All the Devils Are Here [37]
The man he chose to lead this effort was a Swiss executive, Till Guldimann. Like Weatherstone, Guldimann had spent most of his career on trading desks. He, too, developed a keen interest in risk management, which he viewed as woefully unscientific. The traditional way of managing trading risks, for instance, was to impose a limit on how much capital a trader had at his disposal. But as a risk manager, Guldimann was often confronted with the problem of what to do when a trader wanted to increase his limit. “How should I know if he should get his increase?” Guldimann says. “All I could do is ask around. Is he a good guy? Does he know what he’s doing? It was ridiculous.”
There was never any question about how Guldimann and his team would approach this task. They would use statistics and probability theories that had long been popular on Wall Street. (The Black-Scholes formula, for example, developed in the early 1970s for pricing options, had become one of the linchpins of modern Wall Street.) The quants swarming Wall Street were all steeped in those theories—this was the essential building block of virtually everything they did. They knew no other way to approach the subject.
Sure enough, Value at Risk, or VaR, the model the J.P. Morgan quants came up with after years of trial and error, was built on a key tenet of the mathematics of probability, called Gaussian distribution. (It is named after Carl Friedrich Gauss, a German mathematician who introduced it in the early 1800s.) Its daunting name notwithstanding, the Gaussian distribution curve is something we’re all familiar with: it is a simple bell curve, which looks like this:
Why does a bell curve rise as it gets closer to the middle? Because the middle of the graph is where the smallest—and hence the most frequent—changes take place. Take a widely traded stock. It is going to rise or fall by twenty-five cents far more often than it will rise or fall by five dollars. So the twenty-five-cent movements will be clustered near the middle while the less frequent five-dollar movements will be farther along the sides of the curve, on either the plus or the minus side. And the truly enormous moves—the barely imaginable, once-in-a-lifetime events—will be so far outside the scale of the curve that they won’t even show up. These rare events would eventually be called “fat tails” or “black swans.”
Guldimann wasn’t interested in black swans; that was a risk problem for someone else to solve. Instead, VaR was meant to measure market risk from one day to the next, with the working assumption that tomorrow would be more or less like yesterday. Guldimann’s aim was to come up with a single number—a dollar figure—that would represent the amount of money the bank could lose over the next twenty-four hours with a 95 percent probability, assuming a normal market. Of course if it wasn’t a normal market, then all bets were off.
VaR, as Guldimann and his team developed it, had a number of appealing features. First, it could be used to gauge the riskiness of any kind of portfolio, from the simplest loans to the most complex derivatives. Second, it could be used to aggregate risk across the entire firm. Third, it could be used to measure the risks being taken by individual traders. That meant that risk managers no longer had to ask around when a trader wanted to increase his limits. “Once we converted all the limits to VaR limits, we could compare,” says Guldimann. “You could look at the profits the guy made and compare it to his VaR. If the guy who asked for a higher limit was making more money with less VaR, it was a good basis to give him more money.”
Finally, VaR expressed risk