Chapter 1

MORDECAI’S PROPOSITION — A QUESTION OF PRESENT VALUE

“If I gave you $10,000 today would you be willing to give me 1% of all your future paychecks?”

Mordecai Schwartz, FSA, to a young actuarial student

It was 1979 and I had just started my first job out of college as an actuarial student with Connecticut General Life Insurance in Hartford, Connecticut. My boss was a long-haired libertarian from Arkansas who spoke so quietly you had to lean in close to hear him. He was edgy, sarcastic, and rebellious (he had only recently caved in to the company’s insistent demand that he get a haircut and begin wearing decent clothes to work), but he was also one of the top actuaries in the company with a nose for risk and a wizard-like ability to make the numbers sing and dance. He always said that what makes a good actuary is not his or her ability to calculate, or even to use sophisticated mathematical techniques to evaluate risk, but rather to understand the music in the numbers—to hear the melody, to anticipate the chord changes, and most importantly to detect the false note. He said that a good actuary should be able to look at two columns of numbers with vague headings like “prior year actual” or “current year allocated” and, with no knowledge of what the figures were supposed to represent, be able to immediately identify the wrong number.

But before I could even begin to develop those skills, I first had to learn and internalize the concept that is at the heart of all actuarial work—specifically the notion of Present Value. I was, of course, given books and files to read to learn the math behind Present Value,⁴ but Mordecai also wanted to find a way to teach me the practical importance of understanding how Present Value works, and true to his nature, he found a way to permanently embed that concept while at the same time benefiting himself and having some fun, at my expense.

You see, Mordecai was a gambler and game player. An excellent chess player, he was even better at poker, where he could combine his expertise in strategy, psychology, and probability with his fiercely competitive nature to outsmart his colleagues and make a little extra cash. He also enjoyed creating propositions and making bets—from politics to sports, from financial market behavior to actuarial matters, he was always willing to “put his money where his mouth was.” For him, it was often less about the money and more about the elegance and virtues of the proposition itself.

Not surprisingly, most of his bets involved Present Value calculations, at least in an indirect way, and the first one he proposed to me had it at its core. Having just passed the first three (out of ten) actuarial exams with only a minimum of effort, I opined one day that all the talk I’d heard about how long, hard, and treacherous the path was to becoming a Licensed Actuary⁵ was obviously nonsense and that I expected to be able to move through the rest of the exams without any difficulty. Mordecai smiled slyly and asked if I was willing to bet $500 that I would pass all of the final seven exams on my first try. Being overconfident and not understanding either risk or Present Value, I readily agreed. Of course this was an incredibly stupid move on my part. First, I had no idea what the next seven exams were like (Mordecai did). Second, even if my chances of passing any given exam on the first try was 90%, the probability of passing all seven without a miss was less than 50% (0.9 raised to the 7th power is about 0.48). Most importantly, I completely missed the fact that if I failed an exam, I could lose the bet years sooner than if I passed all the exams the first time. In other words, even if I won the bet, I wouldn’t collect for at least another four years (exams were given every 6 months) but if I lost I would have to pay Mordecai as soon as I failed, and this could happen as soon as the next exam. Given that interest rates at that time were well over 10%, this factor alone should have caused me to ask for odds.

So the fourth exam came a few months later and I completely bombed it. I walked out of the room knowing absolutely that I had failed. In a panic about the $500 that I didn’t have but would shortly owe my boss, I considered my options. The only factor that I realized was in my favor was that I knew I had failed but Mordecai did not (results would not be available for another two months) and so I had two months to negotiate a settlement. Eventually, I agreed to pay $50 immediately to extricate myself from the bet. Now to this day I wonder why Mordecai agreed. Perhaps he bought my presentation (I expressed supreme confidence that I’d passed but realized how long I would have to wait for my payoff and how I had underestimated future risks), perhaps he was being kind and/or didn’t want to risk the non-financial fallout when it became known how he’d taken advantage of his naïve young student. Or maybe he was just very risk averse, and having done his own Present Value calculation, decided that $50 was a reasonable estimate of the current worth of the future outcome of the bet. No matter what, it was a lesson well learned and one for which I owe Mordecai a debt far greater than the $50 price.

But Mordecai was not done. He had one more lesson about Present Value that he wanted to teach me, and this was the one that more than any set me on the path that has led to this book.

Mordecai’s Proposition

Shortly before the end of my time working for him, Mordecai came to me with an intriguing proposition. He asked me whether I would be willing to “sell” him a piece of my future earnings. Specifically he offered me $10,000 to enter into a contract with him whereby at the end of each year I would give him 1% of what I’d earned during the prior twelve months. At the time I was making less than $20,000 and so for the current year the bill would be under $200 and even for the next few years it seemed that I would only have to pay him a few hundred dollars. The idea of receiving fifty times the initial amount in one lump sum certainly seemed appealing, but having only just narrowly escaped a financial disaster, I decided this time to consider the question more carefully before I gave him an answer.

For the first time in my life, I tried to think systematically about the future and what it was worth to me in the present. I had to imagine what the rest of my earning career would look like. I had to consider all the possibilities—not only what my career trajectory might look like (e.g., would I rise to some senior actuarial position, change careers and strike it rich, or crash and burn struggling to get by), but also what the future economic world would be like. Would the market for actuaries get better or worse? Would inflation increase, rendering 1% of my future earnings so large as to make the $10,000 I got seem like a pittance? What would I do with the $10,000? If I invested it, what kind of return could I expect to receive and would it offset any inflation that might raise the annual amount I had to pay each year? These were the measurable factors, but there was far more to the proposition that had to be considered.

I needed to think about what it would mean to me to have this additional “tax” burdening me for the rest of my life. One thing I realized was that if I made a lot of money, the bill would be big but I could afford it. On the other hand, if times were tough, I would struggle to make even a modest payment. And then there were the relationships to consider. How would any future wife or family feel about this added “baggage”? And what about my relationship with Mordecai himself? He and I had a decent enough relationship, but what would it mean to be “in business” with him for the next few decades? Assuming my future working career would be at least forty years, lurking in the back of my mind was also another aspect of the proposition that suggested I should grab the money. Specifically, it seemed to me that while the $10,000 was a sure thing, would I really have to pay Mordecai each and every year for the next forty? Wasn’t it possible that some radical change in either his or my circumstance would render the contract unenforceable or moot? The $10,000 could be spent immediately, but were those future payments equally real? And finally, I had to grapple with the most important question in any Present Value calculation—what relative value should I put on amounts payable ten, twenty, or forty years in the future compared to the weight I put on amounts today. I had to figure out, for the first time, what my personal rate of discount was and—interestingly—whether it was different when I considered the value of the next few years’ payments compared to the payments I would be making in the very distant future.

In the end, I made the right decision and turned him down. I won’t go through how each of the five steps played out, but for me, step 4 turned out to be the critical one. The $10,000 just wasn’t as valuable to me as the large payments I expected to make down the road, and the freedom from such a long-term future obligation was too important for me to give up. For this particular decision, I used a relatively low personal rate of discount though others facing the same choice whose discount rate is higher might have done the right thing by accepting the money.

But whether or not I made the right decision is not the point. What is important is that Mordecai’s proposition is the essential question of this book. Namely, what is your future worth, and how do you determine it? For almost forty years I’ve been thinking about this question, and in the next few chapters I will tell you what I’ve discovered about how to answer it.