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Friday, February 18, 2011

Reading List: Fooled by Randomness

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.

Posted at February 18, 2011 22:44