## Monday, January 5, 2009

### Reading List: The Black Swan

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.

Posted at January 5, 2009 23:25