I don’t read much business journalism, but I do generally like Joe Nocera’s writing in the New York Times. I thought his long article on risk management in last Sunday’s Times Magazine was quite good. In particular, I love seeing an article in a nontechnical magazine that actually talks about probability distributions in a reasonably careful and detailed way. If you want to understand how to think about data, you’ve got to learn to love thinking about probabilities.
The hero, so to speak, of the article is Nassim Nicholas Taleb, author of the book The Black Swan. According to the article, he’s been trying to convince people of the inadequacies of a standard risk-assessment method for many years, mostly because the method doesn’t pay attention to the tails of the probability distribution. The standard method, called VaR, is meant to give a sort of 99% confidence estimate of how much money a given set of investments is at risk of losing. Taleb’s point, apparently, is that even if that’s right it doesn’t do you all that much good, because what really matters for risk assessment is how bad the other 1% can be.
That’s an important point, which comes up in other areas too. When people compare health insurance plans, they look at things like copays, which tell you what’ll happen under more or less routine circumstances. It seems to me that by far the more important think to pay attention to in a health plan is how things will play out in the unlikely event that you need, say, a heart transplant followed by a lifetime of anti-rejection drugs. (In fact, extreme events like these are the reason you want insurance at all: if all you were going to need was routine checkups and the like, you’d be better off going without insurance, investing what you would have spent on premiums, and paying out of pocket.)
I do have a couple of observations about the article:
1. Nocera, quoting Taleb, keeps referring to the problem as the “fat tails” of the probability distribution. I think he means “long tails,” though, which is pretty much the opposite. A probability distribution with fat tails would be one in which moderately extreme outcomes were more likely than you might have expected. That wouldn’t be so bad. A distribution with long tails is one in which very very extreme outcomes have non-negligible probabilities. The impression I get from the rest of the article is that this is the problem that Taleb claims is the source of our woes.
2. The article is strong on diagnosis, but I wish it had said more about treatment. Given that standard methods don’t handle the tails very well, what should risk-management types do about it? I fear that the article might leave people with the impression that there’s no way to fix methods like VaR to take better account of the tails, and that we shouldn’t even bother trying to quantify risk with probability theory. That’s certainly not the correct conclusion: There’s no coherent way to think about risk except by modeling probability distributions. If the existing models aren’t good enough, we need better models. I hope that smart quants are thinking about this, not just giving up.
3. Taleb seems like he’s probably very smart and is certainly not a nice guy.