utility. How much? 9% improvement.  Equivalent to 54 basis points a year, net, with certainty.

The third is the use of an annuity. Your withdrawal strategy always needs to be adjusted to allow for the fact that, as you survive year by year, your expected age at death increases. If you don’t allow for this, you have about a 50/50 chance of running out of money before you run out of life. So of course you’re going to make an allowance.  You’re going to be cautious. But if you act very cautiously, and don’t withdraw as much as you can, you’re left with an estate at death, that reduced your potential consumption. Down goes your utility. Buying a lifetime income annuity with some part of the assets, again, enhances the risk-adjusted utility. How much? 4%. Equivalent to 24 basis points a year, guaranteed, net of fees.

The fourth is withdrawal sourcing. A member’s total assets are partly the pension assets and partly other assets. The naïve strategy would be to withdraw assets for spending, proportionately from all sources. A better strategy would take account of different tax rules. Again, improve the utility. How much? With American tax rules, 8%, equivalent to 52 basis points a year, guaranteed.

The fifth and final one is goal-relative optimization. The naïve approach would be to look at the assets only. In that case, an asset class with a low standard deviation of return makes for low risk. But if the stream of desired spending payments, including inflation, is taken as the goal, then an asset allocation that matches that spending pattern is what represents low risk. And that would result in a different set of choices on the efficient frontier. And again, relative to the naïve asset-only case, utility goes up. How much?   2%. Equivalent to 14 basis points a year, with certainty, net of fees.

Let me add it all up, to answer the big question, which of course is: Does the investor care? And, from my post-graduate perspective, the answer is a resounding and heart-felt “Yes”. I haven’t any doubt that if a manager can get investors to increase withdrawals by an aggregate of 29%, that would be huge. And as a reminder, to make the same point in a way even an investment geek would understand, that’s equivalent to an after-fee alpha of 182 basis points, consistently, guaranteed every year. Yes, it’s based on the authors’ input assumptions. Yes, those assumptions refer to American conditions. Do the calculations yourself, for your own country. See what the answer is. And see if you think it’s likely to arrive more reliably than alpha.

What’s more, alpha in the aggregate is a zero-sum game, before fees. These services can be delivered to all investors. Everyone can win, simultaneously.

But fully appreciating the power of this “five actions” message requires measuring investment outcomes that truly matter to investors: the size and certainty of their post-work income stream.



Professionals can help you by taking into account your future work income in the accumulation phase, by nudging your drawdowns to reflect investment returns, by using annuities, by using tax-efficient strategies, and by allocating post-retirement assets to reflect your desired spending. Together these actions can add up to the equivalent of almost 2% a year in higher returns – that’s what matters, much more than attempting to “beat the market.”




[1] The two concepts aren’t quite identical. “Risk” refers to an outcome that arises from a known distribution of possibilities. “Uncertainty” refers to an outcome from a distribution that we have no knowledge of. For example, if we’re tossing coins and have placed a bet on getting two heads in a row, there’s a risk that we’ll lose, and the risk is known (for an unbiased coin) as being one chance in our favor to three chances against us. We know the odds; we just can’t predict the outcome with certainty. In contrast, if we bet that a particular person will fall down next Tuesday, we have no idea what are the odds; that’s simply uncertainty. I won’t take this distinction any further. In this stage I treat the two words as having the same meaning.

[2] Bernstein (2013).

[3] It was given the title “Pension savers – are you prepared for the risk?” on 30 January 2016.

[4] “Shallow risk, deep risk” Commentary by Stuart Fowler, 4 February 2016, at

[5] See, then U.S. Stock Markets 1871-Present and CAPE Ratio, then data series ie_data.xls for real dividends.

[6] The arithmetic average is a little above 2% and the geometric average a little below 2%.

[7] Lo (2005).

[8] Ezra (2011b).

[9] Collie (2015).

[10] The most fascinating book on longevity pools I’ve ever read is Milevsky (2015).

[11] It’s called Mercer LifetimePlus™, in Australia.

[12] Cannon et al (2004).

[13] Mitchell et al (1999)

[14] For a full technical explanation, see Ezra (2016).

[15] Estrada (2015). Here you’ll find a full discussion of both issues, as well as a summary of all the evidence, not only in the US — which is what most tests examine — but also in 19 countries around the world.

[16] Estrada, op. cit. See also Blanchett (2007).

[17] Cohen et al (2010).

[18] Pfau et al (2014).

[19] Estrada, op. cit.

[20] Ezra (2013).

[21] Ezra et al (2009) – see Stage F 02.

[22] Blanchett et al (2012).