Fooled by Randomness
Fooled by Randomness by Nassim Taleb surprised me. I didn't really know what to expect. Originally, I thought it was written by a guy who doesn't have enough gusto to think he is a talented trader, that it was going to be an apology, possibly a confession. In reality, it was a thoughtful meditatation on randomness--determinism even. A treatise on the role determinism plays in life, and especially in trading, it examines various phenomena from the Monte Carlo perpective: a tounge-in-cheek intellectual's view of the meaning of randomness in a social and even historical context, from a quantiative practictioner. The value of this book lies in Taleb's insights into where statistical models diverge from how people perceive and experience the world around them.
The book even started by comparing two traders with different personalities. For example, how can you be so sure of skill, when you can be reasonably sure that competence occurs in society according to a normal distribution. There will always be someone who is exceptional in a large enough sample size. Alexander the Great for example could have been that general with abilities a number of standard deviations away from the mean. Alternatively, the path you can say he took in life was one of a number of alternative sample paths where he surpassed his peers and competitors significantly. This could be construed as a mechanism comparable to the roulette wheel, where he happened to luck out. This could be generalized to the level of historical processes, where what actually happened is actually one of many alternative paths of how history actually did happen.
I think the most useful takeaway for me were his thoughts on probability and how it's perceived. There are a number of traps that thoughttraps people fall into unwittingly, because we as human beings aren't wired or educated properly to think in terms of probabilities. One of my favorite passages:
I was once asked in one of those meetings to express my views on the stock market. I stated, not without a modicum of pomp, that I believed the market would go slightly up over the next week with a high probability. How high? "About 70%". Clearly that was a very strong opinion. But then someone interjected, "But, Nassim, you just boasted being short a very large quanitity of S&P 500 futures, making a bet that the market would go down. What made you change your mind? "I did not change my mind! I have a lot of faith in my bet!"....
The key was that he was expecting a very large drop with a 30% probability, thus he had a high expected value of the short postions despite the fact that the market would probably float up. Many people, even those who are aware of concepts like expected value, perceive the world through distortions such as the one above. These perceptions then drive their decision-making when investing.
Another theme throughout the book was performance records. Taleb claims performance records are effectively meaningless, as a small percentage of investors always outperforms, and they are only really a function of the sample size. In addition, survivorship bias implies that they will be the most visible overshadowing the full picture. Moreover, the cross-sectional problem exists. At any given time in the market , the most successful traders are those who are best fit to the market, so you can make money purely out of randomness. The only way to really evaluate performance histories is via alternative histories, by comparing the opportunity cost of one outcome relative to all possible outcomes.
Taleb seems to have gone through the basic tenets of mathematical finance and very thoroughly tried to apply them to his trading approach. These distortions come from human nature. We aren't wired or educated to think in terms of the "nonlinear aspects of probability". For example, the meaning of a change depends on it's probability, so a 7% drop in the markets is much more significant than a 1% drop, "several billion times more relevant" in fact.
His quanititave insights also extend into money and risk management. Tying risk management strategies to past price activity is foolish. Just because a price hasn't fallen 40% doesn't mean it won't. It's better to size positions conservatively to reduce exposure, as you have control over this. Instead use statistics to identify good trading strategies and trade them aggressively. As a strategy earns more profit, the higher the probability that this profit results for the strategy, and not just pure noise. This effect can also aid in selecting strategies.
Nassim posits that any testable statement should be tested (attributed to Niederhoffer), yet it is always good to maintain a skeptical view of market hypotheses, as they can be proven wrong at any moment by a counterexample. Making a logical leap from "has never gone down" to "never goes down" is difficult. This is one of his key points in the book, which I assume he explores in more detail in his following book, The Black Swan.
Moreover, there are a number of caveats that should be taken into account when performing these tests. Make sure your sample size is large enough before you start to make inferences, as the statistical strength of a hypothesis increases with the number of observations; yet his somewhat breaks down with asymetmetric distributions. For example, if we are estimating the probability of a rare event, we know very little about it until it happens. Until it actually happens, we know much less than the typical square root of n in symmetric distributions. After it happens, our knowledge of the odds dramatically improves. Also, people sometimes generalize too quickly to what they know; for example, random does not necessisarily mean equiprobable. Not all random outcomes are like a coin flip. In finance, the influence of time is also very important as most prices are observed as time series. The shorter the time period under observation, the more noise you see. Also note the emotional effects of exposure to noise. So over the longer the time period, the variability is lower. This is called ergodicity: time eliminates the effects of randomness.
While the book is philosophical and erudite, the real value in the work lies in the insights Taleb shares about the fraility of statistics in a financial context, and also the ease in which they can be abused. The caveats he provides serve as a useful basis for formulating robust trading strategies that ensure that you will stay in the market for the longer term.