Randomness – Part 1

An introduction.

In this series of essays, we’ll explore often unrealized impacts of randomness in life and business, using Nassim Taleb’s Fooled by Randomness: The Hidden Role of Chance in Life and Markets, and Leonard Mlodinow’s The Drunkard’s Walk: How Randomness Rules Our Lives.

These books explain how humans are predisposed to attribute certain causes to certain results, even when those results are driven largely by chance and randomness. As Taleb writes:

Probability is not a mere computation of odds on the dice or more complicated variants; it is the acceptance of the lack of certainty in our knowledge and the development of methods for dealing with our ignorance … [T]his book reflects this author’s drift into becoming a little less of a student of uncertainty (we can learn so little about randomness) and more of a researcher into how people are fooled by it … Consider the left and the right columns of Table P. 1. The best way to summarize the major thesis of this book is that it addresses situations (many of them tragicomical) where the left column is mistaken for the right one. The subsections also illustrate the key areas of discussion on which this book will be based.

As Mlodinow writes:

The title The Drunkard’s Walk comes from a mathematical term describing random motion, such as the paths molecules follow as they fly through space, incessantly bumping, and being bumped by, their sister molecules. That can be a metaphor for our lives, our paths from college to career, from single life to family life, from first hole of golf to eighteenth. The surprise is that the tools used to understand the drunkard’s walk can also be employed to help understand the events of everyday life … A lot of what happens to us— success in our careers, in our investments, and in our life decisions, both major and minor— is as much the result of random factors as the result of skill, preparedness, and hard work. So the reality that we perceive is not a direct reflection of the people or circumstances that underlie it but is instead an image blurred by the randomizing effects of unforeseeable or fluctuating external forces. That is not to say that ability doesn’t matter— it is one of the factors that increase the chances of success— but the connection between actions and results is not as direct as we might like to believe … When we look at extraordinary accomplishments in sports— or elsewhere— we should keep in mind that extraordinary events can happen without extraordinary causes. Random events often look like nonrandom events, and in interpreting human affairs we must take care not to confuse the two … [J]ust as the lessons of persistence, practice, and teamwork that we learn from sports apply equally to all endeavors of life, so do the lessons of randomness.

Our first outing into exploring the ramifications of randomness involves what Taleb describes as the “Number of Monkeys” phenomenon:

If one puts an infinite number of monkeys in front of (strongly built) typewriters, and lets them clap away, there is a certainty that one of them would come out with an exact version of the Iliad. Upon examination, this may be less interesting a concept than it appears at first: Such probability is ridiculously low. But let us carry the reasoning one step beyond. Now that we have found that hero among monkeys, would any reader invest his life’s savings on a bet that the monkey would write the Odyssey next? In this thought experiment, it is the second step that is interesting. How much can past performance (here the typing of the Iliad) be relevant in forecasting future performance? The same applies to any decision based on past performance, merely relying on the attributes of the past time series. Think about the monkey showing up at your door with his impressive past performance. Hey, he wrote the Iliad. The major problem with inference in general is that those whose profession is to derive conclusions from data often fall into the trap faster and more confidently than others. The more data we have, the more likely we are to drown in it. For common wisdom among people with a budding knowledge of probability laws is to base their decision making on the following principle: It is very unlikely for someone to perform considerably well in a consistent fashion without his doing something right. Track records therefore become preeminent. They call on the rule of the likelihood of such a successful run and tell themselves that if someone performed better than the rest in the past then there is a great chance of his performing better than the crowd in the future— and a very great one at that. But, as usual, beware the middlebrow: A small knowledge of probability can lead to worse results than no knowledge at all … I do not deny that if someone performed better than the crowd in the past, there is a presumption of his ability to do better in the future. But the presumption might be weak, very weak, to the point of being useless in decision making. Why? Because it all depends on two factors: The randomness content of his profession and the number of monkeys in operation.

The element of randomness in business, given all the variables regarding consumer preferences and production decisions, is particularly high. As Taleb writes:

This problem enters the business world more viciously than other walks of life, owing to the high dependence on randomness … The greater the number of businessmen, the greater the likelihood of one of them performing in a stellar manner just by luck. I have rarely seen anyone count the monkeys. In the same vein, few count the investors in the market in order to calculate, instead of the probability of success, the conditional probability of successful runs given the number of investors in operation over a given market history … There are other aspects to the monkeys problem; in real life the other monkeys are not countable, let alone visible. They are hidden away, as one sees only the winners— it is natural for those who failed to vanish completely. Accordingly, one sees the survivors, and only the survivors, which imparts such a mistaken perception of the odds. We do not respond to probability, but to society’s assessment of it.

If all this seems too abstract, consider the comments Taleb makes about a best-selling book that profiled various millionaires and claimed to have found the common denominators (persistence and hard work) contributing to their success:

I recently read a bestseller called The Millionaire Next Door, an extremely misleading (but almost enjoyable) book by two “experts,” in which the authors try to infer some attributes that are common to rich people. That all millionaires were persistent, hardworking people does not make persistent hard workers become millionaires: Plenty of unsuccessful entrepreneurs were persistent, hardworking people … In a textbook case of naive empiricism, the author also looked for traits these millionaires had in common and figured out that they shared a taste for risk taking. Clearly risk taking is necessary for large success— but it is also necessary for failure. Had the author done the same study on bankrupt citizens he would certainly have found a predilection for risk taking … I am not saying that Warren Buffett is not skilled; only that a large population of random investors will almost necessarily produce someone with his track records just by luck.

Taleb makes his point more concrete in describing what has become known as “survivorship bias”:

[P]eople may survive owing to traits that momentarily fit the given structure of randomness. Here we take a far simpler situation where we know the structure of randomness; the first such exercise is a finessing of the old popular saying that even a broken clock is right twice a day. We will take it a bit further to show that statistics is a knife that cuts on both sides. Let us use the Monte Carlo generator [a randomness generator] and construct a population of 10,000 fictional investment managers (the generator is not terribly necessary since we can use a coin, or even do plain algebra, but it is considerably more illustrative— and fun). Assume that they each have a perfectly fair game; each one has a 50% probability of making $10,000 at the end of the year, and a 50% probability of losing $10,000. Let us introduce an additional restriction; once a manager has a single bad year, he is thrown out of the sample, good-bye and have a nice life … The Monte Carlo generator will toss a coin; heads and the manager will make $10,000 over the year, tails and he will lose $10,000. We run it for the first year. At the end of the year, we expect 5,000 managers to be up $10,000 each, and 5,000 to be down $10,000. Now we run the game a second year. Again, we can expect 2,500 managers to be up two years in a row; another year, 1,250; a fourth one, 625; a fifth, 313. We have now, simply in a fair game, 313 managers who made money for five years in a row. Out of pure luck. Meanwhile if we throw one of these successful traders into the real world we would get very interesting and helpful comments on his remarkable style, his incisive mind, and the influences that helped him achieve such success. Some analysts may attribute his achievement to precise elements among his childhood experiences. His biographer will dwell on the wonderful role models provided by his parents; we would be supplied with black-and-white pictures in the middle of the book of a great mind in the making. And the following year, should he stop outperforming (recall that his odds of having a good year have stayed at 50%) they would start laying blame, finding fault with the relaxation in his work ethics, or his dissipated lifestyle. They will find something he did before when he was successful that he has subsequently stopped doing, and attribute his failure to that. The truth will be, however, that he simply ran out of luck.

Taleb then shows how even a group of incompetent people can achieve financial investment success through sheer luck:

Let’s push the argument further to make it more interesting. We create a cohort that is composed exclusively of incompetent managers. We will define an incompetent manager as someone who has a negative expected return, the equivalent of the odds being stacked against him. We instruct the Monte Carlo generator now to draw from an urn. The urn has 100 balls, 45 black and 55 red. By drawing with replacement, the ratio of red to black balls will remain the same. If we draw a black ball, the manager will earn $10,000. If we draw a red ball, he will lose $10,000. The manager is thus expected to earn $10,000 with 45% probability, and lose $10,000 with 55%. On average, the manager will lose $1,000 each round— but only on average. At the end of the first year, we still expect to have 4,500 managers turning a profit (45% of them), the second, 45% of that number, 2,025. The third, 911; the fourth, 410; the fifth, 184. Let us give the surviving managers names and dress them in business suits. True, they represent less than 2% of the original cohort. But they will get attention. Nobody will mention the other 98%. What can we conclude? The first counterintuitive point is that a population entirely composed of bad managers will produce a small amount of great track records.

This pattern of randomness producing some good track records extends to business and sports generally. As Mlodinow writes:

In sports we have developed a culture in which, based on intuitive feelings of correlation, a team’s success or failure is often attributed largely to the ability of the coach. As a result, when teams fail, the coach is often fired. Mathematical analysis of firings in all major sports, however, has shown that those firings had, on average, no effect on team performance. An analogous phenomenon occurs in the corporate world, where CEOs are thought to have superhuman power to make or break a company. Yet time and time again at Kodak, Lucent, Xerox, and other companies, that power has proved illusory. In the 1990s, for instance, when he ran GE Capital Services under Jack Welch, Gary Wendt was thought of as one of the smartest businessmen in the country. Wendt parlayed that reputation into a $45 million bonus when he was hired to run the troubled finance company Conseco. Investors apparently agreed that with Wendt at the helm, Conseco’s troubles were over: the company’s stock tripled within a year. But two years after that Wendt abruptly resigned, Conseco went bankrupt, and the stock was trading for pennies. Had Wendt’s task been impossible? Was he asleep at the wheel? Or had his coronation rested on questionable assumptions— for example, that an executive has a near- absolute ability to affect a company or a person’s single past success is a reliable indicator of future performance? On any specific occasion one cannot be confident of the answers without examining the details of the situation at hand.

As Taleb writes, “The virtue of capitalism is that society can take advantage of people’s greed rather than their benevolence, but there is no need to, in addition, extol such greed as a moral (or intellectual) accomplishment.”

Taleb describes what he saw as a stock market trader in the 1980’s and 1990’s:

The story focuses on an unusual episode in history; buying its thesis implies accepting that the current returns in asset values are permanent (the sort of belief that prevailed before the great crash that started in 1929). Remember that asset prices have (still at the time of writing) witnessed the greatest bull market in history and that values did compound astronomically during the past two decades … Virtually all of the subjects [stock trader] became rich from asset price inflation, in other words from the recent inflation in financial paper and assets that started in 1982. An investor who engaged in the same strategy during less august days for the market would certainly have a different story to tell. Imagine the book being written in 1982, after the prolonged erosion of the inflation- adjusted value of the stocks, or in 1935, after the loss of interest in the stock market … The mistake of ignoring the survivorship bias is chronic, even (or perhaps especially) among professionals. How? Because we are trained to take advantage of the information that is lying in front of our eyes, ignoring the information that we do not see [such as, the existence of many more people who went bankrupt while following the same strategy at a slightly different time] … A brief summing up at this point: I showed how we tend to mistake one realization among all possible random histories as the most representative one, forgetting that there may be others. In a nutshell, the survivorship bias implies that the highest performing realization will be the most visible. Why? Because the losers do not show up.

In the next essay in this series, we’ll further explore the role of randomness in people’s financial success and how that understanding should make us more, rather than less, content.