July 2015

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.