Centenarian risk

Worry about the unknown causes people near retirement age to curtail risk exposure, which cuts off their future upside potential.  For most individuals this is not a prudent way to ensure that they have the best use of their retirement savings, in their final stage of life: after they stop working.  What we show in this article is that it would be better to do a handful of things jointly: (A) save much more for retirement throughout one’s career, (B) spend a little less of their savings once you retire, (C) increase one's investments in risky assets for more than nearly two decades into retirement [a risk exposure at this later stage when many suggest one having far lower risk], (D) consider retirement planning for a maximum joint life expectancy of age 100, and (E) become accustomed to “visualizing” one's older self.  Coming off the global financial crisis, and seeing many pension funds in the U.S. underfunded, it is easy to see that Americans have myopically over-estimated the risk intrinsic in the financial markets.  In doing so, they would be missing an inherent amount of stability and growth opportunity that the markets have to offer for one’s nest egg.

To approach this article it is best to discuss aspects of wealth generation throughout one’s career; then discuss aspects of spending in the later stage of life.  Age 66 is used as a rough demarcation of when we cross from one aspect of life, to the other.  We’ll show that roughly 2/3 of all Americans born in 1950 will reach this near-retirement age (66), within the upcoming year of 2016.  Of that 2/3, which will be the focus of this article, only a random handful are expected to reach age 111.  That’s nearly 45 years of retirement.

Let’s start with the wealth generation period, and later we’ll discuss the retirement period.  For many Americans, one begins working after college, and we can use a rough marker of age 21 for when this occurs.  Of course, some individuals start earning a living well before that, and a small portion of others may instead enjoy graduate school or something else and not work full-time until their late 20s.  All of this clearly exposes that slight adjustments will always need to be made when dealing with personal circumstances.  Of course, most readers here are not born in 1950.  Again utilizing age 66 implies a working career of about 45 years (66-21).  So note that for a small extreme group born in any given year, they will endure work and retirement, for nearly 45 years each!

There are a number of poor rules-of-thumbs that exist, chiefly through financial advisers, concerning how much to invest in risky assets during this period of wealth creation.  One popular one is to invest, 100% (or 110%) minus your age, in stocks.  A 66-year old, therefore, would be investing nearly 40% of their portfolio in stocks (linearly drawn down from about 85% when one begins his or her career).  This lower risk level near retirement is to suggest that one should take less risk closer to when they can least afford to.  On the other hand, another trend recently has been to suggest that one should have an even greater level of risk along the way, including leverage, since the time horizon of investment is large enough to encapsulate any risk events that can occur early on.

The approach of the risk modeling research done by this author –and cited by a Board member of Lending Club- is that neither of these two approaches strikes the right balance.  The amount of risk during one’s wealth generation is not at all a linear function; and the “100%-age” type rules underestimate the amount of risk that would be appropriate.  For example, half way through your career to have only about 60% in risky assets overemphasizes the amount of risk from these assets (and by that point you could be living more than an additional half-century!)  Additionally, both this and the second approach described above misunderstand what the risk event is that one is ostensibly protecting themselves from.  We can’t control when markets will fall out of whack, but we must assume that rebounds follow collapses.  Most of our underlying modeling works in a similar fashion and with an economic cycle of about 5-7 years (not 20-25 years prior to retirement), we might assume we already have a full recovery from a risk event.

Another issue with the second approach is the use of leverage, which can run someone into trouble a few different ways.  The first way surrounds the high costs of leverage that drain from returns, an issue that hedge funds generally are having now.  The second way is a market collapse with leverage can have a much more destructive emotional and financial toll on the individual.  See this article for products that have been impacted by both of these two issues.  And a third way is the risk that an early career risk event would behaviorally alter one’s investment thesis, thereby disallowing one to capitalize on whatever high upside the leveraged approach should have offered in the end.

The modeling we show on the first research link above is novel in a couple mathematical respects; it highlights the difficulty in solving this problem in the more rigorous closed-form (using more probability theory versus simulations).  It also reflects that modern random walks offer some nuances that were not previously vetted.  Those erroneous ideas provide some unique assumptions for when we can also model (log)normal distributions of returns in clever ways, which thus far investment and insurance professionals have not taken advantage (e.g., taking products or ratios of normal distributions).

But of course life doesn’t end at retirement!  Just ask anyone who is retired about what happens from there.  So the “recovery” from a risky event is actually more probabilistically complicated, from this age of ~66.  See the illustration below for a survival function [S(t)] of a hypothetical mix of 100 thousand people born in 1950 (the first marker below from the left).  We see that of this birth sample, 95 thousand will live to age 21 (in 1971), and 66 thousand will live to age 66 (in 2016).  After this third marker shown from the left (next to the vertical axis), the additional markers to the right along the curve is something that we’ll describe later as being half-lives.

From this illustration to help clarify the underlying U.S. government actuary table.  Of the 66 thousand who will retire next year, the average life expectancy is only 13 additional years (to age 79 in 2029).  This is higher than the life expectancy in general (age 68) for all of those born in 1950; since we have some typically dying far earlier than average and so others must typically die much later than average in order for balance.

Another implication of this is that the mortality function picks up rapidly by retirement!  In this case the 13 years also happened to be the first half-life of retirees, in the sense that of the 66 thousand sample, we only expect 32 thousand (roughly ½ of them) to survive to age 79.

In order to focus more closely on the mortality function of retirees, we represent below the survival life table again.  It is logarithmically scaled on the vertical axis, and truncated prior to year 2016.  We can see that the survival of retirees doesn’t decay at a fixed rate, but rather accelerates at about year 2050, a time when we get into the centenarians.  On an aside, for year 2039 onwards the actual life tables do not function from actual life and death statistics, but rather mortality functions we’ll describe below.

 

Another way to focus on the mortality function is to line plot the half-life of retirees, starting with the 13 years we noted for those age 66 (next year in 2016).  We note that we can set a simple exponential function (shown in black dots using the left-scale) - not on survival, but on the half-life alone.  We have a high R^2~0.9.  And the actual curve is actually more aggressive versus the line at close to age 100 (the year 2050).

We also show with the illustration above, a complimentary mortality rate function (illustrated exclusively with diamond markers).  Here we can see (using the right-scale) that the table-provided decrements are also more aggressive versus at age ~100.  We have another high R^2~0.9.

In this case the convex exponential curve suggests that the life table, for retirees, can be modeled with an increasing (not fixed) mortality rate with S(t) of the form e^[-f(t)], which if reasonable could provide mortality risk for a pool of the population separately from investment risk (note that here we still need to model both jointly for merely personal situations).  These functions do bring up the interesting advantage insurance companies have for being able to more smartly price an annuity product for your life, taking risks over many birth years.  However as was apparent when running a major PBGC research department, this was seen as an expensive product one can easily auto-manufacture using the ideas here, and very similar to ideas some of the world's wealthiest people (who also read this blog) have for the trustees of their will.  See this research for more on actuarial formulae.  

We’ll continue to use all of this life data and actuarial understanding, to consider the investments and risks as they carry through one’s entire retirement period, on through death.  As opposed to the initial wealth generation period, we have thus far discussed.  And it’s the sort of difficult variance -not in investments but in mortality- that becomes an equally important secondary issue to consider.

Two rungs down based on half-life, would be age 85.  Where the 66 thousand sample (by definition of half-lives) would have been halved nearly twice, to 16 thousand.  Halving twice is a reduction of 75% (½*½=¼).  On setting out to retire, we could create a risk example where we have sufficient funds to pay for retirement in 75% of the cases (with only a ¼ of the cases we would survive beyond age 85).

We’ve had a popular 4% withdrawal rule for example (typically associated with 20th century financial planner Bill Bengen), where we might state that someone with $2 million in retirement savings at age 66 can draw $80 thousand per annum.  If their spending needs rise by 4% and their investments grow by 2%, both conservative estimates and per annum, then we can see (in the yellow curve) below that one would have enough to fund life through age 85.  As with our earlier comment on unique circumstances, here too one can of course be more optimistic on both their own growth forecasts for personal spending and savings levels.  But for the purposes of risk modeling we’ll stay with a more conservative value that get us by for 75% of us (note the double half-life discussion in the previous paragraph.)  And then we can measure the sensitivities about our estimate, based on stressing different variables.

The risk of having risky assets in a retirement context has generally been described as a large market correction early in retirement, which also can not generally be made up for.  This doesn’t make any sense though.  We show above (in orange), a 25% portfolio crash as well as a slow 5-year rebound.  We even reverse the sequence of this variation (in green).  We see that neither version has a large impact on our retirement savings through the later stages of retirement (it’s just + a year and hence well within the range of all the other risk uncertainty we’re modeling!)

What might be more interesting to explore is when the same 2 versions of events occur at age ~79, or 6 years prior to the age 85, we have been focused on recently.  We see a fairly similar overall effect now, though the key point being that at these very low retirement savings levels, the 25% market crash then is simply negligible relative to the drawdowns (in the sense they have the same net impact as if such risk occurred at the start of retirement where the savings levels were at least twice as large.)

The consequence for this is that risky assets could be a larger fraction of one’s portfolio for longer into one’s life, and then into one’s retirement as well.  We are proposing systematic risk here (not stock-picking).  The issue isn’t so much dying prior to age 85, since if one saved enough for retirement a market crash wouldn’t irreparably deplete their funds.  The larger issue is when is “fortunate” enough to survive beyond age 85.  And that is the case for about 25% of retirees (16% of all people born in 1950).

Those people now in superannuation (outliving savings), one could mistakenly argue can not afford to take on more risk.  They are low on savings.  But this is actually improper, since from a retirement risk perspective it is not a matter of taking on less risk to make up for having less money (we’ll address increased savings in a moment).  It’s a matter of appreciating that, if one will have a chance at a high longevity, then they need to take on risky investments in order to provide a greater return that can survive over the long-run.

Hence the balancing act of finding the right combination so that one can not survive just enough to be in the top 16% of their birth year population (age 85), but make it all the way to end of perhaps 111.  To do this, extending retirement from ~20 years, to 45 years, means a dramatic change in perspective.

For example, we’d have to live on perhaps 2/3 our currently presumed retirement spending, which is not easy.  Imagine today downgrading into a worse home in a different location just to better afford the payments, and even then skipping one meal daily.  Not fun but can be done with determination.  Or we could instead save nearly 3 times as much for retirement (e.g., $5.5 million instead of $2 million in our example above).  This is perhaps an even greater economic challenge since more of this challenge is beyond our abilities.  Or even yet, we can imagine having about 7% returns on our investments instead of the current 2% (even an institutional-level feat principally if one is risk averse during retirement).  See the light beige (2/3 spending), dark beige (3x savings), and yellow dotted (5 percentage point extra returns) curves all superimposed below.

Note however that so far we’ve discussed mortality and life tables, as if a household couple would live together as one unit.  In reality joint couples share joint risks, mainly their mortality.  Assuming an opposite-gender couple, we might think of the average longest life expectancy for both people in the marriage to come in closer to 100, so shy of the 111 value assuming we are only examining one person in the population.  This is the last personal circumstance concern that one should consider, in refining their own retirement risk modeling parameters.

When we consider the difficult task in thinking about how we would likely combine taking steps in all of these four directions above (start saving more, start spending less, take increased systematic risk, prepare for being one with a much lengthier life), one should prepare to also appreciate that the risk for your retirement savings is for the investment risk to happen much later in one’s retirement than one might want to plan for.  This implies taking on risk on their larger retirement savings, for a much lengthier amount of time.  Market crashes and sudden death for you and your spouse, before or after the age 85, are hardly an issue from a financial standpoint.  What you should be more concerned about is well outliving an investment or mortality risk.  Start today by becoming more comfortable with and accustomed to a strict financial spending diet, all the while focused on prudent investment risks.  Your older you will deserve it!

And getting comfortable with seeing your future self, particularly at age 100, let’s look at these mid-20th century photos below of a dozen from the Czechoslovakia republic.  Now these could be any of us prior to retirement.  Contentedly living and spending in the moment; and unsure of what tomorrow offers.

The difference is everyone in this mixture are current centenarians.  And a 21st century Prague photographer Jan Langer has taken pictures of all of them, as they look now.  Undoubtedly they look different, and their family relationships and personal concerns are undeniably dissimilar from before.  All the while being “perhaps” the fortunate >0.1% to live so long.  From roughly 150 citizens, in a steady national population of 10 million.  Take the more rigorous path and stay both physically and financially strong.  Envision yourself being one of these fortunate to celebrate a 100-year birthday.  And staunchly make those sacrifices today to ensure this best well-being later.