## Books by Taleb, Nassim Nicholas

Taleb, Nassim Nicholas. The Black Swan. New York: Random House, 2007. ISBN 978-1-4000-6351-2.
If you are interested in financial markets, investing, the philosophy of science, modelling of socioeconomic systems, theories of history and historicism, or the rôle of randomness and contingency in the unfolding of events, this is a must-read book. The author largely avoids mathematics (except in the end notes) and makes his case in quirky and often acerbic prose (there's something about the French that really gets his goat) which works effectively.

The essential message of the book, explained by example in a wide variety of contexts is (and I'll be rather more mathematical here in the interest of concision) is that while many (but certainly not all) natural phenomena can be well modelled by a Gaussian (“bell curve”) distribution, phenomena in human society (for example, the distribution of wealth, population of cities, book sales by authors, casualties in wars, performance of stocks, profitability of companies, frequency of words in language, etc.) are best described by scale-invariant power law distributions. While Gaussian processes converge rapidly upon a mean and standard deviation and rare outliers have little impact upon these measures, in a power law distribution the outliers dominate.

Consider this example. Suppose you wish to determine the mean height of adult males in the United States. If you go out and pick 1000 men at random and measure their height, then compute the average, absent sampling bias (for example, picking them from among college basketball players), you'll obtain a figure which is very close to that you'd get if you included the entire male population of the country. If you replaced one of your sample of 1000 with the tallest man in the country, or with the shortest, his inclusion would have a negligible effect upon the average, as the difference from the mean of the other 999 would be divided by 1000 when computing the average. Now repeat the experiment, but try instead to compute mean net worth. Once again, pick 1000 men at random, compute the net worth of each, and average the numbers. Then, replace one of the 1000 by Bill Gates. Suddenly Bill Gates's net worth dwarfs that of the other 999 (unless one of them randomly happened to be Warren Buffett, say)—the one single outlier dominates the result of the entire sample.

Power laws are everywhere in the human experience (heck, I even found one in AOL search queries), and yet so-called “social scientists” (Thomas Sowell once observed that almost any word is devalued by preceding it with “social”) blithely assume that the Gaussian distribution can be used to model the variability of the things they measure, and that extrapolations from past experience are predictive of the future. The entry of many people trained in physics and mathematics into the field of financial analysis has swelled the ranks of those who naïvely assume human action behaves like inanimate physical systems.

The problem with a power law is that as long as you haven't yet seen the very rare yet stupendously significant outlier, it looks pretty much like a Gaussian, and so your model based upon that (false) assumption works pretty well—until it doesn't. The author calls these unimagined and unmodelled rare events “Black Swans”—you can see a hundred, a thousand, a million white swans and consider each as confirmation of your model that “all swans are white”, but it only takes a single black swan to falsify your model, regardless of how much data you've amassed and how long it has correctly predicted things before it utterly failed.

Moving from ornithology to finance, one of the most common causes of financial calamities in the last few decades has been the appearance of Black Swans, wrecking finely crafted systems built on the assumption of Gaussian behaviour and extrapolation from the past. Much of the current calamity in hedge funds and financial derivatives comes directly from strategies for “making pennies by risking dollars” which never took into account the possibility of the outlier which would wipe out the capital at risk (not to mention that of the lenders to these highly leveraged players who thought they'd quantified and thus tamed the dire risks they were taking).

The Black Swan need not be a destructive bird: for those who truly understand it, it can point the way to investment success. The original business concept of Autodesk was a bet on a Black Swan: I didn't have any confidence in our ability to predict which product would be a success in the early PC market, but I was pretty sure that if we fielded five products or so, one of them would be a hit on which we could concentrate after the market told us which was the winner. A venture capital fund does the same thing: because the upside of a success can be vastly larger than what you lose on a dud, you can win, and win big, while writing off 90% of all of the ventures you back. Investors can fashion a similar strategy using options and option-equivalent investments (for example, resource stocks with a high cost of production), diversifying a small part of their portfolio across a number of extremely high risk investments with unbounded upside while keeping the bulk in instruments (for example sovereign debt) as immune as possible to Black Swans.

There is much more to this book than the matters upon which I have chosen to expound here. What you need to do is lay your hands on this book, read it cover to cover, think it over for a while, then read it again—it is so well written and entertaining that this will be a joy, not a chore. I find it beyond charming that this book was published by Random House.

Taleb, Nassim Nicholas. Fooled by Randomness. 2nd. ed. New York: Random House, [2004] 2005. ISBN 978-0-8129-7521-5.
This book, which preceded the author's bestselling The Black Swan (January 2009), explores a more general topic: randomness and, in particular, how humans perceive and often misperceive its influence in their lives. As with all of Taleb's work, it is simultaneously quirky, immensely entertaining, and so rich in wisdom and insights that you can't possible absorb them all in a single reading.

The author's central thesis, illustrated from real-world examples, tests you perform on yourself, and scholarship in fields ranging from philosophy to neurobiology, is that the human brain evolved in an environment in which assessment of probabilities (and especially conditional probabilities) and nonlinear outcomes was unimportant to reproductive success, and consequently our brains adapted to make decisions according to a set of modular rules called “heuristics”, which researchers have begun to tease out by experimentation. While our brains are capable of abstract thinking and, with the investment of time required to master it, mathematical reasoning about probabilities, the parts of the brain we use to make many of the important decisions in our lives are the much older and more instinctual parts from which our emotions spring. This means that otherwise apparently rational people may do things which, if looked at dispassionately, appear completely insane and against their rational self-interest. This is particularly apparent in the world of finance, in which the author has spent much of his career, and which offers abundant examples of individual and collective delusional behaviour both before and after the publication of this work.

But let's step back from the arcane world of financial derivatives and consider a much simpler and easier to comprehend investment proposition: Russian roulette. A diabolical billionaire makes the following proposition: play a round of Russian roulette (put one cartridge in a six shot revolver, spin the cylinder to randomise its position, put the gun to your temple and pull the trigger). If the gun goes off, you don't receive any payoff and besides, you're dead. If there's just the click of the hammer falling on an empty chamber, you receive one million dollars. Further, as a winner, you're invited to play again on the same date next year, when the payout if you win will be increased by 25%, and so on in subsequent years as long as you wish to keep on playing. You can quit at any time and keep your winnings.

Now suppose a hundred people sign up for this proposition, begin to play the game year after year, and none chooses to take their winnings and walk away from the table. (For connoisseurs of Russian roulette, this is the variety of the game in which the cylinder is spun before each shot, not where the live round continues to advance each time the hammer drops on an empty chamber: in that case there would be no survivors beyond the sixth round.) For each round, on average, 1/6 of the players are killed and out of the game, reducing the number who play next year. Out of the original 100 players in the first round, one would expect, on average, around 83 survivors to participate in the second round, where the payoff will be 1.25 million.

What do we have, then, after ten years of this game? Again, on average, we expect around 16 survivors, each of whom will be paid more than seven million dollars for the tenth round alone, and who will have collected a total of more than 33 million dollars over the ten year period. If the game were to go on for twenty years, we would expect around 3 survivors from the original hundred, each of whom would have “earned” more than a third of a billion dollars each.

Would you expect these people to be regular guests on cable business channels, sought out by reporters from financial publications for their “hot hand insights on Russian roulette”, or lionised for their consistent and rapidly rising financial results? No—they would be immediately recognised as precisely what they were: lucky (and consequently very wealthy) fools who, each year they continue to play the game, run the same 1 in 6 risk of blowing their brains out.

Keep this Russian roulette analogy in mind the next time you see an interview with the “sizzling hot” hedge fund manager who has managed to obtain 25% annual return for his investors over the last five years, or when your broker pitches a mutual fund with a “great track record”, or you read the biography of a businessman or investor who always seems to have made the “right call” at the right time. All of these are circumstances in which randomness, and hence luck, plays an important part. Just as with Russian roulette, there will inevitably be big winners with a great “track record”, and they're the only ones you'll see because the losers have dropped out of the game (and even if they haven't yet they aren't newsworthy). So the question you have to ask yourself is not how great the track record of a given individual is, but rather the size of the original cohort from which the individual was selected at the start of the period of the track record. The rate hedge fund managers “blow up” and lose all of their investors' money in one disastrous market excursion is less than that of the players blown away in Russian roulette, but not all that much. There are a lot of trading strategies which will yield high and consistent returns until they don't, at which time they suffer sudden and disastrous losses which are always reported as “unexpected”. Unexpected by the geniuses who devised the strategy, the fools who put up the money to back it, and the clueless journalists who report the debacle, but entirely predictable to anybody who modelled the risks being run in the light of actual behaviour of markets, not some egghead's ideas of how they “should” behave.

Shall we try another? You go to your doctor for a routine physical, and as part of the laboratory work on your blood, she orders a screening test for a rare but serious disease which afflicts only one person in a thousand but which can be treated if detected early. The screening test has a 5% false positive rate (in 5% of the people tested who do not actually have the disease, it erroneously says that they do) and a 0% false negative rate (if you have the disease, the test will always report that you do). You return to the doctor's office for the follow-up visit and she tells you that you tested positive for the disease. What is the probability you actually have it?

Spoiler warning: Plot and/or ending details follow.
Did you answer 95%? If you did, you're among the large majority of people, not just among the general population but also practising clinicians, who come to the same conclusion. And you'd be just as wrong as them. In fact, the odds you have the disease are a little less than 2%. Here's how it works. Let's assume an ensemble of 10,000 randomly selected people are tested. On average, ten of these people will have the disease, and all of them will test positive for it (no false negatives). But among that population, 500 people who do not have the disease will also test positive due to the 5% false positive rate of the test. That means that, on average (it gets tedious repeating this, but the natterers will be all over me if I don't do so in every instance), there will be, of 10,000 people tested, a total of 510 positive results, of which 10 actually have the disease. Hence, if you're the recipient of a positive test result, the probability you have the disease is 10/510, or a tad less than 2%. So, before embarking upon a demanding and potentially dangerous treatment regime, you're well advised to get some other independent tests to confirm that you are actually afflicted.
Spoilers end here.
In making important decisions in life, we often rely upon information from past performance and reputation without taking into account how much those results may be affected by randomness, luck, and the “survivor effect” (the Russian roulette players who brag of their success in the game are necessarily those who aren't yet dead). When choosing a dentist, you can be pretty sure that a practitioner who is recommended by a variety of his patients whom you respect will do an excellent job drilling your teeth. But this is not the case when choosing an oncologist, since all of the people who give him glowing endorsements are necessarily those who did not die under his care, even if their survival is due to spontaneous remission instead of the treatment they received. In such a situation, you need to, as it were, interview the dead alongside the survivors, or, that being difficult, compare the actual rate of survival among comparable patients with the same condition.

Even when we make decisions with our higher cognitive facilities rather than animal instincts, it's still easy to get it wrong. While the mathematics of probability and statistics have been put into a completely rigorous form, there are assumptions in how they are applied to real world situations which can lead to the kinds of calamities one reads about regularly in the financial press. One of the reasons physical scientists transmogrify so easily into Wall Street “quants” is that they are trained and entirely comfortable with statistical tools and probabilistic analysis. The reason they so frequently run off the cliff, taking their clients' fortunes in the trailer behind them, is that nature doesn't change the rules, nor does she cheat. Most physical processes will exhibit well behaved Gaussian or Poisson distributions, with outliers making a vanishingly small contribution to mean and median values. In financial markets and other human systems none of these conditions obtain: the rules change all the time, and often change profoundly before more than a few participants even perceive they have; any action in the market will provoke a reaction by other actors, often nonlinear and with unpredictable delays; and in human systems the Pareto and other wildly non-Gaussian power law distributions are often the norm.

We live in a world in which randomness reigns in many domains, and where we are bombarded with “news and information” which is probably in excess of 99% noise to 1% signal, with no obvious way to extract the signal except with the benefit of hindsight, which doesn't help in making decisions on what to do today. This book will dramatically deepen your appreciation of this dilemma in our everyday lives, and provide a philosophical foundation for accepting the rôle randomness and luck plays in the world, and how, looked at with the right kind of eyes (and investment strategy) randomness can be your friend.