March 2015

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.

A Message to My Corporate Friends

As I write these words, “What’s Your Future Worth?” is about to be available for purchase. For me, this is the culmination of 3 years of writing, editing, talking, thinking and hoping. I have been advised by people who know far more about these things than me that I need to put up a new post to this blog to mark the occasion and so for the last couple of hours I have been perusing the anecdotes that were left out of the book for one that might be appropriate for the occasion.

Unfortunately I wasn’t able to find one, in part because despite all the thinking and all that I wrote about it in the book itself (step 2 of the Present Value process is “imagine the future”), this was a future that I simply couldn’t envision back when I started writing down some musings every morning; musings that ultimately became “What’s Your Future Worth?”. In fact, most of what I have written, (and will include in future blog posts) is quite specific and very much focused on different aspects of either the actuarial perspective or how to apply Present Value to make better decisions.

Today, however, I want to talk more about why I think “What’s Your Future Worth?” is a worthwhile investment of your time and your money. And while what I am about to say can be appreciated by anyone, I want to direct this post to a particular audience. Specifically I want to speak to my friends in the corporate world who are responsible not only for decisions made by their organizations as entities unto themselves, but also to those who are responsible for decisions that affect the financial well-being of the employees who work for those corporations.

Corporations get a bad name these days, and I fully understand why. Notwithstanding the snide comments that we hear every day (e.g. “Don’t be mean, after all, Corporations are people too”) there is tremendous prejudice against the motivations and ultimate agendas of corporations. I confess that I am not immune from such feelings, but I also want to say that some of my best friends are corporations. I mean that sincerely. In a very real way I feel not only close to many of the individual clients that I have worked with over the years, but also am not ashamed to say that I genuinely like some of the companies they work for. More to the point, I think most corporations have both good intentions and a dark side. It is those good intentions and that “better nature” that I think my book speaks to and for which the actuarial perspective can be extremely useful in providing the means that corporations can use to help improve the world.

At the end of the day, what is a corporation after all? The way I look at it, a corporation is a living entity whose cells are made up of human beings and one whose lifespan is a little (sometimes a lot) longer than ours. Perhaps there is no “soul” within a corporation, but as individual cells, how would we even know if there was one? What is clear, however, is that corporations make decisions and those decisions have future consequences – both for themselves as well as the people who work within them and interact with them. Despite the conventional wisdom that companies only seek “profit maximization”, I think that corporations can and do take into account much much more when they make decisions. Like people and their decisions, the future DOES matter to a corporation and the process they (should) use to evaluate the consequences of those decisions could benefit tremendously from considering Present Value.

I spoke earlier about how we can think of a corporation as a complex multi-cellular organism whose cells are individual human beings. If so, it seems self-evident to me that such an organization should do everything it can to help those cells thrive and be healthy; physically, emotionally and financially. In fact “Financial Wellness” is a buzzword these days and many firms (mine included) are seeking ways to help their employees become financially more healthy by designing compensation and benefit programs that maximize benefits (as valued by the employee) at the minimum possible cost to the employer. This is all well and good, but the fact is that the corporation will never know all they need to know about an employee’s total financial situation to make all the right decisions on their behalf. Even more importantly, the corporation will never know the hopes, dreams, plans and values of each of their employees. At the end of the day it’s the individual employee who has to make the right decision, and the best the employer can do is to design programs that empower and equip those employees to make the right choices to ensure their financial health.

“What’s Your Future Worth?” is a book that will show both corporations and the employees who make them up how to make the decisions that will lead to better futures for everyone, and I truly hope all of you choose to read it.

I am not a salesman at heart and I promise this is the last pitch you will get from me. From now on this blog will only be about Present Value, the actuarial perspective and/or how both can help make the world a better place.