Category Archives: Actuarial

More on Holistic Financial Health – Present Value and the Rest of Your Life

In my last  post I talked about how important it is to use  your personal rate of discount and to think “holistically” about your financial life. In particular, I spoke about how critical this is during your working years when you are accumulating assets of all kinds and incurring both near term and long term liabilities. That need to consider your whole balance sheet does not end when you stop working and consider the rest of your life, and in this post we will talk about that (looming and long) period of your life

While what I said in the last post about holistic financial health might be considered idiosyncratic and contrary to mainstream financial planning, there is one financial expert who, when it comes to the “decumulation” phase of life, has been advocating the holistic approach for nearly a decade. His name is Steve Vernon, and those who read “What’s Your Future Worth?” may remember him as the actuary who wrote 5 excellent books on planning for retirement and started a consulting firm called, appropriately enough, “Rest of Life Communications” ( ). To my mind there is no one better than Steve in helping you think through the challenge of converting all that you have accumulated into income that you can live on.

I had dinner with Steve last week, and I got the opportunity to hear about the fascinating current research projects he is involved in, but mostly our conversation focused on the more general problem of how to help people manage their financial world, both during their working years when income (generally) exceeds outgo as well as afterward when the reverse is true. Steve and I are very much on the same page when it comes to taking a holistic approach to financial decision making and if you want to get his take on the big picture of how to approach the problem, you should check out this article ) as well as this post  where he lays out most of the possible ways to generate retirement income and this example where Steve explains one of his “retirement income generating strategies” .

As extraordinary and on target as Steve is, there are a couple of areas/techniques that Steve generally passes over but I believe should also be considered when you think about your entire financial life and your objectives. It is those areas I would like to briefly describe now, and in future posts I will expand a bit and provide a more complete explanation of why I think they are so important.

Perhaps the most important area that I think needs to be integrated more tightly into a holistic view of financial health is the real estate most of us own. I spoke last time about considering both the value of your house and the mortgage you pay as a key part of your personal balance sheet, but the value of your house goes well beyond being just a (usually) good financial investment and a place to live. Your house can also be used, to use Steve’s term, as another “retirement income generator”. I alluded to this point last time when I introduced the concept of a “reverse mortgage” which is essentially a home equity loan with no need for repayment until you sell or move out of your house. The availability and the effectiveness of this income generator is growing and becoming better known, and in the coming weeks I will devote an entire post to reverse mortgages and the role that they can play in your decumulation strategy, but for now I would just direct you to two links that can provide you with some basic knowledge on the subject. The first is which is an excellent discussion of reverse mortgages and the use of home equity in general put out by a group with no financial interest in having you buy anything. The second is  which is a paper published by Barry Sacks (an expert in the field) that pretty clearly demonstrates the benefits of incorporating a reverse mortgage into your decumulation strategy. In the future we will discuss both of these pieces in greater detail.

As described in the links, contrary to popular myth, taking out a reverse mortgage does not mean that your children will be deprived of their legacy. Beyond that, and implied in much of what passes for financial planning these days, is the notion that the ideal “decumulation” strategy will result in an exact match of your income and your life expectancy, i.e. that if you die without having spent all your assets (except for the house) you will not have gotten the “most” out of your retirement. I disagree, and think that for most of us, our planning horizon does extend beyond our lifetime and includes a concern for both the loved ones we leave behind and the world that they will live in. In fact, to truly take a present value approach to managing your financial life you need to imagine that part of the future (when you are gone but others that you care about are still around) and consider how much value you place on it vs the current time frame and the mid-term future that comprises your retirement years. In terms of the ideas in “What’s Your Future Worth?” this means that when considering your decumulation strategy, you need to make sure you don’t skip step 2 (imagining the future) and step 4 (developing your personal rate of discount) all the while considering a time horizon that extends beyond your death.

Next time we will delve more deeply into this notion and talk about 2 or 3 other financial products that you should consider as well as part of your holistic approach to ensuring your financial health for the rest of your life and beyond.


In Defense of Personal Rates of Discount

As more and more people react to what I’ve written,  it seems that  by far the most controversial aspect (particularly among actuaries) of “What’s Your Future Worth?” has been the notion of a “personal rate of discount” and the proposition that each individual (rather than an expert) should decide how the relative value of amounts that will be received in the future versus those that are received (or paid) in the present is determined. The challenges to the concept have been less about whether or not we all have personal rates of discount (research in behavioral economics over the last 30 years on “time preference” has demonstrated this compellingly) but rather whether we should rely on our own internal time preferences to make important life decisions.

The argument goes as follows. Over the millennia, our biological evolution has produced within us what seem like “programming bugs”. Many of these bugs  have served us well when we roamed the Savannah and needed to avoid starving or being eaten by saber-toothed tigers, but they do not serve us so well in the modern world. Undoubtedly this is true when it comes to our difficulties in evaluating the likelihood of various future scenarios; both on an individual basis (e.g. our risk of getting in an accident, suffering imminent death, disability, or loss of job etc.) and on a more macro-economic basis (e.g. the likelihood of a stock market crash, changes in inflation/interest rates, etc.). Those who take issue with “personal rates of discount” argue that we also are “programmed” to overvalue the present (perhaps because primitive man’s future was so fraught with risk and danger) and therefore a key role of actuaries (and other financial planners ) is to “deprogram” individuals with our expertise and therefore enable individuals to make better decisions that will lead to better outcomes and less regret.

I have two answers to this. The first is that I see a fundamental difference between the objective evaluation of real world risks (like the probability that the plane you are flying on will crash or that you will have a heart attack and die in the next year) and a determination of what is basically an internal set of feelings about the way you live your life. I think it is highly presumptuous for anyone to tell me what I will or will not regret 30 years from now. How many stories have we all heard of people at the end of their life regretting all the “rational” financial decisions they made instead of taking that trip around the world, spending more time with loved ones, and generally experiencing life in the moment? It’s not an easy thing, but I don’t think such tradeoffs between the now and the later should ever be outsourced.

While the above answer might be sufficient for those more philosophically inclined, I also think there is another reason not to rely on outside advice in weighing the present versus the future. Specifically, I think that the ability of actuaries and others to choose the right discount rate even when personal feelings are not at issue is by no means perfect. In fact, in my view, the notion that for a specific question, there is always a “correct” discount rate to be used, even when it’s big companies making important decisions with large sums of money at stake, is an illusion.

Another actuary once confided in me that in his view “Present Value is just a bed time story we tell our clients when they can’t fall asleep at night.” While I wouldn’t go that far, the following cautionary story about how even actuaries can get confused when setting discount rates, illustrates the point in detail.


Jeremy Gold and some “Inconvenient Truths” about discount rates

 “A million dollars of Stocks is worth the same as a million dollars of Bonds, and no amount of actuarial magic will change that “

Jeremy Gold  FSA , PhD to a standing room only crowd of actuaries

“Please tell me you are not going to make Jeremy Gold the hero of your book.”

James Kenney FSA  upon hearing that I might want to tell Jeremy’s story


It was 2003 when I first heard Jeremy Gold speak. I had been working in a small boutique consulting firm and was only vaguely aware of the stir being caused by this actuary who had gone and gotten a Ph.D. in Finance, only to return to tell the world, and the actuarial profession in particular, that the way we had been doing our actuarial valuations, determining contributions  and most especially the Pension Expense for Company Income Statements, was not only wrong, but had been fundamentally flawed for decades and that disaster would ensue  if changes were not made to both the accounting rules, and the investment strategies that companies used to allocate Pension assets. Needless to say most actuaries took issue with what Jeremy was saying.

The debate finally reached my awareness when I received notice that the annual Society of Actuaries meeting that year would be almost entirely devoted to what was being referred to as “The Great Controversy”. The fact that the meeting was being held in Vancouver, a city I had never been to but one that always intrigued me, was enough to convince me to devote 3 days to finding out what all the fuss was about.

Now, actuarial conferences do not have a reputation for being particularly exciting, but the atmosphere in the room for Jeremy’s session was almost electric. By being early I was able to get a seat relatively close to the podium, but many of the late arrivals were relegated to standing in the back and along the side walls. By this time, Jeremy Gold was a notorious figure among actuaries, and many were just aching to engage him in public debate.  Jeremy was tall and lanky and had a head of curly hair and intense dark eyes. He stood at the podium leaning forward staring at the audience with a look of defiance and anticipation. To me, he looked like a middleweight boxer standing in the middle of the ring just daring his opponent to come out of his corner and start fighting.

He began speaking and what he had to say was deceptively simple. He started by explaining how actuaries had historically performed their pension valuations. In particular, he described how the contributions were based on Present Values calculated using a discount rate that essentially was “equal to the ’expected’ annual investment return on a balanced portfolio of stocks and bonds”.  On the other hand, Present Values for company financial accounting purposes utilized a discount rate that was based on corporate AA bond rates (typically 2-3% higher than US Treasury “risk free” rates), but that the expected return on that balanced portfolio (typically another 2% higher than the corporate bond rate) was also directly incorporated into the annual pension accounting calculation as a credit, offsetting the rest of pension expense.

This was all basic information that every actuary in the room knew and used every day. But what came next was not. Jeremy first asked us to consider whether there was any risk associated with the benefits that were promised by the pension plan. Now, by law, all assets in Trust can be used for no other purpose than to pay benefits, and in the unlikely event that the company goes bankrupt and the assets have fallen below the level of the liabilities, the benefits (except for amounts payable to the very highest paid employees) will still get paid because there is a government sponsored program (the Pension Benefit Guarantee Corporation also known as the “PBGC”) that is funded by company paid premiums and provides insurance against such an event. So, except at the margins (ie for benefits higher than the PBGC guaranteed amounts, or in the event the PBGC and/or the US Government defaults on its obligations), pension benefits are fully secure. So why, Jeremy asked, are we as actuaries using a discount rate that is based on AA corporate bond rates that have a material risk of default?

As he quite reasonably pointed out, if long term US Treasury rates are 4% and corporate bond rates are 6%, the 2% difference represents value that the market places on the default risk (including the probability that the bond will actually default). As a result, Jeremy said, rather than overstating pension liabilities (as many actuaries were whispering to their clients) the use of AA Bond rates (in this example 6%) as a discount rate was creating financial statements that grossly understated the pension liabilities of our clients’ pension plans.

Jeremy’s point was that from a theoretical perspective any cash flow should be discounted using a rate obtainable from “a security (or portfolio that) has cash flows that match the liability in amount, timing, and probability of payment”. In this case, with assets in Trust and PBGC guarantees backing up residual underfunding, the obvious security to look at would be returns on US Treasuries, which were as close to risk free as any investment could be.

At that Jeremy stopped and let the implications of what he just said sink in. Many in the audience were aware of this line of attack on standard actuarial practice and presumably were just waiting for the Q&A to unleash their rebuttal, but most of us were not. And the more we considered it, the more we realized that if Jeremy’s point was valid, the consequences were significant, if not game changing. First, virtually all Pension Plans in America would become seriously, if not catastrophically underfunded. The mathematics of Present Value dictates that for every 1% that the discount rate drops, the Present Value of accrued benefits for a typical pension plan will go up by 10%-15%. If, we as actuaries had been complaining about having to value plans using the FASB rules requiring a discount rate as low as nominal bond yields and if these rates that were 2% higher than appropriate (and for many plans in many years the spread between “risk free” and actual rate used was much higher), the typical pension plan, rather than being 80%-90% funded as actuaries and accountants had been presenting to the world (with actuaries secretly saying the plans are even better funded), the average plan would be more like 50% funded, a truly concerning level.

Beyond the embarrassment and impact on the profession’s credibility,revising valuations along the lines Jeremy was suggesting would mean that the health of the US pension system was seriously impaired and had been for decades despite the actuarial profession’s representations to the contrary. How the financial markets (let alone companies’ employees, unions and Boards of Directors) would react would be anybody’s guess, but clearly it would be ugly, and the actuarial profession would not only be in the “blast zone”, we would be sitting at Ground Zero. And then there would be the question of how the Government/PBGC would react to the news that the value of their potential guarantees had suddenly tripled (ie. 15% underfunding becoming 45% underfunding). Would PBGC premiums (about which companies already incessantly complained) triple as well? Would the program be curtailed? The government itself would likely be highly conflicted as significantly higher pension liability would ultimately have to translate into higher employer contributions and less tax revenue (Companies get a tax deduction for pension contributions). Finally, given the fact that companies consider pension benefits a portion of employee compensation and if this component of pay suddenly became 2 or 3 times as expensive as previously thought it would be a pretty good bet that many, if not most, would cut or eliminate these programs entirely. And of course, the last not so minor point, was that if many pension plans were terminated, there would be far fewer actuaries that needed to be employed. It would not be an exaggeration to say that to many in the audience, this vision was apocalyptic.

But Jeremy was far from done. Having just cast serious doubt on our profession’s competence as well as its valuation of a few trillion dollars of pension liabilities (at the time there was about $6 trillion in total private and public pension assets and liabilities in the US, and that number has actually grown substantially since then), he now turned his attention to the assets that were backing these plans. In particular, he took dead aim at the investment strategy most companies took with respect to such assets and how those strategies were not only dangerously misguided, but had been put in place in large part because of the actuarial advice received regarding the impact those strategies had on the calculation of pension expense.

Technically as actuaries we were not responsible for the investment of the assets, but we are often asked to opine about basic asset allocation strategy and so many of us had to rely on portfolio theory to make those recommendations and to do so we used highly sophisticated stochastic projection models that generated the potential outcomes (in terms of pension costs) of each possible investment strategy. For the typical pension plan, the ideal asset allocation always seemed to come out to about 60% stocks/40% bonds. I’m over simplifying a bit, but having been involved in dozens and dozens of large pension plans over the years, prior to 2003 I had rarely seen a plan whose stock allocation was less than 50% or higher than 70% and almost all hovered right around 60%.

Jeremy was saying that not only was this 60/40 allocation wrong it was radically wrong. Over the next 20 minutes he laid out a clear and compelling case for the proposition that virtually all US pension plans should have their assets 100% in US Treasury Bonds.

The centerpiece of his argument was elegant and powerful. It started with a proposition that was very difficult to take issue with; that the value of $1,000,000 worth of stocks was identical to $1,000,000 invested in US Treasury bonds. Despite this, he said, we as actuaries were assuming different annual expected returns on each investment. For this to be the case, the market must believe that any higher expected return available on stocks (or corporate Bonds) would be offset by the risk associated with the investment. And yet by crediting the expected return as an offset to pension expense with no accounting of this extra risk taken on, we were not only distorting the “true” annual cost of the pension, but also were providing strong incentives to our clients to maximize the riskiness of their pension investments. Taking on additional risk in such an opaque way was, in Jeremy’s view, enabling company management to put their enterprises at risk without the stockholders (or the PBGC) being made aware or being party to such a decision

The argument seemed airtight, and yet the implications were even more far reaching than his discussion of what discount rate to use. As noted, there was, at the time, about $6 trillion in pension assets. Probably more than $3 trillion of that was invested in stocks with the remainder mostly in corporate bonds. Now the value of all the publicly traded stocks on the major exchanges in the US was about $13 trillion at the time. While no one could know for sure, it seemed almost certain that the impact on the various markets of the sudden transfer of 25% of invested assets from the stock market to the Treasury bond market would likely be cataclysmic. The shift in immediate demand would almost certainly send stock prices plummeting, bond prices soaring and interest rates plunging. The fallout was frightening to consider, as it would not just be the pension system that collapsed if Jeremy’s recommendations were followed. It was one thing to cast doubt on the professional competence of a few thousand actuaries and to disrupt the mix of benefits that employees received from the companies they worked for. But it was quite another thing to potentially knock out one of the pillars holding up the US Stock market and potentially the economy as a whole. Jeremy was messing with some powerful forces and there was a palpable sense of foreboding that now filled the room.

After dropping his two bombshells on the audience, Jeremy spent the rest of the hour filling in the gaps and addressing potential objections to his thesis, meticulously and systematically dismantling each one until all that seemed left of the standard actuarial model was a pile of smoking rubble. When he finished you could hear a pin drop. With a look of eager anticipation, he said that he would be happy to answer any questions that the audience might have.

Not surprisingly they came at him fast and furiously. Many were not questions at all, but simply prepared rebuttals and challenges for the propositions he had presented. They were sharp, focused and only marginally civil in their trajectory. Like a 19th century gunslinger standing in the town square taking on all the local deputies and concerned citizens intent on maintaining the status quo, Jeremy barely moved as he fired back. He dispatched most of the attacks methodically, and with deadly accuracy. He was nicked by a couple of sharpshooters, but the wounds were superficial. Some pointed out that the portion of benefits not guaranteed by the PBGC were far from risk free. Others noted that in a typical pension plan the payment of benefits would extend far beyond the longest duration of any bond available in the market place rendering his T-Bond investment strategy somewhat impractical. But through it all no one was able to discredit his central premise.

Gradually the tenor of the questions started to change. Rather than attack directly, actuaries started asking practical questions about how Jeremy planned to get us all out of this fix. They started to appeal to him as an actuary, asking what should the profession do and what would he, as a representative of it, propose? He was, after all, one of us, and as such would presumably be just as unhappy as any of us in seeing the demise of the actuarial credential. Jeremy, however, was implacable. A crusader for the Truth, I suspect he viewed himself less as an Old West outlaw and more like Martin Luther out to reform the Catholic Church.

Finally, someone from the audience stood up and wondered aloud about what exactly would happen to the security of all these promised benefits if financial statements were revised, the market crashed and more than a few of the public companies who not only were providing the pensions but whose stock made up the crashing market started to go bankrupt. And in that event, were these pension benefits really so secure after all? For the first time, since the session began, Jeremy hesitated and finally allowed that if, at the end of the day, pension benefits were not as secure as we have all been led to believe then “well maybe in that circumstance using some sort of corporate bond rate to discount liabilities might be appropriate”. And on that somewhat uncertain note, the session ended.



 Whether or not it was a self-fulfilling prophecy we will never know, but subsequent events have shown Jeremy (at least in my opinion) to have been more right than wrong. PBGC premiums have just about tripled since 2003 and the cost of Pension Plans has been recognized as significantly higher than previously thought. Over the last 12 years huge numbers of plans have also been frozen, closed or terminated and the investment of assets  in those Pension Plans that still exist has shifted significantly towards bonds contributing (I believe) to the forces that have pushed interest rates to unprecedentedly low levels. Perhaps coincidentally, the stock market also crashed and we all suffered through a global financial crisis in 2008-9 from which we are now just recovering.

Finally Pension benefits are now recognized not to be the “rock solid guarantee” they once were as some Public Plans have gone broke and recent legislation now allows certain types of Plans to reduce benefits for existing retirees if the Plan is sufficiently distressed.

The above notwithstanding, my point in taking so much space to tell Jeremy’s story is not to say that he was right or wrong about how actuaries should calculate the Present Value of Pension Liabilities or to invest the assets, but rather to demonstrate that the question of how to discount any future event is not 100% clear and actuaries do not necessarily have any special insight into the future that means their opinion should be taken as Gospel. If actuaries themselves can’t decide whether future pension benefits ( a well defined question and something that we are the experts at) should be discounted at 4%, 6% or 8%, why should we believe that there is a “right” discount rate to use when it comes to each of us making important decisions today that will have consequences in our each unique future? I said it before and I will say it again. Don’t let an actuary tell you how to discount your future. By all means ask your friendly actuary to help you frame the issues and evaluate the likelihood of future scenarios, but then think carefully, think long, and know that using your personal rate of discount is the only way you will be able to make decisions that you will not regret.

More About Time Part 2: Personal Rates of Discount and the Time Value of Time

Now that a few people (including some actuaries) have read “What’s Your Future Worth?” I am starting to get questions on one of the more counterintuitive concepts I propose. Specifically, in the book I have taken the position that there is no “correct” discount rate to use when comparing the future to the present and that to make good decisions about the future, each person should introspect deeply and determine their own “personal rate of discount”. No one seems to doubt that if left to their own devices most people will choose not to delay gratification and opt to receive benefits (monetary or otherwise) sooner than they “should” according to traditional economic theory. Many retirement planners and others in the financial world believe that this is simply a mistake and that their job is to help their clients overcome their “emotional barriers” and think objectively about the future.

I disagree and think that what many financial planners are perceiving as emotional errors are often just manifestations of not only our own individual and completely valid “time preferences” but that the traditional “foregone investment” approach to setting a discount rate is in fact based on a specific (and not necessarily correct) assumption as to the nature of time itself.

How time flows and the Time Value of Time

“I just read with great delight your article on ‘the time value of time’…It was a real eye-opener”
John Haley FSA and CEO of Towers Watson

“I wonder …whether you (in your article) meant to be ‘tongue in cheek’”
David Wesley M.D. and Vice President of Cologne Life Reinsurance Company

My ruminations on the nature of Time and how it flows differently for different people began decades ago and in 1996 I was inspired to put some of those thoughts together in my first, and (thus far) only, attempt to add something new to the field of actuarial science. In essence I started from the observation that for most of us, time feels like it is accelerating as we get older, and that while the months and years seemed to drag on forever when we were young, now they seem to fly by in the blink of an eye. I then defined a concept called “perceived time” based on the (hopefully) reasonable assumption that time is perceived to pass at a rate that is proportional to age. In other words a year will “seem” to last twice as long when you are 20 as it does when you are 40. From there I went on to restate a number of actuarial elements (discount rates, life expectancies, annuity values, etc) using “perceived time” instead of the normal definition of time in developing the formulas. The results were interesting, surprising and in my view explained a lot of the “irrational” choices that people make when faced with economic decisions that require them to choose between getting something now versus later (eg whether to take a lump sum payment or a lifetime annuity from their retirement plan)

At the time I was very satisfied with what I’d come up with. My article was published in the Jan/Feb 1997 issue of “Contingencies” a fairly well respected actuarial publication
( ) . The response was reasonably positive and other than Dr. Wesley’s skepticism, most readers took my paper seriously and found its premise intriguing, if not obviously true. Over time, however, I have come to realize that while there may be a kernel of truth in my “theory”, the nature of our relationship to time, is far more complex than I had imagined.

It turns out that there is a pretty extensive amount of academic study devoted to just this question, though it is framed in a slightly different way. Specifically the term “time preference” is defined by economists as the way people value the present as compared with the future and over the last 40 years quite a few economists have conducted a myriad of often ingenious experiments to determine what the average individual’s personal rate of discount rate is and how it varies by circumstance. The results of these experiments show, first, that personal rates of discount are extremely high (14%-179% according to a 2002 survey of all the studies on the subject), but even more confounding is that the rate will vary by all sorts of factors that are “irrational”. For example:

People show dramatically different discount rates when the choices are presented at different points of time (eg today vs one year from now as opposed to one year from now vs two years from now).

People treat decisions affecting expenses (eg whether to pay $100 now vs pay $110 a year from now) very differently than they treat choices about income (eg whether to receive $100 now vs receive $110 a year from now).

The magnitude of the dollars involved has a big impact on the discount rate used to value future payments ($2000 payable a year from now is worth more today (relatively speaking) than $20 payable a year from now)

When multiple time periods and cash payments are considered (eg payments and/or expenses at 3 or 4 different points in time), choices are inconsistent and do not reflect a stable discount rate.

When risk is combined with choices between the present and the future are given, even when the probabilities of outcomes are specified (eg 50% probability of $1000 one year from now vs $200 for certain today), the answers received vary dramatically and unsystematically both when the probabilities are varied as well as the time periods.

So what exactly is going on? Well, one obvious conclusion is that more work is required to understand the way we, as humans, actually process the passage of time and view the future as compared to the present. On the other hand, as scattered and chaotic as the findings above are, there do seem to be two consistent patterns that suggest my original concept of the “Time Value of Time” plays a part. First, the fact that under almost all circumstances there is a positive discount rate suggests that people prefer to receive something now vs. later. There are some limited circumstances where people’s discount rate is actually negative and individuals prefer to delay gratification, (eg the “Christmas Club” savings account that Banks used to set up where people paid a small fee for the opportunity to not access to their money), but these are the exceptions to the rule. In addition, there seems to be a consistent finding that people’s discount rate is lower the longer into the future one looks. For example Leonard Green and others showed that people would choose to receive $100 today rather than $110 a month from now, but would prefer $110 payable 13 months from now vs $100 payable 12 months from today. The phenomenon becomes even more pronounced when the choice is extended out several years in the future. This is most dramatically illustrated by Richard Thaler who showed that over periods up to one year people manifested personal rates of discount of more than 100%, but over a ten year period average discount rates are under 20%. This finding is called “hyperbolic discounting” and one of the consequences of the concept of “perceived time” as I constructed it is that people’s discount rates will be hyperbolic and tend to decrease as both an individual ages and as an individual looks further into the future (all of these findings can be found in “Time Discounting and Time Preferences: A Critical Review” Journal of Economic Literature 40:pp351-401).

The point here is not to determine exactly how we humans perceive and evaluate the passage of time. That will take many more years of research to figure out. But what we can say, and this is the crux of my argument, is that people do seem to have their own “natural” way of perceiving the flow of time and it seems to have very little to do with how much they could earn on money that is set aside. To see this consider that the studies referenced above took place over a 40 year period during which prevailing interest rates and expected investment returns in general varied widely. As far as I could see there was no meaningful correlation between people’s “personal rate of discount” and the prevailing expectations of investment returns at the time of the study.

The financial planners out there may say that all of the above may be valid but people still should factor in their expected rate of returns when determining a discount rate, because by the time the future arrives they will be happy they did so. Maybe so, and there is no doubt that people should be aware of how much they might earn on money that is set aside, but my belief is that we live in the present and not the future and therefore it is important for us to make decisions in the here and now that are most consistent with who we are as human beings and that if we are true to our own internal values (including our time preferences) we will ultimately be making the right decisions for ourselves and be happier for it.

More about Time: Part 1 – On the Importance of Knowing your Time Horizon

I think it’s time to talk more about Time.

In “What’s Your Future Worth?” I talk about the how to develop your own personal rate of discount and how important that is to making good decisions. It’s a hard concept and one that I find does not come naturally to most people. Unfortunately, the nature of Time (in this context) is also more complicated than I presented in the book. In the next few blog posts I will share some of my thoughts on how we humans experience the passage of time and how we should take that awareness into every important decision that we make. But for now, let’s start with one of the most important aspects of Time that we always need to consider and that is –when does time end?

Omega and the Actuarial Perspective on the End of Time

“There’s them that comes in (to the population) and them that goes out. There’s all kind a ways to get in, but there ain’t but one way to get out and that’s to die”
Professor Robert Batten, FSA — explaining the mathematics of Stationary Populations (a key part of “Life Contingencies”) to a class of actuarial students

The essence of actuarial mathematics (at least as it was taught in the 1980’s) and the “Pons Asinorum” for most actuaries of my generation was a subject called “Life Contingencies” explicated in a beautiful book of the same name by C.W. Jordan. Most theoretical mathematicians have never even heard of the subject let alone studied it, but almost all actuaries of a certain age will attest that it is every bit as hard, abstract and “pure” as any undergraduate math course they took in college, and for most of us, a well-thumbed and treasured copy of “Jordan” still resides on our bookshelves. Like most pure math, Life Contingencies has a pristine and pure elegance that richly rewards those who make the effort to learn its intricacies and master the deep and elegant theorems that are at its core. The only small problem that even those of us who loved the math had with Life Contingencies was that in order to become a licensed actuary we had to pass a 5 hour test on the subject that was diabolical in its construction, overwhelming in its scope and contained far more problems than could possibly be completed in the time allowed. Even those who studied for several hundred hours and thought they thoroughly understood the material would come out of the exam feeling like they had only scratched the surface in their preparation. To make matters worse, the Society of Actuaries (who administered the exam) used this particular exam to limit the number actuaries getting licensed and only passed about 25%-30% of those that took it. The test was so hard that most actuaries needed extra course work to pass it, and when my employer offered to send me to Georgia State University to attend a seminar given by Professor Robert Batten designed to help actuarial students like me get “over the hump” and on with our careers I jumped at the chance.

Even considering the wide range of characters inhabiting the profession, Professor Batten was not your typical actuary. A “good ole boy” from somewhere deep in the South, his neck was not just red, but bright red. A rabid Atlanta Braves fan he seemed far more comfortable downing a beer at the ballpark (where he took the class after the seminar ended) than explaining Lindstone’s theorem of annuity values to a bunch of aspiring actuaries. Yet his seminar was riveting. He attacked the subject from two sides. On the one hand, he provided colorful and cogent explanations of the math, almost always punctuated with pointed and often funny stories taken from his obviously less than academic personal history. Somehow his deep southern drawl and down home expressions made the subject approachable and less intimidating.

But the second and most important aspect of his teaching was his dissection of the actual problems from prior exams, where he taught us all kinds of ways to solve problems (or more specifically to get the correct answer) that were not in any book. There was one powerful technique he taught us to use when faced with a particularly inscrutable equation to solve. Specifically, he showed us that when we were faced with such a problem we could simply “special case it”. In his terminology this meant to consider what the expression (which was usually filled with all kinds of variables) would look like at the extreme values (eg if interest rates went to zero or if people became immortal and nobody ever died). Often surprising insights about the nature of the equation could be gained and/or most of the possible answers (it was a multiple choice exam) could be eliminated. In addition to being brutally pragmatic it was a mind expanding way to look at the fundamental equations that governed our profession. It was at this seminar and thinking about this technique that I became intimately familiar and finally understood on a deep level two important concepts that would ultimately inform my thinking about Time and its relationship to actuarial science. One (“Omega”) I will talk about now and the other (“Stationary Populations”) will be discussed in a future blog post.

In actuarial science, Omega, is defined as the limit of the human lifespan. Actuaries need this concept because we use mortality tables that assign a probability of death to every age (eg a 65 year old man has about a 1% chance of dying before turns 66 while approximately one in ten 90 year old women die before reaching age 91) and we need to pick an age where the table ends and the probability of dying within the year is 100%. Whether such an age exists is an interesting philosophical/scientific question, and maybe one day we will know the answer, but for actuaries the concept of Omega is merely the solution to the practical problem of how to keep the calculation of present value tractable. The mathematicians among you may say that a specific Omega is not necessary if one defines mortality as a function of age and in fact there were many early attempts by actuaries to define such a function using ideas like the “force” of mortality (based on an assumed basic law of the universe whereby the “life force” of a human naturally and predictably diminishes over time). Unfortunately none of those attempts were successful in closely modeling the observed mortality rates upon which so much, including the financial solvency of insurance companies, often depends. In the future l may talk more about some of those attempts in the context of how actuaries have historically tried to quantify Risk, but for now suffice it to say that history has shown that the best way to develop a mortality table is to observe the ages at which millions of people actually die and develop tables based on those statistics. This is not as simple as it sounds and in fact there is a whole sub branch of actuarial science called “Mortality Table Construction” that is devoted to that effort.

But what interested me was the broader implications of assuming an age where essentially time stops. Consider an Insurance company that issues an annuity to a 75 year old man that promises to pay him $1000 per month for as long as he lives. Currently most Insurance Companies use an Omega of 110. If we assume the reality of Omega, then the Insurance Company and our 75 year old are not entering into a permanent contract which might end at any time, but rather one that they both assume will end in 35 years. This tension between a timeline with a fixed (certain) endpoint and one that theoretically could go on forever comes up again and again in the actuarial world. It is the fixed timeline that we most often use (sometimes implicitly), but in fact many of the promises made are explicitly indeterminate, and “eternal” in nature. This disconnect has always troubled me and continues to trouble me to this day. I truly believe that no one will live forever, and as a practical matter the cost of the annuity described above won’t change whether we assume a 100% probability of death at 110 or assume a vanishingly small (but still positive) probability of living to 175 or beyond. But what about the Insurance Company that issued that contract? Can we really assume that they will be around to make good on their promise 100 years from now? Is there an Omega for Insurance Companies as well that we should be considering? It might not make a difference from a cost perspective, but it does seem odd to me that we consider the “natural” lifespans of one party to the transactions we value, but blithely ignore the lifespan of the other.

The above is particularly troubling (and relevant to my work as retirement actuary) when we consider the case of a Company sponsored traditional Pension Plan where the Plan promises to pay a fixed pension for life to any employee who renders sufficient service with the Company and then retires. For a 25 year old newly hired employee that promise could extend another 80 years (or even longer if she takes on a younger husband and elects a “joint” annuity). Can anyone really be sure that the Company promising this pension will be around to provide it? That the government that “insures” this promise in the event the company goes bankrupt will make good?

We actuaries pride ourselves on being long term thinkers and in fact have helped keep a few large Life Insurance companies in business for more than a century with our prudent advice on pricing and managing time, risk and money, but the time horizons implicit in our calculations have always struck me as far too long for us to have any real confidence that the promises based on what we are calculating today will have any real meaning 50-80 years from now when some of the consequences of our projections will be fully realized.
The situation is even more acute when we think about our own lives and the decisions we make every day. Beyond the obvious issue of how long we will live, almost every decision we make involves others; either people, institutions, and/or the environment itself. All of those entities have their own “omega” that needs to be taken into account. Sometimes the time horizon is obvious (eg when we consider Climate Change, a subject of a future blog, we need to consider that the earth essentially has no time horizon, or at least none that will matter to us human beings), but in many others it is not.

When we think about a legacy we are leaving to our children and grandchildren or a particular institution, how far in the future should we consider? When we think about investing in our education, our community or even our personal relationships, how long will that knowledge/educational benefit, relationship or community last? We tend to think the answer is “forever” (or at least as long as we and those we are in relationship with are alive), but I would suggest that that is an overestimate and all of us would do well to consider that everything is impermanent, transitory and will eventually cease to exist or transform into something else. We will never know when the end will come, but betting on the permanence and immortality of anything is usually a losing proposition. Be sure to consider this the next time you use Present Value to make a decision.