Professor Nassim Nicholas Taleb recently published an interesting essay in Edge that has relevance for all of us.
The main focus of the essay is on what Taleb calls the Fourth Quadrant. While the name may sound imposing, the concept itself is relatively straightforward.
Taleb identifies two different kinds of environments where events take place. In the first environment, no single event has any significant impact on other events. The example he gives is one of modeling peoples’ weights. Given a population of individuals, say 200 in number, certain statistical frequencies will emerge, such as an average weight, the distribution of weights around this expected weight and so on. Now if you were to introduce to this population a person with an exceptional weight, either very overweight or significantly underweight, the effect this would have on the average weight would not be significant. This is not the case in the second kind of environment where an individual event can have a large impact on statistical properties. Taleb gives the example of modeling wealth distribution. Suppose you look at the same group of 200 people and instead of looking at their weights, you look instead at their wallets. You’ll find that the group has an average income. What happens to this average income if you introduce some incredibly wealthy person like Bill Gates into the mix? You can kiss all of your statistical data and any models based on it goodbye. This is the realm of what are called Fat Tails, or what Taleb calls Black Swans. Bill Gates’s incredible wealth would be a Black Swan to the group’s average wealth. In this second realm you can go for a while and everything will appear predictable, safe, but then one event happens that is deemed impossible according to your statistical models, and all of your predictions are thrown on their head.
So there are two kinds of environments where things happen: the non-sensitive, and the sensitive. The Fourth Quadrant is just the last entry in a two by two matrix. The two kinds of environments can be envisioned as the two columns of the matrix, or the two rows for that matter. To complete the matrix, Taleb goes on to introduce two kinds of events. The first kind are simple in their outcome, like the flip of a coin. There is nothing complicated about the outcome of a coin toss, it’s either heads up or tails. The second kind of events are complicated in their outcomes. A casino bet is like this because there are variables dependent on the outcome of the bet itself. Which card is face up, or which side of the dice rolls up can make the difference between winning a small amount, and taking home a lot. And this can be extended to very complex events, in which the outcomes are not directly related to any observable event, but are dependent on functions of observable outcomes. Derivatives are a great example of this kind of event. A stock option, for example, derives its value from the price movements of the stock it references, and this link is not straightforward but is itself dependent on a combination of factors including the stock price, interest rates and historical volatility to name but a few.
With these two kinds of environments, and these two kinds of events, Taleb goes on to construct a 4 x 4 matrix, where the last entry, the Fourth Quadrant, is where the magic happens. The Fourth Quadrant is where complex and super complex events meet the environment of Black Swans (sensitivity). Taleb argues that in the Fourth Quadrant no reliable statistical models can be developed. While you might be able to apply statistical models for select periods of time, any such validity will be tenuous at best and given enough time will be proven wrong. In the Fourth Quadrant, any and all models will eventually break down.
What makes this relevant to non-statisticians is that we live in a world that very much takes place in the Fourth Quadrant. Very few things in life are simple, many things are complicated. A timely example of complex events taking place in a sensitive environment is the recent financial meltdown. Modern finance has become a terribly complex system with a lot of variables needing to be accounted for. Throw this complexity into an environment which is sensitive to the outcomes of individual events, and well, you have a recipe for disaster. Sure, we can develop models that appear to work if the data is tailored for specific time periods, but no matter how reliable the models may appear to be, there will always be catastrophic events popping up from time to time that defy all statistical models... that defy all odds. There is a real danger in trying to predict future events on the basis of statistical analysis of past events. Taleb illustrates this by the example of a turkey, who grows more confident that he can trust that his keeper has the turkey’s interest at heart, with each passing day of being fed by his keeper, until, on the 1,000th day of that care, the keeper kills the turkey so that he can have him for dinner. The failing of a bank is a catastrophic event, like the slaughtering of the turkey. And it can’t be predicted solely by a statistical analysis of the past occurrences or non‑occurrences of that kind of event. Instead, a proper prediction of the likelihood of that event requires an understanding of the full context of what the banks had been doing, the effects of those actions, as well as the effects of all the other factors in the system. Taleb doesn’t give advice on how to make predictions in such situations; instead, he advises us against the false comfort that comes from relying on statistical ‘experts’, for making predictions about a situation where statistics aren’t a reliable guide.
Taleb does offer up some advice for how we can function in a world that does not always fit into neat mathematical models. His advice is basically Two Fold: 1) Be humble in our approach to complex systems, such as our financial markets; 2) Build redundancy into our society. Instead of striving for increasing efficiency, we should strive for increasing redundancy.
And this brings me to the reason for writing this article. Taleb’s words of wisdom should be heeded as we look to what went wrong with our financial system, and in particular, our banking system. As the bedrock of our capital markets, the US banking system should be simple, so that we can understand it, and it should be stable, so that it can withstand catastrophes when they arise. Our money supply and its administration should be tightly regulated. Banks should be thought of as public institutions serving the interests of society. They should not be placing giant leveraged bets on the back of society.
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