Fragility Detection Heuristic

HOW TO DETECT WHO WILL GO BUST

Let us examine a method to detect fragility—the inverse philosopher’s stone. We can illustrate it with the story of the giant government-sponsored lending firm called Fannie Mae, a corporation that collapsed leaving the United States taxpayer with hundreds of billions of dollars of losses.

One day in 2003, Alex Berenson, a New York Times journalist, came into my office with the secret risk reports of Fannie Mae, given to him by a defector. It was the kind of report getting into the guts of the methodology for risk calculation that only an insider can see—Fannie Mae made its own risk calculations and disclosed what it wanted to whomever it wanted, the public or someone else. But only a defector could show us the guts to see how the risk was calculated.

We looked at the report: simply, a move upward in an economic variable led to massive losses, a move downward (in the opposite direction), to small profits. Further moves upward led to even larger additional losses and further moves downward to even smaller profits. It looked exactly like the story of the stone in Figure 9. Acceleration of harm was obvious—in fact it was monstrous. So we immediately saw that their blowup was inevitable: their exposures were severely “concave,” similar to the graph of traffic in Figure 14: losses that accelerate as one deviates economic variables (I did not even need to understand which one, as fragility to one variable of this magnitude implies fragility to all other parameters). I worked with my emotions, not my brain, and I had a pang before even understanding what numbers I had been looking at. It was the mother of all fragilities and, thanks to Berenson, The New York Times presented my concern. A smear campaign ensued, but nothing too notable. For I had in the meantime called a few key people charlatans and they were not too excited about it.

The key is that the nonlinear is vastly more affected by extreme events—and nobody was interested in extreme events since they had a mental block against them.

I kept telling anyone who would listen to me, including random taxi drivers (well, almost), that the company Fannie Mae was “sitting on a barrel of dynamite.” Of course, blowups don’t happen every day (just as poorly built bridges don’t collapse immediately), and people kept saying that my opinion was wrong and unfounded (using some argument that the stock was going up or something even more circular). I also inferred that other institutions, almost all banks, were in the same situation. After checking similar institutions, and seeing that the problem was general, I realized that a total collapse of the banking system was a certainty. I was so certain I could not see straight and went back to the markets to get my revenge against the turkeys. As in the scene from The Godfather (III), “Just when I thought I was out, they pull me back in.”

Things happened as if they were planned by destiny. Fannie Mae went bust, along with other banks. It just took a bit longer than expected, no big deal.

The stupid part of the story is that I had not seen the link between financial and general fragility—nor did I use the term “fragility.” Maybe I didn’t look at too many porcelain cups. I came to see that the acceleration of harm offered a measure of fragility, with the reverse response pointing toward antifragility.

It all boils down to the following: figuring out if our miscalculations or misforecasts are on balance more harmful than they are beneficial, and how accelerating the damage is. Exactly as in the story of the king, in which the damage from a ten-kilogram stone is more than twice the damage from a five-kilogram one. Such accelerating damage means that a large stone would eventually kill the person. Likewise a large market deviation would eventually kill the company.

Once I figured out that fragility was directly from nonlinearity and convexity effects, and that convexity was measurable, I got all excited. The technique—detecting acceleration of harm—applies to anything that entails decision making under uncertainty, and risk management. While it was the most interesting in medicine and technology, the immediate demand was in economics. So I suggested to the International Monetary Fund a measure of fragility to substitute for their measures of risk that they knew didn’t work. Most people in the risk business had been frustrated by the poor (rather, the random) performance of their models, but they didn’t like my earlier stance: “don’t use any model.” They wanted something. And a risk measure was there.1

So here is something to use. The technique, a simple heuristic called the fragility (and antifragility) detection heuristic, works as follows. Let’s say you want to check whether a town is overoptimized. Say you measure that when traffic increases by ten thousand cars, travel time grows by ten minutes. But if traffic increases by ten thousand more cars, travel time now extends by an extra thirty minutes. Such acceleration of traffic time shows that traffic is fragile and you have too many cars and need to reduce traffic until the acceleration becomes mild (acceleration, I repeat, is acute concavity, or negative convexity effect).

Likewise, government deficits are particularly concave to changes in economic conditions. Every additional deviation in, say, the unemployment rate—particularly when the government has debt—makes deficits incrementally worse. And financial leverage for a company has the same effect: you need to borrow more and more to get the same effect. Just as in a Ponzi scheme.

A fragile company might gain less profit from a 10 percent sales increase than it loses from a 10 percent decline. The relevant question is whether its exposure is asymmetric in this way.

That was in a way the technique I used intuitively to declare that the Highly Respected Firm Fannie Mae was on its way to the cemetery—and it was easy to produce a rule of thumb out of it. Now with the IMF we had a simple measure with a stamp. It looks simple, too simple, so the initial reaction from “experts” was that it was “trivial” (said by people who visibly never detected these risks before—academics and quantitative analysts scorn what they can understand too easily and get ticked off by what they did not think of themselves).

According to the wonderful principle that one should use people’s stupidity to have fun, I invited my friend Raphael Douady to collaborate in expressing this simple idea using the most opaque mathematical derivations, with incomprehensible theorems that would take half a day (for a professional) to understand. Raphael, Bruno Dupire, and I had been involved in an almost two-decades-long continuous conversation on how everything entailing risk—everything—can be seen with a lot more rigor and clarity from the vantage point of an option professional. Raphael and I managed to prove the link between nonlinearity, dislike of volatility, and fragility. Remarkably—as has been shown—if you can say something straightforward in a complicated manner with complex theorems, even if there is no large gain in rigor from these complicated equations, people take the idea very seriously. We got nothing but positive reactions, and we were now told that this simple detection heuristic was “intelligent” (by the same people who had found it trivial). The only problem is that mathematics is addictive.