That’s So Random

Investment Belief #4: Randomness must be actively accounted for as part of the investing equation

For at least the course of my lifetime, we Americans – all of whom are said to be “created equal” – have held to a straightforward construct of the American Dream, where it’s always morning in America. In its telling, we are a people of unlimited power, promise and potential. The keys to our success are not status, wealth or connections, but rather ability, ambition, and drive. Anybody can become whatever he or she wants. Life is thus a ladder, there to be climbed by anybody willing to step up.

James Truslow Adams coined this evocative phrase in his 1931 book, The Epic of America. His American Dream is “that dream of a land in which life should be better and richer and fuller for everyone, with opportunity for each according to ability or achievement. It is…a dream…in which each man and each woman shall be able to attain to the fullest stature of which they are innately capable, and be recognized by others for what they are, regardless of the fortuitous circumstances of birth or position.”

Over the last few decades, a darker vision has grown up. Many of those who claim to have “done their part” by going to school, gaining new skills or working hard do not perceive themselves to have received reward commensurate with their efforts and abilities, leading to great disappointment and some remarkable income inequality. Indeed, since at least the dawning of the 21^st Century, this Dream has turned more nightmarish and been deemed outside the reach of many. Investments haven’t seemed to live up to their earlier promise either, with two major financial crises since 2000 terrifying an entire generation of potential investors. It’s as if (in the words of the critic Andy Greenwald), by some cruel trick, we have come to realize too late that someone or something has tipped the ladder of success sideways, the rungs casting shadows tall as prison bars.

As a consequence, political activists of all stripes actively point blame and propose solutions. But on a personal level, we are all prone to self-serving bias – our tendency to attribute our successes to or own effort and skill but to attribute less desirable outcomes to bad luck. In point of fact, and irrespective of the political conclusions one draws from the current state of the American Dream, luck (and, if you have a spiritual bent, grace) plays an enormous role in our lives – both good and bad – just as luck plays an enormous role in many specific endeavors, from investing to poker to coin-flipping to winning a Nobel Prize. We don’t like to think that much of what happens (and happens to us) is the result of luck – i.e., randomness. We hate the idea of so much that is so important being outside of our control. But how we feel about a given proposition tells us precisely nothing about whether or not it is true and there is no disputing the facts. The random is an important factor in our lives, and, despite how counterintuitive and contradictory it may sound, we need to plan accordingly.

When my kids were teenagers, if something was random, that was a good thing. It was a really good thing, in fact.  Something funny was random. A good party was random. Being more than a bit of a fussbudget, I objected to such usage. I didn’t think it was correct.

But I was wrong.

The Oxford English Dictionary — which is the authority on such matters – has determined as much. In fact, random got its start (so to speak) as a noun in the 14th Century, when its meaning included impetuosity, great speed, force or violence in riding, running, striking, and the like. Its primary usage was in the phrase “with great random.”

Random as slang eventually showed up in the Hacker’s Dictionary and then went mainstream.  It has become a popular colloquial term meaning peculiar, strange, nonsensical, unpredictable or inexplicable; unexpected. As the OED’s Jesse Sheidlower has pointed out, “It was in the movie Clueless in 1995.” He also adds that Random House was established in 1925 specifically to publish books “at random,” in the words of founder Bennett Cerf.

I hate it when my kids are right and I’m wrong.  As if!?

Even so, in the 17th century, random started to mean “lacking a definite purpose.” And by the late 19th century, random came to have the clear and technical mathematical connotation that I favor. In that sense it means being governed by or involving equal chances for each of the actual or hypothetical members of a population as well as having been produced or obtained by such a process and therefore unpredictable in detail.

In investing, it is that unpredictability that really matters, but so does the “in detail” qualifier. As I have stressed before, there are so many variables involved that investing can’t deal in anything like certainty. We might want or even believe in a sure thing investment, but the best we can do is play the probabilities. As in The Hunger Games, the idea is for the odds ever to be in your favor.

The concept is pretty easy to illustrate. The probability of drawing any given poker hand is calculated by dividing the number of ways to draw the hand by the total number of five-card hands. Therefore, since there are four different ways to draw a Royal Flush (one for each suit), the probability of doing so is 4/2,598,960, or about 0.000154 percent. That’s remarkable precision in the aggregate, but we still can’t know when one will be drawn (assuming a fair deck and dealer). That’s why it’s said to be unpredictable in detail.

In blackjack, a player who asks for a hit on 18 deserves to lose, but very occasionally draws a three. Or in poker, sometimes a player draws an inside straight. It’s against the probabilities and can’t be predicted (again, assuming a fair deck and dealer) — it’s utterly random – but it happens.

In the markets, examples are also easy to offer. Sildenafil citrate, now sold as Viagra, was merely a hypertension drug when Pfizer discovered certain significant side effects (essentially by accident) and ended up with one of the more profitable drugs ever.  Talk about random!

As Nassim Taleb makes clear, we often mistake randomness for agency. In fact, the prevalent self-serving bias depends upon it, at least when the results are desirable. Accordingly, we need to account properly for randomness in every investing situation because, much of the time, it really is so random.

Tom Stoppard’s Rosencrantz and Guildenstern are Dead presents Shakespeare’s Hamlet from the bewildered point of view of two of the Bard’s bit players, the comically indistinguishable nobodies who become headliners in Stoppard’s play. The play opens before our heroes have even joined the action in Shakespeare’s epic. They have been “sent for” and are marking time by flipping coins and getting heads each time (the opening scene from the movie version is shown below).

So Guildenstern keeps tossing coins, and Rosencrantz keeps pocketing them. Significantly, Guildenstern is less concerned with his losses than in puzzling out what the defiance of the odds says about chance and fate. “A weaker man might be moved to re-examine his faith, if in nothing else at least in the law of probability.”

This fictional coin tossing streak provides us with a chance to consider the probabilities involved. Guildenstern offers among other explanations the one mathematicians and investors should favor — “a spectacular vindication of the principle that each individual coin spun individually is as likely to come down heads as tails and therefore should cause no surprise each individual time it does.” In other words, past performance is not indicative of future results.

Even so, how unlikely is a streak of this length?

The probability that a fair coin, fairly flipped, will turn up heads is 50 percent (the probability of any two independent sequential events both happening is the product of the probability of both). Thus the odds of it turning up twice in a row is 25 percent (½ x ½), the odds of it turning up three times in a row is 12.5 percent (½ x ½ x ½) and so on.  Accordingly, if we flip a coin 10 times (one “set” of ten), we would only expect to have a set end up with 10 heads in a row once every 1024 sets {(½)¹⁰ = 1/1024}.

Rosencrantz and Guildenstern got heads more than 100 consecutive times. The chances of that happening are thus (½)¹⁰⁰ = 1/7.9 x 1031. In other words, we could expect it to happen once in 79 million million million million million (that’s 79 with 30 zeros after it) sets. By comparison, the universe is about 13.9 billion years old, in which time only about 10¹⁷ seconds (1 with 17 zeros after it) have elapsed. Looked at another way, if every person who ever lived (around 110 billion) had flipped a 100-coin set simultaneously every second since the beginning of the universe until now (again, about 13.9 billion years ago), we could expect all of the 100 coins to have come up heads two times.

If anything like that had happened to you (especially in a bet), you’d agree with Taleb that the probabilities favor a loaded coin. Rosencrantz is similarly suspicious. But then again, while 100 straight heads is less probable than 99, which is less probable than 98, and so on, any exact order of tosses is as likely (actually, unlikely) as 100 heads in a row: (½)¹⁰⁰. We notice the unlikelihood of 100 in a row because of the pattern, and we are pattern-seeking creatures. More “normal” combinations look random and thus expected. We don’t see them as noteworthy. Looked at another way, if there will be one “winner” selected from a stadium of 100,000 people, each person has a 1 in 100,000 chance of winning. But we aren’t surprised when someone does win, even though the individual winner is shocked.

The point here is that the highly improbable happens all the time. In fact, much of what happens is highly improbable. This math explains why we shouldn’t be surprised when the market remains “irrational” far longer than seems possible. But we are.

Much of that difficulty arises because we neglect the limits of induction. Science never fully proves anything. It analyzes the available data, and when the force of the data is strong enough, it suggests tentative conclusions. But these conclusions are always subject to modification or even outright rejection based upon further evidence gathering. Instead, we crave and claim certainty, even when we have no basis for it.

I suspect that our certainty and the leaps of ideological fancy upon which it is so often built are a natural result of our constant search for meaning in an environment where noise is everywhere and signal vanishingly difficult to detect. Randomness is difficult for us to deal with. We are meaning-makers at every level and in nearly every situation. Yet, as I have noted so often, information is cheap and meaning is expensive and elusive. Therefore, we tend to short-circuit good process to get to the end result – typically and not so coincidentally the result we wanted all along.

Even after 100 heads in a row, the odds of the next toss being heads remains one-in-two (the “gambler’s fallacy” is committed when one assumes that a departure from what occurs on average or in the long-term will be corrected in the short-term). We look for patterns (“shiny objects”) to convince ourselves that we have found a “secret sauce” that justifies our making big bets on less likely outcomes. In this regard, we are dumber than rats – literally.

In numerous studies (most prominently those by Edwards and Estes, as reported by Philip Tetlock in his terrific book, Expert Political Judgment), the stated task was predicting which side of a “T-maze” held food for the subject rat.  Unbeknownst both to observers and the rat, the maze was rigged such that the food was randomly placed (without a pattern), but — in the aggregate — 60 percent of the time on one side and 40 percent of the time on the other.

The rat quickly “gets it” and waits at the “60 percent side” every time and is thus correct 60 percent of the time. Human observers kept looking for patterns and chose sides in rough proportion to recent results. As a consequence, the humans were right only 52 percent of the time – they (we!) were (and are, at least in this type of circumstance)much dumber than rats. Overall, we insist on rejecting probabilistic strategies that accept the inevitability of randomness and error.

As I have described previously, the great gambler Billy Walters uses a probabilistic sports betting model that is correct roughly 57 percent of time. He expects and plans for being wrong 43 percent of the time. Since he can’t predict the timing of his successes and failures, he has to be prepared for long losing streaks (although he obviously hopes that none are long as Guildenstern’s). Common gambling practice had been (and often still is) to make fewer bets – to bet only on those games one is most sure of. But that approach is not thinking probabilistically. Walters makes as many bets as he can within the confines of his model (when he thinks the point spread is off by at least one-and-one-half points), with the size of the bets consistent with how wrong he thinks the point spread is.

For investors, the lessons to be gained here relate to diversification, a carefully delineated and bounded process, clear execution rules, and stick-to-it-iveness over the long haul. This doesn’t mean that quants should control everything. Old school analysis and judgment still matter, perhaps more than ever since the pile of available data has gotten so large and the investment universe has gotten so much more educated (on account of the paradox of skill). But it does mean that our conclusions need to be consistent with and supported by the data, no matter how bizarre the numbers or how long the streak.

Even 100 in a row.

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This post is the fifth in a series on Investment Beliefs. Such stated beliefs can suggest a framework for decision-making amidst uncertainty. More specifically, one’s beliefs can provide a basis for strategic investment management, inform priorities, and be used to ensure an alignment of interests among all relevant stakeholders.