Chasing the Tails

There's no way regulators or bankers can estimate every risk correctly. Maybe we should focus on something else.

Daniel Davies, in his characteristically sharp way, puts into words something that has been slinking around the edges of my brain for a while, producing one of those glorious moments of recognition where you say to yourself, not "that's what I was trying to say!" but "that's what i was trying to think!"

Yes, yes, the jokes write themselves. Fire away. And then read this, because it's important.

The point I really liked was on p454 of the technical appendix (p8 of the .pdf file), which is something I ought to have realised myself during a couple of debates a few years ago about exactly what went wrong with the CDO structure. Translating from the mathematical language, I would characterise Taleb’s point as being that the problem with “fat tails” is not that they’re fat; it’s that they’re tails. Even when you’re dealing with a perfectly Gaussian or normal distribution, it’s difficult to say anything with any real confidence about the tails of the distribution, because you have much less data about the shape of the tails (because they’re tails) than about the centre and the region around the mean. So you end up estimating the parameters of your favourite probability distribution based on the mean (central tendency) and variance (spread) of the data you have, and hoping that the tails are going to be roughly in the right place.

But any little errors you make in estimation of the central tendency are going to get blown up to a significant extent when you start trying to use your estimate to try to say something about the 99th percentile of the same distribution. Which is kind of a problem since we have a whole financial regulatory infrastructure built up on “value at risk”, which is a term effectively meaning “trying to say something about the 99th percentile of an empirically estimated distribution.”

Over the last few years, I have been having a lot of earnest conversations with people in the financial industry, and people who cover it, about the extent to which the crisis was produced, and/or worsened, by the attempt to quantify, or at least numerify, the exact amount of risk in the system so that it could be hedged and regulated away. "Value at risk" and its near kin produced the illusion of safety, as Taleb (to whom Davies is responding) has been screaming for years. Worse, it produced a systematically biased illusion of safety; everyone was making pretty much the same mistake. That mistake was to take the sort of risk that is safe 99.995% of the time--but catastrophic when everyone's bets went south at once. We may have minimized the number of bank failures in normal times only by increasing the risk of a single, catastrophic even that took the whole system down.

Or not: there are also those who argue that it played only a minor role.

The wizards of Basel have proposed getting rid of VAR, but it's not clear to me that they're actually planning to replace it with anything more sensible. The problem is somewhat inherent in any regulatory scheme which attempts to de-risk the whole banking system; whatever rules you set will be gamed. (One example: for various not-unreasonable reasons, there's a bias towards sovereign debt in most regulatory rules. This apparently led to European banks taking on a lot of peripheral country sovereign debt which turned out to be just about the riskiest thing they could have bought.) Worse, even when they aren't gamed, they will definitionally produce herding behavior; people are going to be more heavily invested in whatever assets you have deemed "safe". And that herding adds risk to the system.

As one fixed-income manager mordantly noted, "The most dangerous thing in the world is a nominally risk free asset."

So should we give up on ratings agencies, capital standards, and so forth? The anarcho-capitalists in the audience will shout "Yes!"; most of the rest of you will shout "No!" I myself toy with the idea that we should retreat to the much cruder standards of yesteryear. Just require banks to have a lot more capital on their books, the end. Maybe we'll lose banking jobs to countries with looser standards, but we can probably live with that.

But I do recognize that this is probably a fantasy. An old-fashioned bank loan is easy to reserve capital against: your potential loss is the money you loaned out. Some of the more exotic financial instruments are not, because the potential losses are harder to see. And this is true even of some of the less exotic financial instruments, like insturance policies and short selling.

And yet it seems that we could move more in that direction. Reduce the leverage in the system, and hope that means fewer events like 2008.

Notice I said "fewer", not "none". Neither markets nor government are perfectible; the best we're going to get is ones that work pretty well most of the time. In 2005, everyone--homebuyers, bankers, regulators, legislators--was making essentially the same mistake. And while it's more comfortable to believe that this was malevolent, the more prosaic truth is probably that sometimes large groups of people get stuff badly wrong. We can't plan our way to a risk free system. The best we can do is a system that fails a little bit better.

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Which, actually, the US system did. We firehosed money into the financial system, stabilized markets, and provided an economic cushion to those who got hurt. This is, of course, deeply morally unsatisfying, and it raises real questions about moral hazard. But we didn't get bread lines or 25% unemployment. And 25% unemployment stretching for years is even worse than stupid bankers getting to keep their jobs.

That's not ideal. It would be much better if the right regulations, or the power of markets, could transport us to a world where it will always be a sunny afternoon in late 1957, a world where jobs are plentiful and financial crises unimaginable. But it's probably not possible. We're not smart enough to even estimate the tail risk, much less get rid of it. And worse, we never were.